Finite Group Databasebeta

← C7×#26724 #13203940

Subgroups — C7×#26724 #13203940

Order 1792.

826 conjugacy classes of subgroups.

The subgroup lattice has 676 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C7×#2491C211yesmaximal, characteristic
2C7×#2360C211yesmaximal, characteristic, complemented
3C7×#2055C211yesmaximal, characteristic, complemented
4C7×#2035C211yesmaximal, characteristic, complemented
5C7×#2024C211yesmaximal, characteristic, complemented
6C7×#2000C211yesmaximal, characteristic
7C7×#1988C211yesmaximal, characteristic, complemented
8C7×#1934C211yesmaximal, characteristic, complemented
9C7×#1926C211yesmaximal, characteristic, complemented
10C7×#1923C211yesmaximal, characteristic, complemented
11C7×#1920C211yesmaximal, characteristic, complemented
12C7×#1880C211yesmaximal, characteristic, complemented
13C7×#1874C211yesmaximal, characteristic
14C7×#1824C211yesmaximal, characteristic, complemented
15C4×C7×#103C211yesmaximal, characteristic, complemented
16C22×C7×SD16C2211yescharacteristic
17C2×C7×C4⋊Q8C2211yescharacteristic
18C2×C7×#124—21no—
19C2×C7×C22⋊Q8C2211yescharacteristic
20C2×C7×#121C2211yescharacteristic
21C2×C4×C7×Q8C2211yescharacteristic
22C22×C7×C4⋊C4C2211yescharacteristic
23C2×C7×#106C2211yescharacteristic
24C2×C7×C4⋊C8C2211yescharacteristic
25C2×C7×#103C2211yescharacteristic
26C2×C7×#103C2211yescharacteristic
27C2×C7×#103C2211yescharacteristic
28C2×C7×#102C2211yescharacteristic
29C2×C7×#102C2211yescharacteristic
30C2×C7×#102C2211yescharacteristic
31C2×C7×C22⋊C8C2211yescharacteristic
32C2×C7×C22⋊C8C2211yescharacteristic
33C2×C4×C7×C8C2211yescharacteristic
34C7×#394—21no—
35C7×#393—21no—
36C7×#391C2211yescharacteristic
37C7×#390C2211yescharacteristic
38C7×#390C2211yescharacteristic
39C7×#389—21no—
40C7×#389C2211yescharacteristic
41C7×#388—21no—
42C7×#387—21no—
43C7×#385—21no—
44C7×#380C2211yescharacteristic
45C4×C7×C4⋊C4C2211yescharacteristic
46C4×C7×C4⋊C4C2211yescharacteristic
47C4×C7×C22⋊C4—21no—
48C4×C7×C22⋊C4C2211yescharacteristic
49C7×#340C2211yescharacteristic
50C7×#340C2211yescharacteristic
51C7×#340C2211yescharacteristic
52C7×#340C2211yescharacteristic
53C7×#340C2211yescharacteristic
54C7×#340C2211yescharacteristic
55C7×#340C2211yescharacteristic
56C7×#340C2211yescharacteristic
57C7×#336C2211yescharacteristic
58C7×#336C2211yescharacteristic
59#26724C711yesmaximal, characteristic, direct product factor, Sylow
60C22×C7×Q8—21no—
61C22×C7×Q8C2311yescharacteristic
62C22×C7×D4—21no—
63C22×C7×D4C2311yescharacteristic
64C23×C4×C7—21no—
65C23×C4×C7C2311yescharacteristic
66C2×C7×SD16—22no—
67C2×C7×SD16—41no—
68C2×C7×SD16—41no—
69C22×C7×C8C2311yescharacteristic
70C22×C7×C8C2311yescharacteristic
71C22×C7×C8C2311yescharacteristic
72C22×C7×C8C2311yescharacteristic
73C7×C4⋊Q8—22no—
74C7×C4⋊Q8—41no—
75C7×#124—44no—
76C7×C22⋊Q8—22no—
77C7×C22⋊Q8—22no—
78C7×#121—22no—
79C7×#121—41no—
80C4×C7×Q8—22no—
81C4×C7×Q8—41no—
82C2×C7×C4⋊C4—21no—
83C2×C7×C4⋊C4—22no—
84C2×C7×C4⋊C4—21no—
85C2×C7×C4⋊C4—21no—
86C2×C7×C4⋊C4—21no—
87C2×C7×C4⋊C4—21no—
88C2×C7×C4⋊C4—41no—
89C2×C7×C4⋊C4C2311yescharacteristic
90C2×C7×C4⋊C4C2311yescharacteristic
91C2×C7×C4⋊C4C2311yescharacteristic
92C2×C7×C4⋊C4C2311yescharacteristic
93C2×C7×C4⋊C4C2311yescharacteristic
94C2×C7×C4⋊C4C2311yescharacteristic
95C2×C7×C22⋊C4—21no—
96C2×C7×C22⋊C4—21no—
97C2×C7×C22⋊C4—21no—
98C2×C7×C22⋊C4—21no—
99C2×C7×C22⋊C4—21no—
100C2×C7×C22⋊C4—21no—
101C2×C7×C22⋊C4—21no—
102C2×C7×C22⋊C4D411yescharacteristic
103C2×C7×C22⋊C4D411yescharacteristic
104C2×C42×C7—21no—
105C2×C42×C7—21no—
106C2×C42×C7—21no—
107C2×C42×C7C2311yescharacteristic
108C2×C42×C7C2311yescharacteristic
109C7×#106—22no—
110C7×C4⋊C8—41no—
111C7×#103—22no—
112C7×#103—22no—
113C7×#103—41no—
114C7×#102—22no—
115C7×#102—22no—
116C7×#102—41no—
117C7×C22⋊C8—41no—
118C7×C22⋊C8—41no—
119C4×C7×C8—41no—
120C7×#95—21no—
121C7×#95—21no—
122C7×#95—21no—
123C7×#95—21no—
124C7×#95—21no—
125C7×#95—21no—
126C7×#95D411yescharacteristic
127C7×#95D411yescharacteristic
128#2491C2×C711yescharacteristic
129#2360C2×C711yescharacteristic, complemented
130#2055C2×C711yescharacteristic, complemented
131#2035C2×C711yescharacteristic, complemented
132#2024C2×C711yescharacteristic, complemented
133#2000C2×C711yescharacteristic
134#1988C2×C711yescharacteristic, complemented
135#1934C2×C711yescharacteristic, complemented
136#1926C2×C711yescharacteristic, complemented
137#1923C2×C711yescharacteristic, complemented
138#1920C2×C711yescharacteristic, complemented
139#1880C2×C711yescharacteristic, complemented
140#1874C2×C711yescharacteristic
141#1824C2×C711yescharacteristic, complemented
142C4×#103C2×C711yescharacteristic, complemented
143C24×C7—21no—
144C24×C7C2×D411yescharacteristic
145C2×C7×Q8—21no—
146C2×C7×Q8—21no—
147C2×C7×Q8—21no—
148C2×C7×Q8—21no—
149C2×C7×Q8—21no—
150C2×C7×Q8—42no—
151C2×C7×Q8—42no—
152C2×C7×Q8—81no—
153C2×C7×Q8#4112yes—
154C2×C7×D4—21no—
155C2×C7×D4—21no—
156C2×C7×D4—21no—
157C2×C7×D4—21no—
158C2×C7×D4—21no—
159C2×C7×D4—21no—
160C2×C7×D4—42no—
161C2×C7×D4—42no—
162C2×C7×D4—81no—
163C22×C4×C7—21no—
164C22×C4×C7—21no—
165C22×C4×C7—21no—
166C22×C4×C7—21no—
167C22×C4×C7—21no—
168C22×C4×C7—21no—
169C22×C4×C7—21no—
170C22×C4×C7—21no—
171C22×C4×C7—21no—
172C22×C4×C7—21no—
173C22×C4×C7—21no—
174C22×C4×C7—21no—
175C22×C4×C7—21no—
176C22×C4×C7—42no—
177C22×C4×C7—42no—
178C22×C4×C7—81no—
179C22×C4×C7C2×D411yescharacteristic
180C22×C4×C7C2×D411yescharacteristic
181C22×C4×C7C2×D411yescharacteristic
182C22×C4×C7C2×D411yescharacteristic
183C22×C4×C7C2×D411yescharacteristic
184C22×C4×C7C2411yescharacteristic
185C7×SD16—44no—
186C2×C7×C8—21no—
187C2×C7×C8—21no—
188C2×C7×C8—21no—
189C2×C7×C8—21no—
190C2×C7×C8—21no—
191C2×C7×C8—21no—
192C2×C7×C8—21no—
193C2×C7×C8—21no—
194C2×C7×C8—21no—
195C2×C7×C8—21no—
196C2×C7×C8—21no—
197C2×C7×C8—21no—
198C7×C4⋊C4—24no—
199C7×C4⋊C4—21no—
200C7×C4⋊C4—21no—
201C7×C4⋊C4—21no—
202C7×C4⋊C4—21no—
203C7×C4⋊C4—21no—
204C7×C4⋊C4—21no—
205C7×C4⋊C4—21no—
206C7×C4⋊C4—21no—
207C7×C4⋊C4—21no—
208C7×C4⋊C4—42no—
209C7×C4⋊C4—42no—
210C7×C4⋊C4—42no—
211C7×C4⋊C4—81no—
212C7×C4⋊C4#4112yes—
213C7×C4⋊C4#4112yes—
214C7×C4⋊C4#4112yes—
215C7×C22⋊C4—24no—
216C7×C22⋊C4—41no—
217C7×C22⋊C4—42no—
218C7×C22⋊C4—42no—
219C7×C22⋊C4—42no—
220C7×C22⋊C4—42no—
221C7×C22⋊C4—42no—
222C7×C22⋊C4—81no—
223C7×C22⋊C4SD1614yescomplemented
224C42×C7—21no—
225C42×C7—21no—
226C42×C7—21no—
227C42×C7—21no—
228C42×C7—42no—
229C42×C7—42no—
230C42×C7—81no—
231C22×SD16C22×C711yescharacteristic
232C2×C4⋊Q8C22×C711yescharacteristic
233C2×#124—21no—
234C2×C22⋊Q8C22×C711yescharacteristic
235C2×#121C22×C711yescharacteristic
236C2×C4×Q8C22×C711yescharacteristic
237C22×C4⋊C4C22×C711yescharacteristic
238C2×#106C22×C711yescharacteristic
239C2×C4⋊C8C22×C711yescharacteristic
240C2×#103C22×C711yescharacteristic
241C2×#103C22×C711yescharacteristic
242C2×#103C22×C711yescharacteristic
243C2×#102C22×C711yescharacteristic
244C2×#102C22×C711yescharacteristic
245C2×#102C22×C711yescharacteristic
246C2×C22⋊C8C22×C711yescharacteristic
247C2×C22⋊C8C22×C711yescharacteristic
248C2×C4×C8C22×C711yescharacteristic
249#394—21no—
250#393—21no—
251#391C22×C711yescharacteristic
252#390C22×C711yescharacteristic
253#390C22×C711yescharacteristic
254#389—21no—
255#389C22×C711yescharacteristic
256#388—21no—
257#387—21no—
258#385—21no—
259#380C22×C711yescharacteristic
260C4×C4⋊C4C22×C711yescharacteristic
261C4×C4⋊C4C22×C711yescharacteristic
262C4×C22⋊C4—21no—
263C4×C22⋊C4C22×C711yescharacteristic
264#340C22×C711yescharacteristic
265#340C22×C711yescharacteristic
266#340C22×C711yescharacteristic
267#340C22×C711yescharacteristic
268#340C22×C711yescharacteristic
269#340C22×C711yescharacteristic
270#340C22×C711yescharacteristic
271#340C22×C711yescharacteristic
272#336C22×C711yescharacteristic
273#336C22×C711yescharacteristic
274C23×C7—21no—
275C23×C7—21no—
276C23×C7—21no—
277C23×C7—21no—
278C23×C7—21no—
279C23×C7—21no—
280C23×C7—41no—
281C23×C7—41no—
282C23×C7—41no—
283C23×C7—41no—
284C23×C7—41no—
285C23×C7—41no—
286C23×C7—41no—
287C23×C7C2×SD1612yes—
288C23×C7C22×D411yescharacteristic
289C7×Q8—22no—
290C7×Q8—22no—
291C7×Q8—41no—
292C7×Q8—41no—
293C7×Q8—84no—
294C7×D4—41no—
295C7×D4—41no—
296C7×D4—41no—
297C7×D4—41no—
298C7×D4—84no—
299C2×C4×C7—21no—
300C2×C4×C7—21no—
301C2×C4×C7—21no—
302C2×C4×C7—21no—
303C2×C4×C7—22no—
304C2×C4×C7—22no—
305C2×C4×C7—21no—
306C2×C4×C7—21no—
307C2×C4×C7—21no—
308C2×C4×C7—22no—
309C2×C4×C7—21no—
310C2×C4×C7—22no—
311C2×C4×C7—21no—
312C2×C4×C7—21no—
313C2×C4×C7—21no—
314C2×C4×C7—21no—
315C2×C4×C7—21no—
316C2×C4×C7—41no—
317C2×C4×C7—41no—
318C2×C4×C7—41no—
319C2×C4×C7—41no—
320C2×C4×C7—41no—
321C2×C4×C7—41no—
322C2×C4×C7—41no—
323C2×C4×C7—41no—
324C2×C4×C7—41no—
325C2×C4×C7—41no—
326C2×C4×C7—41no—
327C2×C4×C7—41no—
328C2×C4×C7—41no—
329C2×C4×C7—41no—
330C2×C4×C7—41no—
331C2×C4×C7—41no—
332C2×C4×C7—41no—
333C2×C4×C7—41no—
334C2×C4×C7—41no—
335C2×C4×C7—41no—
336C2×C4×C7—41no—
337C2×C4×C7—84no—
338C2×C4×C7C2×SD1612yes—
339C2×C4×C7C2×SD1612yes—
340C2×C4×C7C2×#4111yescharacteristic
341C2×C4×C7C2×#4111yescharacteristic
342C2×C4×C7C2×#4111yescharacteristic
343C2×C4×C7C2×#4111yescharacteristic
344C2×C4×C7H(5,𝔽2)11yescharacteristic
345C2×C4×C7H(5,𝔽2)11yescharacteristic
346C7×C8—41no—
347C7×C8—41no—
348C7×C8—41no—
349C7×C8—41no—
350C22×Q8—21no—
351C22×Q8C23×C711yescharacteristic
352C22×D4—21no—
353C22×D4C23×C711yescharacteristic
354C23×C4—21no—
355C23×C4C23×C711yescharacteristic
356C2×SD16—22no—
357C2×SD16—41no—
358C2×SD16—41no—
359C22×C8C23×C711yescharacteristic
360C22×C8C23×C711yescharacteristic
361C22×C8C23×C711yescharacteristic
362C22×C8C23×C711yescharacteristic
363C4⋊Q8—22no—
364C4⋊Q8—41no—
365#124—44no—
366C22⋊Q8—22no—
367C22⋊Q8—22no—
368#121—22no—
369#121—41no—
370C4×Q8—22no—
371C4×Q8—41no—
372C2×C4⋊C4—21no—
373C2×C4⋊C4—22no—
374C2×C4⋊C4—21no—
375C2×C4⋊C4—21no—
376C2×C4⋊C4—21no—
377C2×C4⋊C4—21no—
378C2×C4⋊C4—41no—
379C2×C4⋊C4C23×C711yescharacteristic
380C2×C4⋊C4C23×C711yescharacteristic
381C2×C4⋊C4C23×C711yescharacteristic
382C2×C4⋊C4C23×C711yescharacteristic
383C2×C4⋊C4C23×C711yescharacteristic
384C2×C4⋊C4C23×C711yescharacteristic
385C2×C22⋊C4—21no—
386C2×C22⋊C4—21no—
387C2×C22⋊C4—21no—
388C2×C22⋊C4—21no—
389C2×C22⋊C4—21no—
390C2×C22⋊C4—21no—
391C2×C22⋊C4—21no—
392C2×C22⋊C4C7×D411yescharacteristic
393C2×C22⋊C4C7×D411yescharacteristic
394C2×C42—21no—
395C2×C42—21no—
396C2×C42—21no—
397C2×C42C23×C711yescharacteristic
398C2×C42C23×C711yescharacteristic
399#106—22no—
400C4⋊C8—41no—
401#103—22no—
402#103—22no—
403#103—41no—
404#102—22no—
405#102—22no—
406#102—41no—
407C22⋊C8—41no—
408C22⋊C8—41no—
409C4×C8—41no—
410#95—21no—
411#95—21no—
412#95—21no—
413#95—21no—
414#95—21no—
415#95—21no—
416#95C7×D411yescharacteristic
417#95C7×D411yescharacteristic
418C22×C7—22no—
419C22×C7—22no—
420C22×C7—22no—
421C22×C7—41no—
422C22×C7—41no—
423C22×C7—41no—
424C22×C7—41no—
425C22×C7—81no—
426C22×C7—81no—
427C22×C7—81no—
428C22×C7—81no—
429C22×C7—81no—
430C22×C7—81no—
431C22×C7—81no—
432C22×C7#52511yescharacteristic
433C22×C7#54611yescharacteristic
434C22×C7#54611yescharacteristic
435C22×C7C22×SD1611yescharacteristic
436C22×C7#57511yescharacteristic
437C22×C7#57611yescharacteristic
438C22×C7#57811yescharacteristic
439C4×C7—22no—
440C4×C7—22no—
441C4×C7—42no—
442C4×C7—41no—
443C4×C7—42no—
444C4×C7—42no—
445C4×C7—41no—
446C4×C7—42no—
447C4×C7—41no—
448C4×C7—81no—
449C4×C7—81no—
450C4×C7—81no—
451C4×C7#52911yescharacteristic
452C4×C7#53811yescharacteristic
453C4×C7#55511yescharacteristic
454C4×C7#55911yescharacteristic
455C24—21no—
456C24C2×C7×D411yescharacteristic
457C2×Q8—21no—
458C2×Q8—21no—
459C2×Q8—21no—
460C2×Q8—21no—
461C2×Q8—21no—
462C2×Q8—42no—
463C2×Q8—42no—
464C2×Q8—81no—
465C2×Q8C7×#4112yes—
466C2×D4—21no—
467C2×D4—21no—
468C2×D4—21no—
469C2×D4—21no—
470C2×D4—21no—
471C2×D4—21no—
472C2×D4—42no—
473C2×D4—42no—
474C2×D4—81no—
475C22×C4—21no—
476C22×C4—21no—
477C22×C4—21no—
478C22×C4—21no—
479C22×C4—21no—
480C22×C4—21no—
481C22×C4—21no—
482C22×C4—21no—
483C22×C4—21no—
484C22×C4—21no—
485C22×C4—21no—
486C22×C4—21no—
487C22×C4—21no—
488C22×C4—42no—
489C22×C4—42no—
490C22×C4—81no—
491C22×C4C2×C7×D411yescharacteristic
492C22×C4C2×C7×D411yescharacteristic
493C22×C4C2×C7×D411yescharacteristic
494C22×C4C2×C7×D411yescharacteristic
495C22×C4C2×C7×D411yescharacteristic
496C22×C4C24×C711yescharacteristic
497SD16—44no—
498C2×C8—21no—
499C2×C8—21no—
500C2×C8—21no—
501C2×C8—21no—
502C2×C8—21no—
503C2×C8—21no—
504C2×C8—21no—
505C2×C8—21no—
506C2×C8—21no—
507C2×C8—21no—
508C2×C8—21no—
509C2×C8—21no—
510C4⋊C4—24no—
511C4⋊C4—21no—
512C4⋊C4—21no—
513C4⋊C4—21no—
514C4⋊C4—21no—
515C4⋊C4—21no—
516C4⋊C4—21no—
517C4⋊C4—21no—
518C4⋊C4—21no—
519C4⋊C4—21no—
520C4⋊C4—42no—
521C4⋊C4—42no—
522C4⋊C4—42no—
523C4⋊C4—81no—
524C4⋊C4C7×#4112yes—
525C4⋊C4C7×#4112yes—
526C4⋊C4C7×#4112yes—
527C22⋊C4—24no—
528C22⋊C4—41no—
529C22⋊C4—42no—
530C22⋊C4—42no—
531C22⋊C4—42no—
532C22⋊C4—42no—
533C22⋊C4—42no—
534C22⋊C4—81no—
535C22⋊C4C7×SD1614yescomplemented
536C42—21no—
537C42—21no—
538C42—21no—
539C42—21no—
540C42—42no—
541C42—42no—
542C42—81no—
543C2×C7—42no—
544C2×C7—161no—
545C2×C7#245911yescharacteristic
546C2×C7#310311yescharacteristic
547C2×C7#312411yescharacteristic
548C2×C7#329511yescharacteristic
549C2×C7#329811yescharacteristic
550C2×C7#331911yescharacteristic
551C2×C7#332711yescharacteristic
552C23—21no—
553C23—21no—
554C23—21no—
555C23—21no—
556C23—21no—
557C23—21no—
558C23—41no—
559C23—41no—
560C23—41no—
561C23—41no—
562C23—41no—
563C23—41no—
564C23—41no—
565C23C2×C7×SD1612yes—
566C23C22×C7×D411yescharacteristic
567Q8—22no—
568Q8—22no—
569Q8—41no—
570Q8—41no—
571Q8—84no—
572D4—41no—
573D4—41no—
574D4—41no—
575D4—41no—
576D4—84no—
577C2×C4—21no—
578C2×C4—21no—
579C2×C4—21no—
580C2×C4—21no—
581C2×C4—22no—
582C2×C4—22no—
583C2×C4—21no—
584C2×C4—21no—
585C2×C4—21no—
586C2×C4—22no—
587C2×C4—21no—
588C2×C4—22no—
589C2×C4—21no—
590C2×C4—21no—
591C2×C4—21no—
592C2×C4—21no—
593C2×C4—21no—
594C2×C4—41no—
595C2×C4—41no—
596C2×C4—41no—
597C2×C4—41no—
598C2×C4—41no—
599C2×C4—41no—
600C2×C4—41no—
601C2×C4—41no—
602C2×C4—41no—
603C2×C4—41no—
604C2×C4—41no—
605C2×C4—41no—
606C2×C4—41no—
607C2×C4—41no—
608C2×C4—41no—
609C2×C4—41no—
610C2×C4—41no—
611C2×C4—41no—
612C2×C4—41no—
613C2×C4—41no—
614C2×C4—41no—
615C2×C4—84no—
616C2×C4C2×C7×SD1612yes—
617C2×C4C2×C7×SD1612yes—
618C2×C4C2×C7×#4111yescharacteristic
619C2×C4C2×C7×#4111yescharacteristic
620C2×C4C2×C7×#4111yescharacteristic
621C2×C4C2×C7×#4111yescharacteristic
622C2×C4C7×H(5,𝔽2)11yescharacteristic
623C2×C4C7×H(5,𝔽2)11yescharacteristic
624C8—41no—
625C8—41no—
626C8—41no—
627C8—41no—
628C7#2672411yescharacteristic, direct product factor, Sylow
629C22—22no—
630C22—22no—
631C22—22no—
632C22—41no—
633C22—41no—
634C22—41no—
635C22—41no—
636C22—81no—
637C22—81no—
638C22—81no—
639C22—81no—
640C22—81no—
641C22—81no—
642C22—81no—
643C22C7×#52511yescharacteristic
644C22C7×#54611yescharacteristic
645C22C7×#54611yescharacteristic
646C22C22×C7×SD1611yescharacteristic
647C22C7×#57511yescharacteristic
648C22C7×#57611yescharacteristic
649C22C7×#57811yescharacteristic
650C4—22no—
651C4—22no—
652C4—41no—
653C4—42no—
654C4—42no—
655C4—41no—
656C4—42no—
657C4—41no—
658C4—42no—
659C4—81no—
660C4—81no—
661C4—81no—
662C4C7×#52911yescharacteristic
663C4C7×#53811yescharacteristic
664C4C7×#55511yescharacteristic
665C4C7×#55911yescharacteristic
666C2—42no—
667C2—161no—
668C2C7×#245911yescharacteristic
669C2C7×#310311yescharacteristic
670C2C7×#312411yescharacteristic
671C2C7×#329511yescharacteristic
672C2C7×#329811yescharacteristic
673C2C7×#331911yescharacteristic
674C2C7×#332711yescharacteristic
subgroupG/H
center, socleC23×C7C22×D4
commutator, Frattini, cosocleC22×C4C24×C7
prime radicalC2×C7×#121C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C7 ◁ C4×C7×C22⋊C4 ◁ G

Complements

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

NH ≅ G/Ntype
2. C7×#2360C2semidirect
3. C7×#2055C2semidirect
4. C7×#2035C2semidirect
5. C7×#2024C2semidirect
7. C7×#1988C2semidirect
8. C7×#1934C2semidirect
9. C7×#1926C2semidirect
10. C7×#1923C2semidirect
11. C7×#1920C2semidirect
12. C7×#1880C2semidirect
14. C7×#1824C2semidirect
15. C4×C7×#103C2semidirect
59. #26724C7direct (N × H)
129. #2360C2×C7semidirect
130. #2055C2×C7semidirect
131. #2035C2×C7semidirect
132. #2024C2×C7semidirect
134. #1988C2×C7semidirect
135. #1934C2×C7semidirect
136. #1926C2×C7semidirect
137. #1923C2×C7semidirect
138. #1920C2×C7semidirect
139. #1880C2×C7semidirect
141. #1824C2×C7semidirect
142. C4×#103C2×C7semidirect
223. C7×C22⋊C4SD16semidirect
535. C22⋊C4C7×SD16semidirect
628. C7#26724direct (N × H)

Maximal subgroups

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

subgroupindex
C7×#24912
C7×#23602
C7×#20552
C7×#20352
C7×#20242
C7×#20002
C7×#19882
C7×#19342
C7×#19262
C7×#19232
C7×#19202
C7×#18802
C7×#18742
C7×#18242
C4×C7×#1032
#267247