Finite Group Databasebeta

← C2×#21454891 #30544792

Subgroups — C2×#21454891 #30544792

Order 15616.

2230 conjugacy classes of subgroups.

The subgroup lattice has 836 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840309C211yesmaximal, characteristic
2#21454891C2116yesmaximal, direct product factor
3C2×#16839838C211yesmaximal, characteristic, complemented
4C2×#16839837C211yesmaximal, characteristic, complemented
5C2×#16839835C211yesmaximal, characteristic, complemented
6C2×#16839834C211yesmaximal, characteristic, complemented
7C2×#16839832C211yesmaximal, characteristic, complemented
8C2×C8×C22⋊D61C211yesmaximal, characteristic, complemented
9C2×#16839825C211yesmaximal, characteristic, complemented
10C2×#16839817C211yesmaximal, characteristic, complemented
11C2×#16839814C211yesmaximal, characteristic, complemented
12C2×#16839730C211yesmaximal, characteristic, complemented
13C2×#16839728C211yesmaximal, characteristic, complemented
14C2×#16839727C211yesmaximal, characteristic, complemented
15C2×#16839727C211yesmaximal, characteristic, complemented
16C2×C61×#435C211yesmaximal, characteristic, complemented
17C22×#11758222C2211yescharacteristic
18C22×#11758222C2211yescharacteristic
19C22×#11758194C2211yescharacteristic
20C22×#11758189C2211yescharacteristic
21C22×#11758189C2211yescharacteristic
22C23×#92418C2211yescharacteristic
23C22×C8×D61C2211yescharacteristic
24C22×C8×D61C2211yescharacteristic
25#16840309C418yes—
26#16840309C2218yes—
27C2×#14519776C411yescharacteristic
28C2×#14519773C411yescharacteristic
29C2×#14519763C411yescharacteristic
30C2×#14519763C411yescharacteristic
31C2×#14519752C411yescharacteristic
32C2×#14519750C411yescharacteristic
33C2×#14519750C411yescharacteristic
34C2×#14519748C411yescharacteristic
35C2×C4×D244C2211yescharacteristic
36C2×C4×C22⋊D61C2211yescharacteristic
37C2×C4×C22⋊D61C2211yescharacteristic
38C2×C42×D61C2211yescharacteristic
39#16839838C2218yescomplemented
40#16839837C2218yescomplemented
41#16839835C2218yescomplemented
42#16839834C2218yescomplemented
43#16839832C2218yescomplemented
44C8×C22⋊D61C2218yescomplemented
45#16839825C2218yescomplemented
46#16839817C2218yescomplemented
47#16839814C2218yescomplemented
48C2×C4⋊#92418C2211yescharacteristic
49C2×#14519706C2211yescharacteristic
50C2×#14519706C2211yescharacteristic
51#16839730C2218yescomplemented
52#16839728C2218yescomplemented
53#16839727C2218yescomplemented
54#16839727C2218yescomplemented
55C2×C22⋊#92418C2211yescharacteristic
56C2×C22⋊#92418C2211yescharacteristic
57C2×#14519689C2211yescharacteristic
58C2×#14519689C2211yescharacteristic
59C2×#14519689C2211yescharacteristic
60C2×#14519689C2211yescharacteristic
61C2×#14519689C2211yescharacteristic
62C2×#14519689C2211yescharacteristic
63C2×#14519689C2211yescharacteristic
64C2×#14519689C2211yescharacteristic
65C2×#14519688C2211yescharacteristic
66C2×C8×Dic61C2211yescharacteristic
67C2×C8×Dic61C2211yescharacteristic
68C22×M16×C61C2211yescharacteristic
69C23×C8×C61C2211yescharacteristic
70C2×C4×D4×C61C2211yescharacteristic
71C61×#435C2218yescomplemented
72C2×C4⋊C8×C61C2211yescharacteristic
73C2×C22⋊C8×C61C2211yescharacteristic
74C2×C22⋊C8×C61C2211yescharacteristic
75C2×#97×C61C2211yescharacteristic
76C2×#11758222—42no—
77C2×#11758222—42no—
78C2×#11758222—42no—
79C2×#11758222—42no—
80C2×#11758222C2×C414yes—
81C2×#11758222C2×C414yes—
82C2×#11758222C2314yes—
83C2×#11758222C2314yes—
84C22×Dic122C2×C411yescharacteristic
85C22×Dic122C2×C411yescharacteristic
86C22×D244C2×C411yescharacteristic
87C22×D244C2×C411yescharacteristic
88C22×D244C2×C411yescharacteristic
89C22×C22⋊D61C2×C411yescharacteristic
90C22×C22⋊D61C2×C411yescharacteristic
91C22×C22⋊D61C2×C411yescharacteristic
92C22×C22⋊D61C2×C411yescharacteristic
93C22×C22⋊D61C2×C411yescharacteristic
94C22×C22⋊D61C2×C411yescharacteristic
95C22×C4×D61C2×C411yescharacteristic
96C22×C4×D61C2×C411yescharacteristic
97C22×C4×D61C2311yescharacteristic
98C22×C4×D61C2311yescharacteristic
99C22×C4×D61C2311yescharacteristic
100C2×#11758194—42no—
101C2×#11758194C2314yes—
102C2×#11758189—42no—
103C2×#11758189—42no—
104C2×#11758189C2314yes—
105C2×#11758189C2314yes—
106C22×#92418—42no—
107C22×#92418C2311yescharacteristic
108C22×#92418C2311yescharacteristic
109C22×#92418C2311yescharacteristic
110C22×#92418C2311yescharacteristic
111C22×#92418C2314yes—
112C2×C8×D61—42no—
113C2×C8×D61—42no—
114C2×C8×D61C2314yes—
115C2×C8×D61C2314yes—
116#14519776C2×C418yes—
117#14519773C2×C418yes—
118#14519763C2×C418yes—
119#14519763C2×C418yes—
120#14519752C2×C418yes—
121#14519750C2×C418yes—
122#14519750C2×C418yes—
123#14519748C2×C418yes—
124C4×D244C2×C414yes—
125C4×D244C2314yes—
126C4×C22⋊D61C2×C414yes—
127C4×C22⋊D61C2×C414yes—
128C4×C22⋊D61C2314yes—
129C4×C22⋊D61C2314yes—
130C2×C4⋊Dic61C2×C411yescharacteristic
131C2×#11758196C2×C411yescharacteristic
132C2×#11758196C2×C411yescharacteristic
133C2×C22⋊Dic61C2×C411yescharacteristic
134C2×C22⋊Dic61C2×C411yescharacteristic
135C2×#11758198C2×C411yescharacteristic
136C2×#11758198C2×C411yescharacteristic
137C2×#11758198C2×C411yescharacteristic
138C2×#11758198C2×C411yescharacteristic
139C2×C4×Dic61C2×C411yescharacteristic
140C2×C4×Dic61C2×C411yescharacteristic
141C2×C4×Dic61C2311yescharacteristic
142C42×D61C2×C414yes—
143C42×D61C2314yes—
144C4⋊#92418C2314yes—
145#14519706C2314yes—
146#14519706C2314yes—
147C22⋊#92418C2314yes—
148C22⋊#92418C2314yes—
149#14519689C2314yes—
150#14519689C2314yes—
151#14519689C2314yes—
152#14519689C2314yes—
153#14519689C2314yes—
154#14519689C2314yes—
155#14519689C2314yes—
156#14519689C2314yes—
157#14519688C2314yes—
158C8×Dic61C2314yes—
159C8×Dic61C2314yes—
160C22×D4×C61C2×C411yescharacteristic
161C23×C4×C61C2311yescharacteristic
162C23×C4×C61C2311yescharacteristic
163C2×M16×C61—42no—
164C2×M16×C61C2314yes—
165C22×C8×C61—42no—
166C22×C8×C61C2311yescharacteristic
167C22×C8×C61C2311yescharacteristic
168C22×C8×C61C2311yescharacteristic
169C22×C8×C61C2311yescharacteristic
170C22×C8×C61C2314yes—
171C4×D4×C61C2×C414yes—
172C4×D4×C61C2314yes—
173C2×C4⋊C4×C61C2×C411yescharacteristic
174C2×C22⋊C4×C61C2×C411yescharacteristic
175C2×C22⋊C4×C61C2×C411yescharacteristic
176C2×C42×C61C2311yescharacteristic
177C4⋊C8×C61C2314yes—
178C22⋊C8×C61C2314yes—
179C22⋊C8×C61C2314yes—
180#97×C61C2314yes—
181C24×C61C22×C411yescharacteristic
182C24×C61C22×C411yescharacteristic
183C23×D61C22×C411yescharacteristic
184C23×D61C22×C411yescharacteristic
185C23×D61C22×C411yescharacteristic
186C2×D4×C61—42no—
187C2×D4×C61C22×C414yes—
188C22×C4×C61—22no—
189C22×C4×C61—22no—
190C22×C4×C61—22no—
191C22×C4×C61—22no—
192C22×C4×C61C22×C411yescharacteristic
193C22×C4×C61C22×C411yescharacteristic
194C22×C4×C61C22×C411yescharacteristic
195C22×C4×C61C22×C411yescharacteristic
196C22×C4×C61C22×C412yes—
197C22×C4×C61C22×C412yes—
198C22×C4×C61C2412yes—
199C22×C4×C61C2412yes—
200C22×C4×C61C2411yescharacteristic
201C2×C22⋊D61—24no—
202C2×C22⋊D61—24no—
203C2×C22⋊D61—42no—
204C2×C22⋊D61—42no—
205C2×C22⋊D61—42no—
206C2×C22⋊D61—42no—
207C2×C22⋊D61C22×C414yes—
208C2×C22⋊D61C22×C414yes—
209C2×C22⋊D61C22×C414yes—
210C2×C22⋊D61C22×C414yes—
211C2×C22⋊D61C22×C414yes—
212C2×C22⋊D61C22×C414yes—
213C22×Dic61C22×C411yescharacteristic
214C22×Dic61C22×C411yescharacteristic
215C22×Dic61C22×C411yescharacteristic
216C22×Dic61C22×C411yescharacteristic
217C22×Dic61C22×C411yescharacteristic
218#11758222—48no—
219#11758222—48no—
220#11758222—44no—
221#11758222—44no—
222#11758222—44no—
223#11758222—44no—
224C2×D244—42no—
225C2×D244—42no—
226C2×D244—42no—
227C2×D244C22×C414yes—
228C2×D244C22×C414yes—
229C2×D244C22×C414yes—
230C2×C4×D61—22no—
231C2×C4×D61—22no—
232C2×C4×D61—22no—
233C2×C4×D61—22no—
234C2×C4×D61—22no—
235C2×C4×D61—22no—
236C2×C4×D61—24no—
237C2×C4×D61—42no—
238C2×C4×D61C22×C414yes—
239C2×C4×D61C22×C412yes—
240C2×C4×D61C22×C412yes—
241C2×C4×D61C22×C412yes—
242C2×C4×D61C22×C414yes—
243C2×C4×D61C2412yes—
244C2×C4×D61C2412yes—
245C2×C4×D61C2412yes—
246C2×Dic122—42no—
247C2×Dic122—42no—
248C2×Dic122C22×C414yes—
249C2×Dic122C22×C414yes—
250M16×C61—44no—
251C2×C8×C61—22no—
252C2×C8×C61—22no—
253C2×C8×C61—22no—
254C2×C8×C61—22no—
255C2×C8×C61—44no—
256C2×C8×C61C2412yes—
257C2×C8×C61C2412yes—
258C2×C8×C61C2412yes—
259C2×C8×C61C2412yes—
260C4⋊C4×C61C22×C414yes—
261C22⋊C4×C61C22×C414yes—
262C22⋊C4×C61C22×C414yes—
263C42×C61C22×C412yes—
264C42×C61C2412yes—
265C22⋊Dic61C22×C414yes—
266C22⋊Dic61C22×C414yes—
267#11758198C22×C414yes—
268#11758198C22×C414yes—
269#11758198C22×C414yes—
270#11758198C22×C414yes—
271C4⋊Dic61C22×C414yes—
272#11758196C22×C414yes—
273#11758196C22×C414yes—
274C4×Dic61C22×C412yes—
275C4×Dic61C22×C414yes—
276C4×Dic61C22×C414yes—
277C4×Dic61C2412yes—
278#11758194—44no—
279C2×#92418—22no—
280C2×#92418—22no—
281C2×#92418—22no—
282C2×#92418—22no—
283C2×#92418—44no—
284C2×#92418C2412yes—
285C2×#92418C2412yes—
286C2×#92418C2412yes—
287C2×#92418C2412yes—
288#11758189—44no—
289#11758189—44no—
290C8×D61—44no—
291C8×D61—44no—
292C23×C61—22no—
293C23×C61—22no—
294C23×C61—22no—
295C23×C61—22no—
296C23×C61—22no—
297C23×C61—22no—
298C23×C61C23×C412yes—
299C23×C61C23×C412yes—
300C23×C61C23×C411yescharacteristic
301C22×D61—22no—
302C22×D61—22no—
303C22×D61—22no—
304C22×D61—22no—
305C22×D61—22no—
306C22×D61—22no—
307C22×D61—22no—
308C22×D61—22no—
309C22×D61—22no—
310C22×D61C23×C412yes—
311C22×D61C23×C412yes—
312C22×D61C23×C412yes—
313D4×C61—44no—
314C2×C4×C61—22no—
315C2×C4×C61—22no—
316C2×C4×C61—22no—
317C2×C4×C61—22no—
318C2×C4×C61—24no—
319C2×C4×C61—24no—
320C2×C4×C61—22no—
321C2×C4×C61—22no—
322C2×C4×C61—22no—
323C2×C4×C61—22no—
324C2×C4×C61C23×C412yes—
325C2×C4×C61C23×C412yes—
326C2×C4×C61C23×C412yes—
327C2×C4×C61C23×C412yes—
328C2×C4×C61C23×C411yescharacteristic
329C2×C4×C61H(5,𝔽2)12yes—
330C2×C4×C61H(5,𝔽2)12yes—
331C2×C4×C61C2511yescharacteristic
332C22⋊D61—28no—
333C22⋊D61—28no—
334C22⋊D61—44no—
335C22⋊D61—44no—
336C22⋊D61—44no—
337C22⋊D61—44no—
338C2×Dic61—22no—
339C2×Dic61—22no—
340C2×Dic61—22no—
341C2×Dic61—22no—
342C2×Dic61#13114yes—
343C2×Dic61C23×C412yes—
344C2×Dic61C23×C412yes—
345C2×Dic61C23×C412yes—
346C2×Dic61C23×C412yes—
347C2×Dic61C23×C412yes—
348D244—44no—
349D244—44no—
350D244—44no—
351C4×D61—24no—
352C4×D61—24no—
353C4×D61—24no—
354C4×D61—22no—
355C4×D61—22no—
356C4×D61—22no—
357C4×D61—22no—
358C4×D61—22no—
359C4×D61—22no—
360C4×D61—28no—
361C4×D61—44no—
362Dic122—44no—
363Dic122—44no—
364C8×C61—22no—
365C8×C61—22no—
366C8×C61—22no—
367C8×C61—22no—
368#92418—22no—
369#92418—22no—
370#92418—22no—
371#92418—22no—
372C2×#2981—611nomaximal, Sylow
373C22×C61—22no—
374C22×C61—22no—
375C22×C61—22no—
376C22×C61—22no—
377C22×C61—22no—
378C22×C61—22no—
379C22×C61—44no—
380C22×C61—44no—
381C22×C61#51812yes—
382C22×C61C2×#13112yes—
383C22×C61#56812yes—
384C22×C61C24×C411yescharacteristic
385C2×D61—22no—
386C2×D61—22no—
387C2×D61—22no—
388C2×D61—22no—
389C2×D61—22no—
390C2×D61—22no—
391C2×D61—22no—
392C2×D61—22no—
393C2×D61—22no—
394C2×D61—44no—
395C2×D61—44no—
396C2×D61—44no—
397C4×C61—22no—
398C4×C61—22no—
399C4×C61—22no—
400C4×C61—22no—
401C4×C61#51812yes—
402C4×C61C2×H(5,𝔽2)11yescharacteristic
403C4×C61C2×H(5,𝔽2)11yescharacteristic
404Dic61—22no—
405Dic61—22no—
406Dic61—22no—
407Dic61—22no—
408Dic61C2×#13114yes—
409C2×#532—611no—
410#2981—6116no—
411C2×#436—611no—
412C2×#436—611no—
413C2×#435—611no—
414C2×#435—611no—
415C2×#435—611no—
416C2×#435D6111yescharacteristic, complemented
417C2×C8×D4—611no—
418C2×C8×D4—611no—
419C2×#432—611no—
420C2×#431—611no—
421C2×#408—611no—
422C2×#408—611no—
423C2×#408—611no—
424C2×#408—611no—
425C2×C61—42no—
426C2×C61—42no—
427C2×C61#298114yescomplemented
428C2×C61C2×#51811yescharacteristic
429C2×C61C22×#13111yescharacteristic
430C2×C61C2×#56811yescharacteristic
431D61—42no—
432D61—42no—
433D61—42no—
434C22×#41—611no—
435C22×#41—611no—
436C22×M16—611no—
437C22×M16—611no—
438C22×M16—611no—
439C22×M16C2×D6111yescharacteristic
440C23×C8—611no—
441C23×C8—611no—
442C23×C8—611no—
443C23×C8C2×D6111yescharacteristic
444#532—618no—
445#532—618no—
446C2×C4⋊Q8—611no—
447C2×#127—611no—
448C2×#124—611no—
449C2×#124—611no—
450C2×#121—611no—
451C2×#121—611no—
452C2×#121—611no—
453C2×#121—611no—
454C2×C4×D4—611no—
455C2×C4×D4—611no—
456C2×C4×D4—611no—
457C2×C4×D4C2×D6111yescharacteristic
458C22×C42—611no—
459#436—618no—
460#436—618no—
461#435—618no—
462#435—618no—
463#435—618no—
464#435C2×D6118yescomplemented
465C8×D4—618no—
466C8×D4—618no—
467#432—618no—
468#431—618no—
469C2×C4⋊C8—611no—
470C2×C4⋊C8—611no—
471C2×C4⋊C8—611no—
472C2×C4⋊C8C2×D6111yescharacteristic
473#408—618no—
474#408—618no—
475#408—618no—
476#408—618no—
477C2×C22⋊C8—611no—
478C2×C22⋊C8—611no—
479C2×C22⋊C8—611no—
480C2×C22⋊C8—611no—
481C2×C22⋊C8—611no—
482C2×C22⋊C8—611no—
483C2×C22⋊C8—611no—
484C2×C22⋊C8—611no—
485C2×C22⋊C8—611no—
486C2×C22⋊C8—611no—
487C2×C22⋊C8C2×D6111yescharacteristic
488C2×C22⋊C8C2×D6111yescharacteristic
489C2×#97—611no—
490C2×#97C2×D6111yescharacteristic
491C2×C4×C8—611no—
492C2×C4×C8—611no—
493C61C2×#298111yescharacteristic, complemented, Sylow
494C2×#41—614no—
495C2×#41—614no—
496C2×#41—614no—
497C2×#41—614no—
498C2×#41—2442no—
499C2×#41—2442no—
500C2×#41—2442no—
501C2×#41—2442no—
502C22×Q8—611no—
503C22×Q8—611no—
504C22×D4—611no—
505C22×D4—611no—
506C22×D4—611no—
507C22×D4—611no—
508C22×D4—611no—
509C22×D4—611no—
510C22×D4—611no—
511C22×D4—611no—
512C22×D4—611no—
513C22×D4C4×D6111yescharacteristic
514C23×C4—611no—
515C23×C4—611no—
516C23×C4—611no—
517C23×C4—611no—
518C23×C4—611no—
519C23×C4C22×D6111yescharacteristic
520C23×C4C22×D6111yescharacteristic
521C2×M16—42no—
522C2×M16—614no—
523C2×M16—614no—
524C2×M16—614no—
525C2×M16—2442no—
526C2×M16—2442no—
527C2×M16—2442no—
528C2×M16C22×D6114yes—
529C22×C8—42no—
530C22×C8—611no—
531C22×C8—611no—
532C22×C8—611no—
533C22×C8—611no—
534C22×C8—614no—
535C22×C8—614no—
536C22×C8—614no—
537C22×C8—2442no—
538C22×C8—2442no—
539C22×C8—2442no—
540C22×C8C22×D6111yescharacteristic
541C22×C8C22×D6111yescharacteristic
542C22×C8C22×D6111yescharacteristic
543C22×C8C22×D6111yescharacteristic
544C22×C8C22×D6114yes—
545C4⋊Q8—618no—
546#127—618no—
547#124—618no—
548#124—618no—
549#121—618no—
550#121—618no—
551#121—618no—
552#121—618no—
553C4×D4—614no—
554C4×D4—614no—
555C4×D4—614no—
556C4×D4—614no—
557C4×D4—614no—
558C4×D4—614no—
559C4×D4C4×D6114yes—
560C4×D4C22×D6114yes—
561C2×C4⋊C4—611no—
562C2×C4⋊C4—611no—
563C2×C4⋊C4—611no—
564C2×C4⋊C4C4×D6111yescharacteristic
565C2×C22⋊C4—611no—
566C2×C22⋊C4—611no—
567C2×C22⋊C4—611no—
568C2×C22⋊C4—611no—
569C2×C22⋊C4—611no—
570C2×C22⋊C4—611no—
571C2×C22⋊C4C4×D6111yescharacteristic
572C2×C22⋊C4C4×D6111yescharacteristic
573C2×C42—611no—
574C2×C42—611no—
575C2×C42—611no—
576C2×C42—614no—
577C2×C42—614no—
578C2×C42C22×D6111yescharacteristic
579C4⋊C8—614no—
580C4⋊C8—614no—
581C4⋊C8—614no—
582C4⋊C8C22×D6114yes—
583C22⋊C8—614no—
584C22⋊C8—614no—
585C22⋊C8—614no—
586C22⋊C8—614no—
587C22⋊C8—614no—
588C22⋊C8—614no—
589C22⋊C8—614no—
590C22⋊C8—614no—
591C22⋊C8—614no—
592C22⋊C8—614no—
593C22⋊C8C22×D6114yes—
594C22⋊C8C22×D6114yes—
595#97—614no—
596#97C22×D6114yes—
597C4×C8—614no—
598C4×C8—614no—
599C24—611no—
600C24—611no—
601C24—611no—
602C24C2×C4×D6111yescharacteristic
603C24C2×C4×D6111yescharacteristic
604#41—2448no—
605#41—2448no—
606#41—2444no—
607#41—2444no—
608#41—2444no—
609#41—2444no—
610C2×Q8—614no—
611C2×Q8—614no—
612C2×Q8—2442no—
613C2×Q8—2442no—
614C2×D4—42no—
615C2×D4—614no—
616C2×D4—614no—
617C2×D4—614no—
618C2×D4—614no—
619C2×D4—614no—
620C2×D4—614no—
621C2×D4—614no—
622C2×D4—614no—
623C2×D4—614no—
624C2×D4—1224no—
625C2×D4—1224no—
626C2×D4—2442no—
627C2×D4—2442no—
628C2×D4—2442no—
629C2×D4—2442no—
630C2×D4—2442no—
631C2×D4—2442no—
632C2×D4—2442no—
633C2×D4C2×C4×D6114yes—
634C22×C4—22no—
635C22×C4—22no—
636C22×C4—22no—
637C22×C4—22no—
638C22×C4—611no—
639C22×C4—611no—
640C22×C4—611no—
641C22×C4—611no—
642C22×C4—611no—
643C22×C4—614no—
644C22×C4—612no—
645C22×C4—612no—
646C22×C4—612no—
647C22×C4—612no—
648C22×C4—612no—
649C22×C4—612no—
650C22×C4—614no—
651C22×C4—1224no—
652C22×C4—1222no—
653C22×C4—1222no—
654C22×C4—1222no—
655C22×C4—1222no—
656C22×C4—1222no—
657C22×C4—1222no—
658C22×C4—2442no—
659C22×C4C2×C4×D6111yescharacteristic
660C22×C4C2×C4×D6111yescharacteristic
661C22×C4C2×C4×D6111yescharacteristic
662C22×C4C2×C4×D6111yescharacteristic
663C22×C4C2×C4×D6112yes—
664C22×C4C2×C4×D6112yes—
665C22×C4C23×D6112yes—
666C22×C4C23×D6112yes—
667C22×C4C23×D6111yescharacteristic
668M16—44no—
669M16—2444no—
670M16—2444no—
671M16—2444no—
672C2×C8—22no—
673C2×C8—22no—
674C2×C8—22no—
675C2×C8—22no—
676C2×C8—44no—
677C2×C8—612no—
678C2×C8—612no—
679C2×C8—612no—
680C2×C8—612no—
681C2×C8—1222no—
682C2×C8—1222no—
683C2×C8—1222no—
684C2×C8—1222no—
685C2×C8—2444no—
686C2×C8—2444no—
687C2×C8—2444no—
688C2×C8C23×D6112yes—
689C2×C8C23×D6112yes—
690C2×C8C23×D6112yes—
691C2×C8C23×D6112yes—
692C4⋊C4—614no—
693C4⋊C4—614no—
694C4⋊C4—614no—
695C4⋊C4C2×C4×D6114yes—
696C22⋊C4—614no—
697C22⋊C4—614no—
698C22⋊C4—614no—
699C22⋊C4—614no—
700C22⋊C4—614no—
701C22⋊C4—614no—
702C22⋊C4C2×C4×D6114yes—
703C22⋊C4C2×C4×D6114yes—
704C42—612no—
705C42—614no—
706C42—614no—
707C42—612no—
708C42C2×C4×D6112yes—
709C42C23×D6112yes—
710C23—22no—
711C23—22no—
712C23—22no—
713C23—22no—
714C23—22no—
715C23—22no—
716C23—612no—
717C23—612no—
718C23—612no—
719C23—1222no—
720C23—1222no—
721C23—1222no—
722C23—1222no—
723C23—1222no—
724C23—1222no—
725C23—1222no—
726C23—1222no—
727C23—1222no—
728C23C22×C4×D6112yes—
729C23C22×C4×D6112yes—
730C23C22×C4×D6111yescharacteristic
731Q8—2444no—
732Q8—2444no—
733D4—44no—
734D4—1228no—
735D4—1228no—
736D4—2444no—
737D4—2444no—
738D4—2444no—
739D4—2444no—
740D4—2444no—
741D4—2444no—
742D4—2444no—
743C2×C4—22no—
744C2×C4—22no—
745C2×C4—22no—
746C2×C4—22no—
747C2×C4—24no—
748C2×C4—24no—
749C2×C4—22no—
750C2×C4—22no—
751C2×C4—22no—
752C2×C4—22no—
753C2×C4—614no—
754C2×C4—612no—
755C2×C4—612no—
756C2×C4—612no—
757C2×C4—612no—
758C2×C4—612no—
759C2×C4—1228no—
760C2×C4—1222no—
761C2×C4—1222no—
762C2×C4—1222no—
763C2×C4—1222no—
764C2×C4—1224no—
765C2×C4—1224no—
766C2×C4—1224no—
767C2×C4—1222no—
768C2×C4—1222no—
769C2×C4—1222no—
770C2×C4—1222no—
771C2×C4—1222no—
772C2×C4—1222no—
773C2×C4—2444no—
774C2×C4C22×C4×D6112yes—
775C2×C4C22×C4×D6112yes—
776C2×C4C22×C4×D6112yes—
777C2×C4C22×C4×D6112yes—
778C2×C4C22×C4×D6111yescharacteristic
779C2×C4#1451982212yes—
780C2×C4#1451982312yes—
781C2×C4C24×D6111yescharacteristic
782C8—22no—
783C8—22no—
784C8—22no—
785C8—22no—
786C8—1222no—
787C8—1222no—
788C8—1222no—
789C8—1222no—
790C22—22no—
791C22—22no—
792C22—22no—
793C22—22no—
794C22—22no—
795C22—22no—
796C22—44no—
797C22—44no—
798C22—1222no—
799C22—1222no—
800C22—1222no—
801C22—1222no—
802C22—1222no—
803C22—1222no—
804C22—1222no—
805C22—1222no—
806C22—1222no—
807C22—2444no—
808C22—2444no—
809C22—2444no—
810C22#1684023412yes—
811C22#131×D6112yes—
812C22#1684052812yes—
813C22C23×C4×D6111yescharacteristic
814C4—22no—
815C4—22no—
816C4—22no—
817C4—22no—
818C4—614no—
819C4—1222no—
820C4—1222no—
821C4—1222no—
822C4—1222no—
823C4#1684023412yes—
824C4C2×#1451982211yescharacteristic
825C4C2×#1451982311yescharacteristic
826C2—42no—
827C2—42no—
828C2—2442no—
829C2—2442no—
830C2—2442no—
831C2#2145489114yesdirect product factor
832C2C2×#1684023411yescharacteristic
833C2C2×#131×D6111yescharacteristic
834C2C2×#1684052811yescharacteristic
subgroupG/H
centerC22×C4C23×D61
commutatorC22×C61C24×C4
FrattiniC2×C4C24×D61
FittingC2×C61×#435C2
socleC23×C61C23×C4
prime radicalC2×#16840309C2
cosocleC2×C4×C61C25
hypercenterC2×#435D61
hypocenterC61C2×#2981
LCSG ▷ C22×C61 ▷ C61
UCSC1 ◁ C22×C4 ◁ C2×#435

Complements

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

NH ≅ G/Ntype
2. #21454891C2direct (N × H)
3. C2×#16839838C2semidirect
4. C2×#16839837C2semidirect
5. C2×#16839835C2semidirect
6. C2×#16839834C2semidirect
7. C2×#16839832C2semidirect
8. C2×C8×C22⋊D61C2semidirect
9. C2×#16839825C2semidirect
10. C2×#16839817C2semidirect
11. C2×#16839814C2semidirect
12. C2×#16839730C2semidirect
13. C2×#16839728C2semidirect
14. C2×#16839727C2semidirect
15. C2×#16839727C2semidirect
16. C2×C61×#435C2semidirect
39. #16839838C22semidirect
40. #16839837C22semidirect
41. #16839835C22semidirect
42. #16839834C22semidirect
43. #16839832C22semidirect
44. C8×C22⋊D61C22semidirect
45. #16839825C22semidirect
46. #16839817C22semidirect
47. #16839814C22semidirect
51. #16839730C22semidirect
52. #16839728C22semidirect
53. #16839727C22semidirect
54. #16839727C22semidirect
71. C61×#435C22semidirect
416. C2×#435D61semidirect
427. C2×C61#2981semidirect
464. #435C2×D61semidirect
493. C61C2×#2981semidirect
831. C2#21454891direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168403092
#214548912
C2×#168398382
C2×#168398372
C2×#168398352
C2×#168398342
C2×#168398322
C2×C8×C22⋊D612
C2×#168398252
C2×#168398172
C2×#168398142
C2×#168397302
C2×#168397282
C2×#168397272
C2×C61×#4352
C2×#298161