Finite Group Databasebeta

← #30616317

Subgroups — #30616317

Order 15616.

1434 conjugacy classes of subgroups.

The subgroup lattice has 918 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1D61⋊#430C211yesmaximal, characteristic, complemented
2#21462439C211yesmaximal, characteristic
3C2×#16840755C211yesmaximal, characteristic, complemented
4D61⋊#413C211yesmaximal, characteristic
5C2×D61⋊#101C211yesmaximal, characteristic, complemented
6#21462382C211yesmaximal, characteristic, complemented
7#21461981C214yesmaximal, complemented
8#21461979C214yesmaximal, complemented
9C2×#137×D61C211yesmaximal, characteristic
10C2×D61⋊M16C2211yescharacteristic
11C2×D61⋊M16C2211yescharacteristic
12C2×D61⋊M16C2211yescharacteristic
13C2×#14519856C2211yescharacteristic
14#16840777—22no—
15#16840777—22no—
16D61⋊#108C2214yes—
17#16840755—22no—
18#16840755C2214yes—
19#16840755C2212yes—
20#16840754C2212yes—
21#16840753—22no—
22#16840752—22no—
23C2×#14519840—22no—
24#16840749—22no—
25#16840748—22no—
26D61⋊#101—22no—
27D61⋊#101C2214yes—
28D61⋊#101C2212yes—
29C2×#14519838—22no—
30D61⋊#100C2212yes—
31#16840728—22no—
32#16840725C2214yes—
33M16×#6923—22no—
34C2×#41×D61C2211yescharacteristic
35C22×Q8×D61C2211yescharacteristic
36C2×#14519810C411yescharacteristic, complemented
37C2×#14519809C412yescomplemented
38C2×#14519808C411yescharacteristic, complemented
39C2×#14519807C411yescharacteristic, complemented
40C2×#14519806C412yescomplemented
41#137×D61—22no—
42#137×D61—22no—
43#137×D61—22no—
44#137×D61—22no—
45C2×Q16×D61C2212yes—
46C2×SD16×D61C2212yes—
47C2×M16×D61C2211yescharacteristic
48C2×#137×C61C411yescharacteristic, complemented
49C2×#11758213—21no—
50C2×#11758213—21no—
51C2×#11758213—21no—
52D61⋊M16—21no—
53D61⋊M16—21no—
54D61⋊M16—21no—
55D61⋊M16—21no—
56D61⋊M16—21no—
57D61⋊M16—21no—
58D61⋊M16—21no—
59D61⋊M16—21no—
60D61⋊M16D412yes—
61D61⋊M16C2312yes—
62D61⋊M16C2312yes—
63D61⋊M16C2312yes—
64C2×#11758217—21no—
65C2×#11758217—21no—
66C2×#11758217D412yes—
67C2×D61⋊C8—21no—
68C2×D61⋊C8—21no—
69C2×D61⋊C8—21no—
70#14519856—21no—
71#14519856—21no—
72#14519856D412yes—
73#14519856C2312yes—
74C2×C4⋊#6923D412yes—
75C2×C22⋊#6923—21no—
76C2×C4×#6923—21no—
77#14519848—24no—
78#14519847—24no—
79#14519840—28no—
80#14519840—24no—
81#14519839—24no—
82#14519838—28no—
83#14519838—24no—
84#14519837—24no—
85#14519831—24no—
86C8×#6923—24no—
87C2×#11758226C2×C411yescharacteristic
88C2×#11758222—21no—
89C2×#11758222C2×C411yescharacteristic
90C2×#11758224—21no—
91C2×#11758224C2×C411yescharacteristic
92#41×D61—21no—
93#41×D61—21no—
94#41×D61—21no—
95#41×D61—21no—
96#41×D61—21no—
97#41×D61—21no—
98#41×D61—21no—
99#41×D61—21no—
100C22×Dic122—21no—
101C22×Dic122C2×C411yescharacteristic
102C2×Q8×D61—21no—
103C2×Q8×D61—21no—
104C2×Q8×D61—21no—
105C2×Q8×D61—21no—
106C2×Q8×D61—21no—
107C2×Q8×D61—21no—
108C2×Q8×D61—21no—
109C2×Q8×D61—21no—
110C2×Q8×D61—21no—
111C2×Q8×D61—21no—
112C2×Q8×D61C2×C412yes—
113C2×Q8×D61C2312yes—
114C2×Q8×D61C2311yescharacteristic
115C2×D4×D61—21no—
116C2×D4×D61C2311yescharacteristic
117C22×C4×D61—21no—
118C22×C4×D61—21no—
119C22×C4×D61C2311yescharacteristic
120#14519810—22no—
121#14519810—22no—
122#14519809—24no—
123#14519809—24no—
124#14519808—22no—
125#14519808—22no—
126#14519807—22no—
127#14519807—22no—
128#14519806—24no—
129#14519806—24no—
130C2×Dic244C2×C412yescomplemented
131C2×#11758202C2×C412yescomplemented
132C2×#11758202C2×C412yescomplemented
133Q16×D61—24no—
134Q16×D61—24no—
135C2×#11758190C2×C412yescomplemented
136C2×#11758200C2×C412yescomplemented
137C2×#11758201C2×C412yescomplemented
138SD16×D61—24no—
139SD16×D61—24no—
140C2×#11758194C2×C411yescharacteristic
141C2×#11758189C2×C412yes—
142M16×D61D412yes—
143M16×D61D412yes—
144M16×D61D412yes—
145M16×D61D412yes—
146C2×C8×D61C2312yes—
147C2×#41×C61C2×C411yescharacteristic
148C22×Q8×C61C2×C411yescharacteristic
149#137×C61—22no—
150#137×C61—22no—
151C2×Q16×C61C2×C412yescomplemented
152C2×SD16×C61C2×C412yescomplemented
153C2×M16×C61C2×C411yescharacteristic
154C23×D61—21no—
155C23×D61#4111yescharacteristic
156C22×#6923—22no—
157#41×C61—21no—
158#41×C61—21no—
159#41×C61—21no—
160#41×C61—21no—
161C2×Q8×C61—21no—
162C2×Q8×C61—21no—
163C2×Q8×C61—21no—
164C2×Q8×C61—21no—
165C2×Q8×C61—21no—
166C2×Q8×C61C22×C412yes—
167C2×Q8×C61C22×C411yescharacteristic
168C2×D4×C61—21no—
169C2×D4×C61C22×C411yescharacteristic
170C22×C4×C61—21no—
171C22×C4×C61—21no—
172C22×C4×C61C22×C411yescharacteristic
173C2×C22⋊D61—21no—
174C2×C22⋊D61—21no—
175C2×C22⋊D61—21no—
176C22×Dic61—21no—
177C22×Dic61—21no—
178C22×Dic61C2×D411yescharacteristic
179#11758226—21no—
180#11758226—21no—
181#11758226—21no—
182#11758226—21no—
183Q8×D61—22no—
184Q8×D61—22no—
185Q8×D61—22no—
186Q8×D61—22no—
187Q8×D61—22no—
188Q8×D61—22no—
189Q8×D61—22no—
190Q8×D61—21no—
191Q8×D61—21no—
192Q8×D61—21no—
193Q8×D61—22no—
194Q8×D61—21no—
195Q8×D61—41no—
196Q8×D61—41no—
197Q8×D61—41no—
198Q8×D61—41no—
199Q8×D61—41no—
200Q8×D61—41no—
201Q8×D61—41no—
202Q8×D61—41no—
203#11758224—21no—
204#11758224—21no—
205#11758224—21no—
206#11758224—21no—
207#11758224—41no—
208#11758224—41no—
209#11758224—41no—
210#11758224—41no—
211D4×D61—21no—
212D4×D61—21no—
213D4×D61—21no—
214D4×D61—21no—
215D4×D61—41no—
216D4×D61—41no—
217D4×D61—41no—
218D4×D61—41no—
219#11758222—21no—
220#11758222—21no—
221#11758222—21no—
222#11758222—21no—
223#11758222—41no—
224#11758222—41no—
225#11758222—41no—
226#11758222—41no—
227C2×D244—21no—
228C2×D244C22×C411yescharacteristic
229C2×C4×D61—22no—
230C2×C4×D61—21no—
231C2×C4×D61—22no—
232C2×C4×D61—21no—
233C2×C4×D61—21no—
234C2×C4×D61—41no—
235C2×C4×D61—41no—
236C2×C4×D61—41no—
237C2×C4×D61—41no—
238C2×C4×D61—41no—
239C2×C4×D61—41no—
240C2×C4×D61—41no—
241C2×C4×D61—41no—
242C2×C4×D61C22×C411yescharacteristic
243C2×C4×D61C2×D411yescharacteristic
244C2×C4×D61C2×D411yescharacteristic
245C2×C4×D61C2×D411yescharacteristic
246C2×C4×D61C2×D411yescharacteristic
247C2×C4×D61C2×D411yescharacteristic
248C2×C4×D61C2×D411yescharacteristic
249C2×C4×D61C2×D411yescharacteristic
250C2×C4×D61#4111yescharacteristic
251C2×C4×D61#4111yescharacteristic
252C2×C4×D61#4111yescharacteristic
253C2×C4×D61C2411yescharacteristic
254C2×Dic122—21no—
255C2×Dic122—21no—
256C2×Dic122—21no—
257C2×Dic122—21no—
258C2×Dic122—21no—
259C2×Dic122—22no—
260C2×Dic122—22no—
261C2×Dic122—21no—
262C2×Dic122—41no—
263C2×Dic122—41no—
264C2×Dic122—41no—
265C2×Dic122—41no—
266C2×Dic122C22×C412yes—
267C2×Dic122C22×C411yescharacteristic
268C22⋊#6923—22no—
269C22⋊#6923—22no—
270#11758217—22no—
271#11758217—22no—
272#11758217—22no—
273#11758217—41no—
274#11758217—41no—
275#11758217C2×D414yes—
276C2×#92420—22no—
277C2×#92420—41no—
278C2×#92420—41no—
279C4⋊#6923—22no—
280C4⋊#6923C2×D414yes—
281C4×#6923—22no—
282C4×#6923—22no—
283#11758213—22no—
284#11758213—22no—
285#11758213—22no—
286#11758213—22no—
287#11758213—41no—
288#11758213—41no—
289D61⋊C8—22no—
290D61⋊C8—22no—
291D61⋊C8—22no—
292D61⋊C8—22no—
293D61⋊C8—41no—
294D61⋊C8—41no—
295Q16×C61—24no—
296SD16×C61—24no—
297M16×C61C22⋊C412yes—
298M16×C61C22⋊C412yes—
299C2×C8×C61C22×C412yes—
300#11758202—24no—
301#11758202—24no—
302#11758201—24no—
303#11758200—24no—
304#11758194C22⋊C412yes—
305#11758194C22⋊C412yes—
306C2×#92418C22×C412yes—
307Dic244—24no—
308#11758190—24no—
309#11758189C22⋊C414yes—
310#11758189C22⋊C414yes—
311C8×D61C2×D414yes—
312C8×D61C2×D414yes—
313C23×C61—21no—
314C23×C61C4×D411yescharacteristic
315C22×D61—21no—
316C22×D61—42no—
317C22×D61—41no—
318C22×D61—41no—
319C22×D61—82no—
320C22×D61C4×D411yescharacteristic
321C22×D61#12111yescharacteristic
322C22×D61#12111yescharacteristic
323C22×D61#12411yescharacteristic
324C22×D61#12411yescharacteristic
325C22×D61C2×#4111yescharacteristic
326C2×#6923—24no—
327C2×#6923—82no—
328Q8×C61—22no—
329Q8×C61—21no—
330Q8×C61—22no—
331Q8×C61—21no—
332Q8×C61—41no—
333Q8×C61—41no—
334D4×C61—21no—
335D4×C61—21no—
336D4×C61—41no—
337D4×C61—41no—
338C2×C4×C61—22no—
339C2×C4×C61—21no—
340C2×C4×C61—41no—
341C2×C4×C61—41no—
342C2×C4×C61—41no—
343C2×C4×C61—41no—
344C2×C4×C61C2×C22⋊C411yescharacteristic
345C2×C4×C61C2×C22⋊C411yescharacteristic
346C2×C4×C61C4×D411yescharacteristic
347C2×C4×C61C4×D411yescharacteristic
348C2×C4×C61C4×D411yescharacteristic
349C2×C4×C61C23×C411yescharacteristic
350C22⋊D61—41no—
351C22⋊D61—41no—
352C22⋊D61—41no—
353C22⋊D61—41no—
354C22⋊D61—41no—
355C22⋊D61—41no—
356C2×Dic61—22no—
357C2×Dic61—21no—
358C2×Dic61—41no—
359C2×Dic61—41no—
360C2×Dic61—41no—
361C2×Dic61—41no—
362C2×Dic61C4×D411yescharacteristic
363C2×Dic61#12111yescharacteristic
364C2×Dic61#12111yescharacteristic
365C2×Dic61#12711yescharacteristic
366C2×Dic61#12711yescharacteristic
367C2×Dic61C22×D411yescharacteristic
368D244—21no—
369D244—21no—
370D244—41no—
371D244—41no—
372C4×D61—41no—
373C4×D61—42no—
374C4×D61—41no—
375C4×D61—42no—
376C4×D61—42no—
377C4×D61—42no—
378C4×D61—41no—
379C4×D61—41no—
380C4×D61—41no—
381C4×D61—41no—
382C4×D61C2×C22⋊C411yescharacteristic
383C4×D61C2×C22⋊C411yescharacteristic
384C4×D61C4×D411yescharacteristic
385C4×D61C4×D411yescharacteristic
386C4×D61#12111yescharacteristic
387C4×D61#12111yescharacteristic
388C4×D61#12111yescharacteristic
389C4×D61#12111yescharacteristic
390C4×D61#12411yescharacteristic
391C4×D61#12411yescharacteristic
392C4×D61#12711yescharacteristic
393C4×D61#12711yescharacteristic
394C4×D61C22×D411yescharacteristic
395C4×D61C22×D411yescharacteristic
396C4×D61C22×D411yescharacteristic
397C4×D61C2×#4111yescharacteristic
398Dic122—22no—
399Dic122—21no—
400Dic122—22no—
401Dic122—21no—
402Dic122—41no—
403Dic122—41no—
404Dic122—42no—
405Dic122—41no—
406Dic122—42no—
407Dic122—41no—
408Dic122—42no—
409Dic122—42no—
410#92420—24no—
411#92420—42no—
412#92420—42no—
413C8×C61C2×C22⋊C414yes—
414#92418C2×C22⋊C414yes—
415#21250—611nomaximal, Sylow
416C22×C61—41no—
417C22×C61—41no—
418C22×C61—81no—
419C22×C61#39011yescharacteristic
420C22×C61#39011yescharacteristic
421C22×C61C2×C4×D411yescharacteristic
422C2×D61—22no—
423C2×D61—22no—
424C2×D61—22no—
425C2×D61—41no—
426C2×D61—41no—
427C2×D61—41no—
428C2×D61—41no—
429C2×D61—82no—
430C2×D61—82no—
431C2×D61—81no—
432C2×D61#39011yescharacteristic
433C2×D61#39011yescharacteristic
434C2×D61C2×#12111yescharacteristic
435C2×D61C2×#12411yescharacteristic
436#6923—44no—
437C4×C61—42no—
438C4×C61—41no—
439C4×C61#39011yescharacteristic
440C4×C61#39011yescharacteristic
441C4×C61C22×C22⋊C411yescharacteristic
442C4×C61C2×C4×D411yescharacteristic
443Dic61—42no—
444Dic61—41no—
445Dic61#39011yescharacteristic
446Dic61#39011yescharacteristic
447Dic61C2×#12111yescharacteristic
448Dic61C2×#12711yescharacteristic
449C22×#137—611no—
450C2×#430—611no—
451#2896—611no—
452C2×#419—611no—
453C2×#413—611no—
454C22×#101—611no—
455#2873—611no—
456#1979—614no—
457#1977—614no—
458C2×C61—21no—
459C2×C61—21no—
460C2×C61—21no—
461C2×C61—81no—
462C2×C61C2×#39011yescharacteristic
463D61—21no—
464D61—21no—
465D61—21no—
466D61—81no—
467D61#306912yes—
468C22×#41—611no—
469C23×Q8—611no—
470C2×#137—611no—
471C2×#137—611no—
472C2×#137—612no—
473C2×#137—612no—
474C2×#137—611no—
475C2×#137—1222no—
476C2×#137—1222no—
477C2×#137—1222no—
478C2×#137—1222no—
479C2×#137#692311yescharacteristic, complemented
480C22×Q16—612no—
481C22×SD16—612no—
482C22×M16—611no—
483C22×M16—611no—
484C22×M16—611no—
485C22×M16—611no—
486C2×#117—611no—
487#430—1222no—
488#430—1222no—
489C2×#108—614no—
490#419—614no—
491#419—612no—
492#419—1222no—
493#418—612no—
494#417—1222no—
495#416—1222no—
496C2×#103—1222no—
497#413—1222no—
498#413—1222no—
499C2×#101—614no—
500C2×#101—612no—
501C2×#101—1222no—
502C2×#101—1222no—
503C2×#100—612no—
504#405—614no—
505#405—1222no—
506C4×M16—1222no—
507C61#2125011yescharacteristic, complemented, Sylow
508C2×#41—611no—
509C2×#41—611no—
510C2×#41—611no—
511C2×#41—1221no—
512C2×#41—1221no—
513C2×#41—1221no—
514C2×#41—1221no—
515C2×#41—1221no—
516C2×#41—1221no—
517C2×#41—1221no—
518C2×#41—1221no—
519C2×#41—1221no—
520C2×#41—1221no—
521C2×#41C2×#692311yescharacteristic
522C22×Q8—612no—
523C22×Q8—612no—
524C22×Q8—611no—
525C22×Q8—611no—
526C22×Q8—1221no—
527C22×Q8—1221no—
528C22×Q8—1221no—
529C22×Q8—1221no—
530C22×Q8—1221no—
531C22×Q8—1221no—
532C22×Q8—1221no—
533C22×Q8—1221no—
534C22×Q8—1221no—
535C22×Q8—1221no—
536C22×Q8—1221no—
537C22×Q8C2×#692311yescharacteristic
538C22×D4—611no—
539C22×D4—1221no—
540C23×C4—611no—
541C23×C4—1221no—
542C23×C4—1221no—
543#137—22no—
544#137—22no—
545#137—1224no—
546#137—1224no—
547#137—1224no—
548#137—1224no—
549#137—1222no—
550#137—1222no—
551#137—1222no—
552#137—1222no—
553#137—1222no—
554#137—1222no—
555C2×Q16—612no—
556C2×Q16—612no—
557C2×Q16—612no—
558C2×Q16—1224no—
559C2×Q16—1224no—
560C2×Q16C2×#692312yescomplemented
561C2×SD16—612no—
562C2×SD16—612no—
563C2×SD16—612no—
564C2×SD16—1224no—
565C2×SD16—1224no—
566C2×SD16C2×#692312yescomplemented
567C2×M16—611no—
568C2×M16—612no—
569C2×M16—612no—
570C2×M16—612no—
571C2×M16—612no—
572C2×M16—612no—
573C2×M16—612no—
574C2×M16—612no—
575C2×M16—612no—
576C2×M16—612no—
577C2×M16—612no—
578C2×M16—1221no—
579C2×M16—1221no—
580C2×M16—1221no—
581C2×M16—1221no—
582C2×M16—1221no—
583C2×M16—1221no—
584C2×M16—1221no—
585C2×M16—1221no—
586C2×M16—1221no—
587C2×M16—1221no—
588C2×M16—1221no—
589C2×M16—1221no—
590C2×M16—1221no—
591C2×M16C2×#692311yescharacteristic
592C22×C8—612no—
593C22×C8—1221no—
594C22×C8—1221no—
595C22×C8—1221no—
596#117—612no—
597#117—612no—
598#117—1221no—
599#117—1221no—
600C2×C4⋊C4—612no—
601C2×C22⋊C4—1221no—
602C2×C42—1221no—
603#108—1224no—
604#108—1224no—
605#103—1228no—
606#103—1224no—
607#102—1224no—
608#101—1228no—
609#101—1224no—
610#100—1224no—
611#97—1224no—
612C4×C8—1224no—
613C24—611no—
614C24—1221no—
615#41—21no—
616#41—21no—
617#41—21no—
618#41—21no—
619#41—1221no—
620#41—1221no—
621#41—1221no—
622#41—1221no—
623#41—1221no—
624#41—1221no—
625#41—1221no—
626#41—1221no—
627#41—1221no—
628#41—1221no—
629#41—1221no—
630#41—1221no—
631#41—2441no—
632#41—2441no—
633#41—2441no—
634#41—2441no—
635#41—2441no—
636#41—2441no—
637#41—2441no—
638#41—2441no—
639C2×Q8—21no—
640C2×Q8—21no—
641C2×Q8—21no—
642C2×Q8—21no—
643C2×Q8—21no—
644C2×Q8—612no—
645C2×Q8—611no—
646C2×Q8—1222no—
647C2×Q8—1221no—
648C2×Q8—1222no—
649C2×Q8—1222no—
650C2×Q8—1221no—
651C2×Q8—1222no—
652C2×Q8—1222no—
653C2×Q8—1221no—
654C2×Q8—1221no—
655C2×Q8—1222no—
656C2×Q8—1222no—
657C2×Q8—1222no—
658C2×Q8—1222no—
659C2×Q8—1222no—
660C2×Q8—1221no—
661C2×Q8—1221no—
662C2×Q8—1221no—
663C2×Q8—1221no—
664C2×Q8—1221no—
665C2×Q8—1221no—
666C2×Q8—2441no—
667C2×Q8—2441no—
668C2×Q8—2441no—
669C2×Q8—2441no—
670C2×Q8—2441no—
671C2×Q8—2441no—
672C2×Q8—2441no—
673C2×Q8—2441no—
674C2×Q8—2441no—
675C2×Q8—2441no—
676C2×Q8—2441no—
677C2×Q8—2441no—
678C2×Q8C22×#692312yes—
679C2×Q8C22×#692311yescharacteristic
680C2×D4—21no—
681C2×D4—611no—
682C2×D4—1221no—
683C2×D4—1221no—
684C2×D4—1221no—
685C2×D4—1221no—
686C2×D4—1221no—
687C2×D4—1221no—
688C2×D4—1221no—
689C2×D4—1221no—
690C2×D4—2441no—
691C2×D4—2441no—
692C2×D4—2441no—
693C2×D4—2441no—
694C2×D4C22×#692311yescharacteristic
695C22×C4—21no—
696C22×C4—21no—
697C22×C4—611no—
698C22×C4—611no—
699C22×C4—611no—
700C22×C4—611no—
701C22×C4—611no—
702C22×C4—611no—
703C22×C4—611no—
704C22×C4—611no—
705C22×C4—611no—
706C22×C4—611no—
707C22×C4—611no—
708C22×C4—611no—
709C22×C4—611no—
710C22×C4—1221no—
711C22×C4—1221no—
712C22×C4—1222no—
713C22×C4—1222no—
714C22×C4—1221no—
715C22×C4—1222no—
716C22×C4—1221no—
717C22×C4—1221no—
718C22×C4—2441no—
719C22×C4—2441no—
720C22×C4—2441no—
721C22×C4—2441no—
722C22×C4—2441no—
723C22×C4—2441no—
724C22×C4—2441no—
725C22×C4—2441no—
726C22×C4C22×#692311yescharacteristic
727Q16—24no—
728Q16—1224no—
729Q16—1224no—
730Q16—1224no—
731SD16—24no—
732SD16—1224no—
733SD16—1224no—
734SD16—1224no—
735M16—612no—
736M16—612no—
737M16—614no—
738M16—614no—
739M16—614no—
740M16—1222no—
741M16—1222no—
742M16—1222no—
743M16—1222no—
744M16—1222no—
745M16—1222no—
746M16—1222no—
747M16—2441no—
748M16—2441no—
749M16—2441no—
750M16—2441no—
751M16C22⋊#692312yes—
752M16C22⋊#692312yes—
753C2×C8—612no—
754C2×C8—614no—
755C2×C8—614no—
756C2×C8—1222no—
757C2×C8—1222no—
758C2×C8—1222no—
759C2×C8—1222no—
760C2×C8—1222no—
761C2×C8—2441no—
762C2×C8—2441no—
763C2×C8—2441no—
764C2×C8—2441no—
765C2×C8C22×#692312yes—
766C4⋊C4—614no—
767C4⋊C4—1222no—
768C22⋊C4—1222no—
769C22⋊C4—1222no—
770C42—1222no—
771C42—1222no—
772C23—21no—
773C23—611no—
774C23—611no—
775C23—611no—
776C23—611no—
777C23—611no—
778C23—611no—
779C23—1221no—
780C23—4882no—
781C23—2441no—
782C23—2441no—
783C23—2442no—
784C23D4×#692311yescharacteristic
785Q8—22no—
786Q8—21no—
787Q8—22no—
788Q8—21no—
789Q8—41no—
790Q8—41no—
791Q8—1222no—
792Q8—1221no—
793Q8—1222no—
794Q8—1221no—
795Q8—2442no—
796Q8—2442no—
797Q8—2442no—
798Q8—2442no—
799Q8—2441no—
800Q8—2441no—
801Q8—2441no—
802Q8—2441no—
803D4—21no—
804D4—21no—
805D4—41no—
806D4—41no—
807D4—1221no—
808D4—1221no—
809D4—2441no—
810D4—2441no—
811D4—2441no—
812D4—2441no—
813D4—2441no—
814D4—2441no—
815D4—2441no—
816D4—2441no—
817C2×C4—21no—
818C2×C4—22no—
819C2×C4—41no—
820C2×C4—41no—
821C2×C4—41no—
822C2×C4—41no—
823C2×C4—611no—
824C2×C4—611no—
825C2×C4—611no—
826C2×C4—611no—
827C2×C4—611no—
828C2×C4—611no—
829C2×C4—611no—
830C2×C4—611no—
831C2×C4—611no—
832C2×C4—611no—
833C2×C4—611no—
834C2×C4—611no—
835C2×C4—611no—
836C2×C4—611no—
837C2×C4—611no—
838C2×C4—611no—
839C2×C4—611no—
840C2×C4—611no—
841C2×C4—611no—
842C2×C4—611no—
843C2×C4—611no—
844C2×C4—611no—
845C2×C4—1224no—
846C2×C4—1221no—
847C2×C4—1222no—
848C2×C4—4882no—
849C2×C4—2441no—
850C2×C4—2441no—
851C2×C4—2441no—
852C2×C4—2441no—
853C2×C4—2442no—
854C2×C4—2442no—
855C2×C4—2442no—
856C2×C4—2442no—
857C2×C4—2441no—
858C2×C4—2441no—
859C2×C4—2441no—
860C2×C4—2441no—
861C2×C4—2441no—
862C2×C4—2441no—
863C2×C4C2×C22⋊#692311yescharacteristic
864C2×C4C2×C22⋊#692311yescharacteristic
865C2×C4D4×#692311yescharacteristic
866C2×C4D4×#692311yescharacteristic
867C2×C4D4×#692311yescharacteristic
868C2×C4C23×#692311yescharacteristic
869C8—614no—
870C8—1224no—
871C8—2442no—
872C8—2442no—
873C8C2×C22⋊#692314yes—
874C22—41no—
875C22—41no—
876C22—81no—
877C22—611no—
878C22—611no—
879C22—611no—
880C22—611no—
881C22—1222no—
882C22—1222no—
883C22—1222no—
884C22—4881no—
885C22—4882no—
886C22—4882no—
887C22—2441no—
888C22—2441no—
889C22—2441no—
890C22—2441no—
891C22#1684071411yescharacteristic
892C22#1684071411yescharacteristic
893C22C2×D4×#692311yescharacteristic
894C4—41no—
895C4—42no—
896C4—611no—
897C4—611no—
898C4—611no—
899C4—611no—
900C4—2444no—
901C4—2441no—
902C4—2442no—
903C4#1684071411yescharacteristic
904C4#1684071411yescharacteristic
905C4C22×C22⋊#692311yescharacteristic
906C4C2×D4×#692311yescharacteristic
907C2—21no—
908C2—21no—
909C2—21no—
910C2—81no—
911C2—612no—
912C2—1221no—
913C2—1221no—
914C2—1221no—
915C2—4881no—
916C2C2×#1684071411yescharacteristic
subgroupG/H
centerC2C2×#16840714
commutatorC2×C4×C61C23×C4
FrattiniC2×C4C23×#6923
FittingC2×#137×C61C4
socleC2×C61C2×#390
prime radicalC2×#41×D61C22
cosocleC2×C4×D61C24
hypercenterC2×#137#6923
hypocenterC61#21250
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2 ◁ C22×C4 ◁ C2×#137

Complements

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

NH ≅ G/Ntype
1. D61⋊#430C2semidirect
3. C2×#16840755C2semidirect
5. C2×D61⋊#101C2semidirect
6. #21462382C2semidirect
7. #21461981C2semidirect
8. #21461979C2semidirect
36. C2×#14519810C4semidirect
37. C2×#14519809C4semidirect
38. C2×#14519808C4semidirect
39. C2×#14519807C4semidirect
40. C2×#14519806C4semidirect
48. C2×#137×C61C4semidirect
130. C2×Dic244C2×C4semidirect
131. C2×#11758202C2×C4semidirect
132. C2×#11758202C2×C4semidirect
135. C2×#11758190C2×C4semidirect
136. C2×#11758200C2×C4semidirect
137. C2×#11758201C2×C4semidirect
151. C2×Q16×C61C2×C4semidirect
152. C2×SD16×C61C2×C4semidirect
479. C2×#137#6923semidirect
507. C61#21250semidirect
560. C2×Q16C2×#6923semidirect
566. C2×SD16C2×#6923semidirect

Maximal subgroups

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

subgroupindex
D61⋊#4302
#214624392
C2×#168407552
D61⋊#4132
C2×D61⋊#1012
#214623822
#214619812
#214619792
C2×#137×D612
#2125061