Finite Group Databasebeta

← #11836001

Subgroups — #11836001

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×C3×#884C211yesmaximal, characteristic, complemented
2C2×#63983C211yesmaximal, characteristic, complemented
3C2×#63978C211yesmaximal, characteristic, complemented
4C2×#63922C211yesmaximal, characteristic, complemented
5#10592658C211yesmaximal, characteristic, complemented
6C3×#4958C211yesmaximal, characteristic, complemented
7#10591723C211yesmaximal, characteristic, complemented
8#10591710C211yesmaximal, characteristic, complemented
9#10591399C211yesmaximal, characteristic, complemented
10#10591382C211yesmaximal, characteristic, complemented
11#10591381C211yesmaximal, characteristic, complemented
12#10591303C211yesmaximal, characteristic, complemented
13#10591302C211yesmaximal, characteristic, complemented
14#10591296C211yesmaximal, characteristic, complemented
15#10591204C211yesmaximal, characteristic, complemented
16#82713—31nomaximal
17#74911—31nomaximal
18C23×D32C2211yescharacteristic
19C22×#638C2211yescharacteristic
20C22×C3×#67C2211yescharacteristic
21C22×C3×#67C2211yescharacteristic
22C22×C3×#67C2211yescharacteristic, complemented
23C23×C3×Dic3C2211yescharacteristic, complemented
24C22×C3×D12C2211yescharacteristic
25C22×C3×C4×D3C2211yescharacteristic, complemented
26C22×#626C2211yescharacteristic
27C22×#625C2211yescharacteristic
28C2×C32×C22⋊C4C2211yescharacteristic, complemented
29C2×#3757C2211yescharacteristic, complemented
30C2×#3752C2211yescharacteristic
31C2×#3752C2211yescharacteristic
32C2×#3750C2211yescharacteristic, complemented
33C2×C3×(C2×D3)⋊C4C2211yescharacteristic
34C2×C3×(C2×D3)⋊C4C2211yescharacteristic
35C2×C3×(C2×D3)⋊C4C2211yescharacteristic
36C2×C3×Dic3⋊C4C2211yescharacteristic, complemented
37C3×#884—24no—
38#63983—24no—
39#63978—24no—
40C2×Dic3⋊Dic3C2211yescharacteristic, 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
52C3×C3⋊#95C2211yescharacteristic, complemented
53C3×C3⋊#95C2211yescharacteristic, complemented
54#63579C2211yescharacteristic, complemented
55#63579C2211yescharacteristic, complemented
56#63579C2211yescharacteristic, complemented
57C2×C3×#121—31no—
58C2×#939—31no—
59C2×#937—31no—
60C2×#937—31no—
61C2×#937—31no—
62C2×#930—31no—
63C2×#884D311yescharacteristic, complemented
64C2×#882—31no—
65C3×#386—31no—
66#5223—31no—
67#5223—31no—
68#5222—31no—
69#5220—31no—
70#5213—31no—
71#5213—31no—
72#5213—31no—
73#4993—31no—
74#4992—31no—
75#4959—31no—
76#4959—31no—
77#4959—61no—
78#4958D311yescharacteristic, complemented
79#4956—31no—
80#4955—31no—
81#4955—31no—
82#4952—31no—
83#4949—31no—
84#4675—31no—
85#4674—31no—
86#4672—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⋊Dic3C2311yescharacteristic
106C22×C3⋊Dic3C2311yescharacteristic
107C22×C3⋊Dic3C2311yescharacteristic
108C2×C3×#67—22no—
109C2×C3×#67—22no—
110C2×C3×#67—22no—
111C2×C3×#67—22no—
112C2×C3×#67—41no—
113C2×C3×#67—41no—
114C2×C3×#67—41no—
115C2×C3×#67—41no—
116C2×C3×#67D414yescomplemented
117C22×C3×Dic3—22no—
118C22×C3×Dic3—41no—
119C22×C3×Dic3—41no—
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—41no—
132C2×#626—41no—
133C2×#626D414yescomplemented
134C2×#625—22no—
135C2×#625—22no—
136C2×#625—41no—
137C32×C22⋊C4—22no—
138#3757—41no—
139#3752—22no—
140#3752—41no—
141#3750—41no—
142C3×(C2×D3)⋊C4—22no—
143C3×(C2×D3)⋊C4—22no—
144C3×(C2×D3)⋊C4—41no—
145C3×Dic3⋊C4—22no—
146Dic3⋊Dic3—22no—
147#3722—22no—
148#3722—22no—
149(C2×D3)⋊Dic3—22no—
150(C2×D3)⋊Dic3—22no—
151(C2×D3)⋊Dic3—22no—
152(C2×D3)⋊Dic3—22no—
153(C2×D3)⋊Dic3—41no—
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—
164C23×C3×C4—31no—
165C22×#67—31no—
166C22×#67—31no—
167C22×#67—31no—
168C22×#67—31no—
169C22×#67—31no—
170C22×#67—61no—
171C22×#67C2×D311yescharacteristic
172C22×#67C2×D311yescharacteristic
173C22×#67C2×D311yescharacteristic, complemented
174C23×Dic3C2×D311yescharacteristic, complemented
175C22×D12—31no—
176C22×D12C2×D311yescharacteristic
177C22×C4×D3C2×D311yescharacteristic, complemented
178C3×#121—64no—
179C2×C3×C4⋊C4—31no—
180C2×C3×C22⋊C4—21no—
181C2×C3×C22⋊C4—31no—
182C2×C3×C22⋊C4—31no—
183C2×C3×C22⋊C4—31no—
184C2×C3×C22⋊C4C2×D311yescharacteristic, complemented
185C2×C3×C22⋊C4C2×D311yescharacteristic, complemented
186C2×#217—31no—
187C2×#217—31no—
188C2×#217—31no—
189C2×#217—31no—
190C2×#217—31no—
191C2×#217—31no—
192C2×#217—31no—
193C2×#217—31no—
194C2×#217—31no—
195C2×#217—61no—
196#939—64no—
197#937—64no—
198#937—64no—
199#937—64no—
200#930—64no—
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—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—61no—
217C2×(C2×D3)⋊C4—61no—
218C2×(C2×D3)⋊C4C2×D311yescharacteristic
219C2×(C2×D3)⋊C4C2×D311yescharacteristic
220C2×(C2×D3)⋊C4C2×D311yescharacteristic
221C2×C4⋊Dic3—31no—
222C2×Dic3⋊C4—31no—
223C2×Dic3⋊C4—31no—
224C2×Dic3⋊C4—31no—
225C2×Dic3⋊C4—61no—
226C2×Dic3⋊C4C2×D311yescharacteristic, complemented
227#884—24no—
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×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⋊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—
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—21no—
301C3×#67—44no—
302C3×#67—44no—
303C3×#67—44no—
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—
317C2×C3×Dic3—44no—
318C2×C3×Dic3C2×D412yes—
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—91no—
332#394—91no—
333#392—91no—
334#386—31no—
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—62no—
386C22×C3×C4—121no—
387C22×C3×C4—121no—
388C22×C3×C4—121no—
389C22×C3×C4—121no—
390C22×C3×C4C22×D311yescharacteristic
391C22×C3×C4C22×D311yescharacteristic
392C22×C3×C4C22×D311yescharacteristic
393C22×C3×C4C22×D311yescharacteristic
394C2×#67—22no—
395C2×#67—22no—
396C2×#67—22no—
397C2×#67—22no—
398C2×#67—34no—
399C2×#67—41no—
400C2×#67—41no—
401C2×#67—41no—
402C2×#67—41no—
403C2×#67—62no—
404C2×#67—62no—
405C2×#67—62no—
406C2×#67—62no—
407C2×#67—62no—
408C2×#67—62no—
409C2×#67—62no—
410C2×#67—62no—
411C2×#67—122no—
412C2×#67—122no—
413C2×#67—121no—
414C2×#67—121no—
415C2×#67—121no—
416C2×#67—121no—
417C2×#67—121no—
418C2×#67—121no—
419C2×#67—122no—
420C2×#67#6714yescomplemented
421C22×Dic3—22no—
422C22×Dic3—31no—
423C22×Dic3—31no—
424C22×Dic3—31no—
425C22×Dic3—31no—
426C22×Dic3—31no—
427C22×Dic3—31no—
428C22×Dic3—41no—
429C22×Dic3—41no—
430C22×Dic3—61no—
431C22×Dic3—61no—
432C22×Dic3—61no—
433C22×Dic3C22×D311yescharacteristic
434C22×Dic3C22×D311yescharacteristic
435C22×Dic3C22×D311yescharacteristic
436C22×Dic3C22×D311yescharacteristic
437C22×Dic3C22×D311yescharacteristic
438C2×D12—22no—
439C2×D12—22no—
440C2×D12—34no—
441C2×D12—41no—
442C2×D12—121no—
443C2×D12—121no—
444C2×C4×D3—22no—
445C2×C4×D3—41no—
446C2×C4×D3—41no—
447C3×C4⋊C4—62no—
448C3×C22⋊C4—22no—
449C3×C22⋊C4—22no—
450C3×C22⋊C4—42no—
451C3×C22⋊C4—62no—
452C3×C22⋊C4—62no—
453C3×C22⋊C4—121no—
454#217—62no—
455#217—62no—
456#217—62no—
457#217—62no—
458#217—121no—
459#217—121no—
460#217—121no—
461#217—121no—
462#217—121no—
463#217—122no—
464(C2×D3)⋊C4—22no—
465(C2×D3)⋊C4—22no—
466(C2×D3)⋊C4—41no—
467(C2×D3)⋊C4—62no—
468(C2×D3)⋊C4—62no—
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—122no—
478(C2×D3)⋊C4—121no—
479(C2×D3)⋊C4—121no—
480(C2×D3)⋊C4—122no—
481(C2×D3)⋊C4—121no—
482(C2×D3)⋊C4—121no—
483(C2×D3)⋊C4—121no—
484C4⋊Dic3—62no—
485Dic3⋊C4—22no—
486Dic3⋊C4—62no—
487Dic3⋊C4—121no—
488Dic3⋊C4—121no—
489Dic3⋊C4—122no—
490C22×C32—22no—
491C22×C32—22no—
492C22×C32—22no—
493C22×C32—41no—
494C22×C32—41no—
495C22×C32—41no—
496C22×C32—41no—
497C22×C32C22×D411yescharacteristic
498C22×C32C22×D411yescharacteristic
499C22×C32C2×#4111yescharacteristic
500C22×C32H(5,𝔽2)11yescharacteristic
501C22×C32H(5,𝔽2)11yescharacteristic
502C22×C32H(5,𝔽2)11yescharacteristic
503C22×C32H(5,𝔽2)11yescharacteristic
504C2×C3⋊D3—22no—
505C2×C3⋊D3—22no—
506C2×C3⋊D3—22no—
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—
535C3⋊Dic3—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—31no—
546C22×D4—31no—
547C22×D4—31no—
548C22×D4—91no—
549C22×D4—91no—
550C22×D4—91no—
551C23×C4—31no—
552C23×C4—31no—
553#121—64no—
554#121—184no—
555#120—184no—
556#120—184no—
557C2×C4⋊C4—31no—
558C2×C4⋊C4—91no—
559C2×C4⋊C4—91no—
560C2×C22⋊C4—31no—
561C2×C22⋊C4—31no—
562C2×C22⋊C4—31no—
563C2×C22⋊C4—91no—
564C2×C22⋊C4—91no—
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⋊C4D3211yescharacteristic, complemented
576#95—31no—
577#95—31no—
578#95—91no—
579#95—91no—
580#95—91no—
581#95—91no—
582C23×C3—21no—
583C23×C3—21no—
584C23×C3—21no—
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—22no—
596C23×C3—32no—
597C23×C3—32no—
598C23×C3—32no—
599C23×C3—41no—
600C23×C3—41no—
601C23×C3—41no—
602C23×C3—41no—
603C23×C3—41no—
604C23×C3—41no—
605C23×C3—61no—
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×C3D3×D412yes—
624C23×C3C2×#6712yes—
625C23×C3C23×D311yescharacteristic
626C23×C3C23×D311yescharacteristic
627C22×D3—21no—
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—32no—
646C22×D3—32no—
647C22×D3—62no—
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—61no—
658C22×D3—61no—
659C22×D3—61no—
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×D3#23512yes—
681C22×D3D3×D412yes—
682C22×D3C2×#6712yes—
683C3×D4—124no—
684C3×D4—124no—
685C3×D4—124no—
686C3×D4—124no—
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—32no—
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—124no—
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—44no—
745C2×Dic3—62no—
746C2×Dic3—62no—
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—61no—
758C2×Dic3—61no—
759C2×Dic3—61no—
760C2×Dic3—61no—
761C2×Dic3—61no—
762C2×Dic3—61no—
763C2×Dic3—61no—
764C2×Dic3—61no—
765C2×Dic3—121no—
766C2×Dic3—121no—
767C2×Dic3—121no—
768C2×Dic3—121no—
769C2×Dic3—121no—
770C2×Dic3—121no—
771C2×Dic3—121no—
772C2×Dic3D3×D412yes—
773C2×Dic3C2×#6712yes—
774D12—44no—
775D12—124no—
776C4×D3—44no—
777C2×C32—42no—
778C2×C32#53411yescharacteristic
779C2×C32#53411yescharacteristic
780C2×C32#53811yescharacteristic
781C2×C32D4211yescharacteristic
782C2×C32#54611yescharacteristic
783C2×C32#54611yescharacteristic
784C2×C32#56011yescharacteristic
785C3⋊D3—42no—
786C3×D3—42no—
787C3×D3—42no—
788C3×D3—42no—
789C24—31no—
790C24—31no—
791C24—31no—
792C24—91no—
793C24—182no—
794C24—182no—
795C24—182no—
796C24—361no—
797C24—361no—
798C24—361no—
799C24—361no—
800C24C2×D3211yescharacteristic
801C2×D4—34no—
802C2×D4—62no—
803C2×D4—62no—
804C2×D4—62no—
805C2×D4—62no—
806C2×D4—62no—
807C2×D4—62no—
808C2×D4—94no—
809C2×D4—121no—
810C2×D4—121no—
811C2×D4—121no—
812C2×D4—121no—
813C2×D4—121no—
814C2×D4—182no—
815C2×D4—182no—
816C2×D4—182no—
817C2×D4—182no—
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—62no—
828C22×C4—62no—
829C22×C4—91no—
830C22×C4—91no—
831C22×C4—91no—
832C22×C4—121no—
833C22×C4—121no—
834C22×C4—121no—
835C22×C4—121no—
836C22×C4C2×D3211yescharacteristic
837C22×C4C2×D3211yescharacteristic
838C4⋊C4—62no—
839C4⋊C4—182no—
840C4⋊C4—361no—
841C22⋊C4—22no—
842C22⋊C4—62no—
843C22⋊C4—62no—
844C22⋊C4—121no—
845C22⋊C4—182no—
846C22⋊C4—182no—
847C22⋊C4—182no—
848C22⋊C4—182no—
849C22⋊C4—182no—
850C22⋊C4—182no—
851C22⋊C4—182no—
852C22⋊C4—361no—
853C22⋊C4—361no—
854C22⋊C4—361no—
855C22⋊C4—361no—
856C22⋊C4—361no—
857C22×C3—22no—
858C22×C3—22no—
859C22×C3—22no—
860C22×C3—22no—
861C22×C3—22no—
862C22×C3—22no—
863C22×C3—21no—
864C22×C3—21no—
865C22×C3—21no—
866C22×C3—21no—
867C22×C3—21no—
868C22×C3—21no—
869C22×C3—21no—
870C22×C3—42no—
871C22×C3—42no—
872C22×C3—42no—
873C22×C3—41no—
874C22×C3—41no—
875C22×C3—41no—
876C22×C3—41no—
877C22×C3—41no—
878C22×C3—41no—
879C22×C3—41no—
880C22×C3—41no—
881C22×C3—62no—
882C22×C3—62no—
883C22×C3—62no—
884C22×C3—62no—
885C22×C3—62no—
886C22×C3—62no—
887C22×C3—62no—
888C22×C3—62no—
889C22×C3—62no—
890C22×C3—81no—
891C22×C3—81no—
892C22×C3—81no—
893C22×C3—81no—
894C22×C3—121no—
895C22×C3—121no—
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×C3C2×#23511yescharacteristic
907C22×C3C2×D3×D411yescharacteristic
908C22×C3C2×D3×D411yescharacteristic
909C22×C3C2×D3×D411yescharacteristic
910C22×C3#100411yescharacteristic
911C22×C3#100411yescharacteristic
912C22×C3#100411yescharacteristic
913C22×C3#100411yescharacteristic
914C22×C3#100411yescharacteristic
915C22×C3D3×#4111yescharacteristic
916C22×C3#100911yescharacteristic
917C22×C3#100911yescharacteristic
918C22×C3#100911yescharacteristic
919C22×C3C22×#6711yescharacteristic
920C2×D3—22no—
921C2×D3—22no—
922C2×D3—22no—
923C2×D3—22no—
924C2×D3—22no—
925C2×D3—22no—
926C2×D3—22no—
927C2×D3—22no—
928C2×D3—22no—
929C2×D3—41no—
930C2×D3—41no—
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—62no—
942C2×D3—62no—
943C2×D3—62no—
944C2×D3—62no—
945C2×D3—62no—
946C2×D3—62no—
947C2×D3—122no—
948C2×D3—122no—
949C2×D3—122no—
950C2×D3—1216no—
951C2×D3—1216no—
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—241no—
961C2×D3—241no—
962C2×D3—241no—
963C2×D3—241no—
964C3×C4—41no—
965C3×C4—41no—
966C3×C4—41no—
967C3×C4—41no—
968C3×C4—62no—
969C3×C4—62no—
970C3×C4—81no—
971C3×C4—81no—
972C3×C4—121no—
973C3×C4—121no—
974C3×C4—121no—
975Dic3—22no—
976Dic3—22no—
977Dic3—41no—
978Dic3—41no—
979Dic3—41no—
980Dic3—122no—
981Dic3—122no—
982Dic3—121no—
983Dic3—121no—
984Dic3—121no—
985Dic3—121no—
986Dic3—121no—
987Dic3—121no—
988Dic3—241no—
989C32#266811yescharacteristic, complemented, Sylow
990C23—21no—
991C23—21no—
992C23—21no—
993C23—21no—
994C23—21no—
995C23—21no—
996C23—32no—
997C23—32no—
998C23—32no—
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—61no—
1014C23—61no—
1015C23—61no—
1016C23—61no—
1017C23—92no—
1018C23—181no—
1019C23—181no—
1020C23—181no—
1021C23—181no—
1022C23—181no—
1023C23—181no—
1024C23—364no—
1025C23—364no—
1026C23—364no—
1027C23—364no—
1028C23—364no—
1029C23—364no—
1030C23—364no—
1031C23D3×#6712yes—
1032C23C22×D3211yescharacteristic
1033D4—124no—
1034D4—124no—
1035D4—124no—
1036D4—124no—
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—32no—
1047C2×C4—32no—
1048C2×C4—61no—
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—124no—
1062C2×C4—124no—
1063C2×C4—181no—
1064C2×C4—181no—
1065C2×C4—181no—
1066C2×C4—181no—
1067C2×C4—181no—
1068C2×C4—181no—
1069C2×C4—181no—
1070C2×C4—181no—
1071C2×C4—181no—
1072C2×C3—21no—
1073C2×C3—21no—
1074C2×C3—21no—
1075C2×C3—21no—
1076C2×C3—21no—
1077C2×C3—21no—
1078C2×C3—21no—
1079C2×C3—42no—
1080C2×C3—42no—
1081C2×C3—82no—
1082C2×C3—122no—
1083C2×C3—122no—
1084C2×C3—122no—
1085C2×C3#549011yescharacteristic
1086C2×C3#555011yescharacteristic
1087C2×C3#556011yescharacteristic
1088C2×C3#558911yescharacteristic
1089C2×C3#560511yescharacteristic
1090C2×C3#560511yescharacteristic
1091C2×C3#560911yescharacteristic
1092C2×C3#561011yescharacteristic
1093C2×C3#561311yescharacteristic
1094C2×C3#562011yescharacteristic
1095C2×C3#566611yescharacteristic
1096C2×C3D4×#6711yescharacteristic
1097C2×C3#580411yescharacteristic
1098C2×C3#582911yescharacteristic
1099D3—42no—
1100D3—42no—
1101D3—42no—
1102D3—122no—
1103D3—122no—
1104D3—242no—
1105C22—22no—
1106C22—22no—
1107C22—22no—
1108C22—41no—
1109C22—41no—
1110C22—41no—
1111C22—41no—
1112C22—62no—
1113C22—62no—
1114C22—62no—
1115C22—62no—
1116C22—62no—
1117C22—62no—
1118C22—62no—
1119C22—62no—
1120C22—62no—
1121C22—121no—
1122C22—121no—
1123C22—121no—
1124C22—121no—
1125C22—121no—
1126C22—121no—
1127C22—121no—
1128C22—121no—
1129C22—121no—
1130C22—121no—
1131C22—121no—
1132C22—121no—
1133C22—182no—
1134C22—182no—
1135C22—182no—
1136C22—3616no—
1137C22—361no—
1138C22—361no—
1139C22—361no—
1140C22—361no—
1141C22D3×#23511yescharacteristic
1142C22#6430711yescharacteristic
1143C22D32×D411yescharacteristic
1144C22#6431311yescharacteristic
1145C22#6431411yescharacteristic
1146C22#6431411yescharacteristic
1147C22C2×D3×#6711yescharacteristic
1148C4—41no—
1149C4—41no—
1150C4—62no—
1151C4—62no—
1152C4—121no—
1153C4—121no—
1154C4—121no—
1155C4—361no—
1156C4—361no—
1157C4—361no—
1158C3—21no—
1159C3#7491111yescharacteristic, complemented
1160C3#8271311yescharacteristic, complemented
1161C2—42no—
1162C2—122no—
1163C2—122no—
1164C2—122no—
1165C2—362no—
1166C2#1059426311yescharacteristic
1167C2#1059428311yescharacteristic
1168C2#1059429711yescharacteristic
1169C2#1059430811yescharacteristic
1170C2#1059506511yescharacteristic
1171C2#1059529111yescharacteristic
1172C2#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×#63978C2semidirect
4. C2×#63922C2semidirect
5. #10592658C2semidirect
6. C3×#4958C2semidirect
7. #10591723C2semidirect
8. #10591710C2semidirect
9. #10591399C2semidirect
10. #10591382C2semidirect
11. #10591381C2semidirect
12. #10591303C2semidirect
13. #10591302C2semidirect
14. #10591296C2semidirect
15. #10591204C2semidirect
22. C22×C3×#67C22semidirect
23. C23×C3×Dic3C22semidirect
25. C22×C3×C4×D3C22semidirect
28. C2×C32×C22⋊C4C22semidirect
29. C2×#3757C22semidirect
32. C2×#3750C22semidirect
36. C2×C3×Dic3⋊C4C22semidirect
40. C2×Dic3⋊Dic3C22semidirect
48. C2×(C2×D3)⋊Dic3C22semidirect
49. C2×(C2×D3)⋊Dic3C22semidirect
51. #63658C22semidirect
52. C3×C3⋊#95C22semidirect
53. C3×C3⋊#95C22semidirect
54. #63579C22semidirect
55. #63579C22semidirect
56. #63579C22semidirect
63. C2×#884D3semidirect
78. #4958D3semidirect
116. C2×C3×#67D4semidirect
133. C2×#626D4semidirect
173. C22×#67C2×D3semidirect
174. C23×Dic3C2×D3semidirect
177. C22×C4×D3C2×D3semidirect
184. C2×C3×C22⋊C4C2×D3semidirect
185. C2×C3×C22⋊C4C2×D3semidirect
226. C2×Dic3⋊C4C2×D3semidirect
240. C3⋊#95C2×D3semidirect
241. C3⋊#95C2×D3semidirect
420. C2×#67#67semidirect
575. C2×C22⋊C4D32semidirect
989. C32#2668semidirect
1159. C3#74911semidirect
1160. 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×#639782
C2×#639222
#105926582
C3×#49582
#105917232
#105917102
#105913992
#105913822
#105913812
#105913032
#105913022
#105912962
#105912042
#827133
#749113