Finite Group Databasebeta

← #14224305

Subgroups — #14224305

Order 1792.

1902 conjugacy classes of subgroups.

The subgroup lattice has 872 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C7×#3511C211yesmaximal, characteristic, complemented
2#11742917C211yesmaximal, characteristic, complemented
3#11740902C214yesmaximal, complemented
4#11740901C214yesmaximal, complemented
5#11740868C212yesmaximal, complemented
6#11740867C212yesmaximal, complemented
7#11740791C212yesmaximal, complemented
8#11740790C212yesmaximal, complemented
9#11740738C212yesmaximal, complemented
10#11740737C212yesmaximal, complemented
11#11740734C211yesmaximal, characteristic, complemented
12#11740727C211yesmaximal, characteristic, complemented
13#11740652C211yesmaximal, characteristic, complemented
14C2×#89861C211yesmaximal, characteristic, complemented
15#11740016C212yesmaximal, complemented
16#11740009C212yesmaximal, complemented
17#11739956C211yesmaximal, characteristic, complemented
18C7×#556—21no—
19C7×#555—21no—
20C7×#554—21no—
21C7×#553—22no—
22C7×#548—22no—
23C7×#547—21no—
24C7×#542C2214yescomplemented
25C7×#537C2212yes—
26C7×#533C2212yescomplemented
27C7×#532C2211yescharacteristic
28C7×#532C2212yescomplemented
29C2×C7×C4⋊Q8C2211yescharacteristic
30C7×#520C2212yes—
31C4×C7×#41C2211yescharacteristic
32#90521C2211yescharacteristic
33#90516C2211yescharacteristic
34C2×#6514C2212yes—
35C2×#6512C2212yes—
36C2×#6511C2212yes—
37#90259—21no—
38#90259—21no—
39#90250—21no—
40#90250—21no—
41#90247—22no—
42#90247—22no—
43#90225C2212yes—
44#90225C2212yes—
45#90212C2211yescharacteristic
46#90207C2211yescharacteristic
47#90170C2212yes—
48#90170C2212yes—
49C2×#6438C2211yescharacteristic
50#90161C2211yescharacteristic
51#90005C2212yes—
52#90005C2212yes—
53#89861C2212yes—
54#89861C2212yes—
55#89861C2214yes—
56#89858C2212yes—
57#89854C2211yescharacteristic, complemented
58#89854C2211yescharacteristic, complemented
59#89852C2212yescomplemented
60#89852C2212yescomplemented
61#89851C2212yescomplemented
62#89850C2212yescomplemented
63#89846C2212yes—
64#89843C2211yescharacteristic, complemented
65#89843C2211yescharacteristic, complemented
66#89831C2214yes—
67#89827C2212yescomplemented
68#89827C2212yescomplemented
69#89824C2214yescomplemented
70#89823C2214yescomplemented
71#89821C2214yes—
72#89820C2214yes—
73#89814C2214yescomplemented
74#89813C2214yescomplemented
75#89811C2214yes—
76#89810C2214yes—
77#89802C2214yescomplemented
78C4×#1144C2214yescomplemented
79#89798C2214yes—
80C4×#1143C2214yes—
81#89790C2214yescomplemented
82C4×#1142C2214yescomplemented
83#89786C2214yes—
84C4×#1141C2214yes—
85#89769C2212yes—
86#89769C2214yescomplemented
87C2×#6384C2212yes—
88C2×#6383C2212yes—
89#89736C2212yes—
90#89736C2212yes—
91C4×#1136C2211yescharacteristic
92C4×#1136C2212yescomplemented
93C2×#6377C2211yescharacteristic
94C2×#6377C2212yescomplemented
95#60727—71nomaximal, Sylow
96C2×C7×#41—22no—
97C2×C7×#41C2312yes—
98C2×C7×#41C2311yescharacteristic
99C22×C7×Q8—21no—
100C22×D28C2311yescharacteristic
101C22×Dic14C2311yescharacteristic
102C7×C4⋊Q8—21no—
103C7×C4⋊Q8—21no—
104C7×C4⋊Q8C2311yescharacteristic
105C7×C4⋊Q8C2312yes—
106C7×C4⋊Q8C2312yes—
107C7×#127C2311yescharacteristic
108C7×#126—24no—
109C7×#125—22no—
110C7×#124—24no—
111C7×#124—22no—
112C7×#124C2312yes—
113C7×#123—24no—
114C7×C22⋊Q8—22no—
115C7×C22⋊Q8—22no—
116C7×C22⋊Q8—24no—
117C7×C22⋊Q8C2314yes—
118C7×#121—22no—
119C7×#121—24no—
120C7×#121—21no—
121C7×#121—21no—
122C7×#121—22no—
123C7×#121C2314yes—
124C4×C7×Q8—22no—
125C4×C7×Q8D411yescharacteristic
126C4×C7×Q8D411yescharacteristic
127C4×C7×Q8C2314yes—
128C4×C7×D4—24no—
129C4×C7×D4—21no—
130C4×C7×D4—21no—
131C4×C7×D4—22no—
132C4×C7×D4D412yes—
133C4×C7×D4D412yes—
134C4×C7×D4D411yescharacteristic
135C4×C7×D4D411yescharacteristic
136C4×C7×D4C2314yes—
137C7×#117—22no—
138C7×#117—22no—
139C7×#117C2311yescharacteristic
140C7×#117C2312yes—
141C2×C7×C4⋊C4—21no—
142C2×C7×C4⋊C4—22no—
143C2×C7×C4⋊C4C2312yes—
144C2×C42×C7C2311yescharacteristic
145C2×C42×C7C2312yes—
146#6514—28no—
147#6512—28no—
148#6511—28no—
149#6510—21no—
150#6507—21no—
151C2×#1144C2314yes—
152C2×#1143C2314yes—
153#6503—21no—
154#6500—22no—
155#6499—21no—
156#6498—22no—
157C2×#1142C2314yes—
158C2×#1141C2314yes—
159#6493C2312yes—
160#6493C2312yes—
161#6492—22no—
162#6492—22no—
163C4×C22⋊D7—22no—
164C4×C22⋊D7—22no—
165C2×(C2×D7)⋊C4—21no—
166C2×(C2×D7)⋊C4—21no—
167#6489C2311yescharacteristic
168#6489C2311yescharacteristic
169#6487—21no—
170#6487—21no—
171#6487C2312yes—
172#6487C2312yes—
173C2×#1136C2314yes—
174C2×#1136C2312yes—
175C22×C7⋊C8C2312yes—
176C22×C7⋊C8C2314yes—
177#6461—22no—
178#6461—22no—
179#6459—22no—
180#6459—22no—
181#6456—21no—
182#6456—21no—
183#6450—21no—
184#6450—21no—
185#6448—22no—
186#6448—22no—
187#6446—22no—
188#6446—22no—
189D7×C22⋊C4—22no—
190#6440—22no—
191#6439—22no—
192#6439—22no—
193#6438—21no—
194#6438—21no—
195#6438C2312yes—
196#6438C2312yes—
197C4×D28C2312yes—
198C4×D28C2312yes—
199#6435—22no—
200#6435—22no—
201#6433C2311yescharacteristic
202#6433C2311yescharacteristic
203#6432C2311yescharacteristic
204#6432C2311yescharacteristic
205C4×Dic14—21no—
206C4×Dic14—21no—
207C4×Dic14C2312yes—
208C4×Dic14C2312yes—
209#6409C2312yes—
210#6409C2312yes—
211#6409C2312yes—
212#6409C2312yes—
213#6406C2312yes—
214#6406C2312yes—
215#6406C2312yes—
216#6406C2312yes—
217#6384C2314yes—
218#6384C2314yes—
219#6383C2314yes—
220#6383C2314yes—
221#6382C2314yes—
222#6382C2314yes—
223#6381C2314yes—
224#6381C2314yes—
225#6377C2312yes—
226#6377C2311yescharacteristic
227#6377C2311yescharacteristic
228#6377C2312yes—
229#6377C2314yes—
230C4×C7⋊C8C2312yes—
231C4×C7⋊C8C2314yes—
232#3511D711yescharacteristic, complemented
233#3510—71no—
234#3181—72no—
235#3180—72no—
236#3175—74no—
237#3173—74no—
238#3172—72no—
239#3171—72no—
240#3165—71no—
241#3153—71no—
242#3135—71no—
243C2×#489—71no—
244#3063—72no—
245#3062—72no—
246#2947—72no—
247#2946—72no—
248#2875—71no—
249C23×D7—21no—
250C7×#41—24no—
251C7×#41—24no—
252C7×#41—24no—
253C7×#41—84no—
254C2×C7×Q8—22no—
255C2×C7×Q8—22no—
256C2×C7×Q8—82no—
257C2×C7×Q8C2×D411yescharacteristic
258C2×C7×Q8C2412yes—
259C2×C7×D4—22no—
260C2×C7×D4—24no—
261C2×C7×D4—21no—
262C2×C7×D4—21no—
263C2×C7×D4C2×D412yes—
264C2×C7×D4C2×D411yescharacteristic
265C2×C7×D4C2412yes—
266C22×C4×C7—22no—
267C22×C4×C7—22no—
268C22×C4×C7—24no—
269C22×C4×C7C2×D411yescharacteristic
270C22×C4×C7C2×D411yescharacteristic
271C22×C4×C7C2×D412yes—
272C22×C4×C7C2×D412yes—
273C22×C4×C7C2412yes—
274C22×C4×C7C2411yescharacteristic
275C2×C22⋊D7—22no—
276C2×C22⋊D7—22no—
277C22×Dic7—21no—
278C2×D28—24no—
279C2×D28—21no—
280C2×D28C2412yes—
281C2×C4×D7—22no—
282C2×C4×D7—22no—
283C2×Dic14—24no—
284C2×Dic14—21no—
285C2×Dic14—21no—
286C2×Dic14—21no—
287C2×Dic14C2412yes—
288C7×C4⋊C4—22no—
289C7×C4⋊C4—22no—
290C7×C4⋊C4—24no—
291C7×C4⋊C4—22no—
292C7×C4⋊C4—21no—
293C7×C4⋊C4—21no—
294C7×C4⋊C4—24no—
295C7×C4⋊C4C2×D411yescharacteristic
296C7×C4⋊C4C2×D411yescharacteristic
297C7×C4⋊C4C2×D412yes—
298C7×C4⋊C4C2×D412yes—
299C7×C4⋊C4C2414yes—
300C7×C22⋊C4—24no—
301C7×C22⋊C4—24no—
302C7×C22⋊C4—24no—
303C7×C22⋊C4—22no—
304C7×C22⋊C4—22no—
305C7×C22⋊C4C2×D412yes—
306C7×C22⋊C4C2×D412yes—
307C7×C22⋊C4C2×D412yes—
308C42×C7—24no—
309C42×C7C2×D411yescharacteristic
310C42×C7C2×D411yescharacteristic
311C42×C7C2×D412yes—
312C42×C7C2×D412yes—
313C42×C7C2412yes—
314C42×C7C2411yescharacteristic
315C42×C7C2411yescharacteristic
316C22⋊Dic7—21no—
317C22⋊Dic7—21no—
318C22⋊Dic7—22no—
319C22⋊Dic7—22no—
320#1144—28no—
321#1143—28no—
322#1142—28no—
323#1141—28no—
324(C2×D7)⋊C4—22no—
325(C2×D7)⋊C4—22no—
326(C2×D7)⋊C4—22no—
327(C2×D7)⋊C4—22no—
328(C2×D7)⋊C4—22no—
329(C2×D7)⋊C4—22no—
330(C2×D7)⋊C4—22no—
331(C2×D7)⋊C4—22no—
332C4⋊Dic7—21no—
333C4⋊Dic7—21no—
334C4⋊Dic7C2411yescharacteristic
335C4⋊Dic7C2411yescharacteristic
336C4⋊Dic7C2411yescharacteristic
337C4⋊Dic7C2411yescharacteristic
338Dic7⋊C4—21no—
339Dic7⋊C4—21no—
340Dic7⋊C4—21no—
341Dic7⋊C4—21no—
342Dic7⋊C4—22no—
343Dic7⋊C4—22no—
344Dic7⋊C4—22no—
345Dic7⋊C4—22no—
346C4×Dic7—21no—
347C4×Dic7—21no—
348C4×Dic7—22no—
349C4×Dic7—22no—
350#1136—28no—
351#1136#4118yescomplemented
352C2×C7⋊C8—24no—
353C2×C7⋊C8—28no—
354C2×C7⋊C8C2412yes—
355C2×C7⋊C8C2412yes—
356C2×C7⋊C8C2414yes—
357C2×#137—72no—
358C2×AGL(1,ℤ/8)—72no—
359C2×#131—72no—
360#559—141no—
361#559—141no—
362#556—21no—
363#556—141no—
364#556—141no—
365#555—21no—
366#554—21no—
367#553—22no—
368#551—142no—
369#551—142no—
370#548—22no—
371#547—21no—
372#542—72no—
373#542—72no—
374#542C2×D714yescomplemented
375#537C2×D712yes—
376#536—71no—
377#535—71no—
378#533—71no—
379#533C2×D712yescomplemented
380#532C2×D711yescharacteristic
381#532C2×D712yescomplemented
382C2×C4⋊Q8C2×D711yescharacteristic
383#529—72no—
384#529—72no—
385C2×#124—71no—
386#520C2×D712yes—
387#519—71no—
388#518—71no—
389C4×#41C2×D711yescharacteristic
390#501—72no—
391#501—72no—
392#500—72no—
393#498—72no—
394#497—72no—
395#496—72no—
396#495—74no—
397#491—71no—
398#491—71no—
399#490—71no—
400#490—71no—
401#489—72no—
402#489—74no—
403#489—72no—
404#489—72no—
405#489—72no—
406#470—74no—
407#469—74no—
408#468—74no—
409#468—74no—
410#467—74no—
411#466—74no—
412#465—74no—
413#465—74no—
414#442—74no—
415#441—74no—
416#440—74no—
417#440—74no—
418C4×Q16—74no—
419C4×SD16—74no—
420C4×SD16—74no—
421C4×D8—74no—
422#428—72no—
423#428—72no—
424#416—72no—
425#416—72no—
426C2×#103—72no—
427C2×#102—72no—
428#405—74no—
429#405—72no—
430C4×M16—71no—
431C4×M16—72no—
432C2×#97—71no—
433C2×#97—72no—
434C23×C7—22no—
435C23×C7C22×D412yes—
436C23×C7C22×D411yescharacteristic
437C22×D7—22no—
438C22×D7—42no—
439C22×D7—81no—
440C22×D7—81no—
441C7×Q8—22no—
442C7×Q8—22no—
443C7×Q8—22no—
444C7×Q8—44no—
445C7×Q8—82no—
446C7×D4—24no—
447C7×D4—22no—
448C7×D4—22no—
449C7×D4—22no—
450C7×D4—42no—
451C7×D4—42no—
452C7×D4—44no—
453C7×D4—84no—
454C2×C4×C7—24no—
455C2×C4×C7—22no—
456C2×C4×C7—24no—
457C2×C4×C7—41no—
458C2×C4×C7—42no—
459C2×C4×C7—41no—
460C2×C4×C7—42no—
461C2×C4×C7—44no—
462C2×C4×C7—84no—
463C2×C4×C7—82no—
464C2×C4×C7C22×D412yes—
465C2×C4×C7C22×D412yes—
466C2×C4×C7C22×D411yescharacteristic
467C2×C4×C7C22×D411yescharacteristic
468C2×C4×C7C22×D412yes—
469C2×C4×C7C22×D411yescharacteristic
470C2×C4×C7C22×D411yescharacteristic
471C2×C4×C7C22×D411yescharacteristic
472C2×C4×C7C2×#4114yes—
473C2×C4×C7C2511yescharacteristic
474C22⋊D7—82no—
475C22⋊D7—82no—
476C2×Dic7—21no—
477C2×Dic7—21no—
478C2×Dic7—22no—
479C2×Dic7—21no—
480C2×Dic7—21no—
481C2×Dic7—42no—
482D28—24no—
483D28—42no—
484C4×D7—82no—
485C4×D7—82no—
486Dic14—24no—
487Dic14—42no—
488Dic14—81no—
489Dic14—81no—
490C7⋊C8—22no—
491C7⋊C8—22no—
492C7⋊C8C2×#4118yes—
493C2×#41—22no—
494C2×#41C22×D712yes—
495C2×#41C22×D711yescharacteristic
496C22×Q8—21no—
497C22×Q8—71no—
498C22×D4—71no—
499#137—148no—
500AGL(1,ℤ/8)—148no—
501C2×Q16—74no—
502C2×SD16—74no—
503C2×SD16—74no—
504C2×D8—74no—
505#131—148no—
506C2×M16—72no—
507C2×M16—74no—
508C22×C8—72no—
509C22×C8—74no—
510C4⋊Q8—21no—
511C4⋊Q8—21no—
512C4⋊Q8—71no—
513C4⋊Q8—71no—
514C4⋊Q8—141no—
515C4⋊Q8C22×D711yescharacteristic
516C4⋊Q8C22×D712yes—
517C4⋊Q8C22×D712yes—
518#127—141no—
519#127C22×D711yescharacteristic
520#126—24no—
521#126—142no—
522#126—142no—
523#126—142no—
524#126—142no—
525#125—22no—
526#125—71no—
527#125—71no—
528#124—24no—
529#124—22no—
530#124—72no—
531#124—72no—
532#124—141no—
533#124—141no—
534#124—142no—
535#124—142no—
536#124—141no—
537#124—141no—
538#124C22×D712yes—
539#123—24no—
540#123—142no—
541#123—142no—
542#123—142no—
543#123—142no—
544#123—142no—
545C22⋊Q8—22no—
546C22⋊Q8—22no—
547C22⋊Q8—24no—
548C22⋊Q8—72no—
549C22⋊Q8—72no—
550C22⋊Q8—141no—
551C22⋊Q8—141no—
552C22⋊Q8—142no—
553C22⋊Q8—142no—
554C22⋊Q8C22×D714yes—
555#121—22no—
556#121—24no—
557#121—21no—
558#121—21no—
559#121—22no—
560#121—72no—
561#121—72no—
562#121C22×D714yes—
563#120—142no—
564C4×Q8—22no—
565C4×Q8—72no—
566C4×Q8—72no—
567C4×Q8—141no—
568C4×Q8—141no—
569C4×Q8—141no—
570C4×Q8—141no—
571C4×Q8C22⋊D711yescharacteristic
572C4×Q8C22⋊D711yescharacteristic
573C4×Q8C22×D714yes—
574C4×D4—24no—
575C4×D4—21no—
576C4×D4—21no—
577C4×D4—22no—
578C4×D4—72no—
579C4×D4—72no—
580C4×D4—142no—
581C4×D4—142no—
582C4×D4—141no—
583C4×D4—141no—
584C4×D4C22⋊D711yescharacteristic
585C4×D4C22⋊D712yes—
586C4×D4C22⋊D712yes—
587C4×D4C22⋊D711yescharacteristic
588C4×D4C22×D714yes—
589#117—22no—
590#117—22no—
591#117—71no—
592#117—71no—
593#117—142no—
594#117—142no—
595#117—142no—
596#117C22×D711yescharacteristic
597#117C22×D712yes—
598C2×C4⋊C4—21no—
599C2×C4⋊C4—22no—
600C2×C4⋊C4C22×D712yes—
601C2×C22⋊C4—141no—
602C2×C22⋊C4—141no—
603C2×C22⋊C4—142no—
604C2×C42C22×D711yescharacteristic
605C2×C42C22×D712yes—
606#107—74no—
607#107—74no—
608#106—74no—
609#106—74no—
610#103—72no—
611#103—72no—
612#103—72no—
613#103—72no—
614#103—74no—
615#103—74no—
616#102—72no—
617#102—72no—
618#102—72no—
619#102—72no—
620#102—74no—
621#102—74no—
622#97—71no—
623#97—71no—
624#97—72no—
625#97—74no—
626#97—72no—
627C4×C8—74no—
628C4×C8—72no—
629C22×C7—21no—
630C22×C7—21no—
631C22×C7—22no—
632C22×C7—22no—
633C22×C7—22no—
634C22×C7—42no—
635C22×C7—42no—
636C22×C7—42no—
637C22×C7#53212yes—
638C22×C7C23×D411yescharacteristic
639C2×D7—42no—
640C2×D7—42no—
641C2×D7—42no—
642C2×D7—162no—
643C4×C7—21no—
644C4×C7—22no—
645C4×C7—21no—
646C4×C7—21no—
647C4×C7—22no—
648C4×C7—21no—
649C4×C7—22no—
650C4×C7—44no—
651C4×C7—42no—
652C4×C7#53212yes—
653C4×C7C22×#4112yes—
654Dic7—41no—
655Dic7—41no—
656Dic7—41no—
657Dic7—41no—
658Dic7—42no—
659C24—141no—
660#41—24no—
661#41—24no—
662#41—24no—
663#41—84no—
664C2×Q8—22no—
665C2×Q8—22no—
666C2×Q8—72no—
667C2×Q8—82no—
668C2×Q8—141no—
669C2×Q8—141no—
670C2×Q8—141no—
671C2×Q8—144no—
672C2×Q8C2×C22⋊D711yescharacteristic
673C2×Q8C23×D712yes—
674C2×D4—22no—
675C2×D4—24no—
676C2×D4—21no—
677C2×D4—21no—
678C2×D4—72no—
679C2×D4—142no—
680C2×D4—142no—
681C2×D4—144no—
682C2×D4—141no—
683C2×D4C2×C22⋊D712yes—
684C2×D4C2×C22⋊D711yescharacteristic
685C2×D4C23×D712yes—
686C22×C4—22no—
687C22×C4—22no—
688C22×C4—24no—
689C22×C4—141no—
690C22×C4—142no—
691C22×C4—142no—
692C22×C4C2×C22⋊D711yescharacteristic
693C22×C4C2×C22⋊D711yescharacteristic
694C22×C4C2×C22⋊D712yes—
695C22×C4C2×C22⋊D712yes—
696C22×C4C23×D712yes—
697C22×C4C23×D711yescharacteristic
698Q16—148no—
699SD16—148no—
700SD16—148no—
701D8—148no—
702M16—78no—
703M16—148no—
704C2×C8—74no—
705C2×C8—72no—
706C2×C8—72no—
707C2×C8—148no—
708C2×C8—144no—
709C4⋊C4—22no—
710C4⋊C4—22no—
711C4⋊C4—24no—
712C4⋊C4—22no—
713C4⋊C4—21no—
714C4⋊C4—21no—
715C4⋊C4—24no—
716C4⋊C4—71no—
717C4⋊C4—71no—
718C4⋊C4—71no—
719C4⋊C4—71no—
720C4⋊C4—141no—
721C4⋊C4—141no—
722C4⋊C4—142no—
723C4⋊C4—142no—
724C4⋊C4—142no—
725C4⋊C4—142no—
726C4⋊C4—141no—
727C4⋊C4—141no—
728C4⋊C4—141no—
729C4⋊C4—141no—
730C4⋊C4C2×C22⋊D711yescharacteristic
731C4⋊C4C2×C22⋊D711yescharacteristic
732C4⋊C4C2×C22⋊D712yes—
733C4⋊C4C2×C22⋊D712yes—
734C4⋊C4C23×D714yes—
735C22⋊C4—24no—
736C22⋊C4—24no—
737C22⋊C4—24no—
738C22⋊C4—22no—
739C22⋊C4—22no—
740C22⋊C4—141no—
741C22⋊C4—141no—
742C22⋊C4—142no—
743C22⋊C4—142no—
744C22⋊C4—142no—
745C22⋊C4—142no—
746C22⋊C4—142no—
747C22⋊C4—142no—
748C22⋊C4—142no—
749C22⋊C4—142no—
750C22⋊C4—142no—
751C22⋊C4—142no—
752C22⋊C4C2×C22⋊D712yes—
753C22⋊C4C2×C22⋊D712yes—
754C22⋊C4C2×C22⋊D712yes—
755C42—24no—
756C42—141no—
757C42—141no—
758C42—142no—
759C42—142no—
760C42C2×C22⋊D712yes—
761C42C2×C22⋊D712yes—
762C42C2×C22⋊D711yescharacteristic
763C42C2×C22⋊D711yescharacteristic
764C42C23×D712yes—
765C42C23×D711yescharacteristic
766C42C23×D711yescharacteristic
767C2×C7—22no—
768C2×C7—42no—
769C2×C7—82no—
770C2×C7C2×#53211yescharacteristic
771C2×C7#358511yescharacteristic
772C2×C7#358611yescharacteristic
773D7—82no—
774C23—22no—
775C23—142no—
776C23—282no—
777C23—561no—
778C23—561no—
779C23C22×C22⋊D712yes—
780C23C22×C22⋊D711yescharacteristic
781Q8—22no—
782Q8—22no—
783Q8—22no—
784Q8—44no—
785Q8—82no—
786Q8—144no—
787Q8—282no—
788Q8—561no—
789Q8—561no—
790D4—24no—
791D4—22no—
792D4—22no—
793D4—22no—
794D4—42no—
795D4—42no—
796D4—44no—
797D4—84no—
798D4—144no—
799D4—282no—
800D4—562no—
801D4—562no—
802C2×C4—24no—
803C2×C4—22no—
804C2×C4—24no—
805C2×C4—42no—
806C2×C4—41no—
807C2×C4—41no—
808C2×C4—42no—
809C2×C4—44no—
810C2×C4—84no—
811C2×C4—82no—
812C2×C4—141no—
813C2×C4—141no—
814C2×C4—142no—
815C2×C4—141no—
816C2×C4—141no—
817C2×C4—282no—
818C2×C4—562no—
819C2×C4—562no—
820C2×C4D7×#4114yes—
821C2×C4C22×C22⋊D712yes—
822C2×C4C22×C22⋊D712yes—
823C2×C4C22×C22⋊D711yescharacteristic
824C2×C4C22×C22⋊D711yescharacteristic
825C2×C4C22×C22⋊D712yes—
826C2×C4C22×C22⋊D711yescharacteristic
827C2×C4C22×C22⋊D711yescharacteristic
828C2×C4C22×C22⋊D711yescharacteristic
829C2×C4C24×D711yescharacteristic
830C8—78no—
831C8—142no—
832C8—142no—
833C7#6072711yescharacteristic, complemented, Sylow
834C22—21no—
835C22—21no—
836C22—22no—
837C22—22no—
838C22—22no—
839C22—42no—
840C22—42no—
841C22—42no—
842C22—282no—
843C22—282no—
844C22—282no—
845C22—1122no—
846C22#9052312yes—
847C22C23×C22⋊D711yescharacteristic
848C4—22no—
849C4—21no—
850C4—22no—
851C4—21no—
852C4—21no—
853C4—22no—
854C4—21no—
855C4—42no—
856C4—44no—
857C4—282no—
858C4—281no—
859C4—281no—
860C4—281no—
861C4—281no—
862C4#9052312yes—
863C4C2×D7×#4112yes—
864C2—22no—
865C2—42no—
866C2—82no—
867C2—562no—
868C2C2×#9052311yescharacteristic
869C2#1174434511yescharacteristic
870C2#1174435511yescharacteristic
subgroupG/H
centerC22C23×C22⋊D7
commutator, cosocleC2×C4×C7C25
FrattiniC2×C4C24×D7
FittingC7×#3511C2
socleC22×C7C23×D4
hypercenter#3511D7
hypocenterC7#60727
LCSG ▷ C2×C4×C7 ▷ C2×C7 ▷ C7
UCSC1 ◁ C22 ◁ C4×#41 ◁ #3511

Complements

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

NH ≅ G/Ntype
1. C7×#3511C2semidirect
2. #11742917C2semidirect
3. #11740902C2semidirect
4. #11740901C2semidirect
5. #11740868C2semidirect
6. #11740867C2semidirect
7. #11740791C2semidirect
8. #11740790C2semidirect
9. #11740738C2semidirect
10. #11740737C2semidirect
11. #11740734C2semidirect
12. #11740727C2semidirect
13. #11740652C2semidirect
14. C2×#89861C2semidirect
15. #11740016C2semidirect
16. #11740009C2semidirect
17. #11739956C2semidirect
24. C7×#542C22semidirect
26. C7×#533C22semidirect
28. C7×#532C22semidirect
57. #89854C22semidirect
58. #89854C22semidirect
59. #89852C22semidirect
60. #89852C22semidirect
61. #89851C22semidirect
62. #89850C22semidirect
64. #89843C22semidirect
65. #89843C22semidirect
67. #89827C22semidirect
68. #89827C22semidirect
69. #89824C22semidirect
70. #89823C22semidirect
73. #89814C22semidirect
74. #89813C22semidirect
77. #89802C22semidirect
78. C4×#1144C22semidirect
81. #89790C22semidirect
82. C4×#1142C22semidirect
86. #89769C22semidirect
92. C4×#1136C22semidirect
94. C2×#6377C22semidirect
232. #3511D7semidirect
351. #1136#41semidirect
374. #542C2×D7semidirect
379. #533C2×D7semidirect
381. #532C2×D7semidirect
833. C7#60727semidirect

Maximal subgroups

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

subgroupindex
C7×#35112
#117429172
#117409022
#117409012
#117408682
#117408672
#117407912
#117407902
#117407382
#117407372
#117407342
#117407272
#117406522
C2×#898612
#117400162
#117400092
#117399562
#607277