Finite Group Databasebeta

← #11807855

Subgroups — #11807855

Order 1152.

1023 conjugacy classes of subgroups.

The subgroup lattice has 799 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#63895C211yesmaximal, characteristic
2#10592689C211yesmaximal, characteristic
3C3×#4978C211yesmaximal, characteristic, complemented
4C3×#4972C211yesmaximal, characteristic, complemented
5#10591396C211yesmaximal, characteristic, complemented
6#10591371C211yesmaximal, characteristic
7#10591367C211yesmaximal, characteristic
8#10591334C211yesmaximal, characteristic, complemented
9#10591327C211yesmaximal, characteristic, complemented
10#10591289C211yesmaximal, characteristic
11#10591270C211yesmaximal, characteristic, complemented
12#10591259C211yesmaximal, characteristic
13#10591235C211yesmaximal, characteristic, complemented
14#10591202C211yesmaximal, characteristic
15#10591201C211yesmaximal, characteristic, complemented
16#75992—31nomaximal
17#75314—31nomaximal
18C22×#627C2211yescharacteristic
19C22×#624C2211yescharacteristic
20C2×C32×C4⋊C4C2211yescharacteristic
21C2×#3752C2211yescharacteristic
22C2×#3752C2211yescharacteristic
23C2×#3752C2211yescharacteristic
24C2×C4×C3⋊Dic3C2211yescharacteristic
25C2×C3×C4⋊Dic3C2211yescharacteristic
26C2×C3×Dic3⋊C4C2211yescharacteristic
27C2×C3×Dic3⋊C4C2211yescharacteristic
28C2×C3×Dic3⋊C4C2211yescharacteristic
29C2×C3×C4×Dic3C2211yescharacteristic
30C2×C3×C4×Dic3C2211yescharacteristic
31C2×#3724C2211yescharacteristic
32C2×Dic3⋊Dic3C2211yescharacteristic
33C2×Dic3⋊Dic3C2211yescharacteristic
34C2×Dic3⋊Dic3C2211yescharacteristic
35C2×#3722C2211yescharacteristic
36C2×#3722C2211yescharacteristic
37C2×#3722C2211yescharacteristic
38C2×Dic32C2211yescharacteristic
39#63895C418yescomplemented
40#63658C2211yescharacteristic
41#63658C2211yescharacteristic
42C3×C3⋊#95C2211yescharacteristic
43C3×C3⋊#95C2211yescharacteristic
44C3×C3⋊#95C2211yescharacteristic
45C3×C3⋊#95C2211yescharacteristic
46C3×C3⋊#95C2211yescharacteristic
47C3×C3⋊#95C2211yescharacteristic
48#63579C2211yescharacteristic
49#63579C2211yescharacteristic
50#63579C2211yescharacteristic
51#63579C2211yescharacteristic
52#63579C2211yescharacteristic
53#63579C2211yescharacteristic
54C2×#897—31no—
55C2×#896—31no—
56C3×#389—31no—
57C3×#387—31no—
58#4990—31no—
59#4990—31no—
60#4990—31no—
61#4990—61no—
62#4987—31no—
63#4980—31no—
64#4980—31no—
65#4978—31no—
66#4978D311yescharacteristic, complemented
67#4973—31no—
68#4972D311yescharacteristic, complemented
69#4940—31no—
70#4940—31no—
71#4933—31no—
72#4928—31no—
73#4670—31no—
74#4669—31no—
75#4669—31no—
76#4667—31no—
77#4664—31no—
78#4664—31no—
79#4654—31no—
80#4653—31no—
81#4647—31no—
82#4646—31no—
83#4646—31no—
84#4646—31no—
85C23×C3⋊D3C2311yescharacteristic
86C22×C32×C4C2311yescharacteristic
87C22×C32×C4C2311yescharacteristic
88C22×C32×C4C2311yescharacteristic
89C22×C3⋊Dic3C2311yescharacteristic
90C22×C3⋊Dic3C2311yescharacteristic
91C22×C3⋊Dic3C2311yescharacteristic
92C22×C3×Dic3C2311yescharacteristic
93C22×C3×Dic3C2311yescharacteristic
94C22×C3×Dic3C2311yescharacteristic
95C22×C3×Dic3C2311yescharacteristic
96C22×C3×Dic3C2311yescharacteristic
97C22×C3×Dic3C2311yescharacteristic
98C22×C3×Dic3C2311yescharacteristic
99C22×C3×Dic3C2311yescharacteristic
100C2×#627—41no—
101C2×#627—41no—
102C2×#627C2×C414yes—
103C2×#624—41no—
104C2×#624—41no—
105C2×#624C2×C414yes—
106C32×C4⋊C4—41no—
107#3752—41no—
108#3752—41no—
109#3752C2×C414yes—
110C4×C3⋊Dic3—41no—
111C3×C4⋊Dic3C2×C414yes—
112C3×Dic3⋊C4—41no—
113C3×Dic3⋊C4—41no—
114C3×Dic3⋊C4C2×C414yes—
115C3×C4×Dic3—41no—
116C3×C4×Dic3—41no—
117#3724—41no—
118Dic3⋊Dic3—41no—
119Dic3⋊Dic3—41no—
120Dic3⋊Dic3C2×C414yes—
121#3722—41no—
122#3722—41no—
123#3722C2×C414yes—
124Dic32—41no—
125#2378—91noSylow
126C22×C4×D3—31no—
127C22×C4×D3—31no—
128C22×Dic6—31no—
129C22×Dic6—31no—
130C2×C3×C4⋊C4—21no—
131C2×C3×C4⋊C4—31no—
132C2×C3×C4⋊C4—31no—
133C2×C3×C4⋊C4—31no—
134C2×C3×C4⋊C4—31no—
135C2×C3×C4⋊C4C2×D311yescharacteristic
136C2×C3×C4⋊C4C2×D311yescharacteristic
137C2×C3×C42—31no—
138C2×C3×C42—31no—
139C2×(C2×D3)⋊C4—31no—
140C2×(C2×D3)⋊C4—31no—
141C2×(C2×D3)⋊C4—31no—
142C2×(C2×D3)⋊C4—31no—
143C2×(C2×D3)⋊C4—31no—
144C2×(C2×D3)⋊C4—31no—
145C2×(C2×D3)⋊C4—31no—
146C2×(C2×D3)⋊C4—31no—
147C2×(C2×D3)⋊C4—31no—
148C2×(C2×D3)⋊C4—31no—
149C2×(C2×D3)⋊C4—31no—
150C2×(C2×D3)⋊C4—31no—
151C2×(C2×D3)⋊C4—61no—
152C2×(C2×D3)⋊C4—61no—
153C2×(C2×D3)⋊C4—61no—
154C2×C4⋊Dic3—31no—
155C2×C4⋊Dic3—31no—
156C2×C4⋊Dic3—31no—
157C2×C4⋊Dic3C2×D311yescharacteristic
158C2×Dic3⋊C4—31no—
159C2×Dic3⋊C4—31no—
160C2×Dic3⋊C4—31no—
161C2×Dic3⋊C4—31no—
162C2×Dic3⋊C4—31no—
163C2×Dic3⋊C4C2×D311yescharacteristic
164C2×Dic3⋊C4C2×D311yescharacteristic
165C2×Dic3⋊C4C2×D311yescharacteristic
166C2×C4×Dic3—31no—
167C2×C4×Dic3—31no—
168C2×C4×Dic3—31no—
169C2×C4×Dic3—31no—
170C2×C4×Dic3—61no—
171C2×C4×Dic3C2×D311yescharacteristic
172C2×C4×Dic3C2×D311yescharacteristic
173#897—38no—
174#896—38no—
175C3×#95—31no—
176C3×#95—31no—
177C3×#95—31no—
178C3×#95—31no—
179C3×#95—31no—
180C3×#95—31no—
181C3⋊#95—31no—
182C3⋊#95—31no—
183C3⋊#95—31no—
184C3⋊#95—31no—
185C3⋊#95—31no—
186C3⋊#95—31no—
187C3⋊#95—31no—
188C3⋊#95—31no—
189C3⋊#95—31no—
190C3⋊#95—31no—
191C3⋊#95—31no—
192C3⋊#95—31no—
193C3⋊#95—31no—
194C3⋊#95—31no—
195C3⋊#95—31no—
196C3⋊#95—31no—
197C3⋊#95—61no—
198C3⋊#95—61no—
199C3⋊#95C2×D311yescharacteristic
200C3⋊#95C2×D311yescharacteristic
201C3⋊#95C2×D311yescharacteristic
202C3⋊#95C2×D311yescharacteristic
203C3⋊#95C2×D311yescharacteristic
204C3⋊#95C2×D311yescharacteristic
205C23×C32C2411yescharacteristic
206C22×C3⋊D3—21no—
207C22×C3⋊D3—21no—
208C22×C3⋊D3—21no—
209C22×C3⋊D3—21no—
210C22×C3⋊D3—21no—
211C22×C3⋊D3—21no—
212C22×C3⋊D3C22×C412yes—
213C2×C32×C4—21no—
214C2×C32×C4—21no—
215C2×C32×C4—21no—
216C2×C32×C4—21no—
217C2×C32×C4—21no—
218C2×C32×C4—21no—
219C2×C32×C4—21no—
220C2×C32×C4—21no—
221C2×C32×C4C22×C412yes—
222C2×C3⋊Dic3—21no—
223C2×C3⋊Dic3—21no—
224C2×C3⋊Dic3—21no—
225C2×C3⋊Dic3—21no—
226C2×C3⋊Dic3—21no—
227C2×C3⋊Dic3—21no—
228C2×C3⋊Dic3—21no—
229C2×C3⋊Dic3—21no—
230C2×C3⋊Dic3C22×C412yes—
231C2×C3×Dic3—21no—
232C2×C3×Dic3—21no—
233C2×C3×Dic3—21no—
234C2×C3×Dic3—21no—
235C2×C3×Dic3—21no—
236C2×C3×Dic3—21no—
237C2×C3×Dic3—21no—
238C2×C3×Dic3—21no—
239C2×C3×Dic3—21no—
240C2×C3×Dic3—21no—
241C2×C3×Dic3—21no—
242C2×C3×Dic3—21no—
243C2×C3×Dic3—21no—
244C2×C3×Dic3—21no—
245C2×C3×Dic3—21no—
246C2×C3×Dic3—21no—
247C2×C3×Dic3—21no—
248C2×C3×Dic3—21no—
249C2×C3×Dic3—21no—
250C2×C3×Dic3—21no—
251C2×C3×Dic3C22×C412yes—
252C2×C3×Dic3C22×C412yes—
253C2×C3×Dic3C22×C412yes—
254C2×C3×Dic3C22×C412yes—
255#627—44no—
256#624—44no—
257C2×C22⋊Q8—91no—
258#391—91no—
259#391—91no—
260#389—31no—
261#389—91no—
262#388—91no—
263#388—91no—
264#388—91no—
265#388—91no—
266#387—31no—
267#387—91no—
268#387—91no—
269#387—91no—
270#381—91no—
271#380—91no—
272C23×D3—31no—
273C23×D3—31no—
274C23×D3—61no—
275C22×C3×C4—21no—
276C22×C3×C4—21no—
277C22×C3×C4—21no—
278C22×C3×C4—31no—
279C22×C3×C4—31no—
280C22×C3×C4—31no—
281C22×C3×C4—31no—
282C22×C3×C4—31no—
283C22×C3×C4—31no—
284C22×C3×C4—31no—
285C22×C3×C4—31no—
286C22×C3×C4C22×D311yescharacteristic
287C22×C3×C4C22×D311yescharacteristic
288C22×C3×C4C22×D311yescharacteristic
289C22×C3×C4C22×D311yescharacteristic
290C22×C3×C4C22×D311yescharacteristic
291C22×C3×C4C22×D311yescharacteristic
292C22×Dic3—31no—
293C22×Dic3—31no—
294C22×Dic3—31no—
295C22×Dic3—31no—
296C22×Dic3—31no—
297C22×Dic3—31no—
298C22×Dic3—61no—
299C22×Dic3—61no—
300C22×Dic3—61no—
301C22×Dic3C22×D311yescharacteristic
302C22×Dic3C22×D311yescharacteristic
303C22×Dic3C22×D311yescharacteristic
304C22×Dic3C22×D311yescharacteristic
305C22×Dic3C22×D311yescharacteristic
306C22×Dic3C22×D311yescharacteristic
307C22×Dic3C22×D311yescharacteristic
308C22×Dic3C22×D311yescharacteristic
309C2×C4×D3—34no—
310C2×C4×D3—34no—
311C2×C4×D3—121no—
312C2×C4×D3—121no—
313C2×C4×D3—121no—
314C2×C4×D3—121no—
315C2×Dic6—34no—
316C2×Dic6—34no—
317C2×Dic6—121no—
318C2×Dic6—121no—
319C2×Dic6—121no—
320C2×Dic6—121no—
321C3×C4⋊C4—34no—
322C3×C4⋊C4—34no—
323C3×C4⋊C4—41no—
324C3×C4⋊C4—41no—
325C3×C4⋊C4—42no—
326C3×C4⋊C4—121no—
327C3×C4⋊C4—121no—
328C3×C42—121no—
329C3×C42—121no—
330(C2×D3)⋊C4—34no—
331(C2×D3)⋊C4—34no—
332(C2×D3)⋊C4—34no—
333(C2×D3)⋊C4—34no—
334(C2×D3)⋊C4—64no—
335(C2×D3)⋊C4—121no—
336(C2×D3)⋊C4—121no—
337(C2×D3)⋊C4—121no—
338(C2×D3)⋊C4—121no—
339(C2×D3)⋊C4—121no—
340(C2×D3)⋊C4—121no—
341(C2×D3)⋊C4—121no—
342(C2×D3)⋊C4—121no—
343(C2×D3)⋊C4—122no—
344(C2×D3)⋊C4—122no—
345C4⋊Dic3—34no—
346C4⋊Dic3—121no—
347C4⋊Dic3—121no—
348C4⋊Dic3C4×D314yes—
349Dic3⋊C4—34no—
350Dic3⋊C4—41no—
351Dic3⋊C4—41no—
352Dic3⋊C4—121no—
353Dic3⋊C4—121no—
354Dic3⋊C4—121no—
355Dic3⋊C4—121no—
356Dic3⋊C4C4×D314yes—
357C4×Dic3—41no—
358C4×Dic3—41no—
359C4×Dic3—121no—
360C4×Dic3—121no—
361C4×Dic3—121no—
362C4×Dic3—121no—
363C4×Dic3—122no—
364C22×C32C23×C411yescharacteristic
365C22×C32H(5,𝔽2)11yescharacteristic
366C22×C32H(5,𝔽2)11yescharacteristic
367C22×C32H(5,𝔽2)11yescharacteristic
368C22×C322−1+411yescharacteristic
369C22×C322−1+411yescharacteristic
370C22×C322−1+411yescharacteristic
371C2×C3⋊D3—22no—
372C2×C3⋊D3—22no—
373C2×C3⋊D3—22no—
374C2×C3⋊D3—41no—
375C2×C3⋊D3—41no—
376C2×C3⋊D3—41no—
377C2×C3⋊D3—41no—
378C32×C4—22no—
379C32×C4—41no—
380C32×C4—41no—
381C3⋊Dic3—22no—
382C3⋊Dic3—41no—
383C3⋊Dic3—41no—
384C3×Dic3—22no—
385C3×Dic3—22no—
386C3×Dic3—22no—
387C3×Dic3—22no—
388C3×Dic3—41no—
389C3×Dic3—41no—
390C3×Dic3—41no—
391C3×Dic3—41no—
392C22×Q8—91no—
393C23×C4—91no—
394C22⋊Q8—98no—
395C2×C4⋊C4—31no—
396C2×C4⋊C4—31no—
397C2×C4⋊C4—31no—
398C2×C4⋊C4—31no—
399C2×C4⋊C4—91no—
400C2×C4⋊C4—91no—
401C2×C4⋊C4—91no—
402C2×C4⋊C4—91no—
403C2×C4⋊C4D3211yescharacteristic
404C2×C22⋊C4—91no—
405C2×C22⋊C4—91no—
406C2×C22⋊C4—91no—
407C2×C22⋊C4—91no—
408C2×C22⋊C4—91no—
409C2×C22⋊C4—91no—
410C2×C42—31no—
411C2×C42—31no—
412C2×C42—91no—
413C2×C42—91no—
414#95—31no—
415#95—31no—
416#95—31no—
417#95—31no—
418#95—31no—
419#95—31no—
420#95—91no—
421#95—91no—
422#95—91no—
423#95—91no—
424#95—91no—
425#95—91no—
426#95—91no—
427#95—91no—
428C23×C3—21no—
429C23×C3C23×D311yescharacteristic
430C23×C3C23×D311yescharacteristic
431C22×D3—32no—
432C22×D3—32no—
433C22×D3—62no—
434C22×D3—61no—
435C22×D3—61no—
436C22×D3—61no—
437C22×D3—61no—
438C22×D3—61no—
439C22×D3—61no—
440C22×D3—61no—
441C22×D3—61no—
442C22×D3—61no—
443C22×D3—61no—
444C22×D3—61no—
445C22×D3—61no—
446C22×D3—121no—
447C22×D3—121no—
448C22×D3—121no—
449C22×D3—121no—
450C22×D3—121no—
451C22×D3—121no—
452C2×C3×C4—21no—
453C2×C3×C4—21no—
454C2×C3×C4—21no—
455C2×C3×C4—21no—
456C2×C3×C4—22no—
457C2×C3×C4—21no—
458C2×C3×C4—21no—
459C2×C3×C4—21no—
460C2×C3×C4—21no—
461C2×C3×C4—21no—
462C2×C3×C4—21no—
463C2×C3×C4—21no—
464C2×C3×C4—21no—
465C2×C3×C4—21no—
466C2×C3×C4—21no—
467C2×C3×C4—21no—
468C2×C3×C4—21no—
469C2×C3×C4—22no—
470C2×C3×C4—32no—
471C2×C3×C4—32no—
472C2×C3×C4—32no—
473C2×C3×C4—32no—
474C2×C3×C4—41no—
475C2×C3×C4—41no—
476C2×C3×C4—41no—
477C2×C3×C4—41no—
478C2×C3×C4—41no—
479C2×C3×C4—41no—
480C2×C3×C4—41no—
481C2×C3×C4—61no—
482C2×C3×C4—61no—
483C2×C3×C4—61no—
484C2×C3×C4—61no—
485C2×C3×C4—61no—
486C2×C3×C4—61no—
487C2×C3×C4—61no—
488C2×C3×C4—61no—
489C2×C3×C4—61no—
490C2×C3×C4—61no—
491C2×C3×C4—61no—
492C2×C3×C4—61no—
493C2×C3×C4—61no—
494C2×C3×C4—61no—
495C2×C3×C4—61no—
496C2×C3×C4—61no—
497C2×C3×C4—61no—
498C2×C3×C4—61no—
499C2×C3×C4—61no—
500C2×C3×C4—61no—
501C2×C3×C4C2×C4×D312yes—
502C2×C3×C4C2×C4×D312yes—
503C2×Dic3—21no—
504C2×Dic3—21no—
505C2×Dic3—21no—
506C2×Dic3—21no—
507C2×Dic3—21no—
508C2×Dic3—21no—
509C2×Dic3—21no—
510C2×Dic3—21no—
511C2×Dic3—21no—
512C2×Dic3—21no—
513C2×Dic3—21no—
514C2×Dic3—21no—
515C2×Dic3—21no—
516C2×Dic3—21no—
517C2×Dic3—21no—
518C2×Dic3—21no—
519C2×Dic3—21no—
520C2×Dic3—21no—
521C2×Dic3—21no—
522C2×Dic3—21no—
523C2×Dic3—32no—
524C2×Dic3—32no—
525C2×Dic3—62no—
526C2×Dic3—61no—
527C2×Dic3—61no—
528C2×Dic3—61no—
529C2×Dic3—61no—
530C2×Dic3—62no—
531C2×Dic3—61no—
532C2×Dic3—61no—
533C2×Dic3—61no—
534C2×Dic3—61no—
535C2×Dic3—61no—
536C2×Dic3—61no—
537C2×Dic3—61no—
538C2×Dic3—61no—
539C2×Dic3—61no—
540C2×Dic3—61no—
541C2×Dic3—61no—
542C2×Dic3—61no—
543C2×Dic3—121no—
544C2×Dic3—121no—
545C2×Dic3—121no—
546C2×Dic3—121no—
547C2×Dic3—121no—
548C2×Dic3—121no—
549C2×Dic3—121no—
550C2×Dic3C2×C4×D312yes—
551C2×Dic3C2×C4×D312yes—
552C2×Dic3C2×C4×D312yes—
553C2×Dic3C2×C4×D312yes—
554C4×D3—124no—
555C4×D3—124no—
556Dic6—124no—
557Dic6—124no—
558C2×C32#51811yescharacteristic
559C2×C32#51911yescharacteristic
560C2×C32#52011yescharacteristic
561C2×C32#56211yescharacteristic
562C2×C32#56211yescharacteristic
563C2×C32#56311yescharacteristic
564C2×C32#56311yescharacteristic
565C3⋊D3—42no—
566C24—91no—
567C2×Q8—94no—
568C2×Q8—361no—
569C2×Q8—361no—
570C22×C4—31no—
571C22×C4—31no—
572C22×C4—31no—
573C22×C4—31no—
574C22×C4—31no—
575C22×C4—31no—
576C22×C4—31no—
577C22×C4—31no—
578C22×C4—94no—
579C22×C4—91no—
580C22×C4—91no—
581C22×C4—91no—
582C22×C4—361no—
583C22×C4—361no—
584C22×C4C2×D3211yescharacteristic
585C22×C4C2×D3211yescharacteristic
586C22×C4C2×D3211yescharacteristic
587C4⋊C4—34no—
588C4⋊C4—34no—
589C4⋊C4—41no—
590C4⋊C4—94no—
591C4⋊C4—121no—
592C4⋊C4—121no—
593C4⋊C4—361no—
594C4⋊C4—361no—
595C4⋊C4—361no—
596C22⋊C4—94no—
597C22⋊C4—94no—
598C22⋊C4—361no—
599C22⋊C4—361no—
600C22⋊C4—361no—
601C22⋊C4—361no—
602C42—121no—
603C42—121no—
604C42—361no—
605C42—361no—
606C22×C3—21no—
607C22×C3—21no—
608C22×C3—21no—
609C22×C3—21no—
610C22×C3—21no—
611C22×C3—21no—
612C22×C3—21no—
613C22×C3C22×C4×D311yescharacteristic
614C22×C3C22×C4×D311yescharacteristic
615C22×C3#100411yescharacteristic
616C22×C3#100411yescharacteristic
617C22×C3#100411yescharacteristic
618C22×C3#100711yescharacteristic
619C22×C3#100711yescharacteristic
620C22×C3#100711yescharacteristic
621C22×C3#100911yescharacteristic
622C22×C3#100911yescharacteristic
623C22×C3#100911yescharacteristic
624C22×C3#101011yescharacteristic
625C22×C3#101011yescharacteristic
626C22×C3#101011yescharacteristic
627C2×D3—62no—
628C2×D3—62no—
629C2×D3—62no—
630C2×D3—62no—
631C2×D3—62no—
632C2×D3—62no—
633C2×D3—122no—
634C2×D3—122no—
635C2×D3—122no—
636C2×D3—121no—
637C2×D3—121no—
638C2×D3—121no—
639C2×D3—121no—
640C2×D3—121no—
641C2×D3—121no—
642C2×D3—121no—
643C2×D3—121no—
644C2×D3—241no—
645C2×D3—241no—
646C2×D3—241no—
647C2×D3—241no—
648C3×C4—22no—
649C3×C4—22no—
650C3×C4—42no—
651C3×C4—42no—
652C3×C4—41no—
653C3×C4—41no—
654C3×C4—41no—
655C3×C4—41no—
656C3×C4—62no—
657C3×C4—62no—
658C3×C4—62no—
659C3×C4—62no—
660C3×C4—81no—
661C3×C4—121no—
662C3×C4—121no—
663C3×C4—121no—
664C3×C4—121no—
665Dic3—22no—
666Dic3—22no—
667Dic3—22no—
668Dic3—22no—
669Dic3—41no—
670Dic3—41no—
671Dic3—41no—
672Dic3—41no—
673Dic3—62no—
674Dic3—62no—
675Dic3—122no—
676Dic3—122no—
677Dic3—121no—
678Dic3—121no—
679Dic3—121no—
680Dic3—121no—
681Dic3—241no—
682C32#237811yescharacteristic, complemented, Sylow
683C23—92no—
684C23—181no—
685C23—181no—
686C23—181no—
687C23—181no—
688C23—181no—
689C23—181no—
690C23C22×D3211yescharacteristic
691Q8—364no—
692C2×C4—21no—
693C2×C4—21no—
694C2×C4—21no—
695C2×C4—21no—
696C2×C4—21no—
697C2×C4—21no—
698C2×C4—21no—
699C2×C4—21no—
700C2×C4—32no—
701C2×C4—32no—
702C2×C4—32no—
703C2×C4—32no—
704C2×C4—61no—
705C2×C4—61no—
706C2×C4—61no—
707C2×C4—61no—
708C2×C4—61no—
709C2×C4—61no—
710C2×C4—61no—
711C2×C4—61no—
712C2×C4—61no—
713C2×C4—61no—
714C2×C4—61no—
715C2×C4—61no—
716C2×C4—61no—
717C2×C4—61no—
718C2×C4—61no—
719C2×C4—61no—
720C2×C4—61no—
721C2×C4—61no—
722C2×C4—61no—
723C2×C4—61no—
724C2×C4—92no—
725C2×C4—181no—
726C2×C4—181no—
727C2×C4—181no—
728C2×C4—181no—
729C2×C4—181no—
730C2×C4—181no—
731C2×C4—181no—
732C2×C4—181no—
733C2×C4—364no—
734C2×C4C4×D3212yes—
735C2×C3—21no—
736C2×C3—21no—
737C2×C3—21no—
738C2×C3—21no—
739C2×C3—21no—
740C2×C3—21no—
741C2×C3—21no—
742C2×C3#550411yescharacteristic
743C2×C3#552111yescharacteristic
744C2×C3#554511yescharacteristic
745C2×C3#554611yescharacteristic
746C2×C3#557211yescharacteristic
747C2×C3#557211yescharacteristic
748C2×C3#562111yescharacteristic
749C2×C3#564711yescharacteristic
750C2×C3#564711yescharacteristic
751C2×C3#566711yescharacteristic
752C2×C3#569911yescharacteristic
753C2×C3#569911yescharacteristic
754C2×C3#571211yescharacteristic
755C2×C3#573511yescharacteristic
756D3—122no—
757D3—122no—
758D3—242no—
759C22—182no—
760C22—182no—
761C22—182no—
762C22—361no—
763C22—361no—
764C22—361no—
765C22—361no—
766C22#6429711yescharacteristic
767C22C2×C4×D3211yescharacteristic
768C22#6430911yescharacteristic
769C22#6431411yescharacteristic
770C22#6431611yescharacteristic
771C22#6432011yescharacteristic
772C22#6433011yescharacteristic
773C4—22no—
774C4—41no—
775C4—41no—
776C4—62no—
777C4—62no—
778C4—62no—
779C4—62no—
780C4—121no—
781C4—121no—
782C4—121no—
783C4—121no—
784C4—182no—
785C4—361no—
786C4—361no—
787C3—21no—
788C3#7531411yescharacteristic, complemented
789C3#7599211yescharacteristic, complemented
790C2—362no—
791C2#1059434711yescharacteristic
792C2#1059435311yescharacteristic
793C2#1059450611yescharacteristic
794C2#1059460411yescharacteristic
795C2#1059487411yescharacteristic
796C2#1059526311yescharacteristic
797C2#1059541811yescharacteristic
subgroupG/H
center, FrattiniC23C22×D32
commutatorC22×C32C23×C4
FittingC2×C32×C4⋊C4C22
socle, cosocleC23×C32C24
prime radicalC23×C3⋊D3C23
hypercenterC2×C4⋊C4D32
hypocenterC32#2378
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
3. C3×#4978C2semidirect
4. C3×#4972C2semidirect
5. #10591396C2semidirect
8. #10591334C2semidirect
9. #10591327C2semidirect
11. #10591270C2semidirect
13. #10591235C2semidirect
15. #10591201C2semidirect
39. #63895C4semidirect
66. #4978D3semidirect
68. #4972D3semidirect
682. C32#2378semidirect
788. C3#75314semidirect
789. C3#75992semidirect

Maximal subgroups

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

subgroupindex
C2×#638952
#105926892
C3×#49782
C3×#49722
#105913962
#105913712
#105913672
#105913342
#105913272
#105912892
#105912702
#105912592
#105912352
#105912022
#105912012
#759923
#753143