Finite Group Databasebeta

← #11807933

Subgroups — #11807933

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×#63979C211yesmaximal, characteristic
2#10592655C211yesmaximal, characteristic, complemented
3C3×#4958C211yesmaximal, characteristic, complemented
4C3×#4956C211yesmaximal, characteristic, complemented
5#10591721C211yesmaximal, characteristic, complemented
6#10591711C211yesmaximal, characteristic, complemented
7#10591710C211yesmaximal, characteristic, complemented
8#10591387C211yesmaximal, characteristic, complemented
9#10591387C211yesmaximal, characteristic, complemented
10#10591382C211yesmaximal, characteristic, complemented
11#10591381C211yesmaximal, characteristic, complemented
12#10591364C211yesmaximal, characteristic, complemented
13#10591363C211yesmaximal, characteristic, complemented
14#10591248C211yesmaximal, characteristic, complemented
15#10591248C211yesmaximal, characteristic, complemented
16#74685—31nomaximal
17#74685—31nomaximal
18C22×#638C2211yescharacteristic
19C22×C4×C3⋊D3C2211yescharacteristic
20C22×C3×#67C2211yescharacteristic
21C22×C3×#67C2211yescharacteristic
22C23×C3×Dic3C2211yescharacteristic
23C22×C3×C4×D3C2211yescharacteristic
24C22×#626C2211yescharacteristic
25C22×#626C2211yescharacteristic
26C22×#625C2211yescharacteristic
27C22×D3×Dic3C2211yescharacteristic
28C2×C32×C22⋊C4C2211yescharacteristic
29C2×#3757C2211yescharacteristic
30C2×#3752C2211yescharacteristic
31C2×C3×#217C2211yescharacteristic
32C2×C3×(C2×D3)⋊C4C2211yescharacteristic
33C2×C3×(C2×D3)⋊C4C2211yescharacteristic
34C2×C3×(C2×D3)⋊C4C2211yescharacteristic
35#63979C418yescomplemented
36C2×#3722C2211yescharacteristic
37C2×#3722C2211yescharacteristic
38C2×(C2×D3)⋊Dic3C2211yescharacteristic
39C2×(C2×D3)⋊Dic3C2211yescharacteristic
40C2×(C2×D3)⋊Dic3C2211yescharacteristic
41C2×Dic32C2211yescharacteristic
42#63658C2211yescharacteristic
43#63658C2211yescharacteristic
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×#940—31no—
55C2×#940—31no—
56C3×#386—31no—
57C3×#386—31no—
58#5220—31no—
59#5220—31no—
60#5213—31no—
61#5213—31no—
62#5213—31no—
63#5213—31no—
64#4958—31no—
65#4958—31no—
66#4958—31no—
67#4958D311yescharacteristic, complemented
68#4956—31no—
69#4956—31no—
70#4956—31no—
71#4956—31no—
72#4956—31no—
73#4956—31no—
74#4956—31no—
75#4956—61no—
76#4956D311yescharacteristic, complemented
77#4665—31no—
78#4665—31no—
79#4665—31no—
80#4665—31no—
81#4651—31no—
82#4651—31no—
83#4651—31no—
84#4651—31no—
85C24×C32C2311yescharacteristic
86C23×C3⋊D3C2311yescharacteristic
87C23×C3×D3C2311yescharacteristic
88C23×C3×D3C2311yescharacteristic
89C22×C32×C4C2311yescharacteristic
90C22×C32×C4C2311yescharacteristic
91C2×#638—41no—
92C2×#638—41no—
93C2×#638C2×C414yescomplemented
94C22×C3⋊Dic3C2311yescharacteristic
95C22×C3⋊Dic3C2311yescharacteristic
96C22×C3⋊Dic3C2311yescharacteristic
97C2×C4×C3⋊D3—41no—
98C2×C4×C3⋊D3—41no—
99C2×C4×C3⋊D3—41no—
100C2×C3×#67—41no—
101C2×C3×#67—41no—
102C2×C3×#67—41no—
103C2×C3×#67—41no—
104C2×C3×#67C2×C414yescomplemented
105C2×C3×#67C2×C414yescomplemented
106C22×C3×Dic3—41no—
107C22×C3×Dic3—41no—
108C22×C3×Dic3—41no—
109C22×C3×Dic3C2311yescharacteristic
110C22×C3×Dic3C2311yescharacteristic
111C22×C3×Dic3C2311yescharacteristic
112C22×C3×Dic3C2311yescharacteristic
113C22×C3×Dic3C2311yescharacteristic
114C22×C3×Dic3C2311yescharacteristic
115C2×C3×C4×D3—41no—
116C2×C3×C4×D3—41no—
117C2×C3×C4×D3—41no—
118C2×#626—41no—
119C2×#626—41no—
120C2×#626—41no—
121C2×#626—41no—
122C2×#626C2×C414yescomplemented
123C2×#626C2×C414yescomplemented
124C2×#625—41no—
125C2×#625—41no—
126C2×#625C2×C414yescomplemented
127C2×D3×Dic3—41no—
128C2×D3×Dic3—41no—
129C2×D3×Dic3—41no—
130C32×C22⋊C4—41no—
131#3757—41no—
132#3752—41no—
133C3×#217—41no—
134C3×(C2×D3)⋊C4—41no—
135C3×(C2×D3)⋊C4—41no—
136C3×(C2×D3)⋊C4—41no—
137#3722—41no—
138#3722—41no—
139(C2×D3)⋊Dic3—41no—
140(C2×D3)⋊Dic3—41no—
141(C2×D3)⋊Dic3—41no—
142Dic32C2×C414yescomplemented
143#2380—91noSylow
144C22×C3×D4—31no—
145C22×C3×D4—31no—
146C23×C3×C4—31no—
147C23×C3×C4—31no—
148C22×#67—31no—
149C22×#67—31no—
150C22×#67—31no—
151C22×#67—31no—
152C22×#67—31no—
153C22×#67—31no—
154C22×#67—61no—
155C22×#67C2×D311yescharacteristic
156C22×#67C2×D311yescharacteristic
157C23×Dic3—31no—
158C23×Dic3C2×D311yescharacteristic
159C22×D12—31no—
160C22×D12—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—21no—
167C2×C3×C22⋊C4—31no—
168C2×C3×C22⋊C4—31no—
169C2×C3×C22⋊C4—31no—
170C2×C3×C22⋊C4—31no—
171C2×C3×C22⋊C4C2×D311yescharacteristic
172C2×C3×C22⋊C4C2×D311yescharacteristic
173C2×#217—31no—
174C2×#217—31no—
175C2×#217—31no—
176C2×#217—31no—
177C2×#217—31no—
178C2×#217—61no—
179C2×#217C2×D311yescharacteristic
180#940—38no—
181#940—38no—
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—31no—
190C2×(C2×D3)⋊C4—31no—
191C2×(C2×D3)⋊C4—61no—
192C2×(C2×D3)⋊C4C2×D311yescharacteristic
193C2×(C2×D3)⋊C4C2×D311yescharacteristic
194C2×(C2×D3)⋊C4C2×D311yescharacteristic
195C2×C4×Dic3—31no—
196C2×C4×Dic3—31no—
197C3×#95—31no—
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⋊#95—31no—
212C3⋊#95—31no—
213C3⋊#95—31no—
214C3⋊#95—31no—
215C3⋊#95—31no—
216C3⋊#95—31no—
217C3⋊#95—61no—
218C3⋊#95—61no—
219C3⋊#95C2×D311yescharacteristic
220C3⋊#95C2×D311yescharacteristic
221C3⋊#95C2×D311yescharacteristic
222C3⋊#95C2×D311yescharacteristic
223C23×C32—21no—
224C23×C32—21no—
225C23×C32—21no—
226C23×C32—21no—
227C23×C32—21no—
228C23×C32—21no—
229C23×C32C22×C412yes—
230C23×C32C2411yescharacteristic
231C22×C3⋊D3—21no—
232C22×C3⋊D3—21no—
233C22×C3⋊D3—21no—
234C22×C3⋊D3—21no—
235C22×C3⋊D3—21no—
236C22×C3⋊D3—21no—
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—
258#638—44no—
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⋊Dic3C22×C412yes—
268C4×C3⋊D3—44no—
269C3×#67—44no—
270C3×#67—44no—
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×Dic3—21no—
286C2×C3×Dic3—21no—
287C2×C3×Dic3—44no—
288C2×C3×Dic3C22×C412yes—
289C2×C3×Dic3C22×C412yes—
290C3×C4×D3—44no—
291#626—44no—
292#626—44no—
293#625—44no—
294D3×Dic3—44no—
295C2×#127—91no—
296#386—31no—
297#386—31no—
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—91no—
309#383—91no—
310C24×C3—21no—
311C24×C3—31no—
312C24×C3—31no—
313C24×C3C22×D311yescharacteristic
314C24×C3C22×D311yescharacteristic
315C23×D3—31no—
316C23×D3—31no—
317C23×D3—61no—
318C23×D3C22×D311yescharacteristic
319C23×D3C22×D311yescharacteristic
320C2×C3×D4—34no—
321C2×C3×D4—34no—
322C2×C3×D4—121no—
323C2×C3×D4—121no—
324C2×C3×D4—121no—
325C2×C3×D4—121no—
326C22×C3×C4—21no—
327C22×C3×C4—21no—
328C22×C3×C4—31no—
329C22×C3×C4—31no—
330C22×C3×C4—31no—
331C22×C3×C4—31no—
332C22×C3×C4—31no—
333C22×C3×C4—31no—
334C22×C3×C4—121no—
335C22×C3×C4—121no—
336C22×C3×C4—121no—
337C22×C3×C4—121no—
338C22×C3×C4—121no—
339C22×C3×C4—121no—
340C22×C3×C4C22×D311yescharacteristic
341C22×C3×C4C22×D311yescharacteristic
342C22×C3×C4C22×D311yescharacteristic
343C22×C3×C4C22×D311yescharacteristic
344C2×#67—34no—
345C2×#67—34no—
346C2×#67—34no—
347C2×#67—34no—
348C2×#67—34no—
349C2×#67—34no—
350C2×#67—41no—
351C2×#67—41no—
352C2×#67—41no—
353C2×#67—41no—
354C2×#67—64no—
355C2×#67—121no—
356C2×#67—121no—
357C2×#67—121no—
358C2×#67—121no—
359C2×#67—121no—
360C2×#67—121no—
361C2×#67—121no—
362C2×#67—121no—
363C2×#67—121no—
364C2×#67—121no—
365C2×#67—121no—
366C2×#67—121no—
367C2×#67—122no—
368C2×#67—122no—
369C2×#67C4×D314yescomplemented
370C2×#67C4×D314yescomplemented
371C22×Dic3—31no—
372C22×Dic3—31no—
373C22×Dic3—31no—
374C22×Dic3—31no—
375C22×Dic3—31no—
376C22×Dic3—31no—
377C22×Dic3—41no—
378C22×Dic3—41no—
379C22×Dic3—41no—
380C22×Dic3—61no—
381C22×Dic3—61no—
382C22×Dic3—61no—
383C22×Dic3—121no—
384C22×Dic3—121no—
385C22×Dic3—121no—
386C22×Dic3C22×D311yescharacteristic
387C22×Dic3C22×D311yescharacteristic
388C22×Dic3C22×D311yescharacteristic
389C22×Dic3C22×D311yescharacteristic
390C22×Dic3C22×D311yescharacteristic
391C22×Dic3C22×D311yescharacteristic
392C2×D12—34no—
393C2×D12—34no—
394C2×D12—121no—
395C2×D12—121no—
396C2×D12—121no—
397C2×D12—121no—
398C2×C4×D3—41no—
399C2×C4×D3—41no—
400C2×C4×D3—41no—
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—41no—
414C3×C22⋊C4—41no—
415C3×C22⋊C4—42no—
416C3×C22⋊C4—121no—
417C3×C22⋊C4—121no—
418C3×C22⋊C4—121no—
419C3×C22⋊C4—121no—
420#217—41no—
421#217—121no—
422#217—121no—
423#217—121no—
424#217—121no—
425#217—121no—
426#217—122no—
427(C2×D3)⋊C4—41no—
428(C2×D3)⋊C4—41no—
429(C2×D3)⋊C4—41no—
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—121no—
436(C2×D3)⋊C4—121no—
437(C2×D3)⋊C4—121no—
438(C2×D3)⋊C4—121no—
439(C2×D3)⋊C4—122no—
440C4×Dic3—34no—
441C4×Dic3—34no—
442C22×C32—22no—
443C22×C32—22no—
444C22×C32—22no—
445C22×C32—41no—
446C22×C32—41no—
447C22×C32—41no—
448C22×C32—41no—
449C22×C32C23×C411yescharacteristic
450C22×C32H(5,𝔽2)11yescharacteristic
451C22×C32H(5,𝔽2)11yescharacteristic
452C22×C32H(5,𝔽2)11yescharacteristic
453C22×C32H(5,𝔽2)11yescharacteristic
454C22×C32H(5,𝔽2)11yescharacteristic
455C22×C32H(5,𝔽2)11yescharacteristic
456C2×C3⋊D3—22no—
457C2×C3⋊D3—22no—
458C2×C3⋊D3—22no—
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—41no—
478C32×C4—41no—
479C3⋊Dic3—22no—
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—31no—
490C22×D4—91no—
491C22×D4—91no—
492C22×D4—91no—
493C22×D4—91no—
494C23×C4—31no—
495C23×C4—31no—
496C23×C4—91no—
497C23×C4—91no—
498#127—98no—
499C2×C22⋊C4—31no—
500C2×C22⋊C4—31no—
501C2×C22⋊C4—31no—
502C2×C22⋊C4—31no—
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⋊C4D3211yescharacteristic
511C2×C42—91no—
512#95—31no—
513#95—31no—
514#95—31no—
515#95—31no—
516#95—91no—
517#95—91no—
518#95—91no—
519#95—91no—
520#95—91no—
521#95—91no—
522#95—91no—
523#95—91no—
524C23×C3—21no—
525C23×C3—21no—
526C23×C3—21no—
527C23×C3—21no—
528C23×C3—21no—
529C23×C3—21no—
530C23×C3—21no—
531C23×C3—21no—
532C23×C3—21no—
533C23×C3—21no—
534C23×C3—21no—
535C23×C3—21no—
536C23×C3—21no—
537C23×C3—22no—
538C23×C3—32no—
539C23×C3—32no—
540C23×C3—41no—
541C23×C3—41no—
542C23×C3—41no—
543C23×C3—41no—
544C23×C3—41no—
545C23×C3—41no—
546C23×C3—61no—
547C23×C3—61no—
548C23×C3—61no—
549C23×C3—61no—
550C23×C3—61no—
551C23×C3—61no—
552C23×C3—61no—
553C23×C3—61no—
554C23×C3—61no—
555C23×C3—61no—
556C23×C3—61no—
557C23×C3—61no—
558C23×C3C2×C4×D312yes—
559C23×C3C2×C4×D312yes—
560C23×C3C23×D311yescharacteristic
561C23×C3C23×D311yescharacteristic
562C22×D3—21no—
563C22×D3—21no—
564C22×D3—21no—
565C22×D3—21no—
566C22×D3—21no—
567C22×D3—21no—
568C22×D3—21no—
569C22×D3—21no—
570C22×D3—21no—
571C22×D3—21no—
572C22×D3—21no—
573C22×D3—21no—
574C22×D3—32no—
575C22×D3—32no—
576C22×D3—62no—
577C22×D3—62no—
578C22×D3—62no—
579C22×D3—61no—
580C22×D3—61no—
581C22×D3—61no—
582C22×D3—61no—
583C22×D3—61no—
584C22×D3—61no—
585C22×D3—61no—
586C22×D3—61no—
587C22×D3—61no—
588C22×D3—61no—
589C22×D3—61no—
590C22×D3—61no—
591C22×D3—121no—
592C22×D3—121no—
593C22×D3—121no—
594C22×D3—121no—
595C22×D3C2×C4×D312yes—
596C22×D3C2×C4×D312yes—
597C3×D4—124no—
598C3×D4—124no—
599C2×C3×C4—22no—
600C2×C3×C4—21no—
601C2×C3×C4—21no—
602C2×C3×C4—21no—
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—32no—
613C2×C3×C4—32no—
614C2×C3×C4—41no—
615C2×C3×C4—41no—
616C2×C3×C4—41no—
617C2×C3×C4—41no—
618C2×C3×C4—41no—
619C2×C3×C4—61no—
620C2×C3×C4—61no—
621C2×C3×C4—61no—
622C2×C3×C4—61no—
623C2×C3×C4—61no—
624C2×C3×C4—61no—
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—124no—
636C2×C3×C4—124no—
637#67—44no—
638#67—44no—
639#67—124no—
640#67—124no—
641#67—124no—
642#67—124no—
643#67—124no—
644#67—124no—
645#67—128no—
646C2×Dic3—21no—
647C2×Dic3—21no—
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—32no—
663C2×Dic3—32no—
664C2×Dic3—44no—
665C2×Dic3—62no—
666C2×Dic3—61no—
667C2×Dic3—61no—
668C2×Dic3—61no—
669C2×Dic3—61no—
670C2×Dic3—62no—
671C2×Dic3—61no—
672C2×Dic3—61no—
673C2×Dic3—61no—
674C2×Dic3—61no—
675C2×Dic3—61no—
676C2×Dic3—61no—
677C2×Dic3—61no—
678C2×Dic3—61no—
679C2×Dic3—61no—
680C2×Dic3—61no—
681C2×Dic3—61no—
682C2×Dic3—61no—
683C2×Dic3—121no—
684C2×Dic3—121no—
685C2×Dic3—121no—
686C2×Dic3—121no—
687C2×Dic3—121no—
688C2×Dic3—121no—
689C2×Dic3—121no—
690C2×Dic3—124no—
691C2×Dic3C2×C4×D312yes—
692C2×Dic3C2×C4×D312yes—
693D12—124no—
694D12—124no—
695C4×D3—44no—
696C4×D3—128no—
697C4×D3—124no—
698C4×D3—124no—
699C4×D3—124no—
700C2×C32—42no—
701C2×C32#51811yescharacteristic
702C2×C32#51811yescharacteristic
703C2×C32#51811yescharacteristic
704C2×C32#56011yescharacteristic
705C2×C32#56011yescharacteristic
706C2×C32#56011yescharacteristic
707C2×C32#56011yescharacteristic
708C3⋊D3—42no—
709C3×D3—42no—
710C3×D3—42no—
711C24—31no—
712C24—31no—
713C24—91no—
714C24C2×D3211yescharacteristic
715C2×D4—34no—
716C2×D4—34no—
717C2×D4—94no—
718C2×D4—94no—
719C2×D4—94no—
720C2×D4—94no—
721C2×D4—121no—
722C2×D4—121no—
723C2×D4—121no—
724C2×D4—121no—
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—91no—
742C22×C4—121no—
743C22×C4—121no—
744C22×C4—121no—
745C22×C4—121no—
746C22×C4—121no—
747C22×C4—121no—
748C22×C4—361no—
749C22×C4—361no—
750C22×C4—361no—
751C22×C4—361no—
752C22×C4—361no—
753C22×C4—361no—
754C22×C4C2×D3211yescharacteristic
755C22×C4C2×D3211yescharacteristic
756C22⋊C4—41no—
757C22⋊C4—121no—
758C22⋊C4—121no—
759C22⋊C4—121no—
760C22⋊C4—121no—
761C22⋊C4—361no—
762C22⋊C4—361no—
763C22⋊C4—361no—
764C22⋊C4—361no—
765C22⋊C4—361no—
766C22⋊C4—361no—
767C22⋊C4—361no—
768C42—94no—
769C22×C3—22no—
770C22×C3—22no—
771C22×C3—22no—
772C22×C3—22no—
773C22×C3—22no—
774C22×C3—22no—
775C22×C3—21no—
776C22×C3—21no—
777C22×C3—21no—
778C22×C3—21no—
779C22×C3—21no—
780C22×C3—21no—
781C22×C3—21no—
782C22×C3—42no—
783C22×C3—42no—
784C22×C3—42no—
785C22×C3—41no—
786C22×C3—41no—
787C22×C3—41no—
788C22×C3—41no—
789C22×C3—41no—
790C22×C3—41no—
791C22×C3—41no—
792C22×C3—41no—
793C22×C3—62no—
794C22×C3—62no—
795C22×C3—62no—
796C22×C3—62no—
797C22×C3—62no—
798C22×C3—62no—
799C22×C3—81no—
800C22×C3—81no—
801C22×C3—81no—
802C22×C3—81no—
803C22×C3—121no—
804C22×C3—121no—
805C22×C3—121no—
806C22×C3—121no—
807C22×C3—121no—
808C22×C3—121no—
809C22×C3—121no—
810C22×C3—121no—
811C22×C3C22×C4×D311yescharacteristic
812C22×C3C22×C4×D311yescharacteristic
813C22×C3#100411yescharacteristic
814C22×C3#100411yescharacteristic
815C22×C3#100411yescharacteristic
816C22×C3#100411yescharacteristic
817C22×C3#100411yescharacteristic
818C22×C3#100411yescharacteristic
819C22×C3#100411yescharacteristic
820C22×C3#100411yescharacteristic
821C22×C3#100911yescharacteristic
822C22×C3#100911yescharacteristic
823C22×C3#100911yescharacteristic
824C22×C3#100911yescharacteristic
825C2×D3—22no—
826C2×D3—22no—
827C2×D3—22no—
828C2×D3—22no—
829C2×D3—22no—
830C2×D3—22no—
831C2×D3—41no—
832C2×D3—41no—
833C2×D3—41no—
834C2×D3—41no—
835C2×D3—41no—
836C2×D3—41no—
837C2×D3—41no—
838C2×D3—41no—
839C2×D3—64no—
840C2×D3—62no—
841C2×D3—62no—
842C2×D3—62no—
843C2×D3—62no—
844C2×D3—62no—
845C2×D3—62no—
846C2×D3—122no—
847C2×D3—122no—
848C2×D3—122no—
849C2×D3—122no—
850C2×D3—122no—
851C2×D3—122no—
852C2×D3—121no—
853C2×D3—121no—
854C2×D3—121no—
855C2×D3—121no—
856C2×D3—121no—
857C2×D3—121no—
858C2×D3—121no—
859C2×D3—121no—
860C3×C4—42no—
861C3×C4—41no—
862C3×C4—41no—
863C3×C4—41no—
864C3×C4—41no—
865C3×C4—62no—
866C3×C4—62no—
867C3×C4—81no—
868C3×C4—121no—
869C3×C4—121no—
870C3×C4—121no—
871C3×C4—121no—
872Dic3—22no—
873Dic3—22no—
874Dic3—41no—
875Dic3—41no—
876Dic3—41no—
877Dic3—41no—
878Dic3—62no—
879Dic3—62no—
880Dic3—122no—
881Dic3—122no—
882Dic3—121no—
883Dic3—121no—
884Dic3—121no—
885Dic3—121no—
886Dic3—241no—
887C32#238011yescharacteristic, complemented, Sylow
888C23—21no—
889C23—21no—
890C23—21no—
891C23—21no—
892C23—21no—
893C23—21no—
894C23—32no—
895C23—32no—
896C23—61no—
897C23—61no—
898C23—61no—
899C23—61no—
900C23—61no—
901C23—61no—
902C23—61no—
903C23—61no—
904C23—61no—
905C23—61no—
906C23—61no—
907C23—61no—
908C23—92no—
909C23—181no—
910C23—181no—
911C23—181no—
912C23—181no—
913C23—181no—
914C23—181no—
915C23C4×D3212yes—
916C23C22×D3211yescharacteristic
917D4—124no—
918D4—124no—
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—32no—
930C2×C4—32no—
931C2×C4—61no—
932C2×C4—61no—
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—92no—
948C2×C4—124no—
949C2×C4—124no—
950C2×C4—181no—
951C2×C4—181no—
952C2×C4—181no—
953C2×C4—181no—
954C2×C4—181no—
955C2×C4—181no—
956C2×C4—181no—
957C2×C4—181no—
958C2×C4—364no—
959C2×C4—364no—
960C2×C3—21no—
961C2×C3—21no—
962C2×C3—21no—
963C2×C3—21no—
964C2×C3—21no—
965C2×C3—21no—
966C2×C3—21no—
967C2×C3—42no—
968C2×C3—42no—
969C2×C3—82no—
970C2×C3—122no—
971C2×C3—122no—
972C2×C3#548611yescharacteristic
973C2×C3#548611yescharacteristic
974C2×C3#554511yescharacteristic
975C2×C3#554511yescharacteristic
976C2×C3#554511yescharacteristic
977C2×C3#554511yescharacteristic
978C2×C3#559511yescharacteristic
979C2×C3#559511yescharacteristic
980C2×C3#562011yescharacteristic
981C2×C3#562011yescharacteristic
982C2×C3#562011yescharacteristic
983C2×C3#562011yescharacteristic
984C2×C3#566611yescharacteristic
985C2×C3#566611yescharacteristic
986D3—42no—
987D3—42no—
988D3—124no—
989D3—122no—
990D3—122no—
991C22—22no—
992C22—22no—
993C22—22no—
994C22—41no—
995C22—41no—
996C22—41no—
997C22—41no—
998C22—62no—
999C22—62no—
1000C22—62no—
1001C22—62no—
1002C22—62no—
1003C22—62no—
1004C22—121no—
1005C22—121no—
1006C22—121no—
1007C22—121no—
1008C22—121no—
1009C22—121no—
1010C22—121no—
1011C22—121no—
1012C22—182no—
1013C22—182no—
1014C22—182no—
1015C22—361no—
1016C22—361no—
1017C22—361no—
1018C22—361no—
1019C22C2×C4×D3211yescharacteristic
1020C22#6430711yescharacteristic
1021C22#6431311yescharacteristic
1022C22#6431411yescharacteristic
1023C22#6431411yescharacteristic
1024C22#6431411yescharacteristic
1025C22#6433011yescharacteristic
1026C4—41no—
1027C4—41no—
1028C4—62no—
1029C4—62no—
1030C4—121no—
1031C4—121no—
1032C4—121no—
1033C4—121no—
1034C4—182no—
1035C4—361no—
1036C4—361no—
1037C3—21no—
1038C3#7468511yescharacteristic, complemented
1039C3#7468511yescharacteristic, complemented
1040C2—42no—
1041C2—122no—
1042C2—122no—
1043C2—362no—
1044C2#1059423311yescharacteristic
1045C2#1059425411yescharacteristic
1046C2#1059425611yescharacteristic
1047C2#1059430811yescharacteristic
1048C2#1059505611yescharacteristic
1049C2#1059525811yescharacteristic
1050C2#1059526411yescharacteristic
subgroupG/H
center, FrattiniC23C22×D32
commutatorC22×C32C23×C4
FittingC2×C32×C22⋊C4C22
socle, cosocleC23×C32C24
prime radicalC2×#63979C2
hypercenterC2×C22⋊C4D32
hypocenterC32#2380
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C2×C22⋊C4

Complements

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

NH ≅ G/Ntype
2. #10592655C2semidirect
3. C3×#4958C2semidirect
4. C3×#4956C2semidirect
5. #10591721C2semidirect
6. #10591711C2semidirect
7. #10591710C2semidirect
8. #10591387C2semidirect
9. #10591387C2semidirect
10. #10591382C2semidirect
11. #10591381C2semidirect
12. #10591364C2semidirect
13. #10591363C2semidirect
14. #10591248C2semidirect
15. #10591248C2semidirect
35. #63979C4semidirect
67. #4958D3semidirect
76. #4956D3semidirect
93. C2×#638C2×C4semidirect
104. C2×C3×#67C2×C4semidirect
105. C2×C3×#67C2×C4semidirect
122. C2×#626C2×C4semidirect
123. C2×#626C2×C4semidirect
126. C2×#625C2×C4semidirect
142. Dic32C2×C4semidirect
369. C2×#67C4×D3semidirect
370. C2×#67C4×D3semidirect
887. C32#2380semidirect
1038. C3#74685semidirect
1039. C3#74685semidirect

Maximal subgroups

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

subgroupindex
C2×#639792
#105926552
C3×#49582
C3×#49562
#105917212
#105917112
#105917102
#105913872
#105913822
#105913812
#105913642
#105913632
#105912482
#746853