Finite Group Databasebeta

← C3×#14187 #10632794

Subgroups — C3×#14187 #10632794

Order 768.

2746 conjugacy classes of subgroups.

The subgroup lattice has 1360 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C3×C4×D4C211yesmaximal, characteristic, complemented
2C2×C3×#392C211yesmaximal, characteristic
3C2×C3×#390C211yesmaximal, characteristic, complemented
4C2×C3×#388C211yesmaximal, characteristic, complemented
5C2×C3×#386C211yesmaximal, characteristic, complemented
6C2×C3×#386C211yesmaximal, characteristic, complemented
7C2×C3×C4×C22⋊C4C211yesmaximal, characteristic, complemented
8C3×#1439C211yesmaximal, characteristic, complemented
9C3×#1438C211yesmaximal, characteristic, complemented
10C3×#1438C211yesmaximal, characteristic, complemented
11C3×#1437C211yesmaximal, characteristic, complemented
12C3×#1437C211yesmaximal, characteristic, complemented
13C3×#1436C211yesmaximal, characteristic, complemented
14C3×#1436C211yesmaximal, characteristic, complemented
15C3×C22⋊#95C211yesmaximal, characteristic, complemented
16#14187C311yesmaximal, characteristic, direct product factor, Sylow
17C23×C3×D4C2211yescharacteristic
18C23×C3×D4C2211yescharacteristic
19C23×C3×D4C2211yescharacteristic
20C24×C3×C4C2211yescharacteristic
21C24×C3×C4C2211yescharacteristic
22C2×C3×C4×D4—24no—
23C2×C3×C4×D4—24no—
24C2×C3×C4×D4—24no—
25C22×C3×C4⋊C4C2211yescharacteristic
26C22×C3×C4⋊C4C2211yescharacteristic
27C22×C3×C22⋊C4C2211yescharacteristic
28C22×C3×C22⋊C4C2211yescharacteristic
29C22×C3×C22⋊C4C2211yescharacteristic
30C22×C3×C22⋊C4C2211yescharacteristic
31C22×C3×C22⋊C4C2211yescharacteristic
32C22×C3×C22⋊C4C2211yescharacteristic
33C22×C3×C22⋊C4C2211yescharacteristic
34C22×C3×C22⋊C4C2211yescharacteristic
35C22×C3×C22⋊C4C2211yescharacteristic
36C22×C3×C22⋊C4C2211yescharacteristic
37C22×C3×C22⋊C4C2211yescharacteristic
38C22×C3×C22⋊C4C2211yescharacteristic
39C22×C3×C22⋊C4C2211yescharacteristic
40C22×C3×C42C2211yescharacteristic
41C22×C3×C42C2211yescharacteristic
42C22×C3×C42C2211yescharacteristic
43C3×#392C418yescomplemented
44C3×#390—24no—
45C3×#388—24no—
46C3×#386—24no—
47C3×#386—24no—
48C3×C4×C22⋊C4—24no—
49C2×C3×#95C2211yescharacteristic
50C2×C3×#95C2211yescharacteristic
51C2×C3×#95C2211yescharacteristic
52C2×C3×#95C2211yescharacteristic
53C2×C3×#95C2211yescharacteristic
54C2×C3×#95C2211yescharacteristic
55C2×C3×#95C2211yescharacteristic
56C2×C3×#95C2211yescharacteristic
57C2×C3×#95C2211yescharacteristic
58C2×C3×#95C2211yescharacteristic
59C2×C3×#95C2211yescharacteristic
60C2×C3×#95C2211yescharacteristic
61C22×C4×D4C2×C311yescharacteristic, complemented
62C2×#392C2×C311yescharacteristic
63C2×#390C2×C311yescharacteristic, complemented
64C2×#388C2×C311yescharacteristic, complemented
65C2×#386C2×C311yescharacteristic, complemented
66C2×#386C2×C311yescharacteristic, complemented
67C2×C4×C22⋊C4C2×C311yescharacteristic, complemented
68#1439C2×C311yescharacteristic, complemented
69#1438C2×C311yescharacteristic, complemented
70#1438C2×C311yescharacteristic, complemented
71#1437C2×C311yescharacteristic, complemented
72#1437C2×C311yescharacteristic, complemented
73#1436C2×C311yescharacteristic, complemented
74#1436C2×C311yescharacteristic, complemented
75C22⋊#95C2×C311yescharacteristic, complemented
76C25×C3C2311yescharacteristic
77C25×C3C2311yescharacteristic
78C25×C3C2311yescharacteristic
79C22×C3×D4—22no—
80C22×C3×D4—22no—
81C22×C3×D4—22no—
82C22×C3×D4—22no—
83C22×C3×D4—22no—
84C22×C3×D4—22no—
85C22×C3×D4—22no—
86C22×C3×D4—22no—
87C22×C3×D4—22no—
88C22×C3×D4—22no—
89C22×C3×D4—22no—
90C22×C3×D4—22no—
91C22×C3×D4—41no—
92C22×C3×D4—41no—
93C22×C3×D4—41no—
94C22×C3×D4—41no—
95C22×C3×D4—41no—
96C22×C3×D4—41no—
97C22×C3×D4C2×C414yes—
98C22×C3×D4C2×C414yescomplemented
99C22×C3×D4C2×C414yescomplemented
100C23×C3×C4—22no—
101C23×C3×C4—22no—
102C23×C3×C4—22no—
103C23×C3×C4—22no—
104C23×C3×C4—22no—
105C23×C3×C4—22no—
106C23×C3×C4—22no—
107C23×C3×C4—22no—
108C23×C3×C4—22no—
109C23×C3×C4—41no—
110C23×C3×C4—41no—
111C23×C3×C4—41no—
112C23×C3×C4—41no—
113C23×C3×C4D414yescomplemented
114C23×C3×C4C2311yescharacteristic
115C23×C3×C4C2311yescharacteristic
116C23×C3×C4C2311yescharacteristic
117C23×C3×C4C2311yescharacteristic
118C23×C3×C4C2311yescharacteristic
119C23×C3×C4C2311yescharacteristic
120C23×C3×C4C2311yescharacteristic
121C23×C3×C4C2311yescharacteristic
122C23×C3×C4C2311yescharacteristic
123C23×C3×C4C2311yescharacteristic
124C23×C3×C4C2311yescharacteristic
125C23×C3×C4C2311yescharacteristic
126C3×C4×D4—232no—
127C2×C3×C4⋊C4—22no—
128C2×C3×C4⋊C4—22no—
129C2×C3×C4⋊C4—22no—
130C2×C3×C4⋊C4—22no—
131C2×C3×C4⋊C4—41no—
132C2×C3×C4⋊C4D414yescomplemented
133C2×C3×C22⋊C4—22no—
134C2×C3×C22⋊C4—22no—
135C2×C3×C22⋊C4—22no—
136C2×C3×C22⋊C4—22no—
137C2×C3×C22⋊C4—22no—
138C2×C3×C22⋊C4—22no—
139C2×C3×C22⋊C4—22no—
140C2×C3×C22⋊C4—22no—
141C2×C3×C22⋊C4—22no—
142C2×C3×C22⋊C4—22no—
143C2×C3×C22⋊C4—22no—
144C2×C3×C22⋊C4—22no—
145C2×C3×C22⋊C4—22no—
146C2×C3×C22⋊C4—22no—
147C2×C3×C22⋊C4—22no—
148C2×C3×C22⋊C4—22no—
149C2×C3×C22⋊C4—22no—
150C2×C3×C22⋊C4—22no—
151C2×C3×C22⋊C4—22no—
152C2×C3×C22⋊C4—22no—
153C2×C3×C22⋊C4—22no—
154C2×C3×C22⋊C4—22no—
155C2×C3×C22⋊C4—22no—
156C2×C3×C22⋊C4—22no—
157C2×C3×C22⋊C4—22no—
158C2×C3×C22⋊C4—22no—
159C2×C3×C22⋊C4—22no—
160C2×C3×C22⋊C4—41no—
161C2×C3×C22⋊C4—41no—
162C2×C3×C22⋊C4—41no—
163C2×C3×C22⋊C4—41no—
164C2×C3×C22⋊C4—41no—
165C2×C3×C22⋊C4—41no—
166C2×C3×C22⋊C4—41no—
167C2×C3×C22⋊C4—41no—
168C2×C3×C22⋊C4C2×C414yescomplemented
169C2×C3×C22⋊C4C2×C414yescomplemented
170C2×C3×C22⋊C4C2×C414yescomplemented
171C2×C3×C22⋊C4D414yescomplemented
172C2×C3×C42—22no—
173C2×C3×C42—22no—
174C2×C3×C42—22no—
175C2×C3×C42—22no—
176C2×C3×C42—22no—
177C2×C3×C42—22no—
178C2×C3×C42—22no—
179C2×C3×C42—41no—
180C2×C3×C42—41no—
181C3×#95—22no—
182C3×#95—22no—
183C3×#95—22no—
184C3×#95—22no—
185C3×#95—22no—
186C3×#95—22no—
187C3×#95—22no—
188C3×#95—41no—
189C3×#95—41no—
190C3×#95—41no—
191C3×#95C2×C414yescomplemented
192C3×#95D414yescomplemented
193C23×D4C22×C311yescharacteristic
194C23×D4C22×C311yescharacteristic
195C23×D4C22×C311yescharacteristic
196C24×C4C22×C311yescharacteristic
197C24×C4C22×C311yescharacteristic
198C2×C4×D4—24no—
199C2×C4×D4—24no—
200C2×C4×D4—24no—
201C22×C4⋊C4C22×C311yescharacteristic
202C22×C4⋊C4C22×C311yescharacteristic
203C22×C22⋊C4C22×C311yescharacteristic
204C22×C22⋊C4C22×C311yescharacteristic
205C22×C22⋊C4C22×C311yescharacteristic
206C22×C22⋊C4C22×C311yescharacteristic
207C22×C22⋊C4C22×C311yescharacteristic
208C22×C22⋊C4C22×C311yescharacteristic
209C22×C22⋊C4C22×C311yescharacteristic
210C22×C22⋊C4C22×C311yescharacteristic
211C22×C22⋊C4C22×C311yescharacteristic
212C22×C22⋊C4C22×C311yescharacteristic
213C22×C22⋊C4C22×C311yescharacteristic
214C22×C22⋊C4C22×C311yescharacteristic
215C22×C22⋊C4C22×C311yescharacteristic
216C22×C42C22×C311yescharacteristic
217C22×C42C22×C311yescharacteristic
218C22×C42C22×C311yescharacteristic
219#392C3×C418yescomplemented
220#390—24no—
221#388—24no—
222#386—24no—
223#386—24no—
224C4×C22⋊C4—24no—
225C2×#95C22×C311yescharacteristic
226C2×#95C22×C311yescharacteristic
227C2×#95C22×C311yescharacteristic
228C2×#95C22×C311yescharacteristic
229C2×#95C22×C311yescharacteristic
230C2×#95C22×C311yescharacteristic
231C2×#95C22×C311yescharacteristic
232C2×#95C22×C311yescharacteristic
233C2×#95C22×C311yescharacteristic
234C2×#95C22×C311yescharacteristic
235C2×#95C22×C311yescharacteristic
236C2×#95C22×C311yescharacteristic
237C24×C3—21no—
238C24×C3—21no—
239C24×C3—21no—
240C24×C3—21no—
241C24×C3—21no—
242C24×C3—21no—
243C24×C3—21no—
244C24×C3—21no—
245C24×C3—21no—
246C24×C3—21no—
247C24×C3—21no—
248C24×C3—21no—
249C24×C3—21no—
250C24×C3—21no—
251C24×C3—21no—
252C24×C3—21no—
253C24×C3—21no—
254C24×C3—21no—
255C24×C3—21no—
256C24×C3—21no—
257C24×C3—21no—
258C24×C3—21no—
259C24×C3—21no—
260C24×C3—21no—
261C24×C3—21no—
262C24×C3—21no—
263C24×C3—21no—
264C24×C3—21no—
265C24×C3—21no—
266C24×C3—21no—
267C24×C3—21no—
268C24×C3—21no—
269C24×C3—21no—
270C24×C3—21no—
271C24×C3—21no—
272C24×C3—21no—
273C24×C3—21no—
274C24×C3—21no—
275C24×C3C22×C412yes—
276C24×C3C22×C412yes—
277C24×C3C22×C412yes—
278C24×C3C2×D412yes—
279C24×C3C2×D412yes—
280C24×C3#4112yes—
281C24×C3#4112yes—
282C24×C3C2411yescharacteristic
283C2×C3×D4—28no—
284C2×C3×D4—28no—
285C2×C3×D4—28no—
286C2×C3×D4—28no—
287C2×C3×D4—28no—
288C2×C3×D4—28no—
289C2×C3×D4—28no—
290C2×C3×D4—28no—
291C2×C3×D4—28no—
292C2×C3×D4—28no—
293C2×C3×D4—44no—
294C2×C3×D4—44no—
295C2×C3×D4—44no—
296C2×C3×D4—44no—
297C2×C3×D4—44no—
298C2×C3×D4—44no—
299C2×C3×D4—44no—
300C2×C3×D4—44no—
301C2×C3×D4—44no—
302C2×C3×D4—44no—
303C2×C3×D4—44no—
304C22×C3×C4—21no—
305C22×C3×C4—21no—
306C22×C3×C4—21no—
307C22×C3×C4—21no—
308C22×C3×C4—21no—
309C22×C3×C4—21no—
310C22×C3×C4—21no—
311C22×C3×C4—21no—
312C22×C3×C4—21no—
313C22×C3×C4—21no—
314C22×C3×C4—21no—
315C22×C3×C4—21no—
316C22×C3×C4—21no—
317C22×C3×C4—21no—
318C22×C3×C4—21no—
319C22×C3×C4—21no—
320C22×C3×C4—28no—
321C22×C3×C4—21no—
322C22×C3×C4—21no—
323C22×C3×C4—21no—
324C22×C3×C4—21no—
325C22×C3×C4—21no—
326C22×C3×C4—21no—
327C22×C3×C4—21no—
328C22×C3×C4—21no—
329C22×C3×C4—21no—
330C22×C3×C4—21no—
331C22×C3×C4—21no—
332C22×C3×C4—21no—
333C22×C3×C4—21no—
334C22×C3×C4—21no—
335C22×C3×C4—21no—
336C22×C3×C4—21no—
337C22×C3×C4—21no—
338C22×C3×C4—21no—
339C22×C3×C4—21no—
340C22×C3×C4—21no—
341C22×C3×C4—21no—
342C22×C3×C4—21no—
343C22×C3×C4—21no—
344C22×C3×C4—21no—
345C22×C3×C4—21no—
346C22×C3×C4—21no—
347C22×C3×C4—21no—
348C22×C3×C4—21no—
349C22×C3×C4—21no—
350C22×C3×C4—21no—
351C22×C3×C4—21no—
352C22×C3×C4—21no—
353C22×C3×C4—21no—
354C22×C3×C4—21no—
355C22×C3×C4—21no—
356C22×C3×C4—21no—
357C22×C3×C4—28no—
358C22×C3×C4—28no—
359C22×C3×C4—21no—
360C22×C3×C4—21no—
361C22×C3×C4—21no—
362C22×C3×C4—21no—
363C22×C3×C4—21no—
364C22×C3×C4—21no—
365C22×C3×C4—21no—
366C22×C3×C4—21no—
367C22×C3×C4—21no—
368C22×C3×C4—21no—
369C22×C3×C4—21no—
370C22×C3×C4—21no—
371C22×C3×C4—21no—
372C22×C3×C4—21no—
373C22×C3×C4—44no—
374C22×C3×C4—44no—
375C22×C3×C4—44no—
376C22×C3×C4—44no—
377C22×C3×C4—44no—
378C22×C3×C4—44no—
379C22×C3×C4—44no—
380C22×C3×C4—44no—
381C22×C3×C4—44no—
382C22×C3×C4—44no—
383C22×C3×C4—44no—
384C22×C3×C4C22×C412yes—
385C22×C3×C4C22×C412yes—
386C22×C3×C4C22×C412yes—
387C22×C3×C4C22×C412yes—
388C22×C3×C4C2×D412yes—
389C22×C3×C4C2×D412yes—
390C22×C3×C4C2×D412yes—
391C22×C3×C4C2×D412yes—
392C22×C3×C4C2×D412yes—
393C22×C3×C4C2×D412yes—
394C22×C3×C4C2×D412yes—
395C22×C3×C4C2×D412yes—
396C22×C3×C4C2×D412yes—
397C22×C3×C4C2×D412yes—
398C22×C3×C4#4112yes—
399C22×C3×C4#4112yes—
400C22×C3×C4#4112yes—
401C22×C3×C4#4112yes—
402C3×C4⋊C4—28no—
403C3×C4⋊C4—44no—
404C3×C22⋊C4—28no—
405C3×C22⋊C4—28no—
406C3×C22⋊C4—28no—
407C3×C22⋊C4—28no—
408C3×C22⋊C4—28no—
409C3×C22⋊C4—44no—
410C3×C22⋊C4—44no—
411C3×C22⋊C4—44no—
412C3×C22⋊C4—44no—
413C3×C22⋊C4—44no—
414C3×C22⋊C4—44no—
415C3×C22⋊C4—44no—
416C3×C22⋊C4—44no—
417C3×C42—28no—
418C3×C42—44no—
419C3×C42—44no—
420C25C23×C311yescharacteristic
421C25C23×C311yescharacteristic
422C25C23×C311yescharacteristic
423C22×D4—22no—
424C22×D4—22no—
425C22×D4—22no—
426C22×D4—22no—
427C22×D4—22no—
428C22×D4—22no—
429C22×D4—22no—
430C22×D4—22no—
431C22×D4—22no—
432C22×D4—22no—
433C22×D4—22no—
434C22×D4—22no—
435C22×D4—41no—
436C22×D4—41no—
437C22×D4—41no—
438C22×D4—41no—
439C22×D4—41no—
440C22×D4—41no—
441C22×D4C2×C3×C414yes—
442C22×D4C2×C3×C414yescomplemented
443C22×D4C2×C3×C414yescomplemented
444C23×C4—22no—
445C23×C4—22no—
446C23×C4—22no—
447C23×C4—22no—
448C23×C4—22no—
449C23×C4—22no—
450C23×C4—22no—
451C23×C4—22no—
452C23×C4—22no—
453C23×C4—41no—
454C23×C4—41no—
455C23×C4—41no—
456C23×C4—41no—
457C23×C4C3×D414yescomplemented
458C23×C4C23×C311yescharacteristic
459C23×C4C23×C311yescharacteristic
460C23×C4C23×C311yescharacteristic
461C23×C4C23×C311yescharacteristic
462C23×C4C23×C311yescharacteristic
463C23×C4C23×C311yescharacteristic
464C23×C4C23×C311yescharacteristic
465C23×C4C23×C311yescharacteristic
466C23×C4C23×C311yescharacteristic
467C23×C4C23×C311yescharacteristic
468C23×C4C23×C311yescharacteristic
469C23×C4C23×C311yescharacteristic
470C4×D4—232no—
471C2×C4⋊C4—22no—
472C2×C4⋊C4—22no—
473C2×C4⋊C4—22no—
474C2×C4⋊C4—22no—
475C2×C4⋊C4—41no—
476C2×C4⋊C4C3×D414yescomplemented
477C2×C22⋊C4—22no—
478C2×C22⋊C4—22no—
479C2×C22⋊C4—22no—
480C2×C22⋊C4—22no—
481C2×C22⋊C4—22no—
482C2×C22⋊C4—22no—
483C2×C22⋊C4—22no—
484C2×C22⋊C4—22no—
485C2×C22⋊C4—22no—
486C2×C22⋊C4—22no—
487C2×C22⋊C4—22no—
488C2×C22⋊C4—22no—
489C2×C22⋊C4—22no—
490C2×C22⋊C4—22no—
491C2×C22⋊C4—22no—
492C2×C22⋊C4—22no—
493C2×C22⋊C4—22no—
494C2×C22⋊C4—22no—
495C2×C22⋊C4—22no—
496C2×C22⋊C4—22no—
497C2×C22⋊C4—22no—
498C2×C22⋊C4—22no—
499C2×C22⋊C4—22no—
500C2×C22⋊C4—22no—
501C2×C22⋊C4—22no—
502C2×C22⋊C4—22no—
503C2×C22⋊C4—22no—
504C2×C22⋊C4—41no—
505C2×C22⋊C4—41no—
506C2×C22⋊C4—41no—
507C2×C22⋊C4—41no—
508C2×C22⋊C4—41no—
509C2×C22⋊C4—41no—
510C2×C22⋊C4—41no—
511C2×C22⋊C4—41no—
512C2×C22⋊C4C2×C3×C414yescomplemented
513C2×C22⋊C4C2×C3×C414yescomplemented
514C2×C22⋊C4C2×C3×C414yescomplemented
515C2×C22⋊C4C3×D414yescomplemented
516C2×C42—22no—
517C2×C42—22no—
518C2×C42—22no—
519C2×C42—22no—
520C2×C42—22no—
521C2×C42—22no—
522C2×C42—22no—
523C2×C42—41no—
524C2×C42—41no—
525#95—22no—
526#95—22no—
527#95—22no—
528#95—22no—
529#95—22no—
530#95—22no—
531#95—22no—
532#95—41no—
533#95—41no—
534#95—41no—
535#95C2×C3×C414yescomplemented
536#95C3×D414yescomplemented
537C23×C3—22no—
538C23×C3—22no—
539C23×C3—22no—
540C23×C3—22no—
541C23×C3—22no—
542C23×C3—22no—
543C23×C3—22no—
544C23×C3—22no—
545C23×C3—22no—
546C23×C3—22no—
547C23×C3—22no—
548C23×C3—22no—
549C23×C3—22no—
550C23×C3—22no—
551C23×C3—22no—
552C23×C3—22no—
553C23×C3—22no—
554C23×C3—22no—
555C23×C3—22no—
556C23×C3—22no—
557C23×C3—22no—
558C23×C3—22no—
559C23×C3—22no—
560C23×C3—22no—
561C23×C3—22no—
562C23×C3—22no—
563C23×C3—22no—
564C23×C3—22no—
565C23×C3—22no—
566C23×C3—22no—
567C23×C3—22no—
568C23×C3—22no—
569C23×C3—22no—
570C23×C3—22no—
571C23×C3—22no—
572C23×C3—22no—
573C23×C3—22no—
574C23×C3—22no—
575C23×C3—22no—
576C23×C3—22no—
577C23×C3—22no—
578C23×C3—22no—
579C23×C3—22no—
580C23×C3—41no—
581C23×C3—41no—
582C23×C3—41no—
583C23×C3—41no—
584C23×C3—41no—
585C23×C3—41no—
586C23×C3—41no—
587C23×C3—41no—
588C23×C3—41no—
589C23×C3—41no—
590C23×C3—41no—
591C23×C3—41no—
592C23×C3—41no—
593C23×C3—41no—
594C23×C3—41no—
595C23×C3—41no—
596C23×C3—41no—
597C23×C3—41no—
598C23×C3—41no—
599C23×C3—41no—
600C23×C3—41no—
601C23×C3—41no—
602C23×C3—41no—
603C23×C3—41no—
604C23×C3—41no—
605C23×C3—41no—
606C23×C3—41no—
607C23×C3—41no—
608C23×C3—41no—
609C23×C3—41no—
610C23×C3—41no—
611C23×C3—41no—
612C23×C3—41no—
613C23×C3—41no—
614C23×C3—41no—
615C23×C3—41no—
616C23×C3—41no—
617C23×C3—41no—
618C23×C3—41no—
619C23×C3—41no—
620C23×C3—41no—
621C23×C3—41no—
622C23×C3—41no—
623C23×C3—41no—
624C23×C3—41no—
625C23×C3—41no—
626C23×C3—41no—
627C23×C3—41no—
628C23×C3—41no—
629C23×C3—41no—
630C23×C3—41no—
631C23×C3—41no—
632C23×C3—41no—
633C23×C3—41no—
634C23×C3—41no—
635C23×C3—41no—
636C23×C3—41no—
637C23×C3—41no—
638C23×C3—41no—
639C23×C3—41no—
640C23×C3C4×D414yes—
641C23×C3C4×D414yes—
642C23×C3C23×C411yescharacteristic
643C23×C3C22×D411yescharacteristic
644C23×C3C22×D411yescharacteristic
645C23×C3C22×D411yescharacteristic
646C23×C3C22×D411yescharacteristic
647C23×C3C2×#4111yescharacteristic
648C23×C3C2×#4111yescharacteristic
649C23×C3C2×#4111yescharacteristic
650C23×C3C2×#4111yescharacteristic
651C23×C3C2×#4111yescharacteristic
652C23×C3C2×#4111yescharacteristic
653C23×C3H(5,𝔽2)11yescharacteristic
654C23×C3H(5,𝔽2)11yescharacteristic
655C23×C3H(5,𝔽2)11yescharacteristic
656C23×C3H(5,𝔽2)11yescharacteristic
657C3×D4—232no—
658C3×D4—416no—
659C3×D4—416no—
660C2×C3×C4—22no—
661C2×C3×C4—22no—
662C2×C3×C4—22no—
663C2×C3×C4—22no—
664C2×C3×C4—22no—
665C2×C3×C4—22no—
666C2×C3×C4—22no—
667C2×C3×C4—22no—
668C2×C3×C4—22no—
669C2×C3×C4—22no—
670C2×C3×C4—22no—
671C2×C3×C4—22no—
672C2×C3×C4—22no—
673C2×C3×C4—22no—
674C2×C3×C4—22no—
675C2×C3×C4—22no—
676C2×C3×C4—22no—
677C2×C3×C4—22no—
678C2×C3×C4—22no—
679C2×C3×C4—22no—
680C2×C3×C4—22no—
681C2×C3×C4—22no—
682C2×C3×C4—22no—
683C2×C3×C4—22no—
684C2×C3×C4—22no—
685C2×C3×C4—22no—
686C2×C3×C4—22no—
687C2×C3×C4—22no—
688C2×C3×C4—22no—
689C2×C3×C4—22no—
690C2×C3×C4—22no—
691C2×C3×C4—22no—
692C2×C3×C4—22no—
693C2×C3×C4—22no—
694C2×C3×C4—22no—
695C2×C3×C4—22no—
696C2×C3×C4—22no—
697C2×C3×C4—22no—
698C2×C3×C4—22no—
699C2×C3×C4—22no—
700C2×C3×C4—22no—
701C2×C3×C4—22no—
702C2×C3×C4—416no—
703C2×C3×C4—416no—
704C2×C3×C4—41no—
705C2×C3×C4—41no—
706C2×C3×C4—41no—
707C2×C3×C4—41no—
708C2×C3×C4—41no—
709C2×C3×C4—41no—
710C2×C3×C4—41no—
711C2×C3×C4—41no—
712C2×C3×C4—41no—
713C2×C3×C4—41no—
714C2×C3×C4—41no—
715C2×C3×C4—41no—
716C2×C3×C4—41no—
717C2×C3×C4—41no—
718C2×C3×C4—41no—
719C2×C3×C4—41no—
720C2×C3×C4—41no—
721C2×C3×C4—41no—
722C2×C3×C4—41no—
723C2×C3×C4—41no—
724C2×C3×C4—41no—
725C2×C3×C4—41no—
726C2×C3×C4—41no—
727C2×C3×C4—41no—
728C2×C3×C4—41no—
729C2×C3×C4—41no—
730C2×C3×C4—41no—
731C2×C3×C4—41no—
732C2×C3×C4—41no—
733C2×C3×C4—41no—
734C2×C3×C4—41no—
735C2×C3×C4—41no—
736C2×C3×C4—41no—
737C2×C3×C4—41no—
738C2×C3×C4—41no—
739C2×C3×C4—41no—
740C2×C3×C4—41no—
741C2×C3×C4—41no—
742C2×C3×C4C4×D414yes—
743C2×C3×C4C4×D414yescomplemented
744C2×C3×C4#12014yes—
745C2×C3×C4#12114yes—
746C24—21no—
747C24—21no—
748C24—21no—
749C24—21no—
750C24—21no—
751C24—21no—
752C24—21no—
753C24—21no—
754C24—21no—
755C24—21no—
756C24—21no—
757C24—21no—
758C24—21no—
759C24—21no—
760C24—21no—
761C24—21no—
762C24—21no—
763C24—21no—
764C24—21no—
765C24—21no—
766C24—21no—
767C24—21no—
768C24—21no—
769C24—21no—
770C24—21no—
771C24—21no—
772C24—21no—
773C24—21no—
774C24—21no—
775C24—21no—
776C24—21no—
777C24—21no—
778C24—21no—
779C24—21no—
780C24—21no—
781C24—21no—
782C24—21no—
783C24—21no—
784C24C22×C3×C412yes—
785C24C22×C3×C412yes—
786C24C22×C3×C412yes—
787C24C2×C3×D412yes—
788C24C2×C3×D412yes—
789C24C3×#4112yes—
790C24C3×#4112yes—
791C24C24×C311yescharacteristic
792C2×D4—28no—
793C2×D4—28no—
794C2×D4—28no—
795C2×D4—28no—
796C2×D4—28no—
797C2×D4—28no—
798C2×D4—28no—
799C2×D4—28no—
800C2×D4—28no—
801C2×D4—28no—
802C2×D4—44no—
803C2×D4—44no—
804C2×D4—44no—
805C2×D4—44no—
806C2×D4—44no—
807C2×D4—44no—
808C2×D4—44no—
809C2×D4—44no—
810C2×D4—44no—
811C2×D4—44no—
812C2×D4—44no—
813C22×C4—21no—
814C22×C4—21no—
815C22×C4—21no—
816C22×C4—21no—
817C22×C4—21no—
818C22×C4—21no—
819C22×C4—21no—
820C22×C4—21no—
821C22×C4—21no—
822C22×C4—21no—
823C22×C4—21no—
824C22×C4—21no—
825C22×C4—21no—
826C22×C4—21no—
827C22×C4—21no—
828C22×C4—21no—
829C22×C4—28no—
830C22×C4—21no—
831C22×C4—21no—
832C22×C4—21no—
833C22×C4—21no—
834C22×C4—21no—
835C22×C4—21no—
836C22×C4—21no—
837C22×C4—21no—
838C22×C4—21no—
839C22×C4—21no—
840C22×C4—21no—
841C22×C4—21no—
842C22×C4—21no—
843C22×C4—21no—
844C22×C4—21no—
845C22×C4—21no—
846C22×C4—21no—
847C22×C4—21no—
848C22×C4—21no—
849C22×C4—21no—
850C22×C4—21no—
851C22×C4—21no—
852C22×C4—21no—
853C22×C4—21no—
854C22×C4—21no—
855C22×C4—21no—
856C22×C4—21no—
857C22×C4—21no—
858C22×C4—21no—
859C22×C4—21no—
860C22×C4—21no—
861C22×C4—21no—
862C22×C4—21no—
863C22×C4—21no—
864C22×C4—21no—
865C22×C4—21no—
866C22×C4—28no—
867C22×C4—28no—
868C22×C4—21no—
869C22×C4—21no—
870C22×C4—21no—
871C22×C4—21no—
872C22×C4—21no—
873C22×C4—21no—
874C22×C4—21no—
875C22×C4—21no—
876C22×C4—21no—
877C22×C4—21no—
878C22×C4—21no—
879C22×C4—21no—
880C22×C4—21no—
881C22×C4—21no—
882C22×C4—44no—
883C22×C4—44no—
884C22×C4—44no—
885C22×C4—44no—
886C22×C4—44no—
887C22×C4—44no—
888C22×C4—44no—
889C22×C4—44no—
890C22×C4—44no—
891C22×C4—44no—
892C22×C4—44no—
893C22×C4C22×C3×C412yes—
894C22×C4C22×C3×C412yes—
895C22×C4C22×C3×C412yes—
896C22×C4C22×C3×C412yes—
897C22×C4C2×C3×D412yes—
898C22×C4C2×C3×D412yes—
899C22×C4C2×C3×D412yes—
900C22×C4C2×C3×D412yes—
901C22×C4C2×C3×D412yes—
902C22×C4C2×C3×D412yes—
903C22×C4C2×C3×D412yes—
904C22×C4C2×C3×D412yes—
905C22×C4C2×C3×D412yes—
906C22×C4C2×C3×D412yes—
907C22×C4C3×#4112yes—
908C22×C4C3×#4112yes—
909C22×C4C3×#4112yes—
910C22×C4C3×#4112yes—
911C4⋊C4—28no—
912C4⋊C4—44no—
913C22⋊C4—28no—
914C22⋊C4—28no—
915C22⋊C4—28no—
916C22⋊C4—28no—
917C22⋊C4—28no—
918C22⋊C4—44no—
919C22⋊C4—44no—
920C22⋊C4—44no—
921C22⋊C4—44no—
922C22⋊C4—44no—
923C22⋊C4—44no—
924C22⋊C4—44no—
925C22⋊C4—44no—
926C42—28no—
927C42—44no—
928C42—44no—
929C22×C3—24no—
930C22×C3—24no—
931C22×C3—24no—
932C22×C3—24no—
933C22×C3—24no—
934C22×C3—24no—
935C22×C3—42no—
936C22×C3—42no—
937C22×C3—42no—
938C22×C3—42no—
939C22×C3—42no—
940C22×C3—42no—
941C22×C3—42no—
942C22×C3—42no—
943C22×C3—42no—
944C22×C3—42no—
945C22×C3—42no—
946C22×C3—42no—
947C22×C3—42no—
948C22×C3—42no—
949C22×C3—42no—
950C22×C3—42no—
951C22×C3—42no—
952C22×C3—42no—
953C22×C3—42no—
954C22×C3—42no—
955C22×C3—42no—
956C22×C3—42no—
957C22×C3—42no—
958C22×C3—42no—
959C22×C3—42no—
960C22×C3—42no—
961C22×C3—42no—
962C22×C3—42no—
963C22×C3—42no—
964C22×C3—42no—
965C22×C3—42no—
966C22×C3—81no—
967C22×C3—81no—
968C22×C3—81no—
969C22×C3—81no—
970C22×C3—81no—
971C22×C3—81no—
972C22×C3—81no—
973C22×C3—81no—
974C22×C3C2×C4×D411yescharacteristic
975C22×C3C2×C4×D411yescharacteristic
976C22×C3C2×C4×D411yescharacteristic
977C22×C3C2×C4×D411yescharacteristic
978C22×C3C4×#4111yescharacteristic
979C22×C3#51811yescharacteristic
980C22×C3#51811yescharacteristic
981C22×C3C2×#12011yescharacteristic
982C22×C3C2×#12111yescharacteristic
983C22×C3#52511yescharacteristic
984C22×C3#52511yescharacteristic
985C22×C3#52511yescharacteristic
986C22×C3#52511yescharacteristic
987C22×C3#52911yescharacteristic
988C22×C3#53211yescharacteristic
989C22×C3#53411yescharacteristic
990C22×C3#53511yescharacteristic
991C22×C3#53811yescharacteristic
992C22×C3#53811yescharacteristic
993C22×C3D4211yescharacteristic
994C22×C3D4211yescharacteristic
995C22×C3#54611yescharacteristic
996C22×C3#54611yescharacteristic
997C22×C3#54611yescharacteristic
998C22×C3#54611yescharacteristic
999C22×C3#54611yescharacteristic
1000C22×C3#55011yescharacteristic
1001C22×C3#55011yescharacteristic
1002C22×C3#55011yescharacteristic
1003C22×C3#55111yescharacteristic
1004C22×C3#55311yescharacteristic
1005C22×C3#55311yescharacteristic
1006C22×C3#55311yescharacteristic
1007C22×C3#55511yescharacteristic
1008C22×C3#55911yescharacteristic
1009C3×C4—24no—
1010C3×C4—24no—
1011C3×C4—24no—
1012C3×C4—24no—
1013C3×C4—42no—
1014C3×C4—42no—
1015C3×C4—42no—
1016C3×C4—42no—
1017C3×C4—42no—
1018C3×C4—42no—
1019C3×C4—81no—
1020C3×C4—81no—
1021C23—22no—
1022C23—22no—
1023C23—22no—
1024C23—22no—
1025C23—22no—
1026C23—22no—
1027C23—22no—
1028C23—22no—
1029C23—22no—
1030C23—22no—
1031C23—22no—
1032C23—22no—
1033C23—22no—
1034C23—22no—
1035C23—22no—
1036C23—22no—
1037C23—22no—
1038C23—22no—
1039C23—22no—
1040C23—22no—
1041C23—22no—
1042C23—22no—
1043C23—22no—
1044C23—22no—
1045C23—22no—
1046C23—22no—
1047C23—22no—
1048C23—22no—
1049C23—22no—
1050C23—22no—
1051C23—22no—
1052C23—22no—
1053C23—22no—
1054C23—22no—
1055C23—22no—
1056C23—22no—
1057C23—22no—
1058C23—22no—
1059C23—22no—
1060C23—22no—
1061C23—22no—
1062C23—22no—
1063C23—22no—
1064C23—41no—
1065C23—41no—
1066C23—41no—
1067C23—41no—
1068C23—41no—
1069C23—41no—
1070C23—41no—
1071C23—41no—
1072C23—41no—
1073C23—41no—
1074C23—41no—
1075C23—41no—
1076C23—41no—
1077C23—41no—
1078C23—41no—
1079C23—41no—
1080C23—41no—
1081C23—41no—
1082C23—41no—
1083C23—41no—
1084C23—41no—
1085C23—41no—
1086C23—41no—
1087C23—41no—
1088C23—41no—
1089C23—41no—
1090C23—41no—
1091C23—41no—
1092C23—41no—
1093C23—41no—
1094C23—41no—
1095C23—41no—
1096C23—41no—
1097C23—41no—
1098C23—41no—
1099C23—41no—
1100C23—41no—
1101C23—41no—
1102C23—41no—
1103C23—41no—
1104C23—41no—
1105C23—41no—
1106C23—41no—
1107C23—41no—
1108C23—41no—
1109C23—41no—
1110C23—41no—
1111C23—41no—
1112C23—41no—
1113C23—41no—
1114C23—41no—
1115C23—41no—
1116C23—41no—
1117C23—41no—
1118C23—41no—
1119C23—41no—
1120C23—41no—
1121C23—41no—
1122C23—41no—
1123C23—41no—
1124C23C3×C4×D414yes—
1125C23C3×C4×D414yes—
1126C23C23×C3×C411yescharacteristic
1127C23C22×C3×D411yescharacteristic
1128C23C22×C3×D411yescharacteristic
1129C23C22×C3×D411yescharacteristic
1130C23C22×C3×D411yescharacteristic
1131C23C2×C3×#4111yescharacteristic
1132C23C2×C3×#4111yescharacteristic
1133C23C2×C3×#4111yescharacteristic
1134C23C2×C3×#4111yescharacteristic
1135C23C2×C3×#4111yescharacteristic
1136C23C2×C3×#4111yescharacteristic
1137C23C3×H(5,𝔽2)11yescharacteristic
1138C23C3×H(5,𝔽2)11yescharacteristic
1139C23C3×H(5,𝔽2)11yescharacteristic
1140C23C3×H(5,𝔽2)11yescharacteristic
1141D4—232no—
1142D4—416no—
1143D4—416no—
1144C2×C4—22no—
1145C2×C4—22no—
1146C2×C4—22no—
1147C2×C4—22no—
1148C2×C4—22no—
1149C2×C4—22no—
1150C2×C4—22no—
1151C2×C4—22no—
1152C2×C4—22no—
1153C2×C4—22no—
1154C2×C4—22no—
1155C2×C4—22no—
1156C2×C4—22no—
1157C2×C4—22no—
1158C2×C4—22no—
1159C2×C4—22no—
1160C2×C4—22no—
1161C2×C4—22no—
1162C2×C4—22no—
1163C2×C4—22no—
1164C2×C4—22no—
1165C2×C4—22no—
1166C2×C4—22no—
1167C2×C4—22no—
1168C2×C4—22no—
1169C2×C4—22no—
1170C2×C4—22no—
1171C2×C4—22no—
1172C2×C4—22no—
1173C2×C4—22no—
1174C2×C4—22no—
1175C2×C4—22no—
1176C2×C4—22no—
1177C2×C4—22no—
1178C2×C4—22no—
1179C2×C4—22no—
1180C2×C4—22no—
1181C2×C4—22no—
1182C2×C4—22no—
1183C2×C4—22no—
1184C2×C4—22no—
1185C2×C4—22no—
1186C2×C4—416no—
1187C2×C4—416no—
1188C2×C4—41no—
1189C2×C4—41no—
1190C2×C4—41no—
1191C2×C4—41no—
1192C2×C4—41no—
1193C2×C4—41no—
1194C2×C4—41no—
1195C2×C4—41no—
1196C2×C4—41no—
1197C2×C4—41no—
1198C2×C4—41no—
1199C2×C4—41no—
1200C2×C4—41no—
1201C2×C4—41no—
1202C2×C4—41no—
1203C2×C4—41no—
1204C2×C4—41no—
1205C2×C4—41no—
1206C2×C4—41no—
1207C2×C4—41no—
1208C2×C4—41no—
1209C2×C4—41no—
1210C2×C4—41no—
1211C2×C4—41no—
1212C2×C4—41no—
1213C2×C4—41no—
1214C2×C4—41no—
1215C2×C4—41no—
1216C2×C4—41no—
1217C2×C4—41no—
1218C2×C4—41no—
1219C2×C4—41no—
1220C2×C4—41no—
1221C2×C4—41no—
1222C2×C4—41no—
1223C2×C4—41no—
1224C2×C4—41no—
1225C2×C4—41no—
1226C2×C4C3×C4×D414yes—
1227C2×C4C3×C4×D414yescomplemented
1228C2×C4C3×#12014yes—
1229C2×C4C3×#12114yes—
1230C2×C3—44no—
1231C2×C3—44no—
1232C2×C3—82no—
1233C2×C3C4×#12011yescharacteristic
1234C2×C3C4×#12111yescharacteristic
1235C2×C3#232111yescharacteristic
1236C2×C3#235811yescharacteristic
1237C2×C3#236311yescharacteristic
1238C2×C3#236411yescharacteristic
1239C2×C3#236611yescharacteristic
1240C2×C3#241011yescharacteristic
1241C2×C3#241411yescharacteristic
1242C2×C3#243111yescharacteristic
1243C2×C3#245611yescharacteristic
1244C2×C3#245611yescharacteristic
1245C2×C3#245911yescharacteristic
1246C2×C3#246711yescharacteristic
1247C2×C3#260211yescharacteristic
1248C22—24no—
1249C22—24no—
1250C22—24no—
1251C22—24no—
1252C22—24no—
1253C22—24no—
1254C22—42no—
1255C22—42no—
1256C22—42no—
1257C22—42no—
1258C22—42no—
1259C22—42no—
1260C22—42no—
1261C22—42no—
1262C22—42no—
1263C22—42no—
1264C22—42no—
1265C22—42no—
1266C22—42no—
1267C22—42no—
1268C22—42no—
1269C22—42no—
1270C22—42no—
1271C22—42no—
1272C22—42no—
1273C22—42no—
1274C22—42no—
1275C22—42no—
1276C22—42no—
1277C22—42no—
1278C22—42no—
1279C22—42no—
1280C22—42no—
1281C22—42no—
1282C22—42no—
1283C22—42no—
1284C22—42no—
1285C22—81no—
1286C22—81no—
1287C22—81no—
1288C22—81no—
1289C22—81no—
1290C22—81no—
1291C22—81no—
1292C22—81no—
1293C22C2×C3×C4×D411yescharacteristic
1294C22C2×C3×C4×D411yescharacteristic
1295C22C2×C3×C4×D411yescharacteristic
1296C22C2×C3×C4×D411yescharacteristic
1297C22C3×C4×#4111yescharacteristic
1298C22C3×#51811yescharacteristic
1299C22C3×#51811yescharacteristic
1300C22C2×C3×#12011yescharacteristic
1301C22C2×C3×#12111yescharacteristic
1302C22C3×#52511yescharacteristic
1303C22C3×#52511yescharacteristic
1304C22C3×#52511yescharacteristic
1305C22C3×#52511yescharacteristic
1306C22C3×#52911yescharacteristic
1307C22C3×#53211yescharacteristic
1308C22C3×#53411yescharacteristic
1309C22C3×#53511yescharacteristic
1310C22C3×#53811yescharacteristic
1311C22C3×#53811yescharacteristic
1312C22C3×D4211yescharacteristic
1313C22C3×D4211yescharacteristic
1314C22C3×#54611yescharacteristic
1315C22C3×#54611yescharacteristic
1316C22C3×#54611yescharacteristic
1317C22C3×#54611yescharacteristic
1318C22C3×#54611yescharacteristic
1319C22C3×#55011yescharacteristic
1320C22C3×#55011yescharacteristic
1321C22C3×#55011yescharacteristic
1322C22C3×#55111yescharacteristic
1323C22C3×#55311yescharacteristic
1324C22C3×#55311yescharacteristic
1325C22C3×#55311yescharacteristic
1326C22C3×#55511yescharacteristic
1327C22C3×#55911yescharacteristic
1328C4—24no—
1329C4—24no—
1330C4—24no—
1331C4—24no—
1332C4—42no—
1333C4—42no—
1334C4—42no—
1335C4—42no—
1336C4—42no—
1337C4—42no—
1338C4—81no—
1339C4—81no—
1340C3#1418711yescharacteristic, direct product factor, Sylow
1341C2—44no—
1342C2—44no—
1343C2—82no—
1344C2C3×C4×#12011yescharacteristic
1345C2C3×C4×#12111yescharacteristic
1346C2C3×#232111yescharacteristic
1347C2C3×#235811yescharacteristic
1348C2C3×#236311yescharacteristic
1349C2C3×#236411yescharacteristic
1350C2C3×#236611yescharacteristic
1351C2C3×#241011yescharacteristic
1352C2C3×#241411yescharacteristic
1353C2C3×#243111yescharacteristic
1354C2C3×#245611yescharacteristic
1355C2C3×#245611yescharacteristic
1356C2C3×#245911yescharacteristic
1357C2C3×#246711yescharacteristic
1358C2C3×#260211yescharacteristic
subgroupG/H
center, socleC24×C3C24
commutatorC23C23×C3×C4
Frattini, cosocleC24C24×C3
prime radicalC2×C3×#392C2
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C24×C3 ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. C22×C3×C4×D4C2semidirect
3. C2×C3×#390C2semidirect
4. C2×C3×#388C2semidirect
5. C2×C3×#386C2semidirect
6. C2×C3×#386C2semidirect
7. C2×C3×C4×C22⋊C4C2semidirect
8. C3×#1439C2semidirect
9. C3×#1438C2semidirect
10. C3×#1438C2semidirect
11. C3×#1437C2semidirect
12. C3×#1437C2semidirect
13. C3×#1436C2semidirect
14. C3×#1436C2semidirect
15. C3×C22⋊#95C2semidirect
16. #14187C3direct (N × H)
43. C3×#392C4semidirect
61. C22×C4×D4C2×C3semidirect
63. C2×#390C2×C3semidirect
64. C2×#388C2×C3semidirect
65. C2×#386C2×C3semidirect
66. C2×#386C2×C3semidirect
67. C2×C4×C22⋊C4C2×C3semidirect
68. #1439C2×C3semidirect
69. #1438C2×C3semidirect
70. #1438C2×C3semidirect
71. #1437C2×C3semidirect
72. #1437C2×C3semidirect
73. #1436C2×C3semidirect
74. #1436C2×C3semidirect
75. C22⋊#95C2×C3semidirect
98. C22×C3×D4C2×C4semidirect
99. C22×C3×D4C2×C4semidirect
113. C23×C3×C4D4semidirect
132. C2×C3×C4⋊C4D4semidirect
168. C2×C3×C22⋊C4C2×C4semidirect
169. C2×C3×C22⋊C4C2×C4semidirect
170. C2×C3×C22⋊C4C2×C4semidirect
171. C2×C3×C22⋊C4D4semidirect
191. C3×#95C2×C4semidirect
192. C3×#95D4semidirect
219. #392C3×C4semidirect
442. C22×D4C2×C3×C4semidirect
443. C22×D4C2×C3×C4semidirect
457. C23×C4C3×D4semidirect
476. C2×C4⋊C4C3×D4semidirect
512. C2×C22⋊C4C2×C3×C4semidirect
513. C2×C22⋊C4C2×C3×C4semidirect
514. C2×C22⋊C4C2×C3×C4semidirect
515. C2×C22⋊C4C3×D4semidirect
535. #95C2×C3×C4semidirect
536. #95C3×D4semidirect
743. C2×C3×C4C4×D4semidirect
1227. C2×C4C3×C4×D4semidirect
1340. C3#14187direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C22×C3×C4×D42
C2×C3×#3922
C2×C3×#3902
C2×C3×#3882
C2×C3×#3862
C2×C3×C4×C22⋊C42
C3×#14392
C3×#14382
C3×#14372
C3×#14362
C3×C22⋊#952
#141873