Finite Group Databasebeta

← C7×#23881 #13201097

Subgroups — C7×#23881 #13201097

Order 1792.

1714 conjugacy classes of subgroups.

The subgroup lattice has 1138 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C7×#575C211yesmaximal, characteristic, complemented
2C7×#3489C211yesmaximal, characteristic, complemented
3C2×C7×#456C211yesmaximal, characteristic, complemented
4C2×C7×#454C211yesmaximal, characteristic, complemented
5C7×#3005C211yesmaximal, characteristic, complemented
6C7×#2432C211yesmaximal, characteristic, complemented
7C7×#2007C211yesmaximal, characteristic, complemented
8C7×#2006C211yesmaximal, characteristic, complemented
9C7×#2005C211yesmaximal, characteristic, complemented
10C7×#2003C211yesmaximal, characteristic, complemented
11C7×#1901C211yesmaximal, characteristic, complemented
12C7×#1883C211yesmaximal, characteristic, complemented
13C7×#1882C211yesmaximal, characteristic, complemented
14C7×#1871C211yesmaximal, characteristic, complemented
15C7×#1789C211yesmaximal, characteristic, complemented
16C2×C7×2−1+4C2211yescharacteristic
17C22×C7×#41C2211yescharacteristic
18C22×C7×#41C2211yescharacteristic
19C7×#575—24no—
20C7×#575—24no—
21C2×C7×#137—21no—
22C2×C7×#137C2211yescharacteristic
23C2×C7×#137C2211yescharacteristic
24C2×C7×#137C2211yescharacteristic, complemented
25C2×C7×AGL(1,ℤ/8)—21no—
26C2×C7×AGL(1,ℤ/8)C2211yescharacteristic
27C2×C7×AGL(1,ℤ/8)C2211yescharacteristic
28C2×C7×AGL(1,ℤ/8)C2211yescharacteristic, complemented
29C2×C7×#135—21no—
30C2×C7×#135—21no—
31C22×C7×M16C2211yescharacteristic
32C7×D4×Q8—21no—
33C7×#548—21no—
34C7×#547—21no—
35C7×#547—22no—
36C7×#546—21no—
37C7×#546—22no—
38C7×#537—21no—
39C7×#537C2211yescharacteristic
40C7×#536—21no—
41C7×#536C2211yescharacteristic
42C2×C7×C4⋊Q8C2211yescharacteristic, complemented
43C2×C7×#124C2211yescharacteristic, complemented
44C7×#525—21no—
45C7×#525C2211yescharacteristic
46C2×C7×C22⋊Q8—21no—
47C2×C7×C22⋊Q8C2211yescharacteristic
48C7×#520C2211yescharacteristic
49C7×#456—24no—
50C7×#454—24no—
51C7×#452—21no—
52C7×#452—21no—
53C7×#449—21no—
54C7×#449—21no—
55C2×C7×#104C2211yescharacteristic
56C2×C7×#104C2211yescharacteristic
57C2×C7×#104C2211yescharacteristic
58C2×C7×#104C2211yescharacteristic
59C2×C7×#104C2211yescharacteristic, complemented
60C2×C7×#104C2211yescharacteristic, complemented
61C7×#419C2211yescharacteristic, complemented
62C7×#418C2211yescharacteristic, complemented
63C2×C7×#101C2211yescharacteristic, complemented
64C2×C7×#101C2211yescharacteristic, complemented
65C7×#407C2211yescharacteristic
66C7×#394—22no—
67C7×#391C2211yescharacteristic, complemented
68C7×#390C2211yescharacteristic, complemented
69C7×#385—22no—
70C4×C7×C22⋊C4C2211yescharacteristic
71C7×#343C2211yescharacteristic, complemented
72C7×#343C2211yescharacteristic, complemented
73C7×#339C2211yescharacteristic, complemented
74C7×#339C2211yescharacteristic, complemented
75#23881C711yesmaximal, characteristic, direct product factor, Sylow
76C7×2−1+4—22no—
77C7×2−1+4—22no—
78C7×2−1+4—41no—
79C7×2−1+4—41no—
80C2×C7×#41—21no—
81C2×C7×#41—21no—
82C2×C7×#41—21no—
83C2×C7×#41—21no—
84C2×C7×#41—22no—
85C2×C7×#41—22no—
86C2×C7×#41—22no—
87C2×C7×#41—22no—
88C2×C7×#41—22no—
89C2×C7×#41—21no—
90C2×C7×#41—21no—
91C2×C7×#41—21no—
92C2×C7×#41—21no—
93C2×C7×#41—41no—
94C2×C7×#41—41no—
95C2×C7×#41—41no—
96C2×C7×#41—41no—
97C2×C7×#41D411yescharacteristic
98C2×C7×#41D411yescharacteristic
99C2×C7×#41C2311yescharacteristic
100C2×C7×#41C2311yescharacteristic
101C2×C7×#41C2311yescharacteristic
102C22×C7×Q8—21no—
103C22×C7×Q8—21no—
104C22×C7×Q8D411yescharacteristic
105C22×C7×Q8C2311yescharacteristic
106C22×C7×Q8C2311yescharacteristic
107C22×C7×D4—21no—
108C22×C7×D4—21no—
109C22×C7×D4D411yescharacteristic
110C22×C7×D4C2311yescharacteristic
111C23×C4×C7—21no—
112C23×C4×C7—21no—
113C23×C4×C7C2311yescharacteristic
114C7×#137—28no—
115C7×#137—22no—
116C7×#137—22no—
117C7×#137—22no—
118C7×#137—22no—
119C7×#137—41no—
120C7×#137D414yescomplemented
121C7×AGL(1,ℤ/8)—28no—
122C7×AGL(1,ℤ/8)—22no—
123C7×AGL(1,ℤ/8)—22no—
124C7×AGL(1,ℤ/8)—22no—
125C7×AGL(1,ℤ/8)—22no—
126C7×AGL(1,ℤ/8)—41no—
127C7×AGL(1,ℤ/8)D414yescomplemented
128C7×#135—28no—
129C7×#135—28no—
130C2×C7×Q16—21no—
131C2×C7×Q16—21no—
132C2×C7×Q16—21no—
133C2×C7×SD16—21no—
134C2×C7×SD16—21no—
135C2×C7×SD16—21no—
136C2×C7×SD16—21no—
137C2×C7×SD16—21no—
138C2×C7×SD16—21no—
139C2×C7×D8—21no—
140C2×C7×D8—21no—
141C2×C7×D8—21no—
142C2×C7×M16—21no—
143C2×C7×M16—22no—
144C2×C7×M16—22no—
145C2×C7×M16C2311yescharacteristic
146C2×C7×M16C2311yescharacteristic
147C2×C7×M16C2311yescharacteristic
148C2×C7×M16C2311yescharacteristic
149C22×C7×C8—21no—
150C7×C4⋊Q8—22no—
151C7×C4⋊Q8—21no—
152C7×C4⋊Q8—22no—
153C7×C4⋊Q8—41no—
154C7×#124—22no—
155C7×#124—21no—
156C7×#124—22no—
157C7×#124—41no—
158C7×#123—22no—
159C7×#123—22no—
160C7×#123—22no—
161C7×#123—21no—
162C7×#123—22no—
163C7×C22⋊Q8—22no—
164C7×C22⋊Q8—22no—
165C7×C22⋊Q8—22no—
166C7×C22⋊Q8—21no—
167C7×C22⋊Q8—21no—
168C7×C22⋊Q8—21no—
169C7×C22⋊Q8—21no—
170C7×C22⋊Q8—21no—
171C7×C22⋊Q8—21no—
172C7×C22⋊Q8—21no—
173C7×C22⋊Q8—21no—
174C7×C22⋊Q8D411yescharacteristic
175C7×C22⋊Q8D411yescharacteristic
176C7×#121—22no—
177C7×#121—22no—
178C7×#121—22no—
179C7×#121—21no—
180C7×#121—21no—
181C7×#121—22no—
182C7×#121D411yescharacteristic
183C7×#121D411yescharacteristic
184C7×#120—22no—
185C7×#120—21no—
186C4×C7×Q8—21no—
187C4×C7×D4—22no—
188C4×C7×D4—22no—
189C4×C7×D4—21no—
190C4×C7×D4—22no—
191C4×C7×D4—21no—
192C4×C7×D4—21no—
193C7×#117—21no—
194C7×#117C2311yescharacteristic
195C2×C7×C4⋊C4—22no—
196C2×C7×C4⋊C4—21no—
197C2×C7×C4⋊C4—22no—
198C2×C7×C4⋊C4D412yes—
199C2×C7×C4⋊C4C2311yescharacteristic
200C2×C7×C22⋊C4—22no—
201C2×C7×C22⋊C4—21no—
202C2×C7×C22⋊C4—22no—
203C2×C7×C22⋊C4—22no—
204C2×C7×C22⋊C4D412yes—
205C2×C42×C7C2311yescharacteristic
206C2×C42×C7C2311yescharacteristic
207C7×#104—22no—
208C7×#104—22no—
209C7×#104—22no—
210C7×#104—22no—
211C7×#104—41no—
212C7×#104—41no—
213C7×#103—21no—
214C7×#103—21no—
215C7×#102—21no—
216C7×#102—21no—
217C7×#101—22no—
218C7×#101—22no—
219C7×C22⋊C8—21no—
220C7×C22⋊C8—21no—
221C7×#95—21no—
222C7×#95—22no—
223C2×#575C2×C711yescharacteristic, complemented
224#3489C2×C711yescharacteristic, complemented
225C2×#456C2×C711yescharacteristic, complemented
226C2×#454C2×C711yescharacteristic, complemented
227#3005C2×C711yescharacteristic, complemented
228#2432C2×C711yescharacteristic, complemented
229#2007C2×C711yescharacteristic, complemented
230#2006C2×C711yescharacteristic, complemented
231#2005C2×C711yescharacteristic, complemented
232#2003C2×C711yescharacteristic, complemented
233#1901C2×C711yescharacteristic, complemented
234#1883C2×C711yescharacteristic, complemented
235#1882C2×C711yescharacteristic, complemented
236#1871C2×C711yescharacteristic, complemented
237#1789C2×C711yescharacteristic, complemented
238C24×C7—21no—
239C24×C7—21no—
240C24×C7C2×D411yescharacteristic
241C7×#41—21no—
242C7×#41—21no—
243C7×#41—24no—
244C7×#41—24no—
245C7×#41—22no—
246C7×#41—22no—
247C7×#41—21no—
248C7×#41—21no—
249C7×#41—21no—
250C7×#41—21no—
251C7×#41—21no—
252C7×#41—21no—
253C7×#41—21no—
254C7×#41—21no—
255C7×#41—42no—
256C7×#41—42no—
257C7×#41—41no—
258C7×#41—41no—
259C7×#41—42no—
260C7×#41—42no—
261C7×#41—42no—
262C7×#41—42no—
263C7×#41—42no—
264C7×#41—42no—
265C7×#41—44no—
266C7×#41—44no—
267C7×#41—42no—
268C7×#41—42no—
269C7×#41—42no—
270C7×#41—42no—
271C7×#41—42no—
272C7×#41—42no—
273C7×#41C2×D412yes—
274C7×#41C2×D412yes—
275C2×C7×Q8—22no—
276C2×C7×Q8—21no—
277C2×C7×Q8—21no—
278C2×C7×Q8—21no—
279C2×C7×Q8—21no—
280C2×C7×Q8—21no—
281C2×C7×Q8—21no—
282C2×C7×Q8—21no—
283C2×C7×Q8—21no—
284C2×C7×Q8—22no—
285C2×C7×Q8—21no—
286C2×C7×Q8—21no—
287C2×C7×Q8—21no—
288C2×C7×Q8—21no—
289C2×C7×Q8—41no—
290C2×C7×Q8—42no—
291C2×C7×Q8—42no—
292C2×C7×Q8—42no—
293C2×C7×Q8—42no—
294C2×C7×Q8C2×D411yescharacteristic
295C2×C7×Q8C2×D411yescharacteristic
296C2×C7×Q8C2×D412yes—
297C2×C7×Q8C2×D411yescharacteristic
298C2×C7×D4—21no—
299C2×C7×D4—22no—
300C2×C7×D4—22no—
301C2×C7×D4—21no—
302C2×C7×D4—21no—
303C2×C7×D4—21no—
304C2×C7×D4—21no—
305C2×C7×D4—21no—
306C2×C7×D4—22no—
307C2×C7×D4—21no—
308C2×C7×D4—21no—
309C2×C7×D4—21no—
310C2×C7×D4—21no—
311C2×C7×D4—21no—
312C2×C7×D4—21no—
313C2×C7×D4—21no—
314C2×C7×D4—41no—
315C2×C7×D4—42no—
316C2×C7×D4—42no—
317C2×C7×D4—42no—
318C2×C7×D4—42no—
319C2×C7×D4—41no—
320C2×C7×D4—41no—
321C2×C7×D4C2×D411yescharacteristic
322C2×C7×D4C2×D411yescharacteristic
323C2×C7×D4C2×D412yes—
324C2×C7×D4C2×D411yescharacteristic
325C22×C4×C7—21no—
326C22×C4×C7—21no—
327C22×C4×C7—21no—
328C22×C4×C7—21no—
329C22×C4×C7—21no—
330C22×C4×C7—22no—
331C22×C4×C7—22no—
332C22×C4×C7—21no—
333C22×C4×C7—21no—
334C22×C4×C7—21no—
335C22×C4×C7—22no—
336C22×C4×C7—21no—
337C22×C4×C7—21no—
338C22×C4×C7—21no—
339C22×C4×C7—21no—
340C22×C4×C7—21no—
341C22×C4×C7—42no—
342C22×C4×C7—42no—
343C22×C4×C7—42no—
344C22×C4×C7—42no—
345C22×C4×C7—41no—
346C22×C4×C7—41no—
347C22×C4×C7C2×D412yes—
348C22×C4×C7C2×D411yescharacteristic
349C22×C4×C7C2×D411yescharacteristic
350C22×C4×C7C2×D411yescharacteristic
351C22×C4×C7C2×D411yescharacteristic
352C22×C4×C7C2×D411yescharacteristic
353C22×C4×C7C2×D412yes—
354C22×C4×C7C2411yescharacteristic
355C7×Q16—24no—
356C7×Q16—24no—
357C7×Q16—42no—
358C7×SD16—24no—
359C7×SD16—24no—
360C7×SD16—24no—
361C7×SD16—24no—
362C7×SD16—42no—
363C7×SD16—42no—
364C7×D8—24no—
365C7×D8—24no—
366C7×D8—42no—
367C7×M16—24no—
368C7×M16—21no—
369C7×M16—21no—
370C7×M16—21no—
371C7×M16—21no—
372C7×M16—21no—
373C7×M16—21no—
374C7×M16C2×D412yes—
375C7×M16C2×D412yes—
376C2×C7×C8—24no—
377C2×C7×C8—21no—
378C2×C7×C8—21no—
379C2×C7×C8—21no—
380C2×C7×C8—21no—
381C7×C4⋊C4—22no—
382C7×C4⋊C4—22no—
383C7×C4⋊C4—22no—
384C7×C4⋊C4—22no—
385C7×C4⋊C4—21no—
386C7×C4⋊C4—22no—
387C7×C4⋊C4—22no—
388C7×C4⋊C4—21no—
389C7×C4⋊C4—21no—
390C7×C4⋊C4—21no—
391C7×C4⋊C4—44no—
392C7×C4⋊C4C2×D411yescharacteristic
393C7×C4⋊C4C2×D411yescharacteristic
394C7×C22⋊C4—22no—
395C7×C22⋊C4—22no—
396C7×C22⋊C4—22no—
397C7×C22⋊C4—22no—
398C7×C22⋊C4—22no—
399C7×C22⋊C4—21no—
400C7×C22⋊C4—22no—
401C7×C22⋊C4—22no—
402C7×C22⋊C4—21no—
403C7×C22⋊C4—21no—
404C7×C22⋊C4—21no—
405C7×C22⋊C4—21no—
406C7×C22⋊C4—44no—
407C7×C22⋊C4—44no—
408C7×C22⋊C4—42no—
409C42×C7—22no—
410C42×C7—21no—
411C42×C7—21no—
412C42×C7—21no—
413C42×C7—21no—
414C42×C7—21no—
415C2×2−1+4C22×C711yescharacteristic
416C22×#41C22×C711yescharacteristic
417C22×#41C22×C711yescharacteristic
418#575—24no—
419#575—24no—
420C2×#137—21no—
421C2×#137C22×C711yescharacteristic
422C2×#137C22×C711yescharacteristic
423C2×#137C22×C711yescharacteristic, complemented
424C2×AGL(1,ℤ/8)—21no—
425C2×AGL(1,ℤ/8)C22×C711yescharacteristic
426C2×AGL(1,ℤ/8)C22×C711yescharacteristic
427C2×AGL(1,ℤ/8)C22×C711yescharacteristic, complemented
428C2×#135—21no—
429C2×#135—21no—
430C22×M16C22×C711yescharacteristic
431D4×Q8—21no—
432#548—21no—
433#547—21no—
434#547—22no—
435#546—21no—
436#546—22no—
437#537—21no—
438#537C22×C711yescharacteristic
439#536—21no—
440#536C22×C711yescharacteristic
441C2×C4⋊Q8C22×C711yescharacteristic, complemented
442C2×#124C22×C711yescharacteristic, complemented
443#525—21no—
444#525C22×C711yescharacteristic
445C2×C22⋊Q8—21no—
446C2×C22⋊Q8C22×C711yescharacteristic
447#520C22×C711yescharacteristic
448#456—24no—
449#454—24no—
450#452—21no—
451#452—21no—
452#449—21no—
453#449—21no—
454C2×#104C22×C711yescharacteristic
455C2×#104C22×C711yescharacteristic
456C2×#104C22×C711yescharacteristic
457C2×#104C22×C711yescharacteristic
458C2×#104C22×C711yescharacteristic, complemented
459C2×#104C22×C711yescharacteristic, complemented
460#419C22×C711yescharacteristic, complemented
461#418C22×C711yescharacteristic, complemented
462C2×#101C22×C711yescharacteristic, complemented
463C2×#101C22×C711yescharacteristic, complemented
464#407C22×C711yescharacteristic
465#394—22no—
466#391C22×C711yescharacteristic, complemented
467#390C22×C711yescharacteristic, complemented
468#385—22no—
469C4×C22⋊C4C22×C711yescharacteristic
470#343C22×C711yescharacteristic, complemented
471#343C22×C711yescharacteristic, complemented
472#339C22×C711yescharacteristic, complemented
473#339C22×C711yescharacteristic, complemented
474C23×C7—21no—
475C23×C7—21no—
476C23×C7—21no—
477C23×C7—21no—
478C23×C7—21no—
479C23×C7—22no—
480C23×C7—41no—
481C23×C7—41no—
482C23×C7—42no—
483C23×C7—42no—
484C23×C7—42no—
485C23×C7—42no—
486C23×C7—41no—
487C23×C7—41no—
488C23×C7—81no—
489C23×C7#12011yescharacteristic
490C23×C7#12011yescharacteristic
491C23×C7C22×D411yescharacteristic
492C7×Q8—21no—
493C7×Q8—21no—
494C7×Q8—22no—
495C7×Q8—21no—
496C7×Q8—21no—
497C7×Q8—22no—
498C7×Q8—21no—
499C7×Q8—42no—
500C7×Q8—44no—
501C7×Q8—41no—
502C7×Q8—41no—
503C7×Q8—41no—
504C7×Q8—41no—
505C7×Q8—41no—
506C7×Q8—41no—
507C7×Q8#12012yes—
508C7×D4—22no—
509C7×D4—22no—
510C7×D4—21no—
511C7×D4—22no—
512C7×D4—21no—
513C7×D4—21no—
514C7×D4—21no—
515C7×D4—22no—
516C7×D4—21no—
517C7×D4—42no—
518C7×D4—42no—
519C7×D4—42no—
520C7×D4—42no—
521C7×D4—44no—
522C7×D4—44no—
523C7×D4—44no—
524C7×D4—41no—
525C7×D4—41no—
526C7×D4—41no—
527C7×D4—41no—
528C7×D4—41no—
529C7×D4—41no—
530C7×D4—81no—
531C7×D4—82no—
532C7×D4#12012yes—
533C2×C4×C7—21no—
534C2×C4×C7—21no—
535C2×C4×C7—21no—
536C2×C4×C7—21no—
537C2×C4×C7—21no—
538C2×C4×C7—21no—
539C2×C4×C7—21no—
540C2×C4×C7—21no—
541C2×C4×C7—21no—
542C2×C4×C7—21no—
543C2×C4×C7—21no—
544C2×C4×C7—22no—
545C2×C4×C7—22no—
546C2×C4×C7—22no—
547C2×C4×C7—21no—
548C2×C4×C7—22no—
549C2×C4×C7—21no—
550C2×C4×C7—21no—
551C2×C4×C7—22no—
552C2×C4×C7—21no—
553C2×C4×C7—22no—
554C2×C4×C7—22no—
555C2×C4×C7—22no—
556C2×C4×C7—42no—
557C2×C4×C7—42no—
558C2×C4×C7—42no—
559C2×C4×C7—44no—
560C2×C4×C7—44no—
561C2×C4×C7—44no—
562C2×C4×C7—41no—
563C2×C4×C7—44no—
564C2×C4×C7—41no—
565C2×C4×C7—41no—
566C2×C4×C7—41no—
567C2×C4×C7—41no—
568C2×C4×C7—41no—
569C2×C4×C7—41no—
570C2×C4×C7—41no—
571C2×C4×C7—42no—
572C2×C4×C7—41no—
573C2×C4×C7—41no—
574C2×C4×C7—41no—
575C2×C4×C7—82no—
576C2×C4×C7#12011yescharacteristic
577C2×C4×C7#12011yescharacteristic
578C2×C4×C7C22×D411yescharacteristic
579C2×C4×C7C22×D411yescharacteristic
580C2×C4×C7C22×D411yescharacteristic
581C2×C4×C7C22×D411yescharacteristic
582C2×C4×C7H(5,𝔽2)11yescharacteristic
583C2×C4×C7H(5,𝔽2)11yescharacteristic
584C7×C8—22no—
585C7×C8—22no—
586C7×C8—41no—
587C7×C8—41no—
5882−1+4—22no—
5892−1+4—22no—
5902−1+4—41no—
5912−1+4—41no—
592C2×#41—21no—
593C2×#41—21no—
594C2×#41—21no—
595C2×#41—22no—
596C2×#41—21no—
597C2×#41—22no—
598C2×#41—22no—
599C2×#41—22no—
600C2×#41—22no—
601C2×#41—21no—
602C2×#41—21no—
603C2×#41—21no—
604C2×#41—21no—
605C2×#41—41no—
606C2×#41—41no—
607C2×#41—41no—
608C2×#41—41no—
609C2×#41C7×D411yescharacteristic
610C2×#41C7×D411yescharacteristic
611C2×#41C23×C711yescharacteristic
612C2×#41C23×C711yescharacteristic
613C2×#41C23×C711yescharacteristic
614C22×Q8—21no—
615C22×Q8—21no—
616C22×Q8C7×D411yescharacteristic
617C22×Q8C23×C711yescharacteristic
618C22×Q8C23×C711yescharacteristic
619C22×D4—21no—
620C22×D4—21no—
621C22×D4C7×D411yescharacteristic
622C22×D4C23×C711yescharacteristic
623C23×C4—21no—
624C23×C4—21no—
625C23×C4C23×C711yescharacteristic
626#137—28no—
627#137—22no—
628#137—22no—
629#137—22no—
630#137—22no—
631#137—41no—
632#137C7×D414yescomplemented
633AGL(1,ℤ/8)—28no—
634AGL(1,ℤ/8)—22no—
635AGL(1,ℤ/8)—22no—
636AGL(1,ℤ/8)—22no—
637AGL(1,ℤ/8)—22no—
638AGL(1,ℤ/8)—41no—
639AGL(1,ℤ/8)C7×D414yescomplemented
640#135—28no—
641#135—28no—
642C2×Q16—21no—
643C2×Q16—21no—
644C2×Q16—21no—
645C2×SD16—21no—
646C2×SD16—21no—
647C2×SD16—21no—
648C2×SD16—21no—
649C2×SD16—21no—
650C2×SD16—21no—
651C2×D8—21no—
652C2×D8—21no—
653C2×D8—21no—
654C2×M16—21no—
655C2×M16—22no—
656C2×M16—22no—
657C2×M16C23×C711yescharacteristic
658C2×M16C23×C711yescharacteristic
659C2×M16C23×C711yescharacteristic
660C2×M16C23×C711yescharacteristic
661C22×C8—21no—
662C4⋊Q8—22no—
663C4⋊Q8—21no—
664C4⋊Q8—22no—
665C4⋊Q8—41no—
666#124—22no—
667#124—21no—
668#124—22no—
669#124—41no—
670#123—22no—
671#123—22no—
672#123—22no—
673#123—21no—
674#123—22no—
675C22⋊Q8—22no—
676C22⋊Q8—22no—
677C22⋊Q8—22no—
678C22⋊Q8—21no—
679C22⋊Q8—21no—
680C22⋊Q8—21no—
681C22⋊Q8—21no—
682C22⋊Q8—21no—
683C22⋊Q8—21no—
684C22⋊Q8—21no—
685C22⋊Q8—21no—
686C22⋊Q8C7×D411yescharacteristic
687C22⋊Q8C7×D411yescharacteristic
688#121—22no—
689#121—22no—
690#121—22no—
691#121—21no—
692#121—21no—
693#121—22no—
694#121C7×D411yescharacteristic
695#121C7×D411yescharacteristic
696#120—22no—
697#120—21no—
698C4×Q8—21no—
699C4×D4—22no—
700C4×D4—22no—
701C4×D4—21no—
702C4×D4—22no—
703C4×D4—21no—
704C4×D4—21no—
705#117—21no—
706#117C23×C711yescharacteristic
707C2×C4⋊C4—22no—
708C2×C4⋊C4—21no—
709C2×C4⋊C4—22no—
710C2×C4⋊C4C7×D412yes—
711C2×C4⋊C4C23×C711yescharacteristic
712C2×C22⋊C4—22no—
713C2×C22⋊C4—21no—
714C2×C22⋊C4—22no—
715C2×C22⋊C4—22no—
716C2×C22⋊C4C7×D412yes—
717C2×C42C23×C711yescharacteristic
718C2×C42C23×C711yescharacteristic
719#104—22no—
720#104—22no—
721#104—22no—
722#104—22no—
723#104—41no—
724#104—41no—
725#103—21no—
726#103—21no—
727#102—21no—
728#102—21no—
729#101—22no—
730#101—22no—
731C22⋊C8—21no—
732C22⋊C8—21no—
733#95—21no—
734#95—22no—
735C22×C7—21no—
736C22×C7—21no—
737C22×C7—21no—
738C22×C7—21no—
739C22×C7—22no—
740C22×C7—21no—
741C22×C7—21no—
742C22×C7—21no—
743C22×C7—21no—
744C22×C7—44no—
745C22×C7—41no—
746C22×C7—41no—
747C22×C7—41no—
748C22×C7—41no—
749C22×C7—42no—
750C22×C7—41no—
751C22×C7—41no—
752C22×C7—41no—
753C22×C7—41no—
754C22×C7—81no—
755C22×C7—81no—
756C22×C7—82no—
757C22×C7—84no—
758C22×C7—81no—
759C22×C7—81no—
760C22×C7C2×#12011yescharacteristic
761C22×C7D4211yescharacteristic
762C22×C7D4211yescharacteristic
763C4×C7—21no—
764C4×C7—21no—
765C4×C7—22no—
766C4×C7—42no—
767C4×C7—42no—
768C4×C7—41no—
769C4×C7—42no—
770C4×C7—41no—
771C4×C7—42no—
772C4×C7—41no—
773C4×C7—41no—
774C4×C7—81no—
775C4×C7C2×#12011yescharacteristic
776C4×C7#53411yescharacteristic
777C4×C7D4211yescharacteristic
778C4×C7D4211yescharacteristic
779C24—21no—
780C24—21no—
781C24C2×C7×D411yescharacteristic
782#41—21no—
783#41—21no—
784#41—24no—
785#41—24no—
786#41—22no—
787#41—22no—
788#41—21no—
789#41—21no—
790#41—21no—
791#41—21no—
792#41—21no—
793#41—21no—
794#41—21no—
795#41—21no—
796#41—42no—
797#41—42no—
798#41—41no—
799#41—41no—
800#41—42no—
801#41—42no—
802#41—42no—
803#41—42no—
804#41—42no—
805#41—42no—
806#41—44no—
807#41—44no—
808#41—42no—
809#41—42no—
810#41—42no—
811#41—42no—
812#41—42no—
813#41—42no—
814#41C2×C7×D412yes—
815#41C2×C7×D412yes—
816C2×Q8—22no—
817C2×Q8—21no—
818C2×Q8—21no—
819C2×Q8—21no—
820C2×Q8—21no—
821C2×Q8—21no—
822C2×Q8—21no—
823C2×Q8—21no—
824C2×Q8—21no—
825C2×Q8—22no—
826C2×Q8—21no—
827C2×Q8—21no—
828C2×Q8—21no—
829C2×Q8—21no—
830C2×Q8—41no—
831C2×Q8—42no—
832C2×Q8—42no—
833C2×Q8—42no—
834C2×Q8—42no—
835C2×Q8C2×C7×D411yescharacteristic
836C2×Q8C2×C7×D411yescharacteristic
837C2×Q8C2×C7×D412yes—
838C2×Q8C2×C7×D411yescharacteristic
839C2×D4—21no—
840C2×D4—22no—
841C2×D4—22no—
842C2×D4—21no—
843C2×D4—21no—
844C2×D4—21no—
845C2×D4—21no—
846C2×D4—21no—
847C2×D4—22no—
848C2×D4—21no—
849C2×D4—21no—
850C2×D4—21no—
851C2×D4—21no—
852C2×D4—21no—
853C2×D4—21no—
854C2×D4—21no—
855C2×D4—41no—
856C2×D4—42no—
857C2×D4—42no—
858C2×D4—42no—
859C2×D4—42no—
860C2×D4—41no—
861C2×D4—41no—
862C2×D4C2×C7×D411yescharacteristic
863C2×D4C2×C7×D411yescharacteristic
864C2×D4C2×C7×D412yes—
865C2×D4C2×C7×D411yescharacteristic
866C22×C4—21no—
867C22×C4—21no—
868C22×C4—21no—
869C22×C4—21no—
870C22×C4—21no—
871C22×C4—22no—
872C22×C4—22no—
873C22×C4—21no—
874C22×C4—21no—
875C22×C4—21no—
876C22×C4—22no—
877C22×C4—21no—
878C22×C4—21no—
879C22×C4—21no—
880C22×C4—21no—
881C22×C4—21no—
882C22×C4—42no—
883C22×C4—42no—
884C22×C4—42no—
885C22×C4—42no—
886C22×C4—41no—
887C22×C4—41no—
888C22×C4C2×C7×D412yes—
889C22×C4C2×C7×D411yescharacteristic
890C22×C4C2×C7×D411yescharacteristic
891C22×C4C2×C7×D411yescharacteristic
892C22×C4C2×C7×D411yescharacteristic
893C22×C4C2×C7×D411yescharacteristic
894C22×C4C2×C7×D412yes—
895C22×C4C24×C711yescharacteristic
896Q16—24no—
897Q16—24no—
898Q16—42no—
899SD16—24no—
900SD16—24no—
901SD16—24no—
902SD16—24no—
903SD16—42no—
904SD16—42no—
905D8—24no—
906D8—24no—
907D8—42no—
908M16—24no—
909M16—21no—
910M16—21no—
911M16—21no—
912M16—21no—
913M16—21no—
914M16—21no—
915M16C2×C7×D412yes—
916M16C2×C7×D412yes—
917C2×C8—24no—
918C2×C8—21no—
919C2×C8—21no—
920C2×C8—21no—
921C2×C8—21no—
922C4⋊C4—22no—
923C4⋊C4—22no—
924C4⋊C4—22no—
925C4⋊C4—22no—
926C4⋊C4—21no—
927C4⋊C4—22no—
928C4⋊C4—22no—
929C4⋊C4—21no—
930C4⋊C4—21no—
931C4⋊C4—21no—
932C4⋊C4—44no—
933C4⋊C4C2×C7×D411yescharacteristic
934C4⋊C4C2×C7×D411yescharacteristic
935C22⋊C4—22no—
936C22⋊C4—22no—
937C22⋊C4—22no—
938C22⋊C4—22no—
939C22⋊C4—22no—
940C22⋊C4—21no—
941C22⋊C4—22no—
942C22⋊C4—22no—
943C22⋊C4—21no—
944C22⋊C4—21no—
945C22⋊C4—21no—
946C22⋊C4—21no—
947C22⋊C4—44no—
948C22⋊C4—44no—
949C22⋊C4—42no—
950C42—22no—
951C42—21no—
952C42—21no—
953C42—21no—
954C42—21no—
955C42—21no—
956C2×C7—21no—
957C2×C7—21no—
958C2×C7—41no—
959C2×C7—41no—
960C2×C7—42no—
961C2×C7—81no—
962C2×C7—82no—
963C2×C7—81no—
964C2×C7#240311yescharacteristic
965C2×C7#301811yescharacteristic
966C2×C7#302011yescharacteristic
967C23—21no—
968C23—21no—
969C23—21no—
970C23—21no—
971C23—21no—
972C23—22no—
973C23—41no—
974C23—41no—
975C23—42no—
976C23—42no—
977C23—42no—
978C23—42no—
979C23—41no—
980C23—41no—
981C23—81no—
982C23C7×#12011yescharacteristic
983C23C7×#12011yescharacteristic
984C23C22×C7×D411yescharacteristic
985Q8—21no—
986Q8—21no—
987Q8—22no—
988Q8—21no—
989Q8—21no—
990Q8—22no—
991Q8—21no—
992Q8—42no—
993Q8—44no—
994Q8—41no—
995Q8—41no—
996Q8—41no—
997Q8—41no—
998Q8—41no—
999Q8—41no—
1000Q8C7×#12012yes—
1001D4—22no—
1002D4—22no—
1003D4—21no—
1004D4—22no—
1005D4—21no—
1006D4—21no—
1007D4—21no—
1008D4—22no—
1009D4—21no—
1010D4—42no—
1011D4—42no—
1012D4—42no—
1013D4—42no—
1014D4—44no—
1015D4—44no—
1016D4—44no—
1017D4—41no—
1018D4—41no—
1019D4—41no—
1020D4—41no—
1021D4—41no—
1022D4—41no—
1023D4—81no—
1024D4—82no—
1025D4C7×#12012yes—
1026C2×C4—21no—
1027C2×C4—21no—
1028C2×C4—21no—
1029C2×C4—21no—
1030C2×C4—21no—
1031C2×C4—21no—
1032C2×C4—21no—
1033C2×C4—21no—
1034C2×C4—21no—
1035C2×C4—21no—
1036C2×C4—21no—
1037C2×C4—22no—
1038C2×C4—22no—
1039C2×C4—22no—
1040C2×C4—21no—
1041C2×C4—22no—
1042C2×C4—21no—
1043C2×C4—21no—
1044C2×C4—22no—
1045C2×C4—21no—
1046C2×C4—22no—
1047C2×C4—22no—
1048C2×C4—22no—
1049C2×C4—42no—
1050C2×C4—42no—
1051C2×C4—42no—
1052C2×C4—44no—
1053C2×C4—44no—
1054C2×C4—44no—
1055C2×C4—41no—
1056C2×C4—44no—
1057C2×C4—41no—
1058C2×C4—41no—
1059C2×C4—41no—
1060C2×C4—41no—
1061C2×C4—41no—
1062C2×C4—41no—
1063C2×C4—41no—
1064C2×C4—42no—
1065C2×C4—41no—
1066C2×C4—41no—
1067C2×C4—41no—
1068C2×C4—82no—
1069C2×C4C7×#12011yescharacteristic
1070C2×C4C7×#12011yescharacteristic
1071C2×C4C22×C7×D411yescharacteristic
1072C2×C4C22×C7×D411yescharacteristic
1073C2×C4C22×C7×D411yescharacteristic
1074C2×C4C22×C7×D411yescharacteristic
1075C2×C4C7×H(5,𝔽2)11yescharacteristic
1076C2×C4C7×H(5,𝔽2)11yescharacteristic
1077C8—22no—
1078C8—22no—
1079C8—41no—
1080C8—41no—
1081C7#2388111yescharacteristic, direct product factor, Sylow
1082C22—21no—
1083C22—21no—
1084C22—21no—
1085C22—21no—
1086C22—22no—
1087C22—21no—
1088C22—21no—
1089C22—21no—
1090C22—21no—
1091C22—44no—
1092C22—41no—
1093C22—41no—
1094C22—41no—
1095C22—41no—
1096C22—42no—
1097C22—41no—
1098C22—41no—
1099C22—41no—
1100C22—41no—
1101C22—81no—
1102C22—81no—
1103C22—82no—
1104C22—84no—
1105C22—81no—
1106C22—81no—
1107C22C2×C7×#12011yescharacteristic
1108C22C7×D4211yescharacteristic
1109C22C7×D4211yescharacteristic
1110C4—21no—
1111C4—21no—
1112C4—22no—
1113C4—42no—
1114C4—42no—
1115C4—41no—
1116C4—42no—
1117C4—41no—
1118C4—42no—
1119C4—41no—
1120C4—41no—
1121C4—81no—
1122C4C2×C7×#12011yescharacteristic
1123C4C7×#53411yescharacteristic
1124C4C7×D4211yescharacteristic
1125C4C7×D4211yescharacteristic
1126C2—21no—
1127C2—21no—
1128C2—41no—
1129C2—41no—
1130C2—42no—
1131C2—82no—
1132C2—81no—
1133C2—81no—
1134C2C7×#240311yescharacteristic
1135C2C7×#301811yescharacteristic
1136C2C7×#302011yescharacteristic
subgroupG/H
center, socleC22×C7C2×#120
commutator, Frattini, cosocleC22×C4C24×C7
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C7 ◁ C23×C4×C7 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C7×#575C2semidirect
2. C7×#3489C2semidirect
3. C2×C7×#456C2semidirect
4. C2×C7×#454C2semidirect
5. C7×#3005C2semidirect
6. C7×#2432C2semidirect
7. C7×#2007C2semidirect
8. C7×#2006C2semidirect
9. C7×#2005C2semidirect
10. C7×#2003C2semidirect
11. C7×#1901C2semidirect
12. C7×#1883C2semidirect
13. C7×#1882C2semidirect
14. C7×#1871C2semidirect
15. C7×#1789C2semidirect
24. C2×C7×#137C22semidirect
28. C2×C7×AGL(1,ℤ/8)C22semidirect
42. C2×C7×C4⋊Q8C22semidirect
43. C2×C7×#124C22semidirect
59. C2×C7×#104C22semidirect
60. C2×C7×#104C22semidirect
61. C7×#419C22semidirect
62. C7×#418C22semidirect
63. C2×C7×#101C22semidirect
64. C2×C7×#101C22semidirect
67. C7×#391C22semidirect
68. C7×#390C22semidirect
71. C7×#343C22semidirect
72. C7×#343C22semidirect
73. C7×#339C22semidirect
74. C7×#339C22semidirect
75. #23881C7direct (N × H)
120. C7×#137D4semidirect
127. C7×AGL(1,ℤ/8)D4semidirect
223. C2×#575C2×C7semidirect
224. #3489C2×C7semidirect
225. C2×#456C2×C7semidirect
226. C2×#454C2×C7semidirect
227. #3005C2×C7semidirect
228. #2432C2×C7semidirect
229. #2007C2×C7semidirect
230. #2006C2×C7semidirect
231. #2005C2×C7semidirect
232. #2003C2×C7semidirect
233. #1901C2×C7semidirect
234. #1883C2×C7semidirect
235. #1882C2×C7semidirect
236. #1871C2×C7semidirect
237. #1789C2×C7semidirect
423. C2×#137C22×C7semidirect
427. C2×AGL(1,ℤ/8)C22×C7semidirect
441. C2×C4⋊Q8C22×C7semidirect
442. C2×#124C22×C7semidirect
458. C2×#104C22×C7semidirect
459. C2×#104C22×C7semidirect
460. #419C22×C7semidirect
461. #418C22×C7semidirect
462. C2×#101C22×C7semidirect
463. C2×#101C22×C7semidirect
466. #391C22×C7semidirect
467. #390C22×C7semidirect
470. #343C22×C7semidirect
471. #343C22×C7semidirect
472. #339C22×C7semidirect
473. #339C22×C7semidirect
632. #137C7×D4semidirect
639. AGL(1,ℤ/8)C7×D4semidirect
1081. C7#23881direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C7×#5752
C7×#34892
C2×C7×#4562
C2×C7×#4542
C7×#30052
C7×#24322
C7×#20072
C7×#20062
C7×#20052
C7×#20032
C7×#19012
C7×#18832
C7×#18822
C7×#18712
C7×#17892
#238817