Finite Group Databasebeta

← #11856273

Subgroups — #11856273

Order 1152.

2347 conjugacy classes of subgroups.

The subgroup lattice has 1136 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C4×D32C211yesmaximal, characteristic, complemented
2C2×C3×#883C211yesmaximal, characteristic, complemented
3C2×#63983C211yesmaximal, characteristic
4C2×#63969C211yesmaximal, characteristic, complemented
5#10592655C211yesmaximal, characteristic, complemented
6C3×#4956C211yesmaximal, characteristic, complemented
7#10591722C211yesmaximal, characteristic, complemented
8#10591721C211yesmaximal, characteristic, complemented
9#10591399C211yesmaximal, characteristic, complemented
10#10591378C211yesmaximal, characteristic, complemented
11#10591377C211yesmaximal, characteristic, complemented
12#10591362C211yesmaximal, characteristic, complemented
13#10591294C211yesmaximal, characteristic, complemented
14#10591290C211yesmaximal, characteristic, complemented
15#10591277C211yesmaximal, characteristic, complemented
16#82912—31nomaximal
17#74936—31nomaximal
18C23×D32C2211yescharacteristic
19C22×#638C2211yescharacteristic
20C22×C4×C3⋊D3C2211yescharacteristic
21C22×C3×#67C2211yescharacteristic
22C22×C3×#67C2211yescharacteristic
23C22×C3×C4×D3C2211yescharacteristic
24C22×C3×C4×D3C2211yescharacteristic
25C22×#624C2211yescharacteristic
26C22×D3×Dic3C2211yescharacteristic
27C22×D3×Dic3C2211yescharacteristic
28C2×C4×D32—24no—
29C2×C4×D32—24no—
30C2×C4×D32—24no—
31C2×C32×C22⋊C4C2211yescharacteristic, complemented
32C2×#3757C2211yescharacteristic, complemented
33C2×#3752C2211yescharacteristic
34C2×C3×#217C2211yescharacteristic, complemented
35C2×C3×#217C2211yescharacteristic, complemented
36C2×C3×(C2×D3)⋊C4C2211yescharacteristic
37C2×C3×(C2×D3)⋊C4C2211yescharacteristic
38C2×C3×C4⋊Dic3C2211yescharacteristic, complemented
39C2×C3×Dic3⋊C4C2211yescharacteristic, complemented
40C3×#883—24no—
41#63983—24no—
42#63969—24no—
43C2×#3724C2211yescharacteristic, complemented
44C2×Dic3⋊Dic3C2211yescharacteristic, complemented
45C2×#3722C2211yescharacteristic
46C2×#3722C2211yescharacteristic
47C2×(C2×D3)⋊Dic3C2211yescharacteristic
48C2×(C2×D3)⋊Dic3C2211yescharacteristic
49C2×(C2×D3)⋊Dic3C2211yescharacteristic
50C2×(C2×D3)⋊Dic3C2211yescharacteristic
51#63658C2211yescharacteristic, complemented
52#63658C2211yescharacteristic, complemented
53C3×C3⋊#95C2211yescharacteristic, complemented
54C3×C3⋊#95C2211yescharacteristic, complemented
55#63579C2211yescharacteristic, complemented
56#63579C2211yescharacteristic, complemented
57#63579C2211yescharacteristic, complemented
58#63579C2211yescharacteristic, complemented
59C23×C4×D3—31no—
60C23×C4×D3—31no—
61C2×C3×#123—31no—
62C2×#937—31no—
63C2×#937—31no—
64C2×#935—31no—
65C2×#883—31no—
66C2×#883D311yescharacteristic, complemented
67C3×#386—31no—
68#5220—31no—
69#5211—31no—
70#5210—31no—
71#4989—31no—
72#4989—31no—
73#4989—31no—
74#4989—31no—
75#4956—31no—
76#4956—31no—
77#4956—31no—
78#4956—31no—
79#4956—31no—
80#4956—61no—
81#4956D311yescharacteristic, complemented
82#4955—31no—
83#4955—31no—
84#4950—31no—
85#4943—31no—
86#4668—31no—
87#4668—31no—
88#4664—31no—
89#4664—31no—
90C24×C32C2311yescharacteristic
91C23×C3⋊D3C2311yescharacteristic
92C23×C3×D3C2311yescharacteristic
93C23×C3×D3C2311yescharacteristic
94C22×D32—22no—
95C22×D32—22no—
96C22×D32—22no—
97C22×D32—22no—
98C22×D32—22no—
99C22×D32—22no—
100C22×D32D414yes—
101C22×C32×C4C2311yescharacteristic
102C22×C32×C4C2311yescharacteristic
103C2×#638—22no—
104C2×#638—22no—
105C2×#638—22no—
106C22×C3⋊Dic3C2311yescharacteristic
107C22×C3⋊Dic3C2311yescharacteristic
108C22×C3⋊Dic3C2311yescharacteristic
109C2×C4×C3⋊D3—22no—
110C2×C4×C3⋊D3—22no—
111C2×C4×C3⋊D3—22no—
112C2×C3×#67—22no—
113C2×C3×#67—22no—
114C2×C3×#67—22no—
115C2×C3×#67—22no—
116C2×C3×#67—22no—
117C2×C3×#67—22no—
118C22×C3×Dic3C2311yescharacteristic
119C22×C3×Dic3C2311yescharacteristic
120C22×C3×Dic3C2311yescharacteristic
121C22×C3×Dic3C2311yescharacteristic
122C22×C3×Dic3C2311yescharacteristic
123C22×C3×Dic3C2311yescharacteristic
124C2×C3×C4×D3—22no—
125C2×C3×C4×D3—22no—
126C2×C3×C4×D3—22no—
127C2×C3×C4×D3—22no—
128C2×C3×C4×D3—22no—
129C2×C3×C4×D3D414yescomplemented
130C2×#624—22no—
131C2×#624—22no—
132C2×#624—22no—
133C2×D3×Dic3—22no—
134C2×D3×Dic3—22no—
135C2×D3×Dic3—22no—
136C2×D3×Dic3—22no—
137C2×D3×Dic3—22no—
138C2×D3×Dic3D414yescomplemented
139C4×D32—232no—
140C32×C22⋊C4—22no—
141#3757—22no—
142#3752—22no—
143C3×#217—22no—
144C3×#217—22no—
145C3×(C2×D3)⋊C4—22no—
146C3×(C2×D3)⋊C4—22no—
147C3×C4⋊Dic3—22no—
148C3×Dic3⋊C4—22no—
149#3724—22no—
150Dic3⋊Dic3—22no—
151#3722—22no—
152#3722—22no—
153(C2×D3)⋊Dic3—22no—
154(C2×D3)⋊Dic3—22no—
155(C2×D3)⋊Dic3—22no—
156(C2×D3)⋊Dic3—22no—
157#2849—91noSylow
158C24×D3—31no—
159C24×D3—31no—
160C22×C3×D4—31no—
161C22×C3×D4—31no—
162C23×C3×C4—31no—
163C23×C3×C4—31no—
164C22×#67—31no—
165C22×#67—31no—
166C22×#67—61no—
167C22×#67C2×D311yescharacteristic
168C22×#67C2×D311yescharacteristic
169C23×Dic3—31no—
170C23×Dic3—31no—
171C22×C4×D3—31no—
172C22×C4×D3—31no—
173C22×C4×D3—31no—
174C22×C4×D3—31no—
175C22×C4×D3—31no—
176C22×C4×D3—31no—
177C22×C4×D3—61no—
178C22×C4×D3—64no—
179C22×C4×D3—64no—
180C22×C4×D3—64no—
181C22×C4×D3—64no—
182C22×C4×D3—64no—
183C22×C4×D3—64no—
184C22×C4×D3C2×D311yescharacteristic
185C22×C4×D3C2×D311yescharacteristic
186C3×#123—64no—
187C2×C3×C4⋊C4—31no—
188C2×C3×C4⋊C4—31no—
189C2×C3×C22⋊C4—21no—
190C2×C3×C22⋊C4—31no—
191C2×C3×C22⋊C4—31no—
192C2×C3×C22⋊C4—31no—
193C2×C3×C22⋊C4—31no—
194C2×C3×C22⋊C4C2×D311yescharacteristic, complemented
195C2×C3×C22⋊C4C2×D311yescharacteristic, complemented
196C2×#217—31no—
197C2×#217—31no—
198C2×#217—31no—
199C2×#217—31no—
200C2×#217—31no—
201C2×#217—31no—
202C2×#217—61no—
203C2×#217C2×D311yescharacteristic, complemented
204C2×#217C2×D311yescharacteristic, complemented
205#937—64no—
206#937—64no—
207#935—64no—
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—31no—
218C2×(C2×D3)⋊C4—61no—
219C2×(C2×D3)⋊C4C2×D311yescharacteristic
220C2×(C2×D3)⋊C4C2×D311yescharacteristic
221C2×C4⋊Dic3—31no—
222C2×C4⋊Dic3C2×D311yescharacteristic, complemented
223C2×Dic3⋊C4—31no—
224C2×Dic3⋊C4—31no—
225C2×Dic3⋊C4—31no—
226C2×Dic3⋊C4C2×D311yescharacteristic, complemented
227#883—24no—
228#883—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—31no—
240C3⋊#95—31no—
241C3⋊#95—31no—
242C3⋊#95—31no—
243C3⋊#95—61no—
244C3⋊#95—61no—
245C3⋊#95C2×D311yescharacteristic, complemented
246C3⋊#95C2×D311yescharacteristic, complemented
247C23×C32—21no—
248C23×C32—21no—
249C23×C32—21no—
250C23×C32—21no—
251C23×C32—21no—
252C23×C32—21no—
253C23×C32—21no—
254C23×C32C2411yescharacteristic
255C22×C3⋊D3—21no—
256C22×C3⋊D3—21no—
257C22×C3⋊D3—21no—
258C22×C3⋊D3—21no—
259C22×C3⋊D3C2×D412yes—
260C22×C3⋊D3#4112yes—
261C22×C3⋊D3#4112yes—
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×D3C2×D412yes—
271C22×C3×D3C2×D412yes—
272C22×C3×D3C2×D412yes—
273C22×C3×D3C2×D412yes—
274C22×C3×D3#4112yes—
275C22×C3×D3#4112yes—
276C2×D32—28no—
277C2×D32—28no—
278C2×D32—28no—
279C2×D32—28no—
280C2×D32—28no—
281C2×D32—28no—
282C2×D32—28no—
283C2×C32×C4—21no—
284C2×C32×C4—21no—
285C2×C32×C4—21no—
286C2×C32×C4—21no—
287C2×C32×C4—21no—
288C2×C32×C4C2×D412yes—
289#638—44no—
290C2×C3⋊Dic3—21no—
291C2×C3⋊Dic3—21no—
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⋊Dic3C2×D412yes—
299C4×C3⋊D3—28no—
300C3×#67—44no—
301C3×#67—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—
317C2×C3×Dic3—21no—
318C2×C3×Dic3C2×D412yes—
319C2×C3×Dic3C2×D412yes—
320C3×C4×D3—28no—
321C3×C4×D3—28no—
322#624—28no—
323D3×Dic3—28no—
324D3×Dic3—28no—
325C24×C4—91no—
326C2×#123—31no—
327C2×#123—91no—
328C2×#120—91no—
329#386—31no—
330#386—91no—
331#386—91no—
332#386—91no—
333#385—91no—
334#385—91no—
335#385—91no—
336#385—91no—
337#381—91no—
338#381—91no—
339#379—91no—
340C24×C3—21no—
341C24×C3—31no—
342C24×C3—31no—
343C24×C3C22×D311yescharacteristic
344C24×C3C22×D311yescharacteristic
345C23×D3—31no—
346C23×D3—31no—
347C23×D3—34no—
348C23×D3—34no—
349C23×D3—61no—
350C23×D3—62no—
351C23×D3—62no—
352C23×D3—62no—
353C23×D3—62no—
354C23×D3—62no—
355C23×D3—62no—
356C23×D3—62no—
357C23×D3—62no—
358C23×D3—62no—
359C23×D3—62no—
360C23×D3—62no—
361C23×D3—62no—
362C23×D3C22×D311yescharacteristic
363C23×D3C22×D311yescharacteristic
364C2×C3×D4—62no—
365C2×C3×D4—62no—
366C2×C3×D4—62no—
367C2×C3×D4—62no—
368C2×C3×D4—62no—
369C2×C3×D4—62no—
370C22×C3×C4—21no—
371C22×C3×C4—21no—
372C22×C3×C4—31no—
373C22×C3×C4—31no—
374C22×C3×C4—34no—
375C22×C3×C4—31no—
376C22×C3×C4—31no—
377C22×C3×C4—31no—
378C22×C3×C4—31no—
379C22×C3×C4—62no—
380C22×C3×C4—62no—
381C22×C3×C4—62no—
382C22×C3×C4—62no—
383C22×C3×C4—62no—
384C22×C3×C4C22×D311yescharacteristic
385C22×C3×C4C22×D311yescharacteristic
386C22×C3×C4C22×D311yescharacteristic
387C22×C3×C4C22×D311yescharacteristic
388C2×#67—22no—
389C2×#67—22no—
390C2×#67—22no—
391C2×#67—22no—
392C2×#67—22no—
393C2×#67—22no—
394C2×#67—62no—
395C2×#67—62no—
396C2×#67—62no—
397C2×#67—62no—
398C2×#67—62no—
399C2×#67—62no—
400C2×#67—64no—
401C2×#67—122no—
402C2×#67—122no—
403C22×Dic3—31no—
404C22×Dic3—31no—
405C22×Dic3—34no—
406C22×Dic3—31no—
407C22×Dic3—31no—
408C22×Dic3—31no—
409C22×Dic3—31no—
410C22×Dic3—61no—
411C22×Dic3—61no—
412C22×Dic3—61no—
413C22×Dic3—62no—
414C22×Dic3—62no—
415C22×Dic3—62no—
416C22×Dic3—62no—
417C22×Dic3—62no—
418C22×Dic3C22×D311yescharacteristic
419C22×Dic3C22×D311yescharacteristic
420C22×Dic3C22×D311yescharacteristic
421C22×Dic3C22×D311yescharacteristic
422C22×Dic3C22×D311yescharacteristic
423C22×Dic3C22×D311yescharacteristic
424C2×C4×D3—22no—
425C2×C4×D3—22no—
426C2×C4×D3—22no—
427C2×C4×D3—22no—
428C2×C4×D3—22no—
429C2×C4×D3—34no—
430C2×C4×D3—632no—
431C2×C4×D3—632no—
432C2×C4×D3—62no—
433C2×C4×D3—62no—
434C2×C4×D3—62no—
435C2×C4×D3—62no—
436C2×C4×D3—62no—
437C2×C4×D3—62no—
438C2×C4×D3—62no—
439C2×C4×D3—62no—
440C2×C4×D3—62no—
441C2×C4×D3—62no—
442C2×C4×D3—62no—
443C2×C4×D3—62no—
444C2×C4×D3—62no—
445C2×C4×D3—62no—
446C2×C4×D3—62no—
447C2×C4×D3—62no—
448C2×C4×D3—62no—
449C2×C4×D3—122no—
450C2×C4×D3—122no—
451C2×C4×D3—122no—
452C2×C4×D3#6714yescomplemented
453C3×C4⋊C4—62no—
454C3×C4⋊C4—62no—
455C3×C22⋊C4—22no—
456C3×C22⋊C4—22no—
457C3×C22⋊C4—42no—
458C3×C22⋊C4—62no—
459C3×C22⋊C4—62no—
460C3×C22⋊C4—62no—
461C3×C22⋊C4—62no—
462#217—22no—
463#217—22no—
464#217—62no—
465#217—62no—
466#217—62no—
467#217—62no—
468#217—62no—
469#217—62no—
470#217—122no—
471(C2×D3)⋊C4—22no—
472(C2×D3)⋊C4—22no—
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—62no—
481(C2×D3)⋊C4—62no—
482(C2×D3)⋊C4—62no—
483(C2×D3)⋊C4—122no—
484C4⋊Dic3—22no—
485C4⋊Dic3—62no—
486Dic3⋊C4—22no—
487Dic3⋊C4—62no—
488Dic3⋊C4—62no—
489Dic3⋊C4—62no—
490C22×C32—41no—
491C22×C32—41no—
492C22×C32—41no—
493C22×C32—41no—
494C22×C32—41no—
495C22×C32—41no—
496C22×C32—41no—
497C22×C32C22×D411yescharacteristic
498C22×C32C22×D411yescharacteristic
499C22×C32C22×D411yescharacteristic
500C22×C32C2×#4111yescharacteristic
501C22×C32C2×#4111yescharacteristic
502C22×C32C2×#4111yescharacteristic
503C22×C32C2×#4111yescharacteristic
504C2×C3⋊D3—22no—
505C2×C3⋊D3—22no—
506C2×C3⋊D3—22no—
507C2×C3⋊D3—22no—
508C2×C3⋊D3—22no—
509C2×C3⋊D3—22no—
510C2×C3⋊D3#12314yescomplemented
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—22no—
521C2×C3×D3—22no—
522C2×C3×D3—22no—
523C2×C3×D3#12014yes—
524C2×C3×D3#12314yescomplemented
525D32—232no—
526C32×C4—22no—
527C32×C4—41no—
528C3⋊Dic3—22no—
529C3⋊Dic3—41no—
530C3⋊Dic3—41no—
531C3×Dic3—22no—
532C3×Dic3—22no—
533C3×Dic3—41no—
534C3×Dic3—41no—
535C3×Dic3—41no—
536C3×Dic3—41no—
537C25—91no—
538C22×D4—31no—
539C22×D4—31no—
540C22×D4—91no—
541C23×C4—31no—
542C23×C4—31no—
543C23×C4—91no—
544C23×C4—91no—
545C23×C4—91no—
546C23×C4—91no—
547C23×C4—184no—
548C23×C4—184no—
549C23×C4—184no—
550#123—64no—
551#123—184no—
552#120—184no—
553C2×C4⋊C4—31no—
554C2×C4⋊C4—31no—
555C2×C4⋊C4—91no—
556C2×C4⋊C4—91no—
557C2×C22⋊C4—31no—
558C2×C22⋊C4—31no—
559C2×C22⋊C4—31no—
560C2×C22⋊C4—31no—
561C2×C22⋊C4—91no—
562C2×C22⋊C4—91no—
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⋊C4D3211yescharacteristic, complemented
570#95—31no—
571#95—31no—
572#95—91no—
573#95—91no—
574#95—91no—
575#95—91no—
576#95—91no—
577#95—91no—
578C23×C3—22no—
579C23×C3—21no—
580C23×C3—21no—
581C23×C3—21no—
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—32no—
595C23×C3—32no—
596C23×C3—32no—
597C23×C3—32no—
598C23×C3—32no—
599C23×C3—32no—
600C23×C3—41no—
601C23×C3—41no—
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×C3C23×D311yescharacteristic
615C23×C3C23×D311yescharacteristic
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—32no—
629C22×D3—32no—
630C22×D3—62no—
631C22×D3—62no—
632C22×D3—62no—
633C22×D3—68no—
634C22×D3—68no—
635C22×D3—68no—
636C22×D3—68no—
637C22×D3—68no—
638C22×D3—68no—
639C22×D3—68no—
640C22×D3—68no—
641C22×D3—68no—
642C22×D3—68no—
643C22×D3—68no—
644C22×D3—68no—
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—68no—
654C22×D3—68no—
655C22×D3—121no—
656C22×D3—121no—
657C22×D3—121no—
658C22×D3—121no—
659C22×D3#23512yes—
660C22×D3D3×D412yes—
661C22×D3D3×D412yes—
662C22×D3D3×D412yes—
663C22×D3#23712yes—
664C22×D3C2×#6712yes—
665C3×D4—124no—
666C3×D4—124no—
667C2×C3×C4—21no—
668C2×C3×C4—21no—
669C2×C3×C4—21no—
670C2×C3×C4—21no—
671C2×C3×C4—21no—
672C2×C3×C4—21no—
673C2×C3×C4—21no—
674C2×C3×C4—21no—
675C2×C3×C4—21no—
676C2×C3×C4—21no—
677C2×C3×C4—22no—
678C2×C3×C4—32no—
679C2×C3×C4—32no—
680C2×C3×C4—41no—
681C2×C3×C4—41no—
682C2×C3×C4—41no—
683C2×C3×C4—41no—
684C2×C3×C4—41no—
685C2×C3×C4—68no—
686C2×C3×C4—68no—
687C2×C3×C4—61no—
688C2×C3×C4—61no—
689C2×C3×C4—61no—
690C2×C3×C4—61no—
691C2×C3×C4—61no—
692C2×C3×C4—61no—
693C2×C3×C4—61no—
694C2×C3×C4—61no—
695C2×C3×C4—61no—
696C2×C3×C4—61no—
697C2×C3×C4—61no—
698C2×C3×C4—61no—
699C2×C3×C4—61no—
700C2×C3×C4—61no—
701C2×C3×C4—61no—
702C2×C3×C4—61no—
703C2×C3×C4D3×D412yes—
704C2×C3×C4C2×#6712yes—
705#67—44no—
706#67—44no—
707#67—124no—
708#67—124no—
709#67—128no—
710C2×Dic3—21no—
711C2×Dic3—21no—
712C2×Dic3—21no—
713C2×Dic3—21no—
714C2×Dic3—21no—
715C2×Dic3—21no—
716C2×Dic3—21no—
717C2×Dic3—21no—
718C2×Dic3—21no—
719C2×Dic3—21no—
720C2×Dic3—21no—
721C2×Dic3—21no—
722C2×Dic3—21no—
723C2×Dic3—21no—
724C2×Dic3—21no—
725C2×Dic3—21no—
726C2×Dic3—32no—
727C2×Dic3—32no—
728C2×Dic3—62no—
729C2×Dic3—68no—
730C2×Dic3—68no—
731C2×Dic3—61no—
732C2×Dic3—61no—
733C2×Dic3—61no—
734C2×Dic3—61no—
735C2×Dic3—62no—
736C2×Dic3—61no—
737C2×Dic3—61no—
738C2×Dic3—61no—
739C2×Dic3—61no—
740C2×Dic3—61no—
741C2×Dic3—61no—
742C2×Dic3—61no—
743C2×Dic3—61no—
744C2×Dic3—61no—
745C2×Dic3—61no—
746C2×Dic3—61no—
747C2×Dic3—61no—
748C2×Dic3—121no—
749C2×Dic3—121no—
750C2×Dic3—121no—
751C2×Dic3—121no—
752C2×Dic3—121no—
753C2×Dic3—121no—
754C2×Dic3—121no—
755C2×Dic3D3×D412yes—
756C2×Dic3C2×#6712yes—
757C4×D3—28no—
758C4×D3—28no—
759C4×D3—68no—
760C4×D3—68no—
761C4×D3—68no—
762C4×D3—68no—
763C4×D3—68no—
764C4×D3—68no—
765C4×D3—128no—
766C2×C32—81no—
767C2×C32C2×#12011yescharacteristic
768C2×C32C2×#12311yescharacteristic
769C2×C32C2×#12311yescharacteristic
770C2×C32#52511yescharacteristic
771C2×C32#52511yescharacteristic
772C2×C32#52511yescharacteristic
773C2×C32#52511yescharacteristic
774C3⋊D3—24no—
775C3×D3—24no—
776C3×D3—24no—
777C24—31no—
778C24—31no—
779C24—94no—
780C24—91no—
781C24—182no—
782C24—182no—
783C24—182no—
784C24—182no—
785C24—182no—
786C24—182no—
787C24C2×D3211yescharacteristic
788C2×D4—62no—
789C2×D4—62no—
790C2×D4—62no—
791C2×D4—62no—
792C2×D4—62no—
793C2×D4—62no—
794C2×D4—182no—
795C2×D4—182no—
796C2×D4—182no—
797C22×C4—31no—
798C22×C4—31no—
799C22×C4—34no—
800C22×C4—31no—
801C22×C4—31no—
802C22×C4—31no—
803C22×C4—31no—
804C22×C4—62no—
805C22×C4—62no—
806C22×C4—62no—
807C22×C4—62no—
808C22×C4—62no—
809C22×C4—94no—
810C22×C4—91no—
811C22×C4—91no—
812C22×C4—91no—
813C22×C4—182no—
814C22×C4—182no—
815C22×C4—182no—
816C22×C4—182no—
817C22×C4—182no—
818C22×C4—182no—
819C22×C4—1832no—
820C22×C4—182no—
821C22×C4—182no—
822C22×C4—182no—
823C22×C4—182no—
824C22×C4—182no—
825C22×C4C2×D3211yescharacteristic
826C22×C4C2×D3211yescharacteristic
827C4⋊C4—62no—
828C4⋊C4—62no—
829C4⋊C4—182no—
830C4⋊C4—182no—
831C22⋊C4—22no—
832C22⋊C4—62no—
833C22⋊C4—62no—
834C22⋊C4—62no—
835C22⋊C4—62no—
836C22⋊C4—182no—
837C22⋊C4—182no—
838C22⋊C4—182no—
839C22⋊C4—182no—
840C22⋊C4—182no—
841C22⋊C4—182no—
842C22⋊C4—182no—
843C22⋊C4—182no—
844C22×C3—21no—
845C22×C3—21no—
846C22×C3—21no—
847C22×C3—21no—
848C22×C3—21no—
849C22×C3—21no—
850C22×C3—21no—
851C22×C3—34no—
852C22×C3—34no—
853C22×C3—42no—
854C22×C3—42no—
855C22×C3—42no—
856C22×C3—41no—
857C22×C3—41no—
858C22×C3—41no—
859C22×C3—41no—
860C22×C3—41no—
861C22×C3—41no—
862C22×C3—41no—
863C22×C3—41no—
864C22×C3—41no—
865C22×C3—41no—
866C22×C3—41no—
867C22×C3—41no—
868C22×C3—41no—
869C22×C3—41no—
870C22×C3—62no—
871C22×C3—62no—
872C22×C3—62no—
873C22×C3—62no—
874C22×C3—62no—
875C22×C3—62no—
876C22×C3—62no—
877C22×C3—62no—
878C22×C3—62no—
879C22×C3—62no—
880C22×C3—62no—
881C22×C3—62no—
882C22×C3—81no—
883C22×C3—81no—
884C22×C3—81no—
885C22×C3—81no—
886C22×C3C2×#23511yescharacteristic
887C22×C3C2×D3×D411yescharacteristic
888C22×C3C2×D3×D411yescharacteristic
889C22×C3C2×D3×D411yescharacteristic
890C22×C3C2×D3×D411yescharacteristic
891C22×C3C2×D3×D411yescharacteristic
892C22×C3C2×#23711yescharacteristic
893C22×C3D3×#4111yescharacteristic
894C22×C3D3×#4111yescharacteristic
895C22×C3D3×#4111yescharacteristic
896C22×C3D3×#4111yescharacteristic
897C22×C3D3×#4111yescharacteristic
898C22×C3D3×#4111yescharacteristic
899C22×C3C22×#6711yescharacteristic
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—22no—
909C2×D3—22no—
910C2×D3—22no—
911C2×D3—22no—
912C2×D3—34no—
913C2×D3—34no—
914C2×D3—64no—
915C2×D3—632no—
916C2×D3—632no—
917C2×D3—62no—
918C2×D3—62no—
919C2×D3—62no—
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—122no—
930C2×D3—122no—
931C2×D3—122no—
932C2×D3—122no—
933C2×D3—122no—
934C2×D3—122no—
935C2×D3#88314yescomplemented
936C2×D3#93714yes—
937C3×C4—22no—
938C3×C4—22no—
939C3×C4—42no—
940C3×C4—41no—
941C3×C4—41no—
942C3×C4—62no—
943C3×C4—62no—
944C3×C4—81no—
945C3×C4—121no—
946C3×C4—121no—
947C3×C4—121no—
948C3×C4—121no—
949Dic3—22no—
950Dic3—22no—
951Dic3—41no—
952Dic3—41no—
953Dic3—41no—
954Dic3—41no—
955Dic3—62no—
956Dic3—62no—
957Dic3—122no—
958Dic3—122no—
959Dic3—121no—
960Dic3—121no—
961Dic3—121no—
962Dic3—121no—
963Dic3—241no—
964C32#284911yescharacteristic, complemented, Sylow
965C23—21no—
966C23—21no—
967C23—21no—
968C23—21no—
969C23—21no—
970C23—21no—
971C23—21no—
972C23—32no—
973C23—32no—
974C23—32no—
975C23—32no—
976C23—32no—
977C23—32no—
978C23—61no—
979C23—61no—
980C23—61no—
981C23—61no—
982C23—61no—
983C23—61no—
984C23—61no—
985C23—61no—
986C23—92no—
987C23—92no—
988C23—92no—
989C23—188no—
990C23—188no—
991C23—188no—
992C23—188no—
993C23—188no—
994C23—188no—
995C23—188no—
996C23—181no—
997C23—181no—
998C23—181no—
999C23—181no—
1000C23C22×D3211yescharacteristic
1001D4—124no—
1002D4—124no—
1003D4—364no—
1004C2×C4—21no—
1005C2×C4—21no—
1006C2×C4—21no—
1007C2×C4—21no—
1008C2×C4—21no—
1009C2×C4—32no—
1010C2×C4—32no—
1011C2×C4—68no—
1012C2×C4—68no—
1013C2×C4—61no—
1014C2×C4—61no—
1015C2×C4—61no—
1016C2×C4—61no—
1017C2×C4—61no—
1018C2×C4—61no—
1019C2×C4—61no—
1020C2×C4—61no—
1021C2×C4—61no—
1022C2×C4—61no—
1023C2×C4—61no—
1024C2×C4—61no—
1025C2×C4—61no—
1026C2×C4—61no—
1027C2×C4—61no—
1028C2×C4—61no—
1029C2×C4—92no—
1030C2×C4—188no—
1031C2×C4—188no—
1032C2×C4—188no—
1033C2×C4—188no—
1034C2×C4—181no—
1035C2×C4—181no—
1036C2×C4—181no—
1037C2×C4—181no—
1038C2×C4—181no—
1039C2×C4—181no—
1040C2×C4—181no—
1041C2×C4—181no—
1042C2×C4D3×#6712yes—
1043C2×C3—21no—
1044C2×C3—21no—
1045C2×C3—21no—
1046C2×C3—21no—
1047C2×C3—21no—
1048C2×C3—21no—
1049C2×C3—21no—
1050C2×C3—64no—
1051C2×C3—64no—
1052C2×C3—82no—
1053C2×C3—81no—
1054C2×C3—81no—
1055C2×C3C2×#88311yescharacteristic
1056C2×C3#554711yescharacteristic
1057C2×C3#554711yescharacteristic
1058C2×C3D3×#12011yescharacteristic
1059C2×C3#560611yescharacteristic
1060C2×C3#560611yescharacteristic
1061C2×C3D3×#12311yescharacteristic
1062C2×C3D3×#12311yescharacteristic
1063C2×C3D3×#12311yescharacteristic
1064C2×C3#565611yescharacteristic
1065C2×C3#565611yescharacteristic
1066C2×C3C2×#93711yescharacteristic
1067C2×C3#582811yescharacteristic
1068C2×C3#582811yescharacteristic
1069D3—24no—
1070D3—24no—
1071D3—64no—
1072D3—64no—
1073D3—124no—
1074C22—34no—
1075C22—34no—
1076C22—41no—
1077C22—41no—
1078C22—41no—
1079C22—41no—
1080C22—41no—
1081C22—41no—
1082C22—41no—
1083C22—62no—
1084C22—62no—
1085C22—62no—
1086C22—62no—
1087C22—62no—
1088C22—62no—
1089C22—62no—
1090C22—62no—
1091C22—62no—
1092C22—62no—
1093C22—62no—
1094C22—62no—
1095C22—94no—
1096C22—1832no—
1097C22—182no—
1098C22—182no—
1099C22—182no—
1100C22—182no—
1101C22—182no—
1102C22—182no—
1103C22D3×#23511yescharacteristic
1104C22#6430611yescharacteristic
1105C22D32×D411yescharacteristic
1106C22D32×D411yescharacteristic
1107C22D3×#23711yescharacteristic
1108C22#6431211yescharacteristic
1109C22C2×D3×#6711yescharacteristic
1110C4—22no—
1111C4—41no—
1112C4—62no—
1113C4—62no—
1114C4—121no—
1115C4—121no—
1116C4—121no—
1117C4—121no—
1118C4—182no—
1119C4—361no—
1120C4—361no—
1121C3—21no—
1122C3#7493611yescharacteristic, complemented
1123C3#8291211yescharacteristic, complemented
1124C2—64no—
1125C2—64no—
1126C2—81no—
1127C2—184no—
1128C2D3×#88311yescharacteristic
1129C2#1059426011yescharacteristic
1130C2#1059426611yescharacteristic
1131C2#1059426711yescharacteristic
1132C2#1059506011yescharacteristic
1133C2D3×#93711yescharacteristic
1134C2#1059530111yescharacteristic
subgroupG/H
center, FrattiniC23C22×D32
commutator, socle, cosocleC23×C32C24
FittingC2×C32×C22⋊C4C22
prime radicalC2×#63983C2
hypercenterC2×C22⋊C4D32
hypocenterC32#2849
LCSG ▷ C23×C32 ▷ C32
UCSC1 ◁ C23 ◁ C2×C22⋊C4

Complements

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

NH ≅ G/Ntype
1. C22×C4×D32C2semidirect
2. C2×C3×#883C2semidirect
4. C2×#63969C2semidirect
5. #10592655C2semidirect
6. C3×#4956C2semidirect
7. #10591722C2semidirect
8. #10591721C2semidirect
9. #10591399C2semidirect
10. #10591378C2semidirect
11. #10591377C2semidirect
12. #10591362C2semidirect
13. #10591294C2semidirect
14. #10591290C2semidirect
15. #10591277C2semidirect
31. C2×C32×C22⋊C4C22semidirect
32. C2×#3757C22semidirect
34. C2×C3×#217C22semidirect
35. C2×C3×#217C22semidirect
38. C2×C3×C4⋊Dic3C22semidirect
39. C2×C3×Dic3⋊C4C22semidirect
43. C2×#3724C22semidirect
44. C2×Dic3⋊Dic3C22semidirect
51. #63658C22semidirect
52. #63658C22semidirect
53. C3×C3⋊#95C22semidirect
54. C3×C3⋊#95C22semidirect
55. #63579C22semidirect
56. #63579C22semidirect
57. #63579C22semidirect
58. #63579C22semidirect
66. C2×#883D3semidirect
81. #4956D3semidirect
129. C2×C3×C4×D3D4semidirect
138. C2×D3×Dic3D4semidirect
194. C2×C3×C22⋊C4C2×D3semidirect
195. C2×C3×C22⋊C4C2×D3semidirect
203. C2×#217C2×D3semidirect
204. C2×#217C2×D3semidirect
222. C2×C4⋊Dic3C2×D3semidirect
226. C2×Dic3⋊C4C2×D3semidirect
245. C3⋊#95C2×D3semidirect
246. C3⋊#95C2×D3semidirect
452. C2×C4×D3#67semidirect
510. C2×C3⋊D3#123semidirect
524. C2×C3×D3#123semidirect
569. C2×C22⋊C4D32semidirect
935. C2×D3#883semidirect
964. C32#2849semidirect
1122. C3#74936semidirect
1123. C3#82912semidirect

Maximal subgroups

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

subgroupindex
C22×C4×D322
C2×C3×#8832
C2×#639832
C2×#639692
#105926552
C3×#49562
#105917222
#105917212
#105913992
#105913782
#105913772
#105913622
#105912942
#105912902
#105912772
#829123
#749363