Finite Group Databasebeta

← #14225893

Subgroups — #14225893

Order 1792.

1800 conjugacy classes of subgroups.

The subgroup lattice has 838 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11742748C211yesmaximal, characteristic
2C2×#90161C211yesmaximal, characteristic, complemented
3C2×C7×#431C211yesmaximal, characteristic, complemented
4#11736720C214yesmaximal, complemented
5#11736719C214yesmaximal, complemented
6#11736718C212yesmaximal, complemented
7#11736717C211yesmaximal, characteristic, complemented
8#11736716C211yesmaximal, characteristic, complemented
9#11736715C212yesmaximal, complemented
10#11736714C211yesmaximal, characteristic, complemented
11#11736713C211yesmaximal, characteristic, complemented
12#11736470C214yesmaximal, complemented
13#11736036C214yesmaximal, complemented
14#11735908C212yesmaximal, complemented
15#11735887C212yesmaximal, complemented
16C22×C42×C7C2211yescharacteristic
17#90482—21no—
18#90482—21no—
19#90482C2212yes—
20C2×#6489C2212yes—
21C2×#6487—21no—
22C2×#6487—21no—
23#90170—21no—
24#90170—21no—
25#90170—21no—
26#90170—21no—
27#90170C2212yes—
28#90170C2212yes—
29#90168C2211yescharacteristic
30#90168C2211yescharacteristic
31#90168C2211yescharacteristic
32C4×#1157—21no—
33C4×#1157—21no—
34C4×#1157C2212yes—
35#90161—21no—
36#90161—21no—
37#90161—21no—
38#90161—21no—
39#90161C2212yes—
40#90161C2212yes—
41#90161C2212yes—
42#90161C2212yes—
43#90161C2211yescharacteristic
44#90161C2211yescharacteristic
45#90161C2211yescharacteristic
46C2×#6433C2212yes—
47C2×#6432C2211yescharacteristic
48C2×#6432C2211yescharacteristic
49C2×C4×Dic14—21no—
50C2×C4×Dic14—21no—
51C7×#431C2211yescharacteristic
52C7×#431C2211yescharacteristic
53C7×#431C2212yes—
54C7×#431C2212yes—
55C7×#431C2212yes—
56C2×C7×C4⋊C8C2212yes—
57C2×C7×C22⋊C8C2212yes—
58C2×C4×C7×C8C2212yes—
59#89885C2218yes—
60#89878C2218yes—
61#89623C2214yescomplemented
62#89622C2214yescomplemented
63#89619C2218yescomplemented
64#89618C2214yescomplemented
65#89614C2214yescomplemented
66#89601C2218yescomplemented
67#89509C2218yes—
68#89508C2214yes—
69#89507C2214yes—
70#89495C2218yes—
71#89494C2214yes—
72#89493C2214yes—
73#89469C2218yescomplemented
74#89466C2212yescomplemented
75#89466C2212yescomplemented
76#89455C2218yescomplemented
77#89454C2212yescomplemented
78#89454C2212yescomplemented
79#89453C2212yescomplemented
80#89453C2212yescomplemented
81#89452C2212yescomplemented
82#89452C2212yescomplemented
83#60846—71nomaximal, Sylow
84C23×C4×C7D411yescharacteristic
85C23×C4×C7D411yescharacteristic
86C23×C4×C7C2311yescharacteristic
87C2×#1157—21no—
88C2×#1157—21no—
89C2×#1157C2312yes—
90C22×Dic14—21no—
91C22×Dic14—21no—
92C22×C7×C8C2314yes—
93C2×C42×C7D411yescharacteristic
94C2×C42×C7D411yescharacteristic
95C2×C42×C7D411yescharacteristic
96C2×C42×C7D411yescharacteristic
97C2×C42×C7D411yescharacteristic
98C2×C42×C7D411yescharacteristic
99C2×C42×C7C2311yescharacteristic
100C2×C42×C7C2311yescharacteristic
101C2×C42×C7C2311yescharacteristic
102C2×C42×C7C2311yescharacteristic
103C2×C42×C7C2311yescharacteristic
104C2×C42×C7C2311yescharacteristic
105#6516—22no—
106C2×C22⋊Dic7—22no—
107#6493—21no—
108#6493—21no—
109#6493—21no—
110#6493—21no—
111#6493C2312yes—
112#6493C2312yes—
113#6492—22no—
114#6492—22no—
115#6492—22no—
116C4×C22⋊D7—22no—
117C4×C22⋊D7—22no—
118C4×C22⋊D7—22no—
119C4×C22⋊D7—22no—
120C4×C22⋊D7—22no—
121C4×C22⋊D7—22no—
122#6489—22no—
123#6489—22no—
124#6489—21no—
125#6489—21no—
126#6489C2312yes—
127#6489C2314yes—
128#6489C2314yes—
129C2×C4⋊Dic7—21no—
130C2×C4⋊Dic7—21no—
131C2×C4⋊Dic7C2312yes—
132C2×C4⋊Dic7C2312yes—
133#6487—22no—
134#6487—22no—
135#6487—22no—
136#6487—22no—
137#6487—22no—
138#6487—22no—
139#6487—22no—
140#6487—22no—
141#6487—21no—
142#6487—21no—
143#6487—21no—
144#6487—21no—
145#6487C2312yes—
146#6487C2312yes—
147C2×Dic7⋊C4—22no—
148C2×Dic7⋊C4—22no—
149C2×C4×Dic7—22no—
150#6439—22no—
151#6439—22no—
152#6438—21no—
153#6438—21no—
154#6438C2312yes—
155#6437C2311yescharacteristic
156C4×D28—21no—
157C4×D28—21no—
158C4×D28—21no—
159C4×D28—21no—
160C4×D28C2312yes—
161C4×D28C2312yes—
162#6435—22no—
163#6435—22no—
164#6435—22no—
165C42×D7—22no—
166#6433—22no—
167#6433—22no—
168#6433—21no—
169#6433—21no—
170#6433C2314yes—
171#6433C2314yes—
172#6433C2312yes—
173#6432—21no—
174#6432—21no—
175#6432—21no—
176#6432—21no—
177#6432C2311yescharacteristic
178#6432C2312yes—
179#6432C2312yes—
180#6432C2312yes—
181#6432C2312yes—
182#6432C2311yescharacteristic
183#6432C2311yescharacteristic
184C4×Dic14—22no—
185C4×Dic14—22no—
186C4×Dic14—22no—
187C4×Dic14—22no—
188C4×Dic14—22no—
189C4×Dic14—22no—
190C4×Dic14—22no—
191C4×Dic14—22no—
192C4×Dic14—21no—
193C4×Dic14—21no—
194C4×Dic14—21no—
195C4×Dic14—21no—
196C4×Dic14C2312yes—
197C4×Dic14C2312yes—
198C7×C4⋊C8C2314yes—
199C7×C4⋊C8C2312yes—
200C7×C4⋊C8C2312yes—
201C7×C22⋊C8C2312yes—
202C7×C22⋊C8C2312yes—
203C7×C22⋊C8C2314yes—
204C4×C7×C8C2312yes—
205C4×C7×C8C2312yes—
206C4×C7×C8C2314yes—
207#6395C2318yes—
208#6395C2318yes—
209#6392C2318yes—
210#6392C2318yes—
211#6391C2318yes—
212#6391C2318yes—
213#6390C2318yes—
214#6390C2318yes—
215#3444—71no—
216C2×#533—71no—
217#3233—74no—
218#3232—74no—
219#3231—72no—
220#3230—71no—
221#3229—71no—
222#3228—72no—
223#3227—71no—
224#3226—71no—
225#3160—72no—
226#3131—72no—
227#3091—74no—
228#3076—74no—
229C2×#431D711yescharacteristic, complemented
230C24×C7C2×D411yescharacteristic
231C22×C4×C7—24no—
232C22×C4×C7—24no—
233C22×C4×C7—42no—
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×C7C2×D411yescharacteristic
247C22×C4×C7C2×D411yescharacteristic
248C22×C4×C7C2×D411yescharacteristic
249C22×C4×C7C2411yescharacteristic
250C22×C4×C7C2411yescharacteristic
251C22×C4×C7C2411yescharacteristic
252C2×C22⋊D7—22no—
253C2×C22⋊D7—22no—
254C2×C22⋊D7—22no—
255C22×Dic7—22no—
256C22×Dic7—22no—
257#1157—28no—
258#1157—44no—
259#1157—44no—
260C2×D28—21no—
261C2×D28—21no—
262C2×D28C2412yes—
263C2×C4×D7—22no—
264C2×C4×D7—22no—
265C2×C4×D7—22no—
266C2×Dic14—22no—
267C2×Dic14—22no—
268C2×Dic14—22no—
269C2×Dic14—22no—
270C2×Dic14—21no—
271C2×Dic14—21no—
272C2×Dic14—44no—
273C2×Dic14—44no—
274C2×Dic14C2412yes—
275C2×C7×C8—28no—
276C2×C7×C8C2414yes—
277C2×C7×C8C2414yes—
278C42×C7C2×D411yescharacteristic
279C42×C7C2×D411yescharacteristic
280C42×C7C2×D411yescharacteristic
281C42×C7C2×D411yescharacteristic
282C42×C7C2×D411yescharacteristic
283C42×C7C2×D411yescharacteristic
284C42×C7C2×D411yescharacteristic
285C42×C7C2×D411yescharacteristic
286C42×C7C2×D411yescharacteristic
287C42×C7C2×D411yescharacteristic
288C42×C7C2×D411yescharacteristic
289C42×C7C2×D411yescharacteristic
290C42×C7C2411yescharacteristic
291C42×C7C2411yescharacteristic
292C42×C7C2411yescharacteristic
293C42×C7C2411yescharacteristic
294C22⋊Dic7—24no—
295C22⋊Dic7—24no—
296C22⋊Dic7—22no—
297C22⋊Dic7—22no—
298C22⋊Dic7—22no—
299(C2×D7)⋊C4—22no—
300(C2×D7)⋊C4—22no—
301(C2×D7)⋊C4—22no—
302(C2×D7)⋊C4—22no—
303(C2×D7)⋊C4—22no—
304(C2×D7)⋊C4—22no—
305C4⋊Dic7—22no—
306C4⋊Dic7—22no—
307C4⋊Dic7—22no—
308C4⋊Dic7—22no—
309C4⋊Dic7—21no—
310C4⋊Dic7—21no—
311C4⋊Dic7—21no—
312C4⋊Dic7—21no—
313C4⋊Dic7—22no—
314C4⋊Dic7—22no—
315C4⋊Dic7C2412yes—
316C4⋊Dic7C2412yes—
317C4⋊Dic7C2414yes—
318C4⋊Dic7C2414yes—
319Dic7⋊C4—24no—
320Dic7⋊C4—24no—
321Dic7⋊C4—24no—
322Dic7⋊C4—24no—
323Dic7⋊C4—22no—
324Dic7⋊C4—22no—
325Dic7⋊C4—22no—
326Dic7⋊C4—22no—
327Dic7⋊C4—22no—
328Dic7⋊C4—22no—
329C4×Dic7—24no—
330C4×Dic7—24no—
331C4×Dic7—22no—
332C4×Dic7—22no—
333C4×Dic7—22no—
334#533—72no—
335#533—72no—
336#533—71no—
337#533—72no—
338#533—72no—
339#533—71no—
340#533—71no—
341#533—141no—
342#533—141no—
343#533—141no—
344#533—141no—
345#532—71no—
346#532—71no—
347#532—71no—
348C2×C4⋊Q8—71no—
349C2×C4⋊Q8—71no—
350#529—72no—
351#529—72no—
352#529—141no—
353#529—141no—
354#529—141no—
355#529—141no—
356C2×#125—72no—
357#525—72no—
358#525—141no—
359#525—141no—
360C2×C22⋊Q8—141no—
361C2×C22⋊Q8—141no—
362C4×#41—72no—
363C4×#41—141no—
364C4×#41—141no—
365C2×C4×Q8—141no—
366C2×C4×Q8—141no—
367C2×#117—72no—
368C22×C42C2×D711yescharacteristic
369#500—72no—
370#500—72no—
371#499—78no—
372#498—72no—
373#498—72no—
374#488—78no—
375#487—72no—
376#487—72no—
377#486—72no—
378#486—72no—
379#485—78no—
380#484—74no—
381#483—74no—
382#482—78no—
383#481—74no—
384#480—74no—
385#479—78no—
386#478—78no—
387#477—74no—
388#476—74no—
389#475—74no—
390#474—74no—
391#431C2×D711yescharacteristic
392#431C2×D711yescharacteristic
393#431C2×D712yes—
394#431C2×D712yes—
395#431C2×D712yes—
396#427—78no—
397C2×C4⋊C8C2×D712yes—
398#416—78no—
399C2×C22⋊C8C2×D712yes—
400C2×C4×C8C2×D712yes—
401C23×C7—22no—
402C23×C7—22no—
403C23×C7—41no—
404C23×C7C22×D411yescharacteristic
405C23×C7C22×D411yescharacteristic
406C23×C7C22×D411yescharacteristic
407C22×D7—22no—
408C2×C4×C7—22no—
409C2×C4×C7—22no—
410C2×C4×C7—22no—
411C2×C4×C7—22no—
412C2×C4×C7—22no—
413C2×C4×C7—22no—
414C2×C4×C7—22no—
415C2×C4×C7—22no—
416C2×C4×C7—22no—
417C2×C4×C7—22no—
418C2×C4×C7—22no—
419C2×C4×C7—22no—
420C2×C4×C7—22no—
421C2×C4×C7—41no—
422C2×C4×C7—41no—
423C2×C4×C7—41no—
424C2×C4×C7#13514yes—
425C2×C4×C7C22×D411yescharacteristic
426C2×C4×C7C22×D411yescharacteristic
427C2×C4×C7C22×D411yescharacteristic
428C2×C4×C7C22×D411yescharacteristic
429C2×C4×C7C22×D411yescharacteristic
430C2×C4×C7C22×D411yescharacteristic
431C2×C4×C7C22×D411yescharacteristic
432C2×C4×C7C22×D411yescharacteristic
433C2×C4×C7C22×D411yescharacteristic
434C2×C4×C7C22×D411yescharacteristic
435C2×C4×C7C22×D411yescharacteristic
436C2×C4×C72−1+414yes—
437C2×C4×C7C2511yescharacteristic
438C22⋊D7—44no—
439C22⋊D7—44no—
440C22⋊D7—44no—
441C2×Dic7—24no—
442C2×Dic7—24no—
443C2×Dic7—22no—
444C2×Dic7—22no—
445C2×Dic7—22no—
446C2×Dic7—44no—
447C2×Dic7—44no—
448D28—24no—
449D28—42no—
450D28—42no—
451C4×D7—44no—
452C4×D7—44no—
453C4×D7—44no—
454Dic14—24no—
455Dic14—44no—
456Dic14—44no—
457Dic14—44no—
458Dic14—42no—
459Dic14—44no—
460Dic14—42no—
461C7×C8—24no—
462C7×C8—24no—
463C2×#41—72no—
464C2×#41—141no—
465C2×#41—141no—
466C22×Q8—141no—
467C22×Q8—141no—
468C23×C4D2811yescharacteristic
469C23×C4D2811yescharacteristic
470C23×C4C22×D711yescharacteristic
471C22×C8C22×D714yes—
472C4⋊Q8—72no—
473C4⋊Q8—72no—
474C4⋊Q8—72no—
475C4⋊Q8—72no—
476C4⋊Q8—71no—
477C4⋊Q8—71no—
478C4⋊Q8—71no—
479C4⋊Q8—141no—
480C4⋊Q8—141no—
481C4⋊Q8—141no—
482C4⋊Q8—141no—
483#127—71no—
484#126—142no—
485#126—142no—
486#125—74no—
487#125—74no—
488#125—72no—
489#125—142no—
490#125—142no—
491#125—141no—
492#125—141no—
493#124—72no—
494#124—141no—
495#124—141no—
496#123—142no—
497#123—142no—
498#123—142no—
499C22⋊Q8—72no—
500C22⋊Q8—72no—
501C22⋊Q8—142no—
502C22⋊Q8—142no—
503C22⋊Q8—142no—
504C22⋊Q8—142no—
505C22⋊Q8—142no—
506C22⋊Q8—142no—
507C22⋊Q8—142no—
508C22⋊Q8—142no—
509C22⋊Q8—141no—
510C22⋊Q8—141no—
511C22⋊Q8—141no—
512C22⋊Q8—141no—
513#121—72no—
514#121—72no—
515#121—141no—
516#121—141no—
517#121—141no—
518#121—141no—
519#120—142no—
520C4×Q8—72no—
521C4×Q8—72no—
522C4×Q8—142no—
523C4×Q8—142no—
524C4×Q8—142no—
525C4×Q8—142no—
526C4×Q8—142no—
527C4×Q8—142no—
528C4×Q8—142no—
529C4×Q8—142no—
530C4×Q8—141no—
531C4×Q8—141no—
532C4×Q8—141no—
533C4×Q8—141no—
534C4×D4—72no—
535C4×D4—72no—
536C4×D4—142no—
537C4×D4—142no—
538C4×D4—142no—
539C4×D4—142no—
540C4×D4—142no—
541C4×D4—142no—
542C4×D4—141no—
543C4×D4—141no—
544C4×D4—141no—
545C4×D4—141no—
546#117—74no—
547#117—74no—
548#117—72no—
549#117—142no—
550#117—142no—
551#117—141no—
552#117—141no—
553#117—142no—
554#117—142no—
555#117—142no—
556C2×C4⋊C4—72no—
557C2×C4⋊C4—72no—
558C2×C4⋊C4—142no—
559C2×C4⋊C4—142no—
560C2×C4⋊C4—141no—
561C2×C4⋊C4—141no—
562C2×C22⋊C4—142no—
563C2×C42—142no—
564C2×C42—142no—
565C2×C42D2811yescharacteristic
566C2×C42D2811yescharacteristic
567C2×C42D2811yescharacteristic
568C2×C42D2811yescharacteristic
569C2×C42D2811yescharacteristic
570C2×C42D2811yescharacteristic
571C2×C42C22×D711yescharacteristic
572C2×C42C22×D711yescharacteristic
573C2×C42C22×D711yescharacteristic
574C2×C42C22×D711yescharacteristic
575C2×C42C22×D711yescharacteristic
576C2×C42C22×D711yescharacteristic
577#107—78no—
578#107—78no—
579#106—78no—
580#106—78no—
581C4⋊C8C22×D712yes—
582C4⋊C8C22×D712yes—
583C4⋊C8C22×D714yes—
584#103—78no—
585#103—78no—
586#102—78no—
587#102—78no—
588C22⋊C8C22×D712yes—
589C22⋊C8C22×D712yes—
590C22⋊C8C22×D714yes—
591C4×C8C22×D712yes—
592C4×C8C22×D712yes—
593C4×C8C22×D714yes—
594C22×C7—21no—
595C22×C7—21no—
596C22×C7—21no—
597C22×C7—21no—
598C22×C7—21no—
599C22×C7—21no—
600C22×C7—21no—
601C22×C7—44no—
602C22×C7#53612yes—
603C22×C7C2×#13512yes—
604C22×C7C23×D411yescharacteristic
605C2×D7—42no—
606C2×D7—42no—
607C2×D7—42no—
608C4×C7—21no—
609C4×C7—21no—
610C4×C7—21no—
611C4×C7—21no—
612C4×C7—21no—
613C4×C7—21no—
614C4×C7—21no—
615C4×C7#53612yes—
616C4×C7C2×#13512yes—
617C4×C7C2×#13512yes—
618C4×C7#57512yes—
619C4×C7C2×2−1+412yes—
620Dic7—42no—
621Dic7—44no—
622Dic7—42no—
623Dic7—44no—
624Dic7—42no—
625C24C2×D2811yescharacteristic
626#41—148no—
627#41—284no—
628#41—284no—
629C2×Q8—72no—
630C2×Q8—141no—
631C2×Q8—141no—
632C2×Q8—142no—
633C2×Q8—142no—
634C2×Q8—142no—
635C2×Q8—142no—
636C2×Q8—284no—
637C2×Q8—284no—
638C2×D4—72no—
639C2×D4—142no—
640C2×D4—142no—
641C2×D4—142no—
642C2×D4—141no—
643C2×D4—141no—
644C22×C4—24no—
645C22×C4—24no—
646C22×C4—42no—
647C22×C4—142no—
648C22×C4—142no—
649C22×C4—142no—
650C22×C4—142no—
651C22×C4—142no—
652C22×C4C2×D2811yescharacteristic
653C22×C4C2×D2811yescharacteristic
654C22×C4C2×D2811yescharacteristic
655C22×C4C2×D2811yescharacteristic
656C22×C4C2×D2811yescharacteristic
657C22×C4C2×D2811yescharacteristic
658C22×C4C2×D2811yescharacteristic
659C22×C4C2×D2811yescharacteristic
660C22×C4C2×D2811yescharacteristic
661C22×C4C2×D2811yescharacteristic
662C22×C4C2×D2811yescharacteristic
663C22×C4C2×D2811yescharacteristic
664C22×C4C2×D2811yescharacteristic
665C22×C4C2×D2811yescharacteristic
666C22×C4C2×D2811yescharacteristic
667C22×C4C23×D711yescharacteristic
668C22×C4C23×D711yescharacteristic
669C22×C4C23×D711yescharacteristic
670C2×C8—28no—
671C2×C8C23×D714yes—
672C2×C8C23×D714yes—
673C4⋊C4—74no—
674C4⋊C4—74no—
675C4⋊C4—72no—
676C4⋊C4—72no—
677C4⋊C4—144no—
678C4⋊C4—144no—
679C4⋊C4—144no—
680C4⋊C4—144no—
681C4⋊C4—142no—
682C4⋊C4—142no—
683C4⋊C4—142no—
684C4⋊C4—142no—
685C4⋊C4—142no—
686C4⋊C4—142no—
687C4⋊C4—142no—
688C4⋊C4—142no—
689C4⋊C4—142no—
690C4⋊C4—142no—
691C4⋊C4—142no—
692C4⋊C4—142no—
693C4⋊C4—141no—
694C4⋊C4—141no—
695C4⋊C4—141no—
696C4⋊C4—141no—
697C22⋊C4—144no—
698C22⋊C4—144no—
699C22⋊C4—142no—
700C22⋊C4—142no—
701C22⋊C4—142no—
702C22⋊C4—142no—
703C22⋊C4—142no—
704C22⋊C4—142no—
705C22⋊C4—142no—
706C22⋊C4—142no—
707C22⋊C4—142no—
708C42—144no—
709C42—142no—
710C42—142no—
711C42—142no—
712C42—144no—
713C42C2×D2811yescharacteristic
714C42C2×D2811yescharacteristic
715C42C2×D2811yescharacteristic
716C42C2×D2811yescharacteristic
717C42C2×D2811yescharacteristic
718C42C2×D2811yescharacteristic
719C42C2×D2811yescharacteristic
720C42C2×D2811yescharacteristic
721C42C2×D2811yescharacteristic
722C42C2×D2811yescharacteristic
723C42C2×D2811yescharacteristic
724C42C2×D2811yescharacteristic
725C42C23×D711yescharacteristic
726C42C23×D711yescharacteristic
727C42C23×D711yescharacteristic
728C42C23×D711yescharacteristic
729C2×C7—22no—
730C2×C7—22no—
731C2×C7—41no—
732C2×C7C2×#53611yescharacteristic
733C2×C7C22×#13511yescharacteristic
734C2×C7C2×#57511yescharacteristic
735D7—82no—
736C23—22no—
737C23—22no—
738C23—41no—
739C23—142no—
740C23C22×D2811yescharacteristic
741C23C22×D2811yescharacteristic
742C23C22×D2811yescharacteristic
743Q8—144no—
744Q8—284no—
745Q8—284no—
746Q8—284no—
747Q8—282no—
748Q8—284no—
749Q8—282no—
750D4—144no—
751D4—284no—
752D4—284no—
753D4—284no—
754D4—282no—
755D4—282no—
756C2×C4—22no—
757C2×C4—22no—
758C2×C4—22no—
759C2×C4—22no—
760C2×C4—22no—
761C2×C4—22no—
762C2×C4—22no—
763C2×C4—22no—
764C2×C4—22no—
765C2×C4—22no—
766C2×C4—22no—
767C2×C4—22no—
768C2×C4—22no—
769C2×C4—41no—
770C2×C4—41no—
771C2×C4—41no—
772C2×C4—142no—
773C2×C4—142no—
774C2×C4—142no—
775C2×C4—144no—
776C2×C4—144no—
777C2×C4—284no—
778C2×C4—284no—
779C2×C4—284no—
780C2×C4—284no—
781C2×C4—284no—
782C2×C4#646714yes—
783C2×C4C22×D2811yescharacteristic
784C2×C4C22×D2811yescharacteristic
785C2×C4C22×D2811yescharacteristic
786C2×C4C22×D2811yescharacteristic
787C2×C4C22×D2811yescharacteristic
788C2×C4C22×D2811yescharacteristic
789C2×C4C22×D2811yescharacteristic
790C2×C4C22×D2811yescharacteristic
791C2×C4C22×D2811yescharacteristic
792C2×C4C22×D2811yescharacteristic
793C2×C4C22×D2811yescharacteristic
794C2×C4#655414yes—
795C2×C4C24×D711yescharacteristic
796C8—24no—
797C8—24no—
798C7#6084611yescharacteristic, complemented, Sylow
799C22—21no—
800C22—21no—
801C22—21no—
802C22—21no—
803C22—21no—
804C22—21no—
805C22—21no—
806C22—44no—
807C22—282no—
808C22—282no—
809C22—282no—
810C22#9021712yes—
811C22C2×#646712yes—
812C22C23×D2811yescharacteristic
813C4—21no—
814C4—21no—
815C4—21no—
816C4—21no—
817C4—21no—
818C4—21no—
819C4—21no—
820C4—282no—
821C4—282no—
822C4—284no—
823C4—282no—
824C4—284no—
825C4#9021712yes—
826C4C2×#646712yes—
827C4C2×#646712yes—
828C4#9043912yes—
829C4C2×#655412yes—
830C2—22no—
831C2—22no—
832C2—41no—
833C2—562no—
834C2C2×#9021711yescharacteristic
835C2C22×#646711yescharacteristic
836C2C2×#9043911yescharacteristic
subgroupG/H
centerC2×C4C22×D28
commutator, cosocleC2×C4×C7C25
FrattiniC2×C4C24×D7
FittingC2×C7×#431C2
socleC22×C7C23×D4
prime radical#11742748C2
hypercenterC2×#431D7
hypocenterC7#60846
LCSG ▷ C2×C4×C7 ▷ C2×C7 ▷ C7
UCSC1 ◁ C2×C4 ◁ C22×C42 ◁ C2×#431

Complements

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

NH ≅ G/Ntype
2. C2×#90161C2semidirect
3. C2×C7×#431C2semidirect
4. #11736720C2semidirect
5. #11736719C2semidirect
6. #11736718C2semidirect
7. #11736717C2semidirect
8. #11736716C2semidirect
9. #11736715C2semidirect
10. #11736714C2semidirect
11. #11736713C2semidirect
12. #11736470C2semidirect
13. #11736036C2semidirect
14. #11735908C2semidirect
15. #11735887C2semidirect
61. #89623C22semidirect
62. #89622C22semidirect
63. #89619C22semidirect
64. #89618C22semidirect
65. #89614C22semidirect
66. #89601C22semidirect
73. #89469C22semidirect
74. #89466C22semidirect
75. #89466C22semidirect
76. #89455C22semidirect
77. #89454C22semidirect
78. #89454C22semidirect
79. #89453C22semidirect
80. #89453C22semidirect
81. #89452C22semidirect
82. #89452C22semidirect
229. C2×#431D7semidirect
798. C7#60846semidirect

Maximal subgroups

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

subgroupindex
#117427482
C2×#901612
C2×C7×#4312
#117367202
#117367192
#117367182
#117367172
#117367162
#117367152
#117367142
#117367132
#117364702
#117360362
#117359082
#117358872
#608467