Finite Group Databasebeta

← #11836006

Subgroups — #11836006

Order 1152.

1751 conjugacy classes of subgroups.

The subgroup lattice has 1174 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×#63910C211yesmaximal, characteristic, complemented
4C2×#63886C211yesmaximal, characteristic, complemented
5#10592690C211yesmaximal, characteristic, complemented
6C3×#4993C211yesmaximal, characteristic, complemented
7C3×#4991C211yesmaximal, characteristic, complemented
8#10591399C211yesmaximal, characteristic, complemented
9#10591393C211yesmaximal, characteristic, complemented
10#10591364C211yesmaximal, characteristic, complemented
11#10591363C211yesmaximal, characteristic, complemented
12#10591301C211yesmaximal, characteristic, complemented
13#10591275C211yesmaximal, characteristic, complemented
14#10591275C211yesmaximal, characteristic, complemented
15#10591204C211yesmaximal, characteristic, complemented
16#78112—31nomaximal
17#77127—31nomaximal
18C23×D32C2211yescharacteristic
19C22×C4⋊(C3⋊D3)C2211yescharacteristic
20C22×C3×D12C2211yescharacteristic
21C22×#626C2211yescharacteristic
22C22×#626C2211yescharacteristic
23C22×#626C2211yescharacteristic
24C22×#626C2211yescharacteristic, complemented
25C22×#625C2211yescharacteristic
26C22×#624C2211yescharacteristic, complemented
27C22×D3×Dic3C2211yescharacteristic, complemented
28C2×C32×C4⋊C4C2211yescharacteristic, complemented
29C2×#3752C2211yescharacteristic
30C2×#3752C2211yescharacteristic
31C2×#3752C2211yescharacteristic, complemented
32C2×#3752C2211yescharacteristic, complemented
33C2×C3×(C2×D3)⋊C4C2211yescharacteristic
34C2×C3×(C2×D3)⋊C4C2211yescharacteristic
35C2×C3×(C2×D3)⋊C4C2211yescharacteristic
36C2×C3×(C2×D3)⋊C4C2211yescharacteristic
37C2×C3×(C2×D3)⋊C4C2211yescharacteristic
38C2×C3×(C2×D3)⋊C4C2211yescharacteristic, complemented
39C2×C3×(C2×D3)⋊C4C2211yescharacteristic, complemented
40C2×C3×Dic3⋊C4C2211yescharacteristic, complemented
41C2×C3×Dic3⋊C4C2211yescharacteristic, complemented
42C2×#3722C2211yescharacteristic
43C2×#3722C2211yescharacteristic
44C2×(C2×D3)⋊Dic3C2211yescharacteristic
45C2×(C2×D3)⋊Dic3C2211yescharacteristic
46C2×(C2×D3)⋊Dic3C2211yescharacteristic
47#63923—24no—
48#63922—24no—
49#63910—24no—
50#63886—24no—
51#63658C2211yescharacteristic, complemented
52C3×C3⋊#95C2211yescharacteristic, complemented
53C3×C3⋊#95C2211yescharacteristic, complemented
54#63579C2211yescharacteristic, complemented
55#63579C2211yescharacteristic, complemented
56#63579C2211yescharacteristic, complemented
57C2×#939—31no—
58C2×#937—31no—
59C2×#895—31no—
60C2×#895—31no—
61C2×#884—31no—
62C2×#882—31no—
63C2×#882—31no—
64C2×#882—31no—
65C3×#399—31no—
66C3×#394—31no—
67#4993D311yescharacteristic, complemented
68#4992—31no—
69#4992—31no—
70#4991—31no—
71#4991—31no—
72#4991—61no—
73#4991D311yescharacteristic, complemented
74#4960—31no—
75#4960—31no—
76#4958—31no—
77#4958—31no—
78#4956—31no—
79#4956—31no—
80#4956—31no—
81#4955—31no—
82#4955—31no—
83#4952—31no—
84#4675—31no—
85#4665—31no—
86#4665—31no—
87#4665—31no—
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)—22no—
106C2×C4⋊(C3⋊D3)—22no—
107C2×C4⋊(C3⋊D3)—41no—
108C22×C3×Dic3C2311yescharacteristic
109C22×C3×Dic3C2311yescharacteristic
110C22×C3×Dic3C2311yescharacteristic
111C22×C3×Dic3C2311yescharacteristic
112C22×C3×Dic3C2311yescharacteristic
113C2×C3×D12—22no—
114C2×C3×D12—22no—
115C2×C3×D12—41no—
116C2×#626—22no—
117C2×#626—22no—
118C2×#626—22no—
119C2×#626—22no—
120C2×#626—41no—
121C2×#626—41no—
122C2×#626—41no—
123C2×#626—41no—
124C2×#626—41no—
125C2×#626—41no—
126C2×#626D414yescomplemented
127C2×#626D414yescomplemented
128C2×#625—22no—
129C2×#625—22no—
130C2×#625—41no—
131C2×#624—22no—
132C2×#624—41no—
133C2×#624—41no—
134C2×D3×Dic3—22no—
135C2×D3×Dic3—41no—
136C2×D3×Dic3—41no—
137C32×C4⋊C4—41no—
138#3752—22no—
139#3752—22no—
140#3752—41no—
141#3752—41no—
142C3×(C2×D3)⋊C4—22no—
143C3×(C2×D3)⋊C4—22no—
144C3×(C2×D3)⋊C4—22no—
145C3×(C2×D3)⋊C4—22no—
146C3×(C2×D3)⋊C4—41no—
147C3×(C2×D3)⋊C4—41no—
148C3×(C2×D3)⋊C4—41no—
149C3×Dic3⋊C4—22no—
150C3×Dic3⋊C4—22no—
151#3722—22no—
152#3722—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—
160C22×#67—31no—
161C22×#67—31no—
162C22×#67—31no—
163C22×#67—31no—
164C22×#67—31no—
165C22×#67—31no—
166C23×Dic3—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—31no—
178C2×C3×C4⋊C4—21no—
179C2×C3×C4⋊C4—31no—
180C2×C3×C4⋊C4—31no—
181C2×C3×C4⋊C4C2×D311yescharacteristic, complemented
182C2×C3×C4⋊C4C2×D311yescharacteristic, complemented
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×C3×C22⋊C4—31no—
189C2×C3×C22⋊C4—31no—
190C2×#217—31no—
191C2×#217—31no—
192C2×#217—31no—
193#939—64no—
194#937—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—61no—
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×(C2×D3)⋊C4C2×D311yescharacteristic, complemented
221C2×Dic3⋊C4C2×D311yescharacteristic, complemented
222C2×Dic3⋊C4C2×D311yescharacteristic, complemented
223#895—64no—
224#895—64no—
225#884—64no—
226#882—64no—
227#882—64no—
228#882—64no—
229C3×#95—31no—
230C3×#95—31no—
231C3⋊#95—31no—
232C3⋊#95—31no—
233C3⋊#95—31no—
234C3⋊#95—31no—
235C3⋊#95—31no—
236C3⋊#95—31no—
237C3⋊#95—31no—
238C3⋊#95—31no—
239C3⋊#95—61no—
240C3⋊#95C2×D311yescharacteristic, complemented
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×C4—21no—
293C2×C32×C4—21no—
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—
301C2×C3×Dic3—21no—
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×Dic3C2×D412yes—
315C2×C3×Dic3C2×D412yes—
316C3×D12—44no—
317#626—44no—
318#626—44no—
319#626—44no—
320#626—44no—
321#625—44no—
322#624—44no—
323D3×Dic3—44no—
324C2×#121—91no—
325C2×#121—91no—
326C2×#120—91no—
327C2×#120—91no—
328#399—31no—
329#397—91no—
330#397—91no—
331#394—31no—
332#394—91no—
333#392—91no—
334#386—91no—
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—62no—
366C2×C3×D4—62no—
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×C4C22×D311yescharacteristic
377C22×C3×C4C22×D311yescharacteristic
378C22×C3×C4C22×D311yescharacteristic
379C22×C3×C4C22×D311yescharacteristic
380C22×C3×C4C22×D311yescharacteristic
381C22×C3×C4C22×D311yescharacteristic
382C2×#67—34no—
383C2×#67—34no—
384C2×#67—62no—
385C2×#67—62no—
386C2×#67—62no—
387C2×#67—62no—
388C2×#67—62no—
389C2×#67—62no—
390C2×#67—62no—
391C2×#67—62no—
392C2×#67—121no—
393C2×#67—121no—
394C2×#67—121no—
395C2×#67—121no—
396C2×#67—121no—
397C2×#67—121no—
398C2×#67—121no—
399C2×#67—121no—
400C22×Dic3—31no—
401C22×Dic3—31no—
402C22×Dic3—31no—
403C22×Dic3—31no—
404C22×Dic3—61no—
405C22×Dic3—61no—
406C22×Dic3—62no—
407C22×Dic3—121no—
408C22×Dic3—121no—
409C22×Dic3C22×D311yescharacteristic
410C22×Dic3C22×D311yescharacteristic
411C22×Dic3C22×D311yescharacteristic
412C22×Dic3C22×D311yescharacteristic
413C22×Dic3C22×D311yescharacteristic
414C2×D12—22no—
415C2×D12—22no—
416C2×D12—34no—
417C2×D12—34no—
418C2×D12—41no—
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—122no—
428C2×D12—122no—
429C2×D12—121no—
430C2×D12—121no—
431C2×D12—122no—
432C2×D12—121no—
433C2×D12—121no—
434C2×D12—121no—
435C2×D12—121no—
436C2×D12—121no—
437C2×D12—121no—
438C2×C4×D3—62no—
439C2×C4×D3—62no—
440C2×C4×D3—62no—
441C2×C4×D3—121no—
442C2×C4×D3—121no—
443C2×C4×D3—121no—
444C2×C4×D3—121no—
445C2×C4×D3—121no—
446C2×C4×D3—121no—
447C3×C4⋊C4—41no—
448C3×C4⋊C4—41no—
449C3×C4⋊C4—42no—
450C3×C4⋊C4—62no—
451C3×C4⋊C4—62no—
452C3×C22⋊C4—62no—
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—121no—
462(C2×D3)⋊C4—22no—
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—122no—
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—121no—
486(C2×D3)⋊C4—122no—
487(C2×D3)⋊C4—122no—
488Dic3⋊C4—22no—
489Dic3⋊C4—22no—
490C22×C32C22×D411yescharacteristic
491C22×C32C22×D411yescharacteristic
492C22×C32C2×#4111yescharacteristic
493C22×C32H(5,𝔽2)11yescharacteristic
494C22×C32H(5,𝔽2)11yescharacteristic
495C22×C32H(5,𝔽2)11yescharacteristic
496C22×C32H(5,𝔽2)11yescharacteristic
497C2×C3⋊D3—22no—
498C2×C3⋊D3—22no—
499C2×C3⋊D3—22no—
500C2×C3⋊D3—22no—
501C2×C3⋊D3—22no—
502C2×C3⋊D3—22no—
503C2×C3⋊D3—41no—
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—22no—
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—41no—
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—
532D32—416no—
533C32×C4—41no—
534C32×C4—41no—
535C32×C4—41no—
536C3⋊Dic3—41no—
537C3⋊Dic3—41no—
538C3×Dic3—22no—
539C3×Dic3—22no—
540C3×Dic3—41no—
541C3×Dic3—41no—
542C3×Dic3—41no—
543C25—91no—
544C22×D4—31no—
545C22×D4—91no—
546C22×D4—91no—
547C22×D4—91no—
548C22×D4—91no—
549C22×D4—91no—
550C22×D4—91no—
551C23×C4—91no—
552C23×C4—91no—
553#121—184no—
554#121—184no—
555#120—184no—
556#120—184no—
557C2×C4⋊C4—31no—
558C2×C4⋊C4—31no—
559C2×C4⋊C4D3211yescharacteristic, complemented
560C2×C22⋊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—
576#95—31no—
577#95—31no—
578#95—91no—
579#95—91no—
580#95—91no—
581#95—91no—
582C23×C3—21no—
583C23×C3—32no—
584C23×C3—32no—
585C23×C3—32no—
586C23×C3—61no—
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×C3C23×D311yescharacteristic
605C23×C3C23×D311yescharacteristic
606C22×D3—21no—
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—32no—
625C22×D3—32no—
626C22×D3—32no—
627C22×D3—32no—
628C22×D3—62no—
629C22×D3—62no—
630C22×D3—61no—
631C22×D3—61no—
632C22×D3—61no—
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—121no—
655C22×D3—121no—
656C22×D3—121no—
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—124no—
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×D3D3×D412yes—
681C22×D3D3×D412yes—
682C22×D3#23912yes—
683C3×D4—124no—
684C2×C3×C4—22no—
685C2×C3×C4—22no—
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—21no—
700C2×C3×C4—21no—
701C2×C3×C4—21no—
702C2×C3×C4—21no—
703C2×C3×C4—21no—
704C2×C3×C4—32no—
705C2×C3×C4—32no—
706C2×C3×C4—41no—
707C2×C3×C4—41no—
708C2×C3×C4—41no—
709C2×C3×C4—41no—
710C2×C3×C4—41no—
711C2×C3×C4—41no—
712C2×C3×C4—41no—
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—61no—
724C2×C3×C4—61no—
725C2×C3×C4—61no—
726#67—124no—
727#67—124no—
728#67—124no—
729#67—124no—
730#67—124no—
731#67—124no—
732C2×Dic3—21no—
733C2×Dic3—21no—
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—61no—
746C2×Dic3—61no—
747C2×Dic3—61no—
748C2×Dic3—61no—
749C2×Dic3—61no—
750C2×Dic3—61no—
751C2×Dic3—61no—
752C2×Dic3—61no—
753C2×Dic3—61no—
754C2×Dic3—61no—
755C2×Dic3—61no—
756C2×Dic3—61no—
757C2×Dic3—121no—
758C2×Dic3—121no—
759C2×Dic3—121no—
760C2×Dic3—121no—
761C2×Dic3—121no—
762C2×Dic3—121no—
763C2×Dic3—124no—
764C2×Dic3D3×D412yes—
765C2×Dic3D3×D412yes—
766D12—44no—
767D12—124no—
768D12—124no—
769D12—128no—
770D12—124no—
771D12—124no—
772D12—124no—
773D12—124no—
774C4×D3—124no—
775C4×D3—124no—
776C4×D3—124no—
777C2×C32#53411yescharacteristic
778C2×C32#53411yescharacteristic
779C2×C32#53811yescharacteristic
780C2×C32D4211yescharacteristic
781C2×C32#54611yescharacteristic
782C2×C32#54611yescharacteristic
783C2×C32#56011yescharacteristic
784C3⋊D3—42no—
785C3⋊D3—42no—
786C3×D3—42no—
787C3×D3—42no—
788C3×D3—42no—
789C24—31no—
790C24—31no—
791C24—31no—
792C24—91no—
793C24—91no—
794C24—182no—
795C24—182no—
796C24—182no—
797C24—361no—
798C24—361no—
799C24—361no—
800C24—361no—
801C2×D4—62no—
802C2×D4—62no—
803C2×D4—94no—
804C2×D4—94no—
805C2×D4—121no—
806C2×D4—182no—
807C2×D4—182no—
808C2×D4—182no—
809C2×D4—182no—
810C2×D4—182no—
811C2×D4—182no—
812C2×D4—182no—
813C2×D4—182no—
814C2×D4—361no—
815C2×D4—361no—
816C2×D4—361no—
817C2×D4—361no—
818C2×D4—361no—
819C2×D4—361no—
820C2×D4—361no—
821C2×D4—361no—
822C22×C4—31no—
823C22×C4—31no—
824C22×C4—31no—
825C22×C4—31no—
826C22×C4—31no—
827C22×C4—91no—
828C22×C4—91no—
829C22×C4—182no—
830C22×C4—182no—
831C22×C4—361no—
832C22×C4—361no—
833C22×C4—361no—
834C22×C4—361no—
835C22×C4C2×D3211yescharacteristic
836C22×C4C2×D3211yescharacteristic
837C22×C4C2×D3211yescharacteristic
838C4⋊C4—41no—
839C4⋊C4—62no—
840C4⋊C4—62no—
841C22⋊C4—62no—
842C22⋊C4—62no—
843C22⋊C4—62no—
844C22⋊C4—62no—
845C22⋊C4—121no—
846C22⋊C4—121no—
847C22⋊C4—121no—
848C22⋊C4—182no—
849C22⋊C4—182no—
850C22⋊C4—182no—
851C22⋊C4—182no—
852C22⋊C4—182no—
853C22⋊C4—182no—
854C22⋊C4—361no—
855C22⋊C4—361no—
856C22⋊C4—361no—
857C22×C3—21no—
858C22×C3—21no—
859C22×C3—21no—
860C22×C3—21no—
861C22×C3—21no—
862C22×C3—21no—
863C22×C3—21no—
864C22×C3—62no—
865C22×C3—62no—
866C22×C3—62no—
867C22×C3—62no—
868C22×C3—62no—
869C22×C3—62no—
870C22×C3—62no—
871C22×C3—62no—
872C22×C3—62no—
873C22×C3—121no—
874C22×C3—121no—
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×C3C2×D3×D411yescharacteristic
886C22×C3C2×D3×D411yescharacteristic
887C22×C3C2×D3×D411yescharacteristic
888C22×C3C2×D3×D411yescharacteristic
889C22×C3#100411yescharacteristic
890C22×C3#100411yescharacteristic
891C22×C3#100411yescharacteristic
892C22×C3C2×#23911yescharacteristic
893C22×C3D3×#4111yescharacteristic
894C22×C3#100911yescharacteristic
895C22×C3#100911yescharacteristic
896C22×C3#100911yescharacteristic
897C22×C3#100911yescharacteristic
898C22×C3#100911yescharacteristic
899C2×D3—22no—
900C2×D3—22no—
901C2×D3—22no—
902C2×D3—22no—
903C2×D3—22no—
904C2×D3—22no—
905C2×D3—22no—
906C2×D3—22no—
907C2×D3—22no—
908C2×D3—41no—
909C2×D3—41no—
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—62no—
921C2×D3—62no—
922C2×D3—62no—
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—122no—
933C2×D3—122no—
934C2×D3—122no—
935C2×D3—122no—
936C2×D3—122no—
937C2×D3—122no—
938C2×D3—1216no—
939C2×D3—1216no—
940C2×D3—121no—
941C2×D3—121no—
942C2×D3—121no—
943C2×D3—121no—
944C2×D3—121no—
945C2×D3—121no—
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—241no—
957C2×D3—241no—
958C2×D3—241no—
959C2×D3—241no—
960C2×D3—241no—
961C2×D3—241no—
962C2×D3—241no—
963C2×D3—241no—
964C3×C4—42no—
965C3×C4—42no—
966C3×C4—41no—
967C3×C4—41no—
968C3×C4—41no—
969C3×C4—41no—
970C3×C4—41no—
971C3×C4—41no—
972C3×C4—62no—
973C3×C4—62no—
974C3×C4—81no—
975C3×C4—121no—
976C3×C4—121no—
977C3×C4—121no—
978Dic3—22no—
979Dic3—22no—
980Dic3—41no—
981Dic3—41no—
982Dic3—41no—
983Dic3—121no—
984Dic3—121no—
985Dic3—121no—
986Dic3—121no—
987Dic3—241no—
988Dic3—241no—
989C32#266811yescharacteristic, complemented, Sylow
990C23—32no—
991C23—32no—
992C23—32no—
993C23—61no—
994C23—61no—
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—92no—
1012C23—92no—
1013C23—181no—
1014C23—181no—
1015C23—181no—
1016C23—181no—
1017C23—181no—
1018C23—181no—
1019C23—181no—
1020C23—181no—
1021C23—181no—
1022C23—181no—
1023C23—181no—
1024C23—181no—
1025C23—364no—
1026C23—364no—
1027C23—364no—
1028C23—364no—
1029C23—364no—
1030C23—364no—
1031C23—364no—
1032C23C22×D3211yescharacteristic
1033D4—124no—
1034D4—364no—
1035D4—364no—
1036D4—364no—
1037D4—364no—
1038D4—364no—
1039D4—364no—
1040C2×C4—21no—
1041C2×C4—21no—
1042C2×C4—21no—
1043C2×C4—21no—
1044C2×C4—21no—
1045C2×C4—21no—
1046C2×C4—21no—
1047C2×C4—21no—
1048C2×C4—21no—
1049C2×C4—32no—
1050C2×C4—32no—
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—181no—
1065C2×C4—181no—
1066C2×C4—181no—
1067C2×C4—181no—
1068C2×C4—181no—
1069C2×C4—181no—
1070C2×C4—364no—
1071C2×C4—364no—
1072C2×C3—21no—
1073C2×C3—21no—
1074C2×C3—21no—
1075C2×C3—21no—
1076C2×C3—21no—
1077C2×C3—21no—
1078C2×C3—21no—
1079C2×C3—122no—
1080C2×C3—122no—
1081C2×C3—122no—
1082C2×C3#559011yescharacteristic
1083C2×C3#560511yescharacteristic
1084C2×C3#561011yescharacteristic
1085C2×C3#562011yescharacteristic
1086C2×C3#563011yescharacteristic
1087C2×C3#563011yescharacteristic
1088C2×C3#564411yescharacteristic
1089C2×C3#565311yescharacteristic
1090C2×C3#565311yescharacteristic
1091C2×C3#565311yescharacteristic
1092C2×C3#565411yescharacteristic
1093C2×C3#566611yescharacteristic
1094C2×C3#567811yescharacteristic
1095C2×C3#571711yescharacteristic
1096D3—42no—
1097D3—42no—
1098D3—42no—
1099D3—122no—
1100D3—122no—
1101D3—122no—
1102D3—122no—
1103D3—242no—
1104D3—242no—
1105C22—62no—
1106C22—62no—
1107C22—62no—
1108C22—62no—
1109C22—62no—
1110C22—62no—
1111C22—62no—
1112C22—62no—
1113C22—62no—
1114C22—121no—
1115C22—121no—
1116C22—121no—
1117C22—121no—
1118C22—121no—
1119C22—121no—
1120C22—121no—
1121C22—121no—
1122C22—121no—
1123C22—121no—
1124C22—121no—
1125C22—121no—
1126C22—182no—
1127C22—182no—
1128C22—182no—
1129C22—182no—
1130C22—182no—
1131C22—182no—
1132C22—3616no—
1133C22—361no—
1134C22—361no—
1135C22—361no—
1136C22—361no—
1137C22—361no—
1138C22—361no—
1139C22—361no—
1140C22—361no—
1141C22#6430711yescharacteristic
1142C22#6430811yescharacteristic
1143C22D32×D411yescharacteristic
1144C22D32×D411yescharacteristic
1145C22D3×#23911yescharacteristic
1146C22#6432011yescharacteristic
1147C22#6433011yescharacteristic
1148C4—41no—
1149C4—41no—
1150C4—41no—
1151C4—62no—
1152C4—62no—
1153C4—121no—
1154C4—121no—
1155C4—121no—
1156C4—361no—
1157C4—361no—
1158C3—21no—
1159C3#7712711yescharacteristic, complemented
1160C3#7811211yescharacteristic, complemented
1161C2—122no—
1162C2—122no—
1163C2—122no—
1164C2—362no—
1165C2—362no—
1166C2#1059461011yescharacteristic
1167C2#1059461111yescharacteristic
1168C2#1059462011yescharacteristic
1169C2#1059462211yescharacteristic
1170C2#1059509011yescharacteristic
1171C2#1059529511yescharacteristic
1172C2#1059543511yescharacteristic
subgroupG/H
center, FrattiniC23C22×D32
commutator, socle, cosocleC23×C32C24
FittingC2×C32×C4⋊C4C22
hypercenterC2×C4⋊C4D32
hypocenterC32#2668
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×#63923C2semidirect
2. C2×#63922C2semidirect
3. C2×#63910C2semidirect
4. C2×#63886C2semidirect
5. #10592690C2semidirect
6. C3×#4993C2semidirect
7. C3×#4991C2semidirect
8. #10591399C2semidirect
9. #10591393C2semidirect
10. #10591364C2semidirect
11. #10591363C2semidirect
12. #10591301C2semidirect
13. #10591275C2semidirect
14. #10591275C2semidirect
15. #10591204C2semidirect
24. C22×#626C22semidirect
26. C22×#624C22semidirect
27. C22×D3×Dic3C22semidirect
28. C2×C32×C4⋊C4C22semidirect
31. C2×#3752C22semidirect
32. C2×#3752C22semidirect
38. C2×C3×(C2×D3)⋊C4C22semidirect
39. C2×C3×(C2×D3)⋊C4C22semidirect
40. C2×C3×Dic3⋊C4C22semidirect
41. C2×C3×Dic3⋊C4C22semidirect
51. #63658C22semidirect
52. C3×C3⋊#95C22semidirect
53. C3×C3⋊#95C22semidirect
54. #63579C22semidirect
55. #63579C22semidirect
56. #63579C22semidirect
67. #4993D3semidirect
73. #4991D3semidirect
126. C2×#626D4semidirect
127. C2×#626D4semidirect
181. C2×C3×C4⋊C4C2×D3semidirect
182. C2×C3×C4⋊C4C2×D3semidirect
219. C2×(C2×D3)⋊C4C2×D3semidirect
220. C2×(C2×D3)⋊C4C2×D3semidirect
221. C2×Dic3⋊C4C2×D3semidirect
222. C2×Dic3⋊C4C2×D3semidirect
240. C3⋊#95C2×D3semidirect
241. C3⋊#95C2×D3semidirect
559. C2×C4⋊C4D32semidirect
989. C32#2668semidirect
1159. C3#77127semidirect
1160. 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×#639102
C2×#638862
#105926902
C3×#49932
C3×#49912
#105913992
#105913932
#105913642
#105913632
#105913012
#105912752
#105912042
#781123
#771273