Finite Group Databasebeta

← C7×#22774 #13199990

Subgroups — C7×#22774 #13199990

Order 1792.

942 conjugacy classes of subgroups.

The subgroup lattice has 664 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C7×#442C211yesmaximal, characteristic
2C7×#2357C211yesmaximal, characteristic, complemented
3C7×D4×C4⋊C4C211yesmaximal, characteristic, complemented
4C7×#1936C211yesmaximal, characteristic, complemented
5C7×#1934C211yesmaximal, characteristic, complemented
6C7×#1920C211yesmaximal, characteristic, complemented
7C7×#1919C211yesmaximal, characteristic, complemented
8C7×#1879C211yesmaximal, characteristic
9C7×#1879C211yesmaximal, characteristic
10C7×#1836C211yesmaximal, characteristic, complemented
11C7×#1804C211yesmaximal, characteristic, complemented
12C7×#1802C211yesmaximal, characteristic, complemented
13C7×#1771C211yesmaximal, characteristic, complemented
14C7×#1762C211yesmaximal, characteristic, complemented
15C4×C7×#102C211yesmaximal, characteristic, complemented
16C22×C7×D8C2211yescharacteristic
17C2×C4×C7×D4C2211yescharacteristic
18C2×C4×C7×D4C2211yescharacteristic
19C2×C4×C7×D4C2211yescharacteristic
20C2×C4×C7×D4C2211yescharacteristic
21C22×C7×C4⋊C4—21no—
22C7×#442C418yescomplemented
23C2×C7×#106C2211yescharacteristic
24C2×C7×C4⋊C8C2211yescharacteristic
25C2×C7×#102C2211yescharacteristic
26C2×C7×#102C2211yescharacteristic
27C2×C7×#102C2211yescharacteristic
28C2×C7×#102C2211yescharacteristic
29C2×C7×#102C2211yescharacteristic
30C2×C7×#102C2211yescharacteristic
31C2×C7×#97C2211yescharacteristic
32C2×C7×#97C2211yescharacteristic
33C2×C4×C7×C8C2211yescharacteristic
34C7×#390C2211yescharacteristic
35C7×#390C2211yescharacteristic
36C7×#389C2211yescharacteristic
37C7×#389C2211yescharacteristic
38C7×#388—21no—
39C7×#388—21no—
40C7×#385—21no—
41C7×#385—21no—
42C7×#384C2211yescharacteristic
43C7×#382C2211yescharacteristic
44C7×#381—21no—
45C7×#380—21no—
46C4×C7×C4⋊C4C2211yescharacteristic
47C4×C7×C4⋊C4C2211yescharacteristic
48C4×C7×C4⋊C4C2211yescharacteristic
49C4×C7×C22⋊C4—21no—
50C7×#340C2211yescharacteristic
51C7×#340C2211yescharacteristic
52C7×#340C2211yescharacteristic
53C7×#340C2211yescharacteristic
54C7×#340C2211yescharacteristic
55C7×#340C2211yescharacteristic
56C7×#340C2211yescharacteristic
57C7×#340C2211yescharacteristic
58C7×#336C2211yescharacteristic
59C7×#336C2211yescharacteristic
60#22774C711yesmaximal, characteristic, direct product factor, Sylow
61C22×C7×D4C2311yescharacteristic
62C22×C7×D4C2311yescharacteristic
63C23×C4×C7—21no—
64C23×C4×C7—21no—
65C23×C4×C7—21no—
66C23×C4×C7—21no—
67C2×C7×D8—22no—
68C2×C7×D8—22no—
69C2×C7×D8C2×C414yes—
70C22×C7×C8C2311yescharacteristic
71C22×C7×C8C2311yescharacteristic
72C22×C7×C8C2311yescharacteristic
73C22×C7×C8C2311yescharacteristic
74C4×C7×D4—22no—
75C4×C7×D4—22no—
76C4×C7×D4—22no—
77C4×C7×D4—22no—
78C4×C7×D4—41no—
79C4×C7×D4—41no—
80C4×C7×D4C2×C414yes—
81C4×C7×D4C2×C414yescomplemented
82C2×C7×C4⋊C4—21no—
83C2×C7×C4⋊C4—21no—
84C2×C7×C4⋊C4—21no—
85C2×C7×C4⋊C4—21no—
86C2×C7×C4⋊C4—44no—
87C2×C7×C4⋊C4D411yescharacteristic
88C2×C7×C4⋊C4D411yescharacteristic
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⋊C4—21no—
103C2×C42×C7—21no—
104C2×C42×C7—21no—
105C2×C42×C7C2311yescharacteristic
106C2×C42×C7C2311yescharacteristic
107C2×C42×C7C2311yescharacteristic
108C7×#106C2×C414yescomplemented
109C7×C4⋊C8—22no—
110C7×#102—22no—
111C7×#102—22no—
112C7×#102—41no—
113C7×#102—41no—
114C7×#102C2×C414yes—
115C7×#102C2×C414yescomplemented
116C7×#97—41no—
117C7×#97C2×C414yescomplemented
118C4×C7×C8—41no—
119C7×#95—21no—
120C7×#95—21no—
121C7×#95—21no—
122C7×#95—21no—
123C7×#95—21no—
124C7×#95—21no—
125C7×#95D411yescharacteristic
126C7×#95D411yescharacteristic
127C2×#442C2×C711yescharacteristic
128#2357C2×C711yescharacteristic, complemented
129D4×C4⋊C4C2×C711yescharacteristic, complemented
130#1936C2×C711yescharacteristic, complemented
131#1934C2×C711yescharacteristic, complemented
132#1920C2×C711yescharacteristic, complemented
133#1919C2×C711yescharacteristic, complemented
134#1879C2×C711yescharacteristic
135#1879C2×C711yescharacteristic
136#1836C2×C711yescharacteristic, complemented
137#1804C2×C711yescharacteristic, complemented
138#1802C2×C711yescharacteristic, complemented
139#1771C2×C711yescharacteristic, complemented
140#1762C2×C711yescharacteristic, complemented
141C4×#102C2×C711yescharacteristic, complemented
142C24×C7—21no—
143C24×C7—21no—
144C2×C7×D4—21no—
145C2×C7×D4—21no—
146C2×C7×D4—21no—
147C2×C7×D4—21no—
148C2×C7×D4—21no—
149C2×C7×D4—21no—
150C2×C7×D4—21no—
151C2×C7×D4—21no—
152C2×C7×D4C22×C412yes—
153C2×C7×D4C22×C412yes—
154C2×C7×D4#4112yes—
155C2×C7×D4#4112yes—
156C22×C4×C7—21no—
157C22×C4×C7—21no—
158C22×C4×C7—24no—
159C22×C4×C7—24no—
160C22×C4×C7—21no—
161C22×C4×C7—21no—
162C22×C4×C7—21no—
163C22×C4×C7—21no—
164C22×C4×C7—42no—
165C22×C4×C7—42no—
166C22×C4×C7—42no—
167C22×C4×C7—42no—
168C22×C4×C7—42no—
169C22×C4×C7—42no—
170C22×C4×C7—81no—
171C22×C4×C7—81no—
172C22×C4×C7—81no—
173C22×C4×C7—81no—
174C22×C4×C7C2×D411yescharacteristic
175C22×C4×C7C2×D411yescharacteristic
176C22×C4×C7C2×D411yescharacteristic
177C22×C4×C7C2×D411yescharacteristic
178C22×C4×C7C2×D411yescharacteristic
179C22×C4×C7C2×D411yescharacteristic
180C22×C4×C7C2411yescharacteristic
181C7×D8—28no—
182C2×C7×C8—21no—
183C2×C7×C8—21no—
184C2×C7×C8—21no—
185C2×C7×C8—21no—
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×C8C22×C412yes—
193C2×C7×C8C22×C412yes—
194C7×C4⋊C4—22no—
195C7×C4⋊C4—21no—
196C7×C4⋊C4—21no—
197C7×C4⋊C4—21no—
198C7×C4⋊C4—21no—
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—41no—
206C7×C4⋊C4—42no—
207C7×C4⋊C4—42no—
208C7×C4⋊C4—42no—
209C7×C4⋊C4—81no—
210C7×C4⋊C4C22×C412yes—
211C7×C4⋊C4C22×C412yes—
212C7×C22⋊C4—24no—
213C7×C22⋊C4—24no—
214C7×C22⋊C4—42no—
215C7×C22⋊C4—42no—
216C7×C22⋊C4—42no—
217C7×C22⋊C4—42no—
218C7×C22⋊C4—81no—
219C7×C22⋊C4—81no—
220C42×C7—21no—
221C42×C7—21no—
222C42×C7—21no—
223C42×C7—21no—
224C42×C7—81no—
225C42×C7—81no—
226C42×C7C22×C412yes—
227C42×C7#4112yes—
228C22×D8C22×C711yescharacteristic
229C2×C4×D4C22×C711yescharacteristic
230C2×C4×D4C22×C711yescharacteristic
231C2×C4×D4C22×C711yescharacteristic
232C2×C4×D4C22×C711yescharacteristic
233C22×C4⋊C4—21no—
234#442C4×C718yescomplemented
235C2×#106C22×C711yescharacteristic
236C2×C4⋊C8C22×C711yescharacteristic
237C2×#102C22×C711yescharacteristic
238C2×#102C22×C711yescharacteristic
239C2×#102C22×C711yescharacteristic
240C2×#102C22×C711yescharacteristic
241C2×#102C22×C711yescharacteristic
242C2×#102C22×C711yescharacteristic
243C2×#97C22×C711yescharacteristic
244C2×#97C22×C711yescharacteristic
245C2×C4×C8C22×C711yescharacteristic
246#390C22×C711yescharacteristic
247#390C22×C711yescharacteristic
248#389C22×C711yescharacteristic
249#389C22×C711yescharacteristic
250#388—21no—
251#388—21no—
252#385—21no—
253#385—21no—
254#384C22×C711yescharacteristic
255#382C22×C711yescharacteristic
256#381—21no—
257#380—21no—
258C4×C4⋊C4C22×C711yescharacteristic
259C4×C4⋊C4C22×C711yescharacteristic
260C4×C4⋊C4C22×C711yescharacteristic
261C4×C22⋊C4—21no—
262#340C22×C711yescharacteristic
263#340C22×C711yescharacteristic
264#340C22×C711yescharacteristic
265#340C22×C711yescharacteristic
266#340C22×C711yescharacteristic
267#340C22×C711yescharacteristic
268#340C22×C711yescharacteristic
269#340C22×C711yescharacteristic
270#336C22×C711yescharacteristic
271#336C22×C711yescharacteristic
272C23×C7—22no—
273C23×C7—22no—
274C23×C7—22no—
275C23×C7—22no—
276C23×C7—41no—
277C23×C7—41no—
278C23×C7—41no—
279C23×C7—41no—
280C23×C7—41no—
281C23×C7—41no—
282C23×C7—41no—
283C23×C7—41no—
284C23×C7—41no—
285C23×C7—41no—
286C23×C7C22×D411yescharacteristic
287C7×D4—22no—
288C7×D4—22no—
289C7×D4—22no—
290C7×D4—22no—
291C7×D4—22no—
292C7×D4—41no—
293C7×D4—41no—
294C7×D4#11714yes—
295C2×C4×C7—21no—
296C2×C4×C7—21no—
297C2×C4×C7—21no—
298C2×C4×C7—21no—
299C2×C4×C7—21no—
300C2×C4×C7—21no—
301C2×C4×C7—22no—
302C2×C4×C7—22no—
303C2×C4×C7—21no—
304C2×C4×C7—21no—
305C2×C4×C7—21no—
306C2×C4×C7—21no—
307C2×C4×C7—21no—
308C2×C4×C7—21no—
309C2×C4×C7—21no—
310C2×C4×C7—21no—
311C2×C4×C7—21no—
312C2×C4×C7—48no—
313C2×C4×C7—41no—
314C2×C4×C7—41no—
315C2×C4×C7—41no—
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—84no—
330C2×C4×C7—84no—
331C2×C4×C7—84no—
332C2×C4×C7C4×D412yes—
333C2×C4×C7C4×D412yes—
334C2×C4×C7AGL(1,ℤ/8)12yes—
335C2×C4×C7C23×C411yescharacteristic
336C2×C4×C7C2×#4111yescharacteristic
337C2×C4×C7C2×#4111yescharacteristic
338C2×C4×C7C2×#4111yescharacteristic
339C2×C4×C7H(5,𝔽2)11yescharacteristic
340C2×C4×C72−1+411yescharacteristic
341C7×C8—22no—
342C7×C8—22no—
343C7×C8—41no—
344C7×C8—41no—
345C22×D4C23×C711yescharacteristic
346C22×D4C23×C711yescharacteristic
347C23×C4—21no—
348C23×C4—21no—
349C23×C4—21no—
350C23×C4—21no—
351C2×D8—22no—
352C2×D8—22no—
353C2×D8C2×C4×C714yes—
354C22×C8C23×C711yescharacteristic
355C22×C8C23×C711yescharacteristic
356C22×C8C23×C711yescharacteristic
357C22×C8C23×C711yescharacteristic
358C4×D4—22no—
359C4×D4—22no—
360C4×D4—22no—
361C4×D4—22no—
362C4×D4—41no—
363C4×D4—41no—
364C4×D4C2×C4×C714yes—
365C4×D4C2×C4×C714yescomplemented
366C2×C4⋊C4—21no—
367C2×C4⋊C4—21no—
368C2×C4⋊C4—21no—
369C2×C4⋊C4—21no—
370C2×C4⋊C4—44no—
371C2×C4⋊C4C7×D411yescharacteristic
372C2×C4⋊C4C7×D411yescharacteristic
373C2×C4⋊C4C23×C711yescharacteristic
374C2×C4⋊C4C23×C711yescharacteristic
375C2×C4⋊C4C23×C711yescharacteristic
376C2×C4⋊C4C23×C711yescharacteristic
377C2×C4⋊C4C23×C711yescharacteristic
378C2×C4⋊C4C23×C711yescharacteristic
379C2×C22⋊C4—21no—
380C2×C22⋊C4—21no—
381C2×C22⋊C4—21no—
382C2×C22⋊C4—21no—
383C2×C22⋊C4—21no—
384C2×C22⋊C4—21no—
385C2×C22⋊C4—21no—
386C2×C22⋊C4—21no—
387C2×C42—21no—
388C2×C42—21no—
389C2×C42C23×C711yescharacteristic
390C2×C42C23×C711yescharacteristic
391C2×C42C23×C711yescharacteristic
392#106C2×C4×C714yescomplemented
393C4⋊C8—22no—
394#102—22no—
395#102—22no—
396#102—41no—
397#102—41no—
398#102C2×C4×C714yes—
399#102C2×C4×C714yescomplemented
400#97—41no—
401#97C2×C4×C714yescomplemented
402C4×C8—41no—
403#95—21no—
404#95—21no—
405#95—21no—
406#95—21no—
407#95—21no—
408#95—21no—
409#95C7×D411yescharacteristic
410#95C7×D411yescharacteristic
411C22×C7—24no—
412C22×C7—42no—
413C22×C7—42no—
414C22×C7—42no—
415C22×C7—42no—
416C22×C7—42no—
417C22×C7—42no—
418C22×C7—42no—
419C22×C7—42no—
420C22×C7—42no—
421C22×C7—81no—
422C22×C7—81no—
423C22×C7—81no—
424C22×C7—81no—
425C22×C7C2×C4×D411yescharacteristic
426C22×C7#54611yescharacteristic
427C22×C7#54811yescharacteristic
428C22×C7C2×AGL(1,ℤ/8)11yescharacteristic
429C22×C7#57511yescharacteristic
430C22×C7#57611yescharacteristic
431C22×C7#57711yescharacteristic
432C4×C7—22no—
433C4×C7—22no—
434C4×C7—22no—
435C4×C7—42no—
436C4×C7—42no—
437C4×C7—41no—
438C4×C7—41no—
439C4×C7—41no—
440C4×C7—81no—
441C4×C7—81no—
442C4×C7—81no—
443C4×C7—81no—
444C4×C7C2×#11711yescharacteristic
445C4×C7#52011yescharacteristic
446C4×C7#55211yescharacteristic
447C4×C7#55311yescharacteristic
448C24—21no—
449C24—21no—
450C2×D4—21no—
451C2×D4—21no—
452C2×D4—21no—
453C2×D4—21no—
454C2×D4—21no—
455C2×D4—21no—
456C2×D4—21no—
457C2×D4—21no—
458C2×D4C22×C4×C712yes—
459C2×D4C22×C4×C712yes—
460C2×D4C7×#4112yes—
461C2×D4C7×#4112yes—
462C22×C4—21no—
463C22×C4—21no—
464C22×C4—24no—
465C22×C4—24no—
466C22×C4—21no—
467C22×C4—21no—
468C22×C4—21no—
469C22×C4—21no—
470C22×C4—42no—
471C22×C4—42no—
472C22×C4—42no—
473C22×C4—42no—
474C22×C4—42no—
475C22×C4—42no—
476C22×C4—81no—
477C22×C4—81no—
478C22×C4—81no—
479C22×C4—81no—
480C22×C4C2×C7×D411yescharacteristic
481C22×C4C2×C7×D411yescharacteristic
482C22×C4C2×C7×D411yescharacteristic
483C22×C4C2×C7×D411yescharacteristic
484C22×C4C2×C7×D411yescharacteristic
485C22×C4C2×C7×D411yescharacteristic
486C22×C4C24×C711yescharacteristic
487D8—28no—
488C2×C8—21no—
489C2×C8—21no—
490C2×C8—21no—
491C2×C8—21no—
492C2×C8—21no—
493C2×C8—21no—
494C2×C8—21no—
495C2×C8—21no—
496C2×C8—21no—
497C2×C8—21no—
498C2×C8C22×C4×C712yes—
499C2×C8C22×C4×C712yes—
500C4⋊C4—22no—
501C4⋊C4—21no—
502C4⋊C4—21no—
503C4⋊C4—21no—
504C4⋊C4—21no—
505C4⋊C4—21no—
506C4⋊C4—21no—
507C4⋊C4—21no—
508C4⋊C4—21no—
509C4⋊C4—21no—
510C4⋊C4—21no—
511C4⋊C4—41no—
512C4⋊C4—42no—
513C4⋊C4—42no—
514C4⋊C4—42no—
515C4⋊C4—81no—
516C4⋊C4C22×C4×C712yes—
517C4⋊C4C22×C4×C712yes—
518C22⋊C4—24no—
519C22⋊C4—24no—
520C22⋊C4—42no—
521C22⋊C4—42no—
522C22⋊C4—42no—
523C22⋊C4—42no—
524C22⋊C4—81no—
525C22⋊C4—81no—
526C42—21no—
527C42—21no—
528C42—21no—
529C42—21no—
530C42—81no—
531C42—81no—
532C42C22×C4×C712yes—
533C42C7×#4112yes—
534C2×C7—44no—
535C2×C7—82no—
536C2×C7#235211yescharacteristic
537C2×C7C4×AGL(1,ℤ/8)11yescharacteristic
538C2×C7#294611yescharacteristic
539C2×C7#330711yescharacteristic
540C2×C7#331811yescharacteristic
541C2×C7#337011yescharacteristic
542C2×C7#337311yescharacteristic
543C23—22no—
544C23—22no—
545C23—22no—
546C23—22no—
547C23—41no—
548C23—41no—
549C23—41no—
550C23—41no—
551C23—41no—
552C23—41no—
553C23—41no—
554C23—41no—
555C23—41no—
556C23—41no—
557C23C22×C7×D411yescharacteristic
558D4—22no—
559D4—22no—
560D4—22no—
561D4—22no—
562D4—22no—
563D4—41no—
564D4—41no—
565D4C7×#11714yes—
566C2×C4—21no—
567C2×C4—21no—
568C2×C4—21no—
569C2×C4—21no—
570C2×C4—21no—
571C2×C4—21no—
572C2×C4—22no—
573C2×C4—22no—
574C2×C4—21no—
575C2×C4—21no—
576C2×C4—21no—
577C2×C4—21no—
578C2×C4—21no—
579C2×C4—21no—
580C2×C4—21no—
581C2×C4—21no—
582C2×C4—21no—
583C2×C4—48no—
584C2×C4—41no—
585C2×C4—41no—
586C2×C4—41no—
587C2×C4—41no—
588C2×C4—41no—
589C2×C4—41no—
590C2×C4—41no—
591C2×C4—41no—
592C2×C4—41no—
593C2×C4—41no—
594C2×C4—41no—
595C2×C4—41no—
596C2×C4—41no—
597C2×C4—41no—
598C2×C4—41no—
599C2×C4—41no—
600C2×C4—84no—
601C2×C4—84no—
602C2×C4—84no—
603C2×C4C4×C7×D412yes—
604C2×C4C4×C7×D412yes—
605C2×C4C7×AGL(1,ℤ/8)12yes—
606C2×C4C23×C4×C711yescharacteristic
607C2×C4C2×C7×#4111yescharacteristic
608C2×C4C2×C7×#4111yescharacteristic
609C2×C4C2×C7×#4111yescharacteristic
610C2×C4C7×H(5,𝔽2)11yescharacteristic
611C2×C4C7×2−1+411yescharacteristic
612C8—22no—
613C8—22no—
614C8—41no—
615C8—41no—
616C7#2277411yescharacteristic, direct product factor, Sylow
617C22—24no—
618C22—42no—
619C22—42no—
620C22—42no—
621C22—42no—
622C22—42no—
623C22—42no—
624C22—42no—
625C22—42no—
626C22—42no—
627C22—81no—
628C22—81no—
629C22—81no—
630C22—81no—
631C22C2×C4×C7×D411yescharacteristic
632C22C7×#54611yescharacteristic
633C22C7×#54811yescharacteristic
634C22C2×C7×AGL(1,ℤ/8)11yescharacteristic
635C22C7×#57511yescharacteristic
636C22C7×#57611yescharacteristic
637C22C7×#57711yescharacteristic
638C4—22no—
639C4—22no—
640C4—22no—
641C4—42no—
642C4—42no—
643C4—41no—
644C4—41no—
645C4—41no—
646C4—81no—
647C4—81no—
648C4—81no—
649C4—81no—
650C4C2×C7×#11711yescharacteristic
651C4C7×#52011yescharacteristic
652C4C7×#55211yescharacteristic
653C4C7×#55311yescharacteristic
654C2—44no—
655C2—82no—
656C2C7×#235211yescharacteristic
657C2C4×C7×AGL(1,ℤ/8)11yescharacteristic
658C2C7×#294611yescharacteristic
659C2C7×#330711yescharacteristic
660C2C7×#331811yescharacteristic
661C2C7×#337011yescharacteristic
662C2C7×#337311yescharacteristic
subgroupG/H
center, socleC23×C7C22×D4
commutatorC2×C4C23×C4×C7
Frattini, cosocleC22×C4C24×C7
prime radicalC22×C7×D8C22
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C7 ◁ C4×C7×C4⋊C4 ◁ G

Complements

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

NH ≅ G/Ntype
2. C7×#2357C2semidirect
3. C7×D4×C4⋊C4C2semidirect
4. C7×#1936C2semidirect
5. C7×#1934C2semidirect
6. C7×#1920C2semidirect
7. C7×#1919C2semidirect
10. C7×#1836C2semidirect
11. C7×#1804C2semidirect
12. C7×#1802C2semidirect
13. C7×#1771C2semidirect
14. C7×#1762C2semidirect
15. C4×C7×#102C2semidirect
22. C7×#442C4semidirect
60. #22774C7direct (N × H)
81. C4×C7×D4C2×C4semidirect
108. C7×#106C2×C4semidirect
115. C7×#102C2×C4semidirect
117. C7×#97C2×C4semidirect
128. #2357C2×C7semidirect
129. D4×C4⋊C4C2×C7semidirect
130. #1936C2×C7semidirect
131. #1934C2×C7semidirect
132. #1920C2×C7semidirect
133. #1919C2×C7semidirect
136. #1836C2×C7semidirect
137. #1804C2×C7semidirect
138. #1802C2×C7semidirect
139. #1771C2×C7semidirect
140. #1762C2×C7semidirect
141. C4×#102C2×C7semidirect
234. #442C4×C7semidirect
365. C4×D4C2×C4×C7semidirect
392. #106C2×C4×C7semidirect
399. #102C2×C4×C7semidirect
401. #97C2×C4×C7semidirect
616. C7#22774direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C7×#4422
C7×#23572
C7×D4×C4⋊C42
C7×#19362
C7×#19342
C7×#19202
C7×#19192
C7×#18792
C7×#18362
C7×#18042
C7×#18022
C7×#17712
C7×#17622
C4×C7×#1022
#227747