Finite Group Databasebeta

← C2×#21458066 #30556860

Subgroups — C2×#21458066 #30556860

Order 15616.

2178 conjugacy classes of subgroups.

The subgroup lattice has 812 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840421C211yesmaximal, characteristic, complemented
2#21458066C2116yesmaximal, direct product factor
3C2×#16840119C211yesmaximal, characteristic, complemented
4C2×#16840086C211yesmaximal, characteristic, complemented
5C2×#16840092C211yesmaximal, characteristic, complemented
6C2×#16840066C211yesmaximal, characteristic, complemented
7C2×#16840013C211yesmaximal, characteristic, complemented
8C2×#16840006C211yesmaximal, characteristic, complemented
9C2×#16839977C211yesmaximal, characteristic, complemented
10C2×#16839905C211yesmaximal, characteristic, complemented
11C2×#16839900C211yesmaximal, characteristic, complemented
12C2×C4×#11758200C211yesmaximal, characteristic, complemented
13C2×#16839840C211yesmaximal, characteristic, complemented
14C2×#16839761C211yesmaximal, characteristic, complemented
15C2×#16839770C211yesmaximal, characteristic, complemented
16C2×C61×#553C211yesmaximal, characteristic, complemented
17C22×#11758222C2211yescharacteristic
18C23×Dic122C2211yescharacteristic
19C22×#11758200C2211yescharacteristic
20C22×#11758200C2211yescharacteristic
21C22×#11758199C2211yescharacteristic
22C22×#11758194C2211yescharacteristic
23C22×#11758194C2211yescharacteristic
24#16840421—24no—
25#16840421C2218yescomplemented
26C2×#14519765C2211yescharacteristic
27C2×#14519763—21no—
28C2×#14519756C2211yescharacteristic
29C2×#14519755—21no—
30C2×#14519751C2211yescharacteristic
31C2×#14519749—21no—
32C2×C4×Dic122C2211yescharacteristic
33C2×#14519737—21no—
34#16840119C2218yescomplemented
35#16840092C2218yescomplemented
36#16840086C2218yescomplemented
37#16840066C2218yescomplemented
38#16840013C2218yescomplemented
39#16840006C2218yescomplemented
40#16839977C2218yescomplemented
41#16839905C2218yescomplemented
42#16839900C2218yescomplemented
43C4×#11758200C2218yescomplemented
44#16839840C2218yescomplemented
45C2×#14519710C2211yescharacteristic
46C2×#14519708C2211yescharacteristic
47C2×#14519708C2211yescharacteristic
48C2×C4⋊#92418C2211yescharacteristic
49#16839770C2218yescomplemented
50#16839761C2218yescomplemented
51C2×#14519700C2211yescharacteristic
52C2×#14519700C2211yescharacteristic
53C2×#14519700C2211yescharacteristic
54C2×#14519700C2211yescharacteristic
55C2×#14519700C2211yescharacteristic
56C2×#14519700C2211yescharacteristic
57C2×#14519698C2211yescharacteristic
58C2×#14519697C2211yescharacteristic
59C2×#14519697C2211yescharacteristic
60C2×#14519697C2211yescharacteristic
61C2×C22⋊#92418C2211yescharacteristic
62C2×C22⋊#92418C2211yescharacteristic
63C2×C4×#92418C2211yescharacteristic
64C61×#553—24no—
65C61×#553C2218yescomplemented
66C2×#126×C61—21no—
67C2×#125×C61C2211yescharacteristic
68C2×#123×C61—21no—
69C2×#121×C61—21no—
70C2×#121×C61C2211yescharacteristic
71C2×#121×C61C2211yescharacteristic
72C2×C4×D4×C61—21no—
73C2×C4×D4×C61C2211yescharacteristic
74C2×C4×D4×C61C2211yescharacteristic
75C2×#117×C61C2211yescharacteristic
76C22×C4⋊C4×C61C2211yescharacteristic
77C2×#11758222—22no—
78C2×#11758222—24no—
79C2×#11758222—42no—
80C2×#11758222C2314yes—
81C22×Dic122—24no—
82C22×Dic122—21no—
83C22×Dic122—22no—
84C22×Dic122—42no—
85C22×Dic122C2311yescharacteristic
86C22×Dic122C2314yes—
87C22×Dic122C2311yescharacteristic
88C22×D244C2311yescharacteristic
89C22×C22⋊D61—21no—
90C22×C22⋊D61—21no—
91C23×Dic61—21no—
92C22×C4×D61—21no—
93C2×#11758200—24no—
94C2×#11758200—42no—
95C2×#11758200C2314yes—
96C2×#11758200C2314yes—
97C2×#11758199—42no—
98C2×#11758199C2314yes—
99C2×#11758194—42no—
100C2×#11758194—42no—
101C2×#11758194C2314yes—
102C2×#11758194C2314yes—
103C22×#92418C2311yescharacteristic
104C22×#92418C2311yescharacteristic
105C22×#92418C2311yescharacteristic
106C22×#92418C2311yescharacteristic
107#14519765—22no—
108#14519765C2314yes—
109#14519763—28no—
110#14519756—22no—
111#14519756C2314yes—
112#14519755—28no—
113#14519751—22no—
114#14519751C2314yes—
115#14519749—28no—
116C4×Dic122—22no—
117C4×Dic122C2314yes—
118#14519737—28no—
119C2×C4⋊Dic61C2311yescharacteristic
120C2×#11758196—21no—
121C2×#11758196—21no—
122C2×C22⋊Dic61—21no—
123C2×#11758198—21no—
124C2×#11758198—21no—
125C2×#11758198—21no—
126C2×C4×Dic61—21no—
127#14519710C2314yes—
128#14519708C2314yes—
129#14519708C2314yes—
130C4⋊#92418C2314yes—
131#14519700C2314yes—
132#14519700C2314yes—
133#14519700C2314yes—
134#14519700C2314yes—
135#14519700C2314yes—
136#14519700C2314yes—
137#14519698C2314yes—
138#14519697C2314yes—
139#14519697C2314yes—
140#14519697C2314yes—
141C22⋊#92418C2314yes—
142C22⋊#92418C2314yes—
143C4×#92418C2314yes—
144C22×D4×C61—21no—
145C22×D4×C61—21no—
146C22×D4×C61D411yescharacteristic
147C22×D4×C61C2311yescharacteristic
148C23×C4×C61—21no—
149C23×C4×C61—21no—
150C23×C4×C61C2311yescharacteristic
151C23×C4×C61C2311yescharacteristic
152#126×C61—28no—
153#125×C61—22no—
154#125×C61C2314yes—
155#123×C61—28no—
156#121×C61—28no—
157#121×C61—22no—
158#121×C61—22no—
159#121×C61C2314yes—
160#121×C61C2314yes—
161C4×D4×C61—28no—
162C4×D4×C61—22no—
163C4×D4×C61D414yes—
164C4×D4×C61C2314yes—
165C4×D4×C61C2314yes—
166#117×C61—22no—
167#117×C61C2314yes—
168C2×C4⋊C4×C61—22no—
169C2×C4⋊C4×C61—21no—
170C2×C4⋊C4×C61—21no—
171C2×C4⋊C4×C61—21no—
172C2×C4⋊C4×C61D411yescharacteristic
173C2×C4⋊C4×C61C2314yes—
174C2×C4⋊C4×C61C2311yescharacteristic
175C2×C4⋊C4×C61C2311yescharacteristic
176C2×C4⋊C4×C61C2311yescharacteristic
177C2×C22⋊C4×C61—21no—
178C2×C22⋊C4×C61—21no—
179C2×C22⋊C4×C61—21no—
180C2×C22⋊C4×C61—21no—
181C2×C22⋊C4×C61D411yescharacteristic
182C2×C22⋊C4×C61D411yescharacteristic
183C2×C42×C61—21no—
184C2×C42×C61C2311yescharacteristic
185C24×C61—21no—
186C24×C61C2×D411yescharacteristic
187C24×C61C2×D411yescharacteristic
188C23×D61—21no—
189C2×D4×C61—24no—
190C2×D4×C61—24no—
191C2×D4×C61—21no—
192C2×D4×C61—22no—
193C2×D4×C61—22no—
194C2×D4×C61—42no—
195C2×D4×C61—44no—
196C2×D4×C61—82no—
197C2×D4×C61C2×D414yes—
198C2×D4×C61C2412yes—
199C22×C4×C61—22no—
200C22×C4×C61—22no—
201C22×C4×C61—22no—
202C22×C4×C61—22no—
203C22×C4×C61—21no—
204C22×C4×C61—21no—
205C22×C4×C61—21no—
206C22×C4×C61—24no—
207C22×C4×C61—24no—
208C22×C4×C61—82no—
209C22×C4×C61—82no—
210C22×C4×C61C2×D411yescharacteristic
211C22×C4×C61C2×D411yescharacteristic
212C22×C4×C61C2×D412yes—
213C22×C4×C61C2×D412yes—
214C22×C4×C61C2×D411yescharacteristic
215C22×C4×C61C2×D411yescharacteristic
216C22×C4×C61C2412yes—
217C22×C4×C61C2412yes—
218C22×C4×C61C2411yescharacteristic
219C2×C22⋊D61—24no—
220C2×C22⋊D61—24no—
221C2×C22⋊D61—44no—
222C2×C22⋊D61—44no—
223C22×Dic61—21no—
224C22×Dic61—21no—
225C22×Dic61—24no—
226C22×Dic61—21no—
227C22×Dic61—44no—
228#11758222—28no—
229#11758222—44no—
230#11758222—48no—
231C2×D244—22no—
232C2×D244—22no—
233C2×D244—21no—
234C2×D244C2412yes—
235C2×C4×D61—24no—
236C2×C4×D61—44no—
237C2×Dic122—21no—
238C2×Dic122—22no—
239C2×Dic122—22no—
240C2×Dic122—22no—
241C2×Dic122—28no—
242C2×Dic122—24no—
243C2×Dic122—21no—
244C2×Dic122—44no—
245C2×Dic122—48no—
246C2×Dic122—44no—
247C2×Dic122#4114yes—
248C2×Dic122C2412yes—
249C2×Dic122C2412yes—
250C4⋊C4×C61—21no—
251C4⋊C4×C61—21no—
252C4⋊C4×C61—24no—
253C4⋊C4×C61—24no—
254C4⋊C4×C61—24no—
255C4⋊C4×C61—21no—
256C4⋊C4×C61C2×D414yes—
257C4⋊C4×C61C2412yes—
258C4⋊C4×C61C2412yes—
259C4⋊C4×C61C2412yes—
260C22⋊C4×C61—24no—
261C22⋊C4×C61—24no—
262C22⋊C4×C61—24no—
263C22⋊C4×C61—24no—
264C22⋊C4×C61C2×D414yes—
265C22⋊C4×C61C2×D414yes—
266C42×C61—24no—
267C42×C61C2×D412yes—
268C42×C61C2412yes—
269C22⋊Dic61—24no—
270#11758200—28no—
271#11758200—44no—
272#11758199—44no—
273#11758198—24no—
274#11758198—24no—
275#11758198—24no—
276C4⋊Dic61—21no—
277C4⋊Dic61C2412yes—
278#11758196—24no—
279#11758196—24no—
280C4×Dic61—24no—
281#11758194—44no—
282#11758194—44no—
283C2×#92418—22no—
284C2×#92418—22no—
285C2×#92418—22no—
286C2×#92418—22no—
287C2×#92418C2412yes—
288C2×#92418C2412yes—
289C2×#92418C2412yes—
290C2×#92418C2412yes—
291C23×C61—22no—
292C23×C61—22no—
293C23×C61—22no—
294C23×C61—22no—
295C23×C61—22no—
296C23×C61—22no—
297C23×C61—22no—
298C23×C61—42no—
299C23×C61—42no—
300C23×C61—42no—
301C23×C61C22×D412yes—
302C23×C61C22×D412yes—
303C23×C61C22×D411yescharacteristic
304C22×D61—22no—
305C22×D61—42no—
306C22×D61—42no—
307C22×D61—42no—
308D4×C61—22no—
309D4×C61—22no—
310D4×C61—44no—
311D4×C61—48no—
312D4×C61—42no—
313D4×C61—84no—
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×C61—22no—
325C2×C4×C61—22no—
326C2×C4×C61—22no—
327C2×C4×C61—42no—
328C2×C4×C61—42no—
329C2×C4×C61—42no—
330C2×C4×C61—84no—
331C2×C4×C61—84no—
332C2×C4×C61C22×D412yes—
333C2×C4×C61C22×D412yes—
334C2×C4×C61C22×D412yes—
335C2×C4×C61C22×D412yes—
336C2×C4×C61C22×D411yescharacteristic
337C2×C4×C61C2×#4112yes—
338C2×C4×C61H(5,𝔽2)12yes—
339C2×C4×C61C2511yescharacteristic
340C22⋊D61—48no—
341C22⋊D61—48no—
342C2×Dic61—24no—
343C2×Dic61—22no—
344C2×Dic61—22no—
345C2×Dic61—22no—
346C2×Dic61—48no—
347C2×Dic61—42no—
348C2×Dic61—42no—
349D244—22no—
350D244—22no—
351D244—42no—
352C4×D61—48no—
353Dic122—24no—
354Dic122—22no—
355Dic122—22no—
356Dic122—22no—
357Dic122—48no—
358Dic122—42no—
359Dic122C2×#4114yes—
360#92418—22no—
361#92418—22no—
362#92418—22no—
363#92418—22no—
364C2×#3326—611nomaximal, Sylow
365C22×C61—22no—
366C22×C61—22no—
367C22×C61—22no—
368C22×C61—22no—
369C22×C61—22no—
370C22×C61—22no—
371C22×C61—44no—
372C22×C61—44no—
373C22×C61—42no—
374C22×C61—42no—
375C22×C61—42no—
376C22×C61—84no—
377C22×C61#54612yes—
378C22×C61#57512yes—
379C22×C61#57712yes—
380C22×C61C23×D411yescharacteristic
381C2×D61—42no—
382C2×D61—42no—
383C2×D61—42no—
384C2×D61—84no—
385C4×C61—22no—
386C4×C61—22no—
387C4×C61—22no—
388C4×C61—22no—
389C4×C61—42no—
390C4×C61—42no—
391C4×C61—42no—
392C4×C61#54612yes—
393C4×C61C22×#4111yescharacteristic
394C4×C61C2×H(5,𝔽2)11yescharacteristic
395Dic61—24no—
396Dic61—42no—
397Dic61—42no—
398C2×#553D6111yescharacteristic, complemented
399C2×#548—611no—
400#3326—6116no—
401C2×#488—611no—
402C2×#482—611no—
403C2×#483—611no—
404C2×#479—611no—
405C2×#469—611no—
406C2×#468—611no—
407C2×#463—611no—
408C2×#449—611no—
409C2×#448—611no—
410C2×C4×SD16—611no—
411C2×#436—611no—
412C2×#417—611no—
413C2×#419—611no—
414C2×C61—42no—
415C2×C61—42no—
416C2×C61—82no—
417C2×C61#332614yescomplemented
418C2×C61C2×#54611yescharacteristic
419C2×C61C2×#57511yescharacteristic
420C2×C61C2×#57711yescharacteristic
421D61—82no—
422C22×#41—611no—
423C23×Q8—611no—
424C22×SD16—611no—
425C22×SD16—611no—
426C22×D8—611no—
427C22×M16—611no—
428C22×M16—611no—
429#553—24no—
430#553C2×D6118yescomplemented
431#548—618no—
432#548—1224no—
433C2×#126—21no—
434C2×#125C2×D6111yescharacteristic
435C2×#124—611no—
436C2×#124—1221no—
437C2×#123—21no—
438C2×C22⋊Q8—611no—
439C2×C22⋊Q8—1221no—
440C2×#121—21no—
441C2×#121—611no—
442C2×#121—1221no—
443C2×#121C2×D6111yescharacteristic
444C2×#121C2×D6111yescharacteristic
445C2×C4×Q8—611no—
446C2×C4×D4—21no—
447C2×C4×D4—1221no—
448C2×C4×D4C2×D6111yescharacteristic
449C2×C4×D4C2×D6111yescharacteristic
450C2×#117C2×D6111yescharacteristic
451C22×C4⋊C4C2×D6111yescharacteristic
452#488—618no—
453#483—618no—
454#482—618no—
455#479—618no—
456#469—618no—
457#468—618no—
458#463—618no—
459#449—618no—
460#448—618no—
461C4×SD16—618no—
462#436—618no—
463C2×#107—611no—
464C2×#106—611no—
465C2×#106—611no—
466C2×C4⋊C8—611no—
467#419—618no—
468#417—618no—
469C2×#103—611no—
470C2×#103—611no—
471C2×#103—611no—
472C2×#103—611no—
473C2×#103—611no—
474C2×#103—611no—
475C2×#102—611no—
476C2×#102—611no—
477C2×#102—611no—
478C2×#102—611no—
479C2×C22⋊C8—611no—
480C2×C22⋊C8—611no—
481C2×C4×C8—611no—
482C61C2×#332611yescharacteristic, complemented, Sylow
483C2×#41—614no—
484C2×#41—1224no—
485C2×#41—1222no—
486C2×#41—2442no—
487C22×Q8—611no—
488C22×Q8—611no—
489C22×Q8—614no—
490C22×Q8—1224no—
491C22×Q8—1221no—
492C22×Q8—1222no—
493C22×Q8—2442no—
494C22×D4—21no—
495C22×D4—21no—
496C22×D4—611no—
497C22×D4—1221no—
498C22×D4—1221no—
499C22×D4C22⋊D6111yescharacteristic
500C22×D4C22×D6111yescharacteristic
501C23×C4—21no—
502C23×C4—21no—
503C23×C4—1221no—
504C23×C4—1221no—
505C23×C4C22×D6111yescharacteristic
506C23×C4C22×D6111yescharacteristic
507C2×SD16—614no—
508C2×SD16—614no—
509C2×SD16—1224no—
510C2×SD16—2442no—
511C2×D8—614no—
512C2×D8—2442no—
513C2×M16—614no—
514C2×M16—614no—
515C2×M16—2442no—
516C2×M16—2442no—
517C22×C8—611no—
518C22×C8—611no—
519C22×C8—611no—
520C22×C8—611no—
521#126—28no—
522#125—22no—
523#125C22×D6114yes—
524#124—614no—
525#124—1228no—
526#124—1222no—
527#123—28no—
528C22⋊Q8—614no—
529C22⋊Q8—1222no—
530C22⋊Q8—1228no—
531#121—28no—
532#121—22no—
533#121—22no—
534#121—614no—
535#121—1228no—
536#121—1222no—
537#121C22×D6114yes—
538#121C22×D6114yes—
539C4×Q8—614no—
540C4×Q8—1222no—
541C4×D4—28no—
542C4×D4—22no—
543C4×D4—1228no—
544C4×D4C22⋊D6114yes—
545C4×D4C22×D6114yes—
546C4×D4C22×D6114yes—
547#117—22no—
548#117C22×D6114yes—
549C2×C4⋊C4—21no—
550C2×C4⋊C4—22no—
551C2×C4⋊C4—21no—
552C2×C4⋊C4—21no—
553C2×C4⋊C4—611no—
554C2×C4⋊C4—1221no—
555C2×C4⋊C4—1221no—
556C2×C4⋊C4C22⋊D6111yescharacteristic
557C2×C4⋊C4C22×D6111yescharacteristic
558C2×C4⋊C4C22×D6111yescharacteristic
559C2×C4⋊C4C22×D6114yes—
560C2×C4⋊C4C22×D6111yescharacteristic
561C2×C22⋊C4—21no—
562C2×C22⋊C4—21no—
563C2×C22⋊C4—21no—
564C2×C22⋊C4—21no—
565C2×C22⋊C4—1221no—
566C2×C22⋊C4—1221no—
567C2×C22⋊C4—1221no—
568C2×C22⋊C4—1221no—
569C2×C22⋊C4C22⋊D6111yescharacteristic
570C2×C22⋊C4C22⋊D6111yescharacteristic
571C2×C42—21no—
572C2×C42—1221no—
573C2×C42C22×D6111yescharacteristic
574#107—614no—
575#106—614no—
576#106—614no—
577C4⋊C8—614no—
578#103—614no—
579#103—614no—
580#103—614no—
581#103—614no—
582#103—614no—
583#103—614no—
584#102—614no—
585#102—614no—
586#102—614no—
587#102—614no—
588C22⋊C8—614no—
589C22⋊C8—614no—
590C4×C8—614no—
591C24—21no—
592C24—1221no—
593C24C2×C22⋊D6111yescharacteristic
594C24C2×C22⋊D6111yescharacteristic
595#41—1228no—
596#41—2444no—
597#41—2448no—
598C2×Q8—614no—
599C2×Q8—612no—
600C2×Q8—612no—
601C2×Q8—1228no—
602C2×Q8—1221no—
603C2×Q8—1224no—
604C2×Q8—1221no—
605C2×Q8—1222no—
606C2×Q8—1222no—
607C2×Q8—1222no—
608C2×Q8—2444no—
609C2×Q8—2444no—
610C2×Q8—2448no—
611C2×D4—24no—
612C2×D4—24no—
613C2×D4—21no—
614C2×D4—22no—
615C2×D4—22no—
616C2×D4—42no—
617C2×D4—44no—
618C2×D4—82no—
619C2×D4—612no—
620C2×D4—1224no—
621C2×D4—1224no—
622C2×D4—1221no—
623C2×D4—1222no—
624C2×D4—1222no—
625C2×D4—2444no—
626C2×D4—2444no—
627C2×D4C2×C22⋊D6114yes—
628C2×D4C23×D6112yes—
629C22×C4—22no—
630C22×C4—22no—
631C22×C4—22no—
632C22×C4—22no—
633C22×C4—21no—
634C22×C4—21no—
635C22×C4—21no—
636C22×C4—24no—
637C22×C4—24no—
638C22×C4—82no—
639C22×C4—82no—
640C22×C4—1221no—
641C22×C4—1224no—
642C22×C4—1221no—
643C22×C4—1221no—
644C22×C4—1224no—
645C22×C4—2444no—
646C22×C4—2444no—
647C22×C4C2×C22⋊D6112yes—
648C22×C4C2×C22⋊D6112yes—
649C22×C4C2×C22⋊D6111yescharacteristic
650C22×C4C2×C22⋊D6111yescharacteristic
651C22×C4C2×C22⋊D6111yescharacteristic
652C22×C4C2×C22⋊D6111yescharacteristic
653C22×C4C23×D6112yes—
654C22×C4C23×D6112yes—
655C22×C4C23×D6111yescharacteristic
656SD16—1228no—
657SD16—2444no—
658D8—2444no—
659M16—2444no—
660M16—2444no—
661C2×C8—612no—
662C2×C8—612no—
663C2×C8—612no—
664C2×C8—612no—
665C2×C8—1222no—
666C2×C8—1222no—
667C2×C8—1222no—
668C2×C8—1222no—
669C4⋊C4—21no—
670C4⋊C4—21no—
671C4⋊C4—24no—
672C4⋊C4—24no—
673C4⋊C4—24no—
674C4⋊C4—21no—
675C4⋊C4—612no—
676C4⋊C4—1221no—
677C4⋊C4—1224no—
678C4⋊C4—1224no—
679C4⋊C4C2×C22⋊D6114yes—
680C4⋊C4C23×D6112yes—
681C4⋊C4C23×D6112yes—
682C4⋊C4C23×D6112yes—
683C22⋊C4—24no—
684C22⋊C4—24no—
685C22⋊C4—24no—
686C22⋊C4—24no—
687C22⋊C4—1224no—
688C22⋊C4—1224no—
689C22⋊C4—1224no—
690C22⋊C4—1224no—
691C22⋊C4C2×C22⋊D6114yes—
692C22⋊C4C2×C22⋊D6114yes—
693C42—24no—
694C42—1224no—
695C42C2×C22⋊D6112yes—
696C42C23×D6112yes—
697C23—22no—
698C23—22no—
699C23—22no—
700C23—22no—
701C23—22no—
702C23—22no—
703C23—22no—
704C23—42no—
705C23—42no—
706C23—42no—
707C23—1222no—
708C23—2442no—
709C23—2442no—
710C23—2442no—
711C23C22×C22⋊D6112yes—
712C23C22×C22⋊D6112yes—
713C23C22×C22⋊D6111yescharacteristic
714Q8—614no—
715Q8—1222no—
716Q8—1224no—
717Q8—1222no—
718Q8—1222no—
719Q8—2448no—
720Q8—2442no—
721D4—22no—
722D4—22no—
723D4—44no—
724D4—48no—
725D4—42no—
726D4—84no—
727D4—1222no—
728D4—1222no—
729D4—2448no—
730D4—2448no—
731D4—2442no—
732C2×C4—22no—
733C2×C4—22no—
734C2×C4—22no—
735C2×C4—22no—
736C2×C4—22no—
737C2×C4—22no—
738C2×C4—22no—
739C2×C4—22no—
740C2×C4—24no—
741C2×C4—24no—
742C2×C4—22no—
743C2×C4—22no—
744C2×C4—22no—
745C2×C4—42no—
746C2×C4—42no—
747C2×C4—42no—
748C2×C4—84no—
749C2×C4—84no—
750C2×C4—1222no—
751C2×C4—1224no—
752C2×C4—1222no—
753C2×C4—1222no—
754C2×C4—2448no—
755C2×C4—2448no—
756C2×C4—2442no—
757C2×C4—2442no—
758C2×C4C22×C22⋊D6112yes—
759C2×C4C22×C22⋊D6112yes—
760C2×C4C22×C22⋊D6112yes—
761C2×C4C22×C22⋊D6112yes—
762C2×C4C22×C22⋊D6111yescharacteristic
763C2×C4#41×D6112yes—
764C2×C4#1451982312yes—
765C2×C4C24×D6111yescharacteristic
766C8—1222no—
767C8—1222no—
768C8—1222no—
769C8—1222no—
770C22—22no—
771C22—22no—
772C22—22no—
773C22—22no—
774C22—22no—
775C22—22no—
776C22—44no—
777C22—44no—
778C22—42no—
779C22—42no—
780C22—42no—
781C22—84no—
782C22—4884no—
783C22—2442no—
784C22—2442no—
785C22—2442no—
786C22#1684040012yes—
787C22#1684056012yes—
788C22#1684057312yes—
789C22C23×C22⋊D6111yescharacteristic
790C4—22no—
791C4—22no—
792C4—22no—
793C4—22no—
794C4—42no—
795C4—42no—
796C4—42no—
797C4—1224no—
798C4—2442no—
799C4—2442no—
800C4#1684040012yes—
801C4C2×#41×D6111yescharacteristic
802C4C2×#1451982311yescharacteristic
803C2—42no—
804C2—42no—
805C2—82no—
806C2—4882no—
807C2#2145806614yesdirect product factor
808C2C2×#1684040011yescharacteristic
809C2C2×#1684056011yescharacteristic
810C2C2×#1684057311yescharacteristic
subgroupG/H
centerC23C22×C22⋊D61
commutator, cosocleC2×C4×C61C25
FrattiniC2×C4C24×D61
FittingC2×C61×#553C2
socleC23×C61C22×D4
hypercenterC2×#553D61
hypocenterC61C2×#3326
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×#553

Complements

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

NH ≅ G/Ntype
1. C2×#16840421C2semidirect
2. #21458066C2direct (N × H)
3. C2×#16840119C2semidirect
4. C2×#16840086C2semidirect
5. C2×#16840092C2semidirect
6. C2×#16840066C2semidirect
7. C2×#16840013C2semidirect
8. C2×#16840006C2semidirect
9. C2×#16839977C2semidirect
10. C2×#16839905C2semidirect
11. C2×#16839900C2semidirect
12. C2×C4×#11758200C2semidirect
13. C2×#16839840C2semidirect
14. C2×#16839761C2semidirect
15. C2×#16839770C2semidirect
16. C2×C61×#553C2semidirect
25. #16840421C22semidirect
34. #16840119C22semidirect
35. #16840092C22semidirect
36. #16840086C22semidirect
37. #16840066C22semidirect
38. #16840013C22semidirect
39. #16840006C22semidirect
40. #16839977C22semidirect
41. #16839905C22semidirect
42. #16839900C22semidirect
43. C4×#11758200C22semidirect
44. #16839840C22semidirect
49. #16839770C22semidirect
50. #16839761C22semidirect
65. C61×#553C22semidirect
398. C2×#553D61semidirect
417. C2×C61#3326semidirect
430. #553C2×D61semidirect
482. C61C2×#3326semidirect
807. C2#21458066direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168404212
#214580662
C2×#168401192
C2×#168400862
C2×#168400922
C2×#168400662
C2×#168400132
C2×#168400062
C2×#168399772
C2×#168399052
C2×#168399002
C2×C4×#117582002
C2×#168398402
C2×#168397612
C2×#168397702
C2×C61×#5532
C2×#332661