Finite Group Databasebeta

← C2×#21454892 #30544793

Subgroups — C2×#21454892 #30544793

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×#16840308C211yesmaximal, characteristic
2#21454892C2116yesmaximal, direct product factor
3C2×#16839838C211yesmaximal, characteristic, complemented
4C2×#16839837C211yesmaximal, characteristic, complemented
5C2×#16839836C211yesmaximal, characteristic, complemented
6C2×#16839833C211yesmaximal, characteristic, complemented
7C2×#16839831C211yesmaximal, characteristic, complemented
8C2×#16839830C211yesmaximal, characteristic, complemented
9C2×C8×C22⋊D61C211yesmaximal, characteristic, complemented
10C2×#16839825C211yesmaximal, characteristic, complemented
11C2×#16839816C211yesmaximal, characteristic, complemented
12C2×#16839812C211yesmaximal, characteristic, complemented
13C2×#16839729C211yesmaximal, characteristic, complemented
14C2×#16839727C211yesmaximal, characteristic, complemented
15C2×#16839727C211yesmaximal, characteristic, complemented
16C2×C61×#408C211yesmaximal, characteristic, complemented
17C22×#11758222C2211yescharacteristic
18C22×#11758194C2211yescharacteristic
19C22×#11758189C2211yescharacteristic
20C22×#11758189C2211yescharacteristic
21C23×#92418C2211yescharacteristic
22C22×C8×D61C2211yescharacteristic
23C22×C8×D61C2211yescharacteristic
24#16840308C418yes—
25#16840308C2218yes—
26C2×#14519775C411yescharacteristic
27C2×#14519773C411yescharacteristic
28C2×#14519766C411yescharacteristic
29C2×#14519764C411yescharacteristic
30C2×#14519749C411yescharacteristic
31C2×#14519749C411yescharacteristic
32C2×#14519749C411yescharacteristic
33C2×#14519749C411yescharacteristic
34C2×C4×C22⋊D61C2211yescharacteristic
35C2×C4×C22⋊D61C2211yescharacteristic
36C2×C4×C22⋊D61C2211yescharacteristic
37C2×C4×C22⋊D61C2211yescharacteristic
38C22×C4×Dic61C2211yescharacteristic
39#16839838C2218yescomplemented
40#16839837C2218yescomplemented
41#16839836C2218yescomplemented
42#16839833C2218yescomplemented
43#16839831C2218yescomplemented
44#16839830C2218yescomplemented
45C8×C22⋊D61C2218yescomplemented
46#16839825C2218yescomplemented
47#16839816C2218yescomplemented
48#16839812C2218yescomplemented
49C2×#14519706C2211yescharacteristic
50C2×#14519706C2211yescharacteristic
51C2×#14519706C2211yescharacteristic
52C2×#14519706C2211yescharacteristic
53#16839729C2218yescomplemented
54#16839727C2218yescomplemented
55#16839727C2218yescomplemented
56C2×C22⋊#92418C2211yescharacteristic
57C2×C22⋊#92418C2211yescharacteristic
58C2×C22⋊#92418C2211yescharacteristic
59C2×C22⋊#92418C2211yescharacteristic
60C2×#14519689C2211yescharacteristic
61C2×#14519689C2211yescharacteristic
62C2×#14519689C2211yescharacteristic
63C2×#14519689C2211yescharacteristic
64C2×#14519687C2211yescharacteristic
65C2×#14519687C2211yescharacteristic
66C2×C8×Dic61C2211yescharacteristic
67C2×C8×Dic61C2211yescharacteristic
68C22×#41×C61C2211yescharacteristic
69C22×M16×C61C2211yescharacteristic
70C23×C8×C61C2211yescharacteristic
71C61×#408C2218yescomplemented
72C2×C22⋊C8×C61C2211yescharacteristic
73C2×C22⋊C8×C61C2211yescharacteristic
74C2×C22⋊C8×C61C2211yescharacteristic
75C2×C22⋊C8×C61C2211yescharacteristic
76C2×#11758222—42no—
77C2×#11758222—42no—
78C2×#11758222C2×C414yes—
79C2×#11758222C2314yes—
80C22×Dic122C2×C411yescharacteristic
81C22×D244C2×C411yescharacteristic
82C22×C22⋊D61C2×C411yescharacteristic
83C22×C22⋊D61C2×C411yescharacteristic
84C22×C22⋊D61C2×C411yescharacteristic
85C22×C22⋊D61C2×C411yescharacteristic
86C22×C22⋊D61C2×C411yescharacteristic
87C22×C22⋊D61C2×C411yescharacteristic
88C23×Dic61C2×C411yescharacteristic
89C23×Dic61C2×C411yescharacteristic
90C22×C4×D61C2311yescharacteristic
91C22×C4×D61C2311yescharacteristic
92C2×#11758194—42no—
93C2×#11758194C2314yes—
94C2×#11758189—42no—
95C2×#11758189—42no—
96C2×#11758189C2314yes—
97C2×#11758189C2314yes—
98C22×#92418—42no—
99C22×#92418C2311yescharacteristic
100C22×#92418C2311yescharacteristic
101C22×#92418C2311yescharacteristic
102C22×#92418C2311yescharacteristic
103C22×#92418C2314yes—
104C2×C8×D61—42no—
105C2×C8×D61—42no—
106C2×C8×D61C2314yes—
107C2×C8×D61C2314yes—
108#14519775C2×C418yes—
109#14519773C2×C418yes—
110#14519766C2×C418yes—
111#14519764C2×C418yes—
112#14519749C2×C418yes—
113#14519749C2×C418yes—
114#14519749C2×C418yes—
115#14519749C2×C418yes—
116C4×C22⋊D61C2×C414yes—
117C4×C22⋊D61C2×C414yes—
118C4×C22⋊D61C2×C414yes—
119C4×C22⋊D61C2×C414yes—
120C4×C22⋊D61C2314yes—
121C4×C22⋊D61C2314yes—
122C4×C22⋊D61C2314yes—
123C4×C22⋊D61C2314yes—
124C2×#11758196C2×C411yescharacteristic
125C2×#11758196C2×C411yescharacteristic
126C2×#11758196C2×C411yescharacteristic
127C2×#11758196C2×C411yescharacteristic
128C2×C22⋊Dic61C2×C411yescharacteristic
129C2×C22⋊Dic61C2×C411yescharacteristic
130C2×C22⋊Dic61C2×C411yescharacteristic
131C2×C22⋊Dic61C2×C411yescharacteristic
132C2×#11758198C2×C411yescharacteristic
133C2×#11758198C2×C411yescharacteristic
134C2×#11758198C2×C411yescharacteristic
135C2×#11758198C2×C411yescharacteristic
136C2×C4×Dic61C2×C411yescharacteristic
137C2×C4×Dic61C2×C411yescharacteristic
138C2×C4×Dic61C2×C414yes—
139C2×C4×Dic61C2311yescharacteristic
140C2×C4×Dic61C2311yescharacteristic
141C2×C4×Dic61C2314yes—
142#14519706C2314yes—
143#14519706C2314yes—
144#14519706C2314yes—
145#14519706C2314yes—
146C22⋊#92418C2314yes—
147C22⋊#92418C2314yes—
148C22⋊#92418C2314yes—
149C22⋊#92418C2314yes—
150#14519689C2314yes—
151#14519689C2314yes—
152#14519689C2314yes—
153#14519689C2314yes—
154#14519687C2314yes—
155#14519687C2314yes—
156C8×Dic61C2314yes—
157C8×Dic61C2314yes—
158C2×#41×C61—42no—
159C2×#41×C61—42no—
160C2×#41×C61C2×C414yes—
161C2×#41×C61C2314yes—
162C22×Q8×C61C2×C411yescharacteristic
163C22×D4×C61C2×C411yescharacteristic
164C22×D4×C61C2×C411yescharacteristic
165C22×D4×C61C2×C411yescharacteristic
166C23×C4×C61C2311yescharacteristic
167C23×C4×C61C2311yescharacteristic
168C23×C4×C61C2311yescharacteristic
169C2×M16×C61—42no—
170C2×M16×C61C2314yes—
171C22×C8×C61—42no—
172C22×C8×C61C2311yescharacteristic
173C22×C8×C61C2311yescharacteristic
174C22×C8×C61C2311yescharacteristic
175C22×C8×C61C2311yescharacteristic
176C22×C8×C61C2314yes—
177C22⋊C8×C61C2314yes—
178C22⋊C8×C61C2314yes—
179C22⋊C8×C61C2314yes—
180C22⋊C8×C61C2314yes—
181C24×C61C22×C411yescharacteristic
182C24×C61C22×C411yescharacteristic
183C24×C61C22×C411yescharacteristic
184C23×D61C22×C411yescharacteristic
185C23×D61C22×C411yescharacteristic
186#41×C61—48no—
187#41×C61—44no—
188#41×C61—44no—
189C2×Q8×C61—42no—
190C2×Q8×C61C22×C414yes—
191C2×D4×C61—42no—
192C2×D4×C61—42no—
193C2×D4×C61—42no—
194C2×D4×C61C22×C414yes—
195C2×D4×C61C22×C414yes—
196C2×D4×C61C22×C414yes—
197C22×C4×C61—22no—
198C22×C4×C61—22no—
199C22×C4×C61—22no—
200C22×C4×C61—22no—
201C22×C4×C61—22no—
202C22×C4×C61—22no—
203C22×C4×C61C22×C411yescharacteristic
204C22×C4×C61C22×C412yes—
205C22×C4×C61C22×C411yescharacteristic
206C22×C4×C61C22×C411yescharacteristic
207C22×C4×C61C22×C412yes—
208C22×C4×C61C22×C412yes—
209C22×C4×C61C2412yes—
210C22×C4×C61C2412yes—
211C22×C4×C61C2412yes—
212C22×C4×C61C2411yescharacteristic
213C2×C22⋊D61—24no—
214C2×C22⋊D61—24no—
215C2×C22⋊D61—42no—
216C2×C22⋊D61—42no—
217C2×C22⋊D61—42no—
218C2×C22⋊D61—42no—
219C2×C22⋊D61C22×C414yes—
220C2×C22⋊D61C22×C414yes—
221C2×C22⋊D61C22×C414yes—
222C2×C22⋊D61C22×C414yes—
223C2×C22⋊D61C22×C414yes—
224C2×C22⋊D61C22×C414yes—
225C22×Dic61—24no—
226C22×Dic61—42no—
227C22×Dic61C22×C411yescharacteristic
228C22×Dic61C22×C411yescharacteristic
229C22×Dic61C22×C411yescharacteristic
230C22×Dic61C22×C411yescharacteristic
231C22×Dic61C22×C411yescharacteristic
232C22×Dic61C22×C414yes—
233C22×Dic61C22×C414yes—
234C22×Dic61C22×C411yescharacteristic
235#11758222—48no—
236#11758222—44no—
237#11758222—44no—
238C2×D244—42no—
239C2×D244C22×C414yes—
240C2×C4×D61—22no—
241C2×C4×D61—22no—
242C2×C4×D61—22no—
243C2×C4×D61—22no—
244C2×C4×D61C22×C412yes—
245C2×C4×D61C22×C412yes—
246C2×C4×D61C2412yes—
247C2×C4×D61C2412yes—
248C2×Dic122—42no—
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—
260C22⋊Dic61C22×C414yes—
261C22⋊Dic61C22×C414yes—
262C22⋊Dic61C22×C414yes—
263C22⋊Dic61C22×C414yes—
264#11758198C22×C414yes—
265#11758198C22×C414yes—
266#11758198C22×C414yes—
267#11758198C22×C414yes—
268#11758196C22×C414yes—
269#11758196C22×C414yes—
270#11758196C22×C414yes—
271#11758196C22×C414yes—
272C4×Dic61C22×C412yes—
273C4×Dic61C22×C412yes—
274C4×Dic61C22×C414yes—
275C4×Dic61C22×C414yes—
276C4×Dic61C2412yes—
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×C61—22no—
299C23×C61—22no—
300C23×C61—22no—
301C23×C61C23×C412yes—
302C23×C61C23×C412yes—
303C23×C61C23×C412yes—
304C23×C61C23×C411yescharacteristic
305C22×D61—22no—
306C22×D61—22no—
307C22×D61—22no—
308C22×D61—22no—
309C22×D61—22no—
310C22×D61—22no—
311C22×D61C23×C412yes—
312C22×D61C23×C412yes—
313Q8×C61—44no—
314D4×C61—44no—
315D4×C61—44no—
316D4×C61—44no—
317C2×C4×C61—22no—
318C2×C4×C61—22no—
319C2×C4×C61—22no—
320C2×C4×C61—24no—
321C2×C4×C61—24no—
322C2×C4×C61—24no—
323C2×C4×C61—22no—
324C2×C4×C61—22no—
325C2×C4×C61—22no—
326C2×C4×C61—22no—
327C2×C4×C61—22no—
328C2×C4×C61—22no—
329C2×C4×C61C23×C412yes—
330C2×C4×C61C23×C412yes—
331C2×C4×C61C23×C412yes—
332C2×C4×C61C23×C411yescharacteristic
333C2×C4×C61H(5,𝔽2)12yes—
334C2×C4×C61H(5,𝔽2)12yes—
335C2×C4×C61C2511yescharacteristic
336C22⋊D61—28no—
337C22⋊D61—28no—
338C22⋊D61—44no—
339C22⋊D61—44no—
340C22⋊D61—44no—
341C22⋊D61—44no—
342C2×Dic61—22no—
343C2×Dic61—22no—
344C2×Dic61—22no—
345C2×Dic61—22no—
346C2×Dic61—22no—
347C2×Dic61—28no—
348C2×Dic61—44no—
349C2×Dic61#13114yes—
350C2×Dic61C23×C412yes—
351C2×Dic61C23×C412yes—
352C2×Dic61C23×C412yes—
353C2×Dic61C23×C412yes—
354C2×Dic61C23×C412yes—
355C2×Dic61C23×C412yes—
356D244—44no—
357C4×D61—24no—
358C4×D61—24no—
359C4×D61—22no—
360C4×D61—22no—
361C4×D61—22no—
362C4×D61—22no—
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—22no—
380C22×C61—22no—
381C22×C61—22no—
382C22×C61—44no—
383C22×C61—44no—
384C22×C61—44no—
385C22×C61#51812yes—
386C22×C61C2×#13112yes—
387C22×C61#56812yes—
388C22×C61C24×C411yescharacteristic
389C2×D61—22no—
390C2×D61—22no—
391C2×D61—22no—
392C2×D61—22no—
393C2×D61—22no—
394C2×D61—22no—
395C2×D61—44no—
396C2×D61—44no—
397C4×C61—22no—
398C4×C61—22no—
399C4×C61—22no—
400C4×C61#51812yes—
401C4×C61C2×H(5,𝔽2)11yescharacteristic
402C4×C61C2×H(5,𝔽2)11yescharacteristic
403Dic61—22no—
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×#435—611no—
417C2×C8×D4—611no—
418C2×C8×D4—611no—
419C2×#432—611no—
420C2×#431—611no—
421C2×#408—611no—
422C2×#408—611no—
423C2×#408—611no—
424C2×#408D6111yescharacteristic, complemented
425C2×C61—42no—
426C2×C61—42no—
427C2×C61—42no—
428C2×C61#298114yescomplemented
429C2×C61C2×#51811yescharacteristic
430C2×C61C22×#13111yescharacteristic
431C2×C61C2×#56811yescharacteristic
432D61—42no—
433D61—42no—
434C22×#41—611no—
435C22×#41C2×D6111yescharacteristic
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×D4—611no—
458C22×C42—611no—
459#436—618no—
460#436—618no—
461#435—618no—
462#435—618no—
463#435—618no—
464#435—618no—
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⋊C8—611no—
473#408—618no—
474#408—618no—
475#408—618no—
476#408C2×D6118yescomplemented
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⋊C8C2×D6111yescharacteristic
486C2×C22⋊C8C2×D6111yescharacteristic
487C2×C22⋊C8C2×D6111yescharacteristic
488C2×C22⋊C8C2×D6111yescharacteristic
489C2×#97—611no—
490C2×#97—611no—
491C2×C4×C8—611no—
492C2×C4×C8—611no—
493C61C2×#298111yescharacteristic, complemented, Sylow
494C2×#41—42no—
495C2×#41—42no—
496C2×#41—614no—
497C2×#41—614no—
498C2×#41—2442no—
499C2×#41—2442no—
500C2×#41C4×D6114yes—
501C2×#41C22×D6114yes—
502C22×Q8—611no—
503C22×Q8C4×D6111yescharacteristic
504C22×D4—611no—
505C22×D4—611no—
506C22×D4—611no—
507C22×D4—611no—
508C22×D4—611no—
509C22×D4—611no—
510C22×D4—611no—
511C22×D4C4×D6111yescharacteristic
512C22×D4C4×D6111yescharacteristic
513C22×D4C4×D6111yescharacteristic
514C23×C4—611no—
515C23×C4—611no—
516C23×C4—611no—
517C23×C4—611no—
518C23×C4C22×D6111yescharacteristic
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×D4—614no—
560C4×D4—614no—
561C2×C4⋊C4—611no—
562C2×C4⋊C4—611no—
563C2×C4⋊C4—611no—
564C2×C4⋊C4—611no—
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⋊C4—611no—
572C2×C22⋊C4—611no—
573C2×C42—611no—
574C2×C42—611no—
575C2×C42—614no—
576C2×C42—614no—
577C2×C42—611no—
578C2×C42—611no—
579C4⋊C8—614no—
580C4⋊C8—614no—
581C4⋊C8—614no—
582C4⋊C8—614no—
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⋊C8C22×D6114yes—
592C22⋊C8C22×D6114yes—
593C22⋊C8C22×D6114yes—
594C22⋊C8C22×D6114yes—
595#97—614no—
596#97—614no—
597C4×C8—614no—
598C4×C8—614no—
599C24—611no—
600C24—611no—
601C24C2×C4×D6111yescharacteristic
602C24C2×C4×D6111yescharacteristic
603C24C2×C4×D6111yescharacteristic
604#41—48no—
605#41—44no—
606#41—44no—
607#41—2448no—
608#41—2444no—
609#41—2444no—
610C2×Q8—42no—
611C2×Q8—614no—
612C2×Q8—2442no—
613C2×Q8C2×C4×D6114yes—
614C2×D4—42no—
615C2×D4—42no—
616C2×D4—42no—
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×D4C2×C4×D6114yes—
632C2×D4C2×C4×D6114yes—
633C2×D4C2×C4×D6114yes—
634C22×C4—22no—
635C22×C4—22no—
636C22×C4—22no—
637C22×C4—22no—
638C22×C4—22no—
639C22×C4—22no—
640C22×C4—611no—
641C22×C4—611no—
642C22×C4—611no—
643C22×C4—611no—
644C22×C4—614no—
645C22×C4—611no—
646C22×C4—611no—
647C22×C4—614no—
648C22×C4—612no—
649C22×C4—612no—
650C22×C4—612no—
651C22×C4—612no—
652C22×C4—1224no—
653C22×C4—1222no—
654C22×C4—1222no—
655C22×C4—1222no—
656C22×C4—1222no—
657C22×C4—2442no—
658C22×C4C2×C4×D6111yescharacteristic
659C22×C4C2×C4×D6112yes—
660C22×C4C2×C4×D6111yescharacteristic
661C22×C4C2×C4×D6111yescharacteristic
662C22×C4C2×C4×D6112yes—
663C22×C4C2×C4×D6112yes—
664C22×C4C23×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⋊C4—614no—
696C22⋊C4—614no—
697C22⋊C4—614no—
698C22⋊C4—614no—
699C22⋊C4—614no—
700C22⋊C4—614no—
701C22⋊C4—614no—
702C22⋊C4—614no—
703C22⋊C4—614no—
704C42—612no—
705C42—612no—
706C42—614no—
707C42—614no—
708C42—612no—
709C42—612no—
710C23—22no—
711C23—22no—
712C23—22no—
713C23—22no—
714C23—22no—
715C23—22no—
716C23—22no—
717C23—22no—
718C23—22no—
719C23—612no—
720C23—612no—
721C23—1222no—
722C23—1222no—
723C23—1222no—
724C23—1222no—
725C23—1222no—
726C23—1222no—
727C23C22×C4×D6112yes—
728C23C22×C4×D6112yes—
729C23C22×C4×D6112yes—
730C23C22×C4×D6111yescharacteristic
731Q8—44no—
732Q8—2444no—
733D4—44no—
734D4—44no—
735D4—44no—
736D4—1228no—
737D4—1228no—
738D4—2444no—
739D4—2444no—
740D4—2444no—
741D4—2444no—
742D4—2444no—
743C2×C4—22no—
744C2×C4—22no—
745C2×C4—22no—
746C2×C4—24no—
747C2×C4—24no—
748C2×C4—24no—
749C2×C4—22no—
750C2×C4—22no—
751C2×C4—22no—
752C2×C4—22no—
753C2×C4—22no—
754C2×C4—22no—
755C2×C4—614no—
756C2×C4—612no—
757C2×C4—612no—
758C2×C4—612no—
759C2×C4—612no—
760C2×C4—612no—
761C2×C4—612no—
762C2×C4—1228no—
763C2×C4—1222no—
764C2×C4—1222no—
765C2×C4—1222no—
766C2×C4—1222no—
767C2×C4—1222no—
768C2×C4—1224no—
769C2×C4—1224no—
770C2×C4—1222no—
771C2×C4—1222no—
772C2×C4—1222no—
773C2×C4—1222no—
774C2×C4—2444no—
775C2×C4C22×C4×D6112yes—
776C2×C4C22×C4×D6112yes—
777C2×C4C22×C4×D6112yes—
778C2×C4C22×C4×D6111yescharacteristic
779C2×C4#1451982212yes—
780C2×C4#1451982212yes—
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—22no—
797C22—22no—
798C22—22no—
799C22—44no—
800C22—44no—
801C22—44no—
802C22—1222no—
803C22—1222no—
804C22—1222no—
805C22—1222no—
806C22—1222no—
807C22—1222no—
808C22—2444no—
809C22—2444no—
810C22#1684023512yes—
811C22#131×D6112yes—
812C22#1684052712yes—
813C22C23×C4×D6111yescharacteristic
814C4—22no—
815C4—22no—
816C4—22no—
817C4—614no—
818C4—1222no—
819C4—1222no—
820C4—1222no—
821C4—1222no—
822C4—1222no—
823C4#1684023512yes—
824C4C2×#1451982211yescharacteristic
825C4C2×#1451982211yescharacteristic
826C2—42no—
827C2—42no—
828C2—42no—
829C2—2442no—
830C2—2442no—
831C2#2145489214yesdirect product factor
832C2C2×#1684023511yescharacteristic
833C2C2×#131×D6111yescharacteristic
834C2C2×#1684052711yescharacteristic
subgroupG/H
centerC22×C4C23×D61
commutatorC22×C61C24×C4
FrattiniC2×C4C24×D61
FittingC2×C61×#408C2
socleC23×C61C23×C4
prime radicalC2×#16840308C2
cosocleC2×C4×C61C25
hypercenterC2×#408D61
hypocenterC61C2×#2981
LCSG ▷ C22×C61 ▷ C61
UCSC1 ◁ C22×C4 ◁ C2×#408

Complements

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

NH ≅ G/Ntype
2. #21454892C2direct (N × H)
3. C2×#16839838C2semidirect
4. C2×#16839837C2semidirect
5. C2×#16839836C2semidirect
6. C2×#16839833C2semidirect
7. C2×#16839831C2semidirect
8. C2×#16839830C2semidirect
9. C2×C8×C22⋊D61C2semidirect
10. C2×#16839825C2semidirect
11. C2×#16839816C2semidirect
12. C2×#16839812C2semidirect
13. C2×#16839729C2semidirect
14. C2×#16839727C2semidirect
15. C2×#16839727C2semidirect
16. C2×C61×#408C2semidirect
39. #16839838C22semidirect
40. #16839837C22semidirect
41. #16839836C22semidirect
42. #16839833C22semidirect
43. #16839831C22semidirect
44. #16839830C22semidirect
45. C8×C22⋊D61C22semidirect
46. #16839825C22semidirect
47. #16839816C22semidirect
48. #16839812C22semidirect
53. #16839729C22semidirect
54. #16839727C22semidirect
55. #16839727C22semidirect
71. C61×#408C22semidirect
424. C2×#408D61semidirect
428. C2×C61#2981semidirect
476. #408C2×D61semidirect
493. C61C2×#2981semidirect
831. C2#21454892direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168403082
#214548922
C2×#168398382
C2×#168398372
C2×#168398362
C2×#168398332
C2×#168398312
C2×#168398302
C2×C8×C22⋊D612
C2×#168398252
C2×#168398162
C2×#168398122
C2×#168397292
C2×#168397272
C2×C61×#4082
C2×#298161