Finite Group Databasebeta

← #14218629

Subgroups — #14218629

Order 1792.

2094 conjugacy classes of subgroups.

The subgroup lattice has 1236 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11743103C211yesmaximal, characteristic
2C7×#2977C211yesmaximal, characteristic, complemented
3#11740366C211yesmaximal, characteristic, complemented
4#11736937C212yesmaximal, complemented
5#11736936C212yesmaximal, complemented
6#11736927C212yesmaximal, complemented
7#11736924C212yesmaximal, complemented
8#11736876C212yesmaximal, complemented
9#11736875C212yesmaximal, complemented
10#11736868C212yesmaximal, complemented
11#11736866C212yesmaximal, complemented
12#11736821C212yesmaximal, complemented
13#11736819C212yesmaximal, complemented
14#11736111C211yesmaximal, characteristic, complemented
15#11736110C211yesmaximal, characteristic, complemented
16#11736107C211yesmaximal, characteristic, complemented
17D7×#408C211yesmaximal, characteristic, complemented
18#11736049C212yesmaximal, complemented
19#11736045C212yesmaximal, complemented
20C2×D7×#41C2211yescharacteristic
21C22×#1157C2211yescharacteristic
22C7×#525C2211yescharacteristic
23#90519C2211yescharacteristic
24#90482C2211yescharacteristic
25C2×D7×M16C2211yescharacteristic, complemented
26C2×D7×M16C2211yescharacteristic, complemented
27C2×#6464C2212yes—
28C2×#6464C2212yes—
29C22×#1131C2211yescharacteristic, complemented
30C22×C8×D7C2211yescharacteristic, complemented
31#90344C411yescharacteristic
32#90344C411yescharacteristic
33#90339C411yescharacteristic
34#90339C411yescharacteristic
35#90320C412yes—
36#90319C412yes—
37#90299C412yes—
38#90298C412yes—
39#90283C411yescharacteristic
40#90283C411yescharacteristic
41#90280C411yescharacteristic
42#90280C411yescharacteristic
43#90239C2212yes—
44#90239C2212yes—
45#90238C2212yes—
46#90238C2212yes—
47#90215C2211yescharacteristic
48D7×#117C2211yescharacteristic
49C7×#435C2212yescomplemented
50C7×#435C2212yescomplemented
51C7×C8×D4C2212yescomplemented
52C7×C8×D4C2212yescomplemented
53C7×#433C2212yescomplemented
54C7×#408C2211yescharacteristic
55C7×#408C2211yescharacteristic
56C2×C7×C22⋊C8C2212yescomplemented
57#90006C2211yescharacteristic
58#90006C2211yescharacteristic
59#89979C2212yescomplemented
60#89901C2211yescharacteristic, complemented
61#89901C2211yescharacteristic, complemented
62#89900C2212yescomplemented
63#89899C2212yescomplemented
64#89883C2212yescomplemented
65#89883C2212yescomplemented
66#89883C2212yescomplemented
67#89882C2211yescharacteristic, complemented
68#89882C2211yescharacteristic, complemented
69#89882C2212yescomplemented
70#89882C2212yescomplemented
71C8×C22⋊D7C2212yescomplemented
72C8×C22⋊D7C2212yescomplemented
73C8×C22⋊D7C2212yescomplemented
74#89784C2212yescomplemented
75#89784C2212yescomplemented
76#89783C2212yescomplemented
77#89783C2212yescomplemented
78#89772C2212yescomplemented
79#89611C2212yescomplemented
80#89611C2212yescomplemented
81#89610C2212yescomplemented
82#89608C2212yescomplemented
83#89608C2212yescomplemented
84#89607C2212yescomplemented
85#89606C2212yescomplemented
86#89605C2212yescomplemented
87#89502C2212yescomplemented
88#89501C2212yescomplemented
89#89501C2212yescomplemented
90#89501C2212yescomplemented
91#89500C2212yescomplemented
92#89500C2212yescomplemented
93#89500C2212yescomplemented
94#89499C2212yes—
95#89499C2212yes—
96#89499C2212yes—
97#89499C2212yes—
98#89499C2212yescomplemented
99#89499C2212yescomplemented
100#89499C2212yescomplemented
101#89499C2212yescomplemented
102#89498C2212yes—
103#89498C2212yescomplemented
104#89498C2212yescomplemented
105(C22⋊D7)⋊C8C2212yescomplemented
106D7×C22⋊C8C2212yes—
107D7×C22⋊C8C2212yescomplemented
108D7×C22⋊C8C2212yescomplemented
109#89492C2212yescomplemented
110#89492C2212yescomplemented
111#89480C2212yescomplemented
112#89478C2212yescomplemented
113#89478C2212yescomplemented
114#89477C2212yescomplemented
115#89461C2212yescomplemented
116#89460C2212yescomplemented
117C8×D28C2212yescomplemented
118#89457C2212yescomplemented
119#60235—71nomaximal, Sylow
120C2×C7×#41C2311yescharacteristic
121C23×C4×C7C2311yescharacteristic
122C22×C22⋊D7C2×C411yescharacteristic
123C22×C22⋊D7C2×C411yescharacteristic
124D7×#41—42no—
125D7×#41—42no—
126C2×#1161C2×C411yescharacteristic
127C2×Q8×D7C2×C411yescharacteristic
128C2×#1159C2×C411yescharacteristic
129C2×#1159C2×C411yescharacteristic
130C2×#1159C2×C411yescharacteristic
131C2×D4×D7C2×C411yescharacteristic
132C2×D4×D7C2×C411yescharacteristic
133C2×D4×D7C2×C411yescharacteristic
134C2×#1157—42no—
135C2×#1157—42no—
136C2×#1157C2×C412yes—
137C2×#1157C2×C412yes—
138C2×#1157C2312yes—
139C2×#1157C2312yes—
140C2×#1157C2311yescharacteristic
141C2×#1157C2311yescharacteristic
142C2×#1157C2311yescharacteristic
143C22×D28C2×C411yescharacteristic
144C22×C4×D7C2311yescharacteristic
145C22×C4×D7C2311yescharacteristic
146C22×C4×D7C2311yescharacteristic
147C22×C4×D7C2311yescharacteristic
148C22×Dic14C2×C411yescharacteristic
149C2×C7×M16C2311yescharacteristic
150C2×C7×M16C2311yescharacteristic
151C22×C7×C8C2311yescharacteristic
152C22×C7×C8C2312yes—
153C22×C7×C8C2311yescharacteristic
154C22×C7×C8C2312yes—
155C7×#123C2×C411yescharacteristic
156C7×#123C2×C411yescharacteristic
157C7×C22⋊Q8C2×C412yes—
158C7×#121C2×C412yes—
159C7×#120C2×C411yescharacteristic
160C7×#120C2×C411yescharacteristic
161C4×C7×D4C2312yes—
162C4×C7×D4C2312yes—
163C7×#117C2311yescharacteristic
164#6516C2×C411yescharacteristic
165#6516C2×C411yescharacteristic
166#6509C2×C412yes—
167#6503C2×C412yes—
168#6503C2×C412yes—
169#6502C2×C412yes—
170#6502C2×C412yes—
171#6501C2×C412yes—
172#6501C2×C412yes—
173#6501C2×C412yes—
174#6500C2×C412yes—
175#6500C2×C412yes—
176#6500C2×C411yescharacteristic
177#6500C2×C411yescharacteristic
178#6498C2×C411yescharacteristic
179#6498C2×C411yescharacteristic
180#6493C2×C412yes—
181#6492C2×C411yescharacteristic
182#6492C2×C411yescharacteristic
183C4×C22⋊D7C2312yes—
184C4×C22⋊D7C2312yes—
185C4×C22⋊D7C2312yes—
186C4×C22⋊D7C2312yes—
187#6489C2311yescharacteristic
188#6487C2×C412yes—
189C2×#1136C2312yes—
190C2×#1136C2312yes—
191C2×#1136C2311yescharacteristic
192C2×#1136C2311yescharacteristic
193C22×C7⋊C8C2311yescharacteristic
194C22×C7⋊C8C2311yescharacteristic
195D7×M16—42no—
196D7×M16—42no—
197#6464—44no—
198#6464—44no—
199C2×#1131—42no—
200C2×#1131C2312yes—
201C2×#1131C2312yes—
202C2×#1131C2312yes—
203C2×#1131C2312yes—
204C2×#1131C2312yes—
205C2×#1131C2312yes—
206C2×C8×D7—42no—
207C2×C8×D7C2312yes—
208C2×C8×D7C2312yes—
209C2×C8×D7C2312yes—
210C2×C8×D7C2312yes—
211C2×C8×D7C2312yes—
212C2×C8×D7C2312yes—
213#6460C2×C412yes—
214#6459C2×C412yes—
215#6459C2×C412yes—
216#6458C2×C412yes—
217#6458C2×C412yes—
218#6458C2×C412yes—
219#6457C2×C412yes—
220#6457C2×C412yes—
221#6455C2×C412yes—
222D7×C4⋊C4C2×C412yes—
223#6451C2×C412yes—
224#6451C2×C412yes—
225#6449C2×C411yescharacteristic
226#6449C2×C411yescharacteristic
227#6448C2×C412yes—
228#6448C2×C412yes—
229#6448C2×C412yes—
230#6448C2×C412yes—
231#6447C2×C412yes—
232#6447C2×C412yes—
233#6447C2×C412yes—
234#6447C2×C412yes—
235#6447C2×C412yes—
236#6447C2×C412yes—
237#6446C2×C412yes—
238#6446C2×C412yes—
239#6445C2×C411yescharacteristic
240#6445C2×C411yescharacteristic
241#6445C2×C412yes—
242#6445C2×C412yes—
243D7×C22⋊C4C2×C411yescharacteristic
244D7×C22⋊C4C2×C411yescharacteristic
245#6441C2×C412yes—
246#6441C2×C412yes—
247#6440C2×C411yescharacteristic
248#6440C2×C411yescharacteristic
249C4×D28C2312yes—
250C4×D28C2312yes—
251#6435C2312yes—
252C42×D7C2312yes—
253C7×C4⋊C8C2312yes—
254C7×C4⋊C8C2312yes—
255C7×C22⋊C8C2312yes—
256C7×C22⋊C8C2312yes—
257C7×C22⋊C8C2312yes—
258C7×C22⋊C8C2312yes—
259C7×C22⋊C8C2312yes—
260C7×C22⋊C8C2312yes—
261C7×#97C2312yes—
262C4×C7×C8C2312yes—
263C22⋊(C7⋊C8)C2312yes—
264C22⋊(C7⋊C8)C2312yes—
265C22⋊(C7⋊C8)C2312yes—
266C22⋊(C7⋊C8)C2312yes—
267C22⋊(C7⋊C8)C2312yes—
268C22⋊(C7⋊C8)C2312yes—
269(C2×D7)⋊C8C2312yes—
270(C2×D7)⋊C8C2312yes—
271(C2×D7)⋊C8C2312yes—
272(C2×D7)⋊C8C2312yes—
273(C2×D7)⋊C8C2312yes—
274(C2×D7)⋊C8C2312yes—
275(C2×D7)⋊C8C2312yes—
276(C2×D7)⋊C8C2312yes—
277(C2×D7)⋊C8C2312yes—
278(C2×D7)⋊C8C2312yes—
279(C2×D7)⋊C8C2312yes—
280(C2×D7)⋊C8C2312yes—
281#6389C2312yes—
282#6389C2312yes—
283Dic7⋊C8C2312yes—
284Dic7⋊C8C2312yes—
285Dic7⋊C8C2312yes—
286Dic7⋊C8C2312yes—
287C8×Dic7C2312yes—
288C8×Dic7C2312yes—
289C4⋊(C7⋊C8)C2312yes—
290C4⋊(C7⋊C8)C2312yes—
291#6377C2312yes—
292C4×C7⋊C8C2312yes—
293#3449—71no—
294#2981—72no—
295#2981—72no—
296#2980—72no—
297#2979—72no—
298#2978—71no—
299#2978—71no—
300#2977—71no—
301#2977D711yescharacteristic, complemented
302#2976—72no—
303#2976—72no—
304#2933—72no—
305#2933—72no—
306#2930—72no—
307#2929—72no—
308#2924—72no—
309#2880—72no—
310#2879—71no—
311C2×#408—71no—
312C24×C7C22×C411yescharacteristic
313C23×D7C22×C411yescharacteristic
314C23×D7C22×C411yescharacteristic
315C23×D7C22×C411yescharacteristic
316C23×D7C22×C411yescharacteristic
317C7×#41—41no—
318C7×#41—41no—
319C2×C7×Q8C22×C411yescharacteristic
320C2×C7×D4C22×C411yescharacteristic
321C2×C7×D4C22×C411yescharacteristic
322C2×C7×D4C22×C412yes—
323C2×C7×D4C22×C412yes—
324C2×C7×D4C22×C411yescharacteristic
325C22×C4×C7—41no—
326C22×C4×C7—41no—
327C22×C4×C7C22×C412yes—
328C22×C4×C7C22×C411yescharacteristic
329C22×C4×C7C2411yescharacteristic
330C22×C4×C7C2411yescharacteristic
331C22×C4×C7C2411yescharacteristic
332C22×C4×C7C2412yes—
333C2×C22⋊D7—42no—
334C2×C22⋊D7—42no—
335C2×C22⋊D7C22×C412yes—
336C2×C22⋊D7C22×C412yes—
337C2×C22⋊D7C22×C412yes—
338C2×C22⋊D7C22×C412yes—
339C2×C22⋊D7C22×C411yescharacteristic
340C2×C22⋊D7C22×C411yescharacteristic
341C2×C22⋊D7C22×C412yes—
342C2×C22⋊D7C22×C412yes—
343C2×C22⋊D7C22×C412yes—
344C2×C22⋊D7C22×C411yescharacteristic
345C2×C22⋊D7C22×C411yescharacteristic
346C2×C22⋊D7C22×C412yes—
347C2×C22⋊D7C22×C411yescharacteristic
348C2×C22⋊D7C22×C411yescharacteristic
349C22×Dic7C22×C411yescharacteristic
350C22×Dic7C22×C411yescharacteristic
351C22×Dic7C22×C411yescharacteristic
352C22×Dic7C22×C411yescharacteristic
353#1161—42no—
354Q8×D7—42no—
355#1159—42no—
356#1159—42no—
357#1159—42no—
358D4×D7—42no—
359D4×D7—42no—
360D4×D7—42no—
361#1157—24no—
362#1157—24no—
363#1157—44no—
364#1157—42no—
365#1157—42no—
366#1157—41no—
367#1157—41no—
368#1157—41no—
369#1157—41no—
370#1157—41no—
371#1157—41no—
372#1157—44no—
373C2×D28—42no—
374C2×D28C22×C412yes—
375C2×D28C22×C412yes—
376C2×D28C22×C412yes—
377C2×D28C22×C412yes—
378C2×D28C22×C411yescharacteristic
379C2×D28C22×C411yescharacteristic
380C2×D28C22×C411yescharacteristic
381C2×C4×D7—22no—
382C2×C4×D7—22no—
383C2×C4×D7—22no—
384C2×C4×D7—22no—
385C2×C4×D7—22no—
386C2×C4×D7—22no—
387C2×C4×D7—41no—
388C2×C4×D7—41no—
389C2×C4×D7C22×C411yescharacteristic
390C2×C4×D7C22×C411yescharacteristic
391C2×C4×D7C22×C411yescharacteristic
392C2×C4×D7C22×C411yescharacteristic
393C2×C4×D7C22×C411yescharacteristic
394C2×C4×D7C22×C411yescharacteristic
395C2×C4×D7C22×C412yes—
396C2×C4×D7C22×C412yes—
397C2×C4×D7C22×C412yes—
398C2×C4×D7C2411yescharacteristic
399C2×C4×D7C2411yescharacteristic
400C2×C4×D7C2411yescharacteristic
401C2×C4×D7C2412yes—
402C2×C4×D7C2411yescharacteristic
403C2×Dic14—42no—
404C2×Dic14C22×C412yes—
405C2×Dic14C22×C412yes—
406C2×Dic14C22×C411yescharacteristic
407C2×Dic14C22×C411yescharacteristic
408C2×Dic14C22×C411yescharacteristic
409C7×M16—41no—
410C7×M16—41no—
411C2×C7×C8—41no—
412C2×C7×C8—41no—
413C2×C7×C8—42no—
414C2×C7×C8—42no—
415C2×C7×C8C2412yes—
416C2×C7×C8C2412yes—
417C2×C7×C8C2412yes—
418C2×C7×C8C2412yes—
419C7×C4⋊C4C22×C412yes—
420C7×C4⋊C4C22×C412yes—
421C7×C4⋊C4C22×C412yes—
422C7×C22⋊C4C22×C411yescharacteristic
423C7×C22⋊C4C22×C411yescharacteristic
424C7×C22⋊C4C22×C412yes—
425C7×C22⋊C4C22×C412yes—
426C7×C22⋊C4C22×C412yes—
427C7×C22⋊C4C22×C412yes—
428C42×C7C2412yes—
429C22⋊Dic7C22×C411yescharacteristic
430C22⋊Dic7C22×C411yescharacteristic
431C22⋊Dic7C22×C412yes—
432C22⋊Dic7C22×C412yes—
433C22⋊Dic7C22×C412yes—
434C22⋊Dic7C22×C412yes—
435(C2×D7)⋊C4C22×C412yes—
436(C2×D7)⋊C4C22×C412yes—
437(C2×D7)⋊C4C22×C412yes—
438(C2×D7)⋊C4C22×C412yes—
439(C2×D7)⋊C4C22×C412yes—
440(C2×D7)⋊C4C22×C412yes—
441(C2×D7)⋊C4C22×C412yes—
442(C2×D7)⋊C4C22×C412yes—
443(C2×D7)⋊C4C22×C412yes—
444(C2×D7)⋊C4C22×C412yes—
445C4⋊Dic7C22×C412yes—
446C4⋊Dic7C22×C412yes—
447C4⋊Dic7C22×C412yes—
448Dic7⋊C4C22×C412yes—
449Dic7⋊C4C22×C412yes—
450Dic7⋊C4C22×C412yes—
451Dic7⋊C4C22×C412yes—
452Dic7⋊C4C22×C412yes—
453Dic7⋊C4C22×C412yes—
454C4×Dic7C22×C412yes—
455C4×Dic7C22×C412yes—
456C4×Dic7C2412yes—
457#1136—42no—
458#1136—42no—
459#1136—41no—
460#1136—41no—
461C2×C7⋊C8—41no—
462C2×C7⋊C8—41no—
463C2×C7⋊C8C2412yes—
464C2×C7⋊C8C2412yes—
465C2×C7⋊C8C2412yes—
466C2×C7⋊C8C2412yes—
467#1131—24no—
468#1131—24no—
469#1131—42no—
470#1131—42no—
471#1131—42no—
472#1131—42no—
473C8×D7—24no—
474C8×D7—24no—
475C8×D7—42no—
476C8×D7—42no—
477C8×D7—42no—
478C8×D7—42no—
479C22×#41—71no—
480C22×#41—71no—
481C2×#131—72no—
482C2×#131—72no—
483C22×M16—71no—
484C22×M16—71no—
485C22×M16—71no—
486C23×C8—71no—
487#537—72no—
488#537—72no—
489#536—71no—
490#536—71no—
491#536—72no—
492#535—72no—
493#535—71no—
494#535—71no—
495#534—71no—
496#534—71no—
497#534—71no—
498#534—71no—
499#532—72no—
500#532—72no—
501#525—71no—
502#525—71no—
503#525—72no—
504#525—72no—
505#525—71no—
506#525C2×D711yescharacteristic
507C2×#117—71no—
508#436—72no—
509#436—72no—
510#436—72no—
511#436—72no—
512#436—72no—
513#436—72no—
514#436—72no—
515#436—72no—
516#435—72no—
517#435—72no—
518#435—72no—
519#435—72no—
520#435—72no—
521#435—72no—
522#435—72no—
523#435—72no—
524#435—72no—
525#435—72no—
526#435—72no—
527#435—72no—
528#435—72no—
529#435—72no—
530#435C2×D712yescomplemented
531#435C2×D712yescomplemented
532C8×D4—72no—
533C8×D4—72no—
534C8×D4—72no—
535C8×D4—72no—
536C8×D4—72no—
537C8×D4—72no—
538C8×D4C2×D712yescomplemented
539C8×D4C2×D712yescomplemented
540#433—72no—
541#433—72no—
542#433—72no—
543#433C2×D712yescomplemented
544#432—72no—
545#432—72no—
546#431—72no—
547#431—72no—
548#424—72no—
549#424—72no—
550#408—71no—
551#408—71no—
552#408—71no—
553#408—71no—
554#408—71no—
555#408—71no—
556#408—72no—
557#408—72no—
558#408—72no—
559#408—72no—
560#408—72no—
561#408—72no—
562#408—72no—
563#408—72no—
564#408—72no—
565#408—72no—
566#408C2×D711yescharacteristic
567#408C2×D711yescharacteristic
568#407—72no—
569#407—72no—
570#407—72no—
571#407—72no—
572C2×C22⋊C8—72no—
573C2×C22⋊C8—72no—
574C2×C22⋊C8—72no—
575C2×C22⋊C8C2×D712yescomplemented
576#405—72no—
577#405—72no—
578C23×C7—41no—
579C23×C7—42no—
580C23×C7C23×C411yescharacteristic
581C23×C7C23×C411yescharacteristic
582C23×C7C23×C411yescharacteristic
583C23×C7C23×C412yes—
584C22×D7—22no—
585C22×D7—22no—
586C22×D7—22no—
587C22×D7—42no—
588C22×D7—41no—
589C22×D7—42no—
590C22×D7—42no—
591C22×D7—42no—
592C22×D7C23×C411yescharacteristic
593C22×D7C23×C411yescharacteristic
594C22×D7C23×C412yes—
595C22×D7C23×C411yescharacteristic
596C22×D7C23×C411yescharacteristic
597C7×Q8—41no—
598C7×D4—41no—
599C7×D4—41no—
600C7×D4—41no—
601C7×D4—42no—
602C7×D4—42no—
603C2×C4×C7—21no—
604C2×C4×C7—21no—
605C2×C4×C7—22no—
606C2×C4×C7—22no—
607C2×C4×C7—21no—
608C2×C4×C7—21no—
609C2×C4×C7—21no—
610C2×C4×C7—21no—
611C2×C4×C7—41no—
612C2×C4×C7—42no—
613C2×C4×C7C23×C412yes—
614C2×C4×C7C23×C412yes—
615C2×C4×C7C23×C412yes—
616C2×C4×C7C23×C411yescharacteristic
617C2×C4×C7C23×C411yescharacteristic
618C2×C4×C7C23×C411yescharacteristic
619C2×C4×C7C2511yescharacteristic
620C22⋊D7—24no—
621C22⋊D7—24no—
622C22⋊D7—42no—
623C22⋊D7—42no—
624C22⋊D7—41no—
625C22⋊D7—41no—
626C22⋊D7—41no—
627C22⋊D7—41no—
628C22⋊D7—41no—
629C22⋊D7—41no—
630C22⋊D7—42no—
631C22⋊D7—42no—
632C22⋊D7—42no—
633C22⋊D7—42no—
634C2×Dic7—22no—
635C2×Dic7—22no—
636C2×Dic7—22no—
637C2×Dic7—41no—
638C2×Dic7C23×C411yescharacteristic
639C2×Dic7C23×C412yes—
640C2×Dic7C23×C412yes—
641C2×Dic7C23×C412yes—
642C2×Dic7C23×C411yescharacteristic
643C2×Dic7C23×C411yescharacteristic
644C2×Dic7C23×C411yescharacteristic
645D28—24no—
646D28—42no—
647D28—42no—
648D28—42no—
649D28—41no—
650D28—41no—
651D28—41no—
652C4×D7—22no—
653C4×D7—22no—
654C4×D7—22no—
655C4×D7—21no—
656C4×D7—21no—
657C4×D7—22no—
658C4×D7—22no—
659C4×D7—21no—
660C4×D7—21no—
661C4×D7—21no—
662C4×D7—21no—
663C4×D7—22no—
664C4×D7—22no—
665C4×D7—22no—
666C4×D7—42no—
667C4×D7—42no—
668C4×D7—42no—
669C4×D7H(5,𝔽2)12yes—
670C4×D7H(5,𝔽2)12yes—
671Dic14—24no—
672Dic14—42no—
673Dic14—41no—
674Dic14—41no—
675Dic14—41no—
676C7×C8—22no—
677C7×C8—22no—
678C7×C8—22no—
679C7×C8—22no—
680C7⋊C8—22no—
681C7⋊C8—22no—
682C7⋊C8—22no—
683C7⋊C8—22no—
684C2×#41—71no—
685C2×#41—71no—
686C2×#41—71no—
687C2×#41—71no—
688C2×#41—72no—
689C2×#41—72no—
690C2×#41—72no—
691C2×#41—71no—
692C2×#41—71no—
693C2×#41—71no—
694C2×#41—72no—
695C2×#41—282no—
696C2×#41—282no—
697C2×#41—282no—
698C2×#41—282no—
699C2×#41C22×D711yescharacteristic
700C22×Q8—71no—
701C22×Q8—71no—
702C22×D4—71no—
703C22×D4—71no—
704C22×D4—71no—
705C22×D4—71no—
706C22×D4—71no—
707C22×D4—71no—
708C23×C4—71no—
709C23×C4—71no—
710C23×C4—71no—
711C23×C4—71no—
712C23×C4C22×D711yescharacteristic
713#131—284no—
714#131—284no—
715C2×M16—71no—
716C2×M16—71no—
717C2×M16—72no—
718C2×M16—72no—
719C2×M16—72no—
720C2×M16—72no—
721C2×M16—72no—
722C2×M16—72no—
723C2×M16—72no—
724C2×M16—72no—
725C2×M16—282no—
726C2×M16—282no—
727C2×M16—282no—
728C2×M16C22×D711yescharacteristic
729C2×M16C22×D711yescharacteristic
730C22×C8—71no—
731C22×C8—71no—
732C22×C8—72no—
733C22×C8—72no—
734C22×C8—72no—
735C22×C8—72no—
736C22×C8—72no—
737C22×C8—72no—
738C22×C8—282no—
739C22×C8C22×D711yescharacteristic
740C22×C8C22×D711yescharacteristic
741C22×C8C22×D712yes—
742C22×C8C22×D712yes—
743C4⋊Q8—72no—
744C4⋊Q8—72no—
745#127—72no—
746#127—72no—
747#124—72no—
748#124—72no—
749#124—72no—
750#124—72no—
751#123—71no—
752#123—71no—
753#123—71no—
754#123—71no—
755#123—72no—
756#123—72no—
757#123—72no—
758#123—72no—
759#123—71no—
760#123—71no—
761#123C4×D711yescharacteristic
762#123C4×D711yescharacteristic
763C22⋊Q8—72no—
764C22⋊Q8—72no—
765C22⋊Q8—72no—
766C22⋊Q8—72no—
767C22⋊Q8—72no—
768C22⋊Q8—72no—
769C22⋊Q8—72no—
770C22⋊Q8C4×D712yes—
771#121—72no—
772#121—72no—
773#121—72no—
774#121—72no—
775#121—72no—
776#121—72no—
777#121—72no—
778#121—72no—
779#121—72no—
780#121—72no—
781#121—72no—
782#121—72no—
783#121—72no—
784#121—72no—
785#121—72no—
786#121C4×D712yes—
787#120—71no—
788#120—71no—
789#120—71no—
790#120—71no—
791#120—72no—
792#120—72no—
793#120—72no—
794#120—72no—
795#120—71no—
796#120—71no—
797#120C4×D711yescharacteristic
798#120C4×D711yescharacteristic
799C4×D4—72no—
800C4×D4—72no—
801C4×D4—72no—
802C4×D4—72no—
803C4×D4—72no—
804C4×D4—72no—
805C4×D4C22×D712yes—
806C4×D4C22×D712yes—
807#117—71no—
808#117—72no—
809#117—71no—
810#117—71no—
811#117—72no—
812#117C22×D711yescharacteristic
813C2×C4⋊C4—72no—
814C2×C22⋊C4—71no—
815C2×C22⋊C4—71no—
816C2×C42—72no—
817C4⋊C8—72no—
818C4⋊C8—72no—
819C4⋊C8—72no—
820C4⋊C8—72no—
821C4⋊C8—72no—
822C4⋊C8—72no—
823C4⋊C8C22×D712yes—
824C4⋊C8C22×D712yes—
825C22⋊C8—72no—
826C22⋊C8—72no—
827C22⋊C8—72no—
828C22⋊C8—72no—
829C22⋊C8—72no—
830C22⋊C8—72no—
831C22⋊C8—72no—
832C22⋊C8—72no—
833C22⋊C8—72no—
834C22⋊C8—72no—
835C22⋊C8—72no—
836C22⋊C8—72no—
837C22⋊C8—72no—
838C22⋊C8—72no—
839C22⋊C8—72no—
840C22⋊C8—72no—
841C22⋊C8—72no—
842C22⋊C8—72no—
843C22⋊C8C22×D712yes—
844C22⋊C8C22×D712yes—
845C22⋊C8C22×D712yes—
846C22⋊C8C22×D712yes—
847C22⋊C8C22×D712yes—
848C22⋊C8C22×D712yes—
849#97—72no—
850#97—72no—
851#97—72no—
852#97C22×D712yes—
853C4×C8—72no—
854C4×C8—72no—
855C4×C8—72no—
856C4×C8C22×D712yes—
857C22×C7—21no—
858C22×C7—21no—
859C22×C7—21no—
860C22×C7—22no—
861C22×C7—22no—
862C22×C7—22no—
863C22×C7—22no—
864C22×C7—22no—
865C22×C7—22no—
866C22×C7—82no—
867C22×C7C24×C411yescharacteristic
868C2×D7—22no—
869C2×D7—21no—
870C2×D7—21no—
871C2×D7—21no—
872C2×D7—22no—
873C2×D7—22no—
874C2×D7—22no—
875C2×D7—22no—
876C2×D7—22no—
877C2×D7—22no—
878C2×D7—44no—
879C2×D7—82no—
880C2×D7—82no—
881C2×D7—82no—
882C2×D7#51812yes—
883C4×C7—22no—
884C4×C7—21no—
885C4×C7—21no—
886C4×C7—21no—
887C4×C7—22no—
888C4×C7—22no—
889C4×C7C2×H(5,𝔽2)11yescharacteristic
890C4×C7C2×H(5,𝔽2)11yescharacteristic
891Dic7—22no—
892Dic7—21no—
893Dic7—21no—
894Dic7—21no—
895Dic7—22no—
896Dic7—22no—
897Dic7#51812yes—
898C24—71no—
899C24—71no—
900C24—71no—
901C24—71no—
902C24C2×C4×D711yescharacteristic
903#41—41no—
904#41—41no—
905#41—144no—
906#41—144no—
907#41—281no—
908#41—281no—
909#41—282no—
910#41—282no—
911#41—281no—
912#41—281no—
913#41—281no—
914#41—281no—
915#41—284no—
916#41—284no—
917#41—282no—
918#41—282no—
919#41—282no—
920#41—282no—
921C2×Q8—72no—
922C2×Q8—71no—
923C2×Q8—71no—
924C2×Q8—71no—
925C2×Q8—72no—
926C2×Q8—282no—
927C2×Q8—282no—
928C2×Q8C2×C4×D711yescharacteristic
929C2×D4—72no—
930C2×D4—72no—
931C2×D4—72no—
932C2×D4—72no—
933C2×D4—72no—
934C2×D4—72no—
935C2×D4—71no—
936C2×D4—71no—
937C2×D4—71no—
938C2×D4—71no—
939C2×D4—72no—
940C2×D4—71no—
941C2×D4—71no—
942C2×D4—72no—
943C2×D4—72no—
944C2×D4—72no—
945C2×D4—72no—
946C2×D4—71no—
947C2×D4—71no—
948C2×D4—72no—
949C2×D4—71no—
950C2×D4—282no—
951C2×D4—282no—
952C2×D4—282no—
953C2×D4—282no—
954C2×D4—282no—
955C2×D4—282no—
956C2×D4C2×C4×D712yes—
957C2×D4C2×C4×D712yes—
958C2×D4C2×C4×D711yescharacteristic
959C2×D4C2×C4×D711yescharacteristic
960C2×D4C2×C4×D711yescharacteristic
961C22×C4—41no—
962C22×C4—41no—
963C22×C4—71no—
964C22×C4—71no—
965C22×C4—71no—
966C22×C4—71no—
967C22×C4—71no—
968C22×C4—71no—
969C22×C4—71no—
970C22×C4—71no—
971C22×C4—71no—
972C22×C4—71no—
973C22×C4—71no—
974C22×C4—71no—
975C22×C4—71no—
976C22×C4—71no—
977C22×C4—72no—
978C22×C4—72no—
979C22×C4—72no—
980C22×C4—72no—
981C22×C4—142no—
982C22×C4—142no—
983C22×C4—142no—
984C22×C4—142no—
985C22×C4—142no—
986C22×C4—142no—
987C22×C4—281no—
988C22×C4—281no—
989C22×C4C2×C4×D712yes—
990C22×C4C2×C4×D711yescharacteristic
991C22×C4C23×D711yescharacteristic
992C22×C4C23×D711yescharacteristic
993C22×C4C23×D711yescharacteristic
994C22×C4C23×D712yes—
995M16—41no—
996M16—41no—
997M16—144no—
998M16—144no—
999M16—282no—
1000M16—282no—
1001M16—282no—
1002M16—282no—
1003M16—281no—
1004M16—281no—
1005M16—282no—
1006M16—282no—
1007C2×C8—41no—
1008C2×C8—41no—
1009C2×C8—42no—
1010C2×C8—42no—
1011C2×C8—72no—
1012C2×C8—72no—
1013C2×C8—72no—
1014C2×C8—72no—
1015C2×C8—144no—
1016C2×C8—144no—
1017C2×C8—282no—
1018C2×C8—282no—
1019C2×C8—282no—
1020C2×C8—282no—
1021C2×C8—281no—
1022C2×C8—281no—
1023C2×C8C23×D712yes—
1024C2×C8C23×D712yes—
1025C2×C8C23×D712yes—
1026C2×C8C23×D712yes—
1027C4⋊C4—72no—
1028C4⋊C4—72no—
1029C4⋊C4—72no—
1030C4⋊C4—72no—
1031C4⋊C4—72no—
1032C4⋊C4—72no—
1033C4⋊C4—72no—
1034C4⋊C4—72no—
1035C4⋊C4—72no—
1036C4⋊C4C2×C4×D712yes—
1037C4⋊C4C2×C4×D712yes—
1038C4⋊C4C2×C4×D712yes—
1039C22⋊C4—71no—
1040C22⋊C4—71no—
1041C22⋊C4—72no—
1042C22⋊C4—72no—
1043C22⋊C4—72no—
1044C22⋊C4—72no—
1045C22⋊C4—72no—
1046C22⋊C4—72no—
1047C22⋊C4—72no—
1048C22⋊C4—72no—
1049C22⋊C4—72no—
1050C22⋊C4—72no—
1051C22⋊C4—72no—
1052C22⋊C4—72no—
1053C22⋊C4—72no—
1054C22⋊C4—72no—
1055C22⋊C4C2×C4×D711yescharacteristic
1056C22⋊C4C2×C4×D711yescharacteristic
1057C22⋊C4C2×C4×D712yes—
1058C22⋊C4C2×C4×D712yes—
1059C22⋊C4C2×C4×D712yes—
1060C22⋊C4C2×C4×D712yes—
1061C42—72no—
1062C42—72no—
1063C42—72no—
1064C42C23×D712yes—
1065C2×C7—41no—
1066C2×C7—41no—
1067C2×C7—41no—
1068C2×C7—42no—
1069C2×C7C2×#51811yescharacteristic
1070C2×C7#357312yes—
1071D7—22no—
1072D7—41no—
1073D7—41no—
1074D7—41no—
1075D7—42no—
1076C23—41no—
1077C23—42no—
1078C23—71no—
1079C23—71no—
1080C23—71no—
1081C23—72no—
1082C23—71no—
1083C23—142no—
1084C23—142no—
1085C23—142no—
1086C23—282no—
1087C23—281no—
1088C23—282no—
1089C23—282no—
1090C23—282no—
1091C23C22×C4×D711yescharacteristic
1092C23C22×C4×D711yescharacteristic
1093C23C22×C4×D711yescharacteristic
1094C23C22×C4×D712yes—
1095Q8—41no—
1096Q8—144no—
1097Q8—281no—
1098Q8—282no—
1099Q8—281no—
1100Q8—281no—
1101D4—41no—
1102D4—41no—
1103D4—41no—
1104D4—42no—
1105D4—42no—
1106D4—144no—
1107D4—144no—
1108D4—144no—
1109D4—282no—
1110D4—282no—
1111D4—281no—
1112D4—282no—
1113D4—281no—
1114D4—281no—
1115D4—282no—
1116D4—282no—
1117D4—282no—
1118D4—282no—
1119D4—282no—
1120D4—281no—
1121D4—281no—
1122D4—281no—
1123D4—281no—
1124D4—281no—
1125D4—281no—
1126D4—282no—
1127C2×C4—21no—
1128C2×C4—21no—
1129C2×C4—22no—
1130C2×C4—22no—
1131C2×C4—21no—
1132C2×C4—21no—
1133C2×C4—21no—
1134C2×C4—21no—
1135C2×C4—41no—
1136C2×C4—42no—
1137C2×C4—71no—
1138C2×C4—72no—
1139C2×C4—72no—
1140C2×C4—71no—
1141C2×C4—72no—
1142C2×C4—72no—
1143C2×C4—71no—
1144C2×C4—71no—
1145C2×C4—72no—
1146C2×C4—142no—
1147C2×C4—142no—
1148C2×C4—142no—
1149C2×C4—142no—
1150C2×C4—142no—
1151C2×C4—142no—
1152C2×C4—142no—
1153C2×C4—142no—
1154C2×C4—142no—
1155C2×C4—141no—
1156C2×C4—141no—
1157C2×C4—142no—
1158C2×C4—142no—
1159C2×C4—141no—
1160C2×C4—141no—
1161C2×C4—141no—
1162C2×C4—141no—
1163C2×C4—282no—
1164C2×C4—282no—
1165C2×C4—282no—
1166C2×C4—281no—
1167C2×C4C22×C4×D712yes—
1168C2×C4C22×C4×D712yes—
1169C2×C4C22×C4×D711yescharacteristic
1170C2×C4C22×C4×D711yescharacteristic
1171C2×C4C22×C4×D712yes—
1172C2×C4C22×C4×D711yescharacteristic
1173C2×C4C24×D711yescharacteristic
1174C8—22no—
1175C8—22no—
1176C8—22no—
1177C8—22no—
1178C8—142no—
1179C8—142no—
1180C8—142no—
1181C8—142no—
1182C7#6023511yescharacteristic, complemented, Sylow
1183C22—21no—
1184C22—22no—
1185C22—21no—
1186C22—21no—
1187C22—22no—
1188C22—22no—
1189C22—22no—
1190C22—22no—
1191C22—22no—
1192C22—72no—
1193C22—82no—
1194C22—142no—
1195C22—141no—
1196C22—141no—
1197C22—141no—
1198C22—142no—
1199C22—142no—
1200C22—142no—
1201C22—142no—
1202C22—142no—
1203C22—142no—
1204C22—284no—
1205C22—562no—
1206C22—562no—
1207C22—562no—
1208C22C23×C4×D711yescharacteristic
1209C4—21no—
1210C4—22no—
1211C4—21no—
1212C4—21no—
1213C4—22no—
1214C4—22no—
1215C4—72no—
1216C4—141no—
1217C4—141no—
1218C4—141no—
1219C4—142no—
1220C4—142no—
1221C4—142no—
1222C4D7×H(5,𝔽2)11yescharacteristic
1223C4D7×H(5,𝔽2)11yescharacteristic
1224C2—41no—
1225C2—42no—
1226C2—41no—
1227C2—41no—
1228C2—142no—
1229C2—281no—
1230C2—281no—
1231C2—281no—
1232C2—282no—
1233C2D7×#51811yescharacteristic
1234C2#1174422812yes—
subgroupG/H
center, FrattiniC2×C4C24×D7
commutator, socleC22×C7C24×C4
FittingC7×#2977C2
prime radical#11743103C2
cosocleC2×C4×C7C25
hypercenter#2977D7
hypocenterC7#60235
LCSG ▷ C22×C7 ▷ C7
UCSC1 ◁ C2×C4 ◁ #2977

Complements

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

NH ≅ G/Ntype
2. C7×#2977C2semidirect
3. #11740366C2semidirect
4. #11736937C2semidirect
5. #11736936C2semidirect
6. #11736927C2semidirect
7. #11736924C2semidirect
8. #11736876C2semidirect
9. #11736875C2semidirect
10. #11736868C2semidirect
11. #11736866C2semidirect
12. #11736821C2semidirect
13. #11736819C2semidirect
14. #11736111C2semidirect
15. #11736110C2semidirect
16. #11736107C2semidirect
17. D7×#408C2semidirect
18. #11736049C2semidirect
19. #11736045C2semidirect
25. C2×D7×M16C22semidirect
26. C2×D7×M16C22semidirect
29. C22×#1131C22semidirect
30. C22×C8×D7C22semidirect
49. C7×#435C22semidirect
50. C7×#435C22semidirect
51. C7×C8×D4C22semidirect
52. C7×C8×D4C22semidirect
53. C7×#433C22semidirect
56. C2×C7×C22⋊C8C22semidirect
59. #89979C22semidirect
60. #89901C22semidirect
61. #89901C22semidirect
62. #89900C22semidirect
63. #89899C22semidirect
64. #89883C22semidirect
65. #89883C22semidirect
66. #89883C22semidirect
67. #89882C22semidirect
68. #89882C22semidirect
69. #89882C22semidirect
70. #89882C22semidirect
71. C8×C22⋊D7C22semidirect
72. C8×C22⋊D7C22semidirect
73. C8×C22⋊D7C22semidirect
74. #89784C22semidirect
75. #89784C22semidirect
76. #89783C22semidirect
77. #89783C22semidirect
78. #89772C22semidirect
79. #89611C22semidirect
80. #89611C22semidirect
81. #89610C22semidirect
82. #89608C22semidirect
83. #89608C22semidirect
84. #89607C22semidirect
85. #89606C22semidirect
86. #89605C22semidirect
87. #89502C22semidirect
88. #89501C22semidirect
89. #89501C22semidirect
90. #89501C22semidirect
91. #89500C22semidirect
92. #89500C22semidirect
93. #89500C22semidirect
98. #89499C22semidirect
99. #89499C22semidirect
100. #89499C22semidirect
101. #89499C22semidirect
103. #89498C22semidirect
104. #89498C22semidirect
105. (C22⋊D7)⋊C8C22semidirect
107. D7×C22⋊C8C22semidirect
108. D7×C22⋊C8C22semidirect
109. #89492C22semidirect
110. #89492C22semidirect
111. #89480C22semidirect
112. #89478C22semidirect
113. #89478C22semidirect
114. #89477C22semidirect
115. #89461C22semidirect
116. #89460C22semidirect
117. C8×D28C22semidirect
118. #89457C22semidirect
301. #2977D7semidirect
530. #435C2×D7semidirect
531. #435C2×D7semidirect
538. C8×D4C2×D7semidirect
539. C8×D4C2×D7semidirect
543. #433C2×D7semidirect
575. C2×C22⋊C8C2×D7semidirect
1182. C7#60235semidirect

Maximal subgroups

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

subgroupindex
#117431032
C7×#29772
#117403662
#117369372
#117369362
#117369272
#117369242
#117368762
#117368752
#117368682
#117368662
#117368212
#117368192
#117361112
#117361102
#117361072
D7×#4082
#117360492
#117360452
#602357