Finite Group Databasebeta

← D7×#3548 #14261585

Subgroups — D7×#3548 #14261585

Order 1792.

7810 conjugacy classes of subgroups.

The subgroup lattice has 1016 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C7×#3548C211yesmaximal, characteristic, complemented
2D7×#562C214yesmaximal, complemented
3#11744167C214yesmaximal, complemented
4D7×#554C214yesmaximal, complemented
5#11744007C214yesmaximal, complemented
6D7×#550C214yesmaximal, complemented
7#11743848C214yesmaximal, complemented
8D7×#547C214yesmaximal, complemented
9#11743761C214yesmaximal, complemented
10D7×#540C214yesmaximal, complemented
11#11743544C214yesmaximal, complemented
12D7×#537C218yesmaximal, complemented
13#11743442C218yesmaximal, complemented
14#11743356C211yesmaximal, characteristic, complemented
15D7×#533C211yesmaximal, characteristic, complemented
16#11743319C212yesmaximal, complemented
17D7×#532C212yesmaximal, complemented
18C2×D7×#41C2218yes—
19C2×D7×#41C2214yes—
20C7×#562C2214yescomplemented
21C7×#554C2214yescomplemented
22C7×#550C2214yescomplemented
23C7×#547C2214yescomplemented
24C7×#540C2214yescomplemented
25C7×#537C2218yescomplemented
26C7×#533C2211yescharacteristic, complemented
27C7×#532C2212yescomplemented
28#90525C2218yescomplemented
29#90524C2218yescomplemented
30#90524C2218yescomplemented
31#90523C2214yescomplemented
32#90515C2218yescomplemented
33#90421C2214yescomplemented
34#90419C2212yescomplemented
35#90417C2214yescomplemented
36#90416C2212yescomplemented
37D7×C4⋊Q8C2212yes—
38D7×C4⋊Q8C2212yes—
39#90410C2214yescomplemented
40#90409C2218yescomplemented
41#90409C2214yescomplemented
42#90407C2212yescomplemented
43D7×#127C2214yes—
44D7×#127C2212yes—
45#90391C2214yescomplemented
46#90389C2214yescomplemented
47#90381C2218yescomplemented
48#90379C2212yescomplemented
49D7×#125C2214yes—
50D7×#125C2212yes—
51#90375C2218yescomplemented
52D7×#124C2214yes—
53#90359C2214yescomplemented
54#90358C22116yescomplemented
55#90354C22116yescomplemented
56#90346C22116yescomplemented
57D7×#123C22116yes—
58#90338C22116yescomplemented
59#90327C22116yescomplemented
60#90326C2218yescomplemented
61#90322C2218yescomplemented
62#90320C2218yescomplemented
63#90320C22116yescomplemented
64#90320C2218yescomplemented
65D7×C22⋊Q8C2218yes—
66D7×C22⋊Q8C22116yes—
67D7×C22⋊Q8C2214yes—
68#90313C2214yescomplemented
69#90312C22116yescomplemented
70#90310C2218yescomplemented
71#90306C22116yescomplemented
72#90302C2218yescomplemented
73#90299C2218yescomplemented
74#90299C22116yescomplemented
75#90299C2218yescomplemented
76D7×#121C2218yes—
77D7×#121C2214yes—
78D7×#121C22116yes—
79D7×#121C2214yes—
80D7×#121C22116yes—
81#90290C2218yescomplemented
82#90290C22116yescomplemented
83#90288C22116yescomplemented
84#90288C22116yescomplemented
85#90287C2214yescomplemented
86#90287C2214yescomplemented
87#90270C2214yescomplemented
88#90269C2214yescomplemented
89#90268C2214yescomplemented
90C4×Q8×D7C2214yes—
91#90253C2218yescomplemented
92#90246C2214yescomplemented
93#90244C2218yescomplemented
94#90244C2214yescomplemented
95#90242C2214yescomplemented
96#90239C2214yescomplemented
97#90239C2214yescomplemented
98C4×D4×D7C2218yes—
99C4×D4×D7C2214yes—
100C4×D4×D7C2214yes—
101#90234C2214yescomplemented
102#90230C2218yescomplemented
103#90226C2214yescomplemented
104D7×#117C2212yes—
105#90208C2212yescomplemented
106#90202C2218yescomplemented
107#90201C2218yescomplemented
108#90198C2218yescomplemented
109C2×D7×C4⋊C4C2218yes—
110#90168C2212yescomplemented
111C2×C42×D7C2211yescharacteristic
112#90161C2211yescharacteristic, complemented
113C2×#3548—71nomaximal, Sylow
114C2×C7×#41C2318yes—
115C2×C7×#41C2314yes—
116D7×#41—416no—
117D7×#41—432no—
118C2×#1161C2314yes—
119C2×#1161C2318yes—
120C2×Q8×D7C2314yes—
121C2×Q8×D7C2314yes—
122C2×#1159C2314yes—
123C2×#1159C2318yes—
124C2×#1159C23116yes—
125C2×#1159C2318yes—
126C2×D4×D7C2314yes—
127C2×D4×D7C2314yes—
128C2×D4×D7C23116yes—
129C2×D4×D7C2314yes—
130C2×D4×D7C2318yes—
131C2×#1157C2314yes—
132C2×#1157C23116yes—
133C2×#1157C2318yes—
134C2×#1157C2318yes—
135C22×C4×D7C2311yescharacteristic
136C22×C4×D7C2312yes—
137C22×C4×D7C2318yes—
138C22×C4×D7C23116yes—
139C7×C4⋊Q8C2312yes—
140C7×C4⋊Q8C2312yes—
141C7×#127C2312yes—
142C7×#127C2314yes—
143C7×#125C2312yes—
144C7×#125C2314yes—
145C7×#124C2314yes—
146C7×#123C23116yes—
147C7×C22⋊Q8C2314yes—
148C7×C22⋊Q8C2318yes—
149C7×C22⋊Q8C23116yes—
150C7×#121C2314yes—
151C7×#121C2314yes—
152C7×#121C23116yes—
153C7×#121C23116yes—
154C7×#121C2318yes—
155C4×C7×Q8C2314yes—
156C4×C7×D4C2318yes—
157C4×C7×D4C2314yes—
158C4×C7×D4C2314yes—
159C7×#117C2312yes—
160C2×C7×C4⋊C4C2318yes—
161C2×C42×C7C2311yescharacteristic
162#6510C2314yes—
163#6509C23116yes—
164#6509C2318yes—
165#6509C2314yes—
166Q8×Dic7C2314yes—
167#6507C2314yes—
168#6507C2314yes—
169#6503C2314yes—
170#6503C2318yes—
171#6503C2314yes—
172#6503C2314yes—
173#6503C23116yes—
174#6502C23116yes—
175#6502C23116yes—
176#6502C23116yes—
177#6502C23116yes—
178#6502C2318yes—
179#6502C2318yes—
180#6502C23116yes—
181#6501C2314yes—
182#6501C2314yes—
183#6501C2318yes—
184#6501C23116yes—
185#6501C23116yes—
186#6499C2314yes—
187#6498C23116yes—
188D4×Dic7C2314yes—
189D4×Dic7C2314yes—
190D4×Dic7C2318yes—
191#6493C2314yes—
192#6493C2314yes—
193#6493C2318yes—
194#6493C23116yes—
195#6493C23116yes—
196#6492C23116yes—
197C4×C22⋊D7C2318yes—
198C4×C22⋊D7C2318yes—
199C4×C22⋊D7C23116yes—
200#6489C2312yes—
201C2×C4⋊Dic7C2318yes—
202#6487C2314yes—
203#6487C23116yes—
204#6487C2318yes—
205C2×Dic7⋊C4C23116yes—
206C2×C4×Dic7C2311yescharacteristic
207C2×C4×Dic7C2312yes—
208#6460C23116yes—
209#6460C2314yes—
210#6460C2318yes—
211#6459C2318yes—
212#6459C23116yes—
213#6459C23116yes—
214#6459C23116yes—
215#6458C2314yes—
216#6458C23116yes—
217#6458C23116yes—
218#6458C2314yes—
219#6458C2318yes—
220#6457C23116yes—
221#6457C23116yes—
222#6456C2314yes—
223#6456C2318yes—
224#6456C2314yes—
225#6455C2314yes—
226D7×C4⋊C4C2314yes—
227D7×C4⋊C4C2314yes—
228D7×C4⋊C4C23116yes—
229D7×C4⋊C4C2318yes—
230D7×C4⋊C4C23116yes—
231D7×C4⋊C4C2314yes—
232D7×C4⋊C4C2314yes—
233D7×C4⋊C4C2318yes—
234D7×C4⋊C4C2318yes—
235#6453C2318yes—
236#6453C2314yes—
237#6452C23116yes—
238#6452C2318yes—
239#6451C2314yes—
240#6451C2314yes—
241#6451C2314yes—
242#6451C2314yes—
243#6450C2318yes—
244#6450C2314yes—
245#6449C23116yes—
246#6448C2318yes—
247#6448C2318yes—
248#6447C23116yes—
249#6447C23116yes—
250#6447C2318yes—
251#6447C2318yes—
252#6447C23116yes—
253#6447C23116yes—
254#6447C23116yes—
255#6446C23116yes—
256#6446C23116yes—
257(C22⋊D7)⋊C4C2318yes—
258(C22⋊D7)⋊C4C2318yes—
259(C22⋊D7)⋊C4C23116yes—
260D7×C22⋊C4C2314yes—
261D7×C22⋊C4C23116yes—
262D7×C22⋊C4C2318yes—
263D7×C22⋊C4C2318yes—
264#6441C23116yes—
265#6441C2318yes—
266#6441C23116yes—
267#6441C23116yes—
268#6440C2314yes—
269#6438C2314yes—
270#6437C2314yes—
271#6437C2312yes—
272C4×D28C2318yes—
273C4×D28C2314yes—
274C4×D28C2314yes—
275#6435C2314yes—
276C42×D7C2311yescharacteristic
277C42×D7C2314yes—
278C42×D7C2311yescharacteristic
279C42×D7C2312yes—
280C42×D7C2312yes—
281C42×D7C2311yescharacteristic
282C42×D7C2311yescharacteristic
283#6433C2312yes—
284#6433C2314yes—
285#6432C2312yes—
286#6432C2312yes—
287C4×Dic14C2318yes—
288C4×Dic14C2314yes—
289#3548—74no—
290#3548—74no—
291#3548—74no—
292#3548—74no—
293#3548—74no—
294#3548—78no—
295#3548—71no—
296#3548—72no—
297#3548D711yescharacteristic, direct product factor
298C2×#562—74no—
299C2×#554—74no—
300C2×#550—74no—
301C2×#547—74no—
302C2×#540—74no—
303C2×#537—78no—
304C2×#533—71no—
305C2×#532—72no—
306C23×D7C2411yescharacteristic
307C23×D7C2418yes—
308C7×#41—48no—
309C7×#41—416no—
310C2×C7×Q8C2414yes—
311C2×C7×Q8C2414yes—
312C2×C7×D4C2414yes—
313C2×C7×D4C2414yes—
314C2×C7×D4C24116yes—
315C2×C7×D4C2414yes—
316C2×C7×D4C2418yes—
317C22×C4×C7C2412yes—
318C22×C4×C7C2411yescharacteristic
319C22×C4×C7C2418yes—
320C22×C4×C7C24116yes—
321C2×C22⋊D7C2418yes—
322C2×C22⋊D7C2418yes—
323C2×C22⋊D7C24116yes—
324C2×C22⋊D7C2418yes—
325C2×C22⋊D7C2418yes—
326C2×C22⋊D7C24116yes—
327C2×C22⋊D7C2418yes—
328C22×Dic7C2411yescharacteristic
329C22×Dic7C2412yes—
330C22×Dic7C2418yes—
331C22×Dic7C24116yes—
332#1161—48no—
333#1161—416no—
334Q8×D7—216no—
335Q8×D7—48no—
336#1159—416no—
337#1159—432no—
338#1159—416no—
339#1159—48no—
340D4×D7—216no—
341D4×D7—216no—
342D4×D7—416no—
343D4×D7—48no—
344D4×D7—432no—
345#1157—432no—
346#1157—416no—
347#1157—416no—
348#1157—48no—
349C2×D28C2414yes—
350C2×D28C2414yes—
351C2×D28C2414yes—
352C2×D28C24116yes—
353C2×D28C2418yes—
354C2×C4×D7—232no—
355C2×C4×D7—28no—
356C2×C4×D7—24no—
357C2×C4×D7—432no—
358C2×C4×D7C2411yescharacteristic
359C2×C4×D7C2411yescharacteristic
360C2×C4×D7C2412yes—
361C2×C4×D7C2411yescharacteristic
362C2×C4×D7C2412yes—
363C2×C4×D7C2412yes—
364C2×C4×D7C2418yes—
365C2×C4×D7C2418yes—
366C2×C4×D7C2418yes—
367C2×C4×D7C2418yes—
368C2×C4×D7C24116yes—
369C2×C4×D7C24116yes—
370C2×C4×D7C2412yes—
371C2×C4×D7C2411yescharacteristic
372C2×Dic14C2414yes—
373C2×Dic14C2418yes—
374C2×Dic14C2414yes—
375C2×Dic14C2418yes—
376C7×C4⋊C4C2414yes—
377C7×C4⋊C4C2418yes—
378C7×C4⋊C4C2414yes—
379C7×C4⋊C4C2414yes—
380C7×C4⋊C4C2414yes—
381C7×C4⋊C4C24116yes—
382C7×C22⋊C4C2414yes—
383C7×C22⋊C4C24116yes—
384C7×C22⋊C4C2418yes—
385C7×C22⋊C4C2418yes—
386C42×C7C2412yes—
387C42×C7C2414yes—
388C42×C7C2411yescharacteristic
389C42×C7C2411yescharacteristic
390C22⋊Dic7C2414yes—
391C22⋊Dic7C24116yes—
392C22⋊Dic7C2418yes—
393C22⋊Dic7C2418yes—
394(C2×D7)⋊C4C2418yes—
395(C2×D7)⋊C4C2418yes—
396(C2×D7)⋊C4C2418yes—
397(C2×D7)⋊C4C24116yes—
398(C2×D7)⋊C4C2418yes—
399(C2×D7)⋊C4C2418yes—
400(C2×D7)⋊C4C24116yes—
401C4⋊Dic7C2414yes—
402C4⋊Dic7C2418yes—
403C4⋊Dic7C2414yes—
404C4⋊Dic7C2414yes—
405C4⋊Dic7C2414yes—
406C4⋊Dic7C24116yes—
407Dic7⋊C4C2418yes—
408Dic7⋊C4C2418yes—
409Dic7⋊C4C2418yes—
410Dic7⋊C4C24116yes—
411Dic7⋊C4C2418yes—
412Dic7⋊C4C2418yes—
413Dic7⋊C4C24116yes—
414Dic7⋊C4C2418yes—
415C4×Dic7C2412yes—
416C4×Dic7C2414yes—
417C4×Dic7C2411yescharacteristic
418C4×Dic7C2412yes—
419C4×Dic7C2411yescharacteristic
420C4×Dic7C2412yes—
421C4×Dic7C2412yes—
422C4×Dic7C2412yes—
423C4×Dic7C2418yes—
424C22×#41—74no—
425C22×#41—78no—
426#562—74no—
427#562—78no—
428#562—716no—
429#562—716no—
430#562—716no—
431#562C2×D714yescomplemented
432#554—74no—
433#554—78no—
434#554—78no—
435#554—716no—
436#554—74no—
437#554—78no—
438#554—74no—
439#554—78no—
440#554C2×D714yescomplemented
441#550—78no—
442#550—78no—
443#550—74no—
444#550—78no—
445#550—716no—
446#550—74no—
447#550—78no—
448#550—74no—
449#550C2×D714yescomplemented
450#547—78no—
451#547—74no—
452#547—716no—
453#547—78no—
454#547—78no—
455#547—74no—
456#547—74no—
457#547—78no—
458#547C2×D714yescomplemented
459#540—74no—
460#540—74no—
461#540—716no—
462#540—716no—
463#540—78no—
464#540—78no—
465#540—74no—
466#540C2×D714yescomplemented
467#537—78no—
468#537—78no—
469#537—78no—
470#537—716no—
471#537—78no—
472#537—716no—
473#537—716no—
474#537—78no—
475#537—716no—
476#537—78no—
477#537—78no—
478#537C2×D718yescomplemented
479#533—72no—
480#533—72no—
481#533—74no—
482#533—74no—
483#533—72no—
484#533—71no—
485#533C2×D711yescharacteristic, complemented
486#532—74no—
487#532—72no—
488#532—72no—
489#532—74no—
490#532—74no—
491#532—74no—
492#532—74no—
493#532—74no—
494#532—72no—
495#532C2×D712yescomplemented
496C2×C4⋊Q8—72no—
497C2×C4⋊Q8—72no—
498C2×#127—72no—
499C2×#127—74no—
500C2×#125—72no—
501C2×#125—74no—
502C2×#124—74no—
503C2×#123—716no—
504C2×C22⋊Q8—74no—
505C2×C22⋊Q8—78no—
506C2×C22⋊Q8—716no—
507C2×#121—74no—
508C2×#121—74no—
509C2×#121—716no—
510C2×#121—78no—
511C2×#121—716no—
512C2×C4×Q8—74no—
513C2×C4×D4—74no—
514C2×C4×D4—74no—
515C2×C4×D4—78no—
516C2×#117—72no—
517C22×C4⋊C4—78no—
518C22×C42—71no—
519C23×C7C2511yescharacteristic
520C23×C7C2518yes—
521C22×D7—24no—
522C22×D7—216no—
523C22×D7—216no—
524C22×D7—22no—
525C22×D7—216no—
526C22×D7C2511yescharacteristic
527C22×D7C2518yes—
528C22×D7C2511yescharacteristic
529C7×Q8—28no—
530C7×Q8—44no—
531C7×D4—28no—
532C7×D4—28no—
533C7×D4—416no—
534C7×D4—44no—
535C7×D4—48no—
536C2×C4×C7—24no—
537C2×C4×C7—216no—
538C2×C4×C7—22no—
539C2×C4×C7—416no—
540C2×C4×C7C2512yes—
541C2×C4×C7C2511yescharacteristic
542C2×C4×C7C2518yes—
543C2×C4×C7C2518yes—
544C2×C4×C7C2512yes—
545C2×C4×C7C2511yescharacteristic
546C22⋊D7—216no—
547C22⋊D7—216no—
548C22⋊D7—416no—
549C22⋊D7—416no—
550C22⋊D7—48no—
551C22⋊D7—48no—
552C22⋊D7—48no—
553C2×Dic7—24no—
554C2×Dic7—216no—
555C2×Dic7—22no—
556C2×Dic7—416no—
557C2×Dic7C2511yescharacteristic
558C2×Dic7C2512yes—
559C2×Dic7C2518yes—
560C2×Dic7C2518yes—
561C2×Dic7C2512yes—
562C2×Dic7C2511yescharacteristic
563D28—28no—
564D28—28no—
565D28—416no—
566D28—44no—
567D28—48no—
568C4×D7—216no—
569C4×D7—24no—
570C4×D7—216no—
571C4×D7—22no—
572C4×D7—24no—
573C4×D7—216no—
574C4×D7—22no—
575C4×D7—216no—
576C4×D7—24no—
577C4×D7—22no—
578C4×D7—416no—
579C4×D7—416no—
580C4×D7H(5,𝔽2)18yes—
581C4×D72−1+414yes—
582Dic14—28no—
583Dic14—216no—
584Dic14—48no—
585Dic14—44no—
586C2×#41—74no—
587C2×#41—78no—
588C2×#41—78no—
589C2×#41—74no—
590C2×#41—716no—
591C2×#41—78no—
592C2×#41—78no—
593C2×#41—74no—
594C2×#41—716no—
595C2×#41—78no—
596C2×#41—2816no—
597C2×#41—2832no—
598C2×#41C22×D714yes—
599C2×#41C22×D718yes—
600C22×Q8—74no—
601C22×Q8—74no—
602C22×D4—74no—
603C22×D4—74no—
604C22×D4—78no—
605C22×D4—716no—
606C22×D4—74no—
607C23×C4—78no—
608C23×C4—71no—
609C23×C4—72no—
610C23×C4—716no—
611C4⋊Q8—74no—
612C4⋊Q8—74no—
613C4⋊Q8—74no—
614C4⋊Q8—74no—
615C4⋊Q8—74no—
616C4⋊Q8—74no—
617C4⋊Q8—72no—
618C4⋊Q8—72no—
619C4⋊Q8C22×D712yes—
620C4⋊Q8C22×D712yes—
621#127—74no—
622#127—74no—
623#127—74no—
624#127—716no—
625#127—78no—
626#127—72no—
627#127—74no—
628#127C22×D712yes—
629#127C22×D714yes—
630#125—78no—
631#125—74no—
632#125—716no—
633#125—78no—
634#125—72no—
635#125—74no—
636#125C22×D712yes—
637#125C22×D714yes—
638#124—74no—
639#124—74no—
640#124—78no—
641#124—78no—
642#124—74no—
643#124C22×D714yes—
644#123—716no—
645#123—716no—
646#123—716no—
647#123—716no—
648#123—716no—
649#123—716no—
650#123—716no—
651#123C22×D7116yes—
652C22⋊Q8—74no—
653C22⋊Q8—78no—
654C22⋊Q8—716no—
655C22⋊Q8—74no—
656C22⋊Q8—78no—
657C22⋊Q8—716no—
658C22⋊Q8—78no—
659C22⋊Q8—74no—
660C22⋊Q8—716no—
661C22⋊Q8—78no—
662C22⋊Q8—716no—
663C22⋊Q8—716no—
664C22⋊Q8—716no—
665C22⋊Q8—78no—
666C22⋊Q8—716no—
667C22⋊Q8—716no—
668C22⋊Q8—716no—
669C22⋊Q8C22×D714yes—
670C22⋊Q8C22×D718yes—
671C22⋊Q8C22×D7116yes—
672#121—74no—
673#121—78no—
674#121—74no—
675#121—78no—
676#121—716no—
677#121—716no—
678#121—716no—
679#121—78no—
680#121—716no—
681#121—716no—
682#121—716no—
683#121—716no—
684#121—74no—
685#121—74no—
686#121—716no—
687#121—78no—
688#121—716no—
689#121—74no—
690#121—74no—
691#121—716no—
692#121—78no—
693#121—716no—
694#121—78no—
695#121—78no—
696#121—716no—
697#121—716no—
698#121—716no—
699#121—716no—
700#121—716no—
701#121C22×D714yes—
702#121C22×D714yes—
703#121C22×D7116yes—
704#121C22×D718yes—
705#121C22×D7116yes—
706C4×Q8—74no—
707C4×Q8—78no—
708C4×Q8—74no—
709C4×Q8—78no—
710C4×Q8—74no—
711C4×Q8C22×D714yes—
712C4×D4—74no—
713C4×D4—74no—
714C4×D4—78no—
715C4×D4—78no—
716C4×D4—78no—
717C4×D4—716no—
718C4×D4—74no—
719C4×D4—74no—
720C4×D4—78no—
721C4×D4—78no—
722C4×D4—78no—
723C4×D4—716no—
724C4×D4—74no—
725C4×D4—74no—
726C4×D4—78no—
727C4×D4C22×D714yes—
728C4×D4C22×D714yes—
729C4×D4C22×D718yes—
730#117—72no—
731#117—74no—
732#117—74no—
733#117—74no—
734#117C22×D712yes—
735C2×C4⋊C4—716no—
736C2×C4⋊C4—78no—
737C2×C4⋊C4—74no—
738C2×C4⋊C4—74no—
739C2×C4⋊C4—716no—
740C2×C4⋊C4—716no—
741C2×C4⋊C4—78no—
742C2×C4⋊C4—78no—
743C2×C4⋊C4—74no—
744C2×C4⋊C4—74no—
745C2×C4⋊C4—78no—
746C2×C4⋊C4C22×D718yes—
747C2×C22⋊C4—74no—
748C2×C22⋊C4—716no—
749C2×C22⋊C4—78no—
750C2×C22⋊C4—78no—
751C2×C42—72no—
752C2×C42—71no—
753C2×C42—74no—
754C2×C42—71no—
755C2×C42—72no—
756C2×C42—71no—
757C2×C42—71no—
758C2×C42—72no—
759C2×C42—71no—
760C2×C42C22×D711yescharacteristic
761C22×C7—22no—
762C22×C7—28no—
763C22×C7—28no—
764C22×C7—21no—
765C22×C7—28no—
766C22×C7C2611yescharacteristic
767C2×D7—22no—
768C2×D7—28no—
769C2×D7—28no—
770C2×D7—21no—
771C2×D7—28no—
772C2×D7—44no—
773C2×D7—432no—
774C2×D7C2×H(5,𝔽2)14yes—
775C2×D7C2×2−1+412yes—
776C4×C7—28no—
777C4×C7—22no—
778C4×C7—28no—
779C4×C7—21no—
780C4×C7C2×H(5,𝔽2)14yes—
781C4×C7C2×2−1+412yes—
782Dic7—28no—
783Dic7—22no—
784Dic7—28no—
785Dic7—21no—
786Dic7C2×H(5,𝔽2)14yes—
787Dic7C2×2−1+412yes—
788C24—71no—
789C24—78no—
790#41—48no—
791#41—416no—
792#41—2816no—
793#41—288no—
794#41—2816no—
795#41—2832no—
796#41—2816no—
797#41—288no—
798#41—288no—
799#41—2816no—
800#41—2832no—
801#41—2816no—
802C2×Q8—78no—
803C2×Q8—74no—
804C2×Q8—78no—
805C2×Q8—74no—
806C2×Q8—1416no—
807C2×Q8—288no—
808C2×Q8C23×D714yes—
809C2×Q8C23×D714yes—
810C2×D4—78no—
811C2×D4—78no—
812C2×D4—78no—
813C2×D4—78no—
814C2×D4—716no—
815C2×D4—716no—
816C2×D4—78no—
817C2×D4—74no—
818C2×D4—74no—
819C2×D4—78no—
820C2×D4—716no—
821C2×D4—74no—
822C2×D4—1416no—
823C2×D4—1416no—
824C2×D4—2816no—
825C2×D4—288no—
826C2×D4—2832no—
827C2×D4C23×D714yes—
828C2×D4C23×D714yes—
829C2×D4C23×D718yes—
830C2×D4C23×D7116yes—
831C2×D4C23×D714yes—
832C22×C4—71no—
833C22×C4—72no—
834C22×C4—71no—
835C22×C4—72no—
836C22×C4—78no—
837C22×C4—716no—
838C22×C4—71no—
839C22×C4—72no—
840C22×C4—71no—
841C22×C4—71no—
842C22×C4—72no—
843C22×C4—72no—
844C22×C4—78no—
845C22×C4—78no—
846C22×C4—78no—
847C22×C4—78no—
848C22×C4—716no—
849C22×C4—716no—
850C22×C4—144no—
851C22×C4—1432no—
852C22×C4—148no—
853C22×C4—2832no—
854C22×C4C23×D711yescharacteristic
855C22×C4C23×D712yes—
856C22×C4C23×D718yes—
857C22×C4C23×D7116yes—
858C4⋊C4—78no—
859C4⋊C4—78no—
860C4⋊C4—716no—
861C4⋊C4—716no—
862C4⋊C4—78no—
863C4⋊C4—78no—
864C4⋊C4—78no—
865C4⋊C4—78no—
866C4⋊C4—74no—
867C4⋊C4—74no—
868C4⋊C4—716no—
869C4⋊C4—74no—
870C4⋊C4—74no—
871C4⋊C4—78no—
872C4⋊C4C23×D714yes—
873C4⋊C4C23×D714yes—
874C4⋊C4C23×D7116yes—
875C4⋊C4C23×D714yes—
876C4⋊C4C23×D714yes—
877C4⋊C4C23×D718yes—
878C22⋊C4—74no—
879C22⋊C4—716no—
880C22⋊C4—78no—
881C22⋊C4—78no—
882C22⋊C4—78no—
883C22⋊C4—716no—
884C22⋊C4—716no—
885C22⋊C4—78no—
886C22⋊C4—78no—
887C22⋊C4—78no—
888C22⋊C4—78no—
889C22⋊C4C23×D714yes—
890C22⋊C4C23×D7116yes—
891C22⋊C4C23×D718yes—
892C22⋊C4C23×D718yes—
893C42—71no—
894C42—72no—
895C42—72no—
896C42—72no—
897C42—72no—
898C42—72no—
899C42—71no—
900C42—78no—
901C42—74no—
902C42C23×D711yescharacteristic
903C42C23×D712yes—
904C42C23×D711yescharacteristic
905C42C23×D714yes—
906C2×C7—41no—
907C2×C7—48no—
908C2×C7C22×H(5,𝔽2)12yes—
909C2×C7C22×2−1+411yescharacteristic
910D7—41no—
911D7—48no—
912D7#354814yesdirect product factor
913C23—71no—
914C23—71no—
915C23—78no—
916C23—144no—
917C23—1416no—
918C23—142no—
919C23—1416no—
920C23—1416no—
921C23C24×D711yescharacteristic
922C23C24×D718yes—
923Q8—28no—
924Q8—44no—
925Q8—1416no—
926Q8—148no—
927Q8—288no—
928Q8—284no—
929D4—28no—
930D4—28no—
931D4—48no—
932D4—44no—
933D4—416no—
934D4—1416no—
935D4—1416no—
936D4—148no—
937D4—148no—
938D4—288no—
939D4—284no—
940D4—2816no—
941D4—288no—
942D4—288no—
943D4—288no—
944D4—2816no—
945D4—2816no—
946C2×C4—216no—
947C2×C4—24no—
948C2×C4—22no—
949C2×C4—416no—
950C2×C4—71no—
951C2×C4—72no—
952C2×C4—78no—
953C2×C4—74no—
954C2×C4—71no—
955C2×C4—72no—
956C2×C4—78no—
957C2×C4—78no—
958C2×C4—142no—
959C2×C4—1416no—
960C2×C4—144no—
961C2×C4—142no—
962C2×C4—1416no—
963C2×C4—144no—
964C2×C4—1416no—
965C2×C4—142no—
966C2×C4—1416no—
967C2×C4—144no—
968C2×C4—1416no—
969C2×C4—144no—
970C2×C4—142no—
971C2×C4—2816no—
972C2×C4—2816no—
973C2×C4—2816no—
974C2×C4C24×D711yescharacteristic
975C2×C4C24×D712yes—
976C2×C4C24×D718yes—
977C2×C4C24×D718yes—
978C2×C4C24×D712yes—
979C2×C4C24×D711yescharacteristic
980C7C2×#354811yescharacteristic, complemented, Sylow
981C22—22no—
982C22—28no—
983C22—28no—
984C22—21no—
985C22—28no—
986C22—74no—
987C22—72no—
988C22—142no—
989C22—148no—
990C22—148no—
991C22—141no—
992C22—148no—
993C22—284no—
994C22—2832no—
995C22C25×D711yescharacteristic
996C4—28no—
997C4—22no—
998C4—28no—
999C4—21no—
1000C4—74no—
1001C4—72no—
1002C4—148no—
1003C4—142no—
1004C4—148no—
1005C4—141no—
1006C4D7×H(5,𝔽2)14yes—
1007C4D7×2−1+412yes—
1008C2—41no—
1009C2—48no—
1010C2—74no—
1011C2—281no—
1012C2—288no—
1013C2C2×D7×H(5,𝔽2)12yes—
1014C2C2×D7×2−1+411yescharacteristic
subgroupG/H
center, FrattiniC22C25×D7
commutator, socle, cosocleC22×C7C26
FittingC7×#3548C2
hypercenter#3548D7
hypocenterC7C2×#3548
LCSG ▷ C22×C7 ▷ C7
UCSC1 ◁ C22 ◁ #3548

Complements

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

NH ≅ G/Ntype
1. C7×#3548C2semidirect
2. D7×#562C2semidirect
3. #11744167C2semidirect
4. D7×#554C2semidirect
5. #11744007C2semidirect
6. D7×#550C2semidirect
7. #11743848C2semidirect
8. D7×#547C2semidirect
9. #11743761C2semidirect
10. D7×#540C2semidirect
11. #11743544C2semidirect
12. D7×#537C2semidirect
13. #11743442C2semidirect
14. #11743356C2semidirect
15. D7×#533C2semidirect
16. #11743319C2semidirect
17. D7×#532C2semidirect
20. C7×#562C22semidirect
21. C7×#554C22semidirect
22. C7×#550C22semidirect
23. C7×#547C22semidirect
24. C7×#540C22semidirect
25. C7×#537C22semidirect
26. C7×#533C22semidirect
27. C7×#532C22semidirect
28. #90525C22semidirect
29. #90524C22semidirect
30. #90524C22semidirect
31. #90523C22semidirect
32. #90515C22semidirect
33. #90421C22semidirect
34. #90419C22semidirect
35. #90417C22semidirect
36. #90416C22semidirect
39. #90410C22semidirect
40. #90409C22semidirect
41. #90409C22semidirect
42. #90407C22semidirect
45. #90391C22semidirect
46. #90389C22semidirect
47. #90381C22semidirect
48. #90379C22semidirect
51. #90375C22semidirect
53. #90359C22semidirect
54. #90358C22semidirect
55. #90354C22semidirect
56. #90346C22semidirect
58. #90338C22semidirect
59. #90327C22semidirect
60. #90326C22semidirect
61. #90322C22semidirect
62. #90320C22semidirect
63. #90320C22semidirect
64. #90320C22semidirect
68. #90313C22semidirect
69. #90312C22semidirect
70. #90310C22semidirect
71. #90306C22semidirect
72. #90302C22semidirect
73. #90299C22semidirect
74. #90299C22semidirect
75. #90299C22semidirect
81. #90290C22semidirect
82. #90290C22semidirect
83. #90288C22semidirect
84. #90288C22semidirect
85. #90287C22semidirect
86. #90287C22semidirect
87. #90270C22semidirect
88. #90269C22semidirect
89. #90268C22semidirect
91. #90253C22semidirect
92. #90246C22semidirect
93. #90244C22semidirect
94. #90244C22semidirect
95. #90242C22semidirect
96. #90239C22semidirect
97. #90239C22semidirect
101. #90234C22semidirect
102. #90230C22semidirect
103. #90226C22semidirect
105. #90208C22semidirect
106. #90202C22semidirect
107. #90201C22semidirect
108. #90198C22semidirect
110. #90168C22semidirect
112. #90161C22semidirect
297. #3548D7direct (N × H)
431. #562C2×D7semidirect
440. #554C2×D7semidirect
449. #550C2×D7semidirect
458. #547C2×D7semidirect
466. #540C2×D7semidirect
478. #537C2×D7semidirect
485. #533C2×D7semidirect
495. #532C2×D7semidirect
912. D7#3548direct (N × H)
980. C7C2×#3548semidirect

Maximal subgroups

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

subgroupindex
C7×#35482
D7×#5622
#117441672
D7×#5542
#117440072
D7×#5502
#117438482
D7×#5472
#117437612
D7×#5402
#117435442
D7×#5372
#117434422
#117433562
D7×#5332
#117433192
D7×#5322
C2×#35487