Finite Group Databasebeta

← #11807780

Subgroups — #11807780

Order 1152.

1365 conjugacy classes of subgroups.

The subgroup lattice has 988 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64093C211yesmaximal, characteristic
2C3×#4951C211yesmaximal, characteristic, complemented
3C3×#4950C211yesmaximal, characteristic, complemented
4#10591722C211yesmaximal, characteristic, complemented
5#10591711C211yesmaximal, characteristic, complemented
6#10591711C211yesmaximal, characteristic, complemented
7#10591704C211yesmaximal, characteristic, complemented
8#10591380C211yesmaximal, characteristic, complemented
9#10591378C211yesmaximal, characteristic, complemented
10#10591325C211yesmaximal, characteristic, complemented
11#10591320C211yesmaximal, characteristic, complemented
12#10591266C211yesmaximal, characteristic, complemented
13#10591263C211yesmaximal, characteristic, complemented
14#10591219C211yesmaximal, characteristic, complemented
15#10591197C211yesmaximal, characteristic, complemented
16#75490—31nomaximal
17#74401—31nomaximal
18C22×#638C2211yescharacteristic
19C22×#638C2211yescharacteristic
20C22×C4⋊(C3⋊D3)C2211yescharacteristic
21C22×C4×C3⋊D3C2211yescharacteristic
22C23×C3×Dic3C2211yescharacteristic
23C22×#624C2211yescharacteristic
24C2×C32×C22⋊C4C2211yescharacteristic
25C2×#3752C2211yescharacteristic
26C2×#3750C2211yescharacteristic
27#64093C418yescomplemented
28C2×C3×#217C2211yescharacteristic
29C2×C3×#217C2211yescharacteristic
30C2×C3×#217C2211yescharacteristic
31C2×C3×C4⋊Dic3C2211yescharacteristic
32C2×C3×C4⋊Dic3C2211yescharacteristic
33C2×C3×C4⋊Dic3C2211yescharacteristic
34C2×C3×C4×Dic3C2211yescharacteristic
35C2×#3724C2211yescharacteristic
36C2×#3722C2211yescharacteristic
37C2×#3722C2211yescharacteristic
38C2×#3722C2211yescharacteristic
39C2×#3722C2211yescharacteristic
40C2×#3722C2211yescharacteristic
41C2×#3722C2211yescharacteristic
42C2×#3722C2211yescharacteristic
43C2×Dic32C2211yescharacteristic
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×#884—31no—
55C2×#884—31no—
56C2×#884—61no—
57C3×#388—31no—
58C3×#385—31no—
59#5213—31no—
60#5213—31no—
61#4990—31no—
62#4989—31no—
63#4988—31no—
64#4987—31no—
65#4987—31no—
66#4978—31no—
67#4958—31no—
68#4958—31no—
69#4957—31no—
70#4957—31no—
71#4956—31no—
72#4956—31no—
73#4951D311yescharacteristic, complemented
74#4950D311yescharacteristic, complemented
75#4939—31no—
76#4933—31no—
77#4670—31no—
78#4668—31no—
79#4665—31no—
80#4665—31no—
81#4664—31no—
82#4664—31no—
83#4655—31no—
84#4652—31no—
85C24×C32C2311yescharacteristic
86C23×C3⋊D3C2311yescharacteristic
87C23×C3⋊D3C2311yescharacteristic
88C22×C32×C4C2311yescharacteristic
89C22×C32×C4C2311yescharacteristic
90C2×#638—41no—
91C2×#638—41no—
92C2×#638—41no—
93C2×#638—41no—
94C2×#638C2×C414yes—
95C2×#638C2×C414yescomplemented
96C22×C3⋊Dic3C2311yescharacteristic
97C22×C3⋊Dic3C2311yescharacteristic
98C2×C4⋊(C3⋊D3)—41no—
99C2×C4⋊(C3⋊D3)—41no—
100C2×C4⋊(C3⋊D3)C2×C414yescomplemented
101C2×C4×C3⋊D3—41no—
102C2×C4×C3⋊D3—41no—
103C2×C4×C3⋊D3C2×C414yescomplemented
104C22×C3×Dic3—41no—
105C22×C3×Dic3—41no—
106C22×C3×Dic3—41no—
107C22×C3×Dic3C2311yescharacteristic
108C22×C3×Dic3C2311yescharacteristic
109C22×C3×Dic3C2311yescharacteristic
110C22×C3×Dic3C2311yescharacteristic
111C22×C3×Dic3C2311yescharacteristic
112C22×C3×Dic3C2311yescharacteristic
113C22×C3×Dic3C2311yescharacteristic
114C22×C3×Dic3C2311yescharacteristic
115C2×#624—41no—
116C2×#624—41no—
117C2×#624—41no—
118C32×C22⋊C4C2×C414yescomplemented
119#3752C2×C414yescomplemented
120#3750C2×C414yescomplemented
121C3×#217—41no—
122C3×#217—41no—
123C3×#217—41no—
124C3×C4⋊Dic3—41no—
125C3×C4⋊Dic3—41no—
126C3×C4⋊Dic3—41no—
127C3×C4×Dic3—41no—
128#3724—41no—
129#3722—41no—
130#3722—41no—
131#3722—41no—
132#3722—41no—
133#3722—41no—
134#3722—41no—
135#3722—41no—
136Dic32—41no—
137#2377—91noSylow
138C23×C3×C4—31no—
139C22×#67—31no—
140C22×#67—31no—
141C22×#67—31no—
142C22×#67—31no—
143C22×#67—61no—
144C22×#67—61no—
145C23×Dic3C2×D311yescharacteristic
146C22×D12—31no—
147C22×D12—31no—
148C22×D12—61no—
149C22×C4×D3—31no—
150C22×C4×D3—31no—
151C22×C4×D3—31no—
152C22×C4×D3—31no—
153C22×C4×D3—61no—
154C2×C3×C4⋊C4—31no—
155C2×C3×C4⋊C4—31no—
156C2×C3×C4⋊C4—31no—
157C2×C3×C22⋊C4—21no—
158C2×C3×C22⋊C4—31no—
159C2×C3×C22⋊C4—31no—
160C2×C3×C22⋊C4—31no—
161C2×C3×C22⋊C4C2×D311yescharacteristic
162C2×C3×C22⋊C4C2×D311yescharacteristic
163C2×C3×C42—31no—
164C2×#217C2×D311yescharacteristic
165C2×#217C2×D311yescharacteristic
166C2×#217C2×D311yescharacteristic
167C2×(C2×D3)⋊C4—31no—
168C2×(C2×D3)⋊C4—31no—
169C2×(C2×D3)⋊C4—31no—
170C2×(C2×D3)⋊C4—31no—
171C2×(C2×D3)⋊C4—31no—
172C2×(C2×D3)⋊C4—31no—
173C2×(C2×D3)⋊C4—31no—
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—61no—
184C2×C4⋊Dic3C2×D311yescharacteristic
185C2×C4⋊Dic3C2×D311yescharacteristic
186C2×C4⋊Dic3C2×D311yescharacteristic
187C2×Dic3⋊C4—31no—
188C2×Dic3⋊C4—31no—
189C2×Dic3⋊C4—31no—
190C2×Dic3⋊C4—31no—
191C2×Dic3⋊C4—61no—
192C2×C4×Dic3—31no—
193C2×C4×Dic3—31no—
194C2×C4×Dic3C2×D311yescharacteristic
195#884—38no—
196#884—38no—
197#884—68no—
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⋊#95C2×D311yescharacteristic
215C3⋊#95C2×D311yescharacteristic
216C3⋊#95C2×D311yescharacteristic
217C3⋊#95C2×D311yescharacteristic
218C23×C32—21no—
219C23×C32—21no—
220C23×C32—21no—
221C23×C32—21no—
222C23×C32—21no—
223C23×C32—21no—
224C23×C32C22×C412yes—
225C23×C32C2411yescharacteristic
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⋊D3—21no—
237C22×C3⋊D3—21no—
238C22×C3⋊D3C22×C412yes—
239C22×C3⋊D3C22×C412yes—
240C2×C32×C4—21no—
241C2×C32×C4—21no—
242C2×C32×C4—21no—
243C2×C32×C4—21no—
244C2×C32×C4C22×C412yes—
245C2×C32×C4C22×C412yes—
246#638—44no—
247#638—44no—
248C2×C3⋊Dic3—21no—
249C2×C3⋊Dic3—21no—
250C2×C3⋊Dic3—21no—
251C2×C3⋊Dic3—21no—
252C2×C3⋊Dic3C22×C412yes—
253C2×C3⋊Dic3C22×C412yes—
254C4⋊(C3⋊D3)—44no—
255C4×C3⋊D3—44no—
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×Dic3—21no—
268C2×C3×Dic3—21no—
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—44no—
281#624—44no—
282C2×#121—91no—
283#390—91no—
284#390—91no—
285#388—31no—
286#388—91no—
287#387—91no—
288#387—91no—
289#386—91no—
290#386—91no—
291#386—91no—
292#386—91no—
293#385—31no—
294#385—91no—
295#381—91no—
296#380—91no—
297C24×C3—21no—
298C24×C3C22×D311yescharacteristic
299C24×C3C22×D311yescharacteristic
300C23×D3—31no—
301C23×D3—31no—
302C23×D3—31no—
303C23×D3—31no—
304C23×D3—61no—
305C23×D3—61no—
306C22×C3×C4—21no—
307C22×C3×C4—21no—
308C22×C3×C4—31no—
309C22×C3×C4—31no—
310C22×C3×C4—31no—
311C22×C3×C4—31no—
312C22×C3×C4—31no—
313C22×C3×C4—31no—
314C22×C3×C4—31no—
315C22×C3×C4—31no—
316C22×C3×C4—121no—
317C22×C3×C4—121no—
318C22×C3×C4—121no—
319C22×C3×C4C22×D311yescharacteristic
320C22×C3×C4C22×D311yescharacteristic
321C22×C3×C4C22×D311yescharacteristic
322C22×C3×C4C22×D311yescharacteristic
323C2×#67—34no—
324C2×#67—34no—
325C2×#67—34no—
326C2×#67—34no—
327C2×#67—64no—
328C2×#67—64no—
329C2×#67—121no—
330C2×#67—121no—
331C2×#67—121no—
332C2×#67—121no—
333C2×#67—121no—
334C2×#67—121no—
335C2×#67—121no—
336C2×#67—121no—
337C2×#67—122no—
338C2×#67—122no—
339C2×#67—122no—
340C2×#67—122no—
341C22×Dic3—31no—
342C22×Dic3—31no—
343C22×Dic3—31no—
344C22×Dic3—31no—
345C22×Dic3—41no—
346C22×Dic3—41no—
347C22×Dic3—41no—
348C22×Dic3—61no—
349C22×Dic3—61no—
350C22×Dic3C22×D311yescharacteristic
351C22×Dic3C22×D311yescharacteristic
352C22×Dic3C22×D311yescharacteristic
353C22×Dic3C22×D311yescharacteristic
354C22×Dic3C22×D311yescharacteristic
355C22×Dic3C22×D311yescharacteristic
356C22×Dic3C22×D311yescharacteristic
357C22×Dic3C22×D311yescharacteristic
358C2×D12—34no—
359C2×D12—34no—
360C2×D12—64no—
361C2×D12—121no—
362C2×D12—121no—
363C2×D12—121no—
364C2×D12—121no—
365C2×D12—122no—
366C2×D12—122no—
367C2×C4×D3—34no—
368C2×C4×D3—34no—
369C2×C4×D3—64no—
370C2×C4×D3—121no—
371C2×C4×D3—121no—
372C2×C4×D3—121no—
373C2×C4×D3—121no—
374C2×C4×D3—121no—
375C2×C4×D3—121no—
376C2×C4×D3—121no—
377C2×C4×D3—121no—
378C2×C4×D3—121no—
379C2×C4×D3—121no—
380C2×C4×D3—122no—
381C2×C4×D3—122no—
382C3×C4⋊C4—121no—
383C3×C4⋊C4—121no—
384C3×C4⋊C4—121no—
385C3×C22⋊C4—24no—
386C3×C22⋊C4—121no—
387C3×C22⋊C4—121no—
388C3×C22⋊C4—121no—
389C3×C22⋊C4C4×D314yescomplemented
390C3×C22⋊C4C4×D314yescomplemented
391C3×C42—121no—
392#217—41no—
393#217—41no—
394#217—41no—
395(C2×D3)⋊C4—34no—
396(C2×D3)⋊C4—34no—
397(C2×D3)⋊C4—64no—
398(C2×D3)⋊C4—121no—
399(C2×D3)⋊C4—121no—
400(C2×D3)⋊C4—121no—
401(C2×D3)⋊C4—121no—
402(C2×D3)⋊C4—121no—
403(C2×D3)⋊C4—121no—
404(C2×D3)⋊C4—121no—
405(C2×D3)⋊C4—121no—
406(C2×D3)⋊C4—121no—
407(C2×D3)⋊C4—121no—
408(C2×D3)⋊C4—121no—
409(C2×D3)⋊C4—121no—
410(C2×D3)⋊C4—121no—
411(C2×D3)⋊C4—121no—
412C4⋊Dic3—41no—
413C4⋊Dic3—41no—
414C4⋊Dic3—41no—
415Dic3⋊C4—34no—
416Dic3⋊C4—34no—
417Dic3⋊C4—64no—
418Dic3⋊C4—121no—
419Dic3⋊C4—121no—
420C4×Dic3—41no—
421C4×Dic3—121no—
422C4×Dic3—121no—
423C22×C32—22no—
424C22×C32—22no—
425C22×C32—22no—
426C22×C32—41no—
427C22×C32—41no—
428C22×C32—41no—
429C22×C32—41no—
430C22×C32C23×C411yescharacteristic
431C22×C32H(5,𝔽2)11yescharacteristic
432C22×C32H(5,𝔽2)11yescharacteristic
433C22×C32H(5,𝔽2)11yescharacteristic
434C22×C32H(5,𝔽2)11yescharacteristic
435C22×C32H(5,𝔽2)11yescharacteristic
436C22×C322−1+411yescharacteristic
437C2×C3⋊D3—22no—
438C2×C3⋊D3—22no—
439C2×C3⋊D3—22no—
440C2×C3⋊D3—22no—
441C2×C3⋊D3—22no—
442C2×C3⋊D3—22no—
443C2×C3⋊D3—41no—
444C2×C3⋊D3—41no—
445C2×C3⋊D3—41no—
446C2×C3⋊D3—41no—
447C2×C3⋊D3—41no—
448C2×C3⋊D3—41no—
449C2×C3⋊D3—41no—
450C2×C3⋊D3—41no—
451C32×C4—22no—
452C32×C4—22no—
453C3⋊Dic3—22no—
454C3⋊Dic3—22no—
455C3×Dic3—41no—
456C3×Dic3—41no—
457C3×Dic3—41no—
458C3×Dic3—41no—
459C3×Dic3—41no—
460C3×Dic3—41no—
461C3×Dic3—41no—
462C3×Dic3—41no—
463C22×D4—91no—
464C22×D4—91no—
465C22×D4—91no—
466C23×C4—31no—
467C23×C4—91no—
468C23×C4—91no—
469#121—98no—
470C2×C4⋊C4—31no—
471C2×C4⋊C4—31no—
472C2×C4⋊C4—31no—
473C2×C4⋊C4—91no—
474C2×C4⋊C4—91no—
475C2×C22⋊C4—31no—
476C2×C22⋊C4—31no—
477C2×C22⋊C4—31no—
478C2×C22⋊C4—91no—
479C2×C22⋊C4—91no—
480C2×C22⋊C4—91no—
481C2×C22⋊C4—91no—
482C2×C22⋊C4—91no—
483C2×C22⋊C4—91no—
484C2×C22⋊C4—91no—
485C2×C22⋊C4—91no—
486C2×C22⋊C4D3211yescharacteristic
487C2×C42—31no—
488C2×C42—91no—
489#95—31no—
490#95—31no—
491#95—31no—
492#95—31no—
493#95—91no—
494#95—91no—
495#95—91no—
496#95—91no—
497#95—91no—
498#95—91no—
499C23×C3—21no—
500C23×C3—21no—
501C23×C3—21no—
502C23×C3—21no—
503C23×C3—21no—
504C23×C3—21no—
505C23×C3—21no—
506C23×C3—21no—
507C23×C3—21no—
508C23×C3—21no—
509C23×C3—21no—
510C23×C3—21no—
511C23×C3—21no—
512C23×C3—22no—
513C23×C3—41no—
514C23×C3—41no—
515C23×C3—41no—
516C23×C3—41no—
517C23×C3—41no—
518C23×C3—41no—
519C23×C3C2×C4×D312yes—
520C23×C3C2×C4×D312yes—
521C23×C3C23×D311yescharacteristic
522C23×C3C23×D311yescharacteristic
523C22×D3—32no—
524C22×D3—32no—
525C22×D3—32no—
526C22×D3—32no—
527C22×D3—62no—
528C22×D3—62no—
529C22×D3—62no—
530C22×D3—62no—
531C22×D3—61no—
532C22×D3—61no—
533C22×D3—61no—
534C22×D3—61no—
535C22×D3—61no—
536C22×D3—61no—
537C22×D3—61no—
538C22×D3—61no—
539C22×D3—61no—
540C22×D3—61no—
541C22×D3—61no—
542C22×D3—61no—
543C22×D3—61no—
544C22×D3—61no—
545C22×D3—61no—
546C22×D3—61no—
547C22×D3—61no—
548C22×D3—61no—
549C22×D3—61no—
550C22×D3—61no—
551C22×D3—61no—
552C22×D3—61no—
553C22×D3—61no—
554C22×D3—61no—
555C22×D3—121no—
556C22×D3—121no—
557C22×D3—121no—
558C22×D3—121no—
559C22×D3—121no—
560C22×D3—121no—
561C22×D3—121no—
562C22×D3—121no—
563C22×D3—121no—
564C22×D3—121no—
565C2×C3×C4—21no—
566C2×C3×C4—21no—
567C2×C3×C4—21no—
568C2×C3×C4—21no—
569C2×C3×C4—21no—
570C2×C3×C4—21no—
571C2×C3×C4—21no—
572C2×C3×C4—21no—
573C2×C3×C4—22no—
574C2×C3×C4—22no—
575C2×C3×C4—41no—
576C2×C3×C4—41no—
577C2×C3×C4—41no—
578C2×C3×C4—41no—
579C2×C3×C4—61no—
580C2×C3×C4—61no—
581C2×C3×C4—61no—
582C2×C3×C4—61no—
583C2×C3×C4—61no—
584C2×C3×C4—61no—
585C2×C3×C4—61no—
586C2×C3×C4—61no—
587C2×C3×C4—61no—
588C2×C3×C4—61no—
589C2×C3×C4—61no—
590C2×C3×C4—61no—
591C2×C3×C4—61no—
592C2×C3×C4—61no—
593C2×C3×C4—61no—
594C2×C3×C4—61no—
595C2×C3×C4—61no—
596C2×C3×C4—61no—
597C2×C3×C4—61no—
598C2×C3×C4—61no—
599C2×C3×C4—61no—
600C2×C3×C4—61no—
601C2×C3×C4—61no—
602C2×C3×C4—61no—
603C2×C3×C4—124no—
604C2×C3×C4C2×C4×D312yes—
605C2×C3×C4C2×C4×D312yes—
606C2×C3×C4C2×C4×D312yes—
607C2×C3×C4C2×C4×D312yes—
608#67—124no—
609#67—124no—
610#67—124no—
611#67—124no—
612#67—128no—
613#67—128no—
614C2×Dic3—21no—
615C2×Dic3—21no—
616C2×Dic3—21no—
617C2×Dic3—21no—
618C2×Dic3—21no—
619C2×Dic3—21no—
620C2×Dic3—21no—
621C2×Dic3—21no—
622C2×Dic3—21no—
623C2×Dic3—21no—
624C2×Dic3—21no—
625C2×Dic3—21no—
626C2×Dic3—21no—
627C2×Dic3—21no—
628C2×Dic3—21no—
629C2×Dic3—21no—
630C2×Dic3—21no—
631C2×Dic3—21no—
632C2×Dic3—21no—
633C2×Dic3—21no—
634C2×Dic3—21no—
635C2×Dic3—21no—
636C2×Dic3—21no—
637C2×Dic3—21no—
638C2×Dic3—32no—
639C2×Dic3—32no—
640C2×Dic3—32no—
641C2×Dic3—32no—
642C2×Dic3—44no—
643C2×Dic3—62no—
644C2×Dic3—62no—
645C2×Dic3—62no—
646C2×Dic3—62no—
647C2×Dic3—61no—
648C2×Dic3—61no—
649C2×Dic3—61no—
650C2×Dic3—61no—
651C2×Dic3—61no—
652C2×Dic3—61no—
653C2×Dic3—61no—
654C2×Dic3—61no—
655C2×Dic3—121no—
656C2×Dic3—121no—
657D12—124no—
658D12—124no—
659D12—128no—
660C4×D3—124no—
661C4×D3—124no—
662C4×D3—124no—
663C4×D3—124no—
664C4×D3—128no—
665C2×C32—42no—
666C2×C32#51811yescharacteristic
667C2×C32#51811yescharacteristic
668C2×C32#52011yescharacteristic
669C2×C32#56011yescharacteristic
670C2×C32#56011yescharacteristic
671C2×C32#56211yescharacteristic
672C2×C32#56211yescharacteristic
673C3⋊D3—42no—
674C3⋊D3—42no—
675C24—91no—
676C24—91no—
677C24C2×D3211yescharacteristic
678C2×D4—94no—
679C2×D4—94no—
680C2×D4—94no—
681C2×D4—361no—
682C2×D4—361no—
683C2×D4—361no—
684C2×D4—361no—
685C2×D4—361no—
686C2×D4—361no—
687C22×C4—31no—
688C22×C4—31no—
689C22×C4—31no—
690C22×C4—31no—
691C22×C4—31no—
692C22×C4—31no—
693C22×C4—31no—
694C22×C4—31no—
695C22×C4—91no—
696C22×C4—91no—
697C22×C4—94no—
698C22×C4—121no—
699C22×C4—121no—
700C22×C4—121no—
701C22×C4—361no—
702C22×C4—361no—
703C22×C4—361no—
704C22×C4—361no—
705C22×C4—361no—
706C22×C4C2×D3211yescharacteristic
707C22×C4C2×D3211yescharacteristic
708C4⋊C4—94no—
709C4⋊C4—121no—
710C4⋊C4—121no—
711C4⋊C4—121no—
712C4⋊C4—361no—
713C22⋊C4—94no—
714C22⋊C4—121no—
715C22⋊C4—121no—
716C22⋊C4—121no—
717C22⋊C4—361no—
718C22⋊C4—361no—
719C22⋊C4—361no—
720C22⋊C4—361no—
721C22⋊C4—361no—
722C22⋊C4—361no—
723C22⋊C4—361no—
724C22⋊C4#62414yescomplemented
725C42—121no—
726C42—361no—
727C22×C3—22no—
728C22×C3—22no—
729C22×C3—22no—
730C22×C3—22no—
731C22×C3—22no—
732C22×C3—22no—
733C22×C3—21no—
734C22×C3—21no—
735C22×C3—21no—
736C22×C3—21no—
737C22×C3—21no—
738C22×C3—21no—
739C22×C3—21no—
740C22×C3—42no—
741C22×C3—42no—
742C22×C3—42no—
743C22×C3—41no—
744C22×C3—41no—
745C22×C3—41no—
746C22×C3—41no—
747C22×C3—41no—
748C22×C3—41no—
749C22×C3—41no—
750C22×C3—41no—
751C22×C3—81no—
752C22×C3—81no—
753C22×C3—81no—
754C22×C3—81no—
755C22×C3C22×C4×D311yescharacteristic
756C22×C3C22×C4×D311yescharacteristic
757C22×C3#100411yescharacteristic
758C22×C3#100411yescharacteristic
759C22×C3#100411yescharacteristic
760C22×C3#100411yescharacteristic
761C22×C3#100411yescharacteristic
762C22×C3#100711yescharacteristic
763C22×C3#100911yescharacteristic
764C22×C3#100911yescharacteristic
765C22×C3#100911yescharacteristic
766C22×C3#100911yescharacteristic
767C22×C3#100911yescharacteristic
768C22×C3#101011yescharacteristic
769C2×D3—64no—
770C2×D3—62no—
771C2×D3—62no—
772C2×D3—62no—
773C2×D3—62no—
774C2×D3—62no—
775C2×D3—62no—
776C2×D3—62no—
777C2×D3—62no—
778C2×D3—62no—
779C2×D3—62no—
780C2×D3—62no—
781C2×D3—62no—
782C2×D3—122no—
783C2×D3—122no—
784C2×D3—122no—
785C2×D3—122no—
786C2×D3—122no—
787C2×D3—122no—
788C2×D3—122no—
789C2×D3—122no—
790C2×D3—122no—
791C2×D3—121no—
792C2×D3—121no—
793C2×D3—121no—
794C2×D3—121no—
795C2×D3—121no—
796C2×D3—121no—
797C2×D3—121no—
798C2×D3—121no—
799C2×D3—121no—
800C2×D3—121no—
801C2×D3—121no—
802C2×D3—121no—
803C2×D3—121no—
804C2×D3—121no—
805C2×D3—121no—
806C2×D3—121no—
807C2×D3—241no—
808C2×D3—241no—
809C2×D3—241no—
810C2×D3—241no—
811C3×C4—22no—
812C3×C4—22no—
813C3×C4—22no—
814C3×C4—22no—
815C3×C4—42no—
816C3×C4—42no—
817C3×C4—121no—
818C3×C4—121no—
819C3×C4—121no—
820C3×C4—121no—
821C3×C4—121no—
822C3×C4—121no—
823C3×C4—121no—
824C3×C4—121no—
825Dic3—41no—
826Dic3—41no—
827Dic3—41no—
828Dic3—41no—
829Dic3—41no—
830Dic3—41no—
831Dic3—41no—
832Dic3—41no—
833Dic3—64no—
834Dic3—62no—
835Dic3—62no—
836Dic3—62no—
837Dic3—62no—
838Dic3—122no—
839C32#237711yescharacteristic, complemented, Sylow
840C23—21no—
841C23—21no—
842C23—21no—
843C23—21no—
844C23—21no—
845C23—21no—
846C23—92no—
847C23—92no—
848C23—181no—
849C23—181no—
850C23—181no—
851C23—181no—
852C23—181no—
853C23—181no—
854C23—181no—
855C23—181no—
856C23—181no—
857C23—181no—
858C23—181no—
859C23—181no—
860C23C2×#62412yes—
861C23C22×D3211yescharacteristic
862D4—364no—
863D4—364no—
864D4—364no—
865C2×C4—21no—
866C2×C4—21no—
867C2×C4—21no—
868C2×C4—21no—
869C2×C4—61no—
870C2×C4—61no—
871C2×C4—61no—
872C2×C4—61no—
873C2×C4—61no—
874C2×C4—61no—
875C2×C4—61no—
876C2×C4—61no—
877C2×C4—61no—
878C2×C4—61no—
879C2×C4—61no—
880C2×C4—61no—
881C2×C4—61no—
882C2×C4—61no—
883C2×C4—61no—
884C2×C4—61no—
885C2×C4—61no—
886C2×C4—61no—
887C2×C4—61no—
888C2×C4—61no—
889C2×C4—61no—
890C2×C4—61no—
891C2×C4—61no—
892C2×C4—61no—
893C2×C4—92no—
894C2×C4—92no—
895C2×C4—124no—
896C2×C4—181no—
897C2×C4—181no—
898C2×C4—181no—
899C2×C4—181no—
900C2×C4—364no—
901C2×C4—364no—
902C2×C4C2×#62412yes—
903C2×C4C2×#62412yes—
904C2×C3—21no—
905C2×C3—21no—
906C2×C3—21no—
907C2×C3—21no—
908C2×C3—21no—
909C2×C3—21no—
910C2×C3—21no—
911C2×C3—42no—
912C2×C3—42no—
913C2×C3—82no—
914C2×C3#550411yescharacteristic
915C2×C3#552311yescharacteristic
916C2×C3#554511yescharacteristic
917C2×C3#554511yescharacteristic
918C2×C3#554511yescharacteristic
919C2×C3#554511yescharacteristic
920C2×C3#559511yescharacteristic
921C2×C3#562011yescharacteristic
922C2×C3#564711yescharacteristic
923C2×C3#564711yescharacteristic
924C2×C3#566611yescharacteristic
925C2×C3#566711yescharacteristic
926C2×C3#568411yescharacteristic
927C2×C3#571111yescharacteristic
928D3—124no—
929D3—122no—
930D3—122no—
931D3—122no—
932D3—122no—
933D3—242no—
934C22—22no—
935C22—22no—
936C22—22no—
937C22—41no—
938C22—41no—
939C22—41no—
940C22—41no—
941C22—182no—
942C22—182no—
943C22—182no—
944C22—182no—
945C22—182no—
946C22—182no—
947C22—361no—
948C22—361no—
949C22—361no—
950C22—361no—
951C22—361no—
952C22—361no—
953C22—361no—
954C22—361no—
955C22#6429711yescharacteristic
956C22#6430711yescharacteristic
957C22#6431411yescharacteristic
958C22#6431411yescharacteristic
959C22#6431411yescharacteristic
960C22#6431411yescharacteristic
961C22C22×#62411yescharacteristic
962C4—22no—
963C4—22no—
964C4—121no—
965C4—121no—
966C4—121no—
967C4—121no—
968C4—121no—
969C4—121no—
970C4—121no—
971C4—121no—
972C4—182no—
973C4—182no—
974C3—21no—
975C3#7440111yescharacteristic, complemented
976C3#7549011yescharacteristic, complemented
977C2—42no—
978C2—362no—
979C2—362no—
980C2#1059404311yescharacteristic
981C2#1059417811yescharacteristic
982C2#1059423611yescharacteristic
983C2#1059430811yescharacteristic
984C2#1059499011yescharacteristic
985C2#1059522311yescharacteristic
986C2#1059522311yescharacteristic
subgroupG/H
center, FrattiniC23C22×D32
commutatorC22×C32C23×C4
FittingC2×C32×C22⋊C4C22
socle, cosocleC23×C32C24
prime radicalC2×#64093C2
hypercenterC2×C22⋊C4D32
hypocenterC32#2377
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C2×C22⋊C4

Complements

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

NH ≅ G/Ntype
2. C3×#4951C2semidirect
3. C3×#4950C2semidirect
4. #10591722C2semidirect
5. #10591711C2semidirect
6. #10591711C2semidirect
7. #10591704C2semidirect
8. #10591380C2semidirect
9. #10591378C2semidirect
10. #10591325C2semidirect
11. #10591320C2semidirect
12. #10591266C2semidirect
13. #10591263C2semidirect
14. #10591219C2semidirect
15. #10591197C2semidirect
27. #64093C4semidirect
73. #4951D3semidirect
74. #4950D3semidirect
95. C2×#638C2×C4semidirect
100. C2×C4⋊(C3⋊D3)C2×C4semidirect
103. C2×C4×C3⋊D3C2×C4semidirect
118. C32×C22⋊C4C2×C4semidirect
119. #3752C2×C4semidirect
120. #3750C2×C4semidirect
389. C3×C22⋊C4C4×D3semidirect
390. C3×C22⋊C4C4×D3semidirect
724. C22⋊C4#624semidirect
839. C32#2377semidirect
975. C3#74401semidirect
976. C3#75490semidirect

Maximal subgroups

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

subgroupindex
C2×#640932
C3×#49512
C3×#49502
#105917222
#105917112
#105917042
#105913802
#105913782
#105913252
#105913202
#105912662
#105912632
#105912192
#105911972
#754903
#744013