Finite Group Databasebeta

← #14226798

Subgroups — #14226798

Order 1792.

2168 conjugacy classes of subgroups.

The subgroup lattice has 898 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11742748C211yesmaximal, characteristic, complemented
2C2×#90168C211yesmaximal, characteristic, complemented
3C2×C7×#423C211yesmaximal, characteristic, complemented
4#11741217C214yesmaximal, complemented
5#11736510C212yesmaximal, complemented
6#11736509C212yesmaximal, complemented
7#11736507C214yesmaximal, complemented
8#11736505C212yesmaximal, complemented
9#11736504C212yesmaximal, complemented
10#11736501C212yesmaximal, complemented
11#11736500C212yesmaximal, complemented
12#11736473C214yesmaximal, complemented
13#11736472C212yesmaximal, complemented
14#11736471C212yesmaximal, complemented
15C22×#1157—21no—
16C22×C7×M16C2212yes—
17C22×C42×C7C2211yescharacteristic
18#90482—21no—
19#90482—21no—
20#90482C2212yes—
21C2×#6493—21no—
22C2×#6493C2212yes—
23C2×#6471C2214yes—
24#90170—21no—
25#90170—21no—
26#90170—21no—
27#90170—21no—
28#90170C2212yescomplemented
29#90170C2212yescomplemented
30#90168—21no—
31#90168—21no—
32#90168—21no—
33#90168—21no—
34#90168C2211yescharacteristic
35#90168C2212yes—
36#90168C2212yes—
37#90168C2212yes—
38#90168C2212yes—
39#90168C2211yescharacteristic, complemented
40#90168C2211yescharacteristic, complemented
41C2×#6438—21no—
42C2×#6437C2211yescharacteristic
43C4×#1157—21no—
44C4×#1157—21no—
45C4×#1157C2212yes—
46C2×C4×D28—21no—
47C2×C4×D28C2212yes—
48#90161C2211yescharacteristic
49#90161C2211yescharacteristic, complemented
50#90161C2211yescharacteristic, complemented
51C2×#6432C2211yescharacteristic
52C7×#423C2212yes—
53C7×#423C2212yes—
54C7×#423C2212yescomplemented
55C7×#423C2212yescomplemented
56C2×C7×C4⋊C8C2212yescomplemented
57C2×C7×C4⋊C8C2212yescomplemented
58#89907C2218yescomplemented
59#89906C2218yescomplemented
60#89905C2214yes—
61#89903C2214yes—
62#89893C2214yes—
63#89887C2218yescomplemented
64#89886C2218yescomplemented
65#89623C2214yescomplemented
66#89622C2214yescomplemented
67#89620C2214yescomplemented
68#89620C2214yescomplemented
69#89619C2218yescomplemented
70#89618C2214yescomplemented
71#89618C2214yescomplemented
72#89616C2218yescomplemented
73#89615C2214yescomplemented
74#89615C2214yescomplemented
75#89615C2214yescomplemented
76#89614C2214yescomplemented
77#89614C2214yescomplemented
78#89613C2214yescomplemented
79#60916—71nomaximal, Sylow
80C23×C4×C7D411yescharacteristic
81C23×C4×C7D411yescharacteristic
82C23×C4×C7C2311yescharacteristic
83C22×C22⋊D7—22no—
84C2×#1157—21no—
85C2×#1157—21no—
86C2×#1157—22no—
87C2×#1157—22no—
88C2×#1157—22no—
89C2×#1157—22no—
90C2×#1157—48no—
91C2×#1157C2312yes—
92C22×D28—21no—
93C22×D28—21no—
94C22×D28C2312yes—
95C22×C4×D7—22no—
96C22×Dic14—21no—
97C2×C7×M16—44no—
98C2×C7×M16C2314yes—
99C2×C7×M16C2314yes—
100C22×C7×C8C2314yes—
101C2×C42×C7D411yescharacteristic
102C2×C42×C7D411yescharacteristic
103C2×C42×C7D411yescharacteristic
104C2×C42×C7D411yescharacteristic
105C2×C42×C7D411yescharacteristic
106C2×C42×C7D411yescharacteristic
107C2×C42×C7C2311yescharacteristic
108C2×C42×C7C2311yescharacteristic
109C2×C42×C7C2311yescharacteristic
110C2×C42×C7C2311yescharacteristic
111C2×C42×C7C2311yescharacteristic
112C2×C42×C7C2311yescharacteristic
113#6516—22no—
114#6493—22no—
115#6493—22no—
116#6493—22no—
117#6493—22no—
118#6493—22no—
119#6493—22no—
120#6493—21no—
121#6493—21no—
122#6493—21no—
123#6493—21no—
124#6493C2314yes—
125#6493C2312yes—
126#6493C2314yes—
127#6493C2312yes—
128#6492—22no—
129#6492—22no—
130#6492—22no—
131C4×C22⋊D7—22no—
132C4×C22⋊D7—22no—
133C4×C22⋊D7—22no—
134C4×C22⋊D7—22no—
135C4×C22⋊D7—22no—
136C4×C22⋊D7—22no—
137C2×(C2×D7)⋊C4—22no—
138C2×(C2×D7)⋊C4—22no—
139#6489—21no—
140#6489—21no—
141#6489C2312yes—
142C2×C4⋊Dic7—21no—
143C2×C4⋊Dic7C2312yes—
144#6487—21no—
145#6487—21no—
146#6487—21no—
147#6487—21no—
148#6487C2312yes—
149#6487C2312yes—
150#6471—48no—
151C2×D56C2318yes—
152C2×#1132C2318yes—
153#6439—22no—
154#6439—22no—
155#6438—22no—
156#6438—22no—
157#6438—22no—
158#6438—22no—
159#6438—21no—
160#6438—21no—
161#6438C2312yes—
162#6437—21no—
163#6437—21no—
164#6437C2311yescharacteristic
165#6437C2312yes—
166#6437C2312yes—
167C4×D28—22no—
168C4×D28—22no—
169C4×D28—22no—
170C4×D28—22no—
171C4×D28—22no—
172C4×D28—22no—
173C4×D28—21no—
174C4×D28—21no—
175C4×D28—21no—
176C4×D28—21no—
177C4×D28C2314yes—
178C4×D28C2312yes—
179C4×D28C2312yes—
180C4×D28C2314yes—
181#6435—22no—
182#6435—22no—
183#6435—22no—
184C42×D7—22no—
185#6433—21no—
186#6433—21no—
187#6433C2312yes—
188#6432—21no—
189#6432—21no—
190#6432C2311yescharacteristic
191#6432C2311yescharacteristic
192#6432C2312yes—
193#6432C2311yescharacteristic
194#6432C2312yes—
195C4×Dic14—21no—
196C4×Dic14—21no—
197C4×Dic14—21no—
198C4×Dic14—21no—
199C4×Dic14C2312yes—
200C4×Dic14C2312yes—
201C7×C4⋊C8C2314yes—
202C7×C4⋊C8C2314yes—
203C7×C4⋊C8C2314yes—
204C7×C4⋊C8C2314yes—
205#6395C2318yes—
206#6395C2318yes—
207#6395C2318yes—
208#6392C2318yes—
209#6391C2318yes—
210#6390C2318yes—
211#3444—71no—
212C2×#532—71no—
213#3254—72no—
214#3253—72no—
215#3251—74no—
216#3247—74no—
217#3246—72no—
218#3245—72no—
219#3079—72no—
220#3077—72no—
221#3055—74no—
222#3038—72no—
223#3036—72no—
224C2×#423D711yescharacteristic, complemented
225C24×C7C2×D411yescharacteristic
226C23×D7—22no—
227C22×C4×C7—24no—
228C22×C4×C7—22no—
229C22×C4×C7—22no—
230C22×C4×C7—42no—
231C22×C4×C7C2×D411yescharacteristic
232C22×C4×C7C2×D411yescharacteristic
233C22×C4×C7C2×D411yescharacteristic
234C22×C4×C7C2×D411yescharacteristic
235C22×C4×C7C2×D411yescharacteristic
236C22×C4×C7C2×D411yescharacteristic
237C22×C4×C7C2×D411yescharacteristic
238C22×C4×C7C2×D411yescharacteristic
239C22×C4×C7C2×D411yescharacteristic
240C22×C4×C7C2×D411yescharacteristic
241C22×C4×C7C2×D411yescharacteristic
242C22×C4×C7C2×D411yescharacteristic
243C22×C4×C7C2×D411yescharacteristic
244C22×C4×C7C2×D411yescharacteristic
245C22×C4×C7C2×D411yescharacteristic
246C22×C4×C7C2411yescharacteristic
247C22×C4×C7C2411yescharacteristic
248C22×C4×C7C2411yescharacteristic
249C2×C22⋊D7—22no—
250C2×C22⋊D7—22no—
251C2×C22⋊D7—22no—
252C2×C22⋊D7—24no—
253C2×C22⋊D7—24no—
254C2×C22⋊D7—48no—
255C22×Dic7—22no—
256#1157—24no—
257#1157—24no—
258#1157—44no—
259#1157—48no—
260#1157—48no—
261#1157—48no—
262#1157—44no—
263#1157—48no—
264C2×D28—24no—
265C2×D28—24no—
266C2×D28—22no—
267C2×D28—22no—
268C2×D28—22no—
269C2×D28—21no—
270C2×D28—21no—
271C2×D28—22no—
272C2×D28—22no—
273C2×D28—44no—
274C2×D28—44no—
275C2×D28C2414yes—
276C2×D28C2412yes—
277C2×C4×D7—22no—
278C2×C4×D7—22no—
279C2×C4×D7—22no—
280C2×C4×D7—24no—
281C2×C4×D7—24no—
282C2×C4×D7—48no—
283C2×Dic14—21no—
284C2×Dic14—21no—
285C2×Dic14—22no—
286C2×Dic14—22no—
287C2×Dic14—44no—
288C2×Dic14C2412yes—
289C7×M16—28no—
290C7×M16—44no—
291C2×C7×C8—44no—
292C2×C7×C8C2418yes—
293C42×C7C2×D411yescharacteristic
294C42×C7C2×D411yescharacteristic
295C42×C7C2×D411yescharacteristic
296C42×C7C2×D411yescharacteristic
297C42×C7C2×D411yescharacteristic
298C42×C7C2×D411yescharacteristic
299C42×C7C2×D411yescharacteristic
300C42×C7C2×D411yescharacteristic
301C42×C7C2×D411yescharacteristic
302C42×C7C2×D411yescharacteristic
303C42×C7C2×D411yescharacteristic
304C42×C7C2×D411yescharacteristic
305C42×C7C2411yescharacteristic
306C42×C7C2411yescharacteristic
307C42×C7C2411yescharacteristic
308C42×C7C2411yescharacteristic
309C22⋊Dic7—22no—
310C22⋊Dic7—22no—
311C22⋊Dic7—22no—
312(C2×D7)⋊C4—22no—
313(C2×D7)⋊C4—22no—
314(C2×D7)⋊C4—22no—
315(C2×D7)⋊C4—22no—
316(C2×D7)⋊C4—22no—
317(C2×D7)⋊C4—22no—
318(C2×D7)⋊C4—24no—
319(C2×D7)⋊C4—24no—
320(C2×D7)⋊C4—24no—
321(C2×D7)⋊C4—24no—
322C4⋊Dic7—21no—
323C4⋊Dic7—21no—
324C4⋊Dic7—21no—
325C4⋊Dic7—21no—
326C4⋊Dic7—22no—
327C4⋊Dic7—22no—
328C4⋊Dic7—22no—
329C4⋊Dic7C2412yes—
330C4⋊Dic7C2412yes—
331C4⋊Dic7C2414yes—
332Dic7⋊C4—22no—
333Dic7⋊C4—22no—
334Dic7⋊C4—22no—
335Dic7⋊C4—22no—
336Dic7⋊C4—22no—
337Dic7⋊C4—22no—
338C4×Dic7—22no—
339C4×Dic7—22no—
340C4×Dic7—22no—
341D56—48no—
342#1132—48no—
343C22×#41—141no—
344C2×AGL(1,ℤ/8)—74no—
345C22×M16C2×D712yes—
346#533—71no—
347#533—71no—
348#533—71no—
349#532—72no—
350#532—72no—
351#532—72no—
352#532—72no—
353#532—71no—
354#532—71no—
355#532—71no—
356#532—141no—
357#532—141no—
358#532—141no—
359#532—141no—
360C2×C4⋊Q8—71no—
361C2×#127—71no—
362#529—72no—
363#529—72no—
364#529—141no—
365#529—141no—
366#529—141no—
367#529—141no—
368C2×#124—141no—
369#525—72no—
370#525—141no—
371#525—141no—
372C2×#121—72no—
373C2×#121—141no—
374C4×#41—72no—
375C4×#41—141no—
376C4×#41—141no—
377C2×C4×D4—72no—
378C2×C4×D4—141no—
379C22×C42C2×D711yescharacteristic
380#478—78no—
381#477—74no—
382#476—74no—
383#476—74no—
384#475—74no—
385#474—74no—
386#474—74no—
387#469—78no—
388#468—78no—
389#466—78no—
390#465—78no—
391#463—78no—
392#461—74no—
393#460—74no—
394#460—74no—
395#459—74no—
396#459—74no—
397#459—74no—
398#428—74no—
399#423C2×D712yes—
400#423C2×D712yes—
401#423C2×D712yescomplemented
402#423C2×D712yescomplemented
403C2×C4⋊C8C2×D712yescomplemented
404C2×C4⋊C8C2×D712yescomplemented
405#418—74no—
406#417—74no—
407C23×C7—22no—
408C23×C7—22no—
409C23×C7—41no—
410C23×C7C22×D411yescharacteristic
411C23×C7C22×D411yescharacteristic
412C23×C7C22×D411yescharacteristic
413C22×D7—22no—
414C22×D7—24no—
415C22×D7—44no—
416C22×D7—44no—
417C22×D7—44no—
418C2×C4×C7—22no—
419C2×C4×C7—22no—
420C2×C4×C7—22no—
421C2×C4×C7—22no—
422C2×C4×C7—22no—
423C2×C4×C7—22no—
424C2×C4×C7—22no—
425C2×C4×C7—22no—
426C2×C4×C7—22no—
427C2×C4×C7—22no—
428C2×C4×C7—22no—
429C2×C4×C7—21no—
430C2×C4×C7—21no—
431C2×C4×C7—21no—
432C2×C4×C7—21no—
433C2×C4×C7—41no—
434C2×C4×C7—41no—
435C2×C4×C7—41no—
436C2×C4×C7AGL(1,ℤ/8)14yescomplemented
437C2×C4×C7C22×D411yescharacteristic
438C2×C4×C7C22×D411yescharacteristic
439C2×C4×C7C22×D411yescharacteristic
440C2×C4×C7C22×D411yescharacteristic
441C2×C4×C7C22×D411yescharacteristic
442C2×C4×C7C22×D411yescharacteristic
443C2×C4×C7C22×D411yescharacteristic
444C2×C4×C7C22×D411yescharacteristic
445C2×C4×C7C22×D411yescharacteristic
446C2×C4×C7C22×D411yescharacteristic
447C2×C4×C7C22×D411yescharacteristic
448C2×C4×C7H(5,𝔽2)12yes—
449C2×C4×C72−1+412yes—
450C2×C4×C7C2511yescharacteristic
451C22⋊D7—48no—
452C22⋊D7—44no—
453C22⋊D7—44no—
454C22⋊D7—48no—
455C22⋊D7—44no—
456C2×Dic7—22no—
457C2×Dic7—22no—
458C2×Dic7—22no—
459C2×Dic7—24no—
460C2×Dic7—44no—
461D28—24no—
462D28—22no—
463D28—24no—
464D28—22no—
465D28—44no—
466D28—44no—
467D28—42no—
468D28—44no—
469D28—44no—
470D28—42no—
471D28—44no—
472C4×D7—48no—
473C4×D7—44no—
474C4×D7—48no—
475C4×D7—44no—
476C4×D7—44no—
477Dic14—22no—
478Dic14—22no—
479Dic14—44no—
480Dic14—42no—
481Dic14—44no—
482Dic14—42no—
483C7×C8—28no—
484C2×#41—72no—
485C2×#41—141no—
486C2×#41—141no—
487C2×#41—142no—
488C2×#41—142no—
489C2×#41—142no—
490C2×#41—142no—
491C2×#41—288no—
492C22×Q8—141no—
493C22×D4—72no—
494C22×D4—142no—
495C22×D4—141no—
496C22×D4—141no—
497C23×C4—142no—
498C23×C4D2811yescharacteristic
499C23×C4D2811yescharacteristic
500C23×C4C22×D711yescharacteristic
501AGL(1,ℤ/8)—288no—
502C2×SD16—78no—
503C2×D8—78no—
504C2×M16—44no—
505C2×M16C22×D714yes—
506C2×M16C22×D714yes—
507C22×C8C22×D714yes—
508C4⋊Q8—72no—
509C4⋊Q8—72no—
510C4⋊Q8—71no—
511C4⋊Q8—71no—
512C4⋊Q8—71no—
513C4⋊Q8—141no—
514C4⋊Q8—141no—
515#127—72no—
516#127—72no—
517#127—71no—
518#127—141no—
519#127—141no—
520#126—142no—
521#126—142no—
522#125—72no—
523#125—141no—
524#125—141no—
525#124—72no—
526#124—142no—
527#124—142no—
528#124—142no—
529#124—142no—
530#124—141no—
531#124—141no—
532#123—142no—
533#123—142no—
534#123—142no—
535C22⋊Q8—72no—
536C22⋊Q8—72no—
537C22⋊Q8—141no—
538C22⋊Q8—141no—
539C22⋊Q8—141no—
540C22⋊Q8—141no—
541#121—74no—
542#121—74no—
543#121—72no—
544#121—72no—
545#121—142no—
546#121—142no—
547#121—142no—
548#121—142no—
549#121—142no—
550#121—142no—
551#121—141no—
552#121—141no—
553#121—141no—
554#121—141no—
555#120—142no—
556C4×Q8—72no—
557C4×Q8—72no—
558C4×Q8—141no—
559C4×Q8—141no—
560C4×Q8—141no—
561C4×Q8—141no—
562C4×D4—74no—
563C4×D4—74no—
564C4×D4—72no—
565C4×D4—72no—
566C4×D4—142no—
567C4×D4—142no—
568C4×D4—142no—
569C4×D4—142no—
570C4×D4—142no—
571C4×D4—142no—
572C4×D4—142no—
573C4×D4—142no—
574C4×D4—142no—
575C4×D4—142no—
576C4×D4—142no—
577C4×D4—142no—
578C4×D4—141no—
579C4×D4—141no—
580C4×D4—141no—
581C4×D4—141no—
582#117—72no—
583#117—141no—
584#117—141no—
585#117—142no—
586#117—142no—
587#117—142no—
588C2×C4⋊C4—72no—
589C2×C4⋊C4—141no—
590C2×C22⋊C4—142no—
591C2×C22⋊C4—142no—
592C2×C42—142no—
593C2×C42D2811yescharacteristic
594C2×C42D2811yescharacteristic
595C2×C42D2811yescharacteristic
596C2×C42D2811yescharacteristic
597C2×C42D2811yescharacteristic
598C2×C42D2811yescharacteristic
599C2×C42C22×D711yescharacteristic
600C2×C42C22×D711yescharacteristic
601C2×C42C22×D711yescharacteristic
602C2×C42C22×D711yescharacteristic
603C2×C42C22×D711yescharacteristic
604C2×C42C22×D711yescharacteristic
605#107—78no—
606#106—78no—
607C4⋊C8C22×D714yes—
608C4⋊C8C22×D714yes—
609C4⋊C8C22×D714yes—
610C4⋊C8C22×D714yes—
611#103—78no—
612#102—78no—
613#102—78no—
614#102—78no—
615C22×C7—21no—
616C22×C7—21no—
617C22×C7—21no—
618C22×C7—21no—
619C22×C7—21no—
620C22×C7—21no—
621C22×C7—21no—
622C22×C7—44no—
623C22×C7#53712yes—
624C22×C7C2×AGL(1,ℤ/8)12yes—
625C22×C7C23×D411yescharacteristic
626C2×D7—42no—
627C2×D7—44no—
628C2×D7—44no—
629C2×D7—42no—
630C2×D7—42no—
631C2×D7—44no—
632C2×D7—88no—
633C4×C7—21no—
634C4×C7—21no—
635C4×C7—21no—
636C4×C7—21no—
637C4×C7—21no—
638C4×C7—21no—
639C4×C7—21no—
640C4×C7#53712yes—
641C4×C7C2×AGL(1,ℤ/8)12yes—
642C4×C7C2×AGL(1,ℤ/8)12yes—
643C4×C7#57512yes—
644C4×C7C2×H(5,𝔽2)11yescharacteristic
645C4×C7C2×2−1+411yescharacteristic
646Dic7—42no—
647Dic7—44no—
648Dic7—42no—
649Dic7—42no—
650C24—142no—
651C24C2×D2811yescharacteristic
652#41—144no—
653#41—144no—
654#41—284no—
655#41—288no—
656#41—288no—
657#41—288no—
658#41—284no—
659#41—288no—
660C2×Q8—72no—
661C2×Q8—141no—
662C2×Q8—141no—
663C2×Q8—142no—
664C2×Q8—142no—
665C2×Q8—284no—
666C2×D4—72no—
667C2×D4—74no—
668C2×D4—142no—
669C2×D4—142no—
670C2×D4—142no—
671C2×D4—144no—
672C2×D4—144no—
673C2×D4—141no—
674C2×D4—141no—
675C2×D4—142no—
676C2×D4—142no—
677C2×D4—142no—
678C2×D4—142no—
679C2×D4—142no—
680C2×D4—144no—
681C2×D4—144no—
682C2×D4—284no—
683C2×D4—284no—
684C2×D4—288no—
685C22×C4—24no—
686C22×C4—22no—
687C22×C4—22no—
688C22×C4—42no—
689C22×C4—142no—
690C22×C4—142no—
691C22×C4—142no—
692C22×C4—142no—
693C22×C4—144no—
694C22×C4—144no—
695C22×C4—288no—
696C22×C4C2×D2811yescharacteristic
697C22×C4C2×D2811yescharacteristic
698C22×C4C2×D2811yescharacteristic
699C22×C4C2×D2811yescharacteristic
700C22×C4C2×D2811yescharacteristic
701C22×C4C2×D2811yescharacteristic
702C22×C4C2×D2811yescharacteristic
703C22×C4C2×D2811yescharacteristic
704C22×C4C2×D2811yescharacteristic
705C22×C4C2×D2811yescharacteristic
706C22×C4C2×D2811yescharacteristic
707C22×C4C2×D2811yescharacteristic
708C22×C4C2×D2811yescharacteristic
709C22×C4C2×D2811yescharacteristic
710C22×C4C2×D2811yescharacteristic
711C22×C4C23×D711yescharacteristic
712C22×C4C23×D711yescharacteristic
713C22×C4C23×D711yescharacteristic
714SD16—288no—
715D8—288no—
716M16—28no—
717M16—44no—
718C2×C8—44no—
719C2×C8C23×D718yes—
720C4⋊C4—72no—
721C4⋊C4—72no—
722C4⋊C4—74no—
723C4⋊C4—142no—
724C4⋊C4—142no—
725C4⋊C4—142no—
726C4⋊C4—142no—
727C4⋊C4—142no—
728C4⋊C4—142no—
729C4⋊C4—142no—
730C4⋊C4—142no—
731C4⋊C4—142no—
732C4⋊C4—141no—
733C4⋊C4—141no—
734C4⋊C4—141no—
735C4⋊C4—141no—
736C22⋊C4—142no—
737C22⋊C4—142no—
738C22⋊C4—142no—
739C22⋊C4—144no—
740C22⋊C4—144no—
741C22⋊C4—144no—
742C22⋊C4—144no—
743C22⋊C4—142no—
744C22⋊C4—142no—
745C22⋊C4—142no—
746C22⋊C4—142no—
747C22⋊C4—142no—
748C22⋊C4—142no—
749C42—142no—
750C42—142no—
751C42—142no—
752C42C2×D2811yescharacteristic
753C42C2×D2811yescharacteristic
754C42C2×D2811yescharacteristic
755C42C2×D2811yescharacteristic
756C42C2×D2811yescharacteristic
757C42C2×D2811yescharacteristic
758C42C2×D2811yescharacteristic
759C42C2×D2811yescharacteristic
760C42C2×D2811yescharacteristic
761C42C2×D2811yescharacteristic
762C42C2×D2811yescharacteristic
763C42C2×D2811yescharacteristic
764C42C23×D711yescharacteristic
765C42C23×D711yescharacteristic
766C42C23×D711yescharacteristic
767C42C23×D711yescharacteristic
768C2×C7—22no—
769C2×C7—22no—
770C2×C7—41no—
771C2×C7C2×#53711yescharacteristic
772C2×C7C22×AGL(1,ℤ/8)11yescharacteristic
773C2×C7C2×#57511yescharacteristic
774D7—82no—
775D7—84no—
776C23—22no—
777C23—22no—
778C23—41no—
779C23—142no—
780C23—144no—
781C23—284no—
782C23—284no—
783C23—284no—
784C23C22×D2811yescharacteristic
785C23C22×D2811yescharacteristic
786C23C22×D2811yescharacteristic
787Q8—142no—
788Q8—142no—
789Q8—284no—
790Q8—282no—
791Q8—284no—
792Q8—282no—
793D4—142no—
794D4—144no—
795D4—144no—
796D4—142no—
797D4—284no—
798D4—284no—
799D4—282no—
800D4—288no—
801D4—284no—
802D4—288no—
803D4—284no—
804D4—284no—
805D4—284no—
806D4—282no—
807D4—284no—
808D4—284no—
809C2×C4—22no—
810C2×C4—22no—
811C2×C4—22no—
812C2×C4—22no—
813C2×C4—22no—
814C2×C4—22no—
815C2×C4—22no—
816C2×C4—22no—
817C2×C4—22no—
818C2×C4—22no—
819C2×C4—22no—
820C2×C4—21no—
821C2×C4—21no—
822C2×C4—21no—
823C2×C4—21no—
824C2×C4—41no—
825C2×C4—41no—
826C2×C4—41no—
827C2×C4—142no—
828C2×C4—142no—
829C2×C4—142no—
830C2×C4—144no—
831C2×C4—288no—
832C2×C4—284no—
833C2×C4—288no—
834C2×C4—284no—
835C2×C4—284no—
836C2×C4—284no—
837C2×C4#647114yescomplemented
838C2×C4C22×D2811yescharacteristic
839C2×C4C22×D2811yescharacteristic
840C2×C4C22×D2811yescharacteristic
841C2×C4C22×D2811yescharacteristic
842C2×C4C22×D2811yescharacteristic
843C2×C4C22×D2811yescharacteristic
844C2×C4C22×D2811yescharacteristic
845C2×C4C22×D2811yescharacteristic
846C2×C4C22×D2811yescharacteristic
847C2×C4C22×D2811yescharacteristic
848C2×C4C22×D2811yescharacteristic
849C2×C4#654812yes—
850C2×C4#655112yes—
851C2×C4C24×D711yescharacteristic
852C8—28no—
853C7#6091611yescharacteristic, complemented, Sylow
854C22—21no—
855C22—21no—
856C22—21no—
857C22—21no—
858C22—21no—
859C22—21no—
860C22—21no—
861C22—44no—
862C22—282no—
863C22—284no—
864C22—284no—
865C22—282no—
866C22—282no—
867C22—284no—
868C22—568no—
869C22#9020112yes—
870C22C2×#647112yes—
871C22C23×D2811yescharacteristic
872C4—21no—
873C4—21no—
874C4—21no—
875C4—21no—
876C4—21no—
877C4—21no—
878C4—21no—
879C4—282no—
880C4—284no—
881C4—282no—
882C4—282no—
883C4#9020112yes—
884C4C2×#647112yes—
885C4C2×#647112yes—
886C4#9043912yes—
887C4C2×#654811yescharacteristic
888C4C2×#655111yescharacteristic
889C2—22no—
890C2—22no—
891C2—41no—
892C2—564no—
893C2—562no—
894C2C2×#9020111yescharacteristic
895C2C22×#647111yescharacteristic
896C2C2×#9043911yescharacteristic
subgroupG/H
centerC22C23×D28
commutator, cosocleC2×C4×C7C25
FrattiniC2×C4C24×D7
FittingC2×C7×#423C2
socleC22×C7C23×D4
hypercenterC2×#423D7
hypocenterC7#60916
LCSG ▷ C2×C4×C7 ▷ C2×C7 ▷ C7
UCSC1 ◁ C22 ◁ C22×C42 ◁ C2×#423

Complements

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

NH ≅ G/Ntype
1. #11742748C2semidirect
2. C2×#90168C2semidirect
3. C2×C7×#423C2semidirect
4. #11741217C2semidirect
5. #11736510C2semidirect
6. #11736509C2semidirect
7. #11736507C2semidirect
8. #11736505C2semidirect
9. #11736504C2semidirect
10. #11736501C2semidirect
11. #11736500C2semidirect
12. #11736473C2semidirect
13. #11736472C2semidirect
14. #11736471C2semidirect
28. #90170C22semidirect
29. #90170C22semidirect
39. #90168C22semidirect
40. #90168C22semidirect
49. #90161C22semidirect
50. #90161C22semidirect
54. C7×#423C22semidirect
55. C7×#423C22semidirect
56. C2×C7×C4⋊C8C22semidirect
57. C2×C7×C4⋊C8C22semidirect
58. #89907C22semidirect
59. #89906C22semidirect
63. #89887C22semidirect
64. #89886C22semidirect
65. #89623C22semidirect
66. #89622C22semidirect
67. #89620C22semidirect
68. #89620C22semidirect
69. #89619C22semidirect
70. #89618C22semidirect
71. #89618C22semidirect
72. #89616C22semidirect
73. #89615C22semidirect
74. #89615C22semidirect
75. #89615C22semidirect
76. #89614C22semidirect
77. #89614C22semidirect
78. #89613C22semidirect
224. C2×#423D7semidirect
401. #423C2×D7semidirect
402. #423C2×D7semidirect
403. C2×C4⋊C8C2×D7semidirect
404. C2×C4⋊C8C2×D7semidirect
436. C2×C4×C7AGL(1,ℤ/8)semidirect
837. C2×C4#6471semidirect
853. C7#60916semidirect

Maximal subgroups

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

subgroupindex
#117427482
C2×#901682
C2×C7×#4232
#117412172
#117365102
#117365092
#117365072
#117365052
#117365042
#117365012
#117365002
#117364732
#117364722
#117364712
#609167