Finite Group Databasebeta

← #11836008

Subgroups — #11836008

Order 1152.

1775 conjugacy classes of subgroups.

The subgroup lattice has 1176 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#63923C211yesmaximal, characteristic, complemented
2C2×#63922C211yesmaximal, characteristic, complemented
3C2×#63916C211yesmaximal, characteristic, complemented
4C2×#63909C211yesmaximal, characteristic, complemented
5#10592364C211yesmaximal, characteristic, complemented
6C3×#4677C211yesmaximal, characteristic, complemented
7C3×#4665C211yesmaximal, characteristic, complemented
8#10591399C211yesmaximal, characteristic, complemented
9#10591393C211yesmaximal, characteristic, complemented
10#10591392C211yesmaximal, characteristic, complemented
11#10591392C211yesmaximal, characteristic, complemented
12#10591387C211yesmaximal, characteristic, complemented
13#10591381C211yesmaximal, characteristic, complemented
14#10591326C211yesmaximal, characteristic, complemented
15#10591314C211yesmaximal, characteristic, complemented
16#78112—31nomaximal
17#74910—31nomaximal
18C23×D32C2211yescharacteristic
19C22×C4⋊(C3⋊D3)C2211yescharacteristic
20C22×C4×C3⋊D3C2211yescharacteristic, complemented
21C22×C3×D12C2211yescharacteristic
22C22×C3×C4×D3C2211yescharacteristic, complemented
23C22×#626C2211yescharacteristic
24C22×#626C2211yescharacteristic
25C22×#626C2211yescharacteristic
26C22×#626C2211yescharacteristic, complemented
27C22×#625C2211yescharacteristic
28C2×#3752C2211yescharacteristic
29C2×#3752C2211yescharacteristic
30C2×#3752C2211yescharacteristic, complemented
31C2×C3×(C2×D3)⋊C4C2211yescharacteristic
32C2×C3×(C2×D3)⋊C4C2211yescharacteristic
33C2×C3×(C2×D3)⋊C4C2211yescharacteristic
34C2×C3×(C2×D3)⋊C4C2211yescharacteristic
35C2×C3×(C2×D3)⋊C4C2211yescharacteristic
36C2×C3×(C2×D3)⋊C4C2211yescharacteristic, complemented
37C2×C3×C4⋊Dic3C2211yescharacteristic, complemented
38C2×C3×C4⋊Dic3C2211yescharacteristic, complemented
39C2×C3×C4⋊Dic3C2211yescharacteristic, complemented
40C2×#3722C2211yescharacteristic
41C2×#3722C2211yescharacteristic
42C2×#3722C2211yescharacteristic, complemented
43C2×(C2×D3)⋊Dic3C2211yescharacteristic
44C2×(C2×D3)⋊Dic3C2211yescharacteristic
45C2×(C2×D3)⋊Dic3C2211yescharacteristic
46C2×(C2×D3)⋊Dic3C2211yescharacteristic, complemented
47#63923—24no—
48#63922—24no—
49#63916—24no—
50#63909—24no—
51C32×#95C2211yescharacteristic, complemented
52#63658C2211yescharacteristic, complemented
53C3×C3⋊#95C2211yescharacteristic, complemented
54#63579C2211yescharacteristic, complemented
55#63579C2211yescharacteristic, complemented
56#63579C2211yescharacteristic, complemented
57C2×#938—31no—
58C2×#937—31no—
59C2×#930—31no—
60C2×#895—31no—
61C2×#895—31no—
62C2×#882—31no—
63C2×#882—31no—
64C2×#882—31no—
65C3×#399—31no—
66C3×#386—31no—
67#5213—31no—
68#4992—31no—
69#4992—31no—
70#4991—31no—
71#4991—31no—
72#4961—31no—
73#4961—31no—
74#4960—31no—
75#4960—31no—
76#4956—31no—
77#4956—31no—
78#4955—31no—
79#4955—31no—
80#4953—31no—
81#4677D311yescharacteristic, complemented
82#4674—31no—
83#4665—31no—
84#4665—31no—
85#4665—31no—
86#4665—61no—
87#4665D311yescharacteristic, complemented
88C23×C3⋊D3C2311yescharacteristic
89C23×C3⋊D3C2311yescharacteristic
90C23×C3×D3C2311yescharacteristic
91C23×C3×D3C2311yescharacteristic
92C23×C3×D3C2311yescharacteristic
93C22×D32—22no—
94C22×D32—22no—
95C22×D32—22no—
96C22×D32—41no—
97C22×D32—41no—
98C22×D32—41no—
99C22×D32—41no—
100C22×C32×C4C2311yescharacteristic
101C22×C32×C4C2311yescharacteristic
102C22×C32×C4C2311yescharacteristic
103C22×C3⋊Dic3C2311yescharacteristic
104C22×C3⋊Dic3C2311yescharacteristic
105C2×C4⋊(C3⋊D3)—41no—
106C2×C4⋊(C3⋊D3)—41no—
107C2×C4⋊(C3⋊D3)D414yescomplemented
108C2×C4×C3⋊D3—22no—
109C2×C4×C3⋊D3—41no—
110C2×C4×C3⋊D3—41no—
111C22×C3×Dic3C2311yescharacteristic
112C22×C3×Dic3C2311yescharacteristic
113C22×C3×Dic3C2311yescharacteristic
114C22×C3×Dic3C2311yescharacteristic
115C22×C3×Dic3C2311yescharacteristic
116C2×C3×D12—41no—
117C2×C3×D12—41no—
118C2×C3×D12D414yescomplemented
119C2×C3×C4×D3—22no—
120C2×C3×C4×D3—41no—
121C2×C3×C4×D3—41no—
122C2×#626—22no—
123C2×#626—22no—
124C2×#626—22no—
125C2×#626—22no—
126C2×#626—22no—
127C2×#626—22no—
128C2×#626—22no—
129C2×#626—22no—
130C2×#626—41no—
131C2×#626—41no—
132C2×#626—41no—
133C2×#626—41no—
134C2×#625—22no—
135C2×#625—22no—
136C2×#625—41no—
137#3752—22no—
138#3752—41no—
139#3752—41no—
140C3×(C2×D3)⋊C4—22no—
141C3×(C2×D3)⋊C4—22no—
142C3×(C2×D3)⋊C4—22no—
143C3×(C2×D3)⋊C4—41no—
144C3×(C2×D3)⋊C4—41no—
145C3×(C2×D3)⋊C4—41no—
146C3×C4⋊Dic3—22no—
147C3×C4⋊Dic3—22no—
148C3×C4⋊Dic3—41no—
149#3722—22no—
150#3722—22no—
151#3722—22no—
152(C2×D3)⋊Dic3—22no—
153(C2×D3)⋊Dic3—22no—
154(C2×D3)⋊Dic3—22no—
155(C2×D3)⋊Dic3—41no—
156#2668—91noSylow
157C24×D3—31no—
158C24×D3—31no—
159C22×C3×D4—31no—
160C23×C3×C4—31no—
161C22×#67—31no—
162C22×#67—31no—
163C22×#67—31no—
164C22×#67—31no—
165C22×#67—31no—
166C22×#67—31no—
167C22×D12—31no—
168C22×D12—31no—
169C22×D12—31no—
170C22×D12—31no—
171C22×D12—31no—
172C22×D12—31no—
173C22×D12—61no—
174C22×D12C2×D311yescharacteristic
175C22×C4×D3—31no—
176C22×C4×D3—31no—
177C22×C4×D3—61no—
178C22×C4×D3C2×D311yescharacteristic, complemented
179C2×C3×C4⋊C4—31no—
180C2×C3×C4⋊C4—31no—
181C2×C3×C4⋊C4—31no—
182C2×C3×C22⋊C4—31no—
183C2×C3×C22⋊C4—31no—
184C2×C3×C22⋊C4—31no—
185C2×C3×C22⋊C4—31no—
186C2×C3×C22⋊C4—31no—
187C2×C3×C22⋊C4—31no—
188C2×#217—31no—
189C2×#217—31no—
190C2×#217—31no—
191C2×#217—31no—
192#938—64no—
193#937—64no—
194#930—64no—
195C2×(C2×D3)⋊C4—31no—
196C2×(C2×D3)⋊C4—31no—
197C2×(C2×D3)⋊C4—31no—
198C2×(C2×D3)⋊C4—31no—
199C2×(C2×D3)⋊C4—31no—
200C2×(C2×D3)⋊C4—31no—
201C2×(C2×D3)⋊C4—31no—
202C2×(C2×D3)⋊C4—31no—
203C2×(C2×D3)⋊C4—31no—
204C2×(C2×D3)⋊C4—31no—
205C2×(C2×D3)⋊C4—31no—
206C2×(C2×D3)⋊C4—31no—
207C2×(C2×D3)⋊C4—31no—
208C2×(C2×D3)⋊C4—31no—
209C2×(C2×D3)⋊C4—31no—
210C2×(C2×D3)⋊C4—31no—
211C2×(C2×D3)⋊C4—61no—
212C2×(C2×D3)⋊C4—61no—
213C2×(C2×D3)⋊C4—61no—
214C2×(C2×D3)⋊C4C2×D311yescharacteristic
215C2×(C2×D3)⋊C4C2×D311yescharacteristic
216C2×(C2×D3)⋊C4C2×D311yescharacteristic
217C2×(C2×D3)⋊C4C2×D311yescharacteristic
218C2×(C2×D3)⋊C4C2×D311yescharacteristic
219C2×(C2×D3)⋊C4C2×D311yescharacteristic, complemented
220C2×C4⋊Dic3C2×D311yescharacteristic, complemented
221C2×C4⋊Dic3C2×D311yescharacteristic, complemented
222C2×C4⋊Dic3C2×D311yescharacteristic, complemented
223#895—64no—
224#895—64no—
225#882—64no—
226#882—64no—
227#882—64no—
228C3×#95—21no—
229C3×#95—31no—
230C3×#95C2×D311yescharacteristic, complemented
231C3×#95C2×D311yescharacteristic, complemented
232C3⋊#95—31no—
233C3⋊#95—31no—
234C3⋊#95—31no—
235C3⋊#95—31no—
236C3⋊#95—31no—
237C3⋊#95—31no—
238C3⋊#95—31no—
239C3⋊#95—31no—
240C3⋊#95—61no—
241C3⋊#95C2×D311yescharacteristic, complemented
242C23×C32C2411yescharacteristic
243C22×C3⋊D3—21no—
244C22×C3⋊D3—21no—
245C22×C3⋊D3—21no—
246C22×C3⋊D3—21no—
247C22×C3⋊D3—21no—
248C22×C3⋊D3—21no—
249C22×C3⋊D3—21no—
250C22×C3⋊D3—21no—
251C22×C3⋊D3—21no—
252C22×C3⋊D3—21no—
253C22×C3⋊D3—21no—
254C22×C3⋊D3—21no—
255C22×C3⋊D3C2×D412yes—
256C22×C3⋊D3C2×D412yes—
257C22×C3×D3—21no—
258C22×C3×D3—21no—
259C22×C3×D3—21no—
260C22×C3×D3—21no—
261C22×C3×D3—21no—
262C22×C3×D3—21no—
263C22×C3×D3—21no—
264C22×C3×D3—21no—
265C22×C3×D3—21no—
266C22×C3×D3—21no—
267C22×C3×D3—21no—
268C22×C3×D3—21no—
269C22×C3×D3—21no—
270C22×C3×D3—21no—
271C22×C3×D3—21no—
272C22×C3×D3—21no—
273C22×C3×D3—21no—
274C22×C3×D3—21no—
275C22×C3×D3C2×D412yes—
276C22×C3×D3C2×D412yes—
277C22×C3×D3#4112yes—
278C2×D32—44no—
279C2×D32—44no—
280C2×D32—44no—
281C2×D32—44no—
282C2×D32—44no—
283C2×D32—44no—
284C2×D32—44no—
285C2×C32×C4—21no—
286C2×C32×C4—21no—
287C2×C32×C4—21no—
288C2×C32×C4—21no—
289C2×C32×C4—21no—
290C2×C32×C4—21no—
291C2×C32×C4—21no—
292C2×C32×C4C2×D412yes—
293C2×C32×C4C2×D412yes—
294C2×C3⋊Dic3—21no—
295C2×C3⋊Dic3—21no—
296C2×C3⋊Dic3—21no—
297C2×C3⋊Dic3—21no—
298C2×C3⋊Dic3—21no—
299C2×C3⋊Dic3—21no—
300C4⋊(C3⋊D3)—44no—
301C4×C3⋊D3—44no—
302C2×C3×Dic3—21no—
303C2×C3×Dic3—21no—
304C2×C3×Dic3—21no—
305C2×C3×Dic3—21no—
306C2×C3×Dic3—21no—
307C2×C3×Dic3—21no—
308C2×C3×Dic3—21no—
309C2×C3×Dic3—21no—
310C2×C3×Dic3—21no—
311C2×C3×Dic3—21no—
312C2×C3×Dic3—21no—
313C2×C3×Dic3—21no—
314C2×C3×Dic3—21no—
315C2×C3×Dic3—21no—
316C2×C3×Dic3—21no—
317C3×D12—44no—
318C3×C4×D3—44no—
319#626—44no—
320#626—44no—
321#626—44no—
322#626—44no—
323#625—44no—
324C2×#121—91no—
325C2×#121—91no—
326C2×#120—91no—
327C2×#120—91no—
328#399—31no—
329#397—91no—
330#397—91no—
331#394—91no—
332#394—91no—
333#392—91no—
334#386—31no—
335#386—91no—
336#386—91no—
337#386—91no—
338#379—91no—
339C24×C3—31no—
340C24×C3—31no—
341C24×C3—31no—
342C23×D3—31no—
343C23×D3—31no—
344C23×D3—31no—
345C23×D3—31no—
346C23×D3—61no—
347C23×D3—61no—
348C23×D3—62no—
349C23×D3—62no—
350C23×D3—62no—
351C23×D3—62no—
352C23×D3—62no—
353C23×D3—62no—
354C23×D3—121no—
355C23×D3—121no—
356C23×D3—121no—
357C23×D3—121no—
358C23×D3—121no—
359C23×D3—121no—
360C23×D3—121no—
361C23×D3—121no—
362C23×D3C22×D311yescharacteristic
363C23×D3C22×D311yescharacteristic
364C23×D3C22×D311yescharacteristic
365C2×C3×D4—34no—
366C2×C3×D4—121no—
367C2×C3×D4—121no—
368C22×C3×C4—21no—
369C22×C3×C4—21no—
370C22×C3×C4—21no—
371C22×C3×C4—31no—
372C22×C3×C4—31no—
373C22×C3×C4—31no—
374C22×C3×C4—31no—
375C22×C3×C4—31no—
376C22×C3×C4—62no—
377C22×C3×C4—121no—
378C22×C3×C4—121no—
379C22×C3×C4C22×D311yescharacteristic
380C22×C3×C4C22×D311yescharacteristic
381C22×C3×C4C22×D311yescharacteristic
382C22×C3×C4C22×D311yescharacteristic
383C22×C3×C4C22×D311yescharacteristic
384C22×C3×C4C22×D311yescharacteristic
385C2×#67—62no—
386C2×#67—62no—
387C2×#67—62no—
388C2×#67—62no—
389C2×#67—62no—
390C2×#67—62no—
391C2×#67—62no—
392C2×#67—62no—
393C2×#67—62no—
394C2×#67—62no—
395C2×#67—62no—
396C2×#67—62no—
397C2×#67—121no—
398C2×#67—121no—
399C2×#67—121no—
400C2×#67—121no—
401C2×#67—121no—
402C2×#67—121no—
403C22×Dic3—31no—
404C22×Dic3—31no—
405C22×Dic3—31no—
406C22×Dic3—31no—
407C22×Dic3—61no—
408C22×Dic3—61no—
409C22×Dic3C22×D311yescharacteristic
410C22×Dic3C22×D311yescharacteristic
411C22×Dic3C22×D311yescharacteristic
412C22×Dic3C22×D311yescharacteristic
413C22×Dic3C22×D311yescharacteristic
414C2×D12—34no—
415C2×D12—34no—
416C2×D12—41no—
417C2×D12—41no—
418C2×D12—64no—
419C2×D12—62no—
420C2×D12—62no—
421C2×D12—62no—
422C2×D12—62no—
423C2×D12—62no—
424C2×D12—62no—
425C2×D12—62no—
426C2×D12—62no—
427C2×D12—121no—
428C2×D12—121no—
429C2×D12—121no—
430C2×D12—121no—
431C2×D12—122no—
432C2×D12—122no—
433C2×D12—121no—
434C2×D12—121no—
435C2×D12—121no—
436C2×D12—121no—
437C2×D12D1214yescomplemented
438C2×C4×D3—22no—
439C2×C4×D3—41no—
440C2×C4×D3—41no—
441C2×C4×D3—62no—
442C2×C4×D3—62no—
443C2×C4×D3—122no—
444C2×C4×D3—121no—
445C2×C4×D3—121no—
446C2×C4×D3—121no—
447C2×C4×D3—121no—
448C2×C4×D3—122no—
449C2×C4×D3—122no—
450C3×C4⋊C4—62no—
451C3×C4⋊C4—62no—
452C3×C4⋊C4—121no—
453C3×C22⋊C4—62no—
454C3×C22⋊C4—62no—
455C3×C22⋊C4—62no—
456C3×C22⋊C4—121no—
457C3×C22⋊C4—121no—
458C3×C22⋊C4—121no—
459#217—62no—
460#217—62no—
461#217—62no—
462#217—121no—
463(C2×D3)⋊C4—22no—
464(C2×D3)⋊C4—22no—
465(C2×D3)⋊C4—22no—
466(C2×D3)⋊C4—41no—
467(C2×D3)⋊C4—41no—
468(C2×D3)⋊C4—41no—
469(C2×D3)⋊C4—62no—
470(C2×D3)⋊C4—62no—
471(C2×D3)⋊C4—62no—
472(C2×D3)⋊C4—62no—
473(C2×D3)⋊C4—62no—
474(C2×D3)⋊C4—62no—
475(C2×D3)⋊C4—62no—
476(C2×D3)⋊C4—62no—
477(C2×D3)⋊C4—62no—
478(C2×D3)⋊C4—62no—
479(C2×D3)⋊C4—62no—
480(C2×D3)⋊C4—122no—
481(C2×D3)⋊C4—121no—
482(C2×D3)⋊C4—121no—
483(C2×D3)⋊C4—121no—
484(C2×D3)⋊C4—121no—
485(C2×D3)⋊C4—122no—
486(C2×D3)⋊C4—121no—
487(C2×D3)⋊C4—122no—
488C4⋊Dic3—22no—
489C4⋊Dic3—22no—
490C4⋊Dic3—41no—
491C22×C32C22×D411yescharacteristic
492C22×C32C22×D411yescharacteristic
493C22×C32C2×#4111yescharacteristic
494C22×C32H(5,𝔽2)11yescharacteristic
495C22×C32H(5,𝔽2)11yescharacteristic
496C22×C32H(5,𝔽2)11yescharacteristic
497C22×C32H(5,𝔽2)11yescharacteristic
498C2×C3⋊D3—22no—
499C2×C3⋊D3—22no—
500C2×C3⋊D3—22no—
501C2×C3⋊D3—22no—
502C2×C3⋊D3—22no—
503C2×C3⋊D3—22no—
504C2×C3⋊D3—41no—
505C2×C3⋊D3—41no—
506C2×C3⋊D3—41no—
507C2×C3⋊D3—41no—
508C2×C3⋊D3—41no—
509C2×C3⋊D3—41no—
510C2×C3⋊D3—41no—
511C2×C3⋊D3—41no—
512C2×C3×D3—22no—
513C2×C3×D3—22no—
514C2×C3×D3—22no—
515C2×C3×D3—22no—
516C2×C3×D3—22no—
517C2×C3×D3—22no—
518C2×C3×D3—22no—
519C2×C3×D3—22no—
520C2×C3×D3—22no—
521C2×C3×D3—41no—
522C2×C3×D3—41no—
523C2×C3×D3—41no—
524C2×C3×D3—41no—
525C2×C3×D3—41no—
526C2×C3×D3—41no—
527C2×C3×D3—41no—
528C2×C3×D3—41no—
529C2×C3×D3—41no—
530C2×C3×D3—41no—
531C2×C3×D3—41no—
532C2×C3×D3—41no—
533D32—416no—
534C32×C4—22no—
535C32×C4—22no—
536C32×C4—41no—
537C3⋊Dic3—41no—
538C3⋊Dic3—41no—
539C3×Dic3—41no—
540C3×Dic3—41no—
541C3×Dic3—41no—
542C3×Dic3—41no—
543C3×Dic3—41no—
544C25—91no—
545C22×D4—31no—
546C22×D4—91no—
547C22×D4—91no—
548C22×D4—91no—
549C22×D4—91no—
550C22×D4—91no—
551C22×D4—91no—
552C23×C4—31no—
553C23×C4—91no—
554#121—184no—
555#121—184no—
556#120—184no—
557#120—184no—
558C2×C4⋊C4—31no—
559C2×C4⋊C4—31no—
560C2×C4⋊C4—31no—
561C2×C22⋊C4—31no—
562C2×C22⋊C4—31no—
563C2×C22⋊C4—31no—
564C2×C22⋊C4—31no—
565C2×C22⋊C4—31no—
566C2×C22⋊C4—31no—
567C2×C22⋊C4—91no—
568C2×C22⋊C4—91no—
569C2×C22⋊C4—91no—
570C2×C22⋊C4—91no—
571C2×C22⋊C4—91no—
572C2×C22⋊C4—91no—
573C2×C22⋊C4—91no—
574C2×C22⋊C4—91no—
575C2×C22⋊C4—91no—
576C2×C22⋊C4—91no—
577#95—31no—
578#95—91no—
579#95—91no—
580#95—91no—
581#95—91no—
582#95D3211yescharacteristic, complemented
583C23×C3—21no—
584C23×C3—32no—
585C23×C3—32no—
586C23×C3—32no—
587C23×C3—61no—
588C23×C3—61no—
589C23×C3—61no—
590C23×C3—61no—
591C23×C3—61no—
592C23×C3—61no—
593C23×C3—61no—
594C23×C3—61no—
595C23×C3—61no—
596C23×C3—61no—
597C23×C3—61no—
598C23×C3—61no—
599C23×C3—61no—
600C23×C3—61no—
601C23×C3—61no—
602C23×C3—61no—
603C23×C3—61no—
604C23×C3—61no—
605C23×C3C23×D311yescharacteristic
606C23×C3C23×D311yescharacteristic
607C22×D3—21no—
608C22×D3—21no—
609C22×D3—21no—
610C22×D3—21no—
611C22×D3—21no—
612C22×D3—21no—
613C22×D3—21no—
614C22×D3—21no—
615C22×D3—21no—
616C22×D3—21no—
617C22×D3—21no—
618C22×D3—21no—
619C22×D3—21no—
620C22×D3—21no—
621C22×D3—21no—
622C22×D3—21no—
623C22×D3—21no—
624C22×D3—21no—
625C22×D3—32no—
626C22×D3—32no—
627C22×D3—32no—
628C22×D3—32no—
629C22×D3—62no—
630C22×D3—62no—
631C22×D3—62no—
632C22×D3—62no—
633C22×D3—61no—
634C22×D3—61no—
635C22×D3—61no—
636C22×D3—61no—
637C22×D3—61no—
638C22×D3—61no—
639C22×D3—61no—
640C22×D3—61no—
641C22×D3—61no—
642C22×D3—61no—
643C22×D3—61no—
644C22×D3—61no—
645C22×D3—61no—
646C22×D3—61no—
647C22×D3—61no—
648C22×D3—61no—
649C22×D3—61no—
650C22×D3—61no—
651C22×D3—61no—
652C22×D3—61no—
653C22×D3—61no—
654C22×D3—61no—
655C22×D3—61no—
656C22×D3—61no—
657C22×D3—121no—
658C22×D3—121no—
659C22×D3—121no—
660C22×D3—121no—
661C22×D3—121no—
662C22×D3—121no—
663C22×D3—121no—
664C22×D3—121no—
665C22×D3—121no—
666C22×D3—121no—
667C22×D3—124no—
668C22×D3—124no—
669C22×D3—124no—
670C22×D3—124no—
671C22×D3—124no—
672C22×D3—124no—
673C22×D3—124no—
674C22×D3—124no—
675C22×D3—124no—
676C22×D3—124no—
677C22×D3—124no—
678C22×D3—124no—
679C22×D3—124no—
680C22×D3—124no—
681C22×D3C2×D1212yes—
682C22×D3C2×D1212yes—
683C22×D3#23912yes—
684C3×D4—124no—
685C2×C3×C4—21no—
686C2×C3×C4—21no—
687C2×C3×C4—21no—
688C2×C3×C4—21no—
689C2×C3×C4—21no—
690C2×C3×C4—21no—
691C2×C3×C4—21no—
692C2×C3×C4—21no—
693C2×C3×C4—21no—
694C2×C3×C4—21no—
695C2×C3×C4—21no—
696C2×C3×C4—21no—
697C2×C3×C4—21no—
698C2×C3×C4—21no—
699C2×C3×C4—22no—
700C2×C3×C4—22no—
701C2×C3×C4—41no—
702C2×C3×C4—41no—
703C2×C3×C4—41no—
704C2×C3×C4—41no—
705C2×C3×C4—41no—
706C2×C3×C4—41no—
707C2×C3×C4—41no—
708C2×C3×C4—61no—
709C2×C3×C4—61no—
710C2×C3×C4—61no—
711C2×C3×C4—61no—
712C2×C3×C4—61no—
713C2×C3×C4—61no—
714C2×C3×C4—61no—
715C2×C3×C4—61no—
716C2×C3×C4—61no—
717C2×C3×C4—61no—
718C2×C3×C4—61no—
719C2×C3×C4—61no—
720C2×C3×C4—61no—
721C2×C3×C4—61no—
722C2×C3×C4—61no—
723C2×C3×C4—124no—
724C2×C3×C4C2×D1212yes—
725C2×C3×C4D3×D412yes—
726C2×C3×C4D3×D412yes—
727C2×C3×C4D3×D412yes—
728#67—124no—
729#67—124no—
730#67—124no—
731#67—124no—
732#67—124no—
733#67—124no—
734C2×Dic3—21no—
735C2×Dic3—21no—
736C2×Dic3—21no—
737C2×Dic3—21no—
738C2×Dic3—21no—
739C2×Dic3—21no—
740C2×Dic3—21no—
741C2×Dic3—21no—
742C2×Dic3—21no—
743C2×Dic3—21no—
744C2×Dic3—21no—
745C2×Dic3—21no—
746C2×Dic3—21no—
747C2×Dic3—21no—
748C2×Dic3—21no—
749C2×Dic3—62no—
750C2×Dic3—61no—
751C2×Dic3—61no—
752C2×Dic3—61no—
753C2×Dic3—61no—
754C2×Dic3—61no—
755C2×Dic3—61no—
756C2×Dic3—61no—
757C2×Dic3—61no—
758C2×Dic3—61no—
759C2×Dic3—61no—
760C2×Dic3—61no—
761C2×Dic3—61no—
762C2×Dic3—121no—
763C2×Dic3—121no—
764C2×Dic3—121no—
765C2×Dic3—121no—
766C2×Dic3—121no—
767D12—44no—
768D12—124no—
769D12—124no—
770D12—128no—
771D12—124no—
772D12—124no—
773D12—124no—
774D12—124no—
775C4×D3—44no—
776C4×D3—124no—
777C4×D3—124no—
778C4×D3—128no—
779C2×C32#53411yescharacteristic
780C2×C32#53411yescharacteristic
781C2×C32#53811yescharacteristic
782C2×C32D4211yescharacteristic
783C2×C32#54611yescharacteristic
784C2×C32#54611yescharacteristic
785C2×C32#56011yescharacteristic
786C3⋊D3—42no—
787C3⋊D3—42no—
788C3×D3—42no—
789C3×D3—42no—
790C3×D3—42no—
791C24—31no—
792C24—31no—
793C24—31no—
794C24—91no—
795C24—91no—
796C24—182no—
797C24—182no—
798C24—182no—
799C24—361no—
800C24—361no—
801C24—361no—
802C24—361no—
803C2×D4—34no—
804C2×D4—94no—
805C2×D4—121no—
806C2×D4—121no—
807C2×D4—182no—
808C2×D4—182no—
809C2×D4—182no—
810C2×D4—182no—
811C2×D4—182no—
812C2×D4—182no—
813C2×D4—182no—
814C2×D4—182no—
815C2×D4—182no—
816C2×D4—182no—
817C2×D4—361no—
818C2×D4—361no—
819C2×D4—361no—
820C2×D4—361no—
821C2×D4—361no—
822C2×D4—361no—
823C2×D4—361no—
824C22×C4—31no—
825C22×C4—31no—
826C22×C4—31no—
827C22×C4—31no—
828C22×C4—31no—
829C22×C4—62no—
830C22×C4—91no—
831C22×C4—91no—
832C22×C4—121no—
833C22×C4—121no—
834C22×C4—182no—
835C22×C4—361no—
836C22×C4—361no—
837C22×C4C2×D3211yescharacteristic
838C22×C4C2×D3211yescharacteristic
839C22×C4C2×D3211yescharacteristic
840C4⋊C4—62no—
841C4⋊C4—62no—
842C4⋊C4—121no—
843C22⋊C4—62no—
844C22⋊C4—62no—
845C22⋊C4—62no—
846C22⋊C4—121no—
847C22⋊C4—121no—
848C22⋊C4—121no—
849C22⋊C4—182no—
850C22⋊C4—182no—
851C22⋊C4—182no—
852C22⋊C4—182no—
853C22⋊C4—182no—
854C22⋊C4—182no—
855C22⋊C4—182no—
856C22⋊C4—361no—
857C22⋊C4—361no—
858C22⋊C4—361no—
859C22×C3—21no—
860C22×C3—21no—
861C22×C3—21no—
862C22×C3—21no—
863C22×C3—21no—
864C22×C3—21no—
865C22×C3—21no—
866C22×C3—62no—
867C22×C3—62no—
868C22×C3—62no—
869C22×C3—62no—
870C22×C3—62no—
871C22×C3—62no—
872C22×C3—62no—
873C22×C3—62no—
874C22×C3—62no—
875C22×C3—121no—
876C22×C3—121no—
877C22×C3—121no—
878C22×C3—121no—
879C22×C3—121no—
880C22×C3—121no—
881C22×C3—121no—
882C22×C3—121no—
883C22×C3—121no—
884C22×C3—121no—
885C22×C3—121no—
886C22×C3—121no—
887C22×C3C22×D1211yescharacteristic
888C22×C3C2×D3×D411yescharacteristic
889C22×C3C2×D3×D411yescharacteristic
890C22×C3C2×D3×D411yescharacteristic
891C22×C3#100411yescharacteristic
892C22×C3#100411yescharacteristic
893C22×C3#100411yescharacteristic
894C22×C3#100411yescharacteristic
895C22×C3C2×#23911yescharacteristic
896C22×C3D3×#4111yescharacteristic
897C22×C3#100911yescharacteristic
898C22×C3#100911yescharacteristic
899C22×C3#100911yescharacteristic
900C22×C3#100911yescharacteristic
901C2×D3—22no—
902C2×D3—22no—
903C2×D3—22no—
904C2×D3—22no—
905C2×D3—22no—
906C2×D3—22no—
907C2×D3—22no—
908C2×D3—22no—
909C2×D3—22no—
910C2×D3—41no—
911C2×D3—41no—
912C2×D3—41no—
913C2×D3—41no—
914C2×D3—41no—
915C2×D3—41no—
916C2×D3—41no—
917C2×D3—41no—
918C2×D3—41no—
919C2×D3—41no—
920C2×D3—41no—
921C2×D3—41no—
922C2×D3—64no—
923C2×D3—62no—
924C2×D3—62no—
925C2×D3—62no—
926C2×D3—62no—
927C2×D3—62no—
928C2×D3—62no—
929C2×D3—62no—
930C2×D3—62no—
931C2×D3—62no—
932C2×D3—62no—
933C2×D3—62no—
934C2×D3—62no—
935C2×D3—122no—
936C2×D3—122no—
937C2×D3—122no—
938C2×D3—122no—
939C2×D3—122no—
940C2×D3—1216no—
941C2×D3—1216no—
942C2×D3—122no—
943C2×D3—122no—
944C2×D3—122no—
945C2×D3—122no—
946C2×D3—121no—
947C2×D3—121no—
948C2×D3—121no—
949C2×D3—121no—
950C2×D3—121no—
951C2×D3—121no—
952C2×D3—121no—
953C2×D3—121no—
954C2×D3—121no—
955C2×D3—121no—
956C2×D3—121no—
957C2×D3—121no—
958C2×D3—121no—
959C2×D3—121no—
960C2×D3—121no—
961C2×D3—121no—
962C2×D3—241no—
963C2×D3—241no—
964C2×D3—241no—
965C2×D3—241no—
966C3×C4—22no—
967C3×C4—22no—
968C3×C4—22no—
969C3×C4—22no—
970C3×C4—42no—
971C3×C4—42no—
972C3×C4—41no—
973C3×C4—41no—
974C3×C4—81no—
975C3×C4—121no—
976C3×C4—121no—
977C3×C4—121no—
978C3×C4—121no—
979C3×C4—121no—
980Dic3—41no—
981Dic3—41no—
982Dic3—41no—
983Dic3—41no—
984Dic3—41no—
985Dic3—122no—
986Dic3—121no—
987Dic3—121no—
988Dic3—121no—
989Dic3—121no—
990Dic3—241no—
991C32#266811yescharacteristic, complemented, Sylow
992C23—32no—
993C23—32no—
994C23—32no—
995C23—61no—
996C23—61no—
997C23—61no—
998C23—61no—
999C23—61no—
1000C23—61no—
1001C23—61no—
1002C23—61no—
1003C23—61no—
1004C23—61no—
1005C23—61no—
1006C23—61no—
1007C23—61no—
1008C23—61no—
1009C23—61no—
1010C23—61no—
1011C23—61no—
1012C23—61no—
1013C23—92no—
1014C23—92no—
1015C23—181no—
1016C23—181no—
1017C23—181no—
1018C23—181no—
1019C23—181no—
1020C23—181no—
1021C23—181no—
1022C23—181no—
1023C23—181no—
1024C23—181no—
1025C23—181no—
1026C23—181no—
1027C23—364no—
1028C23—364no—
1029C23—364no—
1030C23—364no—
1031C23—364no—
1032C23—364no—
1033C23—364no—
1034C23C22×D3211yescharacteristic
1035D4—124no—
1036D4—364no—
1037D4—364no—
1038D4—364no—
1039D4—364no—
1040D4—364no—
1041D4—364no—
1042C2×C4—21no—
1043C2×C4—21no—
1044C2×C4—21no—
1045C2×C4—21no—
1046C2×C4—21no—
1047C2×C4—21no—
1048C2×C4—21no—
1049C2×C4—61no—
1050C2×C4—61no—
1051C2×C4—61no—
1052C2×C4—61no—
1053C2×C4—61no—
1054C2×C4—61no—
1055C2×C4—61no—
1056C2×C4—61no—
1057C2×C4—61no—
1058C2×C4—61no—
1059C2×C4—61no—
1060C2×C4—61no—
1061C2×C4—61no—
1062C2×C4—61no—
1063C2×C4—61no—
1064C2×C4—124no—
1065C2×C4—181no—
1066C2×C4—181no—
1067C2×C4—181no—
1068C2×C4—181no—
1069C2×C4—181no—
1070C2×C4—181no—
1071C2×C4—364no—
1072C2×C4D3×D1212yes—
1073C2×C4#380212yes—
1074C2×C3—21no—
1075C2×C3—21no—
1076C2×C3—21no—
1077C2×C3—21no—
1078C2×C3—21no—
1079C2×C3—21no—
1080C2×C3—21no—
1081C2×C3—122no—
1082C2×C3—122no—
1083C2×C3—122no—
1084C2×C3#549311yescharacteristic
1085C2×C3D4×D1211yescharacteristic
1086C2×C3#555411yescharacteristic
1087C2×C3#558911yescharacteristic
1088C2×C3#561211yescharacteristic
1089C2×C3#562011yescharacteristic
1090C2×C3#563011yescharacteristic
1091C2×C3#563011yescharacteristic
1092C2×C3#564411yescharacteristic
1093C2×C3#565311yescharacteristic
1094C2×C3#565311yescharacteristic
1095C2×C3#565711yescharacteristic
1096C2×C3#566611yescharacteristic
1097C2×C3#571711yescharacteristic
1098D3—42no—
1099D3—42no—
1100D3—42no—
1101D3—124no—
1102D3—122no—
1103D3—122no—
1104D3—122no—
1105D3—122no—
1106D3—242no—
1107C22—62no—
1108C22—62no—
1109C22—62no—
1110C22—62no—
1111C22—62no—
1112C22—62no—
1113C22—62no—
1114C22—62no—
1115C22—62no—
1116C22—121no—
1117C22—121no—
1118C22—121no—
1119C22—121no—
1120C22—121no—
1121C22—121no—
1122C22—121no—
1123C22—121no—
1124C22—121no—
1125C22—121no—
1126C22—121no—
1127C22—121no—
1128C22—182no—
1129C22—182no—
1130C22—182no—
1131C22—182no—
1132C22—182no—
1133C22—182no—
1134C22—3616no—
1135C22—361no—
1136C22—361no—
1137C22—361no—
1138C22—361no—
1139C22—361no—
1140C22—361no—
1141C22—361no—
1142C22—361no—
1143C22C2×D3×D1211yescharacteristic
1144C22C2×#380211yescharacteristic
1145C22#6430711yescharacteristic
1146C22#6431411yescharacteristic
1147C22#6431411yescharacteristic
1148C22#6431411yescharacteristic
1149C22D3×#23911yescharacteristic
1150C4—22no—
1151C4—22no—
1152C4—41no—
1153C4—121no—
1154C4—121no—
1155C4—121no—
1156C4—121no—
1157C4—121no—
1158C4—361no—
1159C4—361no—
1160C3—21no—
1161C3#7491011yescharacteristic, complemented
1162C3#7811211yescharacteristic, complemented
1163C2—122no—
1164C2—122no—
1165C2—122no—
1166C2—362no—
1167C2—362no—
1168C2#1059400411yescharacteristic
1169C2#1059429111yescharacteristic
1170C2#1059429611yescharacteristic
1171C2#1059430811yescharacteristic
1172C2#1059462911yescharacteristic
1173C2#1059463311yescharacteristic
1174C2#1059465011yescharacteristic
subgroupG/H
center, FrattiniC23C22×D32
commutator, socle, cosocleC23×C32C24
FittingC32×#95C22
hypercenter#95D32
hypocenterC32#2668
LCSG ▷ C23×C32 ▷ C32
UCSC1 ◁ C23 ◁ #95

Complements

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

NH ≅ G/Ntype
1. C2×#63923C2semidirect
2. C2×#63922C2semidirect
3. C2×#63916C2semidirect
4. C2×#63909C2semidirect
5. #10592364C2semidirect
6. C3×#4677C2semidirect
7. C3×#4665C2semidirect
8. #10591399C2semidirect
9. #10591393C2semidirect
10. #10591392C2semidirect
11. #10591392C2semidirect
12. #10591387C2semidirect
13. #10591381C2semidirect
14. #10591326C2semidirect
15. #10591314C2semidirect
20. C22×C4×C3⋊D3C22semidirect
22. C22×C3×C4×D3C22semidirect
26. C22×#626C22semidirect
30. C2×#3752C22semidirect
36. C2×C3×(C2×D3)⋊C4C22semidirect
37. C2×C3×C4⋊Dic3C22semidirect
38. C2×C3×C4⋊Dic3C22semidirect
39. C2×C3×C4⋊Dic3C22semidirect
42. C2×#3722C22semidirect
46. C2×(C2×D3)⋊Dic3C22semidirect
51. C32×#95C22semidirect
52. #63658C22semidirect
53. C3×C3⋊#95C22semidirect
54. #63579C22semidirect
55. #63579C22semidirect
56. #63579C22semidirect
81. #4677D3semidirect
87. #4665D3semidirect
107. C2×C4⋊(C3⋊D3)D4semidirect
118. C2×C3×D12D4semidirect
178. C22×C4×D3C2×D3semidirect
219. C2×(C2×D3)⋊C4C2×D3semidirect
220. C2×C4⋊Dic3C2×D3semidirect
221. C2×C4⋊Dic3C2×D3semidirect
222. C2×C4⋊Dic3C2×D3semidirect
230. C3×#95C2×D3semidirect
231. C3×#95C2×D3semidirect
241. C3⋊#95C2×D3semidirect
437. C2×D12D12semidirect
582. #95D32semidirect
991. C32#2668semidirect
1161. C3#74910semidirect
1162. C3#78112semidirect

Maximal subgroups

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

subgroupindex
C2×#639232
C2×#639222
C2×#639162
C2×#639092
#105923642
C3×#46772
C3×#46652
#105913992
#105913932
#105913922
#105913872
#105913812
#105913262
#105913142
#781123
#749103