Finite Group Databasebeta

← #11810268

Subgroups — #11810268

Order 1152.

1439 conjugacy classes of subgroups.

The subgroup lattice has 944 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#63894C211yesmaximal, characteristic
2C2×#63888C211yesmaximal, characteristic, complemented
3C2×#63888C211yesmaximal, characteristic, complemented
4C2×#63883C211yesmaximal, characteristic, complemented
5#10592364C211yesmaximal, characteristic
6C3×#4657C211yesmaximal, characteristic, complemented
7C3×#4646C211yesmaximal, characteristic, complemented
8#10591380C211yesmaximal, characteristic
9#10591367C211yesmaximal, characteristic, complemented
10#10591367C211yesmaximal, characteristic, complemented
11#10591355C211yesmaximal, characteristic, complemented
12#10591347C211yesmaximal, characteristic, complemented
13#10591347C211yesmaximal, characteristic, complemented
14#10591345C211yesmaximal, characteristic, complemented
15#10591327C211yesmaximal, characteristic, complemented
16#77742—31nomaximal
17#76621—31nomaximal
18C22×C4⋊(C3⋊D3)C2211yescharacteristic
19C22×C4×C3⋊D3C2211yescharacteristic
20C22×C3×Dic6C2211yescharacteristic
21C22×#624C2211yescharacteristic
22C22×#624C2211yescharacteristic
23C22×#624C2211yescharacteristic
24C2×#3752C2211yescharacteristic
25C2×#3752C2211yescharacteristic
26C2×#3752C2211yescharacteristic
27C2×C3×C4⋊Dic3C2211yescharacteristic
28C2×C3×Dic3⋊C4C2211yescharacteristic
29C2×C3×Dic3⋊C4C2211yescharacteristic
30C2×C3×Dic3⋊C4C2211yescharacteristic
31C2×C3×Dic3⋊C4C2211yescharacteristic
32C2×C3×C4×Dic3C2211yescharacteristic
33C2×#3724C2211yescharacteristic
34C2×#3724C2211yescharacteristic
35C2×#3724C2211yescharacteristic
36C2×Dic3⋊Dic3C2211yescharacteristic
37C2×Dic3⋊Dic3C2211yescharacteristic
38C2×Dic3⋊Dic3C2211yescharacteristic
39C2×Dic3⋊Dic3C2211yescharacteristic
40C2×#3722C2211yescharacteristic
41C2×#3722C2211yescharacteristic
42C2×#3722C2211yescharacteristic
43C2×#3722C2211yescharacteristic
44C2×#3722C2211yescharacteristic
45#63894—24no—
46#63888—24no—
47#63888—24no—
48#63883—24no—
49C32×#95C2211yescharacteristic
50#63658C2211yescharacteristic
51C3×C3⋊#95C2211yescharacteristic
52C3×C3⋊#95C2211yescharacteristic
53C3×C3⋊#95C2211yescharacteristic
54C3×C3⋊#95C2211yescharacteristic
55C3×C3⋊#95C2211yescharacteristic
56#63579C2211yescharacteristic
57C2×#946—31no—
58C2×#946—31no—
59C2×#896—31no—
60C2×#896—31no—
61C2×#893—31no—
62C2×D3×C4⋊C4—31no—
63C2×D3×C4⋊C4—31no—
64C2×C4×D12—31no—
65C3×#398—31no—
66C3×#391—31no—
67#4994—31no—
68#4994—31no—
69#4987—31no—
70#4987—31no—
71#4982—31no—
72#4928—31no—
73#4676—31no—
74#4676—31no—
75#4667—31no—
76#4667—31no—
77#4667—31no—
78#4667—31no—
79#4665—31no—
80#4665—31no—
81#4665—31no—
82#4665—31no—
83#4665—61no—
84#4657—31no—
85#4657D311yescharacteristic, complemented
86#4647—31no—
87#4646D311yescharacteristic, complemented
88C23×C3⋊D3C2311yescharacteristic
89C23×C3⋊D3C2311yescharacteristic
90C22×C32×C4C2311yescharacteristic
91C22×C32×C4C2311yescharacteristic
92C22×C32×C4C2311yescharacteristic
93C22×C3⋊Dic3C2311yescharacteristic
94C22×C3⋊Dic3C2311yescharacteristic
95C2×C4⋊(C3⋊D3)—22no—
96C2×C4⋊(C3⋊D3)—22no—
97C2×C4⋊(C3⋊D3)Q814yescomplemented
98C2×C4×C3⋊D3—22no—
99C2×C4×C3⋊D3—22no—
100C2×C4×C3⋊D3—41no—
101C22×C3×Dic3C2311yescharacteristic
102C22×C3×Dic3C2311yescharacteristic
103C22×C3×Dic3C2311yescharacteristic
104C22×C3×Dic3C2311yescharacteristic
105C22×C3×Dic3C2311yescharacteristic
106C22×C3×Dic3C2311yescharacteristic
107C22×C3×Dic3C2311yescharacteristic
108C22×C3×Dic3C2311yescharacteristic
109C2×C3×Dic6—22no—
110C2×C3×Dic6—22no—
111C2×C3×Dic6—22no—
112C2×#624—22no—
113C2×#624—22no—
114C2×#624—22no—
115C2×#624—22no—
116C2×#624—22no—
117C2×#624—22no—
118C2×#624—22no—
119C2×#624—41no—
120C2×#624D414yes—
121#3752—22no—
122#3752—22no—
123#3752—41no—
124C3×C4⋊Dic3—22no—
125C3×Dic3⋊C4—22no—
126C3×Dic3⋊C4—22no—
127C3×Dic3⋊C4—22no—
128C3×Dic3⋊C4—22no—
129C3×C4×Dic3—22no—
130#3724—22no—
131#3724—22no—
132#3724—41no—
133Dic3⋊Dic3—22no—
134Dic3⋊Dic3—22no—
135Dic3⋊Dic3—41no—
136Dic3⋊Dic3D414yescomplemented
137#3722—22no—
138#3722—22no—
139#3722—22no—
140#3722—22no—
141#3722—41no—
142#2417—91noSylow
143C22×C3×Q8—31no—
144C22×D12—31no—
145C22×D12—31no—
146C22×D12—61no—
147C22×C4×D3—31no—
148C22×C4×D3—31no—
149C22×C4×D3—31no—
150C22×C4×D3—31no—
151C22×C4×D3—31no—
152C22×C4×D3—31no—
153C22×C4×D3—31no—
154C22×C4×D3—31no—
155C22×C4×D3—61no—
156C22×Dic6C2×D311yescharacteristic
157C2×C3×C4⋊C4—31no—
158C2×C3×C4⋊C4—31no—
159C2×C3×C4⋊C4—31no—
160C2×C3×C4⋊C4—31no—
161C2×C3×C4⋊C4—31no—
162C2×C3×C42—31no—
163#946—64no—
164#946—64no—
165C2×(C2×D3)⋊C4—31no—
166C2×(C2×D3)⋊C4—31no—
167C2×(C2×D3)⋊C4—31no—
168C2×(C2×D3)⋊C4—31no—
169C2×(C2×D3)⋊C4—31no—
170C2×(C2×D3)⋊C4—31no—
171C2×(C2×D3)⋊C4—31no—
172C2×(C2×D3)⋊C4—31no—
173C2×(C2×D3)⋊C4—31no—
174C2×(C2×D3)⋊C4—31no—
175C2×(C2×D3)⋊C4—31no—
176C2×(C2×D3)⋊C4—31no—
177C2×(C2×D3)⋊C4—31no—
178C2×(C2×D3)⋊C4—31no—
179C2×(C2×D3)⋊C4—31no—
180C2×(C2×D3)⋊C4—31no—
181C2×(C2×D3)⋊C4—61no—
182C2×(C2×D3)⋊C4—61no—
183C2×(C2×D3)⋊C4—61no—
184C2×C4⋊Dic3—31no—
185C2×C4⋊Dic3—31no—
186C2×C4⋊Dic3—31no—
187C2×C4⋊Dic3—31no—
188C2×C4⋊Dic3C2×D311yescharacteristic
189C2×Dic3⋊C4—31no—
190C2×Dic3⋊C4—31no—
191C2×Dic3⋊C4—31no—
192C2×Dic3⋊C4—31no—
193C2×Dic3⋊C4—31no—
194C2×Dic3⋊C4—31no—
195C2×Dic3⋊C4—31no—
196C2×Dic3⋊C4—31no—
197C2×Dic3⋊C4—31no—
198C2×Dic3⋊C4—31no—
199C2×Dic3⋊C4C2×D311yescharacteristic
200C2×Dic3⋊C4C2×D311yescharacteristic
201C2×Dic3⋊C4C2×D311yescharacteristic
202C2×Dic3⋊C4C2×D311yescharacteristic
203C2×C4×Dic3C2×D311yescharacteristic
204#896—64no—
205#896—64no—
206#893—64no—
207D3×C4⋊C4—64no—
208D3×C4⋊C4—64no—
209C4×D12—64no—
210C3×#95—21no—
211C3×#95—31no—
212C3×#95—31no—
213C3×#95—31no—
214C3×#95—31no—
215C3×#95—31no—
216C3×#95C2×D311yescharacteristic
217C3×#95C2×D311yescharacteristic
218C3⋊#95—31no—
219C3⋊#95—31no—
220C3⋊#95—31no—
221C3⋊#95—31no—
222C3⋊#95—61no—
223C3⋊#95C2×D311yescharacteristic
224C3⋊#95C2×D311yescharacteristic
225C3⋊#95C2×D311yescharacteristic
226C3⋊#95C2×D311yescharacteristic
227C3⋊#95C2×D311yescharacteristic
228C23×C32C2411yescharacteristic
229C22×C3⋊D3—21no—
230C22×C3⋊D3—21no—
231C22×C3⋊D3—21no—
232C22×C3⋊D3—21no—
233C22×C3⋊D3—21no—
234C22×C3⋊D3—21no—
235C22×C3⋊D3—21no—
236C22×C3⋊D3—21no—
237C22×C3⋊D3—21no—
238C22×C3⋊D3—21no—
239C22×C3⋊D3C2×D412yes—
240C22×C3⋊D3C2×Q812yes—
241C22×C3⋊D3C2×Q812yes—
242C22×C3⋊D3#4112yes—
243C2×C32×C4—21no—
244C2×C32×C4—21no—
245C2×C32×C4—21no—
246C2×C32×C4—21no—
247C2×C32×C4—21no—
248C2×C32×C4—21no—
249C2×C32×C4—21no—
250C2×C32×C4—21no—
251C2×C32×C4C2×Q812yes—
252C2×C3⋊Dic3—21no—
253C2×C3⋊Dic3—21no—
254C2×C3⋊Dic3—21no—
255C2×C3⋊Dic3—21no—
256C2×C3⋊Dic3—21no—
257C2×C3⋊Dic3C2×D412yes—
258C4⋊(C3⋊D3)—28no—
259C4×C3⋊D3—44no—
260C2×C3×Dic3—21no—
261C2×C3×Dic3—21no—
262C2×C3×Dic3—21no—
263C2×C3×Dic3—21no—
264C2×C3×Dic3—21no—
265C2×C3×Dic3—21no—
266C2×C3×Dic3—21no—
267C2×C3×Dic3—21no—
268C2×C3×Dic3—21no—
269C2×C3×Dic3—21no—
270C2×C3×Dic3—21no—
271C2×C3×Dic3—21no—
272C2×C3×Dic3—21no—
273C2×C3×Dic3—21no—
274C2×C3×Dic3—21no—
275C2×C3×Dic3—21no—
276C2×C3×Dic3—21no—
277C2×C3×Dic3—21no—
278C2×C3×Dic3—21no—
279C2×C3×Dic3C2×D412yes—
280C2×C3×Dic3C2×D412yes—
281C2×C3×Dic3C2×D412yes—
282C2×C3×Dic3C2×D412yes—
283C2×C3×Dic3#4112yes—
284C3×Dic6—44no—
285#624—28no—
286#624—44no—
287#624—44no—
288C2×C22⋊Q8—91no—
289C2×C22⋊Q8—91no—
290C2×C4×D4—91no—
291C22×C4⋊C4—91no—
292#398—31no—
293#398—91no—
294#396—91no—
295#396—91no—
296#391—31no—
297#389—91no—
298#386—91no—
299#386—91no—
300#380—91no—
301#380—91no—
302#380—91no—
303C23×D3—31no—
304C23×D3—31no—
305C23×D3—31no—
306C23×D3—31no—
307C23×D3—61no—
308C23×D3—61no—
309C2×C3×Q8—62no—
310C2×C3×Q8—62no—
311C2×C3×Q8—62no—
312C22×C3×C4—21no—
313C22×C3×C4—21no—
314C22×C3×C4—21no—
315C22×C3×C4—31no—
316C22×C3×C4—31no—
317C22×C3×C4—31no—
318C22×C3×C4—31no—
319C22×C3×C4—31no—
320C22×C3×C4—31no—
321C22×C3×C4—31no—
322C22×C3×C4—31no—
323C22×C3×C4C22×D311yescharacteristic
324C22×C3×C4C22×D311yescharacteristic
325C22×C3×C4C22×D311yescharacteristic
326C22×C3×C4C22×D311yescharacteristic
327C22×C3×C4C22×D311yescharacteristic
328C22×C3×C4C22×D311yescharacteristic
329C22×Dic3—31no—
330C22×Dic3—31no—
331C22×Dic3—31no—
332C22×Dic3—31no—
333C22×Dic3—61no—
334C22×Dic3—61no—
335C22×Dic3C22×D311yescharacteristic
336C22×Dic3C22×D311yescharacteristic
337C22×Dic3C22×D311yescharacteristic
338C22×Dic3C22×D311yescharacteristic
339C22×Dic3C22×D311yescharacteristic
340C22×Dic3C22×D311yescharacteristic
341C22×Dic3C22×D311yescharacteristic
342C22×Dic3C22×D311yescharacteristic
343C2×D12—34no—
344C2×D12—34no—
345C2×D12—64no—
346C2×D12—62no—
347C2×D12—62no—
348C2×D12—62no—
349C2×D12—62no—
350C2×D12—122no—
351C2×D12—122no—
352C2×C4×D3—34no—
353C2×C4×D3—34no—
354C2×C4×D3—62no—
355C2×C4×D3—62no—
356C2×C4×D3—62no—
357C2×C4×D3—62no—
358C2×C4×D3—62no—
359C2×C4×D3—62no—
360C2×C4×D3—62no—
361C2×C4×D3—62no—
362C2×C4×D3—62no—
363C2×C4×D3—62no—
364C2×C4×D3—62no—
365C2×C4×D3—62no—
366C2×C4×D3—62no—
367C2×C4×D3—62no—
368C2×C4×D3—62no—
369C2×C4×D3—62no—
370C2×C4×D3—62no—
371C2×C4×D3—62no—
372C2×C4×D3—122no—
373C2×C4×D3—122no—
374C2×C4×D3—121no—
375C2×C4×D3—121no—
376C2×C4×D3—121no—
377C2×C4×D3—121no—
378C2×C4×D3—122no—
379C2×Dic6—22no—
380C2×Dic6—22no—
381C2×Dic6—22no—
382C3×C4⋊C4—62no—
383C3×C4⋊C4—62no—
384C3×C4⋊C4—62no—
385C3×C4⋊C4—62no—
386C3×C4⋊C4—62no—
387C3×C42—62no—
388(C2×D3)⋊C4—62no—
389(C2×D3)⋊C4—62no—
390(C2×D3)⋊C4—62no—
391(C2×D3)⋊C4—62no—
392(C2×D3)⋊C4—62no—
393(C2×D3)⋊C4—62no—
394(C2×D3)⋊C4—62no—
395(C2×D3)⋊C4—62no—
396(C2×D3)⋊C4—62no—
397(C2×D3)⋊C4—62no—
398(C2×D3)⋊C4—62no—
399(C2×D3)⋊C4—62no—
400(C2×D3)⋊C4—122no—
401(C2×D3)⋊C4—122no—
402(C2×D3)⋊C4—121no—
403(C2×D3)⋊C4—121no—
404(C2×D3)⋊C4—121no—
405(C2×D3)⋊C4—121no—
406(C2×D3)⋊C4—122no—
407C4⋊Dic3—22no—
408C4⋊Dic3—34no—
409C4⋊Dic3—62no—
410C4⋊Dic3—62no—
411C4⋊Dic3—121no—
412Dic3⋊C4—22no—
413Dic3⋊C4—22no—
414Dic3⋊C4—22no—
415Dic3⋊C4—22no—
416Dic3⋊C4—34no—
417Dic3⋊C4—62no—
418Dic3⋊C4—62no—
419Dic3⋊C4—62no—
420Dic3⋊C4—62no—
421Dic3⋊C4—62no—
422Dic3⋊C4—62no—
423Dic3⋊C4—121no—
424Dic3⋊C4—121no—
425Dic3⋊C4—121no—
426C4×Dic3—22no—
427C22×C32C22×D411yescharacteristic
428C22×C32C22×D411yescharacteristic
429C22×C32C22×Q811yescharacteristic
430C22×C32C2×#4111yescharacteristic
431C22×C32C2×#4111yescharacteristic
432C22×C32H(5,𝔽2)11yescharacteristic
433C22×C322−1+411yescharacteristic
434C2×C3⋊D3—22no—
435C2×C3⋊D3—22no—
436C2×C3⋊D3—22no—
437C2×C3⋊D3—22no—
438C2×C3⋊D3—22no—
439C2×C3⋊D3—22no—
440C2×C3⋊D3—22no—
441C2×C3⋊D3—22no—
442C2×C3⋊D3—22no—
443C2×C3⋊D3—41no—
444C2×C3⋊D3—41no—
445C2×C3⋊D3—41no—
446C2×C3⋊D3—41no—
447C2×C3⋊D3C22⋊Q814yescomplemented
448C32×C4—22no—
449C32×C4—41no—
450C32×C4—41no—
451C3⋊Dic3—22no—
452C3⋊Dic3—41no—
453C3×Dic3—22no—
454C3×Dic3—22no—
455C3×Dic3—41no—
456C3×Dic3—41no—
457C3×Dic3—41no—
458C3×Dic3—41no—
459C3×Dic3—41no—
460C3×Dic3#12114yes—
461C22×Q8—31no—
462C22×D4—91no—
463C23×C4—91no—
464C23×C4—91no—
465C23×C4—91no—
466C23×C4—91no—
467C22⋊Q8—184no—
468C22⋊Q8—184no—
469C4×D4—184no—
470C2×C4⋊C4—31no—
471C2×C4⋊C4—31no—
472C2×C4⋊C4—31no—
473C2×C4⋊C4—31no—
474C2×C4⋊C4—31no—
475C2×C4⋊C4—91no—
476C2×C4⋊C4—91no—
477C2×C4⋊C4—91no—
478C2×C4⋊C4—91no—
479C2×C4⋊C4—91no—
480C2×C4⋊C4—91no—
481C2×C4⋊C4—91no—
482C2×C4⋊C4—184no—
483C2×C22⋊C4—91no—
484C2×C22⋊C4—91no—
485C2×C22⋊C4—91no—
486C2×C22⋊C4—91no—
487C2×C22⋊C4—91no—
488C2×C22⋊C4—91no—
489C2×C22⋊C4—91no—
490C2×C22⋊C4—91no—
491C2×C42—31no—
492#95—31no—
493#95—31no—
494#95—31no—
495#95—31no—
496#95—31no—
497#95—91no—
498#95—91no—
499#95D3211yescharacteristic
500C23×C3—21no—
501C23×C3C23×D311yescharacteristic
502C23×C3C23×D311yescharacteristic
503C22×D3—32no—
504C22×D3—32no—
505C22×D3—32no—
506C22×D3—32no—
507C22×D3—32no—
508C22×D3—32no—
509C22×D3—32no—
510C22×D3—32no—
511C22×D3—62no—
512C22×D3—62no—
513C22×D3—62no—
514C22×D3—62no—
515C22×D3—61no—
516C22×D3—61no—
517C22×D3—61no—
518C22×D3—61no—
519C22×D3—61no—
520C22×D3—61no—
521C22×D3—61no—
522C22×D3—61no—
523C22×D3—61no—
524C22×D3—61no—
525C22×D3—61no—
526C22×D3—61no—
527C22×D3—61no—
528C22×D3—61no—
529C22×D3—61no—
530C22×D3—61no—
531C22×D3—61no—
532C22×D3—61no—
533C22×D3—61no—
534C22×D3—61no—
535C22×D3—121no—
536C22×D3—121no—
537C22×D3—121no—
538C22×D3—121no—
539C22×D3—121no—
540C22×D3—121no—
541C22×D3—121no—
542C22×D3—121no—
543C22×D3—121no—
544C22×D3—121no—
545C3×Q8—124no—
546C2×C3×C4—21no—
547C2×C3×C4—21no—
548C2×C3×C4—21no—
549C2×C3×C4—21no—
550C2×C3×C4—22no—
551C2×C3×C4—21no—
552C2×C3×C4—21no—
553C2×C3×C4—21no—
554C2×C3×C4—21no—
555C2×C3×C4—21no—
556C2×C3×C4—21no—
557C2×C3×C4—21no—
558C2×C3×C4—21no—
559C2×C3×C4—21no—
560C2×C3×C4—21no—
561C2×C3×C4—21no—
562C2×C3×C4—21no—
563C2×C3×C4—22no—
564C2×C3×C4—32no—
565C2×C3×C4—32no—
566C2×C3×C4—32no—
567C2×C3×C4—32no—
568C2×C3×C4—32no—
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—61no—
577C2×C3×C4—61no—
578C2×C3×C4—61no—
579C2×C3×C4—61no—
580C2×C3×C4—61no—
581C2×C3×C4—61no—
582C2×C3×C4—61no—
583C2×C3×C4—61no—
584C2×C3×C4—61no—
585C2×C3×C4—61no—
586C2×C3×C4—61no—
587C2×C3×C4—61no—
588C2×C3×C4—61no—
589C2×C3×C4—61no—
590C2×C3×C4—61no—
591C2×C3×C4—61no—
592C2×C3×C4—61no—
593C2×C3×C4—61no—
594C2×C3×C4—61no—
595C2×C3×C4D3×Q812yes—
596C2×C3×C4D3×Q812yes—
597C2×Dic3—21no—
598C2×Dic3—21no—
599C2×Dic3—21no—
600C2×Dic3—21no—
601C2×Dic3—21no—
602C2×Dic3—21no—
603C2×Dic3—21no—
604C2×Dic3—21no—
605C2×Dic3—21no—
606C2×Dic3—21no—
607C2×Dic3—21no—
608C2×Dic3—21no—
609C2×Dic3—21no—
610C2×Dic3—21no—
611C2×Dic3—21no—
612C2×Dic3—21no—
613C2×Dic3—21no—
614C2×Dic3—21no—
615C2×Dic3—21no—
616C2×Dic3—32no—
617C2×Dic3—32no—
618C2×Dic3—62no—
619C2×Dic3—61no—
620C2×Dic3—61no—
621C2×Dic3—61no—
622C2×Dic3—61no—
623C2×Dic3—61no—
624C2×Dic3—61no—
625C2×Dic3—61no—
626C2×Dic3—61no—
627C2×Dic3—61no—
628C2×Dic3—61no—
629C2×Dic3—121no—
630C2×Dic3—121no—
631C2×Dic3—121no—
632C2×Dic3—121no—
633C2×Dic3—121no—
634C2×Dic3#23512yes—
635C2×Dic3D3×D412yes—
636C2×Dic3D3×D412yes—
637C2×Dic3D3×D412yes—
638C2×Dic3D3×D412yes—
639D12—68no—
640D12—68no—
641D12—128no—
642C4×D3—68no—
643C4×D3—68no—
644C4×D3—124no—
645C4×D3—124no—
646C4×D3—124no—
647C4×D3—124no—
648C4×D3—124no—
649C4×D3—128no—
650C4×D3—124no—
651Dic6—44no—
652C2×C32C2×#12111yescharacteristic
653C2×C32C2×C22⋊Q811yescharacteristic
654C2×C32#53711yescharacteristic
655C2×C32#54611yescharacteristic
656C2×C32D4×Q811yescharacteristic
657C2×C32#55211yescharacteristic
658C2×C32#55411yescharacteristic
659C3⋊D3—24no—
660C3⋊D3—42no—
661C24—91no—
662C24—91no—
663C2×Q8—62no—
664C2×Q8—62no—
665C2×Q8—62no—
666C2×D4—94no—
667C2×D4—182no—
668C2×D4—182no—
669C22×C4—31no—
670C22×C4—31no—
671C22×C4—31no—
672C22×C4—31no—
673C22×C4—31no—
674C22×C4—31no—
675C22×C4—31no—
676C22×C4—31no—
677C22×C4—94no—
678C22×C4—91no—
679C22×C4—91no—
680C22×C4—182no—
681C22×C4—182no—
682C22×C4—182no—
683C22×C4—182no—
684C22×C4—182no—
685C22×C4—182no—
686C22×C4—182no—
687C22×C4—182no—
688C22×C4—182no—
689C22×C4—361no—
690C22×C4—361no—
691C22×C4C2×D3211yescharacteristic
692C22×C4C2×D3211yescharacteristic
693C22×C4C2×D3211yescharacteristic
694C4⋊C4—62no—
695C4⋊C4—62no—
696C4⋊C4—62no—
697C4⋊C4—62no—
698C4⋊C4—62no—
699C4⋊C4—94no—
700C4⋊C4—182no—
701C4⋊C4—182no—
702C4⋊C4—182no—
703C4⋊C4—182no—
704C4⋊C4—361no—
705C4⋊C4—361no—
706C22⋊C4—182no—
707C22⋊C4—182no—
708C22⋊C4—182no—
709C22⋊C4—182no—
710C22⋊C4—182no—
711C22⋊C4—182no—
712C22⋊C4—361no—
713C22⋊C4—361no—
714C42—62no—
715C22×C3—21no—
716C22×C3—21no—
717C22×C3—21no—
718C22×C3—21no—
719C22×C3—21no—
720C22×C3—21no—
721C22×C3—21no—
722C22×C3C2×#23511yescharacteristic
723C22×C3C2×D3×D411yescharacteristic
724C22×C3C2×D3×D411yescharacteristic
725C22×C3C2×D3×D411yescharacteristic
726C22×C3C2×D3×D411yescharacteristic
727C22×C3C2×D3×Q811yescharacteristic
728C22×C3C2×D3×Q811yescharacteristic
729C22×C3#100711yescharacteristic
730C22×C3#100711yescharacteristic
731C22×C3D3×#4111yescharacteristic
732C22×C3D3×#4111yescharacteristic
733C22×C3D3×#4111yescharacteristic
734C22×C3#100911yescharacteristic
735C22×C3#100911yescharacteristic
736C2×D3—34no—
737C2×D3—34no—
738C2×D3—64no—
739C2×D3—62no—
740C2×D3—62no—
741C2×D3—62no—
742C2×D3—62no—
743C2×D3—62no—
744C2×D3—62no—
745C2×D3—62no—
746C2×D3—62no—
747C2×D3—62no—
748C2×D3—62no—
749C2×D3—62no—
750C2×D3—62no—
751C2×D3—62no—
752C2×D3—62no—
753C2×D3—62no—
754C2×D3—62no—
755C2×D3—62no—
756C2×D3—62no—
757C2×D3—122no—
758C2×D3—122no—
759C2×D3—122no—
760C2×D3—122no—
761C2×D3—122no—
762C2×D3—122no—
763C2×D3—122no—
764C2×D3—122no—
765C2×D3—122no—
766C2×D3—121no—
767C2×D3—121no—
768C2×D3—121no—
769C2×D3—121no—
770C2×D3—121no—
771C2×D3—121no—
772C2×D3—121no—
773C2×D3—121no—
774C2×D3—241no—
775C2×D3—241no—
776C2×D3—241no—
777C2×D3—241no—
778C3×C4—22no—
779C3×C4—22no—
780C3×C4—34no—
781C3×C4—42no—
782C3×C4—42no—
783C3×C4—41no—
784C3×C4—41no—
785C3×C4—41no—
786C3×C4—41no—
787C3×C4—62no—
788C3×C4—62no—
789C3×C4—81no—
790C3×C4—121no—
791C3×C4—121no—
792C3×C4—121no—
793C3×C4—121no—
794C3×C4—121no—
795Dic3—22no—
796Dic3—22no—
797Dic3—41no—
798Dic3—41no—
799Dic3—41no—
800Dic3—41no—
801Dic3—41no—
802Dic3—62no—
803Dic3—62no—
804Dic3—122no—
805Dic3—121no—
806Dic3—121no—
807Dic3—241no—
808Dic3#88414yes—
809C32#241711yescharacteristic, complemented, Sylow
810C23—92no—
811C23—92no—
812C23—92no—
813C23—92no—
814C23—181no—
815C23—181no—
816C23—181no—
817C23—181no—
818C23—181no—
819C23—181no—
820C23—181no—
821C23—181no—
822C23—181no—
823C23—181no—
824C23C22×D3211yescharacteristic
825Q8—124no—
826D4—188no—
827C2×C4—21no—
828C2×C4—21no—
829C2×C4—21no—
830C2×C4—21no—
831C2×C4—21no—
832C2×C4—21no—
833C2×C4—21no—
834C2×C4—21no—
835C2×C4—32no—
836C2×C4—32no—
837C2×C4—32no—
838C2×C4—32no—
839C2×C4—32no—
840C2×C4—61no—
841C2×C4—61no—
842C2×C4—61no—
843C2×C4—61no—
844C2×C4—61no—
845C2×C4—61no—
846C2×C4—61no—
847C2×C4—61no—
848C2×C4—61no—
849C2×C4—61no—
850C2×C4—61no—
851C2×C4—61no—
852C2×C4—61no—
853C2×C4—61no—
854C2×C4—61no—
855C2×C4—61no—
856C2×C4—61no—
857C2×C4—61no—
858C2×C4—61no—
859C2×C4—92no—
860C2×C4—188no—
861C2×C4—181no—
862C2×C4—181no—
863C2×C4—181no—
864C2×C4—181no—
865C2×C4—181no—
866C2×C4—364no—
867C2×C4—364no—
868C2×C4—364no—
869C2×C4#379712yes—
870C2×C3—21no—
871C2×C3—21no—
872C2×C3—21no—
873C2×C3—21no—
874C2×C3—21no—
875C2×C3—21no—
876C2×C3—21no—
877C2×C3C2×#88411yescharacteristic
878C2×C3#557911yescharacteristic
879C2×C3#558111yescharacteristic
880C2×C3D3×#12111yescharacteristic
881C2×C3D3×C22⋊Q811yescharacteristic
882C2×C3D3×C22⋊Q811yescharacteristic
883C2×C3#562911yescharacteristic
884C2×C3#562911yescharacteristic
885C2×C3#565411yescharacteristic
886C2×C3#567611yescharacteristic
887C2×C3#569011yescharacteristic
888C2×C3#569311yescharacteristic
889C2×C3#572711yescharacteristic
890C2×C3#572711yescharacteristic
891D3—64no—
892D3—64no—
893D3—124no—
894D3—122no—
895D3—122no—
896D3—242no—
897C22—94no—
898C22—182no—
899C22—182no—
900C22—182no—
901C22—182no—
902C22—182no—
903C22—182no—
904C22—182no—
905C22—182no—
906C22—182no—
907C22—361no—
908C22—361no—
909C22—361no—
910C22—361no—
911C22C2×#379711yescharacteristic
912C22D3×#23511yescharacteristic
913C22#6430811yescharacteristic
914C22D32×D411yescharacteristic
915C22D32×D411yescharacteristic
916C22#6431211yescharacteristic
917C22#6431611yescharacteristic
918C4—22no—
919C4—34no—
920C4—41no—
921C4—41no—
922C4—62no—
923C4—62no—
924C4—121no—
925C4—121no—
926C4—121no—
927C4—121no—
928C4—121no—
929C4—182no—
930C4—361no—
931C3—21no—
932C3#7662111yescharacteristic, complemented
933C3#7774211yescharacteristic, complemented
934C2—184no—
935C2—362no—
936C2#1059393811yescharacteristic
937C2#1059406711yescharacteristic
938C2D3×#88411yescharacteristic
939C2#1059428211yescharacteristic
940C2#1059434911yescharacteristic
941C2#1059437911yescharacteristic
942C2#1059451911yescharacteristic
subgroupG/H
center, FrattiniC23C22×D32
commutator, socle, cosocleC23×C32C24
FittingC32×#95C22
prime radicalC22×C4⋊(C3⋊D3)C22
hypercenter#95D32
hypocenterC32#2417
LCSG ▷ C23×C32 ▷ C32
UCSC1 ◁ C23 ◁ #95

Complements

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

NH ≅ G/Ntype
2. C2×#63888C2semidirect
3. C2×#63888C2semidirect
4. C2×#63883C2semidirect
6. C3×#4657C2semidirect
7. C3×#4646C2semidirect
9. #10591367C2semidirect
10. #10591367C2semidirect
11. #10591355C2semidirect
12. #10591347C2semidirect
13. #10591347C2semidirect
14. #10591345C2semidirect
15. #10591327C2semidirect
85. #4657D3semidirect
87. #4646D3semidirect
97. C2×C4⋊(C3⋊D3)Q8semidirect
136. Dic3⋊Dic3D4semidirect
447. C2×C3⋊D3C22⋊Q8semidirect
809. C32#2417semidirect
932. C3#76621semidirect
933. C3#77742semidirect

Maximal subgroups

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

subgroupindex
C2×#638942
C2×#638882
C2×#638832
#105923642
C3×#46572
C3×#46462
#105913802
#105913672
#105913552
#105913472
#105913452
#105913272
#777423
#766213