Finite Group Databasebeta

← C3×#15696 #10634303

Subgroups — C3×#15696 #10634303

Order 768.

1814 conjugacy classes of subgroups.

The subgroup lattice has 1166 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#399C211yesmaximal, characteristic, complemented
2C2×C3×#399C211yesmaximal, characteristic, complemented
3C2×C3×#397C211yesmaximal, characteristic, complemented
4C2×C3×#394C211yesmaximal, characteristic
5C2×C3×#390C211yesmaximal, characteristic
6C2×C3×#389C211yesmaximal, characteristic, complemented
7C2×C3×#388C211yesmaximal, characteristic, complemented
8C2×C3×#388C211yesmaximal, characteristic, complemented
9C3×#1444C211yesmaximal, characteristic, complemented
10C3×#1439C211yesmaximal, characteristic, complemented
11C3×#1439C211yesmaximal, characteristic, complemented
12C3×#1439C211yesmaximal, characteristic, complemented
13C3×#1438C211yesmaximal, characteristic
14C3×#1436C211yesmaximal, characteristic, complemented
15C3×C4⋊#95C211yesmaximal, characteristic, complemented
16#15696C311yesmaximal, characteristic, direct product factor, Sylow
17C23×C3×D4C2211yescharacteristic
18C22×C3×C4⋊C4C2211yescharacteristic
19C22×C3×C4⋊C4C2211yescharacteristic
20C22×C3×C4⋊C4C2211yescharacteristic
21C22×C3×C4⋊C4C2211yescharacteristic
22C22×C3×C4⋊C4C2211yescharacteristic
23C22×C3×C4⋊C4C2211yescharacteristic
24C22×C3×C4⋊C4C2211yescharacteristic
25C22×C3×C4⋊C4C2211yescharacteristic
26C22×C3×C22⋊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×C42C2211yescharacteristic
39C22×C3×C42C2211yescharacteristic
40C3×#399—24no—
41C3×#399—24no—
42C3×#397—24no—
43C3×#394—24no—
44C3×#390—24no—
45C3×#389—24no—
46C3×#388—24no—
47C3×#388—24no—
48C2×C3×#95C2211yescharacteristic
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×#399C2×C311yescharacteristic, complemented
61C2×#399C2×C311yescharacteristic, complemented
62C2×#397C2×C311yescharacteristic, complemented
63C2×#394C2×C311yescharacteristic
64C2×#390C2×C311yescharacteristic
65C2×#389C2×C311yescharacteristic, complemented
66C2×#388C2×C311yescharacteristic, complemented
67C2×#388C2×C311yescharacteristic, complemented
68#1444C2×C311yescharacteristic, complemented
69#1439C2×C311yescharacteristic, complemented
70#1439C2×C311yescharacteristic, complemented
71#1439C2×C311yescharacteristic, complemented
72#1438C2×C311yescharacteristic
73#1436C2×C311yescharacteristic, complemented
74C4⋊#95C2×C311yescharacteristic, complemented
75C25×C3C2311yescharacteristic
76C25×C3C2311yescharacteristic
77C22×C3×D4—22no—
78C22×C3×D4—22no—
79C22×C3×D4—22no—
80C22×C3×D4—22no—
81C22×C3×D4—22no—
82C22×C3×D4—41no—
83C22×C3×D4—41no—
84C23×C3×C4C2311yescharacteristic
85C23×C3×C4C2311yescharacteristic
86C23×C3×C4C2311yescharacteristic
87C23×C3×C4C2311yescharacteristic
88C23×C3×C4C2311yescharacteristic
89C23×C3×C4C2311yescharacteristic
90C23×C3×C4C2311yescharacteristic
91C23×C3×C4C2311yescharacteristic
92C23×C3×C4C2311yescharacteristic
93C23×C3×C4C2311yescharacteristic
94C23×C3×C4C2311yescharacteristic
95C23×C3×C4C2311yescharacteristic
96C23×C3×C4C2311yescharacteristic
97C2×C3×C4⋊C4—22no—
98C2×C3×C4⋊C4—22no—
99C2×C3×C4⋊C4—22no—
100C2×C3×C4⋊C4—22no—
101C2×C3×C4⋊C4—22no—
102C2×C3×C4⋊C4—22no—
103C2×C3×C4⋊C4—22no—
104C2×C3×C4⋊C4—22no—
105C2×C3×C4⋊C4—22no—
106C2×C3×C4⋊C4—22no—
107C2×C3×C4⋊C4—22no—
108C2×C3×C4⋊C4—22no—
109C2×C3×C4⋊C4—22no—
110C2×C3×C4⋊C4—22no—
111C2×C3×C4⋊C4—22no—
112C2×C3×C4⋊C4—22no—
113C2×C3×C4⋊C4—22no—
114C2×C3×C4⋊C4—41no—
115C2×C3×C4⋊C4—41no—
116C2×C3×C4⋊C4—41no—
117C2×C3×C4⋊C4—41no—
118C2×C3×C4⋊C4—41no—
119C2×C3×C4⋊C4—41no—
120C2×C3×C4⋊C4D414yes—
121C2×C3×C22⋊C4—22no—
122C2×C3×C22⋊C4—22no—
123C2×C3×C22⋊C4—22no—
124C2×C3×C22⋊C4—22no—
125C2×C3×C22⋊C4—22no—
126C2×C3×C22⋊C4—22no—
127C2×C3×C22⋊C4—22no—
128C2×C3×C22⋊C4—22no—
129C2×C3×C22⋊C4—22no—
130C2×C3×C22⋊C4—22no—
131C2×C3×C22⋊C4—22no—
132C2×C3×C22⋊C4—22no—
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—41no—
149C2×C3×C22⋊C4—41no—
150C2×C3×C22⋊C4—41no—
151C2×C3×C22⋊C4—41no—
152C2×C3×C22⋊C4—41no—
153C2×C3×C22⋊C4—41no—
154C2×C3×C22⋊C4—41no—
155C2×C3×C22⋊C4—41no—
156C2×C3×C22⋊C4D414yes—
157C2×C3×C42—22no—
158C2×C3×C42—22no—
159C2×C3×C42—22no—
160C2×C3×C42—22no—
161C2×C3×C42—22no—
162C2×C3×C42—41no—
163C3×#95—22no—
164C3×#95—22no—
165C3×#95—22no—
166C3×#95—22no—
167C3×#95—22no—
168C3×#95—22no—
169C3×#95—22no—
170C3×#95—22no—
171C3×#95—22no—
172C3×#95—41no—
173C3×#95D414yescomplemented
174C3×#95D414yescomplemented
175C23×D4C22×C311yescharacteristic
176C22×C4⋊C4C22×C311yescharacteristic
177C22×C4⋊C4C22×C311yescharacteristic
178C22×C4⋊C4C22×C311yescharacteristic
179C22×C4⋊C4C22×C311yescharacteristic
180C22×C4⋊C4C22×C311yescharacteristic
181C22×C4⋊C4C22×C311yescharacteristic
182C22×C4⋊C4C22×C311yescharacteristic
183C22×C4⋊C4C22×C311yescharacteristic
184C22×C22⋊C4C22×C311yescharacteristic
185C22×C22⋊C4C22×C311yescharacteristic
186C22×C22⋊C4C22×C311yescharacteristic
187C22×C22⋊C4C22×C311yescharacteristic
188C22×C22⋊C4C22×C311yescharacteristic
189C22×C22⋊C4C22×C311yescharacteristic
190C22×C22⋊C4C22×C311yescharacteristic
191C22×C22⋊C4C22×C311yescharacteristic
192C22×C22⋊C4C22×C311yescharacteristic
193C22×C22⋊C4C22×C311yescharacteristic
194C22×C22⋊C4C22×C311yescharacteristic
195C22×C22⋊C4C22×C311yescharacteristic
196C22×C42C22×C311yescharacteristic
197C22×C42C22×C311yescharacteristic
198#399—24no—
199#399—24no—
200#397—24no—
201#394—24no—
202#390—24no—
203#389—24no—
204#388—24no—
205#388—24no—
206C2×#95C22×C311yescharacteristic
207C2×#95C22×C311yescharacteristic
208C2×#95C22×C311yescharacteristic
209C2×#95C22×C311yescharacteristic
210C2×#95C22×C311yescharacteristic
211C2×#95C22×C311yescharacteristic
212C2×#95C22×C311yescharacteristic
213C2×#95C22×C311yescharacteristic
214C2×#95C22×C311yescharacteristic
215C2×#95C22×C311yescharacteristic
216C2×#95C22×C311yescharacteristic
217C2×#95C22×C311yescharacteristic
218C24×C3—21no—
219C24×C3—21no—
220C24×C3—21no—
221C24×C3—21no—
222C24×C3—21no—
223C24×C3—21no—
224C24×C3—21no—
225C24×C3—21no—
226C24×C3—21no—
227C24×C3—21no—
228C24×C3—21no—
229C24×C3—21no—
230C24×C3—21no—
231C24×C3—21no—
232C24×C3—21no—
233C24×C3—21no—
234C24×C3—21no—
235C24×C3—21no—
236C24×C3—21no—
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×C3C2×D412yes—
247C24×C3#4112yes—
248C24×C3C2411yescharacteristic
249C2×C3×D4—28no—
250C2×C3×D4—44no—
251C2×C3×D4—44no—
252C2×C3×D4—44no—
253C2×C3×D4—44no—
254C2×C3×D4—44no—
255C2×C3×D4—44no—
256C22×C3×C4—21no—
257C22×C3×C4—21no—
258C22×C3×C4—21no—
259C22×C3×C4—21no—
260C22×C3×C4—21no—
261C22×C3×C4—21no—
262C22×C3×C4—21no—
263C22×C3×C4—21no—
264C22×C3×C4—21no—
265C22×C3×C4—21no—
266C22×C3×C4—21no—
267C22×C3×C4—21no—
268C22×C3×C4—21no—
269C22×C3×C4—21no—
270C22×C3×C4—21no—
271C22×C3×C4—21no—
272C22×C3×C4—21no—
273C22×C3×C4—21no—
274C22×C3×C4—21no—
275C22×C3×C4—21no—
276C22×C3×C4—21no—
277C22×C3×C4—21no—
278C22×C3×C4—21no—
279C22×C3×C4—21no—
280C22×C3×C4—21no—
281C22×C3×C4—21no—
282C22×C3×C4—21no—
283C22×C3×C4—21no—
284C22×C3×C4—21no—
285C22×C3×C4—21no—
286C22×C3×C4—21no—
287C22×C3×C4—21no—
288C22×C3×C4—21no—
289C22×C3×C4—21no—
290C22×C3×C4—21no—
291C22×C3×C4—21no—
292C22×C3×C4—21no—
293C22×C3×C4—21no—
294C22×C3×C4—21no—
295C22×C3×C4—21no—
296C22×C3×C4—21no—
297C22×C3×C4—21no—
298C22×C3×C4—21no—
299C22×C3×C4—21no—
300C22×C3×C4—21no—
301C22×C3×C4—21no—
302C22×C3×C4—21no—
303C22×C3×C4—21no—
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—21no—
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×C4C2×D412yes—
333C22×C3×C4C2×D412yes—
334C22×C3×C4C2×D412yes—
335C22×C3×C4C2×D412yes—
336C22×C3×C4C2×D412yes—
337C22×C3×C4C2×D412yes—
338C22×C3×C4C2×D412yes—
339C22×C3×C4C2×D412yes—
340C22×C3×C4C2×D412yes—
341C22×C3×C4C2×D412yes—
342C22×C3×C4C2×D412yes—
343C22×C3×C4#4112yes—
344C22×C3×C4#4112yes—
345C22×C3×C4#4112yes—
346C22×C3×C4#4112yes—
347C3×C4⋊C4—28no—
348C3×C4⋊C4—44no—
349C3×C4⋊C4—44no—
350C3×C4⋊C4—44no—
351C3×C4⋊C4—44no—
352C3×C4⋊C4—44no—
353C3×C4⋊C4—44no—
354C3×C4⋊C4—44no—
355C3×C22⋊C4—28no—
356C3×C22⋊C4—28no—
357C3×C22⋊C4—44no—
358C3×C22⋊C4—44no—
359C3×C22⋊C4—44no—
360C3×C22⋊C4—44no—
361C3×C22⋊C4—44no—
362C3×C22⋊C4—44no—
363C3×C22⋊C4—44no—
364C3×C22⋊C4—44no—
365C3×C22⋊C4—44no—
366C3×C22⋊C4—44no—
367C3×C42—44no—
368C3×C42—44no—
369C25C23×C311yescharacteristic
370C25C23×C311yescharacteristic
371C22×D4—22no—
372C22×D4—22no—
373C22×D4—22no—
374C22×D4—22no—
375C22×D4—22no—
376C22×D4—41no—
377C22×D4—41no—
378C23×C4C23×C311yescharacteristic
379C23×C4C23×C311yescharacteristic
380C23×C4C23×C311yescharacteristic
381C23×C4C23×C311yescharacteristic
382C23×C4C23×C311yescharacteristic
383C23×C4C23×C311yescharacteristic
384C23×C4C23×C311yescharacteristic
385C23×C4C23×C311yescharacteristic
386C23×C4C23×C311yescharacteristic
387C23×C4C23×C311yescharacteristic
388C23×C4C23×C311yescharacteristic
389C23×C4C23×C311yescharacteristic
390C23×C4C23×C311yescharacteristic
391C2×C4⋊C4—22no—
392C2×C4⋊C4—22no—
393C2×C4⋊C4—22no—
394C2×C4⋊C4—22no—
395C2×C4⋊C4—22no—
396C2×C4⋊C4—22no—
397C2×C4⋊C4—22no—
398C2×C4⋊C4—22no—
399C2×C4⋊C4—22no—
400C2×C4⋊C4—22no—
401C2×C4⋊C4—22no—
402C2×C4⋊C4—22no—
403C2×C4⋊C4—22no—
404C2×C4⋊C4—22no—
405C2×C4⋊C4—22no—
406C2×C4⋊C4—22no—
407C2×C4⋊C4—22no—
408C2×C4⋊C4—41no—
409C2×C4⋊C4—41no—
410C2×C4⋊C4—41no—
411C2×C4⋊C4—41no—
412C2×C4⋊C4—41no—
413C2×C4⋊C4—41no—
414C2×C4⋊C4C3×D414yes—
415C2×C22⋊C4—22no—
416C2×C22⋊C4—22no—
417C2×C22⋊C4—22no—
418C2×C22⋊C4—22no—
419C2×C22⋊C4—22no—
420C2×C22⋊C4—22no—
421C2×C22⋊C4—22no—
422C2×C22⋊C4—22no—
423C2×C22⋊C4—22no—
424C2×C22⋊C4—22no—
425C2×C22⋊C4—22no—
426C2×C22⋊C4—22no—
427C2×C22⋊C4—22no—
428C2×C22⋊C4—22no—
429C2×C22⋊C4—22no—
430C2×C22⋊C4—22no—
431C2×C22⋊C4—22no—
432C2×C22⋊C4—22no—
433C2×C22⋊C4—22no—
434C2×C22⋊C4—22no—
435C2×C22⋊C4—22no—
436C2×C22⋊C4—22no—
437C2×C22⋊C4—22no—
438C2×C22⋊C4—22no—
439C2×C22⋊C4—22no—
440C2×C22⋊C4—22no—
441C2×C22⋊C4—22no—
442C2×C22⋊C4—41no—
443C2×C22⋊C4—41no—
444C2×C22⋊C4—41no—
445C2×C22⋊C4—41no—
446C2×C22⋊C4—41no—
447C2×C22⋊C4—41no—
448C2×C22⋊C4—41no—
449C2×C22⋊C4—41no—
450C2×C22⋊C4C3×D414yes—
451C2×C42—22no—
452C2×C42—22no—
453C2×C42—22no—
454C2×C42—22no—
455C2×C42—22no—
456C2×C42—41no—
457#95—22no—
458#95—22no—
459#95—22no—
460#95—22no—
461#95—22no—
462#95—22no—
463#95—22no—
464#95—22no—
465#95—22no—
466#95—41no—
467#95C3×D414yescomplemented
468#95C3×D414yescomplemented
469C23×C3—22no—
470C23×C3—22no—
471C23×C3—22no—
472C23×C3—22no—
473C23×C3—22no—
474C23×C3—22no—
475C23×C3—22no—
476C23×C3—22no—
477C23×C3—22no—
478C23×C3—22no—
479C23×C3—22no—
480C23×C3—22no—
481C23×C3—22no—
482C23×C3—22no—
483C23×C3—41no—
484C23×C3—41no—
485C23×C3—41no—
486C23×C3—41no—
487C23×C3—41no—
488C23×C3—41no—
489C23×C3—41no—
490C23×C3—41no—
491C23×C3—41no—
492C23×C3—41no—
493C23×C3—41no—
494C23×C3—41no—
495C23×C3—41no—
496C23×C3—41no—
497C23×C3—41no—
498C23×C3—41no—
499C23×C3—41no—
500C23×C3—41no—
501C23×C3—41no—
502C23×C3—41no—
503C23×C3—41no—
504C23×C3—41no—
505C23×C3—41no—
506C23×C3—41no—
507C23×C3—41no—
508C23×C3—41no—
509C23×C3—41no—
510C23×C3—41no—
511C23×C3—41no—
512C23×C3—41no—
513C23×C3—41no—
514C23×C3—41no—
515C23×C3—41no—
516C23×C3—41no—
517C23×C3—41no—
518C23×C3—41no—
519C23×C3—41no—
520C23×C3—41no—
521C23×C3—41no—
522C23×C3—41no—
523C23×C3—41no—
524C23×C3—41no—
525C23×C3—41no—
526C23×C3—41no—
527C23×C3—41no—
528C23×C3—41no—
529C23×C3—41no—
530C23×C3—41no—
531C23×C3—41no—
532C23×C3—41no—
533C23×C3—41no—
534C23×C3—41no—
535C23×C3—41no—
536C23×C3—41no—
537C23×C3—41no—
538C23×C3—41no—
539C23×C3C22×D411yescharacteristic
540C23×C3C22×D411yescharacteristic
541C23×C3C22×D411yescharacteristic
542C23×C3C22×D411yescharacteristic
543C23×C3C2×#4111yescharacteristic
544C23×C3C2×#4111yescharacteristic
545C23×C3C2×#4111yescharacteristic
546C23×C3C2×#4111yescharacteristic
547C23×C3C2×#4111yescharacteristic
548C23×C3H(5,𝔽2)11yescharacteristic
549C23×C3H(5,𝔽2)11yescharacteristic
550C23×C3H(5,𝔽2)11yescharacteristic
551C23×C32−1+411yescharacteristic
552C23×C32−1+411yescharacteristic
553C23×C32−1+411yescharacteristic
554C3×D4—416no—
555C2×C3×C4—22no—
556C2×C3×C4—22no—
557C2×C3×C4—22no—
558C2×C3×C4—22no—
559C2×C3×C4—22no—
560C2×C3×C4—22no—
561C2×C3×C4—22no—
562C2×C3×C4—22no—
563C2×C3×C4—22no—
564C2×C3×C4—22no—
565C2×C3×C4—22no—
566C2×C3×C4—22no—
567C2×C3×C4—22no—
568C2×C3×C4—22no—
569C2×C3×C4—22no—
570C2×C3×C4—22no—
571C2×C3×C4—22no—
572C2×C3×C4—22no—
573C2×C3×C4—22no—
574C2×C3×C4—22no—
575C2×C3×C4—22no—
576C2×C3×C4—22no—
577C2×C3×C4—22no—
578C2×C3×C4—22no—
579C2×C3×C4—22no—
580C2×C3×C4—22no—
581C2×C3×C4—22no—
582C2×C3×C4—22no—
583C2×C3×C4—22no—
584C2×C3×C4—22no—
585C2×C3×C4—22no—
586C2×C3×C4—22no—
587C2×C3×C4—22no—
588C2×C3×C4—22no—
589C2×C3×C4—22no—
590C2×C3×C4—22no—
591C2×C3×C4—41no—
592C2×C3×C4—41no—
593C2×C3×C4—41no—
594C2×C3×C4—41no—
595C2×C3×C4—41no—
596C2×C3×C4—41no—
597C2×C3×C4—41no—
598C2×C3×C4—41no—
599C2×C3×C4—41no—
600C2×C3×C4—41no—
601C2×C3×C4—41no—
602C2×C3×C4—41no—
603C2×C3×C4—41no—
604C2×C3×C4—41no—
605C2×C3×C4—41no—
606C2×C3×C4—41no—
607C2×C3×C4—41no—
608C2×C3×C4—41no—
609C2×C3×C4—41no—
610C2×C3×C4—41no—
611C2×C3×C4—41no—
612C2×C3×C4—41no—
613C2×C3×C4—41no—
614C2×C3×C4—41no—
615C2×C3×C4—41no—
616C2×C3×C4—41no—
617C2×C3×C4—41no—
618C2×C3×C4—41no—
619C2×C3×C4—41no—
620C2×C3×C4—41no—
621C2×C3×C4—41no—
622C2×C3×C4—41no—
623C2×C3×C4—41no—
624C2×C3×C4—41no—
625C2×C3×C4—41no—
626C2×C3×C4—41no—
627C2×C3×C4—41no—
628C2×C3×C4—41no—
629C2×C3×C4—41no—
630C2×C3×C4—41no—
631C2×C3×C4—41no—
632C2×C3×C4—41no—
633C2×C3×C4—41no—
634C2×C3×C4—41no—
635C2×C3×C4—41no—
636C2×C3×C4—41no—
637C2×C3×C4—41no—
638C2×C3×C4—41no—
639C2×C3×C4—41no—
640C2×C3×C4—41no—
641C2×C3×C4—41no—
642C2×C3×C4—41no—
643C2×C3×C4#12114yes—
644C2×C3×C4#12314yes—
645C2×C3×C4#12714yes—
646C24—21no—
647C24—21no—
648C24—21no—
649C24—21no—
650C24—21no—
651C24—21no—
652C24—21no—
653C24—21no—
654C24—21no—
655C24—21no—
656C24—21no—
657C24—21no—
658C24—21no—
659C24—21no—
660C24—21no—
661C24—21no—
662C24—21no—
663C24—21no—
664C24—21no—
665C24—21no—
666C24—21no—
667C24—21no—
668C24—21no—
669C24—21no—
670C24—21no—
671C24—21no—
672C24—21no—
673C24—21no—
674C24C2×C3×D412yes—
675C24C3×#4112yes—
676C24C24×C311yescharacteristic
677C2×D4—28no—
678C2×D4—44no—
679C2×D4—44no—
680C2×D4—44no—
681C2×D4—44no—
682C2×D4—44no—
683C2×D4—44no—
684C22×C4—21no—
685C22×C4—21no—
686C22×C4—21no—
687C22×C4—21no—
688C22×C4—21no—
689C22×C4—21no—
690C22×C4—21no—
691C22×C4—21no—
692C22×C4—21no—
693C22×C4—21no—
694C22×C4—21no—
695C22×C4—21no—
696C22×C4—21no—
697C22×C4—21no—
698C22×C4—21no—
699C22×C4—21no—
700C22×C4—21no—
701C22×C4—21no—
702C22×C4—21no—
703C22×C4—21no—
704C22×C4—21no—
705C22×C4—21no—
706C22×C4—21no—
707C22×C4—21no—
708C22×C4—21no—
709C22×C4—21no—
710C22×C4—21no—
711C22×C4—21no—
712C22×C4—21no—
713C22×C4—21no—
714C22×C4—21no—
715C22×C4—21no—
716C22×C4—21no—
717C22×C4—21no—
718C22×C4—21no—
719C22×C4—21no—
720C22×C4—21no—
721C22×C4—21no—
722C22×C4—21no—
723C22×C4—21no—
724C22×C4—21no—
725C22×C4—21no—
726C22×C4—21no—
727C22×C4—21no—
728C22×C4—21no—
729C22×C4—21no—
730C22×C4—21no—
731C22×C4—21no—
732C22×C4—21no—
733C22×C4—21no—
734C22×C4—21no—
735C22×C4—21no—
736C22×C4—21no—
737C22×C4—21no—
738C22×C4—21no—
739C22×C4—21no—
740C22×C4—21no—
741C22×C4—21no—
742C22×C4—21no—
743C22×C4—21no—
744C22×C4—21no—
745C22×C4—21no—
746C22×C4—21no—
747C22×C4—21no—
748C22×C4—21no—
749C22×C4—21no—
750C22×C4—21no—
751C22×C4—21no—
752C22×C4—21no—
753C22×C4—21no—
754C22×C4—21no—
755C22×C4—21no—
756C22×C4—21no—
757C22×C4—21no—
758C22×C4—21no—
759C22×C4—21no—
760C22×C4C2×C3×D412yes—
761C22×C4C2×C3×D412yes—
762C22×C4C2×C3×D412yes—
763C22×C4C2×C3×D412yes—
764C22×C4C2×C3×D412yes—
765C22×C4C2×C3×D412yes—
766C22×C4C2×C3×D412yes—
767C22×C4C2×C3×D412yes—
768C22×C4C2×C3×D412yes—
769C22×C4C2×C3×D412yes—
770C22×C4C2×C3×D412yes—
771C22×C4C3×#4112yes—
772C22×C4C3×#4112yes—
773C22×C4C3×#4112yes—
774C22×C4C3×#4112yes—
775C4⋊C4—28no—
776C4⋊C4—44no—
777C4⋊C4—44no—
778C4⋊C4—44no—
779C4⋊C4—44no—
780C4⋊C4—44no—
781C4⋊C4—44no—
782C4⋊C4—44no—
783C22⋊C4—28no—
784C22⋊C4—28no—
785C22⋊C4—44no—
786C22⋊C4—44no—
787C22⋊C4—44no—
788C22⋊C4—44no—
789C22⋊C4—44no—
790C22⋊C4—44no—
791C22⋊C4—44no—
792C22⋊C4—44no—
793C22⋊C4—44no—
794C22⋊C4—44no—
795C42—44no—
796C42—44no—
797C22×C3—42no—
798C22×C3—42no—
799C22×C3—42no—
800C22×C3—42no—
801C22×C3—42no—
802C22×C3—42no—
803C22×C3—42no—
804C22×C3—42no—
805C22×C3—42no—
806C22×C3—42no—
807C22×C3—42no—
808C22×C3—42no—
809C22×C3—42no—
810C22×C3—42no—
811C22×C3—81no—
812C22×C3—81no—
813C22×C3—81no—
814C22×C3—81no—
815C22×C3—81no—
816C22×C3—81no—
817C22×C3—81no—
818C22×C3—81no—
819C22×C3—81no—
820C22×C3—81no—
821C22×C3—81no—
822C22×C3—81no—
823C22×C3—81no—
824C22×C3—81no—
825C22×C3—81no—
826C22×C3—81no—
827C22×C3C2×#12111yescharacteristic
828C22×C3C2×#12311yescharacteristic
829C22×C3#52511yescharacteristic
830C22×C3#52511yescharacteristic
831C22×C3#52911yescharacteristic
832C22×C3C2×#12711yescharacteristic
833C22×C3#53511yescharacteristic
834C22×C3#53611yescharacteristic
835C22×C3#53611yescharacteristic
836C22×C3#53711yescharacteristic
837C22×C3#53811yescharacteristic
838C22×C3#53911yescharacteristic
839C22×C3#53911yescharacteristic
840C22×C3#54211yescharacteristic
841C22×C3#54211yescharacteristic
842C22×C3D4211yescharacteristic
843C22×C3D4211yescharacteristic
844C22×C3#54611yescharacteristic
845C22×C3#54611yescharacteristic
846C22×C3#54611yescharacteristic
847C22×C3#54711yescharacteristic
848C22×C3#54711yescharacteristic
849C22×C3#54711yescharacteristic
850C22×C3#54711yescharacteristic
851C22×C3#54711yescharacteristic
852C22×C3#54811yescharacteristic
853C22×C3#54811yescharacteristic
854C22×C3#55011yescharacteristic
855C22×C3#55011yescharacteristic
856C22×C3#55111yescharacteristic
857C22×C3#55211yescharacteristic
858C22×C3#55611yescharacteristic
859C22×C3#55911yescharacteristic
860C22×C3#56211yescharacteristic
861C22×C3#56311yescharacteristic
862C3×C4—24no—
863C3×C4—24no—
864C3×C4—24no—
865C3×C4—42no—
866C3×C4—42no—
867C3×C4—42no—
868C3×C4—42no—
869C3×C4—42no—
870C3×C4—42no—
871C3×C4—81no—
872C3×C4—81no—
873C3×C4—81no—
874C3×C4—81no—
875C23—22no—
876C23—22no—
877C23—22no—
878C23—22no—
879C23—22no—
880C23—22no—
881C23—22no—
882C23—22no—
883C23—22no—
884C23—22no—
885C23—22no—
886C23—22no—
887C23—22no—
888C23—22no—
889C23—41no—
890C23—41no—
891C23—41no—
892C23—41no—
893C23—41no—
894C23—41no—
895C23—41no—
896C23—41no—
897C23—41no—
898C23—41no—
899C23—41no—
900C23—41no—
901C23—41no—
902C23—41no—
903C23—41no—
904C23—41no—
905C23—41no—
906C23—41no—
907C23—41no—
908C23—41no—
909C23—41no—
910C23—41no—
911C23—41no—
912C23—41no—
913C23—41no—
914C23—41no—
915C23—41no—
916C23—41no—
917C23—41no—
918C23—41no—
919C23—41no—
920C23—41no—
921C23—41no—
922C23—41no—
923C23—41no—
924C23—41no—
925C23—41no—
926C23—41no—
927C23—41no—
928C23—41no—
929C23—41no—
930C23—41no—
931C23—41no—
932C23—41no—
933C23—41no—
934C23—41no—
935C23—41no—
936C23—41no—
937C23—41no—
938C23—41no—
939C23—41no—
940C23—41no—
941C23—41no—
942C23—41no—
943C23—41no—
944C23—41no—
945C23C22×C3×D411yescharacteristic
946C23C22×C3×D411yescharacteristic
947C23C22×C3×D411yescharacteristic
948C23C22×C3×D411yescharacteristic
949C23C2×C3×#4111yescharacteristic
950C23C2×C3×#4111yescharacteristic
951C23C2×C3×#4111yescharacteristic
952C23C2×C3×#4111yescharacteristic
953C23C2×C3×#4111yescharacteristic
954C23C3×H(5,𝔽2)11yescharacteristic
955C23C3×H(5,𝔽2)11yescharacteristic
956C23C3×H(5,𝔽2)11yescharacteristic
957C23C3×2−1+411yescharacteristic
958C23C3×2−1+411yescharacteristic
959C23C3×2−1+411yescharacteristic
960D4—416no—
961C2×C4—22no—
962C2×C4—22no—
963C2×C4—22no—
964C2×C4—22no—
965C2×C4—22no—
966C2×C4—22no—
967C2×C4—22no—
968C2×C4—22no—
969C2×C4—22no—
970C2×C4—22no—
971C2×C4—22no—
972C2×C4—22no—
973C2×C4—22no—
974C2×C4—22no—
975C2×C4—22no—
976C2×C4—22no—
977C2×C4—22no—
978C2×C4—22no—
979C2×C4—22no—
980C2×C4—22no—
981C2×C4—22no—
982C2×C4—22no—
983C2×C4—22no—
984C2×C4—22no—
985C2×C4—22no—
986C2×C4—22no—
987C2×C4—22no—
988C2×C4—22no—
989C2×C4—22no—
990C2×C4—22no—
991C2×C4—22no—
992C2×C4—22no—
993C2×C4—22no—
994C2×C4—22no—
995C2×C4—22no—
996C2×C4—22no—
997C2×C4—41no—
998C2×C4—41no—
999C2×C4—41no—
1000C2×C4—41no—
1001C2×C4—41no—
1002C2×C4—41no—
1003C2×C4—41no—
1004C2×C4—41no—
1005C2×C4—41no—
1006C2×C4—41no—
1007C2×C4—41no—
1008C2×C4—41no—
1009C2×C4—41no—
1010C2×C4—41no—
1011C2×C4—41no—
1012C2×C4—41no—
1013C2×C4—41no—
1014C2×C4—41no—
1015C2×C4—41no—
1016C2×C4—41no—
1017C2×C4—41no—
1018C2×C4—41no—
1019C2×C4—41no—
1020C2×C4—41no—
1021C2×C4—41no—
1022C2×C4—41no—
1023C2×C4—41no—
1024C2×C4—41no—
1025C2×C4—41no—
1026C2×C4—41no—
1027C2×C4—41no—
1028C2×C4—41no—
1029C2×C4—41no—
1030C2×C4—41no—
1031C2×C4—41no—
1032C2×C4—41no—
1033C2×C4—41no—
1034C2×C4—41no—
1035C2×C4—41no—
1036C2×C4—41no—
1037C2×C4—41no—
1038C2×C4—41no—
1039C2×C4—41no—
1040C2×C4—41no—
1041C2×C4—41no—
1042C2×C4—41no—
1043C2×C4—41no—
1044C2×C4—41no—
1045C2×C4—41no—
1046C2×C4—41no—
1047C2×C4—41no—
1048C2×C4—41no—
1049C2×C4C3×#12114yes—
1050C2×C4C3×#12314yes—
1051C2×C4C3×#12714yes—
1052C2×C3—82no—
1053C2×C3—82no—
1054C2×C3#241511yescharacteristic
1055C2×C3#241811yescharacteristic
1056C2×C3#242511yescharacteristic
1057C2×C3#244811yescharacteristic
1058C2×C3#245511yescharacteristic
1059C2×C3#247911yescharacteristic
1060C2×C3#250111yescharacteristic
1061C2×C3#254011yescharacteristic
1062C2×C3#254111yescharacteristic
1063C2×C3#267211yescharacteristic
1064C2×C3#267411yescharacteristic
1065C2×C3#269411yescharacteristic
1066C2×C3#271011yescharacteristic
1067C2×C3#272311yescharacteristic
1068C2×C3#272711yescharacteristic
1069C22—42no—
1070C22—42no—
1071C22—42no—
1072C22—42no—
1073C22—42no—
1074C22—42no—
1075C22—42no—
1076C22—42no—
1077C22—42no—
1078C22—42no—
1079C22—42no—
1080C22—42no—
1081C22—42no—
1082C22—42no—
1083C22—81no—
1084C22—81no—
1085C22—81no—
1086C22—81no—
1087C22—81no—
1088C22—81no—
1089C22—81no—
1090C22—81no—
1091C22—81no—
1092C22—81no—
1093C22—81no—
1094C22—81no—
1095C22—81no—
1096C22—81no—
1097C22—81no—
1098C22—81no—
1099C22C2×C3×#12111yescharacteristic
1100C22C2×C3×#12311yescharacteristic
1101C22C3×#52511yescharacteristic
1102C22C3×#52511yescharacteristic
1103C22C3×#52911yescharacteristic
1104C22C2×C3×#12711yescharacteristic
1105C22C3×#53511yescharacteristic
1106C22C3×#53611yescharacteristic
1107C22C3×#53611yescharacteristic
1108C22C3×#53711yescharacteristic
1109C22C3×#53811yescharacteristic
1110C22C3×#53911yescharacteristic
1111C22C3×#53911yescharacteristic
1112C22C3×#54211yescharacteristic
1113C22C3×#54211yescharacteristic
1114C22C3×D4211yescharacteristic
1115C22C3×D4211yescharacteristic
1116C22C3×#54611yescharacteristic
1117C22C3×#54611yescharacteristic
1118C22C3×#54611yescharacteristic
1119C22C3×#54711yescharacteristic
1120C22C3×#54711yescharacteristic
1121C22C3×#54711yescharacteristic
1122C22C3×#54711yescharacteristic
1123C22C3×#54711yescharacteristic
1124C22C3×#54811yescharacteristic
1125C22C3×#54811yescharacteristic
1126C22C3×#55011yescharacteristic
1127C22C3×#55011yescharacteristic
1128C22C3×#55111yescharacteristic
1129C22C3×#55211yescharacteristic
1130C22C3×#55611yescharacteristic
1131C22C3×#55911yescharacteristic
1132C22C3×#56211yescharacteristic
1133C22C3×#56311yescharacteristic
1134C4—24no—
1135C4—24no—
1136C4—24no—
1137C4—42no—
1138C4—42no—
1139C4—42no—
1140C4—42no—
1141C4—42no—
1142C4—42no—
1143C4—81no—
1144C4—81no—
1145C4—81no—
1146C4—81no—
1147C3#1569611yescharacteristic, direct product factor, Sylow
1148C2—82no—
1149C2—82no—
1150C2C3×#241511yescharacteristic
1151C2C3×#241811yescharacteristic
1152C2C3×#242511yescharacteristic
1153C2C3×#244811yescharacteristic
1154C2C3×#245511yescharacteristic
1155C2C3×#247911yescharacteristic
1156C2C3×#250111yescharacteristic
1157C2C3×#254011yescharacteristic
1158C2C3×#254111yescharacteristic
1159C2C3×#267211yescharacteristic
1160C2C3×#267411yescharacteristic
1161C2C3×#269411yescharacteristic
1162C2C3×#271011yescharacteristic
1163C2C3×#272311yescharacteristic
1164C2C3×#272711yescharacteristic
subgroupG/H
center, socleC24×C3C24
commutator, Frattini, cosocleC24C24×C3
prime radicalC23×C3×D4C22
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C24×C3 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C3×#399C2semidirect
2. C2×C3×#399C2semidirect
3. C2×C3×#397C2semidirect
6. C2×C3×#389C2semidirect
7. C2×C3×#388C2semidirect
8. C2×C3×#388C2semidirect
9. C3×#1444C2semidirect
10. C3×#1439C2semidirect
11. C3×#1439C2semidirect
12. C3×#1439C2semidirect
14. C3×#1436C2semidirect
15. C3×C4⋊#95C2semidirect
16. #15696C3direct (N × H)
60. C2×#399C2×C3semidirect
61. C2×#399C2×C3semidirect
62. C2×#397C2×C3semidirect
65. C2×#389C2×C3semidirect
66. C2×#388C2×C3semidirect
67. C2×#388C2×C3semidirect
68. #1444C2×C3semidirect
69. #1439C2×C3semidirect
70. #1439C2×C3semidirect
71. #1439C2×C3semidirect
73. #1436C2×C3semidirect
74. C4⋊#95C2×C3semidirect
173. C3×#95D4semidirect
174. C3×#95D4semidirect
467. #95C3×D4semidirect
468. #95C3×D4semidirect
1147. C3#15696direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×#3992
C2×C3×#3972
C2×C3×#3942
C2×C3×#3902
C2×C3×#3892
C2×C3×#3882
C3×#14442
C3×#14392
C3×#14382
C3×#14362
C3×C4⋊#952
#156963