Finite Group Databasebeta

← #11817803

Subgroups — #11817803

Order 1152.

1165 conjugacy classes of subgroups.

The subgroup lattice has 887 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#63956C211yesmaximal, characteristic, complemented
2C2×#63955C211yesmaximal, characteristic, complemented
3#10592920C211yesmaximal, characteristic
4C3×#5222C211yesmaximal, characteristic
5C3×#5220C211yesmaximal, characteristic
6#10591715C211yesmaximal, characteristic, complemented
7#10591715C211yesmaximal, characteristic, complemented
8#10591703C211yesmaximal, characteristic, complemented
9#10591702C211yesmaximal, characteristic, complemented
10#10591702C211yesmaximal, characteristic, complemented
11#10591693C211yesmaximal, characteristic, complemented
12#10591351C211yesmaximal, characteristic, complemented
13#10591334C211yesmaximal, characteristic, complemented
14#10591268C211yesmaximal, characteristic, complemented
15#10591257C211yesmaximal, characteristic, complemented
16#76932—31nomaximal
17#74734—31nomaximal
18C22×C32×D4C2211yescharacteristic
19C23×C3×Dic3C2211yescharacteristic
20C2×#3757C2211yescharacteristic
21C2×#3757C2211yescharacteristic
22C2×#3757C2211yescharacteristic
23C2×#3757C2211yescharacteristic
24C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
25C2×C4×C3⋊Dic3C2211yescharacteristic
26C2×C3×#217C2211yescharacteristic
27C2×C3×#217C2211yescharacteristic
28C2×C3×#217C2211yescharacteristic
29C2×C3×#217C2211yescharacteristic
30C2×C3×#217C2211yescharacteristic
31C2×C3×#217C2211yescharacteristic
32C2×C3×#217C2211yescharacteristic
33C2×C3×Dic3⋊C4C2211yescharacteristic
34C2×#3724C2211yescharacteristic
35C2×#3724C2211yescharacteristic
36C2×#3724C2211yescharacteristic
37C2×Dic3⋊Dic3C2211yescharacteristic
38C2×Dic3⋊Dic3C2211yescharacteristic
39C2×Dic3⋊Dic3C2211yescharacteristic
40C2×Dic3⋊Dic3C2211yescharacteristic
41C2×Dic3⋊Dic3C2211yescharacteristic
42#63956—24no—
43#63955—24no—
44C2×Dic32C2211yescharacteristic
45C2×Dic32C2211yescharacteristic
46C2×Dic32C2211yescharacteristic
47C3×C3⋊#95C2211yescharacteristic
48C3×C3⋊#95C2211yescharacteristic
49C3×C3⋊#95C2211yescharacteristic
50#63579C2211yescharacteristic
51#63579C2211yescharacteristic
52#63579C2211yescharacteristic
53#63579C2211yescharacteristic
54#63579C2211yescharacteristic
55C2×#926—31no—
56C2×#879—31no—
57C2×#879—31no—
58C2×#877—31no—
59C3×#394—31no—
60C3×#386—31no—
61#5222D311yescharacteristic
62#5221—31no—
63#5221—31no—
64#5221—61no—
65#5220D311yescharacteristic
66#5210—31no—
67#4984—31no—
68#4978—31no—
69#4951—31no—
70#4951—31no—
71#4949—31no—
72#4949—31no—
73#4949—31no—
74#4949—31no—
75#4946—31no—
76#4945—31no—
77#4945—31no—
78#4945—31no—
79#4944—31no—
80#4661—31no—
81#4657—31no—
82#4653—31no—
83#4649—31no—
84#4649—31no—
85#4647—31no—
86C24×C32C2311yescharacteristic
87C24×C32C2311yescharacteristic
88C2×C32×D4—22no—
89C2×C32×D4—22no—
90C2×C32×D4—41no—
91C22×C32×C4C2311yescharacteristic
92C22×C3⋊Dic3C2311yescharacteristic
93C22×C3⋊Dic3C2311yescharacteristic
94C22×C3⋊Dic3C2311yescharacteristic
95C22×C3⋊Dic3C2311yescharacteristic
96C22×C3×Dic3—22no—
97C22×C3×Dic3—22no—
98C22×C3×Dic3—22no—
99C22×C3×Dic3C2311yescharacteristic
100C22×C3×Dic3C2311yescharacteristic
101C22×C3×Dic3C2311yescharacteristic
102C22×C3×Dic3C2311yescharacteristic
103C22×C3×Dic3C2311yescharacteristic
104C22×C3×Dic3C2311yescharacteristic
105C22×C3×Dic3C2311yescharacteristic
106C22×C3×Dic3C2311yescharacteristic
107#3757—22no—
108#3757—22no—
109#3757—22no—
110#3757—22no—
111C4⋊(C3⋊Dic3)—41no—
112C4×C3⋊Dic3—22no—
113C3×#217—22no—
114C3×#217—22no—
115C3×#217—22no—
116C3×#217—22no—
117C3×#217—22no—
118C3×#217—41no—
119C3×#217—41no—
120C3×Dic3⋊C4—22no—
121#3724—22no—
122#3724—22no—
123#3724—22no—
124Dic3⋊Dic3—22no—
125Dic3⋊Dic3—22no—
126Dic3⋊Dic3—41no—
127Dic3⋊Dic3—41no—
128Dic3⋊Dic3D414yescomplemented
129Dic32—22no—
130Dic32—22no—
131Dic32—22no—
132#2479—91noSylow
133C22×C3×D4—21no—
134C22×C3×D4C2×D311yescharacteristic
135C22×C3×D4C2×D311yescharacteristic
136C23×C3×C4—31no—
137C23×Dic3C2×D311yescharacteristic
138C2×C3×C4⋊C4—31no—
139C2×C3×C22⋊C4—31no—
140C2×C3×C22⋊C4—31no—
141C2×C3×C22⋊C4—31no—
142C2×C3×C22⋊C4—31no—
143C2×C3×C22⋊C4—31no—
144C2×C3×C22⋊C4—31no—
145C2×C3×C22⋊C4—31no—
146C2×#217—31no—
147C2×#217—31no—
148C2×#217—31no—
149C2×#217—31no—
150C2×#217—31no—
151C2×#217—31no—
152C2×#217—31no—
153C2×#217—31no—
154C2×#217—61no—
155C2×#217—61no—
156C2×#217—61no—
157C2×#217—61no—
158C2×#217C2×D311yescharacteristic
159C2×#217C2×D311yescharacteristic
160C2×#217C2×D311yescharacteristic
161C2×#217C2×D311yescharacteristic
162C2×#217C2×D311yescharacteristic
163C2×#217C2×D311yescharacteristic
164C2×#217C2×D311yescharacteristic
165#926—64no—
166C2×C4⋊Dic3—31no—
167C2×C4⋊Dic3—31no—
168C2×C4⋊Dic3—31no—
169C2×C4⋊Dic3—31no—
170C2×C4⋊Dic3—31no—
171C2×C4⋊Dic3—31no—
172C2×C4⋊Dic3—31no—
173C2×C4⋊Dic3—61no—
174C2×Dic3⋊C4—31no—
175C2×Dic3⋊C4—31no—
176C2×Dic3⋊C4—31no—
177C2×Dic3⋊C4—31no—
178C2×Dic3⋊C4—31no—
179C2×Dic3⋊C4—31no—
180C2×Dic3⋊C4—31no—
181C2×Dic3⋊C4—31no—
182C2×Dic3⋊C4—31no—
183C2×Dic3⋊C4—31no—
184C2×Dic3⋊C4—31no—
185C2×Dic3⋊C4C2×D311yescharacteristic
186C2×C4×Dic3—31no—
187C2×C4×Dic3—31no—
188C2×C4×Dic3—31no—
189C2×C4×Dic3—31no—
190C2×C4×Dic3—31no—
191C2×C4×Dic3—31no—
192C2×C4×Dic3—31no—
193C2×C4×Dic3—31no—
194C2×C4×Dic3—61no—
195#879—64no—
196#879—64no—
197#877—64no—
198C3×#95—31no—
199C3×#95—31no—
200C3×#95—31no—
201C3⋊#95—31no—
202C3⋊#95—31no—
203C3⋊#95—31no—
204C3⋊#95—31no—
205C3⋊#95—31no—
206C3⋊#95—31no—
207C3⋊#95—31no—
208C3⋊#95—31no—
209C3⋊#95—31no—
210C3⋊#95—31no—
211C3⋊#95C2×D311yescharacteristic
212C3⋊#95C2×D311yescharacteristic
213C3⋊#95C2×D311yescharacteristic
214C23×C32—21no—
215C23×C32—21no—
216C23×C32—21no—
217C23×C32—21no—
218C23×C32—21no—
219C23×C32—21no—
220C23×C32—21no—
221C23×C32—21no—
222C23×C32—21no—
223C23×C32—21no—
224C23×C32—21no—
225C23×C32—21no—
226C23×C32—21no—
227C23×C32#4112yes—
228C23×C32C2411yescharacteristic
229C32×D4—44no—
230C2×C32×C4—21no—
231C2×C32×C4—21no—
232C2×C32×C4#4112yes—
233C2×C3⋊Dic3—21no—
234C2×C3⋊Dic3—21no—
235C2×C3⋊Dic3—21no—
236C2×C3⋊Dic3—21no—
237C2×C3⋊Dic3—21no—
238C2×C3⋊Dic3—21no—
239C2×C3⋊Dic3—21no—
240C2×C3⋊Dic3—21no—
241C2×C3⋊Dic3—21no—
242C2×C3⋊Dic3—21no—
243C2×C3⋊Dic3C2×D412yes—
244C2×C3⋊Dic3#4112yes—
245C2×C3×Dic3—28no—
246C2×C3×Dic3—21no—
247C2×C3×Dic3—21no—
248C2×C3×Dic3—21no—
249C2×C3×Dic3—21no—
250C2×C3×Dic3—21no—
251C2×C3×Dic3—21no—
252C2×C3×Dic3—21no—
253C2×C3×Dic3—21no—
254C2×C3×Dic3—21no—
255C2×C3×Dic3—21no—
256C2×C3×Dic3—21no—
257C2×C3×Dic3—21no—
258C2×C3×Dic3—21no—
259C2×C3×Dic3—21no—
260C2×C3×Dic3—21no—
261C2×C3×Dic3—21no—
262C2×C3×Dic3—21no—
263C2×C3×Dic3—21no—
264C2×C3×Dic3—21no—
265C2×C3×Dic3—21no—
266C2×C3×Dic3—21no—
267C2×C3×Dic3C2×D412yes—
268C2×C3×Dic3C2×D412yes—
269C2×C3×Dic3#4112yes—
270C2×#126—91no—
271C2×#117—91no—
272#399—91no—
273#399—91no—
274#398—91no—
275#394—31no—
276#390—91no—
277#389—91no—
278#388—91no—
279#388—91no—
280#388—91no—
281#387—91no—
282#386—31no—
283#385—91no—
284C4×C4⋊C4—91no—
285C24×C3—21no—
286C24×C3—21no—
287C24×C3C22×D311yescharacteristic
288C24×C3C22×D311yescharacteristic
289C24×C3C22×D311yescharacteristic
290C24×C3C22×D311yescharacteristic
291C2×C3×D4—24no—
292C2×C3×D4—22no—
293C2×C3×D4—22no—
294C2×C3×D4—22no—
295C2×C3×D4—22no—
296C2×C3×D4—42no—
297C2×C3×D4—41no—
298C2×C3×D4—41no—
299C2×C3×D4—42no—
300C22×C3×C4—21no—
301C22×C3×C4—31no—
302C22×C3×C4—31no—
303C22×C3×C4—31no—
304C22×C3×C4—31no—
305C22×C3×C4—31no—
306C22×C3×C4—31no—
307C22×C3×C4—31no—
308C22×C3×C4—31no—
309C22×C3×C4—62no—
310C22×C3×C4—62no—
311C22×C3×C4—62no—
312C22×C3×C4C22×D311yescharacteristic
313C22×C3×C4C22×D311yescharacteristic
314C22×Dic3—22no—
315C22×Dic3—22no—
316C22×Dic3—22no—
317C22×Dic3—31no—
318C22×Dic3—31no—
319C22×Dic3—31no—
320C22×Dic3—31no—
321C22×Dic3—31no—
322C22×Dic3—31no—
323C22×Dic3—31no—
324C22×Dic3—31no—
325C22×Dic3—61no—
326C22×Dic3—61no—
327C22×Dic3—61no—
328C22×Dic3—61no—
329C22×Dic3C22×D311yescharacteristic
330C22×Dic3C22×D311yescharacteristic
331C22×Dic3C22×D311yescharacteristic
332C22×Dic3C22×D311yescharacteristic
333C22×Dic3C22×D311yescharacteristic
334C22×Dic3C22×D311yescharacteristic
335C22×Dic3C22×D311yescharacteristic
336C22×Dic3C22×D311yescharacteristic
337C3×C4⋊C4—62no—
338C3×C22⋊C4—62no—
339C3×C22⋊C4—62no—
340C3×C22⋊C4—62no—
341C3×C22⋊C4—62no—
342C3×C22⋊C4—62no—
343C3×C22⋊C4—121no—
344C3×C22⋊C4—121no—
345#217—22no—
346#217—22no—
347#217—22no—
348#217—22no—
349#217—22no—
350#217—41no—
351#217—41no—
352#217—62no—
353#217—62no—
354#217—62no—
355#217—62no—
356#217—62no—
357#217—62no—
358#217—62no—
359#217—62no—
360#217—122no—
361#217—122no—
362#217—122no—
363#217—122no—
364C4⋊Dic3—34no—
365C4⋊Dic3—62no—
366C4⋊Dic3—62no—
367C4⋊Dic3—121no—
368C4⋊Dic3—121no—
369C4⋊Dic3—121no—
370C4⋊Dic3—121no—
371C4⋊Dic3—122no—
372Dic3⋊C4—22no—
373Dic3⋊C4—34no—
374Dic3⋊C4—62no—
375Dic3⋊C4—62no—
376Dic3⋊C4—62no—
377Dic3⋊C4—62no—
378Dic3⋊C4—62no—
379Dic3⋊C4—62no—
380Dic3⋊C4—62no—
381Dic3⋊C4—62no—
382Dic3⋊C4—121no—
383Dic3⋊C4—121no—
384C4×Dic3—62no—
385C4×Dic3—62no—
386C4×Dic3—62no—
387C4×Dic3—62no—
388C4×Dic3—62no—
389C4×Dic3—62no—
390C4×Dic3—62no—
391C4×Dic3—62no—
392C4×Dic3—122no—
393C22×C32—22no—
394C22×C32—22no—
395C22×C32—22no—
396C22×C32—41no—
397C22×C32—41no—
398C22×C32—41no—
399C22×C32—41no—
400C22×C32—41no—
401C22×C32—41no—
402C22×C32—41no—
403C22×C32—41no—
404C22×C32—41no—
405C22×C32—41no—
406C22×C32—41no—
407C22×C32C22×D411yescharacteristic
408C22×C32C2×#4111yescharacteristic
409C22×C32C2×#4111yescharacteristic
410C22×C32C2×#4111yescharacteristic
411C22×C32C2×#4111yescharacteristic
412C22×C32H(5,𝔽2)11yescharacteristic
413C22×C322−1+411yescharacteristic
414C32×C4—22no—
415C3⋊Dic3—22no—
416C3⋊Dic3—22no—
417C3⋊Dic3—41no—
418C3⋊Dic3—41no—
419C3×Dic3—22no—
420C3×Dic3—22no—
421C3×Dic3—22no—
422C3×Dic3—41no—
423C3×Dic3—41no—
424C3×Dic3—41no—
425C3×Dic3—41no—
426C3×Dic3—41no—
427C22×D4D3211yescharacteristic
428C23×C4—31no—
429#126—184no—
430#117—184no—
431C2×C4⋊C4—31no—
432C2×C4⋊C4—91no—
433C2×C4⋊C4—91no—
434C2×C4⋊C4—91no—
435C2×C4⋊C4—91no—
436C2×C4⋊C4—91no—
437C2×C4⋊C4—91no—
438C2×C4⋊C4—91no—
439C2×C4⋊C4—91no—
440C2×C4⋊C4—91no—
441C2×C22⋊C4—31no—
442C2×C22⋊C4—31no—
443C2×C22⋊C4—31no—
444C2×C22⋊C4—31no—
445C2×C22⋊C4—31no—
446C2×C22⋊C4—31no—
447C2×C22⋊C4—31no—
448C2×C22⋊C4—91no—
449C2×C22⋊C4—91no—
450C2×C22⋊C4—91no—
451C2×C22⋊C4—91no—
452C2×C42—91no—
453C2×C42—91no—
454C2×C42—91no—
455C2×C42—91no—
456#95—31no—
457#95—31no—
458#95—31no—
459#95—91no—
460#95—91no—
461#95—91no—
462#95—91no—
463#95—91no—
464C23×C3—21no—
465C23×C3—21no—
466C23×C3—21no—
467C23×C3—21no—
468C23×C3—21no—
469C23×C3—21no—
470C23×C3—21no—
471C23×C3—21no—
472C23×C3—21no—
473C23×C3—21no—
474C23×C3—21no—
475C23×C3—21no—
476C23×C3—22no—
477C23×C3—21no—
478C23×C3—21no—
479C23×C3—21no—
480C23×C3—21no—
481C23×C3—21no—
482C23×C3—21no—
483C23×C3—21no—
484C23×C3—21no—
485C23×C3—21no—
486C23×C3—21no—
487C23×C3—21no—
488C23×C3—21no—
489C23×C3—21no—
490C23×C3—21no—
491C23×C3—21no—
492C23×C3—22no—
493C23×C3—41no—
494C23×C3—41no—
495C23×C3—41no—
496C23×C3—41no—
497C23×C3—41no—
498C23×C3—41no—
499C23×C3—41no—
500C23×C3—41no—
501C23×C3—41no—
502C23×C3—41no—
503C23×C3—41no—
504C23×C3—41no—
505C23×C3#23712yes—
506C23×C3#23712yes—
507C23×C3C23×D311yescharacteristic
508C23×C3C23×D311yescharacteristic
509C3×D4—44no—
510C3×D4—44no—
511C3×D4—48no—
512C2×C3×C4—22no—
513C2×C3×C4—22no—
514C2×C3×C4—21no—
515C2×C3×C4—21no—
516C2×C3×C4—21no—
517C2×C3×C4—21no—
518C2×C3×C4—22no—
519C2×C3×C4—32no—
520C2×C3×C4—32no—
521C2×C3×C4—32no—
522C2×C3×C4—68no—
523C2×C3×C4—61no—
524C2×C3×C4—61no—
525C2×C3×C4—61no—
526C2×C3×C4—61no—
527C2×C3×C4—61no—
528C2×C3×C4—61no—
529C2×C3×C4—61no—
530C2×C3×C4—61no—
531C2×C3×C4—61no—
532C2×C3×C4—61no—
533C2×C3×C4—61no—
534C2×C3×C4—61no—
535C2×C3×C4—61no—
536C2×C3×C4—61no—
537C2×C3×C4—61no—
538C2×C3×C4—61no—
539C2×C3×C4—61no—
540C2×C3×C4—61no—
541C2×C3×C4—61no—
542C2×C3×C4—61no—
543C2×C3×C4—61no—
544C2×C3×C4#23512yes—
545C2×C3×C4#23712yes—
546C2×Dic3—28no—
547C2×Dic3—21no—
548C2×Dic3—21no—
549C2×Dic3—21no—
550C2×Dic3—21no—
551C2×Dic3—21no—
552C2×Dic3—21no—
553C2×Dic3—21no—
554C2×Dic3—21no—
555C2×Dic3—21no—
556C2×Dic3—21no—
557C2×Dic3—21no—
558C2×Dic3—21no—
559C2×Dic3—21no—
560C2×Dic3—21no—
561C2×Dic3—21no—
562C2×Dic3—21no—
563C2×Dic3—21no—
564C2×Dic3—21no—
565C2×Dic3—21no—
566C2×Dic3—21no—
567C2×Dic3—21no—
568C2×Dic3—32no—
569C2×Dic3—32no—
570C2×Dic3—32no—
571C2×Dic3—32no—
572C2×Dic3—62no—
573C2×Dic3—62no—
574C2×Dic3—61no—
575C2×Dic3—61no—
576C2×Dic3—61no—
577C2×Dic3—61no—
578C2×Dic3—61no—
579C2×Dic3—61no—
580C2×Dic3—61no—
581C2×Dic3—61no—
582C2×Dic3—61no—
583C2×Dic3—61no—
584C2×Dic3—61no—
585C2×Dic3—61no—
586C2×Dic3—61no—
587C2×Dic3—61no—
588C2×Dic3—61no—
589C2×Dic3—61no—
590C2×Dic3—61no—
591C2×Dic3—61no—
592C2×Dic3—61no—
593C2×Dic3—61no—
594C2×Dic3—121no—
595C2×Dic3—121no—
596C2×Dic3—121no—
597C2×Dic3—121no—
598C2×Dic3—121no—
599C2×Dic3—121no—
600C2×Dic3—121no—
601C2×Dic3—121no—
602C2×Dic3—121no—
603C2×Dic3—121no—
604C2×Dic3D3×D412yes—
605C2×Dic3D3×D412yes—
606C2×Dic3#23712yes—
607C2×C32—42no—
608C2×C32—81no—
609C2×C32#52511yescharacteristic
610C2×C32#52911yescharacteristic
611C2×C32#54211yescharacteristic
612C2×C32#54711yescharacteristic
613C2×C32#55011yescharacteristic
614C2×C32#55111yescharacteristic
615C2×C32#55211yescharacteristic
616C24C2×D3211yescharacteristic
617C24C2×D3211yescharacteristic
618C2×D4—22no—
619C2×D4—22no—
620C2×D4—41no—
621C22×C4—31no—
622C22×C4—31no—
623C22×C4—31no—
624C22×C4—31no—
625C22×C4—31no—
626C22×C4—31no—
627C22×C4—31no—
628C22×C4—31no—
629C22×C4—62no—
630C22×C4—62no—
631C22×C4—62no—
632C22×C4—91no—
633C22×C4—91no—
634C22×C4—91no—
635C22×C4—91no—
636C22×C4C2×D3211yescharacteristic
637C4⋊C4—62no—
638C4⋊C4—94no—
639C4⋊C4—182no—
640C4⋊C4—182no—
641C4⋊C4—182no—
642C4⋊C4—182no—
643C4⋊C4—182no—
644C4⋊C4—361no—
645C4⋊C4—361no—
646C4⋊C4—361no—
647C22⋊C4—62no—
648C22⋊C4—62no—
649C22⋊C4—62no—
650C22⋊C4—62no—
651C22⋊C4—62no—
652C22⋊C4—121no—
653C22⋊C4—121no—
654C22⋊C4—182no—
655C22⋊C4—182no—
656C22⋊C4—182no—
657C22⋊C4—182no—
658C42—182no—
659C42—182no—
660C42—182no—
661C42—182no—
662C22×C3—22no—
663C22×C3—22no—
664C22×C3—22no—
665C22×C3—22no—
666C22×C3—22no—
667C22×C3—22no—
668C22×C3—21no—
669C22×C3—21no—
670C22×C3—21no—
671C22×C3—21no—
672C22×C3—21no—
673C22×C3—21no—
674C22×C3—21no—
675C22×C3—42no—
676C22×C3—42no—
677C22×C3—42no—
678C22×C3—42no—
679C22×C3—42no—
680C22×C3—42no—
681C22×C3—41no—
682C22×C3—41no—
683C22×C3—41no—
684C22×C3—41no—
685C22×C3—41no—
686C22×C3—41no—
687C22×C3—41no—
688C22×C3—41no—
689C22×C3—41no—
690C22×C3—41no—
691C22×C3—41no—
692C22×C3—41no—
693C22×C3—41no—
694C22×C3—41no—
695C22×C3—41no—
696C22×C3—41no—
697C22×C3—41no—
698C22×C3—41no—
699C22×C3—41no—
700C22×C3—41no—
701C22×C3—41no—
702C22×C3—41no—
703C22×C3—81no—
704C22×C3—81no—
705C22×C3—81no—
706C22×C3—81no—
707C22×C3—81no—
708C22×C3—81no—
709C22×C3—81no—
710C22×C3—81no—
711C22×C3C2×#23511yescharacteristic
712C22×C3C2×D3×D411yescharacteristic
713C22×C3C2×D3×D411yescharacteristic
714C22×C3C2×#23711yescharacteristic
715C22×C3C2×#23711yescharacteristic
716C22×C3C2×#23711yescharacteristic
717C22×C3C2×#23711yescharacteristic
718C22×C3#100411yescharacteristic
719C22×C3#100411yescharacteristic
720C22×C3D3×#4111yescharacteristic
721C22×C3D3×#4111yescharacteristic
722C22×C3D3×#4111yescharacteristic
723C22×C3#101011yescharacteristic
724C22×C3#101011yescharacteristic
725C3×C4—24no—
726C3×C4—22no—
727C3×C4—22no—
728C3×C4—62no—
729C3×C4—62no—
730C3×C4—62no—
731C3×C4—121no—
732C3×C4—121no—
733C3×C4—121no—
734C3×C4—121no—
735C3×C4—121no—
736Dic3—22no—
737Dic3—22no—
738Dic3—22no—
739Dic3—41no—
740Dic3—41no—
741Dic3—41no—
742Dic3—41no—
743Dic3—41no—
744Dic3—62no—
745Dic3—62no—
746Dic3—62no—
747Dic3—62no—
748Dic3—122no—
749Dic3—122no—
750Dic3—121no—
751Dic3—121no—
752Dic3—121no—
753Dic3—121no—
754Dic3—241no—
755Dic3—241no—
756C32#247911yescharacteristic, complemented, Sylow
757C23—21no—
758C23—21no—
759C23—21no—
760C23—21no—
761C23—21no—
762C23—21no—
763C23—21no—
764C23—21no—
765C23—21no—
766C23—21no—
767C23—21no—
768C23—21no—
769C23—21no—
770C23#380512yes—
771C23C22×D3211yescharacteristic
772D4—44no—
773C2×C4—21no—
774C2×C4—21no—
775C2×C4—32no—
776C2×C4—32no—
777C2×C4—32no—
778C2×C4—68no—
779C2×C4—61no—
780C2×C4—61no—
781C2×C4—61no—
782C2×C4—61no—
783C2×C4—61no—
784C2×C4—61no—
785C2×C4—61no—
786C2×C4—61no—
787C2×C4—61no—
788C2×C4—61no—
789C2×C4—61no—
790C2×C4—61no—
791C2×C4—61no—
792C2×C4—61no—
793C2×C4—61no—
794C2×C4—61no—
795C2×C4—61no—
796C2×C4—61no—
797C2×C4—61no—
798C2×C4—61no—
799C2×C4—61no—
800C2×C4—92no—
801C2×C4—92no—
802C2×C4—181no—
803C2×C4—181no—
804C2×C4—181no—
805C2×C4—181no—
806C2×C4—181no—
807C2×C4—181no—
808C2×C4—181no—
809C2×C4—181no—
810C2×C4—181no—
811C2×C4—181no—
812C2×C4#380412yes—
813C2×C3—21no—
814C2×C3—21no—
815C2×C3—21no—
816C2×C3—21no—
817C2×C3—21no—
818C2×C3—21no—
819C2×C3—21no—
820C2×C3—42no—
821C2×C3—42no—
822C2×C3—82no—
823C2×C3—82no—
824C2×C3—81no—
825C2×C3—81no—
826C2×C3#549511yescharacteristic
827C2×C3#555111yescharacteristic
828C2×C3#555711yescharacteristic
829C2×C3#558611yescharacteristic
830C2×C3#558711yescharacteristic
831C2×C3#559911yescharacteristic
832C2×C3#559911yescharacteristic
833C2×C3#560311yescharacteristic
834C2×C3#560611yescharacteristic
835C2×C3#561111yescharacteristic
836C2×C3#565011yescharacteristic
837C2×C3#565011yescharacteristic
838C2×C3#566211yescharacteristic
839C2×C3#568011yescharacteristic
840C22—22no—
841C22—22no—
842C22—22no—
843C22—41no—
844C22—41no—
845C22—41no—
846C22—41no—
847C22—41no—
848C22—41no—
849C22—41no—
850C22—41no—
851C22—41no—
852C22—41no—
853C22—41no—
854C22#6430911yescharacteristic
855C22D32×D411yescharacteristic
856C22D3×#23711yescharacteristic
857C22#6431211yescharacteristic
858C22C2×#380411yescharacteristic
859C22C2×#380511yescharacteristic
860C22#6433011yescharacteristic
861C4—22no—
862C4—62no—
863C4—62no—
864C4—62no—
865C4—121no—
866C4—121no—
867C4—121no—
868C4—121no—
869C4—121no—
870C4—182no—
871C4—182no—
872C4—361no—
873C4—361no—
874C3—21no—
875C3#7473411yescharacteristic, complemented
876C3#7693211yescharacteristic, complemented
877C2—42no—
878C2—81no—
879C2#1059512011yescharacteristic
880C2#1059513011yescharacteristic
881C2#1059513611yescharacteristic
882C2#1059519111yescharacteristic
883C2#1059520311yescharacteristic
884C2#1059526911yescharacteristic
885C2#1059550911yescharacteristic
subgroupG/H
center, FrattiniC23C22×D32
commutator, socle, cosocleC23×C32C24
Fitting, prime radicalC22×C32×D4C22
hypercenterC22×D4D32
hypocenterC32#2479
LCSG ▷ C23×C32 ▷ C32
UCSC1 ◁ C23 ◁ C22×D4

Complements

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

NH ≅ G/Ntype
1. C2×#63956C2semidirect
2. C2×#63955C2semidirect
6. #10591715C2semidirect
7. #10591715C2semidirect
8. #10591703C2semidirect
9. #10591702C2semidirect
10. #10591702C2semidirect
11. #10591693C2semidirect
12. #10591351C2semidirect
13. #10591334C2semidirect
14. #10591268C2semidirect
15. #10591257C2semidirect
128. Dic3⋊Dic3D4semidirect
756. C32#2479semidirect
875. C3#74734semidirect
876. C3#76932semidirect

Maximal subgroups

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

subgroupindex
C2×#639562
C2×#639552
#105929202
C3×#52222
C3×#52202
#105917152
#105917032
#105917022
#105916932
#105913512
#105913342
#105912682
#105912572
#769323
#747343