Finite Group Databasebeta

← #11803038

Subgroups — #11803038

Order 1152.

1279 conjugacy classes of subgroups.

The subgroup lattice has 896 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#63952C211yesmaximal, characteristic
2#10592912C211yesmaximal, characteristic
3C3×#5210C211yesmaximal, characteristic, complemented
4C2×C3×C3⋊#95C211yesmaximal, characteristic, complemented
5#10591718C211yesmaximal, characteristic, complemented
6#10591711C211yesmaximal, characteristic
7Dic3×#217C211yesmaximal, characteristic, complemented
8#10591371C211yesmaximal, characteristic, complemented
9#10591367C211yesmaximal, characteristic, complemented
10#10591259C211yesmaximal, characteristic, complemented
11#10591258C211yesmaximal, characteristic, complemented
12#10591255C211yesmaximal, characteristic, complemented
13#10591249C211yesmaximal, characteristic, complemented
14#10591248C211yesmaximal, characteristic, complemented
15#10591245C211yesmaximal, characteristic, complemented
16#74383—31nomaximal
17#73367—31nomaximal
18C23×C32×C4C2211yescharacteristic
19C22×#638C2211yescharacteristic
20C23×C3×Dic3C2211yescharacteristic
21C23×C3×Dic3C2211yescharacteristic
22C22×#624C2211yescharacteristic
23C2×#3757C2211yescharacteristic
24C2×#3752C2211yescharacteristic
25C2×#3752C2211yescharacteristic
26C2×C3×#217C2211yescharacteristic
27C2×C3×#217C2211yescharacteristic
28C2×C3×Dic3⋊C4C2211yescharacteristic
29C2×C3×Dic3⋊C4C2211yescharacteristic
30C2×#3724C2211yescharacteristic
31C2×Dic3⋊Dic3C2211yescharacteristic
32C2×Dic3⋊Dic3C2211yescharacteristic
33C2×#3722C2211yescharacteristic
34C2×#3722C2211yescharacteristic
35C2×#3722C2211yescharacteristic
36C2×Dic32C2211yescharacteristic
37C2×Dic32C2211yescharacteristic
38C2×Dic32C2211yescharacteristic
39#63952C418yescomplemented
40#63658C2211yescharacteristic
41#63658C2211yescharacteristic
42C3×C3⋊#95C2211yescharacteristic
43C3×C3⋊#95C2211yescharacteristic
44C3×C3⋊#95C2211yescharacteristic
45C3×C3⋊#95C2211yescharacteristic
46C3×C3⋊#95C2211yescharacteristic
47C3×C3⋊#95C2211yescharacteristic
48#63579C2211yescharacteristic
49#63579C2211yescharacteristic
50#63579C2211yescharacteristic
51#63579C2211yescharacteristic
52#63579C2211yescharacteristic
53#63579C2211yescharacteristic
54C2×C4×#67—31no—
55C2×#67⋊C4—31no—
56C3×#385—31no—
57C2×C3×#95—31no—
58#5213—31no—
59#5213—31no—
60#5213—31no—
61#5213—61no—
62#5210—31no—
63#5210D311yescharacteristic, complemented
64C4×#217—31no—
65C2×C3⋊#95D311yescharacteristic, complemented
66#4990—31no—
67#4987—31no—
68#4978—31no—
69#4977—31no—
70#4958—31no—
71#4950—31no—
72Dic3×C22⋊C4—31no—
73#4670—31no—
74#4669—31no—
75#4669—31no—
76#4667—31no—
77#4664—31no—
78#4664—31no—
79#4655—31no—
80#4652—31no—
81#4652—31no—
82#4651—31no—
83#4651—31no—
84#4650—31no—
85C24×C32C2311yescharacteristic
86C23×C3⋊D3C2311yescharacteristic
87C22×C32×C4—22no—
88C22×C32×C4—41no—
89C22×C32×C4—41no—
90C22×C32×C4C2311yescharacteristic
91C22×C32×C4C2311yescharacteristic
92C2×#638—22no—
93C2×#638—22no—
94C2×#638C2×C414yes—
95C22×C3⋊Dic3C2311yescharacteristic
96C22×C3⋊Dic3C2311yescharacteristic
97C22×C3⋊Dic3C2311yescharacteristic
98C22×C3×Dic3—22no—
99C22×C3×Dic3—41no—
100C22×C3×Dic3—41no—
101C22×C3×Dic3—41no—
102C22×C3×Dic3—41no—
103C22×C3×Dic3C2×C414yes—
104C22×C3×Dic3C2311yescharacteristic
105C22×C3×Dic3C2311yescharacteristic
106C22×C3×Dic3C2311yescharacteristic
107C22×C3×Dic3C2311yescharacteristic
108C22×C3×Dic3C2311yescharacteristic
109C22×C3×Dic3C2311yescharacteristic
110C22×C3×Dic3C2311yescharacteristic
111C22×C3×Dic3C2311yescharacteristic
112C2×#624—41no—
113C2×#624—41no—
114C2×#624C2×C414yescomplemented
115#3757—22no—
116#3752—41no—
117#3752—41no—
118C3×#217—22no—
119C3×#217C2×C414yes—
120C3×Dic3⋊C4—41no—
121C3×Dic3⋊C4—41no—
122#3724C2×C414yescomplemented
123Dic3⋊Dic3—41no—
124Dic3⋊Dic3—41no—
125#3722—41no—
126#3722—41no—
127#3722C2×C414yescomplemented
128Dic32—41no—
129Dic32—41no—
130Dic32C2×C414yescomplemented
131#2318—91noSylow
132C23×C3×C4—21no—
133C23×C3×C4—31no—
134C23×C3×C4—31no—
135C23×C3×C4C2×D311yescharacteristic
136C23×C3×C4C2×D311yescharacteristic
137C22×#67—31no—
138C22×#67—31no—
139C22×#67—61no—
140C23×Dic3C2×D311yescharacteristic
141C23×Dic3C2×D311yescharacteristic
142C22×C4×D3—31no—
143C22×C4×D3—31no—
144C2×C3×C4⋊C4—31no—
145C2×C3×C4⋊C4—31no—
146C2×C3×C22⋊C4—31no—
147C2×C3×C22⋊C4—31no—
148C2×#217—31no—
149C2×#217—31no—
150C2×#217—61no—
151C2×#217C2×D311yescharacteristic
152C2×#217C2×D311yescharacteristic
153C4×#67—38no—
154C2×(C2×D3)⋊C4—31no—
155C2×(C2×D3)⋊C4—31no—
156C2×(C2×D3)⋊C4—31no—
157C2×(C2×D3)⋊C4—31no—
158C2×(C2×D3)⋊C4—31no—
159C2×(C2×D3)⋊C4—31no—
160C2×(C2×D3)⋊C4—31no—
161C2×(C2×D3)⋊C4—31no—
162C2×(C2×D3)⋊C4—31no—
163C2×(C2×D3)⋊C4—31no—
164C2×(C2×D3)⋊C4—61no—
165C2×(C2×D3)⋊C4—61no—
166C2×C4⋊Dic3—31no—
167C2×C4⋊Dic3—31no—
168C2×Dic3⋊C4—31no—
169C2×Dic3⋊C4—31no—
170C2×Dic3⋊C4—31no—
171C2×Dic3⋊C4—31no—
172C2×Dic3⋊C4C2×D311yescharacteristic
173C2×Dic3⋊C4C2×D311yescharacteristic
174C2×C4×Dic3—31no—
175C2×C4×Dic3—31no—
176C2×C4×Dic3—31no—
177C2×C4×Dic3—31no—
178C2×C4×Dic3—31no—
179C2×C4×Dic3—31no—
180#67⋊C4—38no—
181C3×#95—31no—
182C3×#95—31no—
183C3×#95—31no—
184C3×#95—31no—
185C3×#95—31no—
186C3×#95—31no—
187C3⋊#95—31no—
188C3⋊#95—31no—
189C3⋊#95—31no—
190C3⋊#95—31no—
191C3⋊#95—31no—
192C3⋊#95—31no—
193C3⋊#95—31no—
194C3⋊#95—31no—
195C3⋊#95—31no—
196C3⋊#95—31no—
197C3⋊#95—31no—
198C3⋊#95—31no—
199C3⋊#95—31no—
200C3⋊#95—31no—
201C3⋊#95—31no—
202C3⋊#95—31no—
203C3⋊#95—61no—
204C3⋊#95—61no—
205C3⋊#95C2×D311yescharacteristic
206C3⋊#95C2×D311yescharacteristic
207C3⋊#95C2×D311yescharacteristic
208C3⋊#95C2×D311yescharacteristic
209C3⋊#95C2×D311yescharacteristic
210C3⋊#95C2×D311yescharacteristic
211C23×C32—21no—
212C23×C32—21no—
213C23×C32—21no—
214C23×C32—21no—
215C23×C32C22×C412yes—
216C23×C32#4112yes—
217C23×C32#4112yes—
218C23×C32C2411yescharacteristic
219C22×C3⋊D3—21no—
220C22×C3⋊D3—21no—
221C22×C3⋊D3—21no—
222C22×C3⋊D3—21no—
223C22×C3⋊D3—21no—
224C22×C3⋊D3—21no—
225C22×C3⋊D3C22×C412yes—
226C2×C32×C4—21no—
227C2×C32×C4—21no—
228C2×C32×C4—21no—
229C2×C32×C4—21no—
230C2×C32×C4—21no—
231C2×C32×C4—21no—
232C2×C32×C4—44no—
233#638—28no—
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⋊Dic3C22×C412yes—
243C2×C3×Dic3—21no—
244C2×C3×Dic3—21no—
245C2×C3×Dic3—21no—
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—44no—
264C2×C3×Dic3—44no—
265C2×C3×Dic3C22×C412yes—
266C2×C3×Dic3C22×C412yes—
267C2×C3×Dic3C22×C412yes—
268C2×C3×Dic3C22×C412yes—
269#624—44no—
270C2×C4×D4—91no—
271#388—91no—
272#388—91no—
273#387—91no—
274#387—91no—
275#386—91no—
276#386—91no—
277#385—31no—
278#385—91no—
279#383—91no—
280#382—91no—
281#381—91no—
282#380—91no—
283C4×C22⋊C4—91no—
284C2×#95—31no—
285C24×C3—21no—
286C24×C3C22×D311yescharacteristic
287C24×C3C22×D311yescharacteristic
288C23×D3—31no—
289C23×D3—31no—
290C23×D3—61no—
291C22×C3×C4—22no—
292C22×C3×C4—22no—
293C22×C3×C4—21no—
294C22×C3×C4—21no—
295C22×C3×C4—31no—
296C22×C3×C4—31no—
297C22×C3×C4—31no—
298C22×C3×C4—31no—
299C22×C3×C4—34no—
300C22×C3×C4—31no—
301C22×C3×C4—31no—
302C22×C3×C4—31no—
303C22×C3×C4—31no—
304C22×C3×C4—42no—
305C22×C3×C4—41no—
306C22×C3×C4—41no—
307C22×C3×C4—41no—
308C22×C3×C4—41no—
309C22×C3×C4—42no—
310C22×C3×C4—42no—
311C22×C3×C4—62no—
312C22×C3×C4—121no—
313C22×C3×C4—121no—
314C22×C3×C4—121no—
315C22×C3×C4—121no—
316C22×C3×C4C22×D311yescharacteristic
317C22×C3×C4C22×D311yescharacteristic
318C22×C3×C4C22×D311yescharacteristic
319C22×C3×C4C22×D311yescharacteristic
320C2×#67—34no—
321C2×#67—34no—
322C2×#67—64no—
323C2×#67—62no—
324C2×#67—62no—
325C2×#67—62no—
326C2×#67—62no—
327C2×#67—122no—
328C2×#67—122no—
329C22×Dic3—22no—
330C22×Dic3—31no—
331C22×Dic3—31no—
332C22×Dic3—31no—
333C22×Dic3—31no—
334C22×Dic3—31no—
335C22×Dic3—31no—
336C22×Dic3—41no—
337C22×Dic3—41no—
338C22×Dic3—41no—
339C22×Dic3—41no—
340C22×Dic3—61no—
341C22×Dic3—61no—
342C22×Dic3—61no—
343C22×Dic3C4×D314yes—
344C22×Dic3C22×D311yescharacteristic
345C22×Dic3C22×D311yescharacteristic
346C22×Dic3C22×D311yescharacteristic
347C22×Dic3C22×D311yescharacteristic
348C22×Dic3C22×D311yescharacteristic
349C22×Dic3C22×D311yescharacteristic
350C22×Dic3C22×D311yescharacteristic
351C22×Dic3C22×D311yescharacteristic
352C2×C4×D3—34no—
353C2×C4×D3—34no—
354C2×C4×D3—121no—
355C2×C4×D3—121no—
356C2×C4×D3—121no—
357C2×C4×D3—121no—
358C3×C4⋊C4—121no—
359C3×C4⋊C4—121no—
360C3×C22⋊C4—34no—
361C3×C22⋊C4—62no—
362#217—22no—
363#217—62no—
364#217—62no—
365#217—122no—
366#217C4×D314yes—
367(C2×D3)⋊C4—34no—
368(C2×D3)⋊C4—34no—
369(C2×D3)⋊C4—121no—
370(C2×D3)⋊C4—121no—
371(C2×D3)⋊C4—121no—
372(C2×D3)⋊C4—121no—
373(C2×D3)⋊C4—121no—
374(C2×D3)⋊C4—121no—
375(C2×D3)⋊C4—121no—
376(C2×D3)⋊C4—121no—
377(C2×D3)⋊C4—122no—
378(C2×D3)⋊C4—122no—
379C4⋊Dic3—121no—
380C4⋊Dic3—121no—
381Dic3⋊C4—34no—
382Dic3⋊C4—34no—
383Dic3⋊C4—41no—
384Dic3⋊C4—41no—
385Dic3⋊C4—121no—
386Dic3⋊C4—121no—
387C4×Dic3—34no—
388C4×Dic3—34no—
389C4×Dic3—121no—
390C4×Dic3—121no—
391C4×Dic3—121no—
392C4×Dic3—121no—
393C22×C32—22no—
394C22×C32—22no—
395C22×C32—22no—
396C22×C32—22no—
397C22×C32—22no—
398C22×C32—22no—
399C22×C32#11714yes—
400C22×C32C23×C411yescharacteristic
401C22×C32C2×#4111yescharacteristic
402C22×C32C2×#4111yescharacteristic
403C22×C32H(5,𝔽2)11yescharacteristic
404C22×C32H(5,𝔽2)11yescharacteristic
405C22×C32H(5,𝔽2)11yescharacteristic
406C22×C322−1+411yescharacteristic
407C2×C3⋊D3—22no—
408C2×C3⋊D3—22no—
409C2×C3⋊D3—22no—
410C2×C3⋊D3—41no—
411C2×C3⋊D3—41no—
412C2×C3⋊D3—41no—
413C2×C3⋊D3—41no—
414C32×C4—41no—
415C32×C4—41no—
416C3⋊Dic3—22no—
417C3⋊Dic3—41no—
418C3⋊Dic3—41no—
419C3×Dic3—22no—
420C3×Dic3—22no—
421C3×Dic3—22no—
422C3×Dic3—22no—
423C3×Dic3—41no—
424C3×Dic3—41no—
425C3×Dic3—41no—
426C3×Dic3—41no—
427C22×D4—91no—
428C23×C4—31no—
429C23×C4—31no—
430C23×C4—91no—
431C23×C4D3211yescharacteristic
432C4×D4—98no—
433C2×C4⋊C4—31no—
434C2×C4⋊C4—31no—
435C2×C4⋊C4—91no—
436C2×C4⋊C4—91no—
437C2×C4⋊C4—91no—
438C2×C22⋊C4—31no—
439C2×C22⋊C4—31no—
440C2×C22⋊C4—91no—
441C2×C22⋊C4—91no—
442C2×C22⋊C4—91no—
443C2×C22⋊C4—91no—
444C2×C22⋊C4—91no—
445C2×C22⋊C4—91no—
446C2×C42—91no—
447C2×C42—91no—
448C2×C42—91no—
449#95—31no—
450#95—31no—
451#95—31no—
452#95—31no—
453#95—31no—
454#95—31no—
455#95—91no—
456#95—91no—
457#95—91no—
458#95—91no—
459#95—91no—
460#95—91no—
461#95—91no—
462#95—91no—
463C23×C3—21no—
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—22no—
473C23×C3—22no—
474C23×C3—22no—
475C23×C3—41no—
476C23×C3—41no—
477C23×C3—41no—
478C23×C3—41no—
479C23×C3C2×C4×D312yes—
480C23×C3C2×C4×D312yes—
481C23×C3#23512yes—
482C23×C3#23512yes—
483C23×C3#23712yes—
484C23×C3#23912yes—
485C23×C3C23×D311yescharacteristic
486C23×C3C23×D311yescharacteristic
487C22×D3—32no—
488C22×D3—32no—
489C22×D3—62no—
490C22×D3—61no—
491C22×D3—61no—
492C22×D3—61no—
493C22×D3—61no—
494C22×D3—61no—
495C22×D3—61no—
496C22×D3—61no—
497C22×D3—61no—
498C22×D3—61no—
499C22×D3—61no—
500C22×D3—61no—
501C22×D3—61no—
502C22×D3—121no—
503C22×D3—121no—
504C22×D3—121no—
505C22×D3—121no—
506C22×D3—121no—
507C22×D3—121no—
508C2×C3×C4—22no—
509C2×C3×C4—22no—
510C2×C3×C4—21no—
511C2×C3×C4—21no—
512C2×C3×C4—21no—
513C2×C3×C4—21no—
514C2×C3×C4—21no—
515C2×C3×C4—21no—
516C2×C3×C4—21no—
517C2×C3×C4—21no—
518C2×C3×C4—21no—
519C2×C3×C4—21no—
520C2×C3×C4—21no—
521C2×C3×C4—21no—
522C2×C3×C4—32no—
523C2×C3×C4—32no—
524C2×C3×C4—32no—
525C2×C3×C4—32no—
526C2×C3×C4—41no—
527C2×C3×C4—41no—
528C2×C3×C4—41no—
529C2×C3×C4—41no—
530C2×C3×C4—44no—
531C2×C3×C4—44no—
532C2×C3×C4—48no—
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—61no—
545C2×C3×C4—61no—
546C2×C3×C4—61no—
547C2×C3×C4—61no—
548C2×C3×C4—61no—
549C2×C3×C4—61no—
550C2×C3×C4—61no—
551C2×C3×C4—61no—
552C2×C3×C4—61no—
553C2×C3×C4—124no—
554C2×C3×C4—124no—
555#67—68no—
556#67—68no—
557#67—128no—
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—21no—
569C2×Dic3—21no—
570C2×Dic3—21no—
571C2×Dic3—21no—
572C2×Dic3—21no—
573C2×Dic3—21no—
574C2×Dic3—21no—
575C2×Dic3—21no—
576C2×Dic3—21no—
577C2×Dic3—21no—
578C2×Dic3—32no—
579C2×Dic3—32no—
580C2×Dic3—44no—
581C2×Dic3—44no—
582C2×Dic3—62no—
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—61no—
595C2×Dic3—61no—
596C2×Dic3—61no—
597C2×Dic3—61no—
598C2×Dic3—61no—
599C2×Dic3—121no—
600C2×Dic3—121no—
601C2×Dic3—121no—
602C2×Dic3—121no—
603C2×Dic3—121no—
604C2×Dic3—121no—
605C2×Dic3—121no—
606C2×Dic3—121no—
607C2×Dic3C2×C4×D312yes—
608C2×Dic3C2×C4×D312yes—
609C2×Dic3C2×C4×D312yes—
610C2×Dic3C2×C4×D312yes—
611C4×D3—124no—
612C4×D3—124no—
613C2×C32—24no—
614C2×C32C2×#11711yescharacteristic
615C2×C32#51811yescharacteristic
616C2×C32#52011yescharacteristic
617C2×C32#53811yescharacteristic
618C2×C32#53811yescharacteristic
619C2×C32#53911yescharacteristic
620C2×C32#53911yescharacteristic
621C3⋊D3—42no—
622C24—91no—
623C24C2×D3211yescharacteristic
624C2×D4—94no—
625C2×D4—182no—
626C2×D4—182no—
627C22×C4—22no—
628C22×C4—31no—
629C22×C4—31no—
630C22×C4—31no—
631C22×C4—31no—
632C22×C4—34no—
633C22×C4—31no—
634C22×C4—31no—
635C22×C4—31no—
636C22×C4—31no—
637C22×C4—41no—
638C22×C4—41no—
639C22×C4—62no—
640C22×C4—94no—
641C22×C4—91no—
642C22×C4—91no—
643C22×C4—91no—
644C22×C4—121no—
645C22×C4—121no—
646C22×C4—121no—
647C22×C4—121no—
648C22×C4—361no—
649C22×C4—361no—
650C22×C4C2×D3211yescharacteristic
651C22×C4C2×D3211yescharacteristic
652C4⋊C4—94no—
653C4⋊C4—121no—
654C4⋊C4—121no—
655C4⋊C4—361no—
656C4⋊C4—361no—
657C22⋊C4—34no—
658C22⋊C4—62no—
659C22⋊C4—94no—
660C22⋊C4—182no—
661C22⋊C4—361no—
662C22⋊C4—361no—
663C22⋊C4—361no—
664C22⋊C4—361no—
665C42—94no—
666C42—361no—
667C42—361no—
668C22×C3—22no—
669C22×C3—22no—
670C22×C3—22no—
671C22×C3—22no—
672C22×C3—22no—
673C22×C3—22no—
674C22×C3—22no—
675C22×C3—22no—
676C22×C3—22no—
677C22×C3—22no—
678C22×C3—22no—
679C22×C3—22no—
680C22×C3—21no—
681C22×C3—21no—
682C22×C3—21no—
683C22×C3—21no—
684C22×C3—21no—
685C22×C3—21no—
686C22×C3—21no—
687C22×C3—24no—
688C22×C3—42no—
689C22×C3—42no—
690C22×C3—42no—
691C22×C3—42no—
692C22×C3—42no—
693C22×C3—42no—
694C22×C3#87214yes—
695C22×C3#89214yes—
696C22×C3C22×C4×D311yescharacteristic
697C22×C3C22×C4×D311yescharacteristic
698C22×C3C2×#23511yescharacteristic
699C22×C3C2×#23511yescharacteristic
700C22×C3C2×#23711yescharacteristic
701C22×C3#100411yescharacteristic
702C22×C3#100411yescharacteristic
703C22×C3#100411yescharacteristic
704C22×C3#100411yescharacteristic
705C22×C3#100411yescharacteristic
706C22×C3C2×#23911yescharacteristic
707C22×C3#100711yescharacteristic
708C22×C3#100911yescharacteristic
709C22×C3#101011yescharacteristic
710C2×D3—62no—
711C2×D3—62no—
712C2×D3—62no—
713C2×D3—62no—
714C2×D3—62no—
715C2×D3—62no—
716C2×D3—122no—
717C2×D3—122no—
718C2×D3—122no—
719C2×D3—121no—
720C2×D3—121no—
721C2×D3—121no—
722C2×D3—121no—
723C2×D3—121no—
724C2×D3—121no—
725C2×D3—121no—
726C2×D3—121no—
727C2×D3—241no—
728C2×D3—241no—
729C2×D3—241no—
730C2×D3—241no—
731C3×C4—42no—
732C3×C4—42no—
733C3×C4—41no—
734C3×C4—41no—
735C3×C4—41no—
736C3×C4—41no—
737C3×C4—62no—
738C3×C4—62no—
739C3×C4—62no—
740C3×C4—62no—
741C3×C4—121no—
742C3×C4—121no—
743C3×C4—121no—
744C3×C4—121no—
745Dic3—22no—
746Dic3—22no—
747Dic3—22no—
748Dic3—22no—
749Dic3—41no—
750Dic3—41no—
751Dic3—41no—
752Dic3—41no—
753Dic3—62no—
754Dic3—62no—
755Dic3—122no—
756Dic3—121no—
757Dic3—121no—
758Dic3—121no—
759Dic3—121no—
760Dic3—241no—
761Dic3—241no—
762C32#231811yescharacteristic, complemented, Sylow
763C23—21no—
764C23—21no—
765C23—21no—
766C23—21no—
767C23—92no—
768C23—181no—
769C23—181no—
770C23—181no—
771C23—181no—
772C23—181no—
773C23—181no—
774C23#379912yes—
775C23C4×D3212yes—
776C23#380412yes—
777C23C22×D3211yescharacteristic
778D4—188no—
779C2×C4—21no—
780C2×C4—21no—
781C2×C4—21no—
782C2×C4—21no—
783C2×C4—21no—
784C2×C4—21no—
785C2×C4—32no—
786C2×C4—32no—
787C2×C4—32no—
788C2×C4—32no—
789C2×C4—44no—
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—61no—
801C2×C4—61no—
802C2×C4—61no—
803C2×C4—61no—
804C2×C4—61no—
805C2×C4—61no—
806C2×C4—61no—
807C2×C4—61no—
808C2×C4—61no—
809C2×C4—61no—
810C2×C4—92no—
811C2×C4—124no—
812C2×C4—124no—
813C2×C4—181no—
814C2×C4—181no—
815C2×C4—181no—
816C2×C4—181no—
817C2×C4—181no—
818C2×C4—181no—
819C2×C4—181no—
820C2×C4—181no—
821C2×C4—364no—
822C2×C3—24no—
823C2×C3—24no—
824C2×C3—21no—
825C2×C3—21no—
826C2×C3—21no—
827C2×C3—21no—
828C2×C3—21no—
829C2×C3—21no—
830C2×C3—21no—
831C2×C3—44no—
832C2×C3C2×#87211yescharacteristic
833C2×C3#548611yescharacteristic
834C2×C3#549411yescharacteristic
835C2×C3#549411yescharacteristic
836C2×C3C2×#89211yescharacteristic
837C2×C3#550411yescharacteristic
838C2×C3#551511yescharacteristic
839C2×C3#551511yescharacteristic
840C2×C3#554511yescharacteristic
841C2×C3#554611yescharacteristic
842C2×C3#559311yescharacteristic
843C2×C3#564411yescharacteristic
844C2×C3#564511yescharacteristic
845C2×C3#566511yescharacteristic
846D3—122no—
847D3—122no—
848D3—242no—
849C22—22no—
850C22—22no—
851C22—22no—
852C22—22no—
853C22—22no—
854C22—22no—
855C22—182no—
856C22—182no—
857C22—182no—
858C22—361no—
859C22—361no—
860C22—361no—
861C22—361no—
862C22#6383614yes—
863C22#6429711yescharacteristic
864C22C2×#379911yescharacteristic
865C22C2×C4×D3211yescharacteristic
866C22#6430711yescharacteristic
867C22C2×#380411yescharacteristic
868C22#6433011yescharacteristic
869C22#6433011yescharacteristic
870C4—41no—
871C4—41no—
872C4—62no—
873C4—62no—
874C4—62no—
875C4—62no—
876C4—121no—
877C4—121no—
878C4—121no—
879C4—121no—
880C4—182no—
881C4—361no—
882C4—361no—
883C3—21no—
884C3#7336711yescharacteristic, complemented
885C3#7438311yescharacteristic, complemented
886C2—24no—
887C2—362no—
888C2C2×#6383611yescharacteristic
889C2#1059487411yescharacteristic
890C2#1059498011yescharacteristic
891C2#1059498711yescharacteristic
892C2#1059503811yescharacteristic
893C2#1059505611yescharacteristic
894C2#1059550711yescharacteristic
subgroupG/H
center, FrattiniC23C22×D32
commutatorC22×C32C23×C4
FittingC23×C32×C4C22
socle, cosocleC23×C32C24
prime radicalC22×#638C22
hypercenterC23×C4D32
hypocenterC32#2318
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C23×C4

Complements

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

NH ≅ G/Ntype
3. C3×#5210C2semidirect
4. C2×C3×C3⋊#95C2semidirect
5. #10591718C2semidirect
7. Dic3×#217C2semidirect
8. #10591371C2semidirect
9. #10591367C2semidirect
10. #10591259C2semidirect
11. #10591258C2semidirect
12. #10591255C2semidirect
13. #10591249C2semidirect
14. #10591248C2semidirect
15. #10591245C2semidirect
39. #63952C4semidirect
63. #5210D3semidirect
65. C2×C3⋊#95D3semidirect
114. C2×#624C2×C4semidirect
122. #3724C2×C4semidirect
127. #3722C2×C4semidirect
130. Dic32C2×C4semidirect
762. C32#2318semidirect
884. C3#73367semidirect
885. C3#74383semidirect

Maximal subgroups

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

subgroupindex
C2×#639522
#105929122
C3×#52102
C2×C3×C3⋊#952
#105917182
#105917112
Dic3×#2172
#105913712
#105913672
#105912592
#105912582
#105912552
#105912492
#105912482
#105912452
#743833
#733673