Finite Group Databasebeta

← #10804434

Subgroups — #10804434

Order 768.

1442 conjugacy classes of subgroups.

The subgroup lattice has 970 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#5547C211yesmaximal, characteristic
2C2×#4840C211yesmaximal, characteristic, complemented
3C2×#4690C211yesmaximal, characteristic, complemented
4C3×#1954C211yesmaximal, characteristic, complemented
5#71615C211yesmaximal, characteristic, complemented
6#70471C211yesmaximal, characteristic, complemented
7#69956C211yesmaximal, characteristic, complemented
8#69956C211yesmaximal, characteristic, complemented
9#69955C211yesmaximal, characteristic, complemented
10#69955C211yesmaximal, characteristic, complemented
11#69917C211yesmaximal, characteristic, complemented
12#69917C211yesmaximal, characteristic, complemented
13#69916C211yesmaximal, characteristic, complemented
14#69916C211yesmaximal, characteristic, complemented
15#69787C211yesmaximal, characteristic, complemented
16#21792—31nomaximal, Sylow
17C22×#235C2211yescharacteristic
18C23×C4×D3C2211yescharacteristic
19C2×C3×C4×D4C2211yescharacteristic
20C2×#939C411yescharacteristic
21C2×#937C411yescharacteristic
22C2×C4×#67C2211yescharacteristic
23C2×C4×#67C2211yescharacteristic
24#5547—24no—
25#5547—24no—
26C2×#896C411yescharacteristic
27C2×#894C411yescharacteristic
28C2×#884C411yescharacteristic
29C2×#883C411yescharacteristic
30C2×#882C411yescharacteristic
31C2×#878C411yescharacteristic
32C2×C4×D12C2211yescharacteristic
33C2×#872C2211yescharacteristic
34C2×C3×C4⋊C8C2211yescharacteristic, complemented
35C2×C3×C22⋊C8C2211yescharacteristic
36C2×C3×C22⋊C8C2211yescharacteristic
37C2×C3×C22⋊C8C2211yescharacteristic, complemented
38C2×C3×C22⋊C8C2211yescharacteristic, complemented
39C2×C3×C4×C8C2211yescharacteristic, complemented
40C2×#830C2211yescharacteristic
41C2×#830C2211yescharacteristic
42C2×#830C2211yescharacteristic, complemented
43C2×#830C2211yescharacteristic, complemented
44C2×(C2×D3)⋊C8C2211yescharacteristic
45C2×(C2×D3)⋊C8C2211yescharacteristic
46C2×(C2×D3)⋊C8C2211yescharacteristic
47C2×(C2×D3)⋊C8C2211yescharacteristic
48C2×(C2×D3)⋊C8C2211yescharacteristic
49C2×(C2×D3)⋊C8C2211yescharacteristic
50C2×(C2×D3)⋊C8C2211yescharacteristic
51C2×(C2×D3)⋊C8C2211yescharacteristic
52C2×(C2×D3)⋊C8C2211yescharacteristic, complemented
53C2×(C2×D3)⋊C8C2211yescharacteristic, complemented
54C2×(C2×D3)⋊C8C2211yescharacteristic, complemented
55C2×(C2×D3)⋊C8C2211yescharacteristic, complemented
56C2×#815C2211yescharacteristic, complemented
57C2×Dic3⋊C8C2211yescharacteristic, complemented
58C2×Dic3⋊C8C2211yescharacteristic, complemented
59C2×C8×Dic3C2211yescharacteristic, complemented
60C2×C4⋊(C3⋊C8)C2211yescharacteristic, complemented
61C2×#803C2211yescharacteristic, complemented
62#4840—24no—
63#4690—24no—
64C2×#525—31no—
65C2×#433—31no—
66C2×#433—31no—
67#1955—31no—
68#1955—31no—
69#1955—31no—
70#1955—31no—
71#1954—31no—
72#1954—31no—
73#1954—31no—
74#1954D311yescharacteristic, complemented
75#1780—31no—
76#1780—31no—
77#1779—31no—
78#1779—31no—
79C24×D3C2×C411yescharacteristic
80C22×C3×D4C2×C411yescharacteristic
81C23×C3×C4C2311yescharacteristic
82C23×C3×C4C2311yescharacteristic
83C22×#67C2×C411yescharacteristic
84C22×#67C2×C411yescharacteristic
85C22×#67C2×C411yescharacteristic
86C22×#67C2×C411yescharacteristic
87C23×Dic3C2×C411yescharacteristic
88C2×#235—22no—
89C2×#235—22no—
90C2×#235—41no—
91C2×#235—41no—
92C2×#235—41no—
93C2×#235—41no—
94C22×D12C2×C411yescharacteristic
95C22×D12C2×C411yescharacteristic
96C22×C4×D3—22no—
97C22×C4×D3—22no—
98C22×C4×D3—41no—
99C22×C4×D3—41no—
100C22×C4×D3—41no—
101C22×C4×D3—41no—
102C22×C4×D3C2×C411yescharacteristic
103C22×C4×D3C2×C411yescharacteristic
104C22×C4×D3C2311yescharacteristic
105C22×C4×D3C2311yescharacteristic
106C22×C4×D3C2311yescharacteristic
107C22×Dic6C2×C411yescharacteristic
108C22×C3×C8C2311yescharacteristic
109C22×C3×C8C2311yescharacteristic
110C22×C3×C8C2311yescharacteristic
111C22×C3×C8C2311yescharacteristic
112C3×C4×D4—22no—
113C3×C4×D4—22no—
114C2×C3×C4⋊C4C2×C411yescharacteristic
115C2×C3×C22⋊C4C2×C411yescharacteristic
116C2×C3×C22⋊C4C2×C411yescharacteristic
117C2×C3×C42C2311yescharacteristic
118C2×#217C2×C411yescharacteristic
119C2×#217C2×C411yescharacteristic
120#939—24no—
121#937—24no—
122C4×#67—22no—
123C4×#67—22no—
124C4×#67—22no—
125C4×#67—22no—
126C2×(C2×D3)⋊C4C2×C411yescharacteristic
127C2×(C2×D3)⋊C4C2×C411yescharacteristic
128C2×(C2×D3)⋊C4C2×C411yescharacteristic
129C2×(C2×D3)⋊C4C2×C411yescharacteristic
130C2×(C2×D3)⋊C4C2×C411yescharacteristic
131C2×(C2×D3)⋊C4C2×C411yescharacteristic
132C2×C4⋊Dic3C2×C411yescharacteristic
133C2×Dic3⋊C4C2×C411yescharacteristic
134C2×Dic3⋊C4C2×C411yescharacteristic
135C2×Dic3⋊C4C2×C411yescharacteristic
136C2×Dic3⋊C4C2×C411yescharacteristic
137C2×C4×Dic3C2311yescharacteristic
138C22×C3⋊C8C2311yescharacteristic
139C22×C3⋊C8C2311yescharacteristic
140C22×C3⋊C8C2311yescharacteristic
141C22×C3⋊C8C2311yescharacteristic
142#896—24no—
143#894—24no—
144#884—24no—
145#883—24no—
146#882—24no—
147#878—24no—
148C4×D12—22no—
149C4×D12—22no—
150#872D414yes—
151#872D414yes—
152C3×C4⋊C8—22no—
153C3×C22⋊C8—41no—
154C3×C22⋊C8—41no—
155C3×C22⋊C8—41no—
156C3×C22⋊C8—41no—
157C3×C4×C8—22no—
158#830—41no—
159#830—41no—
160#830—41no—
161#830—41no—
162(C2×D3)⋊C8—22no—
163(C2×D3)⋊C8—22no—
164(C2×D3)⋊C8—22no—
165(C2×D3)⋊C8—22no—
166(C2×D3)⋊C8—41no—
167(C2×D3)⋊C8—41no—
168(C2×D3)⋊C8—41no—
169(C2×D3)⋊C8—41no—
170(C2×D3)⋊C8—41no—
171(C2×D3)⋊C8—41no—
172(C2×D3)⋊C8—41no—
173(C2×D3)⋊C8—41no—
174#815—22no—
175Dic3⋊C8—22no—
176Dic3⋊C8—22no—
177C8×Dic3—22no—
178C4⋊(C3⋊C8)—22no—
179#803—22no—
180C22×#41—31no—
181C24×C4—31no—
182#525—64no—
183#525—64no—
184C2×#123—31no—
185C2×#123—31no—
186C2×C22⋊Q8—31no—
187C2×C22⋊Q8—31no—
188C2×#121—31no—
189C2×#121—31no—
190C2×#120—31no—
191C2×#120—31no—
192C2×C4×D4—31no—
193C2×C4×D4—31no—
194C2×C4×D4—31no—
195C2×C4×D4C2×D311yescharacteristic
196C2×#117—31no—
197#433—64no—
198#433—64no—
199C2×C4⋊C8—31no—
200C2×C4⋊C8—31no—
201C2×C4⋊C8—31no—
202C2×C4⋊C8C2×D311yescharacteristic, complemented
203C2×C22⋊C8—31no—
204C2×C22⋊C8—31no—
205C2×C22⋊C8—31no—
206C2×C22⋊C8—31no—
207C2×C22⋊C8—31no—
208C2×C22⋊C8—31no—
209C2×C22⋊C8—31no—
210C2×C22⋊C8—31no—
211C2×C22⋊C8—31no—
212C2×C22⋊C8—31no—
213C2×C22⋊C8—31no—
214C2×C22⋊C8—31no—
215C2×C22⋊C8—31no—
216C2×C22⋊C8—31no—
217C2×C22⋊C8—31no—
218C2×C22⋊C8—31no—
219C2×C22⋊C8C2×D311yescharacteristic
220C2×C22⋊C8C2×D311yescharacteristic
221C2×C22⋊C8C2×D311yescharacteristic, complemented
222C2×C22⋊C8C2×D311yescharacteristic, complemented
223C2×#97—31no—
224C2×#97—31no—
225C2×C4×C8—31no—
226C2×C4×C8C2×D311yescharacteristic, complemented
227C24×C3C22×C411yescharacteristic
228C24×C3C22×C411yescharacteristic
229C23×D3—22no—
230C23×D3—22no—
231C23×D3—22no—
232C23×D3—41no—
233C23×D3—41no—
234C23×D3—41no—
235C23×D3—41no—
236C23×D3C22×C411yescharacteristic
237C23×D3C22×C411yescharacteristic
238C23×D3C22×C411yescharacteristic
239C2×C3×D4—22no—
240C2×C3×D4—22no—
241C2×C3×D4—41no—
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×C4C22×C411yescharacteristic
255C22×C3×C4C22×C411yescharacteristic
256C22×C3×C4C22×C411yescharacteristic
257C22×C3×C4C22×C411yescharacteristic
258C22×C3×C4C2411yescharacteristic
259C2×#67—22no—
260C2×#67—22no—
261C2×#67—22no—
262C2×#67—22no—
263C2×#67—22no—
264C2×#67—22no—
265C2×#67—41no—
266C2×#67—41no—
267C2×#67—41no—
268C2×#67—41no—
269C2×#67—41no—
270C2×#67—41no—
271C22×Dic3—22no—
272C22×Dic3—41no—
273C22×Dic3—41no—
274C22×Dic3C22×C411yescharacteristic
275C22×Dic3C22×C411yescharacteristic
276C22×Dic3C22×C411yescharacteristic
277C22×Dic3C22×C411yescharacteristic
278C22×Dic3C22×C411yescharacteristic
279#235—44no—
280#235—44no—
281#235—44no—
282#235—44no—
283C2×D12—22no—
284C2×D12—22no—
285C2×D12—22no—
286C2×D12—41no—
287C2×D12—41no—
288C2×D12—41no—
289C2×C4×D3—21no—
290C2×C4×D3—21no—
291C2×C4×D3—21no—
292C2×C4×D3—21no—
293C2×C4×D3—22no—
294C2×C4×D3—21no—
295C2×C4×D3—21no—
296C2×C4×D3—21no—
297C2×C4×D3—21no—
298C2×C4×D3—21no—
299C2×C4×D3—21no—
300C2×C4×D3—21no—
301C2×C4×D3—21no—
302C2×C4×D3—21no—
303C2×C4×D3—21no—
304C2×C4×D3—21no—
305C2×C4×D3—21no—
306C2×C4×D3—22no—
307C2×C4×D3—44no—
308C2×C4×D3—44no—
309C2×C4×D3—44no—
310C2×C4×D3—44no—
311C2×C4×D3—41no—
312C2×C4×D3—41no—
313C2×C4×D3—41no—
314C2×C4×D3—41no—
315C2×C4×D3C2×D412yes—
316C2×C4×D3C2×D412yes—
317C2×Dic6—22no—
318C2×Dic6—41no—
319C2×Dic6—41no—
320C2×C3×C8—21no—
321C2×C3×C8—21no—
322C2×C3×C8—21no—
323C2×C3×C8—21no—
324C2×C3×C8—21no—
325C2×C3×C8—21no—
326C2×C3×C8—21no—
327C2×C3×C8—21no—
328C2×C3×C8—21no—
329C2×C3×C8—21no—
330C2×C3×C8—21no—
331C2×C3×C8—21no—
332C3×C4⋊C4—22no—
333C3×C22⋊C4—22no—
334C3×C22⋊C4—22no—
335C3×C42C2×D412yes—
336C3×C42C2×D412yes—
337#217—22no—
338#217—22no—
339(C2×D3)⋊C4—22no—
340(C2×D3)⋊C4—22no—
341(C2×D3)⋊C4—22no—
342(C2×D3)⋊C4—22no—
343(C2×D3)⋊C4C22⋊C414yes—
344(C2×D3)⋊C4C22⋊C414yes—
345C4⋊Dic3—22no—
346Dic3⋊C4—22no—
347Dic3⋊C4—22no—
348Dic3⋊C4C22⋊C414yes—
349Dic3⋊C4C22⋊C414yes—
350C4×Dic3C2×D412yes—
351C4×Dic3C2×D412yes—
352C2×C3⋊C8—21no—
353C2×C3⋊C8—21no—
354C2×C3⋊C8—21no—
355C2×C3⋊C8—21no—
356C2×C3⋊C8—21no—
357C2×C3⋊C8—21no—
358C2×C3⋊C8—21no—
359C2×C3⋊C8—21no—
360C2×C3⋊C8—21no—
361C2×C3⋊C8—21no—
362C2×C3⋊C8—21no—
363C2×C3⋊C8—21no—
364C25—31no—
365C2×#41—62no—
366C2×#41—62no—
367C2×#41—121no—
368C2×#41—121no—
369C2×#41—121no—
370C2×#41—121no—
371C22×Q8—31no—
372C22×D4—31no—
373C22×D4—31no—
374C22×D4—31no—
375C22×D4—31no—
376C22×D4—31no—
377C22×D4—31no—
378C22×D4C4×D311yescharacteristic
379C23×C4—31no—
380C23×C4—31no—
381C23×C4—31no—
382C23×C4—31no—
383C23×C4—31no—
384C23×C4—31no—
385C23×C4—62no—
386C23×C4—62no—
387C23×C4—121no—
388C23×C4—121no—
389C23×C4—121no—
390C23×C4—121no—
391C23×C4C22×D311yescharacteristic
392C23×C4C22×D311yescharacteristic
393C22×C8—31no—
394C22×C8—31no—
395C22×C8—31no—
396C22×C8—31no—
397C22×C8C22×D311yescharacteristic
398C22×C8C22×D311yescharacteristic
399C22×C8C22×D311yescharacteristic
400C22×C8C22×D311yescharacteristic
401#123—64no—
402#123—64no—
403C22⋊Q8—64no—
404C22⋊Q8—64no—
405#121—64no—
406#121—64no—
407#120—64no—
408#120—64no—
409C4×D4—22no—
410C4×D4—22no—
411C4×D4—62no—
412C4×D4—62no—
413C4×D4—62no—
414C4×D4—62no—
415C4×D4—62no—
416C4×D4—62no—
417#117—34no—
418#117—34no—
419C2×C4⋊C4—31no—
420C2×C4⋊C4—31no—
421C2×C4⋊C4—31no—
422C2×C4⋊C4—31no—
423C2×C4⋊C4—31no—
424C2×C4⋊C4C4×D311yescharacteristic
425C2×C22⋊C4—31no—
426C2×C22⋊C4—31no—
427C2×C22⋊C4—31no—
428C2×C22⋊C4—31no—
429C2×C22⋊C4—31no—
430C2×C22⋊C4—31no—
431C2×C22⋊C4—31no—
432C2×C22⋊C4—31no—
433C2×C22⋊C4C4×D311yescharacteristic
434C2×C22⋊C4C4×D311yescharacteristic
435C2×C42—31no—
436C2×C42C22×D311yescharacteristic
437C4⋊C8—22no—
438C4⋊C8—62no—
439C4⋊C8—62no—
440C4⋊C8—62no—
441C22⋊C8—41no—
442C22⋊C8—41no—
443C22⋊C8—41no—
444C22⋊C8—41no—
445C22⋊C8—62no—
446C22⋊C8—62no—
447C22⋊C8—62no—
448C22⋊C8—62no—
449C22⋊C8—121no—
450C22⋊C8—121no—
451C22⋊C8—121no—
452C22⋊C8—121no—
453C22⋊C8—121no—
454C22⋊C8—121no—
455C22⋊C8—121no—
456C22⋊C8—121no—
457C22⋊C8—121no—
458C22⋊C8—121no—
459C22⋊C8—121no—
460C22⋊C8—121no—
461#97—62no—
462#97—62no—
463C4×C8—22no—
464C4×C8—62no—
465C23×C3—21no—
466C23×C3—21no—
467C23×C3—21no—
468C23×C3—21no—
469C23×C3—21no—
470C23×C3—21no—
471C23×C3—21no—
472C23×C3—21no—
473C23×C3—21no—
474C23×C3—21no—
475C23×C3—21no—
476C23×C3—21no—
477C23×C3—21no—
478C23×C3#13112yes—
479C23×C3C23×C411yescharacteristic
480C22×D3—21no—
481C22×D3—21no—
482C22×D3—21no—
483C22×D3—21no—
484C22×D3—21no—
485C22×D3—21no—
486C22×D3—21no—
487C22×D3—21no—
488C22×D3—21no—
489C22×D3—21no—
490C22×D3—21no—
491C22×D3—21no—
492C22×D3—21no—
493C22×D3—21no—
494C22×D3—21no—
495C22×D3—21no—
496C22×D3—21no—
497C22×D3—21no—
498C22×D3—21no—
499C22×D3—44no—
500C22×D3—44no—
501C22×D3—44no—
502C22×D3—44no—
503C22×D3—44no—
504C22×D3—44no—
505C22×D3—44no—
506C22×D3C2×C22⋊C412yes—
507C22×D3#13112yes—
508C3×D4—44no—
509C2×C3×C4—21no—
510C2×C3×C4—21no—
511C2×C3×C4—21no—
512C2×C3×C4—21no—
513C2×C3×C4—21no—
514C2×C3×C4—21no—
515C2×C3×C4—21no—
516C2×C3×C4—21no—
517C2×C3×C4—21no—
518C2×C3×C4—21no—
519C2×C3×C4—41no—
520C2×C3×C4—41no—
521C2×C3×C4—41no—
522C2×C3×C4—41no—
523C2×C3×C4—41no—
524C2×C3×C4—41no—
525C2×C3×C4—41no—
526C2×C3×C4—41no—
527C2×C3×C4C2×C22⋊C412yes—
528C2×C3×C4C2×C22⋊C412yes—
529C2×C3×C4C22×D411yescharacteristic
530C2×C3×C4C22×D411yescharacteristic
531C2×C3×C4H(5,𝔽2)11yescharacteristic
532C2×C3×C4H(5,𝔽2)11yescharacteristic
533C2×C3×C4H(5,𝔽2)11yescharacteristic
534C2×C3×C4H(5,𝔽2)11yescharacteristic
535#67—44no—
536#67—44no—
537#67—44no—
538#67—44no—
539C2×Dic3—21no—
540C2×Dic3—21no—
541C2×Dic3—21no—
542C2×Dic3—21no—
543C2×Dic3—21no—
544C2×Dic3—21no—
545C2×Dic3—21no—
546C2×Dic3—21no—
547C2×Dic3—21no—
548C2×Dic3—21no—
549C2×Dic3—21no—
550C2×Dic3—21no—
551C2×Dic3—44no—
552C2×Dic3C2×C22⋊C412yes—
553C2×Dic3C2×C22⋊C412yes—
554C2×Dic3C2×C22⋊C412yes—
555D12—44no—
556D12—44no—
557C4×D3—22no—
558C4×D3—22no—
559C4×D3—22no—
560C4×D3—22no—
561C4×D3—44no—
562C4×D3—44no—
563C4×D3—41no—
564C4×D3—41no—
565C4×D3—41no—
566C4×D3—41no—
567C4×D3—41no—
568C4×D3—41no—
569C4×D3—41no—
570C4×D3—41no—
571Dic6—44no—
572C3×C8—41no—
573C3×C8—41no—
574C3×C8—41no—
575C3×C8—41no—
576C3⋊C8—41no—
577C3⋊C8—41no—
578C3⋊C8—41no—
579C3⋊C8—41no—
580C24—31no—
581C24—31no—
582C24—31no—
583C24—62no—
584C24—62no—
585C24—62no—
586C24—121no—
587C24—121no—
588C24—121no—
589C24—121no—
590C24C2×C4×D311yescharacteristic
591C24C2×C4×D311yescharacteristic
592#41—124no—
593#41—124no—
594#41—124no—
595#41—124no—
596C2×Q8—62no—
597C2×Q8—121no—
598C2×Q8—121no—
599C2×D4—22no—
600C2×D4—22no—
601C2×D4—41no—
602C2×D4—62no—
603C2×D4—62no—
604C2×D4—62no—
605C2×D4—62no—
606C2×D4—62no—
607C2×D4—62no—
608C2×D4—62no—
609C2×D4—62no—
610C2×D4—62no—
611C2×D4—121no—
612C2×D4—121no—
613C2×D4—121no—
614C2×D4—121no—
615C2×D4—121no—
616C2×D4—121no—
617C2×D4—121no—
618C2×D4—121no—
619C2×D4—121no—
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—31no—
633C22×C4—31no—
634C22×C4—31no—
635C22×C4—32no—
636C22×C4—32no—
637C22×C4—31no—
638C22×C4—31no—
639C22×C4—62no—
640C22×C4—62no—
641C22×C4—62no—
642C22×C4—61no—
643C22×C4—61no—
644C22×C4—61no—
645C22×C4—61no—
646C22×C4—61no—
647C22×C4—61no—
648C22×C4—61no—
649C22×C4—61no—
650C22×C4—61no—
651C22×C4—61no—
652C22×C4—61no—
653C22×C4—61no—
654C22×C4—61no—
655C22×C4—61no—
656C22×C4—61no—
657C22×C4—61no—
658C22×C4—121no—
659C22×C4—121no—
660C22×C4—121no—
661C22×C4—121no—
662C22×C4—124no—
663C22×C4—124no—
664C22×C4—124no—
665C22×C4—124no—
666C22×C4—121no—
667C22×C4—121no—
668C22×C4C2×C4×D311yescharacteristic
669C22×C4C2×C4×D311yescharacteristic
670C22×C4C2×C4×D311yescharacteristic
671C22×C4C2×C4×D311yescharacteristic
672C22×C4C23×D311yescharacteristic
673C2×C8—21no—
674C2×C8—21no—
675C2×C8—21no—
676C2×C8—21no—
677C2×C8—21no—
678C2×C8—21no—
679C2×C8—21no—
680C2×C8—21no—
681C2×C8—21no—
682C2×C8—21no—
683C2×C8—21no—
684C2×C8—21no—
685C2×C8—61no—
686C2×C8—61no—
687C2×C8—61no—
688C2×C8—61no—
689C2×C8—61no—
690C2×C8—61no—
691C2×C8—61no—
692C2×C8—61no—
693C2×C8—61no—
694C2×C8—61no—
695C2×C8—61no—
696C2×C8—61no—
697C4⋊C4—22no—
698C4⋊C4—34no—
699C4⋊C4—34no—
700C4⋊C4—62no—
701C4⋊C4—62no—
702C4⋊C4—62no—
703C22⋊C4—22no—
704C22⋊C4—22no—
705C22⋊C4—34no—
706C22⋊C4—34no—
707C22⋊C4—62no—
708C22⋊C4—62no—
709C22⋊C4—62no—
710C22⋊C4—62no—
711C22⋊C4—62no—
712C22⋊C4—62no—
713C42—32no—
714C42—32no—
715C42D3×D412yes—
716C42D3×D412yes—
717C22×C3—22no—
718C22×C3—22no—
719C22×C3—22no—
720C22×C3—41no—
721C22×C3—41no—
722C22×C3—41no—
723C22×C3—41no—
724C22×C3—41no—
725C22×C3—41no—
726C22×C3—41no—
727C22×C3—41no—
728C22×C3—41no—
729C22×C3—41no—
730C22×C3—41no—
731C22×C3C22×C22⋊C411yescharacteristic
732C22×C3#51811yescharacteristic
733C22×C3#51811yescharacteristic
734C22×C3C2×#13111yescharacteristic
735C22×C3C2×#13111yescharacteristic
736C22×C3#56811yescharacteristic
737C22×C3#56811yescharacteristic
738C2×D3—22no—
739C2×D3—22no—
740C2×D3—22no—
741C2×D3—22no—
742C2×D3—22no—
743C2×D3—22no—
744C2×D3—416no—
745C2×D3—41no—
746C2×D3—41no—
747C2×D3—41no—
748C2×D3—41no—
749C2×D3—41no—
750C2×D3—41no—
751C2×D3—41no—
752C2×D3—41no—
753C2×D3—41no—
754C2×D3—41no—
755C2×D3—41no—
756C2×D3—41no—
757C2×D3—41no—
758C2×D3—41no—
759C2×D3—41no—
760C3×C4—22no—
761C3×C4—22no—
762C3×C4—41no—
763C3×C4—41no—
764C3×C4#53511yescharacteristic
765C3×C4#53511yescharacteristic
766C3×C4#53511yescharacteristic
767C3×C4#53511yescharacteristic
768Dic3—22no—
769Dic3—22no—
770Dic3—22no—
771Dic3—41no—
772Dic3—41no—
773C23—21no—
774C23—21no—
775C23—21no—
776C23—21no—
777C23—21no—
778C23—21no—
779C23—21no—
780C23—21no—
781C23—21no—
782C23—21no—
783C23—21no—
784C23—21no—
785C23—21no—
786C23—32no—
787C23—32no—
788C23—61no—
789C23—61no—
790C23—61no—
791C23—61no—
792C23—61no—
793C23—61no—
794C23—61no—
795C23—61no—
796C23—61no—
797C23—61no—
798C23—61no—
799C23—61no—
800C23—61no—
801C23—61no—
802C23—61no—
803C23—61no—
804C23—61no—
805C23—61no—
806C23—61no—
807C23—124no—
808C23—124no—
809C23—124no—
810C23—124no—
811C23—124no—
812C23—124no—
813C23—124no—
814C23#90112yes—
815C23C22×C4×D311yescharacteristic
816Q8—124no—
817D4—44no—
818D4—124no—
819D4—124no—
820D4—124no—
821D4—124no—
822D4—124no—
823D4—124no—
824C2×C4—21no—
825C2×C4—21no—
826C2×C4—21no—
827C2×C4—21no—
828C2×C4—21no—
829C2×C4—21no—
830C2×C4—21no—
831C2×C4—21no—
832C2×C4—21no—
833C2×C4—21no—
834C2×C4—32no—
835C2×C4—32no—
836C2×C4—32no—
837C2×C4—41no—
838C2×C4—41no—
839C2×C4—41no—
840C2×C4—41no—
841C2×C4—41no—
842C2×C4—41no—
843C2×C4—41no—
844C2×C4—41no—
845C2×C4—61no—
846C2×C4—61no—
847C2×C4—61no—
848C2×C4—61no—
849C2×C4—61no—
850C2×C4—61no—
851C2×C4—62no—
852C2×C4—62no—
853C2×C4—62no—
854C2×C4—62no—
855C2×C4—61no—
856C2×C4—61no—
857C2×C4—61no—
858C2×C4—61no—
859C2×C4—61no—
860C2×C4—61no—
861C2×C4—124no—
862C2×C4—124no—
863C2×C4—124no—
864C2×C4—121no—
865C2×C4—121no—
866C2×C4—121no—
867C2×C4—121no—
868C2×C4—121no—
869C2×C4—121no—
870C2×C4—121no—
871C2×C4—121no—
872C2×C4D3×C22⋊C412yes—
873C2×C4D3×C22⋊C412yes—
874C2×C4C2×D3×D411yescharacteristic
875C2×C4C2×D3×D411yescharacteristic
876C2×C4#100411yescharacteristic
877C2×C4#100411yescharacteristic
878C2×C4#100911yescharacteristic
879C2×C4#100911yescharacteristic
880C8—41no—
881C8—41no—
882C8—41no—
883C8—41no—
884C8—121no—
885C8—121no—
886C8—121no—
887C8—121no—
888C2×C3—42no—
889C2×C3—81no—
890C2×C3#230911yescharacteristic
891C2×C3#288011yescharacteristic
892C2×C3#288011yescharacteristic
893C2×C3#297611yescharacteristic
894C2×C3#297611yescharacteristic
895C2×C3#297711yescharacteristic
896C2×C3#297811yescharacteristic
897D3—42no—
898D3—42no—
899D3—81no—
900C22—22no—
901C22—22no—
902C22—22no—
903C22—41no—
904C22—41no—
905C22—41no—
906C22—41no—
907C22—41no—
908C22—41no—
909C22—41no—
910C22—41no—
911C22—41no—
912C22—41no—
913C22—41no—
914C22—62no—
915C22—62no—
916C22—62no—
917C22—62no—
918C22—62no—
919C22—62no—
920C22—1216no—
921C22—121no—
922C22—121no—
923C22—121no—
924C22—121no—
925C22—121no—
926C22—121no—
927C22—121no—
928C22—121no—
929C22—121no—
930C22—121no—
931C22—121no—
932C22—121no—
933C22—121no—
934C22—121no—
935C22—121no—
936C22C2×D3×C22⋊C411yescharacteristic
937C22#554511yescharacteristic
938C22#554511yescharacteristic
939C22C2×#90111yescharacteristic
940C22#574511yescharacteristic
941C22D3×#13111yescharacteristic
942C22#575011yescharacteristic
943C4—22no—
944C4—22no—
945C4—41no—
946C4—41no—
947C4—62no—
948C4—62no—
949C4—62no—
950C4—121no—
951C4—121no—
952C4#560711yescharacteristic
953C4#560711yescharacteristic
954C4#567411yescharacteristic
955C4#571511yescharacteristic
956C3#2179211yescharacteristic, complemented, Sylow
957C2—42no—
958C2—81no—
959C2—122no—
960C2—122no—
961C2—241no—
962C2#7642811yescharacteristic
963C2#7860011yescharacteristic
964C2#7866311yescharacteristic
965C2#7942811yescharacteristic
966C2#7942911yescharacteristic
967C2#7954411yescharacteristic
968C2#7954511yescharacteristic
subgroupG/H
center, FrattiniC22×C4C23×D3
commutator, socleC23×C3C23×C4
FittingC3×#1954C2
prime radicalC2×#5547C2
cosocleC22×C3×C4C24
hypercenter#1954D3
hypocenterC3#21792
LCSG ▷ C23×C3 ▷ C3
UCSC1 ◁ C22×C4 ◁ #1954

Complements

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

NH ≅ G/Ntype
2. C2×#4840C2semidirect
3. C2×#4690C2semidirect
4. C3×#1954C2semidirect
5. #71615C2semidirect
6. #70471C2semidirect
7. #69956C2semidirect
8. #69956C2semidirect
9. #69955C2semidirect
10. #69955C2semidirect
11. #69917C2semidirect
12. #69917C2semidirect
13. #69916C2semidirect
14. #69916C2semidirect
15. #69787C2semidirect
34. C2×C3×C4⋊C8C22semidirect
37. C2×C3×C22⋊C8C22semidirect
38. C2×C3×C22⋊C8C22semidirect
39. C2×C3×C4×C8C22semidirect
42. C2×#830C22semidirect
43. C2×#830C22semidirect
52. C2×(C2×D3)⋊C8C22semidirect
53. C2×(C2×D3)⋊C8C22semidirect
54. C2×(C2×D3)⋊C8C22semidirect
55. C2×(C2×D3)⋊C8C22semidirect
56. C2×#815C22semidirect
57. C2×Dic3⋊C8C22semidirect
58. C2×Dic3⋊C8C22semidirect
59. C2×C8×Dic3C22semidirect
60. C2×C4⋊(C3⋊C8)C22semidirect
61. C2×#803C22semidirect
74. #1954D3semidirect
202. C2×C4⋊C8C2×D3semidirect
221. C2×C22⋊C8C2×D3semidirect
222. C2×C22⋊C8C2×D3semidirect
226. C2×C4×C8C2×D3semidirect
956. C3#21792semidirect

Maximal subgroups

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

subgroupindex
C2×#55472
C2×#48402
C2×#46902
C3×#19542
#716152
#704712
#699562
#699552
#699172
#699162
#697872
#217923