Finite Group Databasebeta

← #10724452

Subgroups — #10724452

Order 768.

1918 conjugacy classes of subgroups.

The subgroup lattice has 1164 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#4939C211yesmaximal, characteristic
2C2×#4665C211yesmaximal, characteristic
3C2×#4665C211yesmaximal, characteristic
4C3×#1436C211yesmaximal, characteristic, complemented
5#71570C211yesmaximal, characteristic, complemented
6#71570C211yesmaximal, characteristic, complemented
7#71536C211yesmaximal, characteristic, complemented
8#69428C211yesmaximal, characteristic, complemented
9#69428C211yesmaximal, characteristic, complemented
10(C2×D3)⋊#95C211yesmaximal, characteristic, complemented
11(C2×D3)⋊#95C211yesmaximal, characteristic, complemented
12(C2×D3)⋊#95C211yesmaximal, characteristic, complemented
13(C2×D3)⋊#95C211yesmaximal, characteristic, complemented
14#69415C211yesmaximal, characteristic, complemented
15#69412C211yesmaximal, characteristic, complemented
16#14513—31nomaximal, Sylow
17C23×D12C2211yescharacteristic
18C23×C4×D3C2211yescharacteristic
19C23×C4×D3C2211yescharacteristic
20C22×C3×C4⋊C4C2211yescharacteristic
21C22×C3×C42C2211yescharacteristic
22C22×(C2×D3)⋊C4C2211yescharacteristic
23C22×(C2×D3)⋊C4C2211yescharacteristic
24C22×(C2×D3)⋊C4C2211yescharacteristic
25C22×(C2×D3)⋊C4C2211yescharacteristic
26C22×(C2×D3)⋊C4C2211yescharacteristic
27C22×(C2×D3)⋊C4C2211yescharacteristic
28C22×(C2×D3)⋊C4C2211yescharacteristic
29C22×(C2×D3)⋊C4C2211yescharacteristic
30C22×(C2×D3)⋊C4C2211yescharacteristic
31C22×(C2×D3)⋊C4C2211yescharacteristic
32C22×C4⋊Dic3C2211yescharacteristic
33C22×Dic3⋊C4C2211yescharacteristic
34C2×C3×#95C2211yescharacteristic
35C2×C3×#95C2211yescharacteristic
36C2×C3×#95C2211yescharacteristic
37C2×C3×#95C2211yescharacteristic
38C2×C3×#95C2211yescharacteristic
39C2×C3⋊#95C2211yescharacteristic
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
52#4939—24no—
53#4665—24no—
54#4665C418yescomplemented
55C2×#390—31no—
56C2×#386—31no—
57C2×#386—31no—
58#1442—31no—
59#1442—31no—
60#1439—31no—
61#1439—31no—
62#1439—31no—
63#1439—31no—
64#1436—31no—
65#1436D311yescharacteristic, complemented
66C22⋊#95—31no—
67C22⋊#95—31no—
68C22⋊#95—31no—
69C22⋊#95—31no—
70C24×D3C2311yescharacteristic
71C24×D3C2311yescharacteristic
72C23×C3×C4C2311yescharacteristic
73C23×C3×C4C2311yescharacteristic
74C23×C3×C4C2311yescharacteristic
75C23×C3×C4C2311yescharacteristic
76C23×C3×C4C2311yescharacteristic
77C23×C3×C4C2311yescharacteristic
78C23×C3×C4C2311yescharacteristic
79C23×Dic3C2311yescharacteristic
80C23×Dic3C2311yescharacteristic
81C23×Dic3C2311yescharacteristic
82C23×Dic3C2311yescharacteristic
83C23×Dic3C2311yescharacteristic
84C23×Dic3C2311yescharacteristic
85C22×D12—41no—
86C22×D12—41no—
87C22×D12—41no—
88C22×D12—41no—
89C22×D12C2×C414yes—
90C22×D12D414yes—
91C22×D12Q814yes—
92C22×C4×D3—22no—
93C22×C4×D3—22no—
94C22×C4×D3—22no—
95C22×C4×D3—41no—
96C22×C4×D3—41no—
97C22×C4×D3—41no—
98C22×C4×D3—41no—
99C22×C4×D3—41no—
100C22×C4×D3—41no—
101C22×C4×D3—41no—
102C22×C4×D3—41no—
103C22×C4×D3—41no—
104C22×C4×D3—41no—
105C22×C4×D3C2×C414yescomplemented
106C2×C3×C4⋊C4—22no—
107C2×C3×C4⋊C4—41no—
108C2×C3×C4⋊C4—41no—
109C2×C3×C42—22no—
110C2×C3×C42—41no—
111C2×C3×C42—41no—
112C2×(C2×D3)⋊C4—22no—
113C2×(C2×D3)⋊C4—22no—
114C2×(C2×D3)⋊C4—22no—
115C2×(C2×D3)⋊C4—22no—
116C2×(C2×D3)⋊C4—22no—
117C2×(C2×D3)⋊C4—22no—
118C2×(C2×D3)⋊C4—22no—
119C2×(C2×D3)⋊C4—22no—
120C2×(C2×D3)⋊C4—22no—
121C2×(C2×D3)⋊C4—22no—
122C2×(C2×D3)⋊C4—22no—
123C2×(C2×D3)⋊C4—22no—
124C2×(C2×D3)⋊C4—22no—
125C2×(C2×D3)⋊C4—41no—
126C2×(C2×D3)⋊C4—41no—
127C2×(C2×D3)⋊C4—41no—
128C2×(C2×D3)⋊C4—41no—
129C2×(C2×D3)⋊C4—41no—
130C2×(C2×D3)⋊C4—41no—
131C2×(C2×D3)⋊C4—41no—
132C2×(C2×D3)⋊C4—41no—
133C2×(C2×D3)⋊C4—41no—
134C2×(C2×D3)⋊C4—41no—
135C2×(C2×D3)⋊C4—41no—
136C2×(C2×D3)⋊C4—41no—
137C2×(C2×D3)⋊C4—41no—
138C2×(C2×D3)⋊C4—41no—
139C2×(C2×D3)⋊C4C2×C414yes—
140C2×(C2×D3)⋊C4C2×C414yes—
141C2×(C2×D3)⋊C4C2×C414yescomplemented
142C2×C4⋊Dic3—22no—
143C2×C4⋊Dic3—41no—
144C2×C4⋊Dic3—41no—
145C2×Dic3⋊C4—22no—
146C2×Dic3⋊C4—41no—
147C2×Dic3⋊C4—41no—
148C3×#95—22no—
149C3×#95—22no—
150C3×#95—41no—
151C3×#95—41no—
152C3×#95C2×C414yescomplemented
153C3⋊#95—22no—
154C3⋊#95—22no—
155C3⋊#95—41no—
156C3⋊#95—41no—
157C3⋊#95—41no—
158C3⋊#95—41no—
159C3⋊#95—41no—
160C3⋊#95—41no—
161C3⋊#95—41no—
162C3⋊#95—41no—
163C3⋊#95—41no—
164C3⋊#95—41no—
165C3⋊#95C2×C414yescomplemented
166C23×D4—31no—
167C24×C4—31no—
168C24×C4—31no—
169C22×C4⋊C4—31no—
170C22×C4⋊C4—31no—
171C22×C4⋊C4C2×D311yescharacteristic
172C22×C22⋊C4—31no—
173C22×C22⋊C4—31no—
174C22×C22⋊C4—31no—
175C22×C22⋊C4—31no—
176C22×C22⋊C4—31no—
177C22×C22⋊C4—31no—
178C22×C22⋊C4—31no—
179C22×C22⋊C4—31no—
180C22×C22⋊C4—31no—
181C22×C22⋊C4—31no—
182C22×C42C2×D311yescharacteristic
183#390—64no—
184#386—38no—
185#386—64no—
186C2×#95—31no—
187C2×#95—31no—
188C2×#95—31no—
189C2×#95—31no—
190C2×#95—31no—
191C2×#95—31no—
192C2×#95—31no—
193C2×#95—31no—
194C2×#95—31no—
195C2×#95—31no—
196C2×#95—31no—
197C2×#95—31no—
198C2×#95—31no—
199C2×#95C2×D311yescharacteristic
200C2×#95C2×D311yescharacteristic
201C2×#95C2×D311yescharacteristic
202C2×#95C2×D311yescharacteristic
203C2×#95C2×D311yescharacteristic
204C24×C3C2411yescharacteristic
205C23×D3—21no—
206C23×D3—21no—
207C23×D3—21no—
208C23×D3—21no—
209C23×D3—21no—
210C23×D3—21no—
211C23×D3—21no—
212C23×D3—21no—
213C23×D3—21no—
214C23×D3—21no—
215C23×D3—21no—
216C23×D3—21no—
217C23×D3—21no—
218C23×D3—21no—
219C23×D3—21no—
220C23×D3—21no—
221C23×D3—21no—
222C23×D3—21no—
223C23×D3—21no—
224C23×D3—21no—
225C23×D3—21no—
226C23×D3—21no—
227C23×D3—21no—
228C23×D3—21no—
229C23×D3C22×C412yes—
230C23×D3C22×C412yes—
231C23×D3C2×D412yes—
232C23×D3C2×D412yes—
233C23×D3C2×Q812yes—
234C23×D3C2×Q812yes—
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×C4C22×C412yes—
277C22×C3×C4C22×C412yes—
278C22×C3×C4C22×C412yes—
279C22×C3×C4C2×D412yes—
280C22×C3×C4C2×Q812yes—
281C22×C3×C4#4112yes—
282C22×C3×C4#4112yes—
283C22×C3×C4#4112yes—
284C22×Dic3—21no—
285C22×Dic3—21no—
286C22×Dic3—21no—
287C22×Dic3—21no—
288C22×Dic3—21no—
289C22×Dic3—21no—
290C22×Dic3—21no—
291C22×Dic3—21no—
292C22×Dic3—21no—
293C22×Dic3—21no—
294C22×Dic3—21no—
295C22×Dic3—21no—
296C22×Dic3—21no—
297C22×Dic3—21no—
298C22×Dic3—21no—
299C22×Dic3—21no—
300C22×Dic3—21no—
301C22×Dic3—21no—
302C22×Dic3—21no—
303C22×Dic3—21no—
304C22×Dic3—21no—
305C22×Dic3—21no—
306C22×Dic3—21no—
307C22×Dic3—21no—
308C22×Dic3—21no—
309C22×Dic3—21no—
310C22×Dic3—21no—
311C22×Dic3—21no—
312C22×Dic3—21no—
313C22×Dic3—21no—
314C22×Dic3—21no—
315C22×Dic3—21no—
316C22×Dic3—21no—
317C22×Dic3—21no—
318C22×Dic3—21no—
319C22×Dic3—21no—
320C22×Dic3—21no—
321C22×Dic3—21no—
322C22×Dic3—21no—
323C22×Dic3C22×C412yes—
324C22×Dic3C22×C412yes—
325C22×Dic3#4112yes—
326C2×D12—44no—
327C2×D12—44no—
328C2×D12—44no—
329C2×D12—44no—
330C2×D12—44no—
331C2×D12—44no—
332C2×D12C4⋊C4116yescomplemented
333C2×C4×D3—44no—
334C2×C4×D3—44no—
335C2×C4×D3—44no—
336C2×C4×D3—44no—
337C2×C4×D3—44no—
338C2×C4×D3—44no—
339C2×C4×D3—44no—
340C2×C4×D3—44no—
341C2×C4×D3—44no—
342C2×C4×D3—44no—
343C2×C4×D3—44no—
344C2×C4×D3—44no—
345C2×C4×D3—44no—
346C2×C4×D3—44no—
347C3×C4⋊C4—44no—
348C3×C42—44no—
349(C2×D3)⋊C4—44no—
350(C2×D3)⋊C4—44no—
351(C2×D3)⋊C4—44no—
352(C2×D3)⋊C4—44no—
353(C2×D3)⋊C4—44no—
354(C2×D3)⋊C4—44no—
355(C2×D3)⋊C4—44no—
356(C2×D3)⋊C4—44no—
357(C2×D3)⋊C4—44no—
358(C2×D3)⋊C4—44no—
359C4⋊Dic3—44no—
360Dic3⋊C4—44no—
361C25—31no—
362C25—31no—
363C22×D4—34no—
364C22×D4—34no—
365C22×D4—34no—
366C22×D4—121no—
367C22×D4—121no—
368C22×D4—121no—
369C22×D4—121no—
370C23×C4—31no—
371C23×C4—31no—
372C23×C4—31no—
373C23×C4—34no—
374C23×C4—31no—
375C23×C4—31no—
376C23×C4—31no—
377C23×C4—62no—
378C23×C4—62no—
379C23×C4—62no—
380C23×C4—121no—
381C23×C4—121no—
382C23×C4—121no—
383C23×C4—121no—
384C23×C4—121no—
385C23×C4—121no—
386C23×C4—121no—
387C23×C4—121no—
388C23×C4—121no—
389C23×C4—121no—
390C23×C4C22×D311yescharacteristic
391C23×C4C22×D311yescharacteristic
392C23×C4C22×D311yescharacteristic
393C23×C4C22×D311yescharacteristic
394C23×C4C22×D311yescharacteristic
395C23×C4C22×D311yescharacteristic
396C23×C4C22×D311yescharacteristic
397C2×C4⋊C4—22no—
398C2×C4⋊C4—41no—
399C2×C4⋊C4—41no—
400C2×C4⋊C4—62no—
401C2×C4⋊C4—62no—
402C2×C4⋊C4—121no—
403C2×C4⋊C4—121no—
404C2×C4⋊C4—121no—
405C2×C4⋊C4—121no—
406C2×C22⋊C4—34no—
407C2×C22⋊C4—34no—
408C2×C22⋊C4—34no—
409C2×C22⋊C4—62no—
410C2×C22⋊C4—62no—
411C2×C22⋊C4—62no—
412C2×C22⋊C4—62no—
413C2×C22⋊C4—62no—
414C2×C22⋊C4—62no—
415C2×C22⋊C4—62no—
416C2×C22⋊C4—62no—
417C2×C22⋊C4—62no—
418C2×C22⋊C4—62no—
419C2×C22⋊C4—62no—
420C2×C22⋊C4—62no—
421C2×C22⋊C4—62no—
422C2×C22⋊C4—121no—
423C2×C22⋊C4—121no—
424C2×C22⋊C4—121no—
425C2×C22⋊C4—121no—
426C2×C22⋊C4—121no—
427C2×C22⋊C4—121no—
428C2×C22⋊C4—121no—
429C2×C22⋊C4—121no—
430C2×C22⋊C4—121no—
431C2×C22⋊C4—121no—
432C2×C22⋊C4—121no—
433C2×C22⋊C4—121no—
434C2×C22⋊C4—121no—
435C2×C22⋊C4—121no—
436C2×C42—22no—
437C2×C42—41no—
438C2×C42—41no—
439#95—22no—
440#95—22no—
441#95—34no—
442#95—41no—
443#95—41no—
444#95—62no—
445#95—62no—
446#95—121no—
447#95—121no—
448#95—121no—
449#95—121no—
450#95—121no—
451#95—121no—
452#95—121no—
453#95—121no—
454#95—121no—
455#95—121no—
456#95C4×D314yescomplemented
457C23×C3C23×C411yescharacteristic
458C23×C3C22×D411yescharacteristic
459C23×C3C22×Q811yescharacteristic
460C23×C3C2×#4111yescharacteristic
461C23×C3C2×#4111yescharacteristic
462C23×C3C2×#4111yescharacteristic
463C23×C3C2×#4111yescharacteristic
464C23×C3H(5,𝔽2)11yescharacteristic
465C23×C3H(5,𝔽2)11yescharacteristic
466C23×C3H(5,𝔽2)11yescharacteristic
467C23×C3H(5,𝔽2)11yescharacteristic
468C23×C3H(5,𝔽2)11yescharacteristic
469C23×C3H(5,𝔽2)11yescharacteristic
470C23×C3H(5,𝔽2)11yescharacteristic
471C23×C3H(5,𝔽2)11yescharacteristic
472C22×D3—22no—
473C22×D3—22no—
474C22×D3—22no—
475C22×D3—22no—
476C22×D3—22no—
477C22×D3—22no—
478C22×D3—22no—
479C22×D3—22no—
480C22×D3—22no—
481C22×D3—22no—
482C22×D3—22no—
483C22×D3—22no—
484C22×D3—22no—
485C22×D3—22no—
486C22×D3—22no—
487C22×D3—22no—
488C22×D3—22no—
489C22×D3—22no—
490C22×D3—22no—
491C22×D3—22no—
492C22×D3—22no—
493C22×D3—22no—
494C22×D3—22no—
495C22×D3—22no—
496C22×D3—22no—
497C22×D3—22no—
498C22×D3—22no—
499C22×D3—22no—
500C22×D3—22no—
501C22×D3—22no—
502C22×D3—22no—
503C22×D3—22no—
504C22×D3—22no—
505C22×D3—22no—
506C22×D3—22no—
507C22×D3—22no—
508C22×D3—41no—
509C22×D3—41no—
510C22×D3—41no—
511C22×D3—41no—
512C22×D3—41no—
513C22×D3—41no—
514C22×D3—41no—
515C22×D3—41no—
516C22×D3—41no—
517C22×D3—41no—
518C22×D3—41no—
519C22×D3—41no—
520C22×D3—41no—
521C22×D3—41no—
522C22×D3—41no—
523C22×D3—41no—
524C22×D3—41no—
525C22×D3—41no—
526C22×D3—41no—
527C22×D3—41no—
528C22×D3—41no—
529C22×D3—41no—
530C22×D3—41no—
531C22×D3—41no—
532C22×D3—41no—
533C22×D3—41no—
534C22×D3—41no—
535C22×D3—41no—
536C22×D3—41no—
537C22×D3—41no—
538C22×D3—41no—
539C22×D3—41no—
540C22×D3C2×C4⋊C414yes—
541C22×D3C2×C4⋊C414yes—
542C2×C3×C4—22no—
543C2×C3×C4—22no—
544C2×C3×C4—22no—
545C2×C3×C4—22no—
546C2×C3×C4—22no—
547C2×C3×C4—22no—
548C2×C3×C4—22no—
549C2×C3×C4—22no—
550C2×C3×C4—22no—
551C2×C3×C4—22no—
552C2×C3×C4—22no—
553C2×C3×C4—22no—
554C2×C3×C4—22no—
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—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—41no—
588C2×C3×C4—41no—
589C2×C3×C4—41no—
590C2×C3×C4C2×C4⋊C414yes—
591C2×Dic3—22no—
592C2×Dic3—22no—
593C2×Dic3—22no—
594C2×Dic3—22no—
595C2×Dic3—22no—
596C2×Dic3—22no—
597C2×Dic3—22no—
598C2×Dic3—22no—
599C2×Dic3—22no—
600C2×Dic3—41no—
601C2×Dic3—41no—
602C2×Dic3—41no—
603C2×Dic3—41no—
604C2×Dic3—41no—
605C2×Dic3—41no—
606C2×Dic3—41no—
607C2×Dic3—41no—
608C2×Dic3—41no—
609C2×Dic3—41no—
610C2×Dic3—41no—
611C2×Dic3—41no—
612C2×Dic3—41no—
613C2×Dic3—41no—
614C2×Dic3—41no—
615C2×Dic3—41no—
616C2×Dic3—41no—
617C2×Dic3—41no—
618C2×Dic3—41no—
619C2×Dic3—41no—
620C2×Dic3—41no—
621C2×Dic3—41no—
622C2×Dic3—41no—
623C2×Dic3—41no—
624C2×Dic3—41no—
625C2×Dic3—41no—
626C2×Dic3—41no—
627C2×Dic3—41no—
628C2×Dic3—41no—
629C2×Dic3—41no—
630C2×Dic3—41no—
631C2×Dic3—41no—
632C2×Dic3—41no—
633D12—416no—
634C4×D3—416no—
635C4×D3—416no—
636C24—32no—
637C24—32no—
638C24—32no—
639C24—32no—
640C24—32no—
641C24—32no—
642C24—61no—
643C24—61no—
644C24—61no—
645C24—61no—
646C24—61no—
647C24—61no—
648C24—61no—
649C24—61no—
650C24—61no—
651C24—61no—
652C24—61no—
653C24—61no—
654C24—61no—
655C24—61no—
656C24—61no—
657C24—61no—
658C24—61no—
659C24—61no—
660C24—61no—
661C24—61no—
662C24—61no—
663C24—61no—
664C24—61no—
665C24—61no—
666C24C23×D311yescharacteristic
667C2×D4—316no—
668C2×D4—124no—
669C2×D4—124no—
670C2×D4—124no—
671C2×D4—124no—
672C2×D4—124no—
673C2×D4—124no—
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—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—32no—
716C22×C4—32no—
717C22×C4—32no—
718C22×C4—61no—
719C22×C4—61no—
720C22×C4—61no—
721C22×C4—61no—
722C22×C4—61no—
723C22×C4—61no—
724C22×C4—61no—
725C22×C4—61no—
726C22×C4—61no—
727C22×C4—61no—
728C22×C4—61no—
729C22×C4—61no—
730C22×C4—61no—
731C22×C4—61no—
732C22×C4—61no—
733C22×C4—61no—
734C22×C4—61no—
735C22×C4—61no—
736C22×C4—61no—
737C22×C4—61no—
738C22×C4—61no—
739C22×C4—61no—
740C22×C4—61no—
741C22×C4—61no—
742C22×C4—61no—
743C22×C4—61no—
744C22×C4—61no—
745C22×C4—61no—
746C22×C4—61no—
747C22×C4—61no—
748C22×C4—61no—
749C22×C4—61no—
750C22×C4—61no—
751C22×C4—61no—
752C22×C4—61no—
753C22×C4—61no—
754C22×C4—61no—
755C22×C4—61no—
756C22×C4—61no—
757C22×C4—124no—
758C22×C4—124no—
759C22×C4—124no—
760C22×C4—124no—
761C22×C4—124no—
762C22×C4—124no—
763C22×C4—124no—
764C22×C4—124no—
765C22×C4—124no—
766C22×C4—124no—
767C22×C4—124no—
768C22×C4—124no—
769C22×C4—124no—
770C22×C4—124no—
771C22×C4C2×C4×D312yes—
772C22×C4C2×C4×D312yes—
773C22×C4C2×C4×D312yes—
774C22×C4#23512yes—
775C22×C4#23512yes—
776C22×C4D3×D412yes—
777C22×C4D3×Q812yes—
778C22×C4#23912yes—
779C4⋊C4—44no—
780C4⋊C4—124no—
781C4⋊C4—124no—
782C22⋊C4—124no—
783C22⋊C4—124no—
784C22⋊C4—124no—
785C22⋊C4—124no—
786C22⋊C4—124no—
787C22⋊C4—124no—
788C22⋊C4—124no—
789C22⋊C4—124no—
790C22⋊C4—124no—
791C22⋊C4—124no—
792C42—44no—
793C22×C3C22×C4⋊C411yescharacteristic
794C22×C3C4×#4111yescharacteristic
795C22×C3C4×#4111yescharacteristic
796C22×C3#51811yescharacteristic
797C22×C3#51811yescharacteristic
798C22×C3#51811yescharacteristic
799C22×C3#51811yescharacteristic
800C22×C3#53411yescharacteristic
801C22×C3#53411yescharacteristic
802C22×C3#53811yescharacteristic
803C22×C3#53811yescharacteristic
804C22×C3#53811yescharacteristic
805C22×C3#53811yescharacteristic
806C22×C3#54011yescharacteristic
807C22×C3#54011yescharacteristic
808C22×C3#54011yescharacteristic
809C22×C3#54011yescharacteristic
810C22×C3#54311yescharacteristic
811C22×C3#54311yescharacteristic
812C22×C3#54611yescharacteristic
813C22×C3#54611yescharacteristic
814C22×C3#54611yescharacteristic
815C22×C3#54611yescharacteristic
816C22×C3#55111yescharacteristic
817C22×C3#55311yescharacteristic
818C22×C3#55311yescharacteristic
819C22×C3#55411yescharacteristic
820C22×C3#55411yescharacteristic
821C22×C3#55411yescharacteristic
822C22×C3#55411yescharacteristic
823C22×C3#55911yescharacteristic
824C22×C3#56011yescharacteristic
825C22×C3#56011yescharacteristic
826C22×C3#56011yescharacteristic
827C22×C3H(3,𝔽4)11yescharacteristic
828C2×D3—24no—
829C2×D3—24no—
830C2×D3—24no—
831C2×D3—24no—
832C2×D3—24no—
833C2×D3—24no—
834C2×D3—42no—
835C2×D3—42no—
836C2×D3—42no—
837C2×D3—42no—
838C2×D3—42no—
839C2×D3—42no—
840C2×D3—42no—
841C2×D3—42no—
842C2×D3—42no—
843C2×D3—42no—
844C2×D3—42no—
845C2×D3—42no—
846C2×D3—42no—
847C2×D3—42no—
848C2×D3—42no—
849C2×D3—42no—
850C2×D3—42no—
851C2×D3—42no—
852C2×D3—42no—
853C2×D3—42no—
854C2×D3—42no—
855C2×D3—42no—
856C2×D3—42no—
857C2×D3—42no—
858C3×C4—24no—
859C3×C4—42no—
860C3×C4—42no—
861C3×C4—42no—
862C3×C4—42no—
863C3×C4—42no—
864C3×C4—81no—
865Dic3—42no—
866Dic3—42no—
867Dic3—42no—
868Dic3—81no—
869Dic3—81no—
870Dic3—81no—
871C23—34no—
872C23—34no—
873C23—62no—
874C23—62no—
875C23—62no—
876C23—62no—
877C23—62no—
878C23—62no—
879C23—62no—
880C23—62no—
881C23—62no—
882C23—62no—
883C23—62no—
884C23—62no—
885C23—62no—
886C23—62no—
887C23—62no—
888C23—62no—
889C23—62no—
890C23—62no—
891C23—62no—
892C23—62no—
893C23—62no—
894C23—62no—
895C23—62no—
896C23—62no—
897C23—62no—
898C23—62no—
899C23—62no—
900C23—62no—
901C23—62no—
902C23—62no—
903C23—62no—
904C23—62no—
905C23—62no—
906C23—62no—
907C23—62no—
908C23—62no—
909C23—121no—
910C23—121no—
911C23—121no—
912C23—121no—
913C23—121no—
914C23—121no—
915C23—121no—
916C23—121no—
917C23—121no—
918C23—121no—
919C23—121no—
920C23—121no—
921C23—121no—
922C23—121no—
923C23—121no—
924C23—121no—
925C23—121no—
926C23—121no—
927C23—121no—
928C23—121no—
929C23—121no—
930C23—121no—
931C23—121no—
932C23—121no—
933C23—121no—
934C23—121no—
935C23—121no—
936C23—121no—
937C23—121no—
938C23—121no—
939C23—121no—
940C23—121no—
941C23C22×C4×D311yescharacteristic
942C23C2×#23511yescharacteristic
943C23C2×#23511yescharacteristic
944C23C2×D3×D411yescharacteristic
945C23#100411yescharacteristic
946C23#100411yescharacteristic
947C23#100411yescharacteristic
948C23C2×D3×Q811yescharacteristic
949C23C2×#23911yescharacteristic
950C23D3×#4111yescharacteristic
951C23#100911yescharacteristic
952C23#100911yescharacteristic
953C23#100911yescharacteristic
954C23#100911yescharacteristic
955C23#100911yescharacteristic
956D4—1216no—
957C2×C4—22no—
958C2×C4—22no—
959C2×C4—22no—
960C2×C4—22no—
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—41no—
979C2×C4—41no—
980C2×C4—41no—
981C2×C4—41no—
982C2×C4—41no—
983C2×C4—41no—
984C2×C4—41no—
985C2×C4—41no—
986C2×C4—41no—
987C2×C4—41no—
988C2×C4—41no—
989C2×C4—41no—
990C2×C4—41no—
991C2×C4—41no—
992C2×C4—41no—
993C2×C4—41no—
994C2×C4—41no—
995C2×C4—41no—
996C2×C4—41no—
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—62no—
1006C2×C4—62no—
1007C2×C4—62no—
1008C2×C4—62no—
1009C2×C4—62no—
1010C2×C4—62no—
1011C2×C4—62no—
1012C2×C4—62no—
1013C2×C4—62no—
1014C2×C4—1216no—
1015C2×C4—1216no—
1016C2×C4—121no—
1017C2×C4—121no—
1018C2×C4—121no—
1019C2×C4—121no—
1020C2×C4—121no—
1021C2×C4—121no—
1022C2×C4—121no—
1023C2×C4—121no—
1024C2×C4—121no—
1025C2×C4—121no—
1026C2×C4—121no—
1027C2×C4—121no—
1028C2×C4—121no—
1029C2×C4—121no—
1030C2×C4—121no—
1031C2×C4—121no—
1032C2×C4—121no—
1033C2×C4—121no—
1034C2×C4—121no—
1035C2×C4—121no—
1036C2×C4—121no—
1037C2×C4—121no—
1038C2×C4—121no—
1039C2×C4—121no—
1040C2×C4—121no—
1041C2×C4—121no—
1042C2×C4—121no—
1043C2×C4—121no—
1044C2×C4—121no—
1045C2×C4—121no—
1046C2×C4—121no—
1047C2×C4—121no—
1048C2×C4—121no—
1049C2×C4D3×C4⋊C414yes—
1050C2×C3#231511yescharacteristic
1051C2×C3#233311yescharacteristic
1052C2×C3#233311yescharacteristic
1053C2×C3#234911yescharacteristic
1054C2×C3#234911yescharacteristic
1055C2×C3#237411yescharacteristic
1056C2×C3#237511yescharacteristic
1057C2×C3#268411yescharacteristic
1058C2×C3#268811yescharacteristic
1059C2×C3#268811yescharacteristic
1060C2×C3#270911yescharacteristic
1061C2×C3#274811yescharacteristic
1062C2×C3#278011yescharacteristic
1063C2×C3#278011yescharacteristic
1064C2×C3#280411yescharacteristic
1065D3—44no—
1066D3—44no—
1067C22—64no—
1068C22—64no—
1069C22—64no—
1070C22—64no—
1071C22—64no—
1072C22—64no—
1073C22—122no—
1074C22—122no—
1075C22—122no—
1076C22—122no—
1077C22—122no—
1078C22—122no—
1079C22—122no—
1080C22—122no—
1081C22—122no—
1082C22—122no—
1083C22—122no—
1084C22—122no—
1085C22—122no—
1086C22—122no—
1087C22—122no—
1088C22—122no—
1089C22—122no—
1090C22—122no—
1091C22—122no—
1092C22—122no—
1093C22—122no—
1094C22—122no—
1095C22—122no—
1096C22—122no—
1097C22C4×#23511yescharacteristic
1098C22#549411yescharacteristic
1099C22C2×D3×C4⋊C411yescharacteristic
1100C22#551411yescharacteristic
1101C22#552111yescharacteristic
1102C22#552711yescharacteristic
1103C22#553511yescharacteristic
1104C22#554011yescharacteristic
1105C22#554511yescharacteristic
1106C22#554511yescharacteristic
1107C22#554511yescharacteristic
1108C22#555011yescharacteristic
1109C22#555011yescharacteristic
1110C22#556011yescharacteristic
1111C22#556211yescharacteristic
1112C22C4×#23911yescharacteristic
1113C22#557911yescharacteristic
1114C22#557911yescharacteristic
1115C22#558511yescharacteristic
1116C22#558911yescharacteristic
1117C22#561211yescharacteristic
1118C22#562011yescharacteristic
1119C22#563011yescharacteristic
1120C22#563411yescharacteristic
1121C22#563411yescharacteristic
1122C22#564411yescharacteristic
1123C22#565311yescharacteristic
1124C22#566311yescharacteristic
1125C22#566611yescharacteristic
1126C22#568311yescharacteristic
1127C22#569011yescharacteristic
1128C22#569711yescharacteristic
1129C22#570411yescharacteristic
1130C22#571111yescharacteristic
1131C22#573011yescharacteristic
1132C4—24no—
1133C4—42no—
1134C4—42no—
1135C4—42no—
1136C4—42no—
1137C4—42no—
1138C4—81no—
1139C4—122no—
1140C4—122no—
1141C4—122no—
1142C4—241no—
1143C4—241no—
1144C4—241no—
1145C3#1451311yescharacteristic, complemented, Sylow
1146C2—124no—
1147C2—124no—
1148C2#7357011yescharacteristic
1149C2#7366711yescharacteristic
1150C2#7377011yescharacteristic
1151C2#7459111yescharacteristic
1152C2#7463411yescharacteristic
1153C2#7492111yescharacteristic
1154C2#7495211yescharacteristic
1155C2#7523711yescharacteristic
1156C2#7539711yescharacteristic
1157C2#7542211yescharacteristic
1158C2#7584011yescharacteristic
1159C2#7591711yescharacteristic
1160C2#7620311yescharacteristic
1161C2#7627811yescharacteristic
1162C2#7665911yescharacteristic
subgroupG/H
center, FrattiniC24C23×D3
commutatorC23×C3C23×C4
FittingC3×#1436C2
socle, cosocleC24×C3C24
prime radicalC23×D12C22
hypercenter#1436D3
hypocenterC3#14513
LCSG ▷ C23×C3 ▷ C3
UCSC1 ◁ C24 ◁ #1436

Complements

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

NH ≅ G/Ntype
4. C3×#1436C2semidirect
5. #71570C2semidirect
6. #71570C2semidirect
7. #71536C2semidirect
8. #69428C2semidirect
9. #69428C2semidirect
10. (C2×D3)⋊#95C2semidirect
11. (C2×D3)⋊#95C2semidirect
12. (C2×D3)⋊#95C2semidirect
13. (C2×D3)⋊#95C2semidirect
14. #69415C2semidirect
15. #69412C2semidirect
54. #4665C4semidirect
65. #1436D3semidirect
105. C22×C4×D3C2×C4semidirect
141. C2×(C2×D3)⋊C4C2×C4semidirect
152. C3×#95C2×C4semidirect
165. C3⋊#95C2×C4semidirect
332. C2×D12C4⋊C4semidirect
456. #95C4×D3semidirect
1145. C3#14513semidirect

Maximal subgroups

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

subgroupindex
C2×#49392
C2×#46652
C3×#14362
#715702
#715362
#694282
(C2×D3)⋊#952
#694152
#694122
#145133