Finite Group Databasebeta

← #30617100

Subgroups — #30617100

Order 15616.

906 conjugacy classes of subgroups.

The subgroup lattice has 880 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#137×#6923C211yesmaximal, characteristic, complemented
2AGL(1,ℤ/8)×#6923C211yesmaximal, characteristic
3C2×#16840801C211yesmaximal, characteristic, complemented
4#21462389C211yesmaximal, characteristic, complemented
5#21461979C211yesmaximal, characteristic, complemented
6#21461937C211yesmaximal, characteristic, complemented
7#21461905C211yesmaximal, characteristic, complemented
8#21461904C211yesmaximal, characteristic, complemented
9#21461859C211yesmaximal, characteristic, complemented
10#21461858C211yesmaximal, characteristic
11#21461708C211yesmaximal, characteristic, complemented
12#21461640C211yesmaximal, characteristic, complemented
13#101×#6923C211yesmaximal, characteristic, complemented
14#100×#6923C211yesmaximal, characteristic, complemented
15#471×D61C211yesmaximal, characteristic
16D61⋊#131C2211yescharacteristic
17#41×#6923C2211yescharacteristic
18C2×Q8×#6923C2211yescharacteristic
19C2×D4×#6923C2211yescharacteristic
20#16840803—21no—
21#16840802—21no—
22#16840801—21no—
23#16840801—21no—
24#16840801—21no—
25#16840801—21no—
26#16840801—21no—
27#16840801—21no—
28Q16×#6923—21no—
29SD16×#6923—21no—
30SD16×#6923—21no—
31D8×#6923—21no—
32D61⋊#108C2211yescharacteristic
33#16840773C2211yescharacteristic
34#16840773C2211yescharacteristic
35C2×#14519846C2211yescharacteristic
36#16840755C2211yescharacteristic
37#16840754C2211yescharacteristic
38#16840753C2211yescharacteristic
39#16840753C2211yescharacteristic
40C2×#14519840C2211yescharacteristic
41C2×#14519839C2211yescharacteristic
42D61⋊#101C2211yescharacteristic
43D61⋊#100C2211yescharacteristic
44#16840728—21no—
45#16840728C2211yescharacteristic
46#16840725—21no—
47#16840725C2211yescharacteristic
48M16×#6923—21no—
49M16×#6923C2211yescharacteristic
50M16×#6923C2211yescharacteristic
51M16×#6923C2211yescharacteristic
52C2×#14519831—21no—
53C2×#14519831C2211yescharacteristic
54#16840641C2211yescharacteristic
55#16840641C2211yescharacteristic
56#16840641C2211yescharacteristic
57#16840641C2211yescharacteristic
58#16840637C2211yescharacteristic
59#16840637C2211yescharacteristic
60#137×D61C2211yescharacteristic
61AGL(1,ℤ/8)×D61C2211yescharacteristic
62C2×SD16×D61C2211yescharacteristic
63#131×D61C2211yescharacteristic
64#16840028C411yescharacteristic, complemented
65#16840027C411yescharacteristic, complemented
66#16840026C411yescharacteristic, complemented
67#16840025C411yescharacteristic, complemented
68#16840024C411yescharacteristic, complemented
69#16840023C411yescharacteristic, complemented
70#16840022C411yescharacteristic, complemented
71#108×D61C2211yescharacteristic
72#101×D61C2211yescharacteristic
73#100×D61C2211yescharacteristic
74C61×#471C411yescharacteristic, complemented
75C23×#6923—21no—
76#14519865—21no—
77#14519864—21no—
78#14519864—22no—
79D61⋊M16—21no—
80D61⋊M16C2311yescharacteristic
81D61⋊M16C2311yescharacteristic
82D61⋊M16C2311yescharacteristic
83C2×D61⋊C8—21no—
84C2×D61⋊C8C2311yescharacteristic
85Q8×#6923—21no—
86Q8×#6923—21no—
87Q8×#6923—21no—
88Q8×#6923—21no—
89Q8×#6923D411yescharacteristic
90Q8×#6923D411yescharacteristic
91D4×#6923—21no—
92D4×#6923—21no—
93D4×#6923—21no—
94D4×#6923—21no—
95D4×#6923—21no—
96D4×#6923—21no—
97D4×#6923D411yescharacteristic
98D4×#6923D411yescharacteristic
99#14519856—21no—
100#14519856C2311yescharacteristic
101C2×C4⋊#6923—21no—
102C2×C4⋊#6923C2311yescharacteristic
103C2×C4⋊#6923C2311yescharacteristic
104C2×C22⋊#6923—21no—
105C2×C4×#6923—21no—
106C2×C4×#6923—21no—
107C2×C4×#6923C2311yescharacteristic
108#14519848—21no—
109#14519847—21no—
110#14519846—21no—
111#14519846—21no—
112#14519846—21no—
113#14519846—21no—
114#14519845—21no—
115#14519845—21no—
116#14519840—21no—
117#14519840—21no—
118#14519840—21no—
119#14519840—21no—
120#14519840—21no—
121#14519840—21no—
122#14519839—21no—
123#14519839—21no—
124#14519839—21no—
125#14519839—21no—
126#14519839—21no—
127#14519839—21no—
128#14519838—22no—
129#14519837—22no—
130#14519831—21no—
131#14519831—21no—
132#14519831—21no—
133#14519831—21no—
134#14519831—21no—
135#14519831D411yescharacteristic
136#14519831D411yescharacteristic
137#14519831D411yescharacteristic
138#14519831D411yescharacteristic
139C8×#6923—21no—
140C8×#6923—21no—
141C8×#6923—21no—
142C8×#6923—21no—
143C8×#6923—21no—
144#41×D61C2311yescharacteristic
145C2×Q8×D61C2311yescharacteristic
146C2×D4×D61C2311yescharacteristic
147#14519810C2×C411yescharacteristic, complemented
148#14519809—21no—
149#14519808C2×C411yescharacteristic, complemented
150#14519807C2×C411yescharacteristic, complemented
151#14519806—21no—
152#14519805C2×C411yescharacteristic
153#14519804—21no—
154#14519803C2×C411yescharacteristic
155#14519802C2×C411yescharacteristic
156#14519801—21no—
157Q16×D61—21no—
158C2×#11758190C2×C411yescharacteristic, complemented
159C2×#11758200C2×C411yescharacteristic, complemented
160C2×#11758201C2×C411yescharacteristic, complemented
161SD16×D61—21no—
162SD16×D61—21no—
163SD16×D61—21no—
164SD16×D61—21no—
165SD16×D61—21no—
166SD16×D61—21no—
167D8×D61—21no—
168#14519785—21no—
169#14519785C2×C411yescharacteristic, complemented
170#14519784C2×C411yescharacteristic, complemented
171#14519783—21no—
172#14519783C2×C411yescharacteristic, complemented
173M16×D61—21no—
174M16×D61C2311yescharacteristic
175M16×D61C2311yescharacteristic
176M16×D61C2311yescharacteristic
177C2×C8×D61—21no—
178C2×C8×D61C2311yescharacteristic
179#14519713C2×C411yescharacteristic, complemented
180#14519712C2×C411yescharacteristic, complemented
181#14519712C2×C411yescharacteristic, complemented
182#14519696C2×C411yescharacteristic, complemented
183#14519695C2×C411yescharacteristic, complemented
184#14519695C2×C411yescharacteristic, complemented
185#14519694C2×C411yescharacteristic, complemented
186#14519693C2×C411yescharacteristic, complemented
187#14519693C2×C411yescharacteristic, complemented
188#137×C61C2×C411yescharacteristic, complemented
189AGL(1,ℤ/8)×C61C2×C411yescharacteristic
190C2×SD16×C61C2×C411yescharacteristic, complemented
191#131×C61C2×C411yescharacteristic, complemented
192#108×C61C2×C411yescharacteristic, complemented
193#101×C61C2×C411yescharacteristic, complemented
194#100×C61C2×C411yescharacteristic, complemented
195C23×D61—21no—
196C22×#6923—21no—
197C22×#6923—21no—
198C22×#6923—21no—
199C22×#6923—21no—
200C22×#6923—41no—
201C22×#6923—41no—
202C22×#6923—82no—
203C22×#6923#4111yescharacteristic
204C22×#6923#4111yescharacteristic
205#41×C61C22×C411yescharacteristic
206C2×Q8×C61C22×C411yescharacteristic
207C2×D4×C61C22×C411yescharacteristic
208C2×C22⋊D61—21no—
209#11758226#4111yescharacteristic
210Q8×D61—21no—
211Q8×D61—21no—
212Q8×D61—21no—
213Q8×D61—21no—
214Q8×D61C2×D411yescharacteristic
215#11758224—21no—
216#11758224#4111yescharacteristic
217D4×D61—21no—
218D4×D61—21no—
219D4×D61—21no—
220D4×D61—21no—
221D4×D61—21no—
222D4×D61C2×D411yescharacteristic
223#11758222—21no—
224#11758222C22×C411yescharacteristic
225C2×D244C22×C411yescharacteristic
226C2×C4×D61—21no—
227C2×C4×D61—21no—
228C2×C4×D61C2411yescharacteristic
229C2×Dic122—21no—
230C2×Dic122C22×C411yescharacteristic
231C22⋊#6923—21no—
232C22⋊#6923—21no—
233C22⋊#6923—21no—
234C22⋊#6923—41no—
235C22⋊#6923—41no—
236#11758217—22no—
237#11758217—21no—
238#11758217—21no—
239#11758217#4112yes—
240C2×#92420—22no—
241C2×#92420—21no—
242C4⋊#6923—21no—
243C4⋊#6923—21no—
244C4⋊#6923—21no—
245C4⋊#6923—21no—
246C4⋊#6923—21no—
247C4⋊#6923—21no—
248C4⋊#6923—41no—
249C4⋊#6923—41no—
250C4⋊#6923C2×D411yescharacteristic
251C4⋊#6923C2×D411yescharacteristic
252C4×#6923—21no—
253C4×#6923—21no—
254C4×#6923—21no—
255C4×#6923—41no—
256C4×#6923—41no—
257C4×#6923C2×D411yescharacteristic
258C4×#6923C2×D411yescharacteristic
259C4×#6923C2×D411yescharacteristic
260C4×#6923C2×D411yescharacteristic
261#11758213—22no—
262#11758213—21no—
263#11758213—21no—
264#11758213—21no—
265D61⋊C8—22no—
266D61⋊C8—21no—
267D61⋊C8—21no—
268D61⋊C8—21no—
269D61⋊C8—21no—
270D61⋊C8C2×D411yescharacteristic
271D61⋊C8C2×D411yescharacteristic
272Q16×C61—21no—
273SD16×C61—21no—
274SD16×C61—21no—
275SD16×C61—21no—
276SD16×C61—21no—
277D8×C61—21no—
278M16×C61—21no—
279M16×C61C22×C411yescharacteristic
280M16×C61C22×C411yescharacteristic
281M16×C61C22×C411yescharacteristic
282C2×C8×C61—21no—
283C2×C8×C61C22×C411yescharacteristic
284#11758202—21no—
285#11758202—21no—
286#11758201—21no—
287#11758201—21no—
288#11758201—21no—
289#11758201—21no—
290#11758200—21no—
291#11758200—21no—
292#11758200—21no—
293#11758200—21no—
294#11758199—21no—
295#11758199—21no—
296#11758194—21no—
297#11758194C22×C411yescharacteristic
298#11758194C22×C411yescharacteristic
299#11758194C22×C411yescharacteristic
300C2×#92418—21no—
301C2×#92418C22×C411yescharacteristic
302Dic244—21no—
303D488—21no—
304#11758190—21no—
305#11758190—21no—
306#11758190—21no—
307#11758190—21no—
308#11758189—21no—
309#11758189—21no—
310#11758189—21no—
311#11758189—21no—
312#11758189—21no—
313C8×D61—21no—
314C8×D61—21no—
315C8×D61—21no—
316C8×D61—21no—
317C8×D61—21no—
318C8×D61C2×D411yescharacteristic
319C8×D61C2×D411yescharacteristic
320C8×D61#4111yescharacteristic
321C8×D61#4111yescharacteristic
322C23×C61—21no—
323C22×D61—21no—
324C22×D61—21no—
325C22×D61—41no—
326C22×D61—41no—
327C22×D61—81no—
328C22×D61—81no—
329C22×D61C2×#4111yescharacteristic
330C2×#6923—21no—
331C2×#6923—21no—
332C2×#6923—41no—
333C2×#6923—41no—
334C2×#6923—41no—
335C2×#6923—41no—
336C2×#6923—81no—
337C2×#6923—81no—
338C2×#6923—82no—
339C2×#6923—82no—
340C2×#6923—81no—
341C2×#6923—81no—
342C2×#6923#12111yescharacteristic
343C2×#6923#12111yescharacteristic
344C2×#6923#12111yescharacteristic
345C2×#6923#12111yescharacteristic
346Q8×C61—21no—
347Q8×C61—21no—
348Q8×C61C4×D411yescharacteristic
349D4×C61—21no—
350D4×C61—21no—
351D4×C61—21no—
352D4×C61C4×D411yescharacteristic
353C2×C4×C61—21no—
354C2×C4×C61—21no—
355C2×C4×C61C23×C411yescharacteristic
356C22⋊D61—21no—
357C22⋊D61—21no—
358C22⋊D61—21no—
359C22⋊D61—41no—
360C22⋊D61—41no—
361C2×Dic61—21no—
362C2×Dic61—21no—
363C2×Dic61C2×#4111yescharacteristic
364D244—21no—
365D244—21no—
366D244—21no—
367D244C4×D411yescharacteristic
368C4×D61—21no—
369C4×D61—21no—
370C4×D61—21no—
371C4×D61—41no—
372C4×D61—41no—
373C4×D61C22×D411yescharacteristic
374C4×D61C22×D411yescharacteristic
375C4×D61C2×#4111yescharacteristic
376C4×D61C2×#4111yescharacteristic
377Dic122—21no—
378Dic122—21no—
379Dic122—21no—
380Dic122—41no—
381Dic122—41no—
382Dic122C4×D411yescharacteristic
383#92420—21no—
384#92420—22no—
385#92420—21no—
386#92420—41no—
387#92420—41no—
388C8×C61—21no—
389C8×C61—21no—
390C8×C61—21no—
391C8×C61C4×D411yescharacteristic
392C8×C61C4×D411yescharacteristic
393#92418—21no—
394#92418—21no—
395#92418—21no—
396#92418C4×D411yescharacteristic
397#92418C4×D411yescharacteristic
398#21557—611nomaximal, Sylow
399C22×C61—21no—
400C22×C61—41no—
401C22×C61—81no—
402C22×C61C4×#4111yescharacteristic
403C2×D61—21no—
404C2×D61—21no—
405C2×D61—21no—
406C2×D61—41no—
407C2×D61—41no—
408C2×D61—41no—
409C2×D61—82no—
410C2×D61—81no—
411C2×D61—81no—
412C2×D61—81no—
413C2×D61C2×#12111yescharacteristic
414C2×D61#52911yescharacteristic
415#6923—21no—
416#6923—21no—
417#6923—21no—
418#6923—21no—
419#6923—41no—
420#6923—41no—
421#6923—81no—
422#6923—81no—
423C4×C61—21no—
424C4×C61—41no—
425C4×C61C2×C4×D411yescharacteristic
426C4×C61C2×C4×D411yescharacteristic
427Dic61—21no—
428Dic61—41no—
429Dic61#52511yescharacteristic
430Dic61#53211yescharacteristic
431C2×#471—611no—
432C4×#137—611no—
433C4×AGL(1,ℤ/8)—611no—
434C2×#440—611no—
435#2875—611no—
436#1977—611no—
437#1952—611no—
438#1931—611no—
439#1930—611no—
440#1908—611no—
441#1907—611no—
442#1816—611no—
443#1778—611no—
444C4×#101—611no—
445C4×#100—611no—
446C2×C61—21no—
447C2×C61—41no—
448C2×C61—81no—
449C2×C61C4×#12111yescharacteristic
450D61—21no—
451D61—41no—
452D61—81no—
453D61#306811yescharacteristic
454D61#306911yescharacteristic
455C2×#137—611no—
456C2×AGL(1,ℤ/8)—611no—
457C22×SD16—611no—
458C2×#131—611no—
459C2×#131—611no—
460C4×#41—611no—
461C2×C4×Q8—611no—
462C2×C4×D4—611no—
463#471—611no—
464#471—611no—
465#471—611no—
466#471—611no—
467#471—611no—
468#471—611no—
469#471—611no—
470#471#692311yescharacteristic, complemented
471#442—1221no—
472#441—1221no—
473#440—1221no—
474#440—1221no—
475#440—1221no—
476#440—1221no—
477#440—1221no—
478#440—1221no—
479C4×Q16—1221no—
480C4×SD16—1221no—
481C4×SD16—1221no—
482C4×D8—1221no—
483C2×#108—611no—
484C2×#108—611no—
485#428—611no—
486#428—611no—
487C2×#107—611no—
488#419—611no—
489#418—611no—
490#417—611no—
491#417—611no—
492C2×#103—611no—
493C2×#102—611no—
494C2×#101—611no—
495C2×#101—611no—
496C2×#100—611no—
497C2×#100—611no—
498#405—611no—
499#405—611no—
500#405—1221no—
501#405—1221no—
502C4×M16—611no—
503C4×M16—611no—
504C4×M16—611no—
505C4×M16—1221no—
506C2×#97—611no—
507C2×#97—1221no—
508#343—611no—
509#343—611no—
510#343—611no—
511#343—611no—
512#341—611no—
513#341—611no—
514C61#2155711yescharacteristic, complemented, Sylow
515C2×#41—611no—
516C22×Q8—611no—
517C22×D4—611no—
518C23×C4—1221no—
519#137—611no—
520#137—611no—
521#137—611no—
522#137—1221no—
523#137—1221no—
524#137C2×#692311yescharacteristic, complemented
525AGL(1,ℤ/8)—611no—
526AGL(1,ℤ/8)—611no—
527AGL(1,ℤ/8)—611no—
528AGL(1,ℤ/8)—1221no—
529AGL(1,ℤ/8)—1221no—
530AGL(1,ℤ/8)C2×#692311yescharacteristic
531C2×Q16—1221no—
532C2×SD16—611no—
533C2×SD16—611no—
534C2×SD16—611no—
535C2×SD16—1221no—
536C2×SD16—1221no—
537C2×SD16—1221no—
538C2×SD16—1221no—
539C2×SD16—1221no—
540C2×SD16—1221no—
541C2×SD16C2×#692311yescharacteristic, complemented
542C2×D8—1221no—
543#131—611no—
544#131—611no—
545#131—611no—
546#131—1221no—
547#131—1221no—
548#131—1222no—
549#131—1221no—
550#131—1221no—
551#131C2×#692311yescharacteristic, complemented
552C2×M16—611no—
553C2×M16—611no—
554C2×M16—611no—
555C2×M16—611no—
556C2×M16—611no—
557C2×M16—611no—
558C2×M16—1221no—
559C2×M16—1221no—
560C22×C8—611no—
561C22×C8—611no—
562C22×C8—1221no—
563C22×C8—1221no—
564C4×Q8—611no—
565C4×Q8—611no—
566C4×Q8—1221no—
567C4×Q8—1221no—
568C4×Q8—1221no—
569C4×Q8—1221no—
570C4×D4—611no—
571C4×D4—611no—
572C4×D4—1221no—
573C4×D4—1221no—
574C4×D4—1221no—
575C4×D4—1221no—
576C4×D4—1221no—
577C4×D4—1221no—
578#117—611no—
579#117—1221no—
580C2×C4⋊C4—611no—
581C2×C4⋊C4—611no—
582C2×C4⋊C4—1221no—
583C2×C22⋊C4—1221no—
584C2×C42—611no—
585C2×C42—1221no—
586C2×C42—1221no—
587#108—611no—
588#108—611no—
589#108—611no—
590#108—1221no—
591#108—1221no—
592#108C2×#692311yescharacteristic, complemented
593#107—1221no—
594#107—1221no—
595#107—1221no—
596#107—1221no—
597#106—1221no—
598#106—1221no—
599#103—1221no—
600#103—1221no—
601#103—1221no—
602#103—1221no—
603#103—1221no—
604#103—1221no—
605#102—1221no—
606#102—1221no—
607#102—1221no—
608#102—1221no—
609#102—1221no—
610#102—1221no—
611#101—611no—
612#101—611no—
613#101—611no—
614#101—1222no—
615#101C2×#692311yescharacteristic, complemented
616#100—611no—
617#100—611no—
618#100—611no—
619#100—1222no—
620#100C2×#692311yescharacteristic, complemented
621#97—611no—
622#97—611no—
623#97—611no—
624#97—611no—
625#97—1221no—
626#97—1221no—
627#97—1221no—
628#97—1221no—
629#97—1221no—
630C4×C8—1221no—
631C4×C8—1221no—
632C4×C8—1221no—
633C4×C8—1221no—
634C4×C8—1221no—
635C24—1221no—
636#41—611no—
637#41—611no—
638#41—611no—
639#41—1221no—
640#41—1221no—
641#41C22×#692311yescharacteristic
642C2×Q8—611no—
643C2×Q8—611no—
644C2×Q8—1221no—
645C2×Q8—1221no—
646C2×Q8—1221no—
647C2×Q8—1221no—
648C2×Q8—1221no—
649C2×Q8C22×#692311yescharacteristic
650C2×D4—611no—
651C2×D4—611no—
652C2×D4—1221no—
653C2×D4—1221no—
654C2×D4—1221no—
655C2×D4—1221no—
656C2×D4—1221no—
657C2×D4—1221no—
658C2×D4C22×#692311yescharacteristic
659C22×C4—611no—
660C22×C4—611no—
661C22×C4—611no—
662C22×C4—1221no—
663C22×C4—1221no—
664C22×C4—1221no—
665C22×C4—1221no—
666C22×C4—1221no—
667C22×C4—1221no—
668C22×C4—4882no—
669C22×C4—2441no—
670C22×C4—2441no—
671Q16—21no—
672Q16—1221no—
673Q16—1221no—
674Q16—1221no—
675SD16—21no—
676SD16—21no—
677SD16—21no—
678SD16—21no—
679SD16—1221no—
680SD16—1221no—
681SD16—1221no—
682SD16—1221no—
683SD16—1221no—
684SD16—1221no—
685SD16—1221no—
686SD16—1221no—
687SD16—1221no—
688SD16—1221no—
689SD16—1221no—
690SD16—1221no—
691D8—21no—
692D8—1221no—
693D8—1221no—
694D8—1221no—
695M16—21no—
696M16—612no—
697M16—611no—
698M16—611no—
699M16—611no—
700M16—1221no—
701M16—1221no—
702M16—1221no—
703M16—1221no—
704M16—1221no—
705M16—1221no—
706M16—1222no—
707M16—1222no—
708M16—1221no—
709M16—1221no—
710M16—1221no—
711M16—1221no—
712M16—1221no—
713M16C22×#692311yescharacteristic
714M16C22×#692311yescharacteristic
715M16C22×#692311yescharacteristic
716C2×C8—21no—
717C2×C8—611no—
718C2×C8—611no—
719C2×C8—611no—
720C2×C8—611no—
721C2×C8—611no—
722C2×C8—611no—
723C2×C8—611no—
724C2×C8—1221no—
725C2×C8—1221no—
726C2×C8—1221no—
727C2×C8—1221no—
728C2×C8—1221no—
729C2×C8—1221no—
730C2×C8—1221no—
731C2×C8—1221no—
732C2×C8—1222no—
733C2×C8—1222no—
734C2×C8—1221no—
735C2×C8—1221no—
736C2×C8—1221no—
737C2×C8C22×#692311yescharacteristic
738C4⋊C4—611no—
739C4⋊C4—611no—
740C4⋊C4—1221no—
741C4⋊C4—1221no—
742C4⋊C4—1221no—
743C4⋊C4—1221no—
744C4⋊C4—1221no—
745C4⋊C4—1221no—
746C4⋊C4—2441no—
747C4⋊C4—2441no—
748C22⋊C4—1221no—
749C22⋊C4—1221no—
750C22⋊C4—1221no—
751C22⋊C4—2441no—
752C22⋊C4—2441no—
753C42—611no—
754C42—611no—
755C42—611no—
756C42—611no—
757C42—1221no—
758C42—1221no—
759C42—1221no—
760C42—2441no—
761C42—2441no—
762C23—21no—
763C23—611no—
764C23—1221no—
765C23—1221no—
766C23—4881no—
767C23—4881no—
768C23—2441no—
769C23—2441no—
770Q8—21no—
771Q8—21no—
772Q8—611no—
773Q8—1221no—
774Q8—1221no—
775Q8—1221no—
776Q8—2441no—
777Q8—2441no—
778Q8D4×#692311yescharacteristic
779D4—21no—
780D4—21no—
781D4—21no—
782D4—611no—
783D4—1221no—
784D4—1221no—
785D4—1221no—
786D4—1221no—
787D4—1221no—
788D4—1221no—
789D4—2441no—
790D4—2441no—
791D4D4×#692311yescharacteristic
792C2×C4—21no—
793C2×C4—21no—
794C2×C4—611no—
795C2×C4—611no—
796C2×C4—611no—
797C2×C4—611no—
798C2×C4—611no—
799C2×C4—611no—
800C2×C4—611no—
801C2×C4—611no—
802C2×C4—611no—
803C2×C4—1221no—
804C2×C4—1221no—
805C2×C4—1221no—
806C2×C4—1221no—
807C2×C4—1221no—
808C2×C4—1221no—
809C2×C4—1221no—
810C2×C4—4882no—
811C2×C4—4882no—
812C2×C4—4881no—
813C2×C4—4881no—
814C2×C4—4881no—
815C2×C4—4881no—
816C2×C4—2441no—
817C2×C4—2441no—
818C2×C4—2441no—
819C2×C4—2441no—
820C2×C4—2441no—
821C2×C4—2441no—
822C2×C4C23×#692311yescharacteristic
823C8—21no—
824C8—21no—
825C8—21no—
826C8—611no—
827C8—611no—
828C8—1221no—
829C8—1221no—
830C8—1222no—
831C8—1221no—
832C8—1221no—
833C8—1221no—
834C8—2441no—
835C8—2441no—
836C8D4×#692311yescharacteristic
837C8D4×#692311yescharacteristic
838C22—21no—
839C22—41no—
840C22—81no—
841C22—611no—
842C22—611no—
843C22—1221no—
844C22—1221no—
845C22—1221no—
846C22—4881no—
847C22—4881no—
848C22—4881no—
849C22—4882no—
850C22—2441no—
851C22—2441no—
852C22—2441no—
853C22#41×#692311yescharacteristic
854C4—21no—
855C4—41no—
856C4—611no—
857C4—611no—
858C4—1221no—
859C4—1221no—
860C4—1221no—
861C4—1221no—
862C4—1221no—
863C4—4881no—
864C4—4881no—
865C4—2441no—
866C4—2441no—
867C4—2441no—
868C4C2×D4×#692311yescharacteristic
869C4C2×D4×#692311yescharacteristic
870C2—21no—
871C2—41no—
872C2—81no—
873C2—611no—
874C2—611no—
875C2—1221no—
876C2—4881no—
877C2—2441no—
878C2#121×#692311yescharacteristic
subgroupG/H
centerC2#121×#6923
commutatorC2×C4×C61C23×C4
FrattiniC2×C4C23×#6923
FittingC61×#471C4
socleC2×C61C4×#121
prime radicalAGL(1,ℤ/8)×D61C22
cosocleC2×C4×D61C24
hypercenter#471#6923
hypocenterC61#21557
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2 ◁ C2×C4 ◁ #471

Complements

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

NH ≅ G/Ntype
1. #137×#6923C2semidirect
3. C2×#16840801C2semidirect
4. #21462389C2semidirect
5. #21461979C2semidirect
6. #21461937C2semidirect
7. #21461905C2semidirect
8. #21461904C2semidirect
9. #21461859C2semidirect
11. #21461708C2semidirect
12. #21461640C2semidirect
13. #101×#6923C2semidirect
14. #100×#6923C2semidirect
64. #16840028C4semidirect
65. #16840027C4semidirect
66. #16840026C4semidirect
67. #16840025C4semidirect
68. #16840024C4semidirect
69. #16840023C4semidirect
70. #16840022C4semidirect
74. C61×#471C4semidirect
147. #14519810C2×C4semidirect
149. #14519808C2×C4semidirect
150. #14519807C2×C4semidirect
158. C2×#11758190C2×C4semidirect
159. C2×#11758200C2×C4semidirect
160. C2×#11758201C2×C4semidirect
169. #14519785C2×C4semidirect
170. #14519784C2×C4semidirect
172. #14519783C2×C4semidirect
179. #14519713C2×C4semidirect
180. #14519712C2×C4semidirect
181. #14519712C2×C4semidirect
182. #14519696C2×C4semidirect
183. #14519695C2×C4semidirect
184. #14519695C2×C4semidirect
185. #14519694C2×C4semidirect
186. #14519693C2×C4semidirect
187. #14519693C2×C4semidirect
188. #137×C61C2×C4semidirect
190. C2×SD16×C61C2×C4semidirect
191. #131×C61C2×C4semidirect
192. #108×C61C2×C4semidirect
193. #101×C61C2×C4semidirect
194. #100×C61C2×C4semidirect
470. #471#6923semidirect
514. C61#21557semidirect
524. #137C2×#6923semidirect
541. C2×SD16C2×#6923semidirect
551. #131C2×#6923semidirect
592. #108C2×#6923semidirect
615. #101C2×#6923semidirect
620. #100C2×#6923semidirect

Maximal subgroups

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

subgroupindex
#137×#69232
AGL(1,ℤ/8)×#69232
C2×#168408012
#214623892
#214619792
#214619372
#214619052
#214619042
#214618592
#214618582
#214617082
#214616402
#101×#69232
#100×#69232
#471×D612
#2155761