Finite Group Databasebeta

← #11817799

Subgroups — #11817799

Order 1152.

1155 conjugacy classes of subgroups.

The subgroup lattice has 886 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#63848C211yesmaximal, characteristic, complemented
2C2×#63836C211yesmaximal, characteristic, complemented
3#10592690C211yesmaximal, characteristic
4C3×#4984C211yesmaximal, characteristic, complemented
5C3×#4978C211yesmaximal, characteristic, complemented
6#10591380C211yesmaximal, characteristic
7#10591375C211yesmaximal, characteristic, complemented
8#10591350C211yesmaximal, characteristic, complemented
9#10591350C211yesmaximal, characteristic, complemented
10#10591348C211yesmaximal, characteristic, complemented
11#10591320C211yesmaximal, characteristic
12#10591266C211yesmaximal, characteristic, complemented
13#10591259C211yesmaximal, characteristic, complemented
14#10591242C211yesmaximal, characteristic, complemented
15#10591194C211yesmaximal, characteristic, complemented
16#76027—31nomaximal
17#75018—31nomaximal
18C22×C4⋊(C3⋊D3)C2211yescharacteristic
19C22×#624C2211yescharacteristic
20C2×C32×C4⋊C4C2211yescharacteristic
21C2×#3752C2211yescharacteristic
22C2×#3752C2211yescharacteristic
23C2×#3752C2211yescharacteristic
24C2×#3752C2211yescharacteristic
25C2×C3×C4⋊Dic3C2211yescharacteristic
26C2×C3×C4⋊Dic3C2211yescharacteristic
27C2×C3×C4⋊Dic3C2211yescharacteristic
28C2×C3×Dic3⋊C4C2211yescharacteristic
29C2×C3×C4×Dic3C2211yescharacteristic
30C2×C3×C4×Dic3C2211yescharacteristic
31C2×Dic3⋊Dic3C2211yescharacteristic
32C2×Dic3⋊Dic3C2211yescharacteristic
33C2×Dic3⋊Dic3C2211yescharacteristic
34C2×Dic3⋊Dic3C2211yescharacteristic
35C2×Dic3⋊Dic3C2211yescharacteristic
36C2×#3722C2211yescharacteristic
37C2×#3722C2211yescharacteristic
38C2×#3722C2211yescharacteristic
39C2×#3722C2211yescharacteristic
40C2×#3722C2211yescharacteristic
41C2×#3722C2211yescharacteristic
42C2×#3722C2211yescharacteristic
43C2×Dic32C2211yescharacteristic
44C2×Dic32C2211yescharacteristic
45#63848—24no—
46#63836—24no—
47#63658C2211yescharacteristic
48C3×C3⋊#95C2211yescharacteristic
49C3×C3⋊#95C2211yescharacteristic
50C3×C3⋊#95C2211yescharacteristic
51C3×C3⋊#95C2211yescharacteristic
52C3×C3⋊#95C2211yescharacteristic
53C3×C3⋊#95C2211yescharacteristic
54#63579C2211yescharacteristic
55C2×#898—31no—
56C2×#898—31no—
57C2×#892—31no—
58C2×#872—31no—
59C3×#389—31no—
60C3×#387—31no—
61#4993—31no—
62#4993—31no—
63#4991—31no—
64#4991—31no—
65#4991—61no—
66#4990—31no—
67#4988—31no—
68#4984D311yescharacteristic, complemented
69#4982—31no—
70#4978D311yescharacteristic, complemented
71#4940—31no—
72#4939—31no—
73C4×C4⋊Dic3—31no—
74#4677—31no—
75#4677—31no—
76#4670—31no—
77#4670—31no—
78#4670—31no—
79#4669—31no—
80#4668—31no—
81#4668—31no—
82#4665—31no—
83#4665—31no—
84#4661—31no—
85#4649—31no—
86C23×C3⋊D3C2311yescharacteristic
87C23×C3⋊D3C2311yescharacteristic
88C22×C32×C4C2311yescharacteristic
89C22×C32×C4C2311yescharacteristic
90C22×C32×C4C2311yescharacteristic
91C22×C3⋊Dic3C2311yescharacteristic
92C22×C3⋊Dic3C2311yescharacteristic
93C2×C4⋊(C3⋊D3)—22no—
94C2×C4⋊(C3⋊D3)—22no—
95C2×C4⋊(C3⋊D3)—41no—
96C22×C3×Dic3C2311yescharacteristic
97C22×C3×Dic3C2311yescharacteristic
98C22×C3×Dic3C2311yescharacteristic
99C22×C3×Dic3C2311yescharacteristic
100C22×C3×Dic3C2311yescharacteristic
101C22×C3×Dic3C2311yescharacteristic
102C22×C3×Dic3C2311yescharacteristic
103C22×C3×Dic3C2311yescharacteristic
104C2×#624—22no—
105C2×#624—22no—
106C2×#624—22no—
107C32×C4⋊C4—22no—
108#3752—22no—
109#3752—22no—
110#3752—22no—
111#3752—41no—
112C3×C4⋊Dic3—22no—
113C3×C4⋊Dic3—41no—
114C3×C4⋊Dic3—41no—
115C3×Dic3⋊C4D414yescomplemented
116C3×C4×Dic3—22no—
117C3×C4×Dic3—22no—
118Dic3⋊Dic3—22no—
119Dic3⋊Dic3—22no—
120Dic3⋊Dic3—22no—
121Dic3⋊Dic3—22no—
122Dic3⋊Dic3—41no—
123#3722—22no—
124#3722—22no—
125#3722—22no—
126#3722—22no—
127#3722—22no—
128#3722—22no—
129#3722—41no—
130Dic32—22no—
131Dic32—22no—
132#2479—91noSylow
133C22×D12—31no—
134C22×D12—31no—
135C22×D12—61no—
136C22×C4×D3—31no—
137C22×C4×D3—31no—
138C2×C3×C4⋊C4—21no—
139C2×C3×C4⋊C4—31no—
140C2×C3×C4⋊C4—31no—
141C2×C3×C4⋊C4—31no—
142C2×C3×C4⋊C4—31no—
143C2×C3×C4⋊C4C2×D311yescharacteristic
144C2×C3×C4⋊C4C2×D311yescharacteristic
145C2×C3×C42—31no—
146C2×C3×C42—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—31no—
152C2×(C2×D3)⋊C4—31no—
153C2×(C2×D3)⋊C4—31no—
154C2×(C2×D3)⋊C4—31no—
155C2×(C2×D3)⋊C4—31no—
156C2×(C2×D3)⋊C4—31no—
157C2×(C2×D3)⋊C4—31no—
158C2×(C2×D3)⋊C4—31no—
159C2×(C2×D3)⋊C4—31no—
160C2×(C2×D3)⋊C4—31no—
161C2×(C2×D3)⋊C4—31no—
162C2×(C2×D3)⋊C4—31no—
163C2×(C2×D3)⋊C4—31no—
164C2×(C2×D3)⋊C4—31no—
165C2×(C2×D3)⋊C4—31no—
166C2×(C2×D3)⋊C4—31no—
167C2×(C2×D3)⋊C4—31no—
168C2×(C2×D3)⋊C4—31no—
169C2×(C2×D3)⋊C4—61no—
170C2×(C2×D3)⋊C4—61no—
171C2×(C2×D3)⋊C4—61no—
172C2×(C2×D3)⋊C4—61no—
173C2×C4⋊Dic3—31no—
174C2×C4⋊Dic3—31no—
175C2×C4⋊Dic3—31no—
176C2×C4⋊Dic3—31no—
177C2×C4⋊Dic3—31no—
178C2×C4⋊Dic3C2×D311yescharacteristic
179C2×C4⋊Dic3C2×D311yescharacteristic
180C2×C4⋊Dic3C2×D311yescharacteristic
181C2×Dic3⋊C4—31no—
182C2×Dic3⋊C4—31no—
183C2×Dic3⋊C4—31no—
184C2×Dic3⋊C4—31no—
185C2×Dic3⋊C4—31no—
186C2×Dic3⋊C4C2×D311yescharacteristic
187C2×C4×Dic3—31no—
188C2×C4×Dic3—31no—
189C2×C4×Dic3—31no—
190C2×C4×Dic3—31no—
191C2×C4×Dic3C2×D311yescharacteristic
192C2×C4×Dic3C2×D311yescharacteristic
193#898—64no—
194#898—64no—
195#892—64no—
196#872—64no—
197C3×#95—31no—
198C3×#95—31no—
199C3×#95—31no—
200C3×#95—31no—
201C3×#95—31no—
202C3×#95—31no—
203C3⋊#95—31no—
204C3⋊#95—31no—
205C3⋊#95—31no—
206C3⋊#95—31no—
207C3⋊#95—61no—
208C3⋊#95C2×D311yescharacteristic
209C3⋊#95C2×D311yescharacteristic
210C3⋊#95C2×D311yescharacteristic
211C3⋊#95C2×D311yescharacteristic
212C3⋊#95C2×D311yescharacteristic
213C3⋊#95C2×D311yescharacteristic
214C23×C32C2411yescharacteristic
215C22×C3⋊D3—21no—
216C22×C3⋊D3—21no—
217C22×C3⋊D3—21no—
218C22×C3⋊D3—21no—
219C22×C3⋊D3—21no—
220C22×C3⋊D3—21no—
221C22×C3⋊D3—21no—
222C22×C3⋊D3—21no—
223C22×C3⋊D3—21no—
224C22×C3⋊D3—21no—
225C22×C3⋊D3—21no—
226C22×C3⋊D3—21no—
227C22×C3⋊D3—21no—
228C22×C3⋊D3#4112yes—
229C2×C32×C4—21no—
230C2×C32×C4—21no—
231C2×C32×C4—21no—
232C2×C32×C4—21no—
233C2×C32×C4—21no—
234C2×C32×C4—21no—
235C2×C32×C4—21no—
236C2×C32×C4C2×D412yes—
237C2×C32×C4#4112yes—
238C2×C3⋊Dic3—21no—
239C2×C3⋊Dic3—21no—
240C2×C3⋊Dic3—21no—
241C2×C3⋊Dic3—21no—
242C2×C3⋊Dic3—21no—
243C2×C3⋊Dic3—21no—
244C4⋊(C3⋊D3)—44no—
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×Dic3—21no—
252C2×C3×Dic3—21no—
253C2×C3×Dic3—21no—
254C2×C3×Dic3—21no—
255C2×C3×Dic3—21no—
256C2×C3×Dic3—21no—
257C2×C3×Dic3—21no—
258C2×C3×Dic3—21no—
259C2×C3×Dic3—21no—
260C2×C3×Dic3—21no—
261C2×C3×Dic3—21no—
262C2×C3×Dic3—21no—
263C2×C3×Dic3—21no—
264C2×C3×Dic3—21no—
265C2×C3×Dic3C2×D412yes—
266C2×C3×Dic3C2×D412yes—
267C2×C3×Dic3#4112yes—
268C2×C3×Dic3#4112yes—
269#624—28no—
270C2×#126—91no—
271C2×#117—91no—
272#399—91no—
273#399—91no—
274#398—91no—
275#394—91no—
276#390—91no—
277#389—31no—
278#388—91no—
279#388—91no—
280#388—91no—
281#387—31no—
282#386—91no—
283#385—91no—
284C4×C4⋊C4—91no—
285C23×D3—31no—
286C23×D3—31no—
287C23×D3—31no—
288C23×D3—31no—
289C23×D3—61no—
290C23×D3—61no—
291C22×C3×C4—21no—
292C22×C3×C4—21no—
293C22×C3×C4—21no—
294C22×C3×C4—31no—
295C22×C3×C4—31no—
296C22×C3×C4—31no—
297C22×C3×C4—31no—
298C22×C3×C4—31no—
299C22×C3×C4—31no—
300C22×C3×C4—31no—
301C22×C3×C4—31no—
302C22×C3×C4C22×D311yescharacteristic
303C22×C3×C4C22×D311yescharacteristic
304C22×C3×C4C22×D311yescharacteristic
305C22×C3×C4C22×D311yescharacteristic
306C22×C3×C4C22×D311yescharacteristic
307C22×C3×C4C22×D311yescharacteristic
308C22×Dic3—31no—
309C22×Dic3—31no—
310C22×Dic3—31no—
311C22×Dic3—31no—
312C22×Dic3—61no—
313C22×Dic3—61no—
314C22×Dic3C22×D311yescharacteristic
315C22×Dic3C22×D311yescharacteristic
316C22×Dic3C22×D311yescharacteristic
317C22×Dic3C22×D311yescharacteristic
318C22×Dic3C22×D311yescharacteristic
319C22×Dic3C22×D311yescharacteristic
320C22×Dic3C22×D311yescharacteristic
321C22×Dic3C22×D311yescharacteristic
322C2×D12—62no—
323C2×D12—62no—
324C2×D12—62no—
325C2×D12—62no—
326C2×D12—122no—
327C2×D12—122no—
328C2×D12—121no—
329C2×D12—121no—
330C2×D12—122no—
331C2×C4×D3—62no—
332C2×C4×D3—62no—
333C2×C4×D3—62no—
334C2×C4×D3—62no—
335C2×C4×D3—62no—
336C2×C4×D3—62no—
337C3×C4⋊C4—22no—
338C3×C4⋊C4—22no—
339C3×C4⋊C4—34no—
340C3×C4⋊C4—42no—
341C3×C4⋊C4—62no—
342C3×C4⋊C4—121no—
343C3×C4⋊C4—121no—
344C3×C42—62no—
345C3×C42—62no—
346(C2×D3)⋊C4—62no—
347(C2×D3)⋊C4—62no—
348(C2×D3)⋊C4—62no—
349(C2×D3)⋊C4—62no—
350(C2×D3)⋊C4—62no—
351(C2×D3)⋊C4—62no—
352(C2×D3)⋊C4—62no—
353(C2×D3)⋊C4—62no—
354(C2×D3)⋊C4—62no—
355(C2×D3)⋊C4—62no—
356(C2×D3)⋊C4—62no—
357(C2×D3)⋊C4—62no—
358(C2×D3)⋊C4—62no—
359(C2×D3)⋊C4—62no—
360(C2×D3)⋊C4—62no—
361(C2×D3)⋊C4—62no—
362(C2×D3)⋊C4—62no—
363(C2×D3)⋊C4—62no—
364(C2×D3)⋊C4—122no—
365(C2×D3)⋊C4—122no—
366(C2×D3)⋊C4—122no—
367(C2×D3)⋊C4—121no—
368(C2×D3)⋊C4—121no—
369(C2×D3)⋊C4—121no—
370(C2×D3)⋊C4—121no—
371(C2×D3)⋊C4—122no—
372C4⋊Dic3—22no—
373C4⋊Dic3—41no—
374C4⋊Dic3—41no—
375C4⋊Dic3—62no—
376C4⋊Dic3—62no—
377C4⋊Dic3—62no—
378C4⋊Dic3—62no—
379C4⋊Dic3—121no—
380Dic3⋊C4—62no—
381Dic3⋊C4—62no—
382Dic3⋊C4—62no—
383Dic3⋊C4—62no—
384Dic3⋊C4—121no—
385Dic3⋊C4D1214yescomplemented
386C4×Dic3—22no—
387C4×Dic3—22no—
388C4×Dic3—62no—
389C4×Dic3—62no—
390C4×Dic3—62no—
391C4×Dic3—62no—
392C22×C32C22×D411yescharacteristic
393C22×C32C2×#4111yescharacteristic
394C22×C32C2×#4111yescharacteristic
395C22×C32C2×#4111yescharacteristic
396C22×C32C2×#4111yescharacteristic
397C22×C32H(5,𝔽2)11yescharacteristic
398C22×C322−1+411yescharacteristic
399C2×C3⋊D3—22no—
400C2×C3⋊D3—22no—
401C2×C3⋊D3—22no—
402C2×C3⋊D3—41no—
403C2×C3⋊D3—41no—
404C2×C3⋊D3—41no—
405C2×C3⋊D3—41no—
406C2×C3⋊D3—41no—
407C2×C3⋊D3—41no—
408C2×C3⋊D3—41no—
409C2×C3⋊D3—41no—
410C2×C3⋊D3—41no—
411C2×C3⋊D3—41no—
412C2×C3⋊D3—41no—
413C32×C4—22no—
414C32×C4—22no—
415C32×C4—41no—
416C3⋊Dic3—41no—
417C3⋊Dic3—41no—
418C3×Dic3—22no—
419C3×Dic3—22no—
420C3×Dic3—22no—
421C3×Dic3—22no—
422C3×Dic3—41no—
423C3×Dic3—41no—
424C3×Dic3—41no—
425C3×Dic3—41no—
426C22×D4—91no—
427C23×C4—91no—
428#126—184no—
429#117—184no—
430C2×C4⋊C4—31no—
431C2×C4⋊C4—31no—
432C2×C4⋊C4—31no—
433C2×C4⋊C4—31no—
434C2×C4⋊C4—91no—
435C2×C4⋊C4—91no—
436C2×C4⋊C4—91no—
437C2×C4⋊C4—91no—
438C2×C4⋊C4—91no—
439C2×C4⋊C4D3211yescharacteristic
440C2×C22⋊C4—91no—
441C2×C22⋊C4—91no—
442C2×C22⋊C4—91no—
443C2×C22⋊C4—91no—
444C2×C22⋊C4—91no—
445C2×C22⋊C4—91no—
446C2×C22⋊C4—91no—
447C2×C22⋊C4—91no—
448C2×C22⋊C4—91no—
449C2×C22⋊C4—91no—
450C2×C22⋊C4—91no—
451C2×C42—31no—
452C2×C42—31no—
453C2×C42—91no—
454C2×C42—91no—
455#95—31no—
456#95—31no—
457#95—31no—
458#95—31no—
459#95—31no—
460#95—31no—
461#95—91no—
462#95—91no—
463C23×C3—21no—
464C23×C3C23×D311yescharacteristic
465C23×C3C23×D311yescharacteristic
466C22×D3—32no—
467C22×D3—32no—
468C22×D3—62no—
469C22×D3—61no—
470C22×D3—61no—
471C22×D3—61no—
472C22×D3—61no—
473C22×D3—61no—
474C22×D3—61no—
475C22×D3—61no—
476C22×D3—61no—
477C22×D3—61no—
478C22×D3—61no—
479C22×D3—61no—
480C22×D3—61no—
481C22×D3—62no—
482C22×D3—61no—
483C22×D3—61no—
484C22×D3—61no—
485C22×D3—61no—
486C22×D3—61no—
487C22×D3—61no—
488C22×D3—61no—
489C22×D3—61no—
490C22×D3—61no—
491C22×D3—61no—
492C22×D3—61no—
493C22×D3—61no—
494C22×D3—61no—
495C22×D3—61no—
496C22×D3—121no—
497C22×D3—121no—
498C22×D3—121no—
499C22×D3—121no—
500C22×D3—121no—
501C22×D3—121no—
502C22×D3—121no—
503C22×D3—121no—
504C22×D3—121no—
505C22×D3—121no—
506C22×D3—121no—
507C22×D3—121no—
508C2×C3×C4—21no—
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—21no—
520C2×C3×C4—21no—
521C2×C3×C4—21no—
522C2×C3×C4—22no—
523C2×C3×C4—22no—
524C2×C3×C4—32no—
525C2×C3×C4—32no—
526C2×C3×C4—32no—
527C2×C3×C4—32no—
528C2×C3×C4—41no—
529C2×C3×C4—41no—
530C2×C3×C4—41no—
531C2×C3×C4—41no—
532C2×C3×C4—41no—
533C2×C3×C4—41no—
534C2×C3×C4—41no—
535C2×C3×C4—61no—
536C2×C3×C4—61no—
537C2×C3×C4—61no—
538C2×C3×C4—61no—
539C2×C3×C4—61no—
540C2×C3×C4—61no—
541C2×C3×C4—61no—
542C2×C3×C4—61no—
543C2×C3×C4—61no—
544C2×C3×C4—61no—
545C2×C3×C4—61no—
546C2×C3×C4—61no—
547C2×C3×C4—61no—
548C2×C3×C4—61no—
549C2×C3×C4—61no—
550C2×C3×C4—61no—
551C2×C3×C4—61no—
552C2×C3×C4—61no—
553C2×C3×C4—61no—
554C2×C3×C4—61no—
555C2×C3×C4C2×D1212yes—
556C2×C3×C4#23512yes—
557C2×C3×C4D3×D412yes—
558C2×C3×C4#23712yes—
559C2×Dic3—21no—
560C2×Dic3—21no—
561C2×Dic3—21no—
562C2×Dic3—21no—
563C2×Dic3—21no—
564C2×Dic3—21no—
565C2×Dic3—21no—
566C2×Dic3—21no—
567C2×Dic3—21no—
568C2×Dic3—21no—
569C2×Dic3—21no—
570C2×Dic3—21no—
571C2×Dic3—21no—
572C2×Dic3—21no—
573C2×Dic3—21no—
574C2×Dic3—21no—
575C2×Dic3—21no—
576C2×Dic3—21no—
577C2×Dic3—21no—
578C2×Dic3—21no—
579C2×Dic3—61no—
580C2×Dic3—61no—
581C2×Dic3—61no—
582C2×Dic3—61no—
583C2×Dic3—61no—
584C2×Dic3—61no—
585C2×Dic3—61no—
586C2×Dic3—61no—
587C2×Dic3—61no—
588C2×Dic3—61no—
589C2×Dic3—61no—
590C2×Dic3—61no—
591C2×Dic3—121no—
592C2×Dic3—121no—
593C2×Dic3—121no—
594C2×Dic3—121no—
595C2×Dic3—121no—
596C2×Dic3—121no—
597C2×Dic3C2×D1212yes—
598C2×Dic3C2×D1212yes—
599C2×Dic3#23912yes—
600C2×Dic3#23912yes—
601D12—124no—
602D12—124no—
603D12—128no—
604C4×D3—68no—
605C4×D3—68no—
606C2×C32#52511yescharacteristic
607C2×C32#52911yescharacteristic
608C2×C32#54211yescharacteristic
609C2×C32#54711yescharacteristic
610C2×C32#55011yescharacteristic
611C2×C32#55111yescharacteristic
612C2×C32#55211yescharacteristic
613C3⋊D3—42no—
614C3⋊D3—81no—
615C24—91no—
616C24—91no—
617C2×D4—182no—
618C2×D4—182no—
619C2×D4—361no—
620C22×C4—31no—
621C22×C4—31no—
622C22×C4—31no—
623C22×C4—31no—
624C22×C4—31no—
625C22×C4—31no—
626C22×C4—31no—
627C22×C4—31no—
628C22×C4—91no—
629C22×C4—91no—
630C22×C4—182no—
631C22×C4—182no—
632C22×C4—182no—
633C22×C4C2×D3211yescharacteristic
634C22×C4C2×D3211yescharacteristic
635C22×C4C2×D3211yescharacteristic
636C4⋊C4—22no—
637C4⋊C4—34no—
638C4⋊C4—62no—
639C4⋊C4—121no—
640C4⋊C4—121no—
641C4⋊C4—182no—
642C4⋊C4—182no—
643C4⋊C4—182no—
644C4⋊C4—182no—
645C4⋊C4—361no—
646C22⋊C4—182no—
647C22⋊C4—182no—
648C22⋊C4—182no—
649C22⋊C4—182no—
650C22⋊C4—182no—
651C22⋊C4—182no—
652C22⋊C4—182no—
653C22⋊C4—182no—
654C22⋊C4—182no—
655C22⋊C4—361no—
656C22⋊C4—361no—
657C42—62no—
658C42—62no—
659C42—182no—
660C42—182no—
661C22×C3—21no—
662C22×C3—21no—
663C22×C3—21no—
664C22×C3—21no—
665C22×C3—21no—
666C22×C3—21no—
667C22×C3—21no—
668C22×C3C22×D1211yescharacteristic
669C22×C3C2×#23511yescharacteristic
670C22×C3C2×D3×D411yescharacteristic
671C22×C3C2×#23711yescharacteristic
672C22×C3#100411yescharacteristic
673C22×C3C2×#23911yescharacteristic
674C22×C3C2×#23911yescharacteristic
675C22×C3#100711yescharacteristic
676C22×C3D3×#4111yescharacteristic
677C22×C3D3×#4111yescharacteristic
678C22×C3D3×#4111yescharacteristic
679C22×C3D3×#4111yescharacteristic
680C22×C3#100911yescharacteristic
681C22×C3#101011yescharacteristic
682C2×D3—62no—
683C2×D3—62no—
684C2×D3—62no—
685C2×D3—62no—
686C2×D3—62no—
687C2×D3—62no—
688C2×D3—122no—
689C2×D3—122no—
690C2×D3—122no—
691C2×D3—121no—
692C2×D3—121no—
693C2×D3—121no—
694C2×D3—121no—
695C2×D3—121no—
696C2×D3—121no—
697C2×D3—121no—
698C2×D3—121no—
699C2×D3—122no—
700C2×D3—122no—
701C2×D3—122no—
702C2×D3—121no—
703C2×D3—121no—
704C2×D3—121no—
705C2×D3—121no—
706C2×D3—121no—
707C2×D3—121no—
708C2×D3—121no—
709C2×D3—121no—
710C2×D3—121no—
711C2×D3—121no—
712C2×D3—121no—
713C2×D3—121no—
714C2×D3—121no—
715C2×D3—121no—
716C2×D3—241no—
717C2×D3—241no—
718C2×D3—241no—
719C2×D3—241no—
720C2×D3—241no—
721C2×D3—241no—
722C2×D3—241no—
723C2×D3—241no—
724C3×C4—22no—
725C3×C4—22no—
726C3×C4—22no—
727C3×C4—22no—
728C3×C4—42no—
729C3×C4—42no—
730C3×C4—41no—
731C3×C4—41no—
732C3×C4—62no—
733C3×C4—62no—
734C3×C4—62no—
735C3×C4—62no—
736C3×C4—81no—
737C3×C4—121no—
738C3×C4—121no—
739C3×C4—121no—
740C3×C4—121no—
741Dic3—22no—
742Dic3—22no—
743Dic3—22no—
744Dic3—22no—
745Dic3—41no—
746Dic3—41no—
747Dic3—41no—
748Dic3—41no—
749Dic3—121no—
750Dic3—121no—
751Dic3—121no—
752Dic3—121no—
753Dic3—241no—
754Dic3—241no—
755C32#247911yescharacteristic, complemented, Sylow
756C23—92no—
757C23—181no—
758C23—181no—
759C23—181no—
760C23—181no—
761C23—181no—
762C23—181no—
763C23—181no—
764C23—181no—
765C23—181no—
766C23—181no—
767C23—181no—
768C23—181no—
769C23—181no—
770C23C22×D3211yescharacteristic
771D4—364no—
772C2×C4—21no—
773C2×C4—21no—
774C2×C4—21no—
775C2×C4—21no—
776C2×C4—21no—
777C2×C4—21no—
778C2×C4—21no—
779C2×C4—32no—
780C2×C4—32no—
781C2×C4—32no—
782C2×C4—32no—
783C2×C4—61no—
784C2×C4—61no—
785C2×C4—61no—
786C2×C4—61no—
787C2×C4—61no—
788C2×C4—61no—
789C2×C4—61no—
790C2×C4—61no—
791C2×C4—61no—
792C2×C4—61no—
793C2×C4—61no—
794C2×C4—61no—
795C2×C4—61no—
796C2×C4—61no—
797C2×C4—61no—
798C2×C4—61no—
799C2×C4—61no—
800C2×C4—61no—
801C2×C4—61no—
802C2×C4—61no—
803C2×C4—188no—
804C2×C4—181no—
805C2×C4—181no—
806C2×C4—181no—
807C2×C4—181no—
808C2×C4—181no—
809C2×C4—181no—
810C2×C4D3×D1212yes—
811C2×C4#380412yes—
812C2×C3—21no—
813C2×C3—21no—
814C2×C3—21no—
815C2×C3—21no—
816C2×C3—21no—
817C2×C3—21no—
818C2×C3—21no—
819C2×C3#550711yescharacteristic
820C2×C3#552411yescharacteristic
821C2×C3#555511yescharacteristic
822C2×C3#555611yescharacteristic
823C2×C3#557711yescharacteristic
824C2×C3#558011yescharacteristic
825C2×C3#559911yescharacteristic
826C2×C3#562411yescharacteristic
827C2×C3#562711yescharacteristic
828C2×C3#565811yescharacteristic
829C2×C3#569311yescharacteristic
830C2×C3#569411yescharacteristic
831C2×C3#571011yescharacteristic
832C2×C3#573311yescharacteristic
833D3—122no—
834D3—122no—
835D3—242no—
836D3—242no—
837D3—241no—
838D3—241no—
839C22—182no—
840C22—182no—
841C22—182no—
842C22—361no—
843C22—361no—
844C22—361no—
845C22—361no—
846C22—361no—
847C22—361no—
848C22—361no—
849C22—361no—
850C22—361no—
851C22—361no—
852C22—361no—
853C22#6429711yescharacteristic
854C22C2×D3×D1211yescharacteristic
855C22#6431211yescharacteristic
856C22#6431411yescharacteristic
857C22D3×#23911yescharacteristic
858C22D3×#23911yescharacteristic
859C22C2×#380411yescharacteristic
860C4—22no—
861C4—22no—
862C4—41no—
863C4—62no—
864C4—62no—
865C4—62no—
866C4—62no—
867C4—121no—
868C4—121no—
869C4—121no—
870C4—121no—
871C4—361no—
872C4—361no—
873C3—21no—
874C3#7501811yescharacteristic, complemented
875C3#7602711yescharacteristic, complemented
876C2—362no—
877C2—721no—
878C2#1059446611yescharacteristic
879C2#1059446911yescharacteristic
880C2#1059452411yescharacteristic
881C2#1059462711yescharacteristic
882C2#1059490611yescharacteristic
883C2#1059511811yescharacteristic
884C2#1059537611yescharacteristic
subgroupG/H
center, FrattiniC23C22×D32
commutator, socle, cosocleC23×C32C24
FittingC2×C32×C4⋊C4C22
prime radicalC22×C4⋊(C3⋊D3)C22
hypercenterC2×C4⋊C4D32
hypocenterC32#2479
LCSG ▷ C23×C32 ▷ C32
UCSC1 ◁ C23 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
1. C2×#63848C2semidirect
2. C2×#63836C2semidirect
4. C3×#4984C2semidirect
5. C3×#4978C2semidirect
7. #10591375C2semidirect
8. #10591350C2semidirect
9. #10591350C2semidirect
10. #10591348C2semidirect
12. #10591266C2semidirect
13. #10591259C2semidirect
14. #10591242C2semidirect
15. #10591194C2semidirect
68. #4984D3semidirect
70. #4978D3semidirect
115. C3×Dic3⋊C4D4semidirect
385. Dic3⋊C4D12semidirect
755. C32#2479semidirect
874. C3#75018semidirect
875. C3#76027semidirect

Maximal subgroups

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

subgroupindex
C2×#638482
C2×#638362
#105926902
C3×#49842
C3×#49782
#105913802
#105913752
#105913502
#105913482
#105913202
#105912662
#105912592
#105912422
#105911942
#760273
#750183