Finite Group Databasebeta

← C2×#21454691 #30544164

Subgroups — C2×#21454691 #30544164

Order 15616.

2806 conjugacy classes of subgroups.

The subgroup lattice has 798 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14519798C211yesmaximal, characteristic
2C2×#16840244C211yesmaximal, characteristic, complemented
3C2×#16840241C211yesmaximal, characteristic, complemented
4#21454691C2116yesmaximal, direct product factor
5C2×#16839864C211yesmaximal, characteristic, complemented
6C2×#16839863C211yesmaximal, characteristic, complemented
7C2×#16839861C211yesmaximal, characteristic, complemented
8C2×C4×#11758202C211yesmaximal, characteristic, complemented
9C2×#16839854C211yesmaximal, characteristic, complemented
10C2×C4×#11758199C211yesmaximal, characteristic, complemented
11C2×#16839842C211yesmaximal, characteristic, complemented
12C2×#107×D61C211yesmaximal, characteristic, complemented
13C2×#16839762C211yesmaximal, characteristic, complemented
14C2×#16839760C211yesmaximal, characteristic, complemented
15C2×#16839719C211yesmaximal, characteristic, complemented
16C2×C61×#440C211yesmaximal, characteristic, complemented
17C22×#11758226C2211yescharacteristic
18C22×#11758224C2211yescharacteristic
19C2×#14519798C4116yescomplemented
20C2×#14519798C2218yes—
21C22×#11758202C2211yescharacteristic
22C22×#11758190C2211yescharacteristic
23C22×#11758199C2211yescharacteristic
24C22×#11758189C2211yescharacteristic
25C22×C8×D61C2211yescharacteristic
26#16840244—24no—
27#16840244C2218yescomplemented
28#16840241—24no—
29#16840241C2218yescomplemented
30C2×Q8×Dic61C2211yescharacteristic
31C2×C4×Dic122C2211yescharacteristic
32C2×#14519742C2211yescharacteristic
33C2×C4×D244—21no—
34C2×C4×D244C2211yescharacteristic
35C2×D4×Dic61C2211yescharacteristic
36C2×#14519739—21no—
37C2×#14519739C2211yescharacteristic
38C2×C4×C22⋊D61—21no—
39C2×#14519737—21no—
40C2×#14519734—21no—
41C2×#14519734C2211yescharacteristic
42C2×#14519733—21no—
43C22×#11758196—21no—
44C2×C4⋊C4×D61—21no—
45C2×C4⋊C4×D61C2211yescharacteristic
46C2×C4⋊C4×D61C2211yescharacteristic
47#16839864C2218yescomplemented
48#16839863C2218yescomplemented
49#16839861C2218yescomplemented
50C4×#11758202C2218yescomplemented
51#16839854C2218yescomplemented
52C4×#11758199C2218yescomplemented
53#16839842C2218yescomplemented
54C2×#14519711C2211yescharacteristic
55C2×#14519710C2211yescharacteristic
56C2×#14519710C2211yescharacteristic
57#107×D61C2218yescomplemented
58#16839762C2218yescomplemented
59#16839760C2218yescomplemented
60C2×#14519702C2211yescharacteristic
61C2×#14519701C2211yescharacteristic
62C2×#14519700C2211yescharacteristic
63C2×#14519699C2211yescharacteristic
64C2×#14519698C2211yescharacteristic
65C2×#14519697C2211yescharacteristic
66#16839719C2218yescomplemented
67C2×#14519687C2211yescharacteristic
68C2×C4×#92418C2211yescharacteristic
69C2×C8×Dic61C2211yescharacteristic
70C22×SD16×C61C2211yescharacteristic
71C2×C4×Q8×C61C2211yescharacteristic
72C2×C4×D4×C61C2211yescharacteristic
73C61×#440C2218yescomplemented
74C2×#107×C61C2211yescharacteristic
75C2×#103×C61C2211yescharacteristic
76C2×#102×C61C2211yescharacteristic
77C2×#97×C61C2211yescharacteristic
78C2×#11758226—22no—
79C2×#11758226—24no—
80C2×#11758226C2×C418yescomplemented
81C2×#11758226C2314yes—
82C2×#11758224—22no—
83C2×#11758224—24no—
84C2×#11758224C2×C418yescomplemented
85C2×#11758224C2314yes—
86C22×Dic122C2311yescharacteristic
87C22×D244—21no—
88C22×D244C2311yescharacteristic
89C22×C22⋊D61—21no—
90C23×Dic61—21no—
91C23×Dic61—21no—
92C22×C4×D61—21no—
93C22×C4×D61—21no—
94C22×C4×D61—21no—
95C22×C4×D61—21no—
96C22×C4×D61—21no—
97C22×C4×D61C2311yescharacteristic
98#14519798C2×C4164yescomplemented
99C2×#11758202C2×C418yescomplemented
100C2×#11758202C2314yes—
101C2×#11758190C2×C418yescomplemented
102C2×#11758190C2314yes—
103C2×#11758199C2×C418yescomplemented
104C2×#11758199C2314yes—
105C2×#11758189—24no—
106C2×#11758189C2314yes—
107C22×#92418C2311yescharacteristic
108C22×#92418C2311yescharacteristic
109C2×C8×D61C2×C418yescomplemented
110C2×C8×D61C2314yes—
111Q8×Dic61—22no—
112Q8×Dic61C2314yes—
113C4×Dic122—22no—
114C4×Dic122C2314yes—
115#14519742—22no—
116#14519742C2314yes—
117C4×D244—22no—
118C4×D244—28no—
119C4×D244C2314yes—
120D4×Dic61—22no—
121D4×Dic61C2314yes—
122#14519739—28no—
123#14519739—22no—
124#14519739C2314yes—
125C4×C22⋊D61—28no—
126#14519737—28no—
127#14519734—28no—
128#14519734D414yes—
129#14519734C2314yes—
130#14519733—28no—
131C2×C4⋊Dic61—21no—
132C2×C4⋊Dic61C2311yescharacteristic
133C2×C4⋊Dic61C2311yescharacteristic
134C2×#11758196—21no—
135C2×#11758196—21no—
136C2×#11758196—21no—
137C2×#11758196—21no—
138C2×#11758196—28no—
139C2×#11758196D411yescharacteristic
140C2×#11758196D411yescharacteristic
141C4⋊C4×D61—22no—
142C4⋊C4×D61—22no—
143C4⋊C4×D61—28no—
144C4⋊C4×D61C2314yes—
145C4⋊C4×D61C2314yes—
146C2×C22⋊Dic61—21no—
147C2×#11758198—21no—
148C2×#11758198—21no—
149C2×#11758198D411yescharacteristic
150C2×#11758198D411yescharacteristic
151C2×C4×Dic61—21no—
152C2×C4×Dic61—21no—
153C2×C4×Dic61—21no—
154C2×C4×Dic61C2311yescharacteristic
155#14519711C2314yes—
156#14519710C2314yes—
157#14519710C2314yes—
158#14519702C2314yes—
159#14519701C2314yes—
160#14519700C2314yes—
161#14519699C2314yes—
162#14519698C2314yes—
163#14519697C2314yes—
164#14519687C2314yes—
165C4×#92418C2314yes—
166C8×Dic61C2314yes—
167C22×Q8×C61C2311yescharacteristic
168C22×D4×C61C2311yescharacteristic
169C23×C4×C61—21no—
170C2×SD16×C61C2×C418yescomplemented
171C2×SD16×C61C2314yes—
172C22×C8×C61C2311yescharacteristic
173C22×C8×C61C2311yescharacteristic
174C4×Q8×C61—22no—
175C4×Q8×C61C2314yes—
176C4×D4×C61—22no—
177C4×D4×C61C2314yes—
178C2×C4⋊C4×C61—21no—
179C2×C4⋊C4×C61C2311yescharacteristic
180C2×C4⋊C4×C61C2311yescharacteristic
181C2×C22⋊C4×C61—21no—
182C2×C42×C61—21no—
183C2×C42×C61C2311yescharacteristic
184#107×C61C2314yes—
185#103×C61C2314yes—
186#102×C61C2314yes—
187#97×C61C2314yes—
188C24×C61—21no—
189C23×D61—21no—
190C23×D61C2×D411yescharacteristic
191C2×Q8×C61—21no—
192C2×Q8×C61—22no—
193C2×Q8×C61C22×C414yes—
194C2×Q8×C61C2412yes—
195C2×D4×C61—21no—
196C2×D4×C61—22no—
197C2×D4×C61C22×C414yes—
198C2×D4×C61C2412yes—
199C22×C4×C61—21no—
200C22×C4×C61—21no—
201C22×C4×C61—21no—
202C22×C4×C61—24no—
203C22×C4×C61—82no—
204C22×C4×C61C2×D411yescharacteristic
205C22×C4×C61C2×D411yescharacteristic
206C22×C4×C61C2411yescharacteristic
207C2×C22⋊D61—28no—
208C2×C22⋊D61—24no—
209C22×Dic61—21no—
210C22×Dic61—28no—
211C22×Dic61—24no—
212C22×Dic61—21no—
213C22×Dic61—21no—
214C22×Dic61—24no—
215C22×Dic61—82no—
216C22×Dic61C2×D411yescharacteristic
217C22×Dic61C2×D411yescharacteristic
218C22×Dic61C2×D411yescharacteristic
219#11758226—216no—
220#11758226—28no—
221#11758226C22×C4116yescomplemented
222#11758224—216no—
223#11758224—28no—
224#11758224C22×C4116yescomplemented
225C2×D244—28no—
226C2×D244—24no—
227C2×D244—21no—
228C2×D244—22no—
229C2×D244C22×C414yes—
230C2×D244C2412yes—
231C2×C4×D61—28no—
232C2×C4×D61—24no—
233C2×C4×D61—24no—
234C2×C4×D61—24no—
235C2×C4×D61—24no—
236C2×C4×D61—24no—
237C2×C4×D61—82no—
238C2×C4×D61—82no—
239C2×C4×D61—82no—
240C2×C4×D61—82no—
241C2×C4×D61C22×C414yes—
242C2×C4×D61C2×D412yes—
243C2×C4×D61#4114yes—
244C2×C4×D61C2412yes—
245C2×Dic122—21no—
246C2×Dic122—22no—
247C2×Dic122C22×C414yes—
248C2×Dic122C2412yes—
249SD16×C61C22×C4116yescomplemented
250C2×C8×C61—22no—
251C2×C8×C61C22×C414yes—
252C2×C8×C61C2412yes—
253C2×C8×C61C2412yes—
254C4⋊C4×C61—24no—
255C4⋊C4×C61—21no—
256C4⋊C4×C61—21no—
257C4⋊C4×C61C2412yes—
258C4⋊C4×C61C2412yes—
259C22⋊C4×C61—24no—
260C42×C61—24no—
261C42×C61C2×D412yes—
262C42×C61C2412yes—
263C22⋊Dic61—24no—
264#11758202C22×C4116yescomplemented
265#11758199C22×C4116yescomplemented
266#11758198—24no—
267#11758198—24no—
268#11758198C2×D414yes—
269#11758198C2×D414yes—
270C4⋊Dic61—21no—
271C4⋊Dic61—21no—
272C4⋊Dic61—24no—
273C4⋊Dic61C2412yes—
274C4⋊Dic61C2412yes—
275#11758196—24no—
276#11758196—24no—
277#11758196—24no—
278#11758196—24no—
279#11758196C2×D414yes—
280#11758196C2×D414yes—
281C4×Dic61—24no—
282C4×Dic61—24no—
283C4×Dic61—24no—
284C4×Dic61C2×D412yes—
285C4×Dic61C2412yes—
286C2×#92418—22no—
287C2×#92418C22×C414yes—
288C2×#92418C2412yes—
289C2×#92418C2412yes—
290#11758190C22×C4116yescomplemented
291#11758189—28no—
292C8×D61C22×C4116yescomplemented
293C23×C61—24no—
294C23×C61—22no—
295C23×C61—42no—
296C23×C61—42no—
297C23×C61C22×D411yescharacteristic
298C22×D61—22no—
299C22×D61—22no—
300C22×D61—24no—
301C22×D61—22no—
302C22×D61—42no—
303C22×D61—42no—
304C22×D61C4×D414yes—
305C22×D61C22×D412yes—
306Q8×C61—24no—
307Q8×C61—22no—
308Q8×C61C23×C414yes—
309D4×C61—24no—
310D4×C61—22no—
311D4×C61C23×C414yes—
312C2×C4×C61—24no—
313C2×C4×C61—22no—
314C2×C4×C61—22no—
315C2×C4×C61—22no—
316C2×C4×C61—22no—
317C2×C4×C61—22no—
318C2×C4×C61—42no—
319C2×C4×C61—42no—
320C2×C4×C61—84no—
321C2×C4×C61C23×C412yes—
322C2×C4×C61C22×D412yes—
323C2×C4×C61C22×D412yes—
324C2×C4×C61C22×D411yescharacteristic
325C2×C4×C61C2×#4112yes—
326C2×C4×C61C2511yescharacteristic
327C22⋊D61—216no—
328C2×Dic61—24no—
329C2×Dic61—22no—
330C2×Dic61—22no—
331C2×Dic61—22no—
332C2×Dic61—216no—
333C2×Dic61—22no—
334C2×Dic61—22no—
335C2×Dic61—42no—
336C2×Dic61—42no—
337C2×Dic61—84no—
338C2×Dic61C4×D414yes—
339C2×Dic61C22×D412yes—
340C2×Dic61C22×D412yes—
341C2×Dic61C22×D412yes—
342D244—216no—
343D244—24no—
344D244—22no—
345D244C23×C414yes—
346C4×D61—216no—
347C4×D61—84no—
348C4×D61—84no—
349C4×D61—84no—
350C4×D61—84no—
351C4×D61C4×D418yes—
352C4×D61C23×C414yes—
353C4×D61C2×#4114yes—
354Dic122—24no—
355Dic122—22no—
356Dic122C23×C414yes—
357C8×C61—22no—
358C8×C61C23×C414yes—
359#92418—22no—
360#92418C23×C414yes—
361C2×#2951—611nomaximal, Sylow
362C22×C61—24no—
363C22×C61—48no—
364C22×C61—42no—
365C22×C61—42no—
366C22×C61C2×C4×D412yes—
367C22×C61#57612yes—
368C22×C61#57812yes—
369C22×C61C23×D411yescharacteristic
370C2×D61—28no—
371C2×D61—22no—
372C2×D61—22no—
373C2×D61—24no—
374C2×D61—48no—
375C2×D61—42no—
376C2×D61—42no—
377C2×D61C2×C4×D414yes—
378C4×C61—24no—
379C4×C61—22no—
380C4×C61—22no—
381C4×C61—42no—
382C4×C61—42no—
383C4×C61C2×C4×D412yes—
384C4×C61C24×C411yescharacteristic
385C4×C61C22×#4111yescharacteristic
386Dic61—24no—
387Dic61—22no—
388Dic61—22no—
389Dic61—42no—
390Dic61—42no—
391Dic61C2×C4×D414yes—
392C22×#135—611no—
393C2×#520—611no—
394C2×#520—611no—
395#2951—6116no—
396C2×#440—611no—
397C2×#440—611no—
398C2×#440—611no—
399C2×#440D6111yescharacteristic, complemented
400C2×C4×Q16—611no—
401C2×C4×Q16—611no—
402C2×C4×D8—611no—
403C2×C4×D8—611no—
404C22×#107—611no—
405C2×#417—611no—
406C2×#417—611no—
407C2×#405—611no—
408C2×C61—44no—
409C2×C61#295114yescomplemented
410C2×C61C22×C4×D411yescharacteristic
411C2×C61C2×#57611yescharacteristic
412C2×C61C2×#57811yescharacteristic
413D61—24no—
414D61—44no—
415C22×#41—611no—
416C22×#41—611no—
417C2×#135—6116no—
418C2×#135—618no—
419C22×Q16—611no—
420C22×SD16—611no—
421C22×SD16C2×D6111yescharacteristic
422C22×D8—611no—
423C22×M16—611no—
424C23×C8—611no—
425#520—618no—
426#520—618no—
427#520—1224no—
428#520—1224no—
429C2×C4×Q8—611no—
430C2×C4×Q8—611no—
431C2×C4×Q8—611no—
432C2×C4×Q8C2×D6111yescharacteristic
433C2×C4×D4—611no—
434C2×C4×D4—611no—
435C2×C4×D4—611no—
436C2×C4×D4—1221no—
437C2×C4×D4—1221no—
438C2×C4×D4—1221no—
439C2×C4×D4—1221no—
440C2×C4×D4C2×D6111yescharacteristic
441C2×#117—611no—
442C2×#117—1221no—
443C2×#117—1221no—
444C22×C4⋊C4—611no—
445C22×C4⋊C4—611no—
446C22×C4⋊C4—1221no—
447C22×C4⋊C4—1221no—
448#440—618no—
449#440—618no—
450#440—618no—
451#440C2×D6118yescomplemented
452C4×Q16—618no—
453C4×Q16—618no—
454C4×D8—618no—
455C4×D8—618no—
456C2×#107—611no—
457C2×#107—611no—
458C2×#107—611no—
459C2×#107—618no—
460C2×#107C2×D6111yescharacteristic
461#417—618no—
462#417—618no—
463C2×#103—611no—
464C2×#103—611no—
465C2×#103—611no—
466C2×#103C2×D6111yescharacteristic
467C2×#102—611no—
468C2×#102—611no—
469C2×#102—611no—
470C2×#102C2×D6111yescharacteristic
471#405—618no—
472C2×#97—611no—
473C2×#97C2×D6111yescharacteristic
474C2×C4×C8—611no—
475C2×C4×C8—611no—
476C61C2×#295111yescharacteristic, complemented, Sylow
477C2×#41—618no—
478C2×#41—614no—
479C2×#41—618no—
480C2×#41—614no—
481C2×#41—1222no—
482C2×#41—1224no—
483C2×#41—1222no—
484C2×#41—1224no—
485C22×Q8—611no—
486C22×Q8C22×D6111yescharacteristic
487C22×D4—611no—
488C22×D4—1221no—
489C22×D4—1221no—
490C22×D4C22×D6111yescharacteristic
491C23×C4—21no—
492C23×C4—611no—
493C23×C4—1221no—
494C23×C4—1221no—
495C23×C4—1221no—
496C23×C4—1221no—
497C23×C4—1221no—
498C23×C4—1221no—
499C23×C4—1221no—
500#135—6164no—
501C2×Q16—618no—
502C2×Q16—614no—
503C2×SD16—618no—
504C2×SD16—614no—
505C2×SD16C4×D6118yescomplemented
506C2×SD16C22×D6114yes—
507C2×D8—618no—
508C2×D8—614no—
509C2×M16—614no—
510C2×M16—1224no—
511C22×C8—611no—
512C22×C8—618no—
513C22×C8—614no—
514C22×C8—611no—
515C22×C8C22×D6111yescharacteristic
516C22×C8C22×D6111yescharacteristic
517C4×Q8—22no—
518C4×Q8—614no—
519C4×Q8—614no—
520C4×Q8—614no—
521C4×Q8—1222no—
522C4×Q8—1222no—
523C4×Q8—1222no—
524C4×Q8C22×D6114yes—
525C4×D4—22no—
526C4×D4—614no—
527C4×D4—614no—
528C4×D4—614no—
529C4×D4—1228no—
530C4×D4—1222no—
531C4×D4—1222no—
532C4×D4—1228no—
533C4×D4—1228no—
534C4×D4—1228no—
535C4×D4—1222no—
536C4×D4C22×D6114yes—
537#117—614no—
538#117—614no—
539#117—1228no—
540#117—1228no—
541C2×C4⋊C4—21no—
542C2×C4⋊C4—611no—
543C2×C4⋊C4—611no—
544C2×C4⋊C4—611no—
545C2×C4⋊C4—611no—
546C2×C4⋊C4—614no—
547C2×C4⋊C4—614no—
548C2×C4⋊C4—1228no—
549C2×C4⋊C4—1222no—
550C2×C4⋊C4—1222no—
551C2×C4⋊C4—1228no—
552C2×C4⋊C4—1221no—
553C2×C4⋊C4—1221no—
554C2×C4⋊C4—1221no—
555C2×C4⋊C4—1221no—
556C2×C4⋊C4—1221no—
557C2×C4⋊C4C22×D6111yescharacteristic
558C2×C4⋊C4C22×D6111yescharacteristic
559C2×C22⋊C4—21no—
560C2×C22⋊C4—611no—
561C2×C22⋊C4—611no—
562C2×C22⋊C4—1221no—
563C2×C22⋊C4—1221no—
564C2×C22⋊C4—1221no—
565C2×C42—21no—
566C2×C42—611no—
567C2×C42—1221no—
568C2×C42—1221no—
569C2×C42—1221no—
570C2×C42C22×D6111yescharacteristic
571#107—614no—
572#107—614no—
573#107—614no—
574#107C22×D6114yes—
575#103—614no—
576#103—614no—
577#103—614no—
578#103C22×D6114yes—
579#102—614no—
580#102—614no—
581#102—614no—
582#102C22×D6114yes—
583#97—614no—
584#97C22×D6114yes—
585C4×C8—614no—
586C4×C8—614no—
587C24—21no—
588C24—611no—
589C24—1221no—
590#41—6116no—
591#41—6116no—
592#41—12216no—
593#41—1228no—
594#41—12216no—
595#41—1228no—
596C2×Q8—21no—
597C2×Q8—22no—
598C2×Q8—614no—
599C2×Q8—612no—
600C2×Q8—1221no—
601C2×Q8—1222no—
602C2×Q8C2×C4×D6114yes—
603C2×Q8C23×D6112yes—
604C2×D4—21no—
605C2×D4—22no—
606C2×D4—614no—
607C2×D4—612no—
608C2×D4—1224no—
609C2×D4—1228no—
610C2×D4—1224no—
611C2×D4—1228no—
612C2×D4—1221no—
613C2×D4—1222no—
614C2×D4C2×C4×D6114yes—
615C2×D4C23×D6112yes—
616C22×C4—21no—
617C22×C4—21no—
618C22×C4—21no—
619C22×C4—24no—
620C22×C4—82no—
621C22×C4—611no—
622C22×C4—614no—
623C22×C4—612no—
624C22×C4—614no—
625C22×C4—612no—
626C22×C4—611no—
627C22×C4—611no—
628C22×C4—1224no—
629C22×C4—1228no—
630C22×C4—1224no—
631C22×C4—1224no—
632C22×C4—1224no—
633C22×C4—1224no—
634C22×C4—1228no—
635C22×C4—1224no—
636C22×C4—1221no—
637C22×C4—1221no—
638C22×C4—1221no—
639C22×C4—1224no—
640C22×C4—4882no—
641C22×C4—4882no—
642C22×C4—4882no—
643C22×C4—4882no—
644C22×C4—4882no—
645C22×C4D4×D6111yescharacteristic
646C22×C4D4×D6111yescharacteristic
647C22×C4C23×D6111yescharacteristic
648Q16—6116no—
649SD16—6116no—
650SD16C2×C4×D61116yescomplemented
651D8—6116no—
652M16—1228no—
653C2×C8—22no—
654C2×C8—614no—
655C2×C8—612no—
656C2×C8—6116no—
657C2×C8—612no—
658C2×C8—1222no—
659C2×C8C2×C4×D6114yes—
660C2×C8C23×D6112yes—
661C2×C8C23×D6112yes—
662C4⋊C4—24no—
663C4⋊C4—21no—
664C4⋊C4—21no—
665C4⋊C4—614no—
666C4⋊C4—614no—
667C4⋊C4—612no—
668C4⋊C4—612no—
669C4⋊C4—1224no—
670C4⋊C4—1224no—
671C4⋊C4—1224no—
672C4⋊C4—1224no—
673C4⋊C4—1221no—
674C4⋊C4—1221no—
675C4⋊C4—1224no—
676C4⋊C4C23×D6112yes—
677C4⋊C4C23×D6112yes—
678C22⋊C4—24no—
679C22⋊C4—614no—
680C22⋊C4—614no—
681C22⋊C4—1224no—
682C22⋊C4—1224no—
683C22⋊C4—1224no—
684C42—24no—
685C42—612no—
686C42—612no—
687C42—1224no—
688C42—1224no—
689C42—1224no—
690C42D4×D6112yes—
691C42C23×D6112yes—
692C23—24no—
693C23—22no—
694C23—42no—
695C23—42no—
696C23—614no—
697C23—612no—
698C23—1222no—
699C23—1222no—
700C23—1224no—
701C23—1222no—
702C23—2442no—
703C23—2442no—
704C23C2×D4×D6111yescharacteristic
705Q8—24no—
706Q8—22no—
707Q8—614no—
708Q8—1224no—
709Q8—1222no—
710Q8C22×C4×D6114yes—
711D4—24no—
712D4—22no—
713D4—614no—
714D4—12216no—
715D4—12216no—
716D4—1224no—
717D4—1222no—
718D4C22×C4×D6114yes—
719C2×C4—24no—
720C2×C4—22no—
721C2×C4—22no—
722C2×C4—22no—
723C2×C4—22no—
724C2×C4—22no—
725C2×C4—42no—
726C2×C4—42no—
727C2×C4—84no—
728C2×C4—614no—
729C2×C4—612no—
730C2×C4—618no—
731C2×C4—614no—
732C2×C4—614no—
733C2×C4—612no—
734C2×C4—612no—
735C2×C4—12216no—
736C2×C4—12216no—
737C2×C4—1224no—
738C2×C4—1222no—
739C2×C4—1222no—
740C2×C4—1222no—
741C2×C4—1222no—
742C2×C4—1222no—
743C2×C4—4884no—
744C2×C4—4884no—
745C2×C4—4884no—
746C2×C4—4884no—
747C2×C4—4884no—
748C2×C4—2442no—
749C2×C4—2442no—
750C2×C4C22×C4×D6112yes—
751C2×C4C2×D4×D6112yes—
752C2×C4C2×D4×D6112yes—
753C2×C4C2×D4×D6111yescharacteristic
754C2×C4#41×D6112yes—
755C2×C4C24×D6111yescharacteristic
756C8—22no—
757C8—614no—
758C8—1222no—
759C8C22×C4×D6114yes—
760C22—24no—
761C22—42no—
762C22—48no—
763C22—42no—
764C22—614no—
765C22—1222no—
766C22—1228no—
767C22—1222no—
768C22—1224no—
769C22—2442no—
770C22—2448no—
771C22—2442no—
772C22C4×D4×D6112yes—
773C22#1684056612yes—
774C22#1684057812yes—
775C22C22×D4×D6111yescharacteristic
776C4—24no—
777C4—22no—
778C4—22no—
779C4—42no—
780C4—42no—
781C4—614no—
782C4—1224no—
783C4—1222no—
784C4—1222no—
785C4—2442no—
786C4—2442no—
787C4C4×D4×D6112yes—
788C4C23×C4×D6111yescharacteristic
789C4C2×#41×D6111yescharacteristic
790C2—44no—
791C2—1224no—
792C2—2444no—
793C2#2145469114yesdirect product factor
794C2C2×C4×D4×D6111yescharacteristic
795C2C2×#1684056611yescharacteristic
796C2C2×#1684057811yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutatorC4×C61C24×C4
FrattiniC2×C4C24×D61
FittingC2×C61×#440C2
socleC23×C61C22×D4
prime radicalC22×#14519798C2
cosocleC2×C4×C61C25
hypercenterC2×#440D61
hypocenterC61C2×#2951
LCSG ▷ C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#440

Complements

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

NH ≅ G/Ntype
2. C2×#16840244C2semidirect
3. C2×#16840241C2semidirect
4. #21454691C2direct (N × H)
5. C2×#16839864C2semidirect
6. C2×#16839863C2semidirect
7. C2×#16839861C2semidirect
8. C2×C4×#11758202C2semidirect
9. C2×#16839854C2semidirect
10. C2×C4×#11758199C2semidirect
11. C2×#16839842C2semidirect
12. C2×#107×D61C2semidirect
13. C2×#16839762C2semidirect
14. C2×#16839760C2semidirect
15. C2×#16839719C2semidirect
16. C2×C61×#440C2semidirect
19. C2×#14519798C4semidirect
27. #16840244C22semidirect
29. #16840241C22semidirect
47. #16839864C22semidirect
48. #16839863C22semidirect
49. #16839861C22semidirect
50. C4×#11758202C22semidirect
51. #16839854C22semidirect
52. C4×#11758199C22semidirect
53. #16839842C22semidirect
57. #107×D61C22semidirect
58. #16839762C22semidirect
59. #16839760C22semidirect
66. #16839719C22semidirect
73. C61×#440C22semidirect
80. C2×#11758226C2×C4semidirect
84. C2×#11758224C2×C4semidirect
98. #14519798C2×C4semidirect
99. C2×#11758202C2×C4semidirect
101. C2×#11758190C2×C4semidirect
103. C2×#11758199C2×C4semidirect
109. C2×C8×D61C2×C4semidirect
170. C2×SD16×C61C2×C4semidirect
221. #11758226C22×C4semidirect
224. #11758224C22×C4semidirect
249. SD16×C61C22×C4semidirect
264. #11758202C22×C4semidirect
265. #11758199C22×C4semidirect
290. #11758190C22×C4semidirect
292. C8×D61C22×C4semidirect
399. C2×#440D61semidirect
409. C2×C61#2951semidirect
451. #440C2×D61semidirect
476. C61C2×#2951semidirect
505. C2×SD16C4×D61semidirect
650. SD16C2×C4×D61semidirect
793. C2#21454691direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#145197982
C2×#168402442
C2×#168402412
#214546912
C2×#168398642
C2×#168398632
C2×#168398612
C2×C4×#117582022
C2×#168398542
C2×C4×#117581992
C2×#168398422
C2×#107×D612
C2×#168397622
C2×#168397602
C2×#168397192
C2×C61×#4402
C2×#295161