Finite Group Databasebeta

← #13355708

Subgroups — #13355708

Order 1792.

1704 conjugacy classes of subgroups.

The subgroup lattice has 840 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#90513C211yesmaximal, characteristic
2#11742799C211yesmaximal, characteristic, complemented
3C2×C7×#410C211yesmaximal, characteristic, complemented
4C2×#90008C211yesmaximal, characteristic, complemented
5C2×#89777C211yesmaximal, characteristic, complemented
6C2×#89328C211yesmaximal, characteristic, complemented
7#11729328C211yesmaximal, characteristic, complemented
8#11727809C218yesmaximal, complemented
9C22×C7×#41C2211yescharacteristic
10C22×#1157C2211yescharacteristic
11C2×C7×#117C2211yescharacteristic
12C2×C7×#117C2211yescharacteristic
13C2×#6514—21no—
14#90513—22no—
15#90513—22no—
16#90513C414yescomplemented
17#90513C2214yes—
18C2×#6513—22no—
19C2×#6512—21no—
20C2×#6505C412yescomplemented
21C2×#6495C412yescomplemented
22C2×#6489C2211yescharacteristic
23C22×#1136C2211yescharacteristic
24C22×#1136C2211yescharacteristic
25#90214—22no—
26#90213C2214yescomplemented
27#90212—21no—
28D7×#117—22no—
29#90207—21no—
30#90195—22no—
31#90177—22no—
32C4×#1157—22no—
33C7×#410—22no—
34C7×#410C2214yescomplemented
35C2×C7×#99—22no—
36#90008—22no—
37#90008—22no—
38C2×#6411C2214yescomplemented
39#89777—22no—
40#89777C2214yescomplemented
41C2×#6379—22no—
42#89328C2214yescomplemented
43#89327C2214yescomplemented
44#21000—71nomaximal, Sylow
45C2×C7×#41—21no—
46C2×C7×#41—21no—
47C2×C7×#41—21no—
48C2×C7×#41—21no—
49C2×C7×#41—21no—
50C2×C7×#41—21no—
51C2×C7×#41—21no—
52C2×C7×#41—21no—
53C2×C7×#41—21no—
54C2×C7×#41—21no—
55C2×C7×#41C2×C412yescomplemented
56C2×C7×#41C2312yes—
57C22×C7×Q8C2×C411yescharacteristic, complemented
58C22×C7×D4—21no—
59C22×C7×D4C2×C411yescharacteristic, complemented
60C23×C4×C7—21no—
61C23×C4×C7C2311yescharacteristic
62C22×C22⋊D7—21no—
63C2×#1157—21no—
64C2×#1157—21no—
65C2×#1157—21no—
66C2×#1157—21no—
67C2×#1157—21no—
68C2×#1157—21no—
69C2×#1157C2×C412yes—
70C2×#1157C2×C412yes—
71C2×#1157D412yes—
72C2×#1157D412yes—
73C2×#1157D412yes—
74C2×#1157C2312yes—
75C22×D28D411yescharacteristic
76C22×C4×D7—21no—
77C22×Dic14D411yescharacteristic
78C7×#117—21no—
79C7×#117—21no—
80C7×#117—21no—
81C7×#117—21no—
82C7×#117—21no—
83C7×#117D412yes—
84C7×#117C2312yes—
85C7×#117C2312yes—
86C2×C7×C4⋊C4—21no—
87C2×C7×C4⋊C4—21no—
88C2×C7×C22⋊C4—21no—
89C2×C7×C22⋊C4D412yes—
90C2×C42×C7—21no—
91C2×C42×C7—21no—
92C2×C22⋊Dic7—21no—
93#6514—24no—
94#6514—24no—
95#6513—28no—
96#6513—28no—
97#6512—24no—
98#6512—24no—
99C2×#1144—22no—
100#6505—24no—
101#6505C2×C418yescomplemented
102C2×#1143—22no—
103C2×#1142—22no—
104#6495—24no—
105#6495C2×C418yescomplemented
106C2×#1141—22no—
107C4×C22⋊D7—28no—
108#6489—21no—
109#6489—21no—
110#6489D412yes—
111#6489D412yes—
112C2×C4⋊Dic7—21no—
113C2×C4×Dic7C2312yes—
114C2×#1136—21no—
115C2×#1136—21no—
116C2×#1136—21no—
117C2×#1136—21no—
118C2×#1136—21no—
119C2×#1136—21no—
120C2×#1136—21no—
121C2×#1136—21no—
122C2×#1136C2×C412yescomplemented
123C2×#1136C2×C412yescomplemented
124C2×#1136C2312yes—
125C2×#1136C2312yes—
126C22×C7⋊C8—21no—
127C22×C7⋊C8—21no—
128#6456—24no—
129#6455—24no—
130D7×C4⋊C4—24no—
131#6450—24no—
132(C22⋊D7)⋊C4—28no—
133D7×C22⋊C4—24no—
134#6440—24no—
135C4×D28—24no—
136#6435—24no—
137C42×D7—24no—
138C4×Dic14—24no—
139C7×#99—28no—
140#6411—28no—
141#6379—28no—
142C2×#575—71no—
143#3428—71no—
144C2×#421—71no—
145C2×#421—71no—
146C2×#410D711yescharacteristic, complemented
147#1906—78no—
148C2×#344—71no—
149#1733—71no—
150C24×C7—21no—
151C24×C7C2×D411yescharacteristic
152C23×D7—21no—
153C7×#41—22no—
154C7×#41—22no—
155C7×#41—22no—
156C7×#41—22no—
157C7×#41—22no—
158C7×#41—22no—
159C7×#41—22no—
160C7×#41—22no—
161C7×#41—41no—
162C7×#41—41no—
163C7×#41—41no—
164C7×#41—41no—
165C7×#41—41no—
166C7×#41—41no—
167C7×#41—41no—
168C7×#41—41no—
169C2×C7×Q8—21no—
170C2×C7×Q8—21no—
171C2×C7×Q8—21no—
172C2×C7×Q8—21no—
173C2×C7×Q8—21no—
174C2×C7×Q8C22×C412yes—
175C2×C7×D4—22no—
176C2×C7×D4—22no—
177C2×C7×D4—21no—
178C2×C7×D4—21no—
179C2×C7×D4—21no—
180C2×C7×D4—21no—
181C2×C7×D4—21no—
182C2×C7×D4—41no—
183C2×C7×D4—41no—
184C2×C7×D4—41no—
185C2×C7×D4—41no—
186C2×C7×D4C22×C412yes—
187C22×C4×C7—21no—
188C22×C4×C7—22no—
189C22×C4×C7—22no—
190C22×C4×C7—22no—
191C22×C4×C7—41no—
192C22×C4×C7—41no—
193C22×C4×C7—41no—
194C22×C4×C7—41no—
195C22×C4×C7—41no—
196C22×C4×C7C22×C411yescharacteristic
197C22×C4×C7C22×C411yescharacteristic
198C22×C4×C7C2×D411yescharacteristic
199C22×C4×C7C2×D411yescharacteristic
200C22×C4×C7C2×D411yescharacteristic
201C22×C4×C7C2×D411yescharacteristic
202C22×C4×C7C2×D411yescharacteristic
203C22×C4×C7C2×D411yescharacteristic
204C22×C4×C7C2×D411yescharacteristic
205C22×C4×C7#4111yescharacteristic
206C22×C4×C7#4111yescharacteristic
207C22×C4×C7#4111yescharacteristic
208C22×C4×C7#4111yescharacteristic
209C22×C4×C7C2411yescharacteristic
210C2×C22⋊D7—22no—
211C2×C22⋊D7—22no—
212C2×C22⋊D7—22no—
213C2×C22⋊D7—22no—
214C2×C22⋊D7—22no—
215C2×C22⋊D7—22no—
216C22×Dic7—21no—
217C22×Dic7—22no—
218#1157—22no—
219#1157—22no—
220#1157—22no—
221#1157—22no—
222#1157—22no—
223#1157—22no—
224#1157—22no—
225#1157—22no—
226#1157—22no—
227#1157—22no—
228#1157—22no—
229#1157—22no—
230#1157C22⋊C414yes—
231#1157C22⋊C414yes—
232#1157C22×C414yes—
233#1157C2×D414yes—
234C2×D28—21no—
235C2×D28—21no—
236C2×D28—21no—
237C2×D28C22⋊C412yes—
238C2×D28C22⋊C412yes—
239C2×D28C2×D412yes—
240C2×C4×D7—22no—
241C2×C4×D7—22no—
242C2×C4×D7—22no—
243C2×C4×D7—22no—
244C2×C4×D7—22no—
245C2×C4×D7—22no—
246C2×C4×D7—28no—
247C2×Dic14—21no—
248C2×Dic14—21no—
249C2×Dic14—21no—
250C2×Dic14C22⋊C412yes—
251C2×Dic14C22⋊C412yes—
252C2×Dic14C2×D412yes—
253C7×C4⋊C4—22no—
254C7×C4⋊C4—22no—
255C7×C4⋊C4—22no—
256C7×C4⋊C4—41no—
257C7×C22⋊C4—22no—
258C7×C22⋊C4—22no—
259C7×C22⋊C4—41no—
260C7×C22⋊C4C2×D414yes—
261C42×C7—22no—
262C42×C7—22no—
263C42×C7—22no—
264C42×C7—41no—
265C22⋊Dic7—22no—
266C22⋊Dic7—22no—
267#1144—28no—
268#1143—28no—
269#1142—28no—
270#1141—28no—
271(C2×D7)⋊C4—28no—
272C4⋊Dic7—22no—
273C4⋊Dic7—22no—
274Dic7⋊C4—28no—
275C4×Dic7—28no—
276C4×Dic7—22no—
277C4×Dic7C2×D414yes—
278#1136—22no—
279#1136—22no—
280#1136—22no—
281#1136—22no—
282#1136—22no—
283#1136—41no—
284#1136—41no—
285#1136C22×C414yes—
286C2×C7⋊C8—22no—
287C2×C7⋊C8—22no—
288C2×C7⋊C8—22no—
289C2×C7⋊C8—22no—
290C2×C7⋊C8—41no—
291C2×C7⋊C8—41no—
292C22×#41—71no—
293C22×#41C2×D711yescharacteristic
294#575—74no—
295#575—74no—
296#575—142no—
297#575—142no—
298C2×#137—72no—
299C2×#137—141no—
300C2×AGL(1,ℤ/8)—72no—
301C2×AGL(1,ℤ/8)—141no—
302C2×#135—142no—
303C22×M16—71no—
304C22×M16—71no—
305#520—142no—
306#520—142no—
307#519—141no—
308#518—141no—
309#518—142no—
310C4×#41—74no—
311C4×#41—142no—
312C2×#117—71no—
313C2×#117—142no—
314C2×#117C2×D711yescharacteristic
315C2×#117C2×D711yescharacteristic
316#421—74no—
317#421—142no—
318#421—142no—
319#421—142no—
320C2×#104—74no—
321C2×#104—142no—
322#410—22no—
323#410C2×D714yescomplemented
324C2×#99—22no—
325#344—74no—
326#339—74no—
327C23×C7—22no—
328C23×C7—41no—
329C23×C7—41no—
330C23×C7—81no—
331C23×C7—82no—
332C23×C7C4×D411yescharacteristic
333C23×C7C4×D411yescharacteristic
334C23×C7#12011yescharacteristic
335C23×C7#12011yescharacteristic
336C23×C7#12111yescharacteristic
337C23×C7#12111yescharacteristic
338C23×C7C22×D411yescharacteristic
339C22×D7—22no—
340C22×D7—22no—
341C22×D7—22no—
342C22×D7—82no—
343C7×Q8—22no—
344C7×Q8—22no—
345C7×Q8—41no—
346C7×Q8—41no—
347C7×D4—22no—
348C7×D4—22no—
349C7×D4—42no—
350C7×D4—42no—
351C7×D4—42no—
352C7×D4—42no—
353C7×D4—41no—
354C7×D4—41no—
355C2×C4×C7—22no—
356C2×C4×C7—24no—
357C2×C4×C7—41no—
358C2×C4×C7—41no—
359C2×C4×C7—42no—
360C2×C4×C7—42no—
361C2×C4×C7—42no—
362C2×C4×C7—42no—
363C2×C4×C7—42no—
364C2×C4×C7—82no—
365C2×C4×C7—82no—
366C2×C4×C7C2×C22⋊C411yescharacteristic
367C2×C4×C7C2×C22⋊C411yescharacteristic
368C2×C4×C7C2×C22⋊C411yescharacteristic
369C2×C4×C7C2×C22⋊C411yescharacteristic
370C2×C4×C7C4×D411yescharacteristic
371C2×C4×C7C4×D411yescharacteristic
372C2×C4×C7C4×D411yescharacteristic
373C2×C4×C7C4×D411yescharacteristic
374C2×C4×C7C4×D411yescharacteristic
375C2×C4×C7C4×D411yescharacteristic
376C2×C4×C7#12011yescharacteristic
377C2×C4×C7#12011yescharacteristic
378C2×C4×C7#12111yescharacteristic
379C2×C4×C7#12111yescharacteristic
380C2×C4×C7#12111yescharacteristic
381C2×C4×C7#12111yescharacteristic
382C2×C4×C7#12111yescharacteristic
383C2×C4×C7#12111yescharacteristic
384C2×C4×C7#12311yescharacteristic
385C2×C4×C7#12311yescharacteristic
386C2×C4×C7#12311yescharacteristic
387C2×C4×C7#12311yescharacteristic
388C2×C4×C7C23×C411yescharacteristic
389C2×C4×C7C22×D411yescharacteristic
390C2×C4×C7C22×D411yescharacteristic
391C2×C4×C7C22×D411yescharacteristic
392C2×C4×C7C2×#4111yescharacteristic
393C2×C4×C7C2×#4111yescharacteristic
394C22⋊D7—24no—
395C22⋊D7—24no—
396C22⋊D7—24no—
397C22⋊D7—24no—
398C2×Dic7—22no—
399C2×Dic7—22no—
400C2×Dic7—22no—
401C2×Dic7—24no—
402C2×Dic7—82no—
403D28—22no—
404D28—22no—
405D28—22no—
406D28C2×C22⋊C414yes—
407C4×D7—24no—
408C4×D7—24no—
409C4×D7—24no—
410C4×D7—24no—
411C4×D7—88no—
412Dic14—22no—
413Dic14—22no—
414Dic14—22no—
415Dic14C2×C22⋊C414yes—
416C7⋊C8—24no—
417C7⋊C8—42no—
418C2×#41—21no—
419C2×#41—21no—
420C2×#41—21no—
421C2×#41—21no—
422C2×#41—21no—
423C2×#41—21no—
424C2×#41—21no—
425C2×#41—21no—
426C2×#41—21no—
427C2×#41—21no—
428C2×#41—72no—
429C2×#41—72no—
430C2×#41—72no—
431C2×#41—72no—
432C2×#41—72no—
433C2×#41—72no—
434C2×#41—141no—
435C2×#41—141no—
436C2×#41—141no—
437C2×#41—141no—
438C2×#41—141no—
439C2×#41—141no—
440C2×#41C4×D712yescomplemented
441C2×#41C22×D712yes—
442C22×Q8—71no—
443C22×Q8C4×D711yescharacteristic, complemented
444C22×D4—21no—
445C22×D4—71no—
446C22×D4—141no—
447C22×D4C4×D711yescharacteristic, complemented
448C23×C4—21no—
449C23×C4—141no—
450C23×C4C22×D711yescharacteristic
451#137—78no—
452#137—144no—
453#137—144no—
454#137—144no—
455AGL(1,ℤ/8)—78no—
456AGL(1,ℤ/8)—144no—
457AGL(1,ℤ/8)—144no—
458AGL(1,ℤ/8)—144no—
459#135—148no—
460#135—148no—
461C2×Q16—142no—
462C2×SD16—142no—
463C2×SD16—142no—
464C2×D8—142no—
465C2×M16—72no—
466C2×M16—72no—
467C2×M16—72no—
468C2×M16—72no—
469C2×M16—141no—
470C2×M16—141no—
471C2×M16—141no—
472C2×M16—141no—
473C2×M16—141no—
474C2×M16—141no—
475C2×M16—141no—
476C2×M16—141no—
477C22×C8—141no—
478C22×C8—141no—
479C4×Q8—144no—
480C4×Q8—144no—
481C4×D4—144no—
482C4×D4—144no—
483C4×D4—148no—
484C4×D4—148no—
485#117—21no—
486#117—21no—
487#117—21no—
488#117—21no—
489#117—21no—
490#117—72no—
491#117—72no—
492#117—144no—
493#117—144no—
494#117—144no—
495#117—141no—
496#117—141no—
497#117C22⋊D712yes—
498#117C22×D712yes—
499#117C22×D712yes—
500C2×C4⋊C4—21no—
501C2×C4⋊C4—21no—
502C2×C4⋊C4—144no—
503C2×C4⋊C4—141no—
504C2×C22⋊C4—21no—
505C2×C22⋊C4—144no—
506C2×C22⋊C4—141no—
507C2×C22⋊C4C22⋊D712yes—
508C2×C42—21no—
509C2×C42—21no—
510C2×C42—72no—
511C2×C42—144no—
512#104—148no—
513#104—148no—
514#99—28no—
515C22×C7—41no—
516C22×C7—41no—
517C22×C7—41no—
518C22×C7—41no—
519C22×C7—41no—
520C22×C7—41no—
521C22×C7—41no—
522C22×C7—42no—
523C22×C7—82no—
524C22×C7—82no—
525C22×C7—82no—
526C22×C7#38611yescharacteristic
527C22×C7#38611yescharacteristic
528C22×C7#38611yescharacteristic
529C22×C7#38611yescharacteristic
530C22×C7C2×C4×D411yescharacteristic
531C22×C7C2×#12011yescharacteristic
532C22×C7C2×#12111yescharacteristic
533C2×D7—24no—
534C2×D7—44no—
535C2×D7—82no—
536C2×D7—82no—
537C4×C7—44no—
538C4×C7—42no—
539C4×C7—82no—
540C4×C7#38611yescharacteristic
541C4×C7#38611yescharacteristic
542C4×C7#38611yescharacteristic
543C4×C7#38611yescharacteristic
544C4×C7C22×C22⋊C411yescharacteristic
545C4×C7C2×C4×D411yescharacteristic
546C4×C7C2×#12111yescharacteristic
547C4×C7C2×#12311yescharacteristic
548Dic7—24no—
549Dic7—44no—
550C24—21no—
551C24—141no—
552C24C2×C22⋊D711yescharacteristic
553#41—22no—
554#41—22no—
555#41—22no—
556#41—22no—
557#41—22no—
558#41—22no—
559#41—22no—
560#41—22no—
561#41—41no—
562#41—41no—
563#41—41no—
564#41—41no—
565#41—41no—
566#41—41no—
567#41—41no—
568#41—41no—
569#41—74no—
570#41—74no—
571#41—74no—
572#41—74no—
573#41—142no—
574#41—142no—
575#41—142no—
576#41—142no—
577#41—142no—
578#41—142no—
579#41—142no—
580#41—142no—
581#41—142no—
582#41—142no—
583#41—142no—
584#41—142no—
585C2×Q8—21no—
586C2×Q8—21no—
587C2×Q8—21no—
588C2×Q8—21no—
589C2×Q8—21no—
590C2×Q8—72no—
591C2×Q8—72no—
592C2×Q8—72no—
593C2×Q8—141no—
594C2×Q8—141no—
595C2×Q8—141no—
596C2×Q8C2×C4×D712yes—
597C2×D4—22no—
598C2×D4—22no—
599C2×D4—21no—
600C2×D4—21no—
601C2×D4—21no—
602C2×D4—21no—
603C2×D4—21no—
604C2×D4—41no—
605C2×D4—41no—
606C2×D4—41no—
607C2×D4—41no—
608C2×D4—72no—
609C2×D4—72no—
610C2×D4—72no—
611C2×D4—142no—
612C2×D4—142no—
613C2×D4—142no—
614C2×D4—142no—
615C2×D4—142no—
616C2×D4—142no—
617C2×D4—141no—
618C2×D4—141no—
619C2×D4—141no—
620C2×D4C2×C4×D712yes—
621C22×C4—21no—
622C22×C4—22no—
623C22×C4—22no—
624C22×C4—22no—
625C22×C4—41no—
626C22×C4—41no—
627C22×C4—41no—
628C22×C4—41no—
629C22×C4—41no—
630C22×C4—148no—
631C22×C4—141no—
632C22×C4—142no—
633C22×C4—142no—
634C22×C4—142no—
635C22×C4—142no—
636C22×C4—142no—
637C22×C4—142no—
638C22×C4—142no—
639C22×C4C2×C4×D711yescharacteristic
640C22×C4C2×C4×D711yescharacteristic
641C22×C4#115711yescharacteristic
642C22×C4#115711yescharacteristic
643C22×C4D4×D711yescharacteristic
644C22×C4D4×D711yescharacteristic
645C22×C4D4×D711yescharacteristic
646C22×C4D4×D711yescharacteristic
647C22×C4D4×D711yescharacteristic
648C22×C4D4×D711yescharacteristic
649C22×C4#115911yescharacteristic
650C22×C4#115911yescharacteristic
651C22×C4C2×C22⋊D711yescharacteristic
652C22×C4C23×D711yescharacteristic
653Q16—148no—
654SD16—148no—
655SD16—148no—
656D8—148no—
657M16—74no—
658M16—142no—
659M16—142no—
660M16—142no—
661M16—142no—
662M16—142no—
663M16—281no—
664M16—281no—
665C2×C8—142no—
666C2×C8—142no—
667C2×C8—142no—
668C2×C8—142no—
669C2×C8—281no—
670C2×C8—281no—
671C4⋊C4—22no—
672C4⋊C4—22no—
673C4⋊C4—22no—
674C4⋊C4—41no—
675C4⋊C4—148no—
676C4⋊C4—142no—
677C4⋊C4—142no—
678C22⋊C4—22no—
679C22⋊C4—22no—
680C22⋊C4—41no—
681C22⋊C4—148no—
682C22⋊C4—142no—
683C22⋊C4—142no—
684C22⋊C4C2×C22⋊D714yes—
685C42—22no—
686C42—22no—
687C42—22no—
688C42—41no—
689C42—74no—
690C42—148no—
691C42—142no—
692C2×C7—21no—
693C2×C7—21no—
694C2×C7—21no—
695C2×C7—21no—
696C2×C7—21no—
697C2×C7—21no—
698C2×C7—21no—
699C2×C7—82no—
700C2×C7C2×#38611yescharacteristic
701D7—44no—
702C23—22no—
703C23—41no—
704C23—41no—
705C23—81no—
706C23—82no—
707C23—142no—
708C23—142no—
709C23—142no—
710C23—562no—
711C23C4×C22⋊D711yescharacteristic
712C23C4×C22⋊D711yescharacteristic
713C23#650011yescharacteristic
714C23#650011yescharacteristic
715C23#650111yescharacteristic
716C23#650111yescharacteristic
717C23C22×C22⋊D711yescharacteristic
718Q8—22no—
719Q8—22no—
720Q8—41no—
721Q8—41no—
722Q8—74no—
723Q8—142no—
724Q8—142no—
725Q8—142no—
726D4—22no—
727D4—22no—
728D4—42no—
729D4—42no—
730D4—42no—
731D4—42no—
732D4—41no—
733D4—41no—
734D4—74no—
735D4—144no—
736D4—144no—
737D4—144no—
738D4—144no—
739D4—142no—
740D4—142no—
741D4—142no—
742C2×C4—22no—
743C2×C4—24no—
744C2×C4—41no—
745C2×C4—41no—
746C2×C4—42no—
747C2×C4—42no—
748C2×C4—42no—
749C2×C4—42no—
750C2×C4—42no—
751C2×C4—82no—
752C2×C4—82no—
753C2×C4—142no—
754C2×C4—142no—
755C2×C4—142no—
756C2×C4—144no—
757C2×C4—144no—
758C2×C4—144no—
759C2×C4—144no—
760C2×C4—144no—
761C2×C4—568no—
762C2×C4—562no—
763C2×C4D7×C22⋊C411yescharacteristic
764C2×C4D7×C22⋊C411yescharacteristic
765C2×C4D7×C22⋊C411yescharacteristic
766C2×C4D7×C22⋊C411yescharacteristic
767C2×C4(C22⋊D7)⋊C411yescharacteristic
768C2×C4(C22⋊D7)⋊C411yescharacteristic
769C2×C4(C22⋊D7)⋊C411yescharacteristic
770C2×C4(C22⋊D7)⋊C411yescharacteristic
771C2×C4#644611yescharacteristic
772C2×C4#644611yescharacteristic
773C2×C4#644611yescharacteristic
774C2×C4#644611yescharacteristic
775C2×C4#644711yescharacteristic
776C2×C4#644711yescharacteristic
777C2×C4#644711yescharacteristic
778C2×C4#644711yescharacteristic
779C2×C4C4×C22⋊D711yescharacteristic
780C2×C4C4×C22⋊D711yescharacteristic
781C2×C4#650011yescharacteristic
782C2×C4#650011yescharacteristic
783C2×C4#650111yescharacteristic
784C2×C4#650111yescharacteristic
785C2×C4C22×C4×D711yescharacteristic
786C2×C4C2×#115711yescharacteristic
787C2×C4C2×D4×D711yescharacteristic
788C2×C4C2×D4×D711yescharacteristic
789C2×C4C2×D4×D711yescharacteristic
790C2×C4C2×#115911yescharacteristic
791C8—144no—
792C8—282no—
793C7#2100011yescharacteristic, complemented, Sylow
794C22—41no—
795C22—41no—
796C22—41no—
797C22—41no—
798C22—41no—
799C22—41no—
800C22—41no—
801C22—42no—
802C22—82no—
803C22—82no—
804C22—82no—
805C22—144no—
806C22—284no—
807C22—562no—
808C22—562no—
809C22#8972811yescharacteristic
810C22#8972811yescharacteristic
811C22#8972811yescharacteristic
812C22#8972811yescharacteristic
813C22C2×C4×C22⋊D711yescharacteristic
814C22C2×#650011yescharacteristic
815C22C2×#650111yescharacteristic
816C4—44no—
817C4—42no—
818C4—82no—
819C4—144no—
820C4—284no—
821C4#8972811yescharacteristic
822C4#8972811yescharacteristic
823C4#8972811yescharacteristic
824C4#8972811yescharacteristic
825C4C2×D7×C22⋊C411yescharacteristic
826C4C2×(C22⋊D7)⋊C411yescharacteristic
827C4C2×#644611yescharacteristic
828C4C2×#644711yescharacteristic
829C2—21no—
830C2—21no—
831C2—21no—
832C2—21no—
833C2—21no—
834C2—21no—
835C2—21no—
836C2—82no—
837C2—284no—
838C2C2×#8972811yescharacteristic
subgroupG/H
centerC4C2×#6447
commutatorC2×C4×C7C23×C4
FrattiniC22×C4C23×D7
FittingC2×C7×#410C2
socleC2×C7C2×#386
prime radicalC2×#90513C2
cosocleC22×C4×C7C24
hypercenterC2×#410D7
hypocenterC7#21000
LCSG ▷ C2×C4×C7 ▷ C2×C7 ▷ C7
UCSC1 ◁ C4 ◁ C23×C4 ◁ C2×#410

Complements

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

NH ≅ G/Ntype
2. #11742799C2semidirect
3. C2×C7×#410C2semidirect
4. C2×#90008C2semidirect
5. C2×#89777C2semidirect
6. C2×#89328C2semidirect
7. #11729328C2semidirect
8. #11727809C2semidirect
16. #90513C4semidirect
20. C2×#6505C4semidirect
21. C2×#6495C4semidirect
26. #90213C22semidirect
34. C7×#410C22semidirect
38. C2×#6411C22semidirect
40. #89777C22semidirect
42. #89328C22semidirect
43. #89327C22semidirect
55. C2×C7×#41C2×C4semidirect
57. C22×C7×Q8C2×C4semidirect
59. C22×C7×D4C2×C4semidirect
101. #6505C2×C4semidirect
105. #6495C2×C4semidirect
122. C2×#1136C2×C4semidirect
123. C2×#1136C2×C4semidirect
146. C2×#410D7semidirect
323. #410C2×D7semidirect
440. C2×#41C4×D7semidirect
443. C22×Q8C4×D7semidirect
447. C22×D4C4×D7semidirect
793. C7#21000semidirect

Maximal subgroups

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

subgroupindex
C2×#905132
#117427992
C2×C7×#4102
C2×#900082
C2×#897772
C2×#893282
#117293282
#117278092
#210007