Finite Group Databasebeta

← #11817841

Subgroups — #11817841

Order 1152.

1131 conjugacy classes of subgroups.

The subgroup lattice has 871 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#63878C211yesmaximal, characteristic, complemented
2C2×#63848C211yesmaximal, characteristic, complemented
3#10592369C211yesmaximal, characteristic, complemented
4C3×#4677C211yesmaximal, characteristic, complemented
5C3×#4655C211yesmaximal, characteristic, complemented
6#10591392C211yesmaximal, characteristic
7#10591383C211yesmaximal, characteristic
8#10591379C211yesmaximal, characteristic, complemented
9#10591364C211yesmaximal, characteristic
10#10591357C211yesmaximal, characteristic, complemented
11#10591350C211yesmaximal, characteristic, complemented
12#10591348C211yesmaximal, characteristic, complemented
13#10591284C211yesmaximal, characteristic, complemented
14Dic3×C4⋊Dic3C211yesmaximal, characteristic, complemented
15#10591266C211yesmaximal, characteristic, complemented
16#78028—31nomaximal
17#75018—31nomaximal
18C22×#626C2211yescharacteristic
19C22×D3×Dic3C2211yescharacteristic
20C2×#3752C2211yescharacteristic
21C2×#3752C2211yescharacteristic
22C2×#3752C2211yescharacteristic
23C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
24C2×C4×C3⋊Dic3C2211yescharacteristic
25C2×C3×(C2×D3)⋊C4C2211yescharacteristic
26C2×C3×(C2×D3)⋊C4C2211yescharacteristic
27C2×C3×(C2×D3)⋊C4C2211yescharacteristic
28C2×C3×C4⋊Dic3C2211yescharacteristic
29C2×C3×C4⋊Dic3C2211yescharacteristic
30C2×C3×C4⋊Dic3C2211yescharacteristic
31C2×C3×C4⋊Dic3C2211yescharacteristic
32C2×C3×Dic3⋊C4C2211yescharacteristic
33C2×C3×C4×Dic3C2211yescharacteristic
34C2×Dic3⋊Dic3C2211yescharacteristic
35C2×Dic3⋊Dic3C2211yescharacteristic
36C2×Dic3⋊Dic3C2211yescharacteristic
37C2×Dic3⋊Dic3C2211yescharacteristic
38C2×#3722C2211yescharacteristic
39C2×#3722C2211yescharacteristic
40C2×#3722C2211yescharacteristic
41C2×(C2×D3)⋊Dic3C2211yescharacteristic
42C2×(C2×D3)⋊Dic3C2211yescharacteristic
43C2×Dic32C2211yescharacteristic
44C2×Dic32C2211yescharacteristic
45#63878—24no—
46#63848—24no—
47C32×#95C2211yescharacteristic
48#63658C2211yescharacteristic
49C3×C3⋊#95C2211yescharacteristic
50C3×C3⋊#95C2211yescharacteristic
51C3×C3⋊#95C2211yescharacteristic
52#63579C2211yescharacteristic
53#63579C2211yescharacteristic
54#63579C2211yescharacteristic
55C2×#898—31no—
56C2×#898—31no—
57C2×#892—31no—
58C2×#877—31no—
59C3×#399—31no—
60C3×#387—31no—
61#4993—31no—
62#4991—31no—
63#4990—31no—
64#4984—31no—
65#4982—31no—
66Dic3×C4⋊C4—31no—
67#4972—31no—
68#4961—31no—
69#4958—31no—
70#4957—31no—
71#4950—31no—
72#4945—31no—
73#4939—31no—
74C4×C4⋊Dic3—31no—
75#4677—31no—
76#4677D311yescharacteristic, complemented
77#4670—31no—
78#4670—31no—
79#4670—31no—
80#4670—31no—
81#4670—61no—
82#4668—31no—
83#4665—31no—
84#4661—31no—
85#4655D311yescharacteristic, complemented
86C23×C3⋊D3C2311yescharacteristic
87C23×C3×D3C2311yescharacteristic
88C22×C32×C4C2311yescharacteristic
89C22×C32×C4C2311yescharacteristic
90C22×C32×C4C2311yescharacteristic
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
100C22×C3×Dic3C2311yescharacteristic
101C2×#626—22no—
102C2×#626—22no—
103C2×#626—41no—
104C2×D3×Dic3—22no—
105C2×D3×Dic3—22no—
106C2×D3×Dic3—22no—
107#3752—22no—
108#3752—22no—
109#3752—22no—
110C4⋊(C3⋊Dic3)—22no—
111C4×C3⋊Dic3—22no—
112C3×(C2×D3)⋊C4—22no—
113C3×(C2×D3)⋊C4—22no—
114C3×(C2×D3)⋊C4—41no—
115C3×C4⋊Dic3—22no—
116C3×C4⋊Dic3—22no—
117C3×C4⋊Dic3—22no—
118C3×C4⋊Dic3—41no—
119C3×Dic3⋊C4D414yescomplemented
120C3×C4×Dic3—22no—
121Dic3⋊Dic3—22no—
122Dic3⋊Dic3—22no—
123Dic3⋊Dic3—41no—
124Dic3⋊Dic3—41no—
125#3722—22no—
126#3722—22no—
127#3722—41no—
128(C2×D3)⋊Dic3—22no—
129(C2×D3)⋊Dic3—22no—
130Dic32—22no—
131Dic32—22no—
132#2479—91noSylow
133C22×#67—31no—
134C23×Dic3—31no—
135C22×D12—31no—
136C22×C4×D3—31no—
137C2×C3×C4⋊C4—31no—
138C2×C3×C4⋊C4—31no—
139C2×C3×C4⋊C4—31no—
140C2×C3×C4⋊C4—31no—
141C2×C3×C4⋊C4—31no—
142C2×C3×C22⋊C4—31no—
143C2×C3×C22⋊C4—31no—
144C2×C3×C22⋊C4—31no—
145C2×C3×C42—31no—
146C2×#217—31no—
147C2×#217—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—61no—
163C2×(C2×D3)⋊C4—61no—
164C2×(C2×D3)⋊C4—61no—
165C2×(C2×D3)⋊C4C2×D311yescharacteristic
166C2×(C2×D3)⋊C4C2×D311yescharacteristic
167C2×(C2×D3)⋊C4C2×D311yescharacteristic
168C2×C4⋊Dic3—31no—
169C2×C4⋊Dic3—31no—
170C2×C4⋊Dic3—31no—
171C2×C4⋊Dic3—31no—
172C2×C4⋊Dic3—31no—
173C2×C4⋊Dic3—31no—
174C2×C4⋊Dic3—61no—
175C2×C4⋊Dic3C2×D311yescharacteristic
176C2×C4⋊Dic3C2×D311yescharacteristic
177C2×C4⋊Dic3C2×D311yescharacteristic
178C2×C4⋊Dic3C2×D311yescharacteristic
179C2×Dic3⋊C4—31no—
180C2×Dic3⋊C4—31no—
181C2×Dic3⋊C4—31no—
182C2×Dic3⋊C4—31no—
183C2×Dic3⋊C4C2×D311yescharacteristic
184C2×C4×Dic3—31no—
185C2×C4×Dic3—31no—
186C2×C4×Dic3—31no—
187C2×C4×Dic3—31no—
188C2×C4×Dic3—31no—
189C2×C4×Dic3—31no—
190C2×C4×Dic3—61no—
191C2×C4×Dic3C2×D311yescharacteristic
192#898—64no—
193#898—64no—
194#892—64no—
195#877—64no—
196C3×#95—21no—
197C3×#95—31no—
198C3×#95—31no—
199C3×#95—31no—
200C3×#95C2×D311yescharacteristic
201C3×#95C2×D311yescharacteristic
202C3⋊#95—31no—
203C3⋊#95—31no—
204C3⋊#95—31no—
205C3⋊#95—31no—
206C3⋊#95—31no—
207C3⋊#95—31no—
208C3⋊#95—31no—
209C3⋊#95—31no—
210C3⋊#95—61no—
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—
244C2×C3⋊Dic3—21no—
245C2×C3⋊Dic3—21no—
246C2×C3⋊Dic3#4112yes—
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—
268#626—44no—
269D3×Dic3—28no—
270C2×#126—91no—
271C2×#117—91no—
272#399—31no—
273#399—91no—
274#398—91no—
275#394—91no—
276#390—91no—
277#389—91no—
278#388—91no—
279#388—91no—
280#388—91no—
281#387—31no—
282#386—91no—
283#385—91no—
284C4×C4⋊C4—91no—
285C24×C3—31no—
286C23×D3—31no—
287C23×D3—31no—
288C23×D3—61no—
289C23×D3C22×D311yescharacteristic
290C22×C3×C4—21no—
291C22×C3×C4—21no—
292C22×C3×C4—21no—
293C22×C3×C4—31no—
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×C4C22×D311yescharacteristic
301C22×C3×C4C22×D311yescharacteristic
302C22×C3×C4C22×D311yescharacteristic
303C22×C3×C4C22×D311yescharacteristic
304C22×C3×C4C22×D311yescharacteristic
305C22×C3×C4C22×D311yescharacteristic
306C2×#67—62no—
307C2×#67—62no—
308C2×#67—121no—
309C22×Dic3—31no—
310C22×Dic3—31no—
311C22×Dic3—31no—
312C22×Dic3—31no—
313C22×Dic3—31no—
314C22×Dic3—31no—
315C22×Dic3—61no—
316C22×Dic3—61no—
317C22×Dic3—61no—
318C22×Dic3—62no—
319C22×Dic3—62no—
320C22×Dic3—62no—
321C22×Dic3C22×D311yescharacteristic
322C22×Dic3C22×D311yescharacteristic
323C22×Dic3C22×D311yescharacteristic
324C22×Dic3C22×D311yescharacteristic
325C22×Dic3C22×D311yescharacteristic
326C22×Dic3C22×D311yescharacteristic
327C22×Dic3C22×D311yescharacteristic
328C2×D12—62no—
329C2×D12—62no—
330C2×D12—121no—
331C2×C4×D3—62no—
332C2×C4×D3—62no—
333C2×C4×D3—62no—
334C3×C4⋊C4—34no—
335C3×C4⋊C4—62no—
336C3×C4⋊C4—62no—
337C3×C4⋊C4—62no—
338C3×C4⋊C4—121no—
339C3×C22⋊C4—62no—
340C3×C22⋊C4—62no—
341C3×C22⋊C4—121no—
342C3×C42—62no—
343#217—62no—
344#217—62no—
345(C2×D3)⋊C4—22no—
346(C2×D3)⋊C4—22no—
347(C2×D3)⋊C4—41no—
348(C2×D3)⋊C4—62no—
349(C2×D3)⋊C4—62no—
350(C2×D3)⋊C4—62no—
351(C2×D3)⋊C4—62no—
352(C2×D3)⋊C4—64no—
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—122no—
362(C2×D3)⋊C4—122no—
363(C2×D3)⋊C4—121no—
364(C2×D3)⋊C4—121no—
365C4⋊Dic3—22no—
366C4⋊Dic3—22no—
367C4⋊Dic3—22no—
368C4⋊Dic3—41no—
369C4⋊Dic3—62no—
370C4⋊Dic3—62no—
371C4⋊Dic3—62no—
372C4⋊Dic3—62no—
373C4⋊Dic3—122no—
374C4⋊Dic3—121no—
375C4⋊Dic3—121no—
376Dic3⋊C4—62no—
377Dic3⋊C4—62no—
378Dic3⋊C4—121no—
379Dic3⋊C4—121no—
380Dic3⋊C4D1214yescomplemented
381C4×Dic3—22no—
382C4×Dic3—62no—
383C4×Dic3—62no—
384C4×Dic3—62no—
385C4×Dic3—62no—
386C4×Dic3—62no—
387C4×Dic3—62no—
388C4×Dic3—122no—
389C22×C32C22×D411yescharacteristic
390C22×C32C2×#4111yescharacteristic
391C22×C32C2×#4111yescharacteristic
392C22×C32C2×#4111yescharacteristic
393C22×C32C2×#4111yescharacteristic
394C22×C32H(5,𝔽2)11yescharacteristic
395C22×C322−1+411yescharacteristic
396C2×C3⋊D3—41no—
397C2×C3⋊D3—41no—
398C2×C3⋊D3—41no—
399C2×C3⋊D3—41no—
400C2×C3⋊D3—41no—
401C2×C3⋊D3—41no—
402C2×C3⋊D3—41no—
403C2×C3×D3—22no—
404C2×C3×D3—22no—
405C2×C3×D3—22no—
406C2×C3×D3—41no—
407C2×C3×D3—41no—
408C2×C3×D3—41no—
409C2×C3×D3—41no—
410C32×C4—22no—
411C32×C4—22no—
412C32×C4—41no—
413C3⋊Dic3—22no—
414C3⋊Dic3—41no—
415C3⋊Dic3—41no—
416C3×Dic3—22no—
417C3×Dic3—22no—
418C3×Dic3—22no—
419C3×Dic3—41no—
420C3×Dic3—41no—
421C3×Dic3—41no—
422C3×Dic3—41no—
423C22×D4—91no—
424C23×C4—91no—
425#126—184no—
426#117—184no—
427C2×C4⋊C4—31no—
428C2×C4⋊C4—31no—
429C2×C4⋊C4—31no—
430C2×C4⋊C4—31no—
431C2×C4⋊C4—31no—
432C2×C4⋊C4—91no—
433C2×C4⋊C4—91no—
434C2×C4⋊C4—91no—
435C2×C4⋊C4—91no—
436C2×C4⋊C4—91no—
437C2×C22⋊C4—31no—
438C2×C22⋊C4—31no—
439C2×C22⋊C4—31no—
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×C42—31no—
449C2×C42—91no—
450C2×C42—91no—
451C2×C42—91no—
452#95—31no—
453#95—31no—
454#95—31no—
455#95—91no—
456#95—91no—
457#95—91no—
458#95—91no—
459#95D3211yescharacteristic
460C23×C3—21no—
461C23×C3—32no—
462C23×C3—61no—
463C23×C3—61no—
464C23×C3—61no—
465C23×C3—61no—
466C23×C3—61no—
467C23×C3—61no—
468C23×C3C23×D311yescharacteristic
469C23×C3C23×D311yescharacteristic
470C22×D3—21no—
471C22×D3—21no—
472C22×D3—21no—
473C22×D3—21no—
474C22×D3—21no—
475C22×D3—21no—
476C22×D3—62no—
477C22×D3—61no—
478C22×D3—61no—
479C22×D3—61no—
480C22×D3—61no—
481C22×D3—61no—
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—121no—
492C22×D3—121no—
493C22×D3—121no—
494C22×D3—121no—
495C22×D3—121no—
496C22×D3—121no—
497C22×D3#23912yes—
498C2×C3×C4—21no—
499C2×C3×C4—21no—
500C2×C3×C4—21no—
501C2×C3×C4—21no—
502C2×C3×C4—21no—
503C2×C3×C4—21no—
504C2×C3×C4—21no—
505C2×C3×C4—21no—
506C2×C3×C4—21no—
507C2×C3×C4—21no—
508C2×C3×C4—21no—
509C2×C3×C4—21no—
510C2×C3×C4—21no—
511C2×C3×C4—21no—
512C2×C3×C4—22no—
513C2×C3×C4—22no—
514C2×C3×C4—32no—
515C2×C3×C4—32no—
516C2×C3×C4—32no—
517C2×C3×C4—41no—
518C2×C3×C4—41no—
519C2×C3×C4—41no—
520C2×C3×C4—41no—
521C2×C3×C4—41no—
522C2×C3×C4—41no—
523C2×C3×C4—41no—
524C2×C3×C4—61no—
525C2×C3×C4—61no—
526C2×C3×C4—61no—
527C2×C3×C4—61no—
528C2×C3×C4—61no—
529C2×C3×C4—61no—
530C2×C3×C4—61no—
531C2×C3×C4—61no—
532C2×C3×C4—61no—
533C2×C3×C4—61no—
534C2×C3×C4—61no—
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×C4C2×D1212yes—
543C2×C3×C4D3×D412yes—
544C2×C3×C4#23712yes—
545C2×C3×C4#23912yes—
546#67—124no—
547C2×Dic3—21no—
548C2×Dic3—21no—
549C2×Dic3—21no—
550C2×Dic3—21no—
551C2×Dic3—21no—
552C2×Dic3—21no—
553C2×Dic3—21no—
554C2×Dic3—21no—
555C2×Dic3—21no—
556C2×Dic3—21no—
557C2×Dic3—21no—
558C2×Dic3—21no—
559C2×Dic3—21no—
560C2×Dic3—21no—
561C2×Dic3—21no—
562C2×Dic3—21no—
563C2×Dic3—21no—
564C2×Dic3—21no—
565C2×Dic3—32no—
566C2×Dic3—32no—
567C2×Dic3—62no—
568C2×Dic3—68no—
569C2×Dic3—61no—
570C2×Dic3—61no—
571C2×Dic3—61no—
572C2×Dic3—61no—
573C2×Dic3—62no—
574C2×Dic3—61no—
575C2×Dic3—61no—
576C2×Dic3—61no—
577C2×Dic3—61no—
578C2×Dic3—61no—
579C2×Dic3—61no—
580C2×Dic3—61no—
581C2×Dic3—61no—
582C2×Dic3—61no—
583C2×Dic3—61no—
584C2×Dic3—61no—
585C2×Dic3—61no—
586C2×Dic3—121no—
587C2×Dic3—121no—
588C2×Dic3—121no—
589C2×Dic3—121no—
590C2×Dic3—121no—
591C2×Dic3—121no—
592C2×Dic3—121no—
593C2×Dic3C2×D1212yes—
594C2×Dic3C2×D1212yes—
595C2×Dic3#23712yes—
596D12—124no—
597C4×D3—68no—
598C2×C32#52511yescharacteristic
599C2×C32#52911yescharacteristic
600C2×C32#54211yescharacteristic
601C2×C32#54711yescharacteristic
602C2×C32#55011yescharacteristic
603C2×C32#55111yescharacteristic
604C2×C32#55211yescharacteristic
605C3⋊D3—81no—
606C3×D3—42no—
607C24—31no—
608C24—91no—
609C2×D4—182no—
610C2×D4—182no—
611C2×D4—361no—
612C22×C4—31no—
613C22×C4—31no—
614C22×C4—31no—
615C22×C4—31no—
616C22×C4—31no—
617C22×C4—31no—
618C22×C4—31no—
619C22×C4—91no—
620C22×C4—91no—
621C22×C4—91no—
622C22×C4—182no—
623C22×C4—182no—
624C22×C4—182no—
625C22×C4C2×D3211yescharacteristic
626C22×C4C2×D3211yescharacteristic
627C22×C4C2×D3211yescharacteristic
628C4⋊C4—34no—
629C4⋊C4—62no—
630C4⋊C4—62no—
631C4⋊C4—62no—
632C4⋊C4—121no—
633C4⋊C4—182no—
634C4⋊C4—182no—
635C4⋊C4—182no—
636C4⋊C4—361no—
637C4⋊C4—361no—
638C22⋊C4—62no—
639C22⋊C4—62no—
640C22⋊C4—121no—
641C22⋊C4—182no—
642C22⋊C4—182no—
643C22⋊C4—182no—
644C22⋊C4—182no—
645C22⋊C4—182no—
646C22⋊C4—182no—
647C22⋊C4—182no—
648C22⋊C4—361no—
649C42—62no—
650C42—182no—
651C42—182no—
652C42—182no—
653C22×C3—21no—
654C22×C3—21no—
655C22×C3—21no—
656C22×C3—21no—
657C22×C3—21no—
658C22×C3—21no—
659C22×C3—21no—
660C22×C3—62no—
661C22×C3—62no—
662C22×C3—62no—
663C22×C3—121no—
664C22×C3—121no—
665C22×C3—121no—
666C22×C3—121no—
667C22×C3C22×D1211yescharacteristic
668C22×C3C2×D3×D411yescharacteristic
669C22×C3C2×#23711yescharacteristic
670C22×C3C2×#23711yescharacteristic
671C22×C3#100411yescharacteristic
672C22×C3C2×#23911yescharacteristic
673C22×C3C2×#23911yescharacteristic
674C22×C3D3×#4111yescharacteristic
675C22×C3D3×#4111yescharacteristic
676C22×C3D3×#4111yescharacteristic
677C22×C3D3×#4111yescharacteristic
678C22×C3#100911yescharacteristic
679C22×C3#101011yescharacteristic
680C22×C3#101011yescharacteristic
681C2×D3—22no—
682C2×D3—22no—
683C2×D3—22no—
684C2×D3—41no—
685C2×D3—41no—
686C2×D3—41no—
687C2×D3—41no—
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—121no—
700C2×D3—121no—
701C2×D3—121no—
702C2×D3—121no—
703C2×D3—121no—
704C2×D3—121no—
705C2×D3—241no—
706C2×D3—241no—
707C2×D3—241no—
708C2×D3—241no—
709C3×C4—22no—
710C3×C4—22no—
711C3×C4—22no—
712C3×C4—22no—
713C3×C4—42no—
714C3×C4—42no—
715C3×C4—41no—
716C3×C4—41no—
717C3×C4—62no—
718C3×C4—62no—
719C3×C4—62no—
720C3×C4—81no—
721C3×C4—121no—
722C3×C4—121no—
723C3×C4—121no—
724C3×C4—121no—
725Dic3—22no—
726Dic3—22no—
727Dic3—22no—
728Dic3—41no—
729Dic3—41no—
730Dic3—41no—
731Dic3—41no—
732Dic3—62no—
733Dic3—62no—
734Dic3—122no—
735Dic3—122no—
736Dic3—121no—
737Dic3—121no—
738Dic3—121no—
739Dic3—121no—
740Dic3—241no—
741C32#247911yescharacteristic, complemented, Sylow
742C23—32no—
743C23—61no—
744C23—61no—
745C23—61no—
746C23—61no—
747C23—61no—
748C23—61no—
749C23—181no—
750C23—181no—
751C23—181no—
752C23—181no—
753C23—181no—
754C23—181no—
755C23—181no—
756C23C22×D3211yescharacteristic
757D4—364no—
758C2×C4—21no—
759C2×C4—21no—
760C2×C4—21no—
761C2×C4—21no—
762C2×C4—21no—
763C2×C4—21no—
764C2×C4—21no—
765C2×C4—32no—
766C2×C4—32no—
767C2×C4—32no—
768C2×C4—61no—
769C2×C4—61no—
770C2×C4—61no—
771C2×C4—61no—
772C2×C4—61no—
773C2×C4—61no—
774C2×C4—61no—
775C2×C4—61no—
776C2×C4—61no—
777C2×C4—61no—
778C2×C4—61no—
779C2×C4—61no—
780C2×C4—61no—
781C2×C4—61no—
782C2×C4—61no—
783C2×C4—61no—
784C2×C4—61no—
785C2×C4—61no—
786C2×C4—92no—
787C2×C4—188no—
788C2×C4—181no—
789C2×C4—181no—
790C2×C4—181no—
791C2×C4—181no—
792C2×C4—181no—
793C2×C4—181no—
794C2×C4—181no—
795C2×C4—181no—
796C2×C4#379612yes—
797C2×C4D3×D1212yes—
798C2×C3—21no—
799C2×C3—21no—
800C2×C3—21no—
801C2×C3—21no—
802C2×C3—21no—
803C2×C3—21no—
804C2×C3—21no—
805C2×C3—122no—
806C2×C3#552411yescharacteristic
807C2×C3#555511yescharacteristic
808C2×C3#557711yescharacteristic
809C2×C3#562411yescharacteristic
810C2×C3#562711yescharacteristic
811C2×C3#563711yescharacteristic
812C2×C3#564211yescharacteristic
813C2×C3#564911yescharacteristic
814C2×C3#565511yescharacteristic
815C2×C3#565811yescharacteristic
816C2×C3#566211yescharacteristic
817C2×C3#569411yescharacteristic
818C2×C3#571011yescharacteristic
819C2×C3#571811yescharacteristic
820D3—42no—
821D3—242no—
822D3—241no—
823D3—241no—
824C22—62no—
825C22—62no—
826C22—62no—
827C22—121no—
828C22—121no—
829C22—121no—
830C22—121no—
831C22—361no—
832C22—361no—
833C22—361no—
834C22—361no—
835C22—361no—
836C22—361no—
837C22—361no—
838C22C2×#379611yescharacteristic
839C22C2×D3×D1211yescharacteristic
840C22#6430711yescharacteristic
841C22#6430911yescharacteristic
842C22D3×#23711yescharacteristic
843C22#6431211yescharacteristic
844C22D3×#23911yescharacteristic
845C4—22no—
846C4—22no—
847C4—41no—
848C4—62no—
849C4—62no—
850C4—62no—
851C4—121no—
852C4—121no—
853C4—121no—
854C4—121no—
855C4—182no—
856C4—361no—
857C4—361no—
858C3—21no—
859C3#7501811yescharacteristic, complemented
860C3#7802811yescharacteristic, complemented
861C2—122no—
862C2—721no—
863C2#1059390011yescharacteristic
864C2#1059407711yescharacteristic
865C2#1059414411yescharacteristic
866C2#1059423011yescharacteristic
867C2#1059445711yescharacteristic
868C2#1059462711yescharacteristic
869C2#1059464711yescharacteristic
subgroupG/H
center, FrattiniC23C22×D32
commutator, socle, cosocleC23×C32C24
FittingC32×#95C22
prime radicalC22×#626C22
hypercenter#95D32
hypocenterC32#2479
LCSG ▷ C23×C32 ▷ C32
UCSC1 ◁ C23 ◁ #95

Complements

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

NH ≅ G/Ntype
1. C2×#63878C2semidirect
2. C2×#63848C2semidirect
3. #10592369C2semidirect
4. C3×#4677C2semidirect
5. C3×#4655C2semidirect
8. #10591379C2semidirect
10. #10591357C2semidirect
11. #10591350C2semidirect
12. #10591348C2semidirect
13. #10591284C2semidirect
14. Dic3×C4⋊Dic3C2semidirect
15. #10591266C2semidirect
76. #4677D3semidirect
85. #4655D3semidirect
119. C3×Dic3⋊C4D4semidirect
380. Dic3⋊C4D12semidirect
741. C32#2479semidirect
859. C3#75018semidirect
860. C3#78028semidirect

Maximal subgroups

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

subgroupindex
C2×#638782
C2×#638482
#105923692
C3×#46772
C3×#46552
#105913922
#105913832
#105913792
#105913642
#105913572
#105913502
#105913482
#105912842
Dic3×C4⋊Dic32
#105912662
#780283
#750183