Finite Group Databasebeta

← C2×#21457249 #30552943

Subgroups — C2×#21457249 #30552943

Order 15616.

1818 conjugacy classes of subgroups.

The subgroup lattice has 734 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840377C211yesmaximal, characteristic
2C2×#16840375C211yesmaximal, characteristic, complemented
3#21457249C2116yesmaximal, direct product factor
4C2×#16840066C211yesmaximal, characteristic, complemented
5C2×#16840056C211yesmaximal, characteristic, complemented
6C2×#16840046C211yesmaximal, characteristic, complemented
7C2×#16840021C211yesmaximal, characteristic, complemented
8C2×#16840007C211yesmaximal, characteristic
9C2×#16840004C211yesmaximal, characteristic, complemented
10C2×#16839990C211yesmaximal, characteristic
11C2×#16839983C211yesmaximal, characteristic, complemented
12C2×#16839983C211yesmaximal, characteristic, complemented
13C2×#16839973C211yesmaximal, characteristic, complemented
14C2×#16839967C211yesmaximal, characteristic, complemented
15C2×#16839787C211yesmaximal, characteristic, complemented
16C2×C61×#478C211yesmaximal, characteristic, complemented
17C22×Dic244C2211yescharacteristic
18C22×Dic244C2211yescharacteristic
19C22×#11758200C2211yescharacteristic
20C22×#11758200C2211yescharacteristic
21C22×#11758189C2211yescharacteristic
22C22×C8×D61C2211yescharacteristic
23#16840377—24no—
24#16840377C2218yes—
25#16840375—24no—
26#16840375C2218yescomplemented
27C2×#14519777C2211yescharacteristic
28C2×#14519776C2211yescharacteristic
29C2×#14519772—21no—
30C2×#14519772—21no—
31C2×#14519770—21no—
32C2×#14519768—21no—
33C2×#14519768—21no—
34C2×#14519764C2211yescharacteristic
35C2×#14519763—21no—
36C2×#14519760—21no—
37C2×#14519757C2211yescharacteristic
38C2×#14519757C2211yescharacteristic
39C2×#14519757C2211yescharacteristic
40C2×#14519756—21no—
41C2×#14519748C2211yescharacteristic
42C2×C4×Dic122C2211yescharacteristic
43C2×#14519742C2211yescharacteristic
44C2×#14519742C2211yescharacteristic
45C2×#14519734C2211yescharacteristic
46#16840066C2218yescomplemented
47#16840056C2218yescomplemented
48#16840046C2218yescomplemented
49#16840021C2218yescomplemented
50#16840007C2218yes—
51#16840004C2218yescomplemented
52#16839990C2218yes—
53#16839983C2218yescomplemented
54#16839983C2218yescomplemented
55#16839973C2218yescomplemented
56#16839967C2218yescomplemented
57C2×#14519710C2211yescharacteristic
58C2×#14519708C2211yescharacteristic
59#16839787C2218yescomplemented
60C2×C4⋊#92418C2211yescharacteristic
61C2×#14519706C2211yescharacteristic
62C2×#14519706C2211yescharacteristic
63C2×#14519702C2211yescharacteristic
64C2×#14519702C2211yescharacteristic
65C2×#14519700C2211yescharacteristic
66C2×#14519700C2211yescharacteristic
67C2×#14519700C2211yescharacteristic
68C2×#14519700C2211yescharacteristic
69C2×#125×C61C2211yescharacteristic
70C2×C4×D4×C61C2211yescharacteristic
71C61×#478C2218yescomplemented
72C2×#107×C61C2211yescharacteristic
73C2×#106×C61C2211yescharacteristic
74C2×C4⋊C8×C61C2211yescharacteristic
75C2×#102×C61C2211yescharacteristic
76C2×#102×C61C2211yescharacteristic
77C22×Dic122—21no—
78C22×Dic122C2311yescharacteristic
79C22×Dic122C2311yescharacteristic
80C22×Dic122C2311yescharacteristic
81C22×C22⋊D61—21no—
82C22×C4×D61C2311yescharacteristic
83C2×Dic244—42no—
84C2×Dic244—42no—
85C2×Dic244C2314yes—
86C2×Dic244C2314yes—
87C2×#11758200—42no—
88C2×#11758200—42no—
89C2×#11758200C2314yes—
90C2×#11758200C2314yes—
91C2×#11758189—42no—
92C2×#11758189C2314yes—
93C22×#92418C2311yescharacteristic
94C22×#92418C2311yescharacteristic
95C2×C8×D61—42no—
96C2×C8×D61C2314yes—
97#14519777—22no—
98#14519777C2314yes—
99#14519776—22no—
100#14519776C2314yes—
101#14519772—28no—
102#14519772—28no—
103#14519770—28no—
104#14519768—28no—
105#14519768—28no—
106#14519764—22no—
107#14519764C2314yes—
108#14519763—28no—
109#14519760—28no—
110#14519757—22no—
111#14519757—22no—
112#14519757—22no—
113#14519757C2314yes—
114#14519757C2314yes—
115#14519757C2314yes—
116#14519756—28no—
117#14519748—22no—
118#14519748C2314yes—
119C4×Dic122—22no—
120C4×Dic122C2314yes—
121#14519742—22no—
122#14519742—22no—
123#14519742C2314yes—
124#14519742C2314yes—
125#14519734D414yes—
126#14519734C2314yes—
127C2×C4⋊Dic61—21no—
128C2×C4⋊Dic61—21no—
129C2×C4⋊Dic61—21no—
130C2×C4⋊Dic61—21no—
131C2×C4⋊Dic61—21no—
132C2×C4⋊Dic61C2311yescharacteristic
133C2×#11758196—21no—
134C2×#11758196—21no—
135C2×#11758196—21no—
136C2×#11758196—21no—
137C2×#11758196D411yescharacteristic
138C2×#11758196D411yescharacteristic
139C2×C22⋊Dic61—21no—
140C2×C22⋊Dic61—21no—
141C2×C22⋊Dic61—21no—
142C2×#11758198—21no—
143C2×#11758198—21no—
144C2×#11758198—21no—
145C2×#11758198D411yescharacteristic
146C2×#11758198D411yescharacteristic
147C2×C4×Dic61—21no—
148C2×C4×Dic61—21no—
149C2×C4×Dic61—21no—
150C2×C4×Dic61C2311yescharacteristic
151#14519710C2314yes—
152#14519708C2314yes—
153C4⋊#92418C2314yes—
154#14519706C2314yes—
155#14519706C2314yes—
156#14519702C2314yes—
157#14519702C2314yes—
158#14519700C2314yes—
159#14519700C2314yes—
160#14519700C2314yes—
161#14519700C2314yes—
162C22×D4×C61C2311yescharacteristic
163C23×C4×C61—21no—
164C22×C8×C61C2311yescharacteristic
165C22×C8×C61C2311yescharacteristic
166#125×C61—22no—
167#125×C61C2314yes—
168C4×D4×C61—22no—
169C4×D4×C61C2314yes—
170C2×C4⋊C4×C61—21no—
171C2×C4⋊C4×C61—21no—
172C2×C4⋊C4×C61C2311yescharacteristic
173C2×C4⋊C4×C61C2311yescharacteristic
174C2×C4⋊C4×C61C2311yescharacteristic
175C2×C22⋊C4×C61—21no—
176C2×C42×C61C2311yescharacteristic
177#107×C61C2314yes—
178#106×C61C2314yes—
179C4⋊C8×C61C2314yes—
180#102×C61C2314yes—
181#102×C61C2314yes—
182C24×C61—21no—
183C23×D61C2×D411yescharacteristic
184C2×D4×C61—21no—
185C2×D4×C61—22no—
186C2×D4×C61—22no—
187C2×D4×C61C2412yes—
188C22×C4×C61—21no—
189C22×C4×C61—21no—
190C22×C4×C61—21no—
191C22×C4×C61—24no—
192C22×C4×C61—82no—
193C22×C4×C61C2×D411yescharacteristic
194C22×C4×C61C2×D411yescharacteristic
195C22×C4×C61C2411yescharacteristic
196C2×C22⋊D61—24no—
197C2×C22⋊D61—82no—
198C22×Dic61—21no—
199C22×Dic61—21no—
200C22×Dic61—21no—
201C22×Dic61—21no—
202C22×Dic61C2×D411yescharacteristic
203C22×Dic61C2×D411yescharacteristic
204C22×Dic61C2×D411yescharacteristic
205C2×C4×D61—22no—
206C2×C4×D61—22no—
207C2×C4×D61C2×D412yes—
208C2×C4×D61C2412yes—
209C2×Dic122—22no—
210C2×Dic122—22no—
211C2×Dic122—22no—
212C2×Dic122—22no—
213C2×Dic122—22no—
214C2×Dic122—22no—
215C2×Dic122—21no—
216C2×Dic122—21no—
217C2×Dic122—21no—
218C2×Dic122—24no—
219C2×Dic122—82no—
220C2×Dic122C2412yes—
221C2×Dic122C2412yes—
222C2×Dic122C2412yes—
223C2×C8×C61—22no—
224C2×C8×C61—22no—
225C2×C8×C61C2412yes—
226C2×C8×C61C2412yes—
227C4⋊C4×C61—24no—
228C4⋊C4×C61—24no—
229C4⋊C4×C61—21no—
230C4⋊C4×C61—21no—
231C4⋊C4×C61—21no—
232C4⋊C4×C61C2412yes—
233C4⋊C4×C61C2412yes—
234C4⋊C4×C61C2412yes—
235C22⋊C4×C61—24no—
236C42×C61C2×D412yes—
237C42×C61C2412yes—
238C22⋊Dic61—24no—
239C22⋊Dic61—24no—
240C22⋊Dic61—24no—
241#11758200—44no—
242#11758200—44no—
243#11758198—24no—
244#11758198—24no—
245#11758198—24no—
246#11758198C2×D414yes—
247#11758198C2×D414yes—
248C4⋊Dic61—24no—
249C4⋊Dic61—24no—
250C4⋊Dic61—21no—
251C4⋊Dic61—24no—
252C4⋊Dic61—24no—
253C4⋊Dic61—24no—
254C4⋊Dic61C2412yes—
255#11758196—24no—
256#11758196—24no—
257#11758196—24no—
258#11758196—24no—
259#11758196C2×D414yes—
260#11758196C2×D414yes—
261C4×Dic61—24no—
262C4×Dic61—24no—
263C4×Dic61—24no—
264C4×Dic61C2×D412yes—
265C4×Dic61C2412yes—
266C2×#92418—22no—
267C2×#92418—22no—
268C2×#92418C2412yes—
269C2×#92418C2412yes—
270Dic244—44no—
271Dic244—44no—
272#11758189—44no—
273C8×D61—44no—
274C23×C61—22no—
275C23×C61—42no—
276C23×C61—42no—
277C23×C61—42no—
278C23×C61C22×D411yescharacteristic
279C22×D61—22no—
280C22×D61—22no—
281C22×D61—22no—
282C22×D61C22×D412yes—
283D4×C61—22no—
284D4×C61—22no—
285D4×C61—42no—
286C2×C4×C61—22no—
287C2×C4×C61—22no—
288C2×C4×C61—22no—
289C2×C4×C61—22no—
290C2×C4×C61—22no—
291C2×C4×C61—42no—
292C2×C4×C61—42no—
293C2×C4×C61—42no—
294C2×C4×C61—84no—
295C2×C4×C61C22×D412yes—
296C2×C4×C61C22×D412yes—
297C2×C4×C61C22×D411yescharacteristic
298C2×C4×C61H(5,𝔽2)12yes—
299C2×C4×C612−1+412yes—
300C2×C4×C61C2511yescharacteristic
301C22⋊D61—84no—
302C2×Dic61—22no—
303C2×Dic61—22no—
304C2×Dic61—22no—
305C2×Dic61—22no—
306C2×Dic61—22no—
307C2×Dic61—22no—
308C2×Dic61—22no—
309C2×Dic61—42no—
310C2×Dic61—42no—
311C2×Dic61—42no—
312C2×Dic61—42no—
313C2×Dic61C22×D412yes—
314C2×Dic61C22×D412yes—
315C2×Dic61C22×D412yes—
316C4×D61—24no—
317C4×D61—22no—
318C4×D61—22no—
319Dic122—22no—
320Dic122—22no—
321Dic122—22no—
322Dic122—22no—
323Dic122—22no—
324Dic122—22no—
325Dic122—42no—
326Dic122—42no—
327Dic122—42no—
328Dic122—84no—
329C8×C61—22no—
330C8×C61—22no—
331#92418—22no—
332#92418—22no—
333C2×#3258—611nomaximal, Sylow
334C22×C61—42no—
335C22×C61—42no—
336C22×C61—42no—
337C22×C61—84no—
338C22×C61#53712yes—
339C22×C61#57712yes—
340C22×C61#57812yes—
341C22×C61C23×D411yescharacteristic
342C2×D61—22no—
343C2×D61—22no—
344C2×D61—22no—
345C2×D61—44no—
346C4×C61—22no—
347C4×C61—22no—
348C4×C61—42no—
349C4×C61—42no—
350C4×C61—42no—
351C4×C61#53712yes—
352C4×C61C2×H(5,𝔽2)11yescharacteristic
353C4×C61C2×2−1+411yescharacteristic
354Dic61—22no—
355Dic61—22no—
356Dic61—22no—
357Dic61—42no—
358Dic61—42no—
359Dic61—42no—
360Dic61—42no—
361C2×#542—611no—
362C2×#541—611no—
363#3258—6116no—
364C2×#479—611no—
365C2×#477—611no—
366C2×#475—611no—
367C2×#478D6111yescharacteristic, complemented
368C2×#470—611no—
369C2×#468—611no—
370C2×#467—611no—
371C2×#465—611no—
372C2×#464—611no—
373C2×#464—611no—
374C2×#462—611no—
375C2×#461—611no—
376C2×#424—611no—
377C2×C61—82no—
378C2×C61#325814yescomplemented
379C2×C61C2×#53711yescharacteristic
380C2×C61C2×#57711yescharacteristic
381C2×C61C2×#57811yescharacteristic
382D61—42no—
383C22×Q16—611no—
384C22×Q16—611no—
385C22×SD16—611no—
386C22×SD16—611no—
387C22×M16—611no—
388C23×C8—611no—
389#542—618no—
390#542—1224no—
391#541—618no—
392#541—1224no—
393C2×C4⋊Q8—611no—
394C2×C4⋊Q8—611no—
395C2×#126—1221no—
396C2×#126—1221no—
397C2×#126—1221no—
398C2×#125—1221no—
399C2×#125—1221no—
400C2×#125C2×D6111yescharacteristic
401C2×#124—611no—
402C2×#124—1221no—
403C2×#123—1221no—
404C2×C22⋊Q8—611no—
405C2×C22⋊Q8—611no—
406C2×C22⋊Q8—611no—
407C2×C22⋊Q8—1221no—
408C2×#121—611no—
409C2×C4×Q8—611no—
410C2×C4×Q8—611no—
411C2×C4×Q8—611no—
412C2×C4×D4C2×D6111yescharacteristic
413C2×#117—611no—
414#479—618no—
415#478C2×D6118yescomplemented
416#477—618no—
417#475—618no—
418#470—618no—
419#468—618no—
420#467—618no—
421#465—618no—
422#464—618no—
423#464—618no—
424#462—618no—
425#461—618no—
426C2×#107—611no—
427C2×#107C2×D6111yescharacteristic
428C2×#106—611no—
429C2×#106C2×D6111yescharacteristic
430#424—618no—
431C2×C4⋊C8—611no—
432C2×C4⋊C8—611no—
433C2×C4⋊C8—611no—
434C2×C4⋊C8C2×D6111yescharacteristic
435C2×#103—611no—
436C2×#103—611no—
437C2×#103—611no—
438C2×#103—611no—
439C2×#103—611no—
440C2×#103—611no—
441C2×#102C2×D6111yescharacteristic
442C2×#102C2×D6111yescharacteristic
443C61C2×#325811yescharacteristic, complemented, Sylow
444C22×Q8—611no—
445C22×Q8—611no—
446C22×Q8—611no—
447C22×Q8—1221no—
448C22×D4—1221no—
449C22×D4C22×D6111yescharacteristic
450C23×C4—21no—
451C23×C4—611no—
452C2×Q16—614no—
453C2×Q16—614no—
454C2×Q16—2442no—
455C2×Q16—2442no—
456C2×SD16—614no—
457C2×SD16—614no—
458C2×SD16—2442no—
459C2×SD16—2442no—
460C2×M16—614no—
461C2×M16—2442no—
462C22×C8—611no—
463C22×C8—611no—
464C22×C8—614no—
465C22×C8—2442no—
466C22×C8C22×D6111yescharacteristic
467C22×C8C22×D6111yescharacteristic
468C4⋊Q8—614no—
469C4⋊Q8—614no—
470C4⋊Q8—1222no—
471C4⋊Q8—1222no—
472#126—1228no—
473#126—1228no—
474#126—1228no—
475#125—22no—
476#125—1228no—
477#125—1228no—
478#125C22×D6114yes—
479#124—614no—
480#124—1222no—
481#124—1228no—
482#123—1228no—
483C22⋊Q8—614no—
484C22⋊Q8—614no—
485C22⋊Q8—614no—
486C22⋊Q8—1222no—
487C22⋊Q8—1222no—
488C22⋊Q8—1222no—
489C22⋊Q8—1228no—
490#121—614no—
491#121—1222no—
492C4×Q8—614no—
493C4×Q8—614no—
494C4×Q8—614no—
495C4×Q8—1222no—
496C4×Q8—1222no—
497C4×Q8—1222no—
498C4×D4—22no—
499C4×D4C22×D6114yes—
500#117—614no—
501#117—614no—
502C2×C4⋊C4—21no—
503C2×C4⋊C4—21no—
504C2×C4⋊C4—611no—
505C2×C4⋊C4—611no—
506C2×C4⋊C4—611no—
507C2×C4⋊C4—1221no—
508C2×C4⋊C4—1221no—
509C2×C4⋊C4—1221no—
510C2×C4⋊C4—1221no—
511C2×C4⋊C4—1221no—
512C2×C4⋊C4—1221no—
513C2×C4⋊C4—1221no—
514C2×C4⋊C4—1221no—
515C2×C4⋊C4—1221no—
516C2×C4⋊C4C22×D6111yescharacteristic
517C2×C4⋊C4C22×D6111yescharacteristic
518C2×C4⋊C4C22×D6111yescharacteristic
519C2×C22⋊C4—21no—
520C2×C22⋊C4—611no—
521C2×C22⋊C4—611no—
522C2×C22⋊C4—1221no—
523C2×C22⋊C4—1221no—
524C2×C22⋊C4—1221no—
525C2×C22⋊C4—1221no—
526C2×C22⋊C4—1221no—
527C2×C22⋊C4—1221no—
528C2×C42—611no—
529C2×C42—1221no—
530C2×C42—1221no—
531C2×C42—1221no—
532C2×C42C22×D6111yescharacteristic
533#107—614no—
534#107C22×D6114yes—
535#106—614no—
536#106C22×D6114yes—
537C4⋊C8—614no—
538C4⋊C8—614no—
539C4⋊C8—614no—
540C4⋊C8C22×D6114yes—
541#103—614no—
542#103—614no—
543#103—614no—
544#103—614no—
545#103—614no—
546#103—614no—
547#102C22×D6114yes—
548#102C22×D6114yes—
549C24—21no—
550C24—611no—
551C2×Q8—612no—
552C2×Q8—612no—
553C2×Q8—612no—
554C2×Q8—1224no—
555C2×Q8—1221no—
556C2×Q8—1221no—
557C2×Q8—1221no—
558C2×Q8—1222no—
559C2×Q8—1222no—
560C2×Q8—1222no—
561C2×Q8—1222no—
562C2×Q8—1222no—
563C2×Q8—1222no—
564C2×Q8—4882no—
565C2×D4—21no—
566C2×D4—22no—
567C2×D4—22no—
568C2×D4—1224no—
569C2×D4—4882no—
570C2×D4C23×D6112yes—
571C22×C4—21no—
572C22×C4—21no—
573C22×C4—21no—
574C22×C4—24no—
575C22×C4—82no—
576C22×C4—611no—
577C22×C4—611no—
578C22×C4—611no—
579C22×C4—612no—
580C22×C4—612no—
581C22×C4—1222no—
582C22×C4—1222no—
583C22×C4—1221no—
584C22×C4—1221no—
585C22×C4—1221no—
586C22×C4—1221no—
587C22×C4D4×D6111yescharacteristic
588C22×C4D4×D6111yescharacteristic
589C22×C4C23×D6111yescharacteristic
590Q16—2444no—
591Q16—2444no—
592SD16—2444no—
593SD16—2444no—
594M16—2444no—
595C2×C8—22no—
596C2×C8—22no—
597C2×C8—612no—
598C2×C8—612no—
599C2×C8—1222no—
600C2×C8—1222no—
601C2×C8—2444no—
602C2×C8C23×D6112yes—
603C2×C8C23×D6112yes—
604C4⋊C4—24no—
605C4⋊C4—24no—
606C4⋊C4—21no—
607C4⋊C4—21no—
608C4⋊C4—21no—
609C4⋊C4—614no—
610C4⋊C4—614no—
611C4⋊C4—612no—
612C4⋊C4—1224no—
613C4⋊C4—1224no—
614C4⋊C4—1224no—
615C4⋊C4—1224no—
616C4⋊C4—1224no—
617C4⋊C4—1224no—
618C4⋊C4—1221no—
619C4⋊C4—1224no—
620C4⋊C4—1224no—
621C4⋊C4—1224no—
622C4⋊C4C23×D6112yes—
623C4⋊C4C23×D6112yes—
624C4⋊C4C23×D6112yes—
625C22⋊C4—24no—
626C22⋊C4—614no—
627C22⋊C4—614no—
628C22⋊C4—1224no—
629C22⋊C4—1224no—
630C22⋊C4—1224no—
631C22⋊C4—1224no—
632C22⋊C4—1224no—
633C22⋊C4—1224no—
634C42—612no—
635C42—612no—
636C42—1224no—
637C42—1224no—
638C42—1224no—
639C42D4×D6112yes—
640C42C23×D6112yes—
641C23—22no—
642C23—42no—
643C23—42no—
644C23—42no—
645C23—612no—
646C23—1222no—
647C23—1222no—
648C23—1222no—
649C23C2×D4×D6111yescharacteristic
650Q8—1222no—
651Q8—1222no—
652Q8—1222no—
653Q8—1222no—
654Q8—1222no—
655Q8—1222no—
656Q8—4884no—
657Q8—2442no—
658Q8—2442no—
659Q8—2442no—
660D4—22no—
661D4—22no—
662D4—42no—
663D4—4884no—
664C2×C4—22no—
665C2×C4—22no—
666C2×C4—22no—
667C2×C4—22no—
668C2×C4—22no—
669C2×C4—42no—
670C2×C4—42no—
671C2×C4—42no—
672C2×C4—84no—
673C2×C4—612no—
674C2×C4—612no—
675C2×C4—612no—
676C2×C4—1222no—
677C2×C4—1222no—
678C2×C4—1222no—
679C2×C4—1222no—
680C2×C4—1222no—
681C2×C4—1224no—
682C2×C4—1222no—
683C2×C4—1222no—
684C2×C4—1222no—
685C2×C4—1222no—
686C2×C4—2442no—
687C2×C4—2442no—
688C2×C4—2442no—
689C2×C4—2442no—
690C2×C4C2×D4×D6112yes—
691C2×C4C2×D4×D6112yes—
692C2×C4C2×D4×D6111yescharacteristic
693C2×C4#1451982312yes—
694C2×C4#1451982512yes—
695C2×C4C24×D6111yescharacteristic
696C8—22no—
697C8—22no—
698C8—1222no—
699C8—1222no—
700C22—42no—
701C22—42no—
702C22—42no—
703C22—84no—
704C22—1222no—
705C22—1222no—
706C22—1222no—
707C22—2444no—
708C22#1684034212yes—
709C22#1684057212yes—
710C22#1684057612yes—
711C22C22×D4×D6111yescharacteristic
712C4—22no—
713C4—22no—
714C4—42no—
715C4—42no—
716C4—42no—
717C4—1222no—
718C4—1222no—
719C4—1222no—
720C4—2442no—
721C4—2442no—
722C4—2442no—
723C4—2442no—
724C4#1684034212yes—
725C4C2×#1451982311yescharacteristic
726C4C2×#1451982511yescharacteristic
727C2—82no—
728C2—2442no—
729C2#2145724914yesdirect product factor
730C2C2×#1684034211yescharacteristic
731C2C2×#1684057211yescharacteristic
732C2C2×#1684057611yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutator, cosocleC2×C4×C61C25
FrattiniC2×C4C24×D61
FittingC2×C61×#478C2
socleC23×C61C22×D4
prime radicalC2×#14519748C22
hypercenterC2×#478D61
hypocenterC61C2×#3258
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#478

Complements

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

NH ≅ G/Ntype
2. C2×#16840375C2semidirect
3. #21457249C2direct (N × H)
4. C2×#16840066C2semidirect
5. C2×#16840056C2semidirect
6. C2×#16840046C2semidirect
7. C2×#16840021C2semidirect
9. C2×#16840004C2semidirect
11. C2×#16839983C2semidirect
12. C2×#16839983C2semidirect
13. C2×#16839973C2semidirect
14. C2×#16839967C2semidirect
15. C2×#16839787C2semidirect
16. C2×C61×#478C2semidirect
26. #16840375C22semidirect
46. #16840066C22semidirect
47. #16840056C22semidirect
48. #16840046C22semidirect
49. #16840021C22semidirect
51. #16840004C22semidirect
53. #16839983C22semidirect
54. #16839983C22semidirect
55. #16839973C22semidirect
56. #16839967C22semidirect
59. #16839787C22semidirect
71. C61×#478C22semidirect
367. C2×#478D61semidirect
378. C2×C61#3258semidirect
415. #478C2×D61semidirect
443. C61C2×#3258semidirect
729. C2#21457249direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168403772
C2×#168403752
#214572492
C2×#168400662
C2×#168400562
C2×#168400462
C2×#168400212
C2×#168400072
C2×#168400042
C2×#168399902
C2×#168399832
C2×#168399732
C2×#168399672
C2×#168397872
C2×C61×#4782
C2×#325861