Finite Group Databasebeta

← #11835999

Subgroups — #11835999

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×C3×#884C211yesmaximal, characteristic, complemented
2C2×#63983C211yesmaximal, characteristic, complemented
3C2×#63980C211yesmaximal, characteristic, complemented
4C2×#63922C211yesmaximal, characteristic, complemented
5#10592657C211yesmaximal, characteristic, complemented
6C3×#4959C211yesmaximal, characteristic, complemented
7#10591724C211yesmaximal, characteristic, complemented
8#10591713C211yesmaximal, characteristic, complemented
9#10591399C211yesmaximal, characteristic, complemented
10#10591382C211yesmaximal, characteristic, complemented
11#10591381C211yesmaximal, characteristic, complemented
12#10591301C211yesmaximal, characteristic, complemented
13#10591300C211yesmaximal, characteristic, complemented
14#10591299C211yesmaximal, characteristic, complemented
15#10591203C211yesmaximal, characteristic, complemented
16#82713—31nomaximal
17#77127—31nomaximal
18C23×D32C2211yescharacteristic
19C22×#638C2211yescharacteristic
20C23×C3⋊Dic3C2211yescharacteristic, complemented
21C22×C3×#67C2211yescharacteristic
22C22×C3×#67C2211yescharacteristic
23C22×C3×#67C2211yescharacteristic, complemented
24C22×C3×D12C2211yescharacteristic
25C22×C3×C4×D3C2211yescharacteristic, complemented
26C22×#626C2211yescharacteristic
27C22×#625C2211yescharacteristic
28C2×C32×C22⋊C4C2211yescharacteristic, complemented
29C2×#3752C2211yescharacteristic
30C2×#3752C2211yescharacteristic
31C2×C3×#217C2211yescharacteristic, complemented
32C2×C3×(C2×D3)⋊C4C2211yescharacteristic
33C2×C3×(C2×D3)⋊C4C2211yescharacteristic
34C2×C3×(C2×D3)⋊C4C2211yescharacteristic
35C2×C3×Dic3⋊C4C2211yescharacteristic, complemented
36C2×C3×Dic3⋊C4C2211yescharacteristic, complemented
37C3×#884—24no—
38#63983—24no—
39#63980—24no—
40C2×#3724C2211yescharacteristic, complemented
41C2×#3722C2211yescharacteristic
42C2×#3722C2211yescharacteristic
43C2×(C2×D3)⋊Dic3C2211yescharacteristic
44C2×(C2×D3)⋊Dic3C2211yescharacteristic
45C2×(C2×D3)⋊Dic3C2211yescharacteristic
46C2×(C2×D3)⋊Dic3C2211yescharacteristic
47C2×(C2×D3)⋊Dic3C2211yescharacteristic
48C2×(C2×D3)⋊Dic3C2211yescharacteristic, complemented
49C2×(C2×D3)⋊Dic3C2211yescharacteristic, complemented
50#63922—24no—
51#63658C2211yescharacteristic, complemented
52#63658C2211yescharacteristic, complemented
53C3×C3⋊#95C2211yescharacteristic, complemented
54#63579C2211yescharacteristic, complemented
55#63579C2211yescharacteristic, complemented
56#63579C2211yescharacteristic, complemented
57C2×C3×#121—31no—
58C2×#939—31no—
59C2×#939—31no—
60C2×#937—31no—
61C2×#937—31no—
62C2×#937—31no—
63C2×#884D311yescharacteristic, complemented
64C2×#882—31no—
65C3×#394—31no—
66#5223—31no—
67#5222—31no—
68#5220—31no—
69#5213—31no—
70#5213—31no—
71#4993—31no—
72#4993—31no—
73#4992—31no—
74#4991—31no—
75#4960—31no—
76#4959D311yescharacteristic, complemented
77#4958—31no—
78#4958—31no—
79#4958—31no—
80#4958—61no—
81#4956—31no—
82#4955—31no—
83#4955—31no—
84#4952—31no—
85#4952—31no—
86#4675—31no—
87#4665—31no—
88C24×C32C2311yescharacteristic
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
102C2×#638—22no—
103C2×#638—22no—
104C2×#638—41no—
105C22×C3⋊Dic3—22no—
106C22×C3⋊Dic3—41no—
107C22×C3⋊Dic3—41no—
108C22×C3⋊Dic3C2311yescharacteristic
109C22×C3⋊Dic3C2311yescharacteristic
110C22×C3⋊Dic3C2311yescharacteristic
111C2×C3×#67—22no—
112C2×C3×#67—22no—
113C2×C3×#67—22no—
114C2×C3×#67—22no—
115C2×C3×#67—41no—
116C2×C3×#67—41no—
117C2×C3×#67—41no—
118C2×C3×#67—41no—
119C2×C3×#67D414yescomplemented
120C22×C3×Dic3C2311yescharacteristic
121C22×C3×Dic3C2311yescharacteristic
122C22×C3×Dic3C2311yescharacteristic
123C22×C3×Dic3C2311yescharacteristic
124C22×C3×Dic3C2311yescharacteristic
125C2×C3×D12—22no—
126C2×C3×D12—22no—
127C2×C3×D12—41no—
128C2×C3×C4×D3—22no—
129C2×C3×C4×D3—41no—
130C2×C3×C4×D3—41no—
131C2×#626—22no—
132C2×#626—22no—
133C2×#626—41no—
134C2×#625—41no—
135C2×#625—41no—
136C2×#625D414yescomplemented
137C32×C22⋊C4—22no—
138#3752—22no—
139#3752—41no—
140C3×#217—41no—
141C3×(C2×D3)⋊C4—22no—
142C3×(C2×D3)⋊C4—22no—
143C3×(C2×D3)⋊C4—41no—
144C3×Dic3⋊C4—22no—
145C3×Dic3⋊C4—41no—
146#3724—22no—
147#3722—22no—
148#3722—41no—
149(C2×D3)⋊Dic3—22no—
150(C2×D3)⋊Dic3—22no—
151(C2×D3)⋊Dic3—22no—
152(C2×D3)⋊Dic3—22no—
153(C2×D3)⋊Dic3—22no—
154(C2×D3)⋊Dic3—41no—
155(C2×D3)⋊Dic3—41no—
156#2668—91noSylow
157C24×D3—31no—
158C24×D3—31no—
159C22×C3×D4—31no—
160C22×C3×D4—31no—
161C22×C3×D4—31no—
162C22×C3×D4—31no—
163C23×C3×C4—31no—
164C22×#67—31no—
165C22×#67—31no—
166C22×#67—31no—
167C22×#67—31no—
168C22×#67—31no—
169C22×#67—61no—
170C22×#67C2×D311yescharacteristic
171C22×#67C2×D311yescharacteristic
172C22×#67C2×D311yescharacteristic, complemented
173C23×Dic3—31no—
174C23×Dic3—31no—
175C23×Dic3—61no—
176C22×D12—31no—
177C22×D12C2×D311yescharacteristic
178C22×C4×D3C2×D311yescharacteristic, complemented
179C3×#121—64no—
180C2×C3×C4⋊C4—31no—
181C2×C3×C4⋊C4—31no—
182C2×C3×C22⋊C4—21no—
183C2×C3×C22⋊C4—31no—
184C2×C3×C22⋊C4—31no—
185C2×C3×C22⋊C4—31no—
186C2×C3×C22⋊C4—31no—
187C2×C3×C22⋊C4C2×D311yescharacteristic, complemented
188C2×C3×C22⋊C4C2×D311yescharacteristic, complemented
189C2×#217—31no—
190C2×#217—31no—
191C2×#217—31no—
192C2×#217—31no—
193C2×#217—31no—
194C2×#217—31no—
195C2×#217—31no—
196C2×#217C2×D311yescharacteristic, complemented
197#939—64no—
198#939—64no—
199#937—64no—
200#937—64no—
201#937—64no—
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—31no—
212C2×(C2×D3)⋊C4—31no—
213C2×(C2×D3)⋊C4—31no—
214C2×(C2×D3)⋊C4—31no—
215C2×(C2×D3)⋊C4—31no—
216C2×(C2×D3)⋊C4—31no—
217C2×(C2×D3)⋊C4—61no—
218C2×(C2×D3)⋊C4—61no—
219C2×(C2×D3)⋊C4C2×D311yescharacteristic
220C2×(C2×D3)⋊C4C2×D311yescharacteristic
221C2×(C2×D3)⋊C4C2×D311yescharacteristic
222C2×Dic3⋊C4—31no—
223C2×Dic3⋊C4—31no—
224C2×Dic3⋊C4C2×D311yescharacteristic, complemented
225C2×Dic3⋊C4C2×D311yescharacteristic, complemented
226#884—24no—
227#882—64no—
228C3×#95—31no—
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⋊#95—61no—
241C3⋊#95C2×D311yescharacteristic, complemented
242C23×C32—21no—
243C23×C32—21no—
244C23×C32—21no—
245C23×C32—21no—
246C23×C32—21no—
247C23×C32—21no—
248C23×C32C2×D412yes—
249C23×C32C2411yescharacteristic
250C22×C3⋊D3—21no—
251C22×C3⋊D3—21no—
252C22×C3⋊D3—21no—
253C22×C3⋊D3—21no—
254C22×C3⋊D3—21no—
255C22×C3⋊D3—21no—
256C22×C3⋊D3#4112yes—
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×D3C2×D412yes—
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—
291#638—44no—
292C2×C3⋊Dic3—21no—
293C2×C3⋊Dic3—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—
300C2×C3⋊Dic3—44no—
301C2×C3⋊Dic3C2×D412yes—
302C3×#67—44no—
303C3×#67—44no—
304C3×#67—44no—
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—
317C2×C3×Dic3—21no—
318C2×C3×Dic3—21no—
319C2×C3×Dic3C2×D412yes—
320C3×D12—44no—
321C3×C4×D3—44no—
322#626—44no—
323#625—44no—
324C2×#121—31no—
325C2×#121—91no—
326C2×#120—91no—
327C2×#120—91no—
328#399—91no—
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—21no—
340C24×C3—31no—
341C24×C3—31no—
342C24×C3—31no—
343C24×C3C22×D311yescharacteristic
344C24×C3C22×D311yescharacteristic
345C23×D3—31no—
346C23×D3—31no—
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—62no—
367C2×C3×D4—62no—
368C2×C3×D4—62no—
369C2×C3×D4—62no—
370C2×C3×D4—62no—
371C2×C3×D4—62no—
372C2×C3×D4—121no—
373C2×C3×D4—121no—
374C2×C3×D4—121no—
375C2×C3×D4—121no—
376C2×C3×D4—121no—
377C22×C3×C4—21no—
378C22×C3×C4—21no—
379C22×C3×C4—31no—
380C22×C3×C4—31no—
381C22×C3×C4—31no—
382C22×C3×C4—31no—
383C22×C3×C4—31no—
384C22×C3×C4—62no—
385C22×C3×C4—121no—
386C22×C3×C4—121no—
387C22×C3×C4C22×D311yescharacteristic
388C22×C3×C4C22×D311yescharacteristic
389C22×C3×C4C22×D311yescharacteristic
390C22×C3×C4C22×D311yescharacteristic
391C2×#67—22no—
392C2×#67—22no—
393C2×#67—22no—
394C2×#67—22no—
395C2×#67—34no—
396C2×#67—34no—
397C2×#67—41no—
398C2×#67—41no—
399C2×#67—41no—
400C2×#67—41no—
401C2×#67—62no—
402C2×#67—62no—
403C2×#67—62no—
404C2×#67—62no—
405C2×#67—64no—
406C2×#67—62no—
407C2×#67—62no—
408C2×#67—122no—
409C2×#67—121no—
410C2×#67—121no—
411C2×#67—121no—
412C2×#67—121no—
413C2×#67—121no—
414C2×#67—121no—
415C2×#67—121no—
416C2×#67—122no—
417C2×#67#6714yescomplemented
418C22×Dic3—31no—
419C22×Dic3—31no—
420C22×Dic3—31no—
421C22×Dic3—31no—
422C22×Dic3—31no—
423C22×Dic3—31no—
424C22×Dic3—61no—
425C22×Dic3—61no—
426C22×Dic3—61no—
427C22×Dic3—62no—
428C22×Dic3—62no—
429C22×Dic3—122no—
430C22×Dic3—121no—
431C22×Dic3—121no—
432C22×Dic3—121no—
433C22×Dic3—121no—
434C22×Dic3—122no—
435C22×Dic3—122no—
436C22×Dic3C22×D311yescharacteristic
437C22×Dic3C22×D311yescharacteristic
438C22×Dic3C22×D311yescharacteristic
439C22×Dic3C22×D311yescharacteristic
440C22×Dic3C22×D311yescharacteristic
441C2×D12—22no—
442C2×D12—22no—
443C2×D12—41no—
444C2×D12—62no—
445C2×D12—62no—
446C2×D12—121no—
447C2×C4×D3—22no—
448C2×C4×D3—41no—
449C2×C4×D3—41no—
450C3×C4⋊C4—62no—
451C3×C4⋊C4—121no—
452C3×C22⋊C4—22no—
453C3×C22⋊C4—22no—
454C3×C22⋊C4—42no—
455C3×C22⋊C4—62no—
456C3×C22⋊C4—62no—
457C3×C22⋊C4—121no—
458C3×C22⋊C4—121no—
459#217—41no—
460#217—62no—
461#217—62no—
462#217—62no—
463#217—62no—
464#217—62no—
465#217—121no—
466#217—121no—
467(C2×D3)⋊C4—22no—
468(C2×D3)⋊C4—22no—
469(C2×D3)⋊C4—41no—
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—121no—
481(C2×D3)⋊C4—121no—
482(C2×D3)⋊C4—121no—
483(C2×D3)⋊C4—121no—
484(C2×D3)⋊C4—122no—
485(C2×D3)⋊C4—121no—
486(C2×D3)⋊C4—121no—
487Dic3⋊C4—22no—
488Dic3⋊C4—41no—
489Dic3⋊C4—62no—
490Dic3⋊C4—62no—
491C22×C32—22no—
492C22×C32—22no—
493C22×C32—22no—
494C22×C32—41no—
495C22×C32—41no—
496C22×C32—41no—
497C22×C32—41no—
498C22×C32C22×D411yescharacteristic
499C22×C32C22×D411yescharacteristic
500C22×C32C2×#4111yescharacteristic
501C22×C32H(5,𝔽2)11yescharacteristic
502C22×C32H(5,𝔽2)11yescharacteristic
503C22×C32H(5,𝔽2)11yescharacteristic
504C22×C32H(5,𝔽2)11yescharacteristic
505C2×C3⋊D3—22no—
506C2×C3⋊D3—22no—
507C2×C3⋊D3—22no—
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—41no—
535C32×C4—41no—
536C3⋊Dic3—22no—
537C3⋊Dic3—41no—
538C3⋊Dic3—41no—
539C3×Dic3—22no—
540C3×Dic3—41no—
541C3×Dic3—41no—
542C3×Dic3—41no—
543C3×Dic3—41no—
544C25—91no—
545C22×D4—31no—
546C22×D4—31no—
547C22×D4—31no—
548C22×D4—31no—
549C22×D4—91no—
550C22×D4—91no—
551C22×D4—91no—
552C23×C4—31no—
553C23×C4—91no—
554#121—64no—
555#121—184no—
556#120—184no—
557#120—184no—
558C2×C4⋊C4—31no—
559C2×C4⋊C4—31no—
560C2×C4⋊C4—91no—
561C2×C22⋊C4—31no—
562C2×C22⋊C4—31no—
563C2×C22⋊C4—31no—
564C2×C22⋊C4—31no—
565C2×C22⋊C4—91no—
566C2×C22⋊C4—91no—
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⋊C4D3211yescharacteristic, complemented
577#95—31no—
578#95—91no—
579#95—91no—
580#95—91no—
581#95—91no—
582#95—91no—
583C23×C3—22no—
584C23×C3—22no—
585C23×C3—21no—
586C23×C3—21no—
587C23×C3—21no—
588C23×C3—21no—
589C23×C3—21no—
590C23×C3—21no—
591C23×C3—21no—
592C23×C3—21no—
593C23×C3—21no—
594C23×C3—21no—
595C23×C3—21no—
596C23×C3—21no—
597C23×C3—21no—
598C23×C3—22no—
599C23×C3—32no—
600C23×C3—32no—
601C23×C3—32no—
602C23×C3—41no—
603C23×C3—41no—
604C23×C3—41no—
605C23×C3—41no—
606C23×C3—61no—
607C23×C3—61no—
608C23×C3—61no—
609C23×C3—61no—
610C23×C3—61no—
611C23×C3—61no—
612C23×C3—61no—
613C23×C3—61no—
614C23×C3—61no—
615C23×C3—61no—
616C23×C3—61no—
617C23×C3—61no—
618C23×C3—61no—
619C23×C3—61no—
620C23×C3—61no—
621C23×C3—61no—
622C23×C3—61no—
623C23×C3—61no—
624C23×C3D3×D412yes—
625C23×C3C2×#6712yes—
626C23×C3C23×D311yescharacteristic
627C23×C3C23×D311yescharacteristic
628C22×D3—21no—
629C22×D3—21no—
630C22×D3—21no—
631C22×D3—21no—
632C22×D3—21no—
633C22×D3—21no—
634C22×D3—21no—
635C22×D3—21no—
636C22×D3—21no—
637C22×D3—21no—
638C22×D3—21no—
639C22×D3—21no—
640C22×D3—21no—
641C22×D3—21no—
642C22×D3—21no—
643C22×D3—21no—
644C22×D3—21no—
645C22×D3—21no—
646C22×D3—32no—
647C22×D3—32no—
648C22×D3—62no—
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—61no—
658C22×D3—61no—
659C22×D3—61no—
660C22×D3—61no—
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×D3D3×D412yes—
682C22×D3D3×D412yes—
683C22×D3C2×#6712yes—
684C3×D4—124no—
685C3×D4—124no—
686C3×D4—124no—
687C3×D4—124no—
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—32no—
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—61no—
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—124no—
722#67—44no—
723#67—44no—
724#67—44no—
725#67—124no—
726#67—124no—
727#67—124no—
728#67—124no—
729#67—124no—
730#67—128no—
731C2×Dic3—21no—
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—32no—
746C2×Dic3—32no—
747C2×Dic3—62no—
748C2×Dic3—61no—
749C2×Dic3—61no—
750C2×Dic3—61no—
751C2×Dic3—61no—
752C2×Dic3—62no—
753C2×Dic3—62no—
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—61no—
763C2×Dic3—61no—
764C2×Dic3—61no—
765C2×Dic3—61no—
766C2×Dic3—121no—
767C2×Dic3—121no—
768C2×Dic3—121no—
769C2×Dic3—121no—
770C2×Dic3—121no—
771C2×Dic3—121no—
772C2×Dic3—124no—
773C2×Dic3—124no—
774C2×Dic3—128no—
775C2×Dic3C2×#6712yes—
776D12—44no—
777D12—124no—
778C4×D3—44no—
779C2×C32—42no—
780C2×C32#53411yescharacteristic
781C2×C32#53411yescharacteristic
782C2×C32#53811yescharacteristic
783C2×C32D4211yescharacteristic
784C2×C32#54611yescharacteristic
785C2×C32#54611yescharacteristic
786C2×C32#56011yescharacteristic
787C3⋊D3—42no—
788C3×D3—42no—
789C3×D3—42no—
790C3×D3—42no—
791C24—31no—
792C24—31no—
793C24—31no—
794C24—91no—
795C24—182no—
796C24—182no—
797C24—182no—
798C24—361no—
799C24—361no—
800C24—361no—
801C24—361no—
802C24C2×D3211yescharacteristic
803C2×D4—34no—
804C2×D4—62no—
805C2×D4—62no—
806C2×D4—62no—
807C2×D4—62no—
808C2×D4—62no—
809C2×D4—62no—
810C2×D4—94no—
811C2×D4—121no—
812C2×D4—121no—
813C2×D4—121no—
814C2×D4—121no—
815C2×D4—121no—
816C2×D4—182no—
817C2×D4—182no—
818C2×D4—182no—
819C2×D4—182no—
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—91no—
833C22×C4—121no—
834C22×C4—121no—
835C22×C4—182no—
836C22×C4—361no—
837C22×C4—361no—
838C22×C4C2×D3211yescharacteristic
839C22×C4C2×D3211yescharacteristic
840C4⋊C4—62no—
841C4⋊C4—121no—
842C4⋊C4—182no—
843C22⋊C4—22no—
844C22⋊C4—62no—
845C22⋊C4—62no—
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—182no—
855C22⋊C4—361no—
856C22⋊C4—361no—
857C22⋊C4—361no—
858C22⋊C4—361no—
859C22×C3—24no—
860C22×C3—22no—
861C22×C3—22no—
862C22×C3—22no—
863C22×C3—22no—
864C22×C3—22no—
865C22×C3—22no—
866C22×C3—21no—
867C22×C3—21no—
868C22×C3—21no—
869C22×C3—21no—
870C22×C3—21no—
871C22×C3—21no—
872C22×C3—21no—
873C22×C3—42no—
874C22×C3—42no—
875C22×C3—42no—
876C22×C3—42no—
877C22×C3—42no—
878C22×C3—42no—
879C22×C3—41no—
880C22×C3—41no—
881C22×C3—41no—
882C22×C3—41no—
883C22×C3—41no—
884C22×C3—41no—
885C22×C3—41no—
886C22×C3—41no—
887C22×C3—62no—
888C22×C3—62no—
889C22×C3—62no—
890C22×C3—62no—
891C22×C3—62no—
892C22×C3—62no—
893C22×C3—62no—
894C22×C3—62no—
895C22×C3—62no—
896C22×C3—121no—
897C22×C3—121no—
898C22×C3—121no—
899C22×C3—121no—
900C22×C3—121no—
901C22×C3—121no—
902C22×C3—121no—
903C22×C3—121no—
904C22×C3—121no—
905C22×C3—121no—
906C22×C3—121no—
907C22×C3—121no—
908C22×C3C2×D3×D411yescharacteristic
909C22×C3C2×D3×D411yescharacteristic
910C22×C3C2×D3×D411yescharacteristic
911C22×C3#100411yescharacteristic
912C22×C3#100411yescharacteristic
913C22×C3#100411yescharacteristic
914C22×C3#100411yescharacteristic
915C22×C3#100411yescharacteristic
916C22×C3D3×#4111yescharacteristic
917C22×C3D3×#4111yescharacteristic
918C22×C3#100911yescharacteristic
919C22×C3#100911yescharacteristic
920C22×C3#100911yescharacteristic
921C22×C3C22×#6711yescharacteristic
922C2×D3—22no—
923C2×D3—22no—
924C2×D3—22no—
925C2×D3—22no—
926C2×D3—22no—
927C2×D3—22no—
928C2×D3—22no—
929C2×D3—22no—
930C2×D3—22no—
931C2×D3—41no—
932C2×D3—41no—
933C2×D3—41no—
934C2×D3—41no—
935C2×D3—41no—
936C2×D3—41no—
937C2×D3—41no—
938C2×D3—41no—
939C2×D3—41no—
940C2×D3—41no—
941C2×D3—41no—
942C2×D3—41no—
943C2×D3—62no—
944C2×D3—62no—
945C2×D3—62no—
946C2×D3—62no—
947C2×D3—62no—
948C2×D3—62no—
949C2×D3—122no—
950C2×D3—122no—
951C2×D3—122no—
952C2×D3—1216no—
953C2×D3—1216no—
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—41no—
967C3×C4—41no—
968C3×C4—41no—
969C3×C4—41no—
970C3×C4—62no—
971C3×C4—81no—
972C3×C4—81no—
973C3×C4—121no—
974C3×C4—121no—
975C3×C4—121no—
976C3×C4—121no—
977Dic3—22no—
978Dic3—41no—
979Dic3—41no—
980Dic3—41no—
981Dic3—41no—
982Dic3—62no—
983Dic3—62no—
984Dic3—122no—
985Dic3—122no—
986Dic3—122no—
987Dic3—121no—
988Dic3—121no—
989Dic3—121no—
990Dic3—121no—
991C32#266811yescharacteristic, complemented, Sylow
992C23—21no—
993C23—21no—
994C23—21no—
995C23—21no—
996C23—21no—
997C23—21no—
998C23—32no—
999C23—32no—
1000C23—32no—
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—61no—
1014C23—61no—
1015C23—61no—
1016C23—61no—
1017C23—61no—
1018C23—61no—
1019C23—92no—
1020C23—181no—
1021C23—181no—
1022C23—181no—
1023C23—181no—
1024C23—181no—
1025C23—181no—
1026C23—364no—
1027C23—364no—
1028C23—364no—
1029C23—364no—
1030C23—364no—
1031C23—364no—
1032C23—364no—
1033C23D3×#6712yes—
1034C23C22×D3211yescharacteristic
1035D4—124no—
1036D4—124no—
1037D4—124no—
1038D4—124no—
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—32no—
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—92no—
1064C2×C4—124no—
1065C2×C4—181no—
1066C2×C4—181no—
1067C2×C4—181no—
1068C2×C4—181no—
1069C2×C4—181no—
1070C2×C4—181no—
1071C2×C4—181no—
1072C2×C4—181no—
1073C2×C4—364no—
1074C2×C3—21no—
1075C2×C3—21no—
1076C2×C3—21no—
1077C2×C3—21no—
1078C2×C3—21no—
1079C2×C3—21no—
1080C2×C3—21no—
1081C2×C3—44no—
1082C2×C3—42no—
1083C2×C3—42no—
1084C2×C3—122no—
1085C2×C3—122no—
1086C2×C3—122no—
1087C2×C3#559011yescharacteristic
1088C2×C3#560511yescharacteristic
1089C2×C3#560511yescharacteristic
1090C2×C3#561011yescharacteristic
1091C2×C3#561011yescharacteristic
1092C2×C3#561311yescharacteristic
1093C2×C3#562011yescharacteristic
1094C2×C3#562011yescharacteristic
1095C2×C3#565311yescharacteristic
1096C2×C3#565411yescharacteristic
1097C2×C3#567811yescharacteristic
1098C2×C3D4×#6711yescharacteristic
1099C2×C3#580411yescharacteristic
1100C2×C3#582911yescharacteristic
1101D3—42no—
1102D3—42no—
1103D3—42no—
1104D3—122no—
1105D3—122no—
1106D3—242no—
1107C22—22no—
1108C22—22no—
1109C22—22no—
1110C22—41no—
1111C22—41no—
1112C22—41no—
1113C22—41no—
1114C22—62no—
1115C22—62no—
1116C22—62no—
1117C22—62no—
1118C22—62no—
1119C22—62no—
1120C22—62no—
1121C22—62no—
1122C22—62no—
1123C22—121no—
1124C22—121no—
1125C22—121no—
1126C22—121no—
1127C22—121no—
1128C22—121no—
1129C22—121no—
1130C22—121no—
1131C22—121no—
1132C22—121no—
1133C22—121no—
1134C22—121no—
1135C22—182no—
1136C22—182no—
1137C22—182no—
1138C22—3616no—
1139C22—361no—
1140C22—361no—
1141C22—361no—
1142C22—361no—
1143C22#6430611yescharacteristic
1144C22#6430811yescharacteristic
1145C22D32×D411yescharacteristic
1146C22#6431311yescharacteristic
1147C22#6431311yescharacteristic
1148C22#6431411yescharacteristic
1149C22C2×D3×#6711yescharacteristic
1150C4—41no—
1151C4—41no—
1152C4—62no—
1153C4—121no—
1154C4—121no—
1155C4—121no—
1156C4—121no—
1157C4—182no—
1158C4—361no—
1159C4—361no—
1160C3—21no—
1161C3#7712711yescharacteristic, complemented
1162C3#8271311yescharacteristic, complemented
1163C2—42no—
1164C2—122no—
1165C2—122no—
1166C2—122no—
1167C2—362no—
1168C2#1059426411yescharacteristic
1169C2#1059427611yescharacteristic
1170C2#1059430611yescharacteristic
1171C2#1059431011yescharacteristic
1172C2#1059506811yescharacteristic
1173C2#1059528711yescharacteristic
1174C2#1059530211yescharacteristic
subgroupG/H
center, FrattiniC23C22×D32
commutator, socle, cosocleC23×C32C24
FittingC2×C32×C22⋊C4C22
hypercenterC2×C22⋊C4D32
hypocenterC32#2668
LCSG ▷ C23×C32 ▷ C32
UCSC1 ◁ C23 ◁ C2×C22⋊C4

Complements

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

NH ≅ G/Ntype
1. C2×C3×#884C2semidirect
2. C2×#63983C2semidirect
3. C2×#63980C2semidirect
4. C2×#63922C2semidirect
5. #10592657C2semidirect
6. C3×#4959C2semidirect
7. #10591724C2semidirect
8. #10591713C2semidirect
9. #10591399C2semidirect
10. #10591382C2semidirect
11. #10591381C2semidirect
12. #10591301C2semidirect
13. #10591300C2semidirect
14. #10591299C2semidirect
15. #10591203C2semidirect
20. C23×C3⋊Dic3C22semidirect
23. C22×C3×#67C22semidirect
25. C22×C3×C4×D3C22semidirect
28. C2×C32×C22⋊C4C22semidirect
31. C2×C3×#217C22semidirect
35. C2×C3×Dic3⋊C4C22semidirect
36. C2×C3×Dic3⋊C4C22semidirect
40. C2×#3724C22semidirect
48. C2×(C2×D3)⋊Dic3C22semidirect
49. C2×(C2×D3)⋊Dic3C22semidirect
51. #63658C22semidirect
52. #63658C22semidirect
53. C3×C3⋊#95C22semidirect
54. #63579C22semidirect
55. #63579C22semidirect
56. #63579C22semidirect
63. C2×#884D3semidirect
76. #4959D3semidirect
119. C2×C3×#67D4semidirect
136. C2×#625D4semidirect
172. C22×#67C2×D3semidirect
178. C22×C4×D3C2×D3semidirect
187. C2×C3×C22⋊C4C2×D3semidirect
188. C2×C3×C22⋊C4C2×D3semidirect
196. C2×#217C2×D3semidirect
224. C2×Dic3⋊C4C2×D3semidirect
225. C2×Dic3⋊C4C2×D3semidirect
241. C3⋊#95C2×D3semidirect
417. C2×#67#67semidirect
576. C2×C22⋊C4D32semidirect
991. C32#2668semidirect
1161. C3#77127semidirect
1162. C3#82713semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#8842
C2×#639832
C2×#639802
C2×#639222
#105926572
C3×#49592
#105917242
#105917132
#105913992
#105913822
#105913812
#105913012
#105913002
#105912992
#105912032
#827133
#771273