Finite Group Databasebeta

← #11807935

Subgroups — #11807935

Order 1152.

1439 conjugacy classes of subgroups.

The subgroup lattice has 1052 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#63911C211yesmaximal, characteristic
2#10592364C211yesmaximal, characteristic, complemented
3C3×#4665C211yesmaximal, characteristic, complemented
4C3×#4651C211yesmaximal, characteristic, complemented
5#10591387C211yesmaximal, characteristic, complemented
6#10591387C211yesmaximal, characteristic, complemented
7#10591382C211yesmaximal, characteristic, complemented
8#10591382C211yesmaximal, characteristic, complemented
9#10591380C211yesmaximal, characteristic, complemented
10#10591376C211yesmaximal, characteristic, complemented
11#10591364C211yesmaximal, characteristic, complemented
12#10591364C211yesmaximal, characteristic, complemented
13#10591275C211yesmaximal, characteristic, complemented
14#10591275C211yesmaximal, characteristic, complemented
15#10591223C211yesmaximal, characteristic, complemented
16#74685—31nomaximal
17#74298—31nomaximal
18C22×C4⋊(C3⋊D3)C2211yescharacteristic
19C22×C4×C3⋊D3C2211yescharacteristic
20C22×C3×D12C2211yescharacteristic
21C22×C3×C4×D3C2211yescharacteristic
22C22×#626C2211yescharacteristic
23C22×#626C2211yescharacteristic
24C22×#626C2211yescharacteristic
25C22×#626C2211yescharacteristic
26C22×#624C2211yescharacteristic
27C22×D3×Dic3C2211yescharacteristic
28C2×#3752C2211yescharacteristic
29C2×#3752C2211yescharacteristic
30C2×#3752C2211yescharacteristic
31C2×C3×(C2×D3)⋊C4C2211yescharacteristic
32C2×C3×(C2×D3)⋊C4C2211yescharacteristic
33C2×C3×(C2×D3)⋊C4C2211yescharacteristic
34C2×C3×C4×Dic3C2211yescharacteristic
35C2×#3722C2211yescharacteristic
36C2×#3722C2211yescharacteristic
37C2×#3722C2211yescharacteristic
38C2×(C2×D3)⋊Dic3C2211yescharacteristic
39C2×(C2×D3)⋊Dic3C2211yescharacteristic
40C2×(C2×D3)⋊Dic3C2211yescharacteristic
41#63911C418yescomplemented
42C32×#95C2211yescharacteristic
43#63658C2211yescharacteristic
44C3×C3⋊#95C2211yescharacteristic
45C3×C3⋊#95C2211yescharacteristic
46C3×C3⋊#95C2211yescharacteristic
47C3×C3⋊#95C2211yescharacteristic
48C3×C3⋊#95C2211yescharacteristic
49C3×C3⋊#95C2211yescharacteristic
50#63579C2211yescharacteristic
51#63579C2211yescharacteristic
52#63579C2211yescharacteristic
53#63579C2211yescharacteristic
54C2×#940—31no—
55C2×#874—31no—
56C3×#386—31no—
57C3×#383—31no—
58#5220—31no—
59#5213—31no—
60#5213—31no—
61#4958—31no—
62#4958—31no—
63#4956—31no—
64#4956—31no—
65#4956—31no—
66#4956—31no—
67#4937—31no—
68#4665—31no—
69#4665—31no—
70#4665—31no—
71#4665—31no—
72#4665—31no—
73#4665—31no—
74#4665—31no—
75#4665—31no—
76#4665—31no—
77#4665—31no—
78#4665—31no—
79#4665—31no—
80#4665—31no—
81#4665—61no—
82#4665D311yescharacteristic, complemented
83#4651—31no—
84#4651D311yescharacteristic, complemented
85C23×C3⋊D3C2311yescharacteristic
86C23×C3⋊D3C2311yescharacteristic
87C23×C3×D3C2311yescharacteristic
88C23×C3×D3C2311yescharacteristic
89C22×C32×C4C2311yescharacteristic
90C22×C32×C4C2311yescharacteristic
91C22×C32×C4C2311yescharacteristic
92C22×C3⋊Dic3C2311yescharacteristic
93C22×C3⋊Dic3C2311yescharacteristic
94C2×C4⋊(C3⋊D3)—41no—
95C2×C4⋊(C3⋊D3)—41no—
96C2×C4⋊(C3⋊D3)C2×C414yescomplemented
97C2×C4×C3⋊D3—41no—
98C2×C4×C3⋊D3—41no—
99C2×C4×C3⋊D3—41no—
100C22×C3×Dic3C2311yescharacteristic
101C22×C3×Dic3C2311yescharacteristic
102C22×C3×Dic3C2311yescharacteristic
103C22×C3×Dic3C2311yescharacteristic
104C22×C3×Dic3C2311yescharacteristic
105C22×C3×Dic3C2311yescharacteristic
106C2×C3×D12—41no—
107C2×C3×D12—41no—
108C2×C3×D12C2×C414yescomplemented
109C2×C3×C4×D3—41no—
110C2×C3×C4×D3—41no—
111C2×C3×C4×D3—41no—
112C2×#626—41no—
113C2×#626—41no—
114C2×#626—41no—
115C2×#626—41no—
116C2×#626—41no—
117C2×#626—41no—
118C2×#626—41no—
119C2×#626—41no—
120C2×#626C2×C414yescomplemented
121C2×#626C2×C414yescomplemented
122C2×#626C2×C414yescomplemented
123C2×#626C2×C414yescomplemented
124C2×#624—41no—
125C2×#624—41no—
126C2×#624—41no—
127C2×D3×Dic3—41no—
128C2×D3×Dic3—41no—
129C2×D3×Dic3—41no—
130#3752—41no—
131#3752—41no—
132#3752—41no—
133C3×(C2×D3)⋊C4—41no—
134C3×(C2×D3)⋊C4—41no—
135C3×(C2×D3)⋊C4—41no—
136C3×C4×Dic3C2×C414yescomplemented
137#3722—41no—
138#3722—41no—
139#3722—41no—
140(C2×D3)⋊Dic3—41no—
141(C2×D3)⋊Dic3—41no—
142(C2×D3)⋊Dic3—41no—
143#2380—91noSylow
144C22×C3×D4—31no—
145C23×C3×C4—31no—
146C22×#67—31no—
147C22×#67—31no—
148C22×#67—31no—
149C22×#67—31no—
150C23×Dic3—31no—
151C22×D12—31no—
152C22×D12—31no—
153C22×D12—31no—
154C22×D12—31no—
155C22×D12—31no—
156C22×D12—31no—
157C22×D12—61no—
158C22×D12C2×D311yescharacteristic
159C22×C4×D3—31no—
160C22×C4×D3—31no—
161C22×C4×D3—31no—
162C22×C4×D3—31no—
163C22×C4×D3—31no—
164C22×C4×D3—61no—
165C22×C4×D3C2×D311yescharacteristic
166C2×C3×C22⋊C4—31no—
167C2×C3×C22⋊C4—31no—
168C2×C3×C22⋊C4—31no—
169C2×C3×C42—31no—
170C2×#217—31no—
171C2×#217—31no—
172C2×#217—31no—
173#940—38no—
174C2×(C2×D3)⋊C4—31no—
175C2×(C2×D3)⋊C4—31no—
176C2×(C2×D3)⋊C4—31no—
177C2×(C2×D3)⋊C4—31no—
178C2×(C2×D3)⋊C4—31no—
179C2×(C2×D3)⋊C4—31no—
180C2×(C2×D3)⋊C4—31no—
181C2×(C2×D3)⋊C4—31no—
182C2×(C2×D3)⋊C4—31no—
183C2×(C2×D3)⋊C4—31no—
184C2×(C2×D3)⋊C4—31no—
185C2×(C2×D3)⋊C4—31no—
186C2×(C2×D3)⋊C4—31no—
187C2×(C2×D3)⋊C4—31no—
188C2×(C2×D3)⋊C4—31no—
189C2×(C2×D3)⋊C4—61no—
190C2×(C2×D3)⋊C4—61no—
191C2×(C2×D3)⋊C4—61no—
192C2×(C2×D3)⋊C4C2×D311yescharacteristic
193C2×(C2×D3)⋊C4C2×D311yescharacteristic
194C2×(C2×D3)⋊C4C2×D311yescharacteristic
195C2×C4×Dic3C2×D311yescharacteristic
196#874—38no—
197C3×#95—21no—
198C3×#95—31no—
199C3×#95—31no—
200C3×#95—31no—
201C3×#95—31no—
202C3×#95—31no—
203C3×#95—31no—
204C3×#95C2×D311yescharacteristic
205C3×#95C2×D311yescharacteristic
206C3⋊#95—31no—
207C3⋊#95—31no—
208C3⋊#95—31no—
209C3⋊#95—31no—
210C3⋊#95—31no—
211C3⋊#95—31no—
212C3⋊#95—31no—
213C3⋊#95—31no—
214C3⋊#95—31no—
215C3⋊#95—31no—
216C3⋊#95—61no—
217C3⋊#95C2×D311yescharacteristic
218C3⋊#95C2×D311yescharacteristic
219C3⋊#95C2×D311yescharacteristic
220C3⋊#95C2×D311yescharacteristic
221C3⋊#95C2×D311yescharacteristic
222C3⋊#95C2×D311yescharacteristic
223C23×C32C2411yescharacteristic
224C22×C3⋊D3—21no—
225C22×C3⋊D3—21no—
226C22×C3⋊D3—21no—
227C22×C3⋊D3—21no—
228C22×C3⋊D3—21no—
229C22×C3⋊D3—21no—
230C22×C3⋊D3—21no—
231C22×C3⋊D3—21no—
232C22×C3⋊D3—21no—
233C22×C3⋊D3—21no—
234C22×C3⋊D3—21no—
235C22×C3⋊D3—21no—
236C22×C3⋊D3C22×C412yes—
237C22×C3⋊D3C22×C412yes—
238C22×C3×D3—21no—
239C22×C3×D3—21no—
240C22×C3×D3—21no—
241C22×C3×D3—21no—
242C22×C3×D3—21no—
243C22×C3×D3—21no—
244C22×C3×D3—21no—
245C22×C3×D3—21no—
246C22×C3×D3—21no—
247C22×C3×D3—21no—
248C22×C3×D3—21no—
249C22×C3×D3—21no—
250C22×C3×D3C22×C412yes—
251C22×C3×D3C22×C412yes—
252C2×C32×C4—21no—
253C2×C32×C4—21no—
254C2×C32×C4—21no—
255C2×C32×C4—21no—
256C2×C32×C4—21no—
257C2×C32×C4—21no—
258C2×C32×C4—21no—
259C2×C32×C4—21no—
260C2×C32×C4C22×C412yes—
261C2×C3⋊Dic3—21no—
262C2×C3⋊Dic3—21no—
263C2×C3⋊Dic3—21no—
264C2×C3⋊Dic3—21no—
265C2×C3⋊Dic3—21no—
266C2×C3⋊Dic3—21no—
267C4⋊(C3⋊D3)—44no—
268C4×C3⋊D3—44no—
269C2×C3×Dic3—21no—
270C2×C3×Dic3—21no—
271C2×C3×Dic3—21no—
272C2×C3×Dic3—21no—
273C2×C3×Dic3—21no—
274C2×C3×Dic3—21no—
275C2×C3×Dic3—21no—
276C2×C3×Dic3—21no—
277C2×C3×Dic3—21no—
278C2×C3×Dic3—21no—
279C2×C3×Dic3—21no—
280C2×C3×Dic3—21no—
281C2×C3×Dic3—21no—
282C2×C3×Dic3—21no—
283C2×C3×Dic3—21no—
284C2×C3×Dic3—21no—
285C2×C3×Dic3C22×C412yes—
286C2×C3×Dic3C22×C412yes—
287C3×D12—44no—
288C3×C4×D3—44no—
289#626—44no—
290#626—44no—
291#626—44no—
292#626—44no—
293#624—44no—
294D3×Dic3—44no—
295C2×#127—91no—
296#386—31no—
297#386—91no—
298#386—91no—
299#386—91no—
300#386—91no—
301#386—91no—
302#386—91no—
303#386—91no—
304#386—91no—
305#386—91no—
306#386—91no—
307#386—91no—
308#383—31no—
309#383—91no—
310C24×C3—31no—
311C24×C3—31no—
312C23×D3—31no—
313C23×D3—31no—
314C23×D3—31no—
315C23×D3—31no—
316C23×D3—61no—
317C23×D3—61no—
318C23×D3C22×D311yescharacteristic
319C23×D3C22×D311yescharacteristic
320C2×C3×D4—34no—
321C2×C3×D4—121no—
322C2×C3×D4—121no—
323C22×C3×C4—21no—
324C22×C3×C4—21no—
325C22×C3×C4—21no—
326C22×C3×C4—31no—
327C22×C3×C4—31no—
328C22×C3×C4—31no—
329C22×C3×C4—31no—
330C22×C3×C4—31no—
331C22×C3×C4—31no—
332C22×C3×C4—121no—
333C22×C3×C4—121no—
334C22×C3×C4—121no—
335C22×C3×C4C22×D311yescharacteristic
336C22×C3×C4C22×D311yescharacteristic
337C22×C3×C4C22×D311yescharacteristic
338C22×C3×C4C22×D311yescharacteristic
339C22×C3×C4C22×D311yescharacteristic
340C22×C3×C4C22×D311yescharacteristic
341C2×#67—34no—
342C2×#67—34no—
343C2×#67—34no—
344C2×#67—34no—
345C2×#67—121no—
346C2×#67—121no—
347C2×#67—121no—
348C2×#67—121no—
349C2×#67—121no—
350C2×#67—121no—
351C2×#67—121no—
352C2×#67—121no—
353C22×Dic3—31no—
354C22×Dic3—31no—
355C22×Dic3—31no—
356C22×Dic3—31no—
357C22×Dic3—61no—
358C22×Dic3—61no—
359C22×Dic3—121no—
360C22×Dic3—121no—
361C22×Dic3—121no—
362C22×Dic3C22×D311yescharacteristic
363C22×Dic3C22×D311yescharacteristic
364C22×Dic3C22×D311yescharacteristic
365C22×Dic3C22×D311yescharacteristic
366C22×Dic3C22×D311yescharacteristic
367C22×Dic3C22×D311yescharacteristic
368C2×D12—34no—
369C2×D12—34no—
370C2×D12—34no—
371C2×D12—34no—
372C2×D12—34no—
373C2×D12—34no—
374C2×D12—41no—
375C2×D12—41no—
376C2×D12—64no—
377C2×D12—121no—
378C2×D12—121no—
379C2×D12—121no—
380C2×D12—121no—
381C2×D12—122no—
382C2×D12—122no—
383C2×D12—121no—
384C2×D12—121no—
385C2×D12—121no—
386C2×D12—121no—
387C2×D12—121no—
388C2×D12—121no—
389C2×D12—121no—
390C2×D12—121no—
391C2×D12C4×D314yescomplemented
392C2×C4×D3—41no—
393C2×C4×D3—41no—
394C2×C4×D3—41no—
395C2×C4×D3—121no—
396C2×C4×D3—121no—
397C2×C4×D3—121no—
398C2×C4×D3—121no—
399C2×C4×D3—121no—
400C2×C4×D3—121no—
401C2×C4×D3—121no—
402C2×C4×D3—121no—
403C2×C4×D3—121no—
404C2×C4×D3—121no—
405C2×C4×D3—121no—
406C2×C4×D3—121no—
407C2×C4×D3—122no—
408C2×C4×D3—121no—
409C2×C4×D3—121no—
410C2×C4×D3—121no—
411C2×C4×D3—122no—
412C2×C4×D3—122no—
413C3×C22⋊C4—121no—
414C3×C22⋊C4—121no—
415C3×C22⋊C4—121no—
416C3×C42—34no—
417#217—121no—
418#217—121no—
419#217—121no—
420(C2×D3)⋊C4—41no—
421(C2×D3)⋊C4—41no—
422(C2×D3)⋊C4—41no—
423(C2×D3)⋊C4—121no—
424(C2×D3)⋊C4—121no—
425(C2×D3)⋊C4—121no—
426(C2×D3)⋊C4—121no—
427(C2×D3)⋊C4—121no—
428(C2×D3)⋊C4—121no—
429(C2×D3)⋊C4—121no—
430(C2×D3)⋊C4—121no—
431(C2×D3)⋊C4—121no—
432(C2×D3)⋊C4—121no—
433(C2×D3)⋊C4—121no—
434(C2×D3)⋊C4—121no—
435(C2×D3)⋊C4—122no—
436(C2×D3)⋊C4—121no—
437(C2×D3)⋊C4—121no—
438(C2×D3)⋊C4—121no—
439(C2×D3)⋊C4—122no—
440(C2×D3)⋊C4—122no—
441C4×Dic3C4×D314yescomplemented
442C22×C32C23×C411yescharacteristic
443C22×C32H(5,𝔽2)11yescharacteristic
444C22×C32H(5,𝔽2)11yescharacteristic
445C22×C32H(5,𝔽2)11yescharacteristic
446C22×C32H(5,𝔽2)11yescharacteristic
447C22×C32H(5,𝔽2)11yescharacteristic
448C22×C32H(5,𝔽2)11yescharacteristic
449C2×C3⋊D3—22no—
450C2×C3⋊D3—22no—
451C2×C3⋊D3—22no—
452C2×C3⋊D3—22no—
453C2×C3⋊D3—22no—
454C2×C3⋊D3—22no—
455C2×C3⋊D3—41no—
456C2×C3⋊D3—41no—
457C2×C3⋊D3—41no—
458C2×C3⋊D3—41no—
459C2×C3⋊D3—41no—
460C2×C3⋊D3—41no—
461C2×C3⋊D3—41no—
462C2×C3⋊D3—41no—
463C2×C3×D3—22no—
464C2×C3×D3—22no—
465C2×C3×D3—22no—
466C2×C3×D3—22no—
467C2×C3×D3—22no—
468C2×C3×D3—22no—
469C2×C3×D3—41no—
470C2×C3×D3—41no—
471C2×C3×D3—41no—
472C2×C3×D3—41no—
473C2×C3×D3—41no—
474C2×C3×D3—41no—
475C2×C3×D3—41no—
476C2×C3×D3—41no—
477C32×C4—22no—
478C32×C4—41no—
479C32×C4—41no—
480C3⋊Dic3—41no—
481C3⋊Dic3—41no—
482C3×Dic3—22no—
483C3×Dic3—22no—
484C3×Dic3—41no—
485C3×Dic3—41no—
486C3×Dic3—41no—
487C3×Dic3—41no—
488C22×D4—31no—
489C22×D4—91no—
490C22×D4—91no—
491C22×D4—91no—
492C22×D4—91no—
493C22×D4—91no—
494C23×C4—31no—
495C23×C4—91no—
496C23×C4—91no—
497C23×C4—91no—
498#127—98no—
499C2×C22⋊C4—31no—
500C2×C22⋊C4—31no—
501C2×C22⋊C4—31no—
502C2×C22⋊C4—91no—
503C2×C22⋊C4—91no—
504C2×C22⋊C4—91no—
505C2×C22⋊C4—91no—
506C2×C22⋊C4—91no—
507C2×C22⋊C4—91no—
508C2×C22⋊C4—91no—
509C2×C22⋊C4—91no—
510C2×C22⋊C4—91no—
511C2×C42—31no—
512#95—31no—
513#95—31no—
514#95—31no—
515#95—31no—
516#95—31no—
517#95—31no—
518#95—91no—
519#95—91no—
520#95—91no—
521#95—91no—
522#95—91no—
523#95D3211yescharacteristic
524C23×C3—21no—
525C23×C3—32no—
526C23×C3—32no—
527C23×C3—61no—
528C23×C3—61no—
529C23×C3—61no—
530C23×C3—61no—
531C23×C3—61no—
532C23×C3—61no—
533C23×C3—61no—
534C23×C3—61no—
535C23×C3—61no—
536C23×C3—61no—
537C23×C3—61no—
538C23×C3—61no—
539C23×C3C23×D311yescharacteristic
540C23×C3C23×D311yescharacteristic
541C22×D3—21no—
542C22×D3—21no—
543C22×D3—21no—
544C22×D3—21no—
545C22×D3—21no—
546C22×D3—21no—
547C22×D3—21no—
548C22×D3—21no—
549C22×D3—21no—
550C22×D3—21no—
551C22×D3—21no—
552C22×D3—21no—
553C22×D3—32no—
554C22×D3—32no—
555C22×D3—32no—
556C22×D3—32no—
557C22×D3—62no—
558C22×D3—62no—
559C22×D3—62no—
560C22×D3—62no—
561C22×D3—61no—
562C22×D3—61no—
563C22×D3—61no—
564C22×D3—61no—
565C22×D3—61no—
566C22×D3—61no—
567C22×D3—61no—
568C22×D3—61no—
569C22×D3—61no—
570C22×D3—61no—
571C22×D3—61no—
572C22×D3—61no—
573C22×D3—61no—
574C22×D3—61no—
575C22×D3—61no—
576C22×D3—61no—
577C22×D3—61no—
578C22×D3—61no—
579C22×D3—61no—
580C22×D3—61no—
581C22×D3—61no—
582C22×D3—61no—
583C22×D3—61no—
584C22×D3—61no—
585C22×D3—121no—
586C22×D3—121no—
587C22×D3—121no—
588C22×D3—121no—
589C22×D3—121no—
590C22×D3—121no—
591C22×D3—121no—
592C22×D3—121no—
593C22×D3—121no—
594C22×D3—121no—
595C22×D3C2×C4×D312yes—
596C22×D3C2×C4×D312yes—
597C3×D4—124no—
598C2×C3×C4—21no—
599C2×C3×C4—21no—
600C2×C3×C4—21no—
601C2×C3×C4—21no—
602C2×C3×C4—22no—
603C2×C3×C4—21no—
604C2×C3×C4—21no—
605C2×C3×C4—21no—
606C2×C3×C4—21no—
607C2×C3×C4—21no—
608C2×C3×C4—21no—
609C2×C3×C4—21no—
610C2×C3×C4—21no—
611C2×C3×C4—21no—
612C2×C3×C4—21no—
613C2×C3×C4—21no—
614C2×C3×C4—21no—
615C2×C3×C4—22no—
616C2×C3×C4—32no—
617C2×C3×C4—32no—
618C2×C3×C4—41no—
619C2×C3×C4—41no—
620C2×C3×C4—41no—
621C2×C3×C4—41no—
622C2×C3×C4—41no—
623C2×C3×C4—41no—
624C2×C3×C4—41no—
625C2×C3×C4—61no—
626C2×C3×C4—61no—
627C2×C3×C4—61no—
628C2×C3×C4—61no—
629C2×C3×C4—61no—
630C2×C3×C4—61no—
631C2×C3×C4—61no—
632C2×C3×C4—61no—
633C2×C3×C4—61no—
634C2×C3×C4—61no—
635C2×C3×C4—61no—
636C2×C3×C4—61no—
637C2×C3×C4—61no—
638C2×C3×C4—61no—
639C2×C3×C4—61no—
640C2×C3×C4—61no—
641C2×C3×C4—124no—
642C2×C3×C4C2×C4×D312yes—
643C2×C3×C4C2×C4×D312yes—
644#67—124no—
645#67—124no—
646#67—124no—
647#67—124no—
648C2×Dic3—21no—
649C2×Dic3—21no—
650C2×Dic3—21no—
651C2×Dic3—21no—
652C2×Dic3—21no—
653C2×Dic3—21no—
654C2×Dic3—21no—
655C2×Dic3—21no—
656C2×Dic3—21no—
657C2×Dic3—21no—
658C2×Dic3—21no—
659C2×Dic3—21no—
660C2×Dic3—21no—
661C2×Dic3—21no—
662C2×Dic3—21no—
663C2×Dic3—21no—
664C2×Dic3—62no—
665C2×Dic3—61no—
666C2×Dic3—61no—
667C2×Dic3—61no—
668C2×Dic3—61no—
669C2×Dic3—61no—
670C2×Dic3—61no—
671C2×Dic3—61no—
672C2×Dic3—61no—
673C2×Dic3—61no—
674C2×Dic3—61no—
675C2×Dic3—61no—
676C2×Dic3—61no—
677C2×Dic3—121no—
678C2×Dic3—121no—
679C2×Dic3—121no—
680C2×Dic3—121no—
681C2×Dic3—121no—
682C2×Dic3—124no—
683C2×Dic3C2×C4×D312yes—
684C2×Dic3C2×C4×D312yes—
685D12—44no—
686D12—124no—
687D12—124no—
688D12—128no—
689D12—124no—
690D12—124no—
691D12—124no—
692D12—124no—
693C4×D3—44no—
694C4×D3—124no—
695C4×D3—124no—
696C4×D3—128no—
697C4×D3—124no—
698C4×D3—124no—
699C4×D3—124no—
700C2×C32#51811yescharacteristic
701C2×C32#51811yescharacteristic
702C2×C32#51811yescharacteristic
703C2×C32#56011yescharacteristic
704C2×C32#56011yescharacteristic
705C2×C32#56011yescharacteristic
706C2×C32#56011yescharacteristic
707C3⋊D3—42no—
708C3⋊D3—42no—
709C3×D3—42no—
710C3×D3—42no—
711C24—31no—
712C24—31no—
713C24—91no—
714C24—91no—
715C2×D4—34no—
716C2×D4—94no—
717C2×D4—94no—
718C2×D4—94no—
719C2×D4—94no—
720C2×D4—94no—
721C2×D4—121no—
722C2×D4—121no—
723C2×D4—361no—
724C2×D4—361no—
725C2×D4—361no—
726C2×D4—361no—
727C2×D4—361no—
728C2×D4—361no—
729C2×D4—361no—
730C2×D4—361no—
731C2×D4—361no—
732C2×D4—361no—
733C22×C4—31no—
734C22×C4—31no—
735C22×C4—31no—
736C22×C4—31no—
737C22×C4—31no—
738C22×C4—31no—
739C22×C4—91no—
740C22×C4—91no—
741C22×C4—121no—
742C22×C4—121no—
743C22×C4—121no—
744C22×C4—361no—
745C22×C4—361no—
746C22×C4—361no—
747C22×C4—361no—
748C22×C4—361no—
749C22×C4—361no—
750C22×C4—361no—
751C22×C4—361no—
752C22×C4—361no—
753C22×C4C2×D3211yescharacteristic
754C22×C4C2×D3211yescharacteristic
755C22×C4C2×D3211yescharacteristic
756C22⋊C4—121no—
757C22⋊C4—121no—
758C22⋊C4—121no—
759C22⋊C4—361no—
760C22⋊C4—361no—
761C22⋊C4—361no—
762C22⋊C4—361no—
763C22⋊C4—361no—
764C22⋊C4—361no—
765C22⋊C4—361no—
766C22⋊C4—361no—
767C22⋊C4—361no—
768C42—34no—
769C22×C3—21no—
770C22×C3—21no—
771C22×C3—21no—
772C22×C3—21no—
773C22×C3—21no—
774C22×C3—21no—
775C22×C3—21no—
776C22×C3—62no—
777C22×C3—62no—
778C22×C3—62no—
779C22×C3—62no—
780C22×C3—62no—
781C22×C3—62no—
782C22×C3—121no—
783C22×C3—121no—
784C22×C3—121no—
785C22×C3—121no—
786C22×C3—121no—
787C22×C3—121no—
788C22×C3—121no—
789C22×C3—121no—
790C22×C3C22×C4×D311yescharacteristic
791C22×C3C22×C4×D311yescharacteristic
792C22×C3#100411yescharacteristic
793C22×C3#100411yescharacteristic
794C22×C3#100411yescharacteristic
795C22×C3#100411yescharacteristic
796C22×C3#100911yescharacteristic
797C22×C3#100911yescharacteristic
798C22×C3#100911yescharacteristic
799C22×C3#100911yescharacteristic
800C22×C3#100911yescharacteristic
801C22×C3#100911yescharacteristic
802C22×C3#100911yescharacteristic
803C22×C3#100911yescharacteristic
804C2×D3—22no—
805C2×D3—22no—
806C2×D3—22no—
807C2×D3—22no—
808C2×D3—22no—
809C2×D3—22no—
810C2×D3—41no—
811C2×D3—41no—
812C2×D3—41no—
813C2×D3—41no—
814C2×D3—41no—
815C2×D3—41no—
816C2×D3—41no—
817C2×D3—41no—
818C2×D3—64no—
819C2×D3—62no—
820C2×D3—62no—
821C2×D3—62no—
822C2×D3—62no—
823C2×D3—62no—
824C2×D3—62no—
825C2×D3—62no—
826C2×D3—62no—
827C2×D3—62no—
828C2×D3—62no—
829C2×D3—62no—
830C2×D3—62no—
831C2×D3—122no—
832C2×D3—122no—
833C2×D3—122no—
834C2×D3—122no—
835C2×D3—122no—
836C2×D3—122no—
837C2×D3—122no—
838C2×D3—122no—
839C2×D3—122no—
840C2×D3—121no—
841C2×D3—121no—
842C2×D3—121no—
843C2×D3—121no—
844C2×D3—121no—
845C2×D3—121no—
846C2×D3—121no—
847C2×D3—121no—
848C2×D3—121no—
849C2×D3—121no—
850C2×D3—121no—
851C2×D3—121no—
852C2×D3—121no—
853C2×D3—121no—
854C2×D3—121no—
855C2×D3—121no—
856C2×D3—241no—
857C2×D3—241no—
858C2×D3—241no—
859C2×D3—241no—
860C3×C4—22no—
861C3×C4—22no—
862C3×C4—42no—
863C3×C4—42no—
864C3×C4—41no—
865C3×C4—41no—
866C3×C4—41no—
867C3×C4—41no—
868C3×C4—62no—
869C3×C4—62no—
870C3×C4—81no—
871C3×C4—121no—
872C3×C4—121no—
873C3×C4—121no—
874C3×C4—121no—
875Dic3—22no—
876Dic3—22no—
877Dic3—41no—
878Dic3—41no—
879Dic3—41no—
880Dic3—41no—
881Dic3—122no—
882Dic3—121no—
883Dic3—121no—
884Dic3—121no—
885Dic3—121no—
886Dic3—241no—
887C32#238011yescharacteristic, complemented, Sylow
888C23—32no—
889C23—32no—
890C23—61no—
891C23—61no—
892C23—61no—
893C23—61no—
894C23—61no—
895C23—61no—
896C23—61no—
897C23—61no—
898C23—61no—
899C23—61no—
900C23—61no—
901C23—61no—
902C23—92no—
903C23—92no—
904C23—181no—
905C23—181no—
906C23—181no—
907C23—181no—
908C23—181no—
909C23—181no—
910C23—181no—
911C23—181no—
912C23—181no—
913C23—181no—
914C23—181no—
915C23—181no—
916C23C22×D3211yescharacteristic
917D4—124no—
918D4—364no—
919D4—364no—
920D4—364no—
921D4—364no—
922D4—364no—
923C2×C4—21no—
924C2×C4—21no—
925C2×C4—21no—
926C2×C4—21no—
927C2×C4—21no—
928C2×C4—21no—
929C2×C4—21no—
930C2×C4—21no—
931C2×C4—32no—
932C2×C4—32no—
933C2×C4—61no—
934C2×C4—61no—
935C2×C4—61no—
936C2×C4—61no—
937C2×C4—61no—
938C2×C4—61no—
939C2×C4—61no—
940C2×C4—61no—
941C2×C4—61no—
942C2×C4—61no—
943C2×C4—61no—
944C2×C4—61no—
945C2×C4—61no—
946C2×C4—61no—
947C2×C4—61no—
948C2×C4—61no—
949C2×C4—124no—
950C2×C4—181no—
951C2×C4—181no—
952C2×C4—181no—
953C2×C4—181no—
954C2×C4—181no—
955C2×C4—181no—
956C2×C4—364no—
957C2×C4—364no—
958C2×C4—364no—
959C2×C4C4×D3212yes—
960C2×C3—21no—
961C2×C3—21no—
962C2×C3—21no—
963C2×C3—21no—
964C2×C3—21no—
965C2×C3—21no—
966C2×C3—21no—
967C2×C3—122no—
968C2×C3—122no—
969C2×C3#548611yescharacteristic
970C2×C3#552111yescharacteristic
971C2×C3#552111yescharacteristic
972C2×C3#552111yescharacteristic
973C2×C3#554511yescharacteristic
974C2×C3#554511yescharacteristic
975C2×C3#559511yescharacteristic
976C2×C3#562011yescharacteristic
977C2×C3#562011yescharacteristic
978C2×C3#566611yescharacteristic
979C2×C3#571111yescharacteristic
980C2×C3#571111yescharacteristic
981C2×C3#571111yescharacteristic
982C2×C3#571111yescharacteristic
983D3—42no—
984D3—42no—
985D3—124no—
986D3—122no—
987D3—122no—
988D3—122no—
989D3—122no—
990D3—242no—
991C22—62no—
992C22—62no—
993C22—62no—
994C22—62no—
995C22—62no—
996C22—62no—
997C22—121no—
998C22—121no—
999C22—121no—
1000C22—121no—
1001C22—121no—
1002C22—121no—
1003C22—121no—
1004C22—121no—
1005C22—182no—
1006C22—182no—
1007C22—182no—
1008C22—182no—
1009C22—182no—
1010C22—182no—
1011C22—361no—
1012C22—361no—
1013C22—361no—
1014C22—361no—
1015C22—361no—
1016C22—361no—
1017C22—361no—
1018C22—361no—
1019C22C2×C4×D3211yescharacteristic
1020C22#6430711yescharacteristic
1021C22#6430811yescharacteristic
1022C22#6431411yescharacteristic
1023C22#6431411yescharacteristic
1024C22#6431411yescharacteristic
1025C22#6432011yescharacteristic
1026C4—22no—
1027C4—41no—
1028C4—41no—
1029C4—62no—
1030C4—62no—
1031C4—121no—
1032C4—121no—
1033C4—121no—
1034C4—121no—
1035C4—361no—
1036C4—361no—
1037C3—21no—
1038C3#7429811yescharacteristic, complemented
1039C3#7468511yescharacteristic, complemented
1040C2—122no—
1041C2—122no—
1042C2—362no—
1043C2—362no—
1044C2#1059399411yescharacteristic
1045C2#1059418211yescharacteristic
1046C2#1059423611yescharacteristic
1047C2#1059424211yescharacteristic
1048C2#1059460411yescharacteristic
1049C2#1059466111yescharacteristic
1050C2#1059466311yescharacteristic
subgroupG/H
center, FrattiniC23C22×D32
commutatorC22×C32C23×C4
FittingC32×#95C22
socle, cosocleC23×C32C24
prime radicalC2×#63911C2
hypercenter#95D32
hypocenterC32#2380
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ #95

Complements

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

NH ≅ G/Ntype
2. #10592364C2semidirect
3. C3×#4665C2semidirect
4. C3×#4651C2semidirect
5. #10591387C2semidirect
6. #10591387C2semidirect
7. #10591382C2semidirect
8. #10591382C2semidirect
9. #10591380C2semidirect
10. #10591376C2semidirect
11. #10591364C2semidirect
12. #10591364C2semidirect
13. #10591275C2semidirect
14. #10591275C2semidirect
15. #10591223C2semidirect
41. #63911C4semidirect
82. #4665D3semidirect
84. #4651D3semidirect
96. C2×C4⋊(C3⋊D3)C2×C4semidirect
108. C2×C3×D12C2×C4semidirect
120. C2×#626C2×C4semidirect
121. C2×#626C2×C4semidirect
122. C2×#626C2×C4semidirect
123. C2×#626C2×C4semidirect
136. C3×C4×Dic3C2×C4semidirect
391. C2×D12C4×D3semidirect
441. C4×Dic3C4×D3semidirect
887. C32#2380semidirect
1038. C3#74298semidirect
1039. C3#74685semidirect

Maximal subgroups

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

subgroupindex
C2×#639112
#105923642
C3×#46652
C3×#46512
#105913872
#105913822
#105913802
#105913762
#105913642
#105912752
#105912232
#746853
#742983