Finite Group Databasebeta

← C2×#21458194 #30558456

Subgroups — C2×#21458194 #30558456

Order 15616.

1930 conjugacy classes of subgroups.

The subgroup lattice has 736 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840460C211yesmaximal, characteristic
2C2×#16840447C211yesmaximal, characteristic, complemented
3#21458194C2116yesmaximal, direct product factor
4C2×#16840162C211yesmaximal, characteristic, complemented
5C2×#16840097C211yesmaximal, characteristic, complemented
6C2×#16840106C211yesmaximal, characteristic, complemented
7C2×#16840088C211yesmaximal, characteristic, complemented
8C2×#16840075C211yesmaximal, characteristic, complemented
9C2×#16840072C211yesmaximal, characteristic, complemented
10C2×#16840061C211yesmaximal, characteristic, complemented
11C2×#16839992C211yesmaximal, characteristic, complemented
12C2×#16839991C211yesmaximal, characteristic, complemented
13C2×#16839849C211yesmaximal, characteristic, complemented
14C2×C8×C22⋊D61C211yesmaximal, characteristic, complemented
15C2×#16839797C211yesmaximal, characteristic, complemented
16C22×#106×C61C211yesmaximal, characteristic, complemented
17C22×#11758190C2211yescharacteristic
18C22×C8×D61C2211yescharacteristic
19#16840460—24no—
20#16840460C2218yes—
21#16840447—24no—
22#16840447C2218yescomplemented
23C2×#14519772—21no—
24C2×#14519772—21no—
25C2×#14519768C2211yescharacteristic
26C2×#14519768C2211yescharacteristic
27C2×#14519767—21no—
28C2×#14519762—21no—
29C2×#14519760—21no—
30C2×#14519757C2211yescharacteristic
31C2×#14519756C2211yescharacteristic
32C2×#14519752C2211yescharacteristic
33C2×#14519751—21no—
34C2×#14519751C2211yescharacteristic
35C2×#14519742C2211yescharacteristic
36C2×#14519739C2211yescharacteristic
37C2×C4×C22⋊D61—21no—
38C2×C4×C22⋊D61C2211yescharacteristic
39C2×#14519736—21no—
40C2×#14519735C2211yescharacteristic
41C2×#14519735C2211yescharacteristic
42#16840162C2218yescomplemented
43#16840106C2218yescomplemented
44#16840097C2218yescomplemented
45#16840088C2218yescomplemented
46#16840075C2218yescomplemented
47#16840072C2218yescomplemented
48#16840061C2218yescomplemented
49#16839992C2218yescomplemented
50#16839991C2218yescomplemented
51#16839849C2218yescomplemented
52C8×C22⋊D61C2218yescomplemented
53#16839797C2218yescomplemented
54C2×#14519710C2211yescharacteristic
55C2×#14519710C2211yescharacteristic
56C2×#14519710C2211yescharacteristic
57C2×#14519710C2211yescharacteristic
58C2×#14519709C2211yescharacteristic
59C2×#14519706C2211yescharacteristic
60C2×#14519702C2211yescharacteristic
61C2×#14519700C2211yescharacteristic
62C2×#14519700C2211yescharacteristic
63C2×#14519699C2211yescharacteristic
64C2×#14519697C2211yescharacteristic
65C2×#14519697C2211yescharacteristic
66C2×C22⋊#92418C2211yescharacteristic
67C2×#14519689C2211yescharacteristic
68C2×C8×Dic61C2211yescharacteristic
69C23×C8×C61C2211yescharacteristic
70C22×C4⋊C4×C61C2211yescharacteristic
71C22×C4⋊C4×C61C2211yescharacteristic
72C2×#106×C61C2211yescharacteristic
73C2×#106×C61C2211yescharacteristic
74C2×#106×C61C2211yescharacteristic
75C2×#106×C61C2211yescharacteristic
76C2×#106×C61C2218yescomplemented
77C22×Dic122C2311yescharacteristic
78C22×D244—21no—
79C22×D244C2311yescharacteristic
80C22×C22⋊D61—21no—
81C22×C22⋊D61D411yescharacteristic
82C22×C4×D61—21no—
83C22×C4×D61C2311yescharacteristic
84C2×#11758190—24no—
85C2×#11758190C2314yes—
86C22×#92418C2311yescharacteristic
87C22×#92418C2311yescharacteristic
88C2×C8×D61—24no—
89C2×C8×D61C2314yes—
90#14519772—28no—
91#14519772—28no—
92#14519768—22no—
93#14519768—22no—
94#14519768C2314yes—
95#14519768C2314yes—
96#14519767—28no—
97#14519762—28no—
98#14519760—28no—
99#14519757—22no—
100#14519757C2314yes—
101#14519756—22no—
102#14519756C2314yes—
103#14519752—22no—
104#14519752C2314yes—
105#14519751—22no—
106#14519751—28no—
107#14519751C2314yes—
108#14519742—22no—
109#14519742C2314yes—
110#14519739—22no—
111#14519739C2314yes—
112C4×C22⋊D61—28no—
113C4×C22⋊D61D414yes—
114C4×C22⋊D61C2314yes—
115#14519736—28no—
116#14519735—22no—
117#14519735—22no—
118#14519735C2314yes—
119#14519735C2314yes—
120C2×C4⋊Dic61—21no—
121C2×C4⋊Dic61—21no—
122C2×C4⋊Dic61—21no—
123C2×C4⋊Dic61C2311yescharacteristic
124C2×C4⋊Dic61C2311yescharacteristic
125C2×#11758196—21no—
126C2×#11758196—21no—
127C2×#11758196—21no—
128C2×#11758196—21no—
129C2×#11758196D411yescharacteristic
130C2×C22⋊Dic61—21no—
131C2×C22⋊Dic61D411yescharacteristic
132C2×#11758198—21no—
133C2×#11758198—21no—
134C2×#11758198—21no—
135C2×#11758198—21no—
136C2×#11758198—21no—
137C2×#11758198—21no—
138C2×#11758198D411yescharacteristic
139C2×C4×Dic61—21no—
140C2×C4×Dic61—21no—
141C2×C4×Dic61—21no—
142C2×C4×Dic61C2311yescharacteristic
143#14519710C2314yes—
144#14519710C2314yes—
145#14519710C2314yes—
146#14519710C2314yes—
147#14519709C2314yes—
148#14519706C2314yes—
149#14519702C2314yes—
150#14519700C2314yes—
151#14519700C2314yes—
152#14519699C2314yes—
153#14519697C2314yes—
154#14519697C2314yes—
155C22⋊#92418C2314yes—
156#14519689C2314yes—
157C8×Dic61C2314yes—
158C23×C4×C61—21no—
159C23×C4×C61—21no—
160C23×C4×C61C2311yescharacteristic
161C22×C8×C61—24no—
162C22×C8×C61C2311yescharacteristic
163C22×C8×C61C2314yes—
164C22×C8×C61C2311yescharacteristic
165C2×C4⋊C4×C61—22no—
166C2×C4⋊C4×C61—21no—
167C2×C4⋊C4×C61—21no—
168C2×C4⋊C4×C61—22no—
169C2×C4⋊C4×C61C2314yes—
170C2×C4⋊C4×C61C2311yescharacteristic
171C2×C4⋊C4×C61C2311yescharacteristic
172C2×C4⋊C4×C61C2311yescharacteristic
173C2×C4⋊C4×C61C2311yescharacteristic
174C2×C4⋊C4×C61C2314yes—
175#106×C61C2314yes—
176#106×C61C2314yes—
177#106×C61C2314yes—
178#106×C61C2314yes—
179C24×C61C2×D411yescharacteristic
180C23×D61—21no—
181C23×D61C2×D411yescharacteristic
182C22×C4×C61—22no—
183C22×C4×C61—22no—
184C22×C4×C61—21no—
185C22×C4×C61—21no—
186C22×C4×C61—21no—
187C22×C4×C61—21no—
188C22×C4×C61—24no—
189C22×C4×C61—24no—
190C22×C4×C61—44no—
191C22×C4×C61—82no—
192C22×C4×C61C2×D411yescharacteristic
193C22×C4×C61C2×D412yes—
194C22×C4×C61C2412yes—
195C22×C4×C61C2411yescharacteristic
196C2×C22⋊D61—24no—
197C2×C22⋊D61—24no—
198C2×C22⋊D61—44no—
199C2×C22⋊D61C2×D414yes—
200C22×Dic61—21no—
201C22×Dic61—21no—
202C22×Dic61—21no—
203C22×Dic61C2×D411yescharacteristic
204C22×Dic61C2×D411yescharacteristic
205C22×Dic61C2×D411yescharacteristic
206C2×D244—22no—
207C2×D244—22no—
208C2×D244—21no—
209C2×D244—24no—
210C2×D244—82no—
211C2×D244C2412yes—
212C2×C4×D61—22no—
213C2×C4×D61—22no—
214C2×C4×D61—24no—
215C2×C4×D61—82no—
216C2×C4×D61C2×D412yes—
217C2×C4×D61C2412yes—
218C2×Dic122—22no—
219C2×Dic122—22no—
220C2×Dic122—21no—
221C2×Dic122C2412yes—
222C2×C8×C61—22no—
223C2×C8×C61—28no—
224C2×C8×C61#4114yes—
225C2×C8×C61C2412yes—
226C2×C8×C61C2412yes—
227C4⋊C4×C61—21no—
228C4⋊C4×C61—21no—
229C4⋊C4×C61—21no—
230C4⋊C4×C61—21no—
231C4⋊C4×C61—24no—
232C4⋊C4×C61—24no—
233C4⋊C4×C61C2412yes—
234C4⋊C4×C61C2412yes—
235C4⋊C4×C61C2412yes—
236C4⋊C4×C61C2412yes—
237C22⋊Dic61—24no—
238C22⋊Dic61C2×D414yes—
239#11758198—24no—
240#11758198—24no—
241#11758198—24no—
242#11758198—24no—
243#11758198—24no—
244#11758198—24no—
245#11758198C2×D414yes—
246C4⋊Dic61—21no—
247C4⋊Dic61—21no—
248C4⋊Dic61—24no—
249C4⋊Dic61—24no—
250C4⋊Dic61—24no—
251C4⋊Dic61C2412yes—
252C4⋊Dic61C2412yes—
253#11758196—24no—
254#11758196—24no—
255#11758196—24no—
256#11758196—24no—
257#11758196C2×D414yes—
258C4×Dic61—24no—
259C4×Dic61—24no—
260C4×Dic61—24no—
261C4×Dic61C2×D412yes—
262C4×Dic61C2412yes—
263C2×#92418—22no—
264C2×#92418—22no—
265C2×#92418C2412yes—
266C2×#92418C2412yes—
267#11758190—28no—
268C8×D61—28no—
269C23×C61—22no—
270C23×C61—22no—
271C23×C61#13514yes—
272C23×C61C22×D412yes—
273C23×C61C22×D411yescharacteristic
274C22×D61—22no—
275C22×D61—22no—
276C22×D61—22no—
277C22×D61—22no—
278C22×D61—42no—
279C22×D61—42no—
280C22×D61—42no—
281C22×D61C22×D412yes—
282C2×C4×C61—22no—
283C2×C4×C61—24no—
284C2×C4×C61—22no—
285C2×C4×C61—22no—
286C2×C4×C61—22no—
287C2×C4×C61—22no—
288C2×C4×C61—22no—
289C2×C4×C61—22no—
290C2×C4×C61—48no—
291C2×C4×C61—42no—
292C2×C4×C61—42no—
293C2×C4×C61—42no—
294C2×C4×C61—42no—
295C2×C4×C61—84no—
296C2×C4×C61C22×D412yes—
297C2×C4×C61C22×D411yescharacteristic
298C2×C4×C61C2×#4112yes—
299C2×C4×C612−1+412yes—
300C2×C4×C61C2511yescharacteristic
301C22⋊D61—28no—
302C22⋊D61—48no—
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×Dic61C22×D412yes—
313C2×Dic61C22×D412yes—
314C2×Dic61C22×D412yes—
315D244—22no—
316D244—22no—
317D244—42no—
318D244—84no—
319C4×D61—24no—
320C4×D61—22no—
321C4×D61—22no—
322C4×D61—84no—
323Dic122—22no—
324Dic122—22no—
325Dic122—42no—
326C8×C61—22no—
327C8×C61C2×#4114yes—
328#92418—22no—
329#92418—22no—
330C2×#3337—611nomaximal, Sylow
331C22×C61—28no—
332C22×C61—22no—
333C22×C61—22no—
334C22×C61#54712yes—
335C22×C61C2×#13514yes—
336C22×C61C2×#13512yes—
337C22×C61#57712yes—
338C22×C61C23×D411yescharacteristic
339C2×D61—22no—
340C2×D61—22no—
341C2×D61—22no—
342C2×D61—44no—
343C2×D61—42no—
344C2×D61—42no—
345C2×D61—42no—
346C2×D61—84no—
347C4×C61—22no—
348C4×C61—42no—
349C4×C61—42no—
350C4×C61—42no—
351C4×C61—42no—
352C4×C61#54712yes—
353C4×C61C22×#4111yescharacteristic
354C4×C61C2×2−1+411yescharacteristic
355Dic61—22no—
356Dic61—22no—
357Dic61—22no—
358Dic61—42no—
359Dic61—42no—
360Dic61—42no—
361C2×#553—611no—
362C2×#552—611no—
363#3337—6116no—
364C2×#499—611no—
365C2×#484—611no—
366C2×#485—611no—
367C2×#482—611no—
368C2×#480—611no—
369C2×#479—611no—
370C2×#478—611no—
371C2×#465—611no—
372C2×#465—611no—
373C2×C4×SD16—611no—
374C2×C8×D4—611no—
375C2×#427—611no—
376C22×#106D6111yescharacteristic, complemented
377C2×C61—24no—
378C2×C61#333714yescomplemented
379C2×C61C2×#54711yescharacteristic
380C2×C61C22×#13511yescharacteristic
381C2×C61C2×#57711yescharacteristic
382D61—42no—
383D61—82no—
384C22×SD16—611no—
385C23×C8—611no—
386C23×C8C2×D6111yescharacteristic
387#553—618no—
388#553—1224no—
389#552—618no—
390#552—1224no—
391C2×#126—1221no—
392C2×#126—1221no—
393C2×#125—611no—
394C2×#125—611no—
395C2×#125—1221no—
396C2×#123—1221no—
397C2×#123—1221no—
398C2×C22⋊Q8—611no—
399C2×C22⋊Q8—611no—
400C2×#121—611no—
401C2×#121—611no—
402C2×#121—1221no—
403C2×C4×Q8—611no—
404C2×C4×D4—611no—
405C2×C4×D4—611no—
406C2×C4×D4—1221no—
407C2×#117—611no—
408C2×#117—611no—
409C2×#117—1221no—
410C22×C4⋊C4C2×D6111yescharacteristic
411C22×C4⋊C4C2×D6111yescharacteristic
412#499—618no—
413#485—618no—
414#484—618no—
415#482—618no—
416#480—618no—
417#479—618no—
418#478—618no—
419#465—618no—
420#465—618no—
421C4×SD16—618no—
422C8×D4—618no—
423#427—618no—
424C2×#107—611no—
425C2×#107—611no—
426C2×#107—611no—
427C2×#107—611no—
428C2×#106—611no—
429C2×#106C2×D6111yescharacteristic
430C2×#106C2×D6111yescharacteristic
431C2×#106C2×D6111yescharacteristic
432C2×#106C2×D6111yescharacteristic
433C2×#106C2×D6118yescomplemented
434C2×C4⋊C8—611no—
435C2×#103—611no—
436C2×#103—611no—
437C2×#103—611no—
438C2×#102—611no—
439C2×#102—611no—
440C2×#102—611no—
441C2×C22⋊C8—611no—
442C2×C22⋊C8—611no—
443C2×C4×C8—611no—
444C61C2×#333711yescharacteristic, complemented, Sylow
445C22×Q8—611no—
446C22×D4—611no—
447C22×D4—611no—
448C22×D4—1221no—
449C22×D4—1221no—
450C23×C4—21no—
451C23×C4—21no—
452C23×C4—611no—
453C23×C4—1221no—
454C23×C4C22×D6111yescharacteristic
455C2×SD16—614no—
456C2×SD16—1224no—
457C22×C8—24no—
458C22×C8—611no—
459C22×C8—611no—
460C22×C8—614no—
461C22×C8—1224no—
462C22×C8C22×D6111yescharacteristic
463C22×C8C22×D6114yes—
464C22×C8C22×D6111yescharacteristic
465#126—1228no—
466#126—1228no—
467#125—614no—
468#125—614no—
469#125—1222no—
470#125—1222no—
471#125—1228no—
472#123—1228no—
473#123—1228no—
474C22⋊Q8—614no—
475C22⋊Q8—614no—
476C22⋊Q8—1222no—
477C22⋊Q8—1222no—
478#121—614no—
479#121—614no—
480#121—1222no—
481#121—1228no—
482#121—1222no—
483C4×Q8—614no—
484C4×Q8—1222no—
485C4×D4—614no—
486C4×D4—614no—
487C4×D4—614no—
488C4×D4—1222no—
489C4×D4—1228no—
490#117—614no—
491#117—614no—
492#117—1228no—
493#117—1222no—
494#117—1222no—
495C2×C4⋊C4—21no—
496C2×C4⋊C4—21no—
497C2×C4⋊C4—22no—
498C2×C4⋊C4—22no—
499C2×C4⋊C4—611no—
500C2×C4⋊C4—611no—
501C2×C4⋊C4—611no—
502C2×C4⋊C4—1221no—
503C2×C4⋊C4—1221no—
504C2×C4⋊C4—1221no—
505C2×C4⋊C4—1221no—
506C2×C4⋊C4—1221no—
507C2×C4⋊C4—1221no—
508C2×C4⋊C4—1221no—
509C2×C4⋊C4C22×D6111yescharacteristic
510C2×C4⋊C4C22×D6111yescharacteristic
511C2×C4⋊C4C22×D6111yescharacteristic
512C2×C4⋊C4C22×D6111yescharacteristic
513C2×C4⋊C4C22×D6114yes—
514C2×C4⋊C4C22×D6114yes—
515C2×C22⋊C4—611no—
516C2×C22⋊C4—611no—
517C2×C22⋊C4—1221no—
518C2×C22⋊C4—1221no—
519C2×C22⋊C4—1221no—
520C2×C22⋊C4—1221no—
521C2×C22⋊C4—1221no—
522C2×C22⋊C4—1221no—
523C2×C22⋊C4—1221no—
524C2×C42—611no—
525C2×C42—1221no—
526C2×C42—1221no—
527C2×C42—1221no—
528#107—614no—
529#107—614no—
530#107—614no—
531#107—614no—
532#106—614no—
533#106C22×D6114yes—
534#106C22×D6114yes—
535#106C22×D6114yes—
536#106C22×D6114yes—
537C4⋊C8—614no—
538#103—614no—
539#103—614no—
540#103—614no—
541#102—614no—
542#102—614no—
543#102—614no—
544C22⋊C8—614no—
545C22⋊C8—614no—
546C4×C8—614no—
547C24—611no—
548C24—1221no—
549C24D4×D6111yescharacteristic
550C2×Q8—612no—
551C2×Q8—1221no—
552C2×Q8—1222no—
553C2×Q8—1222no—
554C2×D4—614no—
555C2×D4—612no—
556C2×D4—1224no—
557C2×D4—1224no—
558C2×D4—1224no—
559C2×D4—1221no—
560C2×D4—1222no—
561C2×D4—1222no—
562C2×D4—4882no—
563C2×D4—2444no—
564C22×C4—22no—
565C22×C4—22no—
566C22×C4—24no—
567C22×C4—21no—
568C22×C4—21no—
569C22×C4—21no—
570C22×C4—21no—
571C22×C4—24no—
572C22×C4—44no—
573C22×C4—82no—
574C22×C4—611no—
575C22×C4—611no—
576C22×C4—611no—
577C22×C4—612no—
578C22×C4—612no—
579C22×C4—1224no—
580C22×C4—1222no—
581C22×C4—1222no—
582C22×C4—1221no—
583C22×C4—1221no—
584C22×C4—1221no—
585C22×C4—4882no—
586C22×C4D4×D6112yes—
587C22×C4D4×D6111yescharacteristic
588C22×C4C23×D6112yes—
589C22×C4C23×D6111yescharacteristic
590SD16—1228no—
591C2×C8—22no—
592C2×C8—28no—
593C2×C8—612no—
594C2×C8—612no—
595C2×C8—1222no—
596C2×C8—1222no—
597C2×C8—1228no—
598C2×C8#1175822214yes—
599C2×C8C23×D6112yes—
600C2×C8C23×D6112yes—
601C4⋊C4—21no—
602C4⋊C4—21no—
603C4⋊C4—21no—
604C4⋊C4—21no—
605C4⋊C4—24no—
606C4⋊C4—24no—
607C4⋊C4—614no—
608C4⋊C4—612no—
609C4⋊C4—612no—
610C4⋊C4—1224no—
611C4⋊C4—1224no—
612C4⋊C4—1224no—
613C4⋊C4—1224no—
614C4⋊C4—1224no—
615C4⋊C4—1224no—
616C4⋊C4—1221no—
617C4⋊C4—1221no—
618C4⋊C4—1224no—
619C4⋊C4C23×D6112yes—
620C4⋊C4C23×D6112yes—
621C4⋊C4C23×D6112yes—
622C4⋊C4C23×D6112yes—
623C22⋊C4—614no—
624C22⋊C4—614no—
625C22⋊C4—1224no—
626C22⋊C4—1224no—
627C22⋊C4—1224no—
628C22⋊C4—1224no—
629C22⋊C4—1224no—
630C22⋊C4—1224no—
631C22⋊C4—1224no—
632C42—612no—
633C42—612no—
634C42—1224no—
635C42—1224no—
636C42—1224no—
637C23—22no—
638C23—22no—
639C23—612no—
640C23—1222no—
641C23—1222no—
642C23—1222no—
643C23—1222no—
644C23—2442no—
645C23—2442no—
646C23—2442no—
647C23#1451979814yes—
648C23C2×D4×D6112yes—
649C23C2×D4×D6111yescharacteristic
650Q8—1222no—
651Q8—1222no—
652Q8—2442no—
653D4—1228no—
654D4—1222no—
655D4—1222no—
656D4—4884no—
657D4—2448no—
658D4—2442no—
659C2×C4—22no—
660C2×C4—22no—
661C2×C4—22no—
662C2×C4—24no—
663C2×C4—22no—
664C2×C4—22no—
665C2×C4—22no—
666C2×C4—22no—
667C2×C4—48no—
668C2×C4—42no—
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—4884no—
686C2×C4—2442no—
687C2×C4—2442no—
688C2×C4—2442no—
689C2×C4C2×D4×D6112yes—
690C2×C4C2×D4×D6111yescharacteristic
691C2×C4C2×#1175822212yes—
692C2×C4#1451982512yes—
693C2×C4C24×D6111yescharacteristic
694C8—22no—
695C8—1222no—
696C8—1222no—
697C8C2×#1175822214yes—
698C22—28no—
699C22—22no—
700C22—22no—
701C22—1222no—
702C22—1222no—
703C22—1222no—
704C22—4884no—
705C22—2442no—
706C22—2442no—
707C22—2442no—
708C22—2444no—
709C22#1684041312yes—
710C22C2×#1451979814yes—
711C22C2×#1451979812yes—
712C22#1684056812yes—
713C22C22×D4×D6111yescharacteristic
714C4—22no—
715C4—42no—
716C4—42no—
717C4—42no—
718C4—42no—
719C4—1222no—
720C4—1222no—
721C4—1222no—
722C4—2442no—
723C4—2442no—
724C4—2442no—
725C4#1684041312yes—
726C4C22×#1175822211yescharacteristic
727C4C2×#1451982511yescharacteristic
728C2—24no—
729C2—4882no—
730C2—2442no—
731C2#2145819414yesdirect product factor
732C2C2×#1684041311yescharacteristic
733C2C22×#1451979811yescharacteristic
734C2C2×#1684056811yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutator, cosocleC2×C4×C61C25
FrattiniC2×C4C24×D61
FittingC22×#106×C61C2
socleC23×C61C22×D4
prime radicalC2×#16840460C2
hypercenterC22×#106D61
hypocenterC61C2×#3337
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C23×C4 ◁ C22×#106

Complements

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

NH ≅ G/Ntype
2. C2×#16840447C2semidirect
3. #21458194C2direct (N × H)
4. C2×#16840162C2semidirect
5. C2×#16840097C2semidirect
6. C2×#16840106C2semidirect
7. C2×#16840088C2semidirect
8. C2×#16840075C2semidirect
9. C2×#16840072C2semidirect
10. C2×#16840061C2semidirect
11. C2×#16839992C2semidirect
12. C2×#16839991C2semidirect
13. C2×#16839849C2semidirect
14. C2×C8×C22⋊D61C2semidirect
15. C2×#16839797C2semidirect
16. C22×#106×C61C2semidirect
22. #16840447C22semidirect
42. #16840162C22semidirect
43. #16840106C22semidirect
44. #16840097C22semidirect
45. #16840088C22semidirect
46. #16840075C22semidirect
47. #16840072C22semidirect
48. #16840061C22semidirect
49. #16839992C22semidirect
50. #16839991C22semidirect
51. #16839849C22semidirect
52. C8×C22⋊D61C22semidirect
53. #16839797C22semidirect
76. C2×#106×C61C22semidirect
376. C22×#106D61semidirect
378. C2×C61#3337semidirect
433. C2×#106C2×D61semidirect
444. C61C2×#3337semidirect
731. C2#21458194direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168404602
C2×#168404472
#214581942
C2×#168401622
C2×#168400972
C2×#168401062
C2×#168400882
C2×#168400752
C2×#168400722
C2×#168400612
C2×#168399922
C2×#168399912
C2×#168398492
C2×C8×C22⋊D612
C2×#168397972
C22×#106×C612
C2×#333761