Finite Group Databasebeta

← C3×#14770 #10633377

Subgroups — C3×#14770 #10633377

Order 768.

1770 conjugacy classes of subgroups.

The subgroup lattice has 1046 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#396C211yesmaximal, characteristic
2C2×C3×#395C211yesmaximal, characteristic, complemented
3C2×C3×#393C211yesmaximal, characteristic
4C2×C3×#391C211yesmaximal, characteristic, complemented
5C2×C3×#380C211yesmaximal, characteristic
6C2×C3×C4×C22⋊C4C211yesmaximal, characteristic
7C3×#1444C211yesmaximal, characteristic, complemented
8C3×#1442C211yesmaximal, characteristic, complemented
9C3×#1441C211yesmaximal, characteristic, complemented
10C3×#1439C211yesmaximal, characteristic
11C3×#1439C211yesmaximal, characteristic
12C3×#1436C211yesmaximal, characteristic, complemented
13C3×#1436C211yesmaximal, characteristic, complemented
14C3×C4⋊#95C211yesmaximal, characteristic, complemented
15C3×C22⋊#95C211yesmaximal, characteristic
16#14770C311yesmaximal, characteristic, direct product factor, Sylow
17C23×C3×Q8C2211yescharacteristic
18C24×C3×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×C42C2211yescharacteristic
33C22×C3×C42C2211yescharacteristic
34C3×#396—24no—
35C3×#395—24no—
36C3×#393—24no—
37C3×#391—24no—
38C3×#380—24no—
39C3×C4×C22⋊C4—24no—
40C2×C3×#95C2211yescharacteristic
41C2×C3×#95C2211yescharacteristic
42C2×C3×#95C2211yescharacteristic
43C2×C3×#95C2211yescharacteristic
44C2×C3×#95C2211yescharacteristic
45C2×C3×#95C2211yescharacteristic
46C2×C3×#95C2211yescharacteristic
47C2×C3×#95C2211yescharacteristic
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×#396C2×C311yescharacteristic
59C2×#395C2×C311yescharacteristic, complemented
60C2×#393C2×C311yescharacteristic
61C2×#391C2×C311yescharacteristic, complemented
62C2×#380C2×C311yescharacteristic
63C2×C4×C22⋊C4C2×C311yescharacteristic
64#1444C2×C311yescharacteristic, complemented
65#1442C2×C311yescharacteristic, complemented
66#1441C2×C311yescharacteristic, complemented
67#1439C2×C311yescharacteristic
68#1439C2×C311yescharacteristic
69#1436C2×C311yescharacteristic, complemented
70#1436C2×C311yescharacteristic, complemented
71C4⋊#95C2×C311yescharacteristic, complemented
72C22⋊#95C2×C311yescharacteristic
73C25×C3C2311yescharacteristic
74C22×C3×Q8—22no—
75C22×C3×Q8—22no—
76C22×C3×Q8—22no—
77C22×C3×Q8—22no—
78C22×C3×Q8—22no—
79C22×C3×Q8—41no—
80C22×C3×Q8—41no—
81C23×C3×C4—22no—
82C23×C3×C4—22no—
83C23×C3×C4—22no—
84C23×C3×C4—22no—
85C23×C3×C4—41no—
86C23×C3×C4—41no—
87C23×C3×C4Q814yescomplemented
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
97C23×C3×C4C2311yescharacteristic
98C23×C3×C4C2311yescharacteristic
99C23×C3×C4C2311yescharacteristic
100C23×C3×C4C2311yescharacteristic
101C23×C3×C4C2311yescharacteristic
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—22no—
115C2×C3×C4⋊C4—22no—
116C2×C3×C4⋊C4—41no—
117C2×C3×C4⋊C4—41no—
118C2×C3×C4⋊C4—41no—
119C2×C3×C4⋊C4—41no—
120C2×C3×C4⋊C4—41no—
121C2×C3×C4⋊C4—41no—
122C2×C3×C4⋊C4—41no—
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—41no—
136C2×C3×C22⋊C4—41no—
137C2×C3×C22⋊C4—41no—
138C2×C3×C22⋊C4—41no—
139C2×C3×C22⋊C4D414yes—
140C2×C3×C22⋊C4Q814yescomplemented
141C2×C3×C42—22no—
142C2×C3×C42—22no—
143C2×C3×C42—22no—
144C2×C3×C42—22no—
145C2×C3×C42—41no—
146C2×C3×C42—41no—
147C3×#95—22no—
148C3×#95—22no—
149C3×#95—22no—
150C3×#95—22no—
151C3×#95—22no—
152C3×#95—22no—
153C3×#95—22no—
154C3×#95—22no—
155C3×#95—22no—
156C3×#95—22no—
157C3×#95—22no—
158C3×#95—22no—
159C3×#95—22no—
160C3×#95—22no—
161C3×#95—22no—
162C3×#95—41no—
163C3×#95D414yes—
164C3×#95D414yes—
165C23×Q8C22×C311yescharacteristic
166C24×C4C22×C311yescharacteristic
167C22×C4⋊C4C22×C311yescharacteristic
168C22×C4⋊C4C22×C311yescharacteristic
169C22×C4⋊C4C22×C311yescharacteristic
170C22×C4⋊C4C22×C311yescharacteristic
171C22×C4⋊C4C22×C311yescharacteristic
172C22×C4⋊C4C22×C311yescharacteristic
173C22×C4⋊C4C22×C311yescharacteristic
174C22×C22⋊C4C22×C311yescharacteristic
175C22×C22⋊C4C22×C311yescharacteristic
176C22×C22⋊C4C22×C311yescharacteristic
177C22×C22⋊C4C22×C311yescharacteristic
178C22×C22⋊C4C22×C311yescharacteristic
179C22×C22⋊C4C22×C311yescharacteristic
180C22×C42C22×C311yescharacteristic
181C22×C42C22×C311yescharacteristic
182#396—24no—
183#395—24no—
184#393—24no—
185#391—24no—
186#380—24no—
187C4×C22⋊C4—24no—
188C2×#95C22×C311yescharacteristic
189C2×#95C22×C311yescharacteristic
190C2×#95C22×C311yescharacteristic
191C2×#95C22×C311yescharacteristic
192C2×#95C22×C311yescharacteristic
193C2×#95C22×C311yescharacteristic
194C2×#95C22×C311yescharacteristic
195C2×#95C22×C311yescharacteristic
196C2×#95C22×C311yescharacteristic
197C2×#95C22×C311yescharacteristic
198C2×#95C22×C311yescharacteristic
199C2×#95C22×C311yescharacteristic
200C2×#95C22×C311yescharacteristic
201C2×#95C22×C311yescharacteristic
202C2×#95C22×C311yescharacteristic
203C2×#95C22×C311yescharacteristic
204C2×#95C22×C311yescharacteristic
205C2×#95C22×C311yescharacteristic
206C24×C3—21no—
207C24×C3—21no—
208C24×C3—21no—
209C24×C3—21no—
210C24×C3—21no—
211C24×C3—21no—
212C24×C3—21no—
213C24×C3—21no—
214C24×C3—21no—
215C24×C3—21no—
216C24×C3—21no—
217C24×C3—21no—
218C24×C3C2×D412yes—
219C24×C3C2×Q812yes—
220C24×C3C2×Q812yes—
221C24×C3C2411yescharacteristic
222C2×C3×Q8—28no—
223C2×C3×Q8—44no—
224C2×C3×Q8—44no—
225C2×C3×Q8—44no—
226C2×C3×Q8—44no—
227C2×C3×Q8—44no—
228C2×C3×Q8—44no—
229C22×C3×C4—21no—
230C22×C3×C4—21no—
231C22×C3×C4—21no—
232C22×C3×C4—21no—
233C22×C3×C4—21no—
234C22×C3×C4—21no—
235C22×C3×C4—21no—
236C22×C3×C4—21no—
237C22×C3×C4—21no—
238C22×C3×C4—21no—
239C22×C3×C4—21no—
240C22×C3×C4—21no—
241C22×C3×C4—21no—
242C22×C3×C4—21no—
243C22×C3×C4—21no—
244C22×C3×C4—21no—
245C22×C3×C4—21no—
246C22×C3×C4—21no—
247C22×C3×C4—21no—
248C22×C3×C4—21no—
249C22×C3×C4—21no—
250C22×C3×C4—21no—
251C22×C3×C4—21no—
252C22×C3×C4—21no—
253C22×C3×C4—21no—
254C22×C3×C4—21no—
255C22×C3×C4—21no—
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—28no—
282C22×C3×C4—28no—
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—44no—
312C22×C3×C4—44no—
313C22×C3×C4—44no—
314C22×C3×C4—44no—
315C22×C3×C4—44no—
316C22×C3×C4C2×D412yes—
317C22×C3×C4C2×D412yes—
318C22×C3×C4C2×D412yes—
319C22×C3×C4C2×D412yes—
320C22×C3×C4C2×D412yes—
321C22×C3×C4C2×D412yes—
322C22×C3×C4C2×D412yes—
323C22×C3×C4C2×D412yes—
324C22×C3×C4C2×Q812yes—
325C22×C3×C4C2×Q812yes—
326C22×C3×C4C2×Q812yes—
327C22×C3×C4C2×Q812yes—
328C22×C3×C4#4112yes—
329C22×C3×C4#4112yes—
330C22×C3×C4#4112yes—
331C22×C3×C4#4112yes—
332C22×C3×C4#4112yes—
333C22×C3×C4#4112yes—
334C3×C4⋊C4—44no—
335C3×C4⋊C4—44no—
336C3×C4⋊C4—44no—
337C3×C4⋊C4—44no—
338C3×C4⋊C4—44no—
339C3×C4⋊C4—44no—
340C3×C4⋊C4—44no—
341C3×C22⋊C4—28no—
342C3×C22⋊C4—28no—
343C3×C22⋊C4—44no—
344C3×C22⋊C4—44no—
345C3×C22⋊C4—44no—
346C3×C22⋊C4—44no—
347C3×C42—44no—
348C3×C42—44no—
349C25C23×C311yescharacteristic
350C22×Q8—22no—
351C22×Q8—22no—
352C22×Q8—22no—
353C22×Q8—22no—
354C22×Q8—22no—
355C22×Q8—41no—
356C22×Q8—41no—
357C23×C4—22no—
358C23×C4—22no—
359C23×C4—22no—
360C23×C4—22no—
361C23×C4—41no—
362C23×C4—41no—
363C23×C4C3×Q814yescomplemented
364C23×C4C23×C311yescharacteristic
365C23×C4C23×C311yescharacteristic
366C23×C4C23×C311yescharacteristic
367C23×C4C23×C311yescharacteristic
368C23×C4C23×C311yescharacteristic
369C23×C4C23×C311yescharacteristic
370C23×C4C23×C311yescharacteristic
371C23×C4C23×C311yescharacteristic
372C23×C4C23×C311yescharacteristic
373C23×C4C23×C311yescharacteristic
374C23×C4C23×C311yescharacteristic
375C23×C4C23×C311yescharacteristic
376C23×C4C23×C311yescharacteristic
377C23×C4C23×C311yescharacteristic
378C2×C4⋊C4—22no—
379C2×C4⋊C4—22no—
380C2×C4⋊C4—22no—
381C2×C4⋊C4—22no—
382C2×C4⋊C4—22no—
383C2×C4⋊C4—22no—
384C2×C4⋊C4—22no—
385C2×C4⋊C4—22no—
386C2×C4⋊C4—22no—
387C2×C4⋊C4—22no—
388C2×C4⋊C4—22no—
389C2×C4⋊C4—22no—
390C2×C4⋊C4—22no—
391C2×C4⋊C4—22no—
392C2×C4⋊C4—41no—
393C2×C4⋊C4—41no—
394C2×C4⋊C4—41no—
395C2×C4⋊C4—41no—
396C2×C4⋊C4—41no—
397C2×C4⋊C4—41no—
398C2×C4⋊C4—41no—
399C2×C22⋊C4—22no—
400C2×C22⋊C4—22no—
401C2×C22⋊C4—22no—
402C2×C22⋊C4—22no—
403C2×C22⋊C4—22no—
404C2×C22⋊C4—22no—
405C2×C22⋊C4—22no—
406C2×C22⋊C4—22no—
407C2×C22⋊C4—22no—
408C2×C22⋊C4—22no—
409C2×C22⋊C4—22no—
410C2×C22⋊C4—22no—
411C2×C22⋊C4—41no—
412C2×C22⋊C4—41no—
413C2×C22⋊C4—41no—
414C2×C22⋊C4—41no—
415C2×C22⋊C4C3×D414yes—
416C2×C22⋊C4C3×Q814yescomplemented
417C2×C42—22no—
418C2×C42—22no—
419C2×C42—22no—
420C2×C42—22no—
421C2×C42—41no—
422C2×C42—41no—
423#95—22no—
424#95—22no—
425#95—22no—
426#95—22no—
427#95—22no—
428#95—22no—
429#95—22no—
430#95—22no—
431#95—22no—
432#95—22no—
433#95—22no—
434#95—22no—
435#95—22no—
436#95—22no—
437#95—22no—
438#95—41no—
439#95C3×D414yes—
440#95C3×D414yes—
441C23×C3—22no—
442C23×C3—22no—
443C23×C3—22no—
444C23×C3—22no—
445C23×C3—22no—
446C23×C3—22no—
447C23×C3—22no—
448C23×C3—22no—
449C23×C3—22no—
450C23×C3—22no—
451C23×C3—22no—
452C23×C3—22no—
453C23×C3—22no—
454C23×C3—22no—
455C23×C3—22no—
456C23×C3—22no—
457C23×C3—22no—
458C23×C3—22no—
459C23×C3—41no—
460C23×C3—41no—
461C23×C3—41no—
462C23×C3—41no—
463C23×C3—41no—
464C23×C3—41no—
465C23×C3—41no—
466C23×C3—41no—
467C23×C3—41no—
468C23×C3—41no—
469C23×C3—41no—
470C23×C3—41no—
471C23×C3—41no—
472C23×C3—41no—
473C23×C3—41no—
474C23×C3—41no—
475C23×C3C4⋊Q814yes—
476C23×C3C22×D411yescharacteristic
477C23×C3C22×D411yescharacteristic
478C23×C3C22×D411yescharacteristic
479C23×C3C22×Q811yescharacteristic
480C23×C3C22×Q811yescharacteristic
481C23×C3C2×#4111yescharacteristic
482C23×C3C2×#4111yescharacteristic
483C23×C3C2×#4111yescharacteristic
484C23×C3C2×#4111yescharacteristic
485C23×C3C2×#4111yescharacteristic
486C23×C3C2×#4111yescharacteristic
487C23×C3H(5,𝔽2)11yescharacteristic
488C23×C3H(5,𝔽2)11yescharacteristic
489C23×C3H(5,𝔽2)11yescharacteristic
490C23×C32−1+411yescharacteristic
491C3×Q8—416no—
492C2×C3×C4—22no—
493C2×C3×C4—22no—
494C2×C3×C4—22no—
495C2×C3×C4—22no—
496C2×C3×C4—22no—
497C2×C3×C4—22no—
498C2×C3×C4—22no—
499C2×C3×C4—22no—
500C2×C3×C4—22no—
501C2×C3×C4—22no—
502C2×C3×C4—22no—
503C2×C3×C4—22no—
504C2×C3×C4—22no—
505C2×C3×C4—22no—
506C2×C3×C4—22no—
507C2×C3×C4—22no—
508C2×C3×C4—22no—
509C2×C3×C4—22no—
510C2×C3×C4—22no—
511C2×C3×C4—22no—
512C2×C3×C4—22no—
513C2×C3×C4—22no—
514C2×C3×C4—22no—
515C2×C3×C4—22no—
516C2×C3×C4—22no—
517C2×C3×C4—22no—
518C2×C3×C4—22no—
519C2×C3×C4—22no—
520C2×C3×C4—22no—
521C2×C3×C4—22no—
522C2×C3×C4—22no—
523C2×C3×C4—22no—
524C2×C3×C4—22no—
525C2×C3×C4—22no—
526C2×C3×C4—22no—
527C2×C3×C4—22no—
528C2×C3×C4—22no—
529C2×C3×C4—22no—
530C2×C3×C4—22no—
531C2×C3×C4—22no—
532C2×C3×C4—22no—
533C2×C3×C4—22no—
534C2×C3×C4—416no—
535C2×C3×C4—41no—
536C2×C3×C4—41no—
537C2×C3×C4—41no—
538C2×C3×C4—41no—
539C2×C3×C4—41no—
540C2×C3×C4—41no—
541C2×C3×C4—41no—
542C2×C3×C4—41no—
543C2×C3×C4—41no—
544C2×C3×C4—41no—
545C2×C3×C4—41no—
546C2×C3×C4—41no—
547C2×C3×C4—41no—
548C2×C3×C4—41no—
549C2×C3×C4—41no—
550C2×C3×C4—41no—
551C2×C3×C4—41no—
552C2×C3×C4—41no—
553C2×C3×C4—41no—
554C2×C3×C4—41no—
555C2×C3×C4—41no—
556C2×C3×C4—41no—
557C2×C3×C4—41no—
558C2×C3×C4—41no—
559C2×C3×C4—41no—
560C2×C3×C4—41no—
561C2×C3×C4—41no—
562C2×C3×C4—41no—
563C2×C3×C4—41no—
564C2×C3×C4—41no—
565C2×C3×C4—41no—
566C2×C3×C4—41no—
567C2×C3×C4—41no—
568C2×C3×C4—41no—
569C2×C3×C4—41no—
570C2×C3×C4—41no—
571C2×C3×C4—41no—
572C2×C3×C4—41no—
573C2×C3×C4—41no—
574C2×C3×C4—41no—
575C2×C3×C4—41no—
576C2×C3×C4—41no—
577C2×C3×C4—41no—
578C2×C3×C4—41no—
579C2×C3×C4—41no—
580C2×C3×C4—41no—
581C2×C3×C4—41no—
582C2×C3×C4—41no—
583C2×C3×C4—41no—
584C2×C3×C4—41no—
585C2×C3×C4—41no—
586C2×C3×C4—41no—
587C2×C3×C4#12114yes—
588C2×C3×C4C22⋊Q814yes—
589C2×C3×C4C22⋊Q814yes—
590C2×C3×C4C22⋊Q814yes—
591C24—21no—
592C24—21no—
593C24—21no—
594C24—21no—
595C24—21no—
596C24—21no—
597C24—21no—
598C24—21no—
599C24—21no—
600C24—21no—
601C24—21no—
602C24—21no—
603C24C2×C3×D412yes—
604C24C2×C3×Q812yes—
605C24C2×C3×Q812yes—
606C24C24×C311yescharacteristic
607C2×Q8—28no—
608C2×Q8—44no—
609C2×Q8—44no—
610C2×Q8—44no—
611C2×Q8—44no—
612C2×Q8—44no—
613C2×Q8—44no—
614C22×C4—21no—
615C22×C4—21no—
616C22×C4—21no—
617C22×C4—21no—
618C22×C4—21no—
619C22×C4—21no—
620C22×C4—21no—
621C22×C4—21no—
622C22×C4—21no—
623C22×C4—21no—
624C22×C4—21no—
625C22×C4—21no—
626C22×C4—21no—
627C22×C4—21no—
628C22×C4—21no—
629C22×C4—21no—
630C22×C4—21no—
631C22×C4—21no—
632C22×C4—21no—
633C22×C4—21no—
634C22×C4—21no—
635C22×C4—21no—
636C22×C4—21no—
637C22×C4—21no—
638C22×C4—21no—
639C22×C4—21no—
640C22×C4—21no—
641C22×C4—21no—
642C22×C4—21no—
643C22×C4—21no—
644C22×C4—21no—
645C22×C4—21no—
646C22×C4—21no—
647C22×C4—21no—
648C22×C4—21no—
649C22×C4—21no—
650C22×C4—21no—
651C22×C4—21no—
652C22×C4—21no—
653C22×C4—21no—
654C22×C4—21no—
655C22×C4—21no—
656C22×C4—21no—
657C22×C4—21no—
658C22×C4—21no—
659C22×C4—21no—
660C22×C4—21no—
661C22×C4—21no—
662C22×C4—21no—
663C22×C4—21no—
664C22×C4—21no—
665C22×C4—21no—
666C22×C4—28no—
667C22×C4—28no—
668C22×C4—21no—
669C22×C4—21no—
670C22×C4—21no—
671C22×C4—21no—
672C22×C4—21no—
673C22×C4—21no—
674C22×C4—21no—
675C22×C4—21no—
676C22×C4—21no—
677C22×C4—21no—
678C22×C4—21no—
679C22×C4—21no—
680C22×C4—21no—
681C22×C4—21no—
682C22×C4—21no—
683C22×C4—21no—
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—44no—
697C22×C4—44no—
698C22×C4—44no—
699C22×C4—44no—
700C22×C4—44no—
701C22×C4C2×C3×D412yes—
702C22×C4C2×C3×D412yes—
703C22×C4C2×C3×D412yes—
704C22×C4C2×C3×D412yes—
705C22×C4C2×C3×D412yes—
706C22×C4C2×C3×D412yes—
707C22×C4C2×C3×D412yes—
708C22×C4C2×C3×D412yes—
709C22×C4C2×C3×Q812yes—
710C22×C4C2×C3×Q812yes—
711C22×C4C2×C3×Q812yes—
712C22×C4C2×C3×Q812yes—
713C22×C4C3×#4112yes—
714C22×C4C3×#4112yes—
715C22×C4C3×#4112yes—
716C22×C4C3×#4112yes—
717C22×C4C3×#4112yes—
718C22×C4C3×#4112yes—
719C4⋊C4—44no—
720C4⋊C4—44no—
721C4⋊C4—44no—
722C4⋊C4—44no—
723C4⋊C4—44no—
724C4⋊C4—44no—
725C4⋊C4—44no—
726C22⋊C4—28no—
727C22⋊C4—28no—
728C22⋊C4—44no—
729C22⋊C4—44no—
730C22⋊C4—44no—
731C22⋊C4—44no—
732C42—44no—
733C42—44no—
734C22×C3—24no—
735C22×C3—24no—
736C22×C3—24no—
737C22×C3—42no—
738C22×C3—42no—
739C22×C3—42no—
740C22×C3—42no—
741C22×C3—42no—
742C22×C3—42no—
743C22×C3—42no—
744C22×C3—42no—
745C22×C3—42no—
746C22×C3—42no—
747C22×C3—42no—
748C22×C3—42no—
749C22×C3C2×#12111yescharacteristic
750C22×C3C2×C22⋊Q811yescharacteristic
751C22×C3C2×C22⋊Q811yescharacteristic
752C22×C3C2×C22⋊Q811yescharacteristic
753C22×C3#52511yescharacteristic
754C22×C3#52911yescharacteristic
755C22×C3#52911yescharacteristic
756C22×C3C2×C4⋊Q811yescharacteristic
757C22×C3#53211yescharacteristic
758C22×C3#53211yescharacteristic
759C22×C3#53311yescharacteristic
760C22×C3#53311yescharacteristic
761C22×C3#53311yescharacteristic
762C22×C3#53811yescharacteristic
763C22×C3#53811yescharacteristic
764C22×C3#54211yescharacteristic
765C22×C3#54211yescharacteristic
766C22×C3#54311yescharacteristic
767C22×C3#54411yescharacteristic
768C22×C3D4211yescharacteristic
769C22×C3D4211yescharacteristic
770C22×C3#54611yescharacteristic
771C22×C3#54611yescharacteristic
772C22×C3#54611yescharacteristic
773C22×C3#54611yescharacteristic
774C22×C3#54611yescharacteristic
775C22×C3#54711yescharacteristic
776C22×C3#54811yescharacteristic
777C22×C3D4×Q811yescharacteristic
778C22×C3#55111yescharacteristic
779C22×C3#55411yescharacteristic
780C22×C3#55411yescharacteristic
781C22×C3#55411yescharacteristic
782C22×C3#55511yescharacteristic
783C22×C3#55611yescharacteristic
784C3×C4—24no—
785C3×C4—24no—
786C3×C4—24no—
787C3×C4—24no—
788C3×C4—42no—
789C3×C4—42no—
790C3×C4—42no—
791C3×C4—42no—
792C3×C4—42no—
793C3×C4—42no—
794C3×C4—81no—
795C3×C4—81no—
796C3×C4—81no—
797C3×C4—81no—
798C23—22no—
799C23—22no—
800C23—22no—
801C23—22no—
802C23—22no—
803C23—22no—
804C23—22no—
805C23—22no—
806C23—22no—
807C23—22no—
808C23—22no—
809C23—22no—
810C23—22no—
811C23—22no—
812C23—22no—
813C23—22no—
814C23—22no—
815C23—22no—
816C23—41no—
817C23—41no—
818C23—41no—
819C23—41no—
820C23—41no—
821C23—41no—
822C23—41no—
823C23—41no—
824C23—41no—
825C23—41no—
826C23—41no—
827C23—41no—
828C23—41no—
829C23—41no—
830C23—41no—
831C23—41no—
832C23C3×C4⋊Q814yes—
833C23C22×C3×D411yescharacteristic
834C23C22×C3×D411yescharacteristic
835C23C22×C3×D411yescharacteristic
836C23C22×C3×Q811yescharacteristic
837C23C22×C3×Q811yescharacteristic
838C23C2×C3×#4111yescharacteristic
839C23C2×C3×#4111yescharacteristic
840C23C2×C3×#4111yescharacteristic
841C23C2×C3×#4111yescharacteristic
842C23C2×C3×#4111yescharacteristic
843C23C2×C3×#4111yescharacteristic
844C23C3×H(5,𝔽2)11yescharacteristic
845C23C3×H(5,𝔽2)11yescharacteristic
846C23C3×H(5,𝔽2)11yescharacteristic
847C23C3×2−1+411yescharacteristic
848Q8—416no—
849C2×C4—22no—
850C2×C4—22no—
851C2×C4—22no—
852C2×C4—22no—
853C2×C4—22no—
854C2×C4—22no—
855C2×C4—22no—
856C2×C4—22no—
857C2×C4—22no—
858C2×C4—22no—
859C2×C4—22no—
860C2×C4—22no—
861C2×C4—22no—
862C2×C4—22no—
863C2×C4—22no—
864C2×C4—22no—
865C2×C4—22no—
866C2×C4—22no—
867C2×C4—22no—
868C2×C4—22no—
869C2×C4—22no—
870C2×C4—22no—
871C2×C4—22no—
872C2×C4—22no—
873C2×C4—22no—
874C2×C4—22no—
875C2×C4—22no—
876C2×C4—22no—
877C2×C4—22no—
878C2×C4—22no—
879C2×C4—22no—
880C2×C4—22no—
881C2×C4—22no—
882C2×C4—22no—
883C2×C4—22no—
884C2×C4—22no—
885C2×C4—22no—
886C2×C4—22no—
887C2×C4—22no—
888C2×C4—22no—
889C2×C4—22no—
890C2×C4—22no—
891C2×C4—416no—
892C2×C4—41no—
893C2×C4—41no—
894C2×C4—41no—
895C2×C4—41no—
896C2×C4—41no—
897C2×C4—41no—
898C2×C4—41no—
899C2×C4—41no—
900C2×C4—41no—
901C2×C4—41no—
902C2×C4—41no—
903C2×C4—41no—
904C2×C4—41no—
905C2×C4—41no—
906C2×C4—41no—
907C2×C4—41no—
908C2×C4—41no—
909C2×C4—41no—
910C2×C4—41no—
911C2×C4—41no—
912C2×C4—41no—
913C2×C4—41no—
914C2×C4—41no—
915C2×C4—41no—
916C2×C4—41no—
917C2×C4—41no—
918C2×C4—41no—
919C2×C4—41no—
920C2×C4—41no—
921C2×C4—41no—
922C2×C4—41no—
923C2×C4—41no—
924C2×C4—41no—
925C2×C4—41no—
926C2×C4—41no—
927C2×C4—41no—
928C2×C4—41no—
929C2×C4—41no—
930C2×C4—41no—
931C2×C4—41no—
932C2×C4—41no—
933C2×C4—41no—
934C2×C4—41no—
935C2×C4—41no—
936C2×C4—41no—
937C2×C4—41no—
938C2×C4—41no—
939C2×C4—41no—
940C2×C4—41no—
941C2×C4—41no—
942C2×C4—41no—
943C2×C4—41no—
944C2×C4C3×#12114yes—
945C2×C4C3×C22⋊Q814yes—
946C2×C4C3×C22⋊Q814yes—
947C2×C4C3×C22⋊Q814yes—
948C2×C3—44no—
949C2×C3#239611yescharacteristic
950C2×C3#242411yescharacteristic
951C2×C3#242711yescharacteristic
952C2×C3#243711yescharacteristic
953C2×C3#243911yescharacteristic
954C2×C3#244011yescharacteristic
955C2×C3#245011yescharacteristic
956C2×C3#245211yescharacteristic
957C2×C3#246511yescharacteristic
958C2×C3#252111yescharacteristic
959C2×C3#254911yescharacteristic
960C2×C3#255511yescharacteristic
961C2×C3#257411yescharacteristic
962C2×C3#266511yescharacteristic
963C2×C3#285711yescharacteristic
964C22—24no—
965C22—24no—
966C22—24no—
967C22—42no—
968C22—42no—
969C22—42no—
970C22—42no—
971C22—42no—
972C22—42no—
973C22—42no—
974C22—42no—
975C22—42no—
976C22—42no—
977C22—42no—
978C22—42no—
979C22C2×C3×#12111yescharacteristic
980C22C2×C3×C22⋊Q811yescharacteristic
981C22C2×C3×C22⋊Q811yescharacteristic
982C22C2×C3×C22⋊Q811yescharacteristic
983C22C3×#52511yescharacteristic
984C22C3×#52911yescharacteristic
985C22C3×#52911yescharacteristic
986C22C2×C3×C4⋊Q811yescharacteristic
987C22C3×#53211yescharacteristic
988C22C3×#53211yescharacteristic
989C22C3×#53311yescharacteristic
990C22C3×#53311yescharacteristic
991C22C3×#53311yescharacteristic
992C22C3×#53811yescharacteristic
993C22C3×#53811yescharacteristic
994C22C3×#54211yescharacteristic
995C22C3×#54211yescharacteristic
996C22C3×#54311yescharacteristic
997C22C3×#54411yescharacteristic
998C22C3×D4211yescharacteristic
999C22C3×D4211yescharacteristic
1000C22C3×#54611yescharacteristic
1001C22C3×#54611yescharacteristic
1002C22C3×#54611yescharacteristic
1003C22C3×#54611yescharacteristic
1004C22C3×#54611yescharacteristic
1005C22C3×#54711yescharacteristic
1006C22C3×#54811yescharacteristic
1007C22C3×D4×Q811yescharacteristic
1008C22C3×#55111yescharacteristic
1009C22C3×#55411yescharacteristic
1010C22C3×#55411yescharacteristic
1011C22C3×#55411yescharacteristic
1012C22C3×#55511yescharacteristic
1013C22C3×#55611yescharacteristic
1014C4—24no—
1015C4—24no—
1016C4—24no—
1017C4—24no—
1018C4—42no—
1019C4—42no—
1020C4—42no—
1021C4—42no—
1022C4—42no—
1023C4—42no—
1024C4—81no—
1025C4—81no—
1026C4—81no—
1027C4—81no—
1028C3#1477011yescharacteristic, direct product factor, Sylow
1029C2—44no—
1030C2C3×#239611yescharacteristic
1031C2C3×#242411yescharacteristic
1032C2C3×#242711yescharacteristic
1033C2C3×#243711yescharacteristic
1034C2C3×#243911yescharacteristic
1035C2C3×#244011yescharacteristic
1036C2C3×#245011yescharacteristic
1037C2C3×#245211yescharacteristic
1038C2C3×#246511yescharacteristic
1039C2C3×#252111yescharacteristic
1040C2C3×#254911yescharacteristic
1041C2C3×#255511yescharacteristic
1042C2C3×#257411yescharacteristic
1043C2C3×#266511yescharacteristic
1044C2C3×#285711yescharacteristic
subgroupG/H
center, socleC24×C3C24
commutator, Frattini, cosocleC24C24×C3
prime radicalC25×C3C23
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C24×C3 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C3×#395C2semidirect
4. C2×C3×#391C2semidirect
7. C3×#1444C2semidirect
8. C3×#1442C2semidirect
9. C3×#1441C2semidirect
12. C3×#1436C2semidirect
13. C3×#1436C2semidirect
14. C3×C4⋊#95C2semidirect
16. #14770C3direct (N × H)
59. C2×#395C2×C3semidirect
61. C2×#391C2×C3semidirect
64. #1444C2×C3semidirect
65. #1442C2×C3semidirect
66. #1441C2×C3semidirect
69. #1436C2×C3semidirect
70. #1436C2×C3semidirect
71. C4⋊#95C2×C3semidirect
87. C23×C3×C4Q8semidirect
140. C2×C3×C22⋊C4Q8semidirect
363. C23×C4C3×Q8semidirect
416. C2×C22⋊C4C3×Q8semidirect
1028. C3#14770direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×#3962
C2×C3×#3952
C2×C3×#3932
C2×C3×#3912
C2×C3×#3802
C2×C3×C4×C22⋊C42
C3×#14442
C3×#14422
C3×#14412
C3×#14392
C3×#14362
C3×C4⋊#952
C3×C22⋊#952
#147703