Finite Group Databasebeta

← C7×#22862 #13200078

Subgroups — C7×#22862 #13200078

Order 1792.

1134 conjugacy classes of subgroups.

The subgroup lattice has 742 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C7×#452C211yesmaximal, characteristic
2C2×C7×#440C211yesmaximal, characteristic, complemented
3C2×C7×#417C211yesmaximal, characteristic
4C7×#2360C211yesmaximal, characteristic, complemented
5C7×#2339C211yesmaximal, characteristic
6C7×#1969C211yesmaximal, characteristic, complemented
7C7×#1935C211yesmaximal, characteristic, complemented
8C7×#1928C211yesmaximal, characteristic, complemented
9C7×#1894C211yesmaximal, characteristic, complemented
10C7×#1878C211yesmaximal, characteristic, complemented
11C7×#1877C211yesmaximal, characteristic, complemented
12C7×#1862C211yesmaximal, characteristic, complemented
13C7×#1852C211yesmaximal, characteristic, complemented
14C4×C7×#102C211yesmaximal, characteristic, complemented
15C7×#1753C211yesmaximal, characteristic, complemented
16C22×C7×#41C2211yescharacteristic
17C22×C7×Q16C2211yescharacteristic
18C22×C7×SD16C2211yescharacteristic
19C22×C7×M16C2211yescharacteristic
20C2×C7×C22⋊Q8C2211yescharacteristic
21C2×C4×C7×Q8C2211yescharacteristic
22C2×C4×C7×D4C2211yescharacteristic
23C2×C4×C7×D4C2211yescharacteristic
24C22×C7×C4⋊C4C2211yescharacteristic
25C7×#452C418yescomplemented
26C7×#440—24no—
27C2×C7×#107C2211yescharacteristic
28C2×C7×#107C2211yescharacteristic
29C7×#417—24no—
30C2×C7×#103C2211yescharacteristic
31C2×C7×#103C2211yescharacteristic
32C2×C7×#103C2211yescharacteristic
33C2×C7×#103C2211yescharacteristic
34C2×C7×#103C2211yescharacteristic
35C2×C7×#102C2211yescharacteristic
36C2×C7×#102C2211yescharacteristic
37C2×C7×#102C2211yescharacteristic
38C2×C7×C22⋊C8C2211yescharacteristic
39C2×C7×#97C2211yescharacteristic
40C2×C4×C7×C8C2211yescharacteristic
41C7×#391C2211yescharacteristic
42C7×#391C2211yescharacteristic
43C7×#391C2211yescharacteristic
44C7×#389—21no—
45C7×#389C2211yescharacteristic
46C7×#387—21no—
47C7×#386—21no—
48C7×#386—21no—
49C7×#385—21no—
50C7×#381—21no—
51C7×#380C2211yescharacteristic
52C4×C7×C4⋊C4C2211yescharacteristic
53C4×C7×C22⋊C4—21no—
54C4×C7×C22⋊C4C2211yescharacteristic
55C2×C7×#95—21no—
56C7×#340C2211yescharacteristic
57C7×#340C2211yescharacteristic
58C7×#340C2211yescharacteristic
59C7×#340C2211yescharacteristic
60C7×#336C2211yescharacteristic
61C7×#336C2211yescharacteristic
62#22862C711yesmaximal, characteristic, direct product factor, Sylow
63C2×C7×#41—22no—
64C2×C7×#41—22no—
65C2×C7×#41—22no—
66C2×C7×#41—41no—
67C2×C7×#41—41no—
68C2×C7×#41C2×C414yes—
69C22×C7×Q8C2311yescharacteristic
70C22×C7×Q8C2311yescharacteristic
71C22×C7×D4—21no—
72C22×C7×D4C2311yescharacteristic
73C23×C4×C7—21no—
74C23×C4×C7—21no—
75C23×C4×C7—21no—
76C23×C4×C7—21no—
77C23×C4×C7C2311yescharacteristic
78C2×C7×Q16—41no—
79C2×C7×Q16—41no—
80C2×C7×Q16C2×C414yescomplemented
81C2×C7×SD16—22no—
82C2×C7×SD16—22no—
83C2×C7×SD16C2×C414yescomplemented
84C2×C7×M16—22no—
85C2×C7×M16—22no—
86C2×C7×M16—41no—
87C22×C7×C8C2311yescharacteristic
88C22×C7×C8C2311yescharacteristic
89C22×C7×C8C2311yescharacteristic
90C22×C7×C8C2311yescharacteristic
91C7×C22⋊Q8—22no—
92C7×C22⋊Q8C2×C414yescomplemented
93C4×C7×Q8—22no—
94C4×C7×Q8—41no—
95C4×C7×D4—22no—
96C4×C7×D4—22no—
97C4×C7×D4—41no—
98C4×C7×D4—41no—
99C2×C7×C4⋊C4—21no—
100C2×C7×C4⋊C4—22no—
101C2×C7×C4⋊C4—21no—
102C2×C7×C4⋊C4—21no—
103C2×C7×C4⋊C4—21no—
104C2×C7×C4⋊C4—41no—
105C2×C7×C4⋊C4C2311yescharacteristic
106C2×C7×C4⋊C4C2311yescharacteristic
107C2×C7×C4⋊C4C2311yescharacteristic
108C2×C7×C4⋊C4C2311yescharacteristic
109C2×C7×C4⋊C4C2311yescharacteristic
110C2×C7×C22⋊C4—21no—
111C2×C7×C22⋊C4—21no—
112C2×C7×C22⋊C4—21no—
113C2×C7×C22⋊C4—21no—
114C2×C7×C22⋊C4D411yescharacteristic
115C2×C7×C22⋊C4D411yescharacteristic
116C2×C42×C7—21no—
117C2×C42×C7—21no—
118C2×C42×C7C2311yescharacteristic
119C2×C42×C7C2311yescharacteristic
120C7×#107—22no—
121C7×#107—41no—
122C7×#103—22no—
123C7×#103—22no—
124C7×#103—22no—
125C7×#103—41no—
126C7×#103C2×C414yescomplemented
127C7×#102—22no—
128C7×#102C2×C414yescomplemented
129C7×#102D414yes—
130C7×C22⋊C8C2×C414yescomplemented
131C7×#97—22no—
132C4×C7×C8—41no—
133C7×#95—21no—
134C7×#95—21no—
135C7×#95—21no—
136C7×#95—21no—
137C7×#95—21no—
138C7×#95—21no—
139C7×#95—21no—
140C7×#95—21no—
141C7×#95—21no—
142C7×#95D411yescharacteristic
143C7×#95D411yescharacteristic
144C2×#452C2×C711yescharacteristic
145C2×#440C2×C711yescharacteristic, complemented
146C2×#417C2×C711yescharacteristic
147#2360C2×C711yescharacteristic, complemented
148#2339C2×C711yescharacteristic
149#1969C2×C711yescharacteristic, complemented
150#1935C2×C711yescharacteristic, complemented
151#1928C2×C711yescharacteristic, complemented
152#1894C2×C711yescharacteristic, complemented
153#1878C2×C711yescharacteristic, complemented
154#1877C2×C711yescharacteristic, complemented
155#1862C2×C711yescharacteristic, complemented
156#1852C2×C711yescharacteristic, complemented
157C4×#102C2×C711yescharacteristic, complemented
158#1753C2×C711yescharacteristic, complemented
159C24×C7—21no—
160C24×C7C2×D411yescharacteristic
161C7×#41—28no—
162C7×#41—44no—
163C7×#41—44no—
164C7×#41—44no—
165C2×C7×Q8—21no—
166C2×C7×Q8—21no—
167C2×C7×Q8—21no—
168C2×C7×Q8—21no—
169C2×C7×Q8—21no—
170C2×C7×Q8—21no—
171C2×C7×Q8—21no—
172C2×C7×Q8—21no—
173C2×C7×Q8—21no—
174C2×C7×Q8—21no—
175C2×C7×Q8C22×C412yes—
176C2×C7×Q8C22×C412yes—
177C2×C7×D4—24no—
178C2×C7×D4—21no—
179C2×C7×D4—21no—
180C2×C7×D4—21no—
181C2×C7×D4—42no—
182C2×C7×D4—42no—
183C2×C7×D4C22×C412yes—
184C2×C7×D4C2×D412yes—
185C2×C7×D4#4112yes—
186C22×C4×C7—21no—
187C22×C4×C7—21no—
188C22×C4×C7—21no—
189C22×C4×C7—21no—
190C22×C4×C7—21no—
191C22×C4×C7—21no—
192C22×C4×C7—21no—
193C22×C4×C7—21no—
194C22×C4×C7—24no—
195C22×C4×C7—21no—
196C22×C4×C7—21no—
197C22×C4×C7—21no—
198C22×C4×C7—42no—
199C22×C4×C7—42no—
200C22×C4×C7—42no—
201C22×C4×C7—42no—
202C22×C4×C7—42no—
203C22×C4×C7—42no—
204C22×C4×C7—42no—
205C22×C4×C7—42no—
206C22×C4×C7—81no—
207C22×C4×C7—81no—
208C22×C4×C7—81no—
209C22×C4×C7C22×C412yes—
210C22×C4×C7C2×D411yescharacteristic
211C22×C4×C7C2×D411yescharacteristic
212C22×C4×C7C2×D411yescharacteristic
213C22×C4×C7C2×D411yescharacteristic
214C22×C4×C7C2×D411yescharacteristic
215C22×C4×C7#4112yes—
216C22×C4×C7C2411yescharacteristic
217C7×Q16—44no—
218C7×SD16—28no—
219C7×M16—44no—
220C2×C7×C8—21no—
221C2×C7×C8—21no—
222C2×C7×C8—21no—
223C2×C7×C8—21no—
224C2×C7×C8—21no—
225C2×C7×C8—21no—
226C2×C7×C8—21no—
227C2×C7×C8—21no—
228C2×C7×C8—21no—
229C2×C7×C8C22×C412yes—
230C2×C7×C8C22×C412yes—
231C2×C7×C8C2×D412yes—
232C7×C4⋊C4—24no—
233C7×C4⋊C4—21no—
234C7×C4⋊C4—21no—
235C7×C4⋊C4—21no—
236C7×C4⋊C4—21no—
237C7×C4⋊C4—21no—
238C7×C4⋊C4—21no—
239C7×C4⋊C4—21no—
240C7×C4⋊C4—21no—
241C7×C4⋊C4—42no—
242C7×C4⋊C4—42no—
243C7×C4⋊C4—81no—
244C7×C4⋊C4C22×C412yes—
245C7×C4⋊C4C2×D412yes—
246C7×C22⋊C4—24no—
247C7×C22⋊C4—22no—
248C7×C22⋊C4—41no—
249C7×C22⋊C4—42no—
250C7×C22⋊C4—42no—
251C7×C22⋊C4—81no—
252C42×C7—21no—
253C42×C7—21no—
254C42×C7—21no—
255C42×C7—21no—
256C42×C7—42no—
257C42×C7—81no—
258C22×#41C22×C711yescharacteristic
259C22×Q16C22×C711yescharacteristic
260C22×SD16C22×C711yescharacteristic
261C22×M16C22×C711yescharacteristic
262C2×C22⋊Q8C22×C711yescharacteristic
263C2×C4×Q8C22×C711yescharacteristic
264C2×C4×D4C22×C711yescharacteristic
265C2×C4×D4C22×C711yescharacteristic
266C22×C4⋊C4C22×C711yescharacteristic
267#452C4×C718yescomplemented
268#440—24no—
269C2×#107C22×C711yescharacteristic
270C2×#107C22×C711yescharacteristic
271#417—24no—
272C2×#103C22×C711yescharacteristic
273C2×#103C22×C711yescharacteristic
274C2×#103C22×C711yescharacteristic
275C2×#103C22×C711yescharacteristic
276C2×#103C22×C711yescharacteristic
277C2×#102C22×C711yescharacteristic
278C2×#102C22×C711yescharacteristic
279C2×#102C22×C711yescharacteristic
280C2×C22⋊C8C22×C711yescharacteristic
281C2×#97C22×C711yescharacteristic
282C2×C4×C8C22×C711yescharacteristic
283#391C22×C711yescharacteristic
284#391C22×C711yescharacteristic
285#391C22×C711yescharacteristic
286#389—21no—
287#389C22×C711yescharacteristic
288#387—21no—
289#386—21no—
290#386—21no—
291#385—21no—
292#381—21no—
293#380C22×C711yescharacteristic
294C4×C4⋊C4C22×C711yescharacteristic
295C4×C22⋊C4—21no—
296C4×C22⋊C4C22×C711yescharacteristic
297C2×#95—21no—
298#340C22×C711yescharacteristic
299#340C22×C711yescharacteristic
300#340C22×C711yescharacteristic
301#340C22×C711yescharacteristic
302#336C22×C711yescharacteristic
303#336C22×C711yescharacteristic
304C23×C7—22no—
305C23×C7—22no—
306C23×C7—21no—
307C23×C7—22no—
308C23×C7—21no—
309C23×C7—21no—
310C23×C7—21no—
311C23×C7—21no—
312C23×C7—21no—
313C23×C7—41no—
314C23×C7—41no—
315C23×C7—41no—
316C23×C7—41no—
317C23×C7C4×D412yes—
318C23×C7C22×D411yescharacteristic
319C7×Q8—22no—
320C7×Q8—22no—
321C7×Q8—22no—
322C7×Q8—22no—
323C7×Q8—41no—
324C7×Q8—41no—
325C7×Q8—41no—
326C7×Q8—41no—
327C7×D4—22no—
328C7×D4—22no—
329C7×D4—22no—
330C7×D4—48no—
331C7×D4C4×D414yes—
332C2×C4×C7—21no—
333C2×C4×C7—21no—
334C2×C4×C7—21no—
335C2×C4×C7—21no—
336C2×C4×C7—22no—
337C2×C4×C7—22no—
338C2×C4×C7—22no—
339C2×C4×C7—22no—
340C2×C4×C7—22no—
341C2×C4×C7—22no—
342C2×C4×C7—22no—
343C2×C4×C7—21no—
344C2×C4×C7—21no—
345C2×C4×C7—22no—
346C2×C4×C7—21no—
347C2×C4×C7—21no—
348C2×C4×C7—21no—
349C2×C4×C7—21no—
350C2×C4×C7—21no—
351C2×C4×C7—21no—
352C2×C4×C7—21no—
353C2×C4×C7—48no—
354C2×C4×C7—41no—
355C2×C4×C7—41no—
356C2×C4×C7—41no—
357C2×C4×C7—41no—
358C2×C4×C7—41no—
359C2×C4×C7—41no—
360C2×C4×C7—41no—
361C2×C4×C7—41no—
362C2×C4×C7—41no—
363C2×C4×C7—41no—
364C2×C4×C7—41no—
365C2×C4×C7—41no—
366C2×C4×C7—41no—
367C2×C4×C7—41no—
368C2×C4×C7—41no—
369C2×C4×C7—41no—
370C2×C4×C7—41no—
371C2×C4×C7—84no—
372C2×C4×C7—84no—
373C2×C4×C7—84no—
374C2×C4×C7C4×D412yes—
375C2×C4×C7#13712yes—
376C2×C4×C7C23×C411yescharacteristic
377C2×C4×C7C22×D411yescharacteristic
378C2×C4×C7C2×#4111yescharacteristic
379C2×C4×C7C2×#4111yescharacteristic
380C2×C4×C7H(5,𝔽2)11yescharacteristic
381C2×C4×C7H(5,𝔽2)11yescharacteristic
382C7×C8—22no—
383C7×C8—22no—
384C7×C8—22no—
385C7×C8—41no—
386C2×#41—22no—
387C2×#41—22no—
388C2×#41—22no—
389C2×#41—41no—
390C2×#41—41no—
391C2×#41C2×C4×C714yes—
392C22×Q8C23×C711yescharacteristic
393C22×Q8C23×C711yescharacteristic
394C22×D4—21no—
395C22×D4C23×C711yescharacteristic
396C23×C4—21no—
397C23×C4—21no—
398C23×C4—21no—
399C23×C4—21no—
400C23×C4C23×C711yescharacteristic
401C2×Q16—41no—
402C2×Q16—41no—
403C2×Q16C2×C4×C714yescomplemented
404C2×SD16—22no—
405C2×SD16—22no—
406C2×SD16C2×C4×C714yescomplemented
407C2×M16—22no—
408C2×M16—22no—
409C2×M16—41no—
410C22×C8C23×C711yescharacteristic
411C22×C8C23×C711yescharacteristic
412C22×C8C23×C711yescharacteristic
413C22×C8C23×C711yescharacteristic
414C22⋊Q8—22no—
415C22⋊Q8C2×C4×C714yescomplemented
416C4×Q8—22no—
417C4×Q8—41no—
418C4×D4—22no—
419C4×D4—22no—
420C4×D4—41no—
421C4×D4—41no—
422C2×C4⋊C4—21no—
423C2×C4⋊C4—22no—
424C2×C4⋊C4—21no—
425C2×C4⋊C4—21no—
426C2×C4⋊C4—21no—
427C2×C4⋊C4—41no—
428C2×C4⋊C4C23×C711yescharacteristic
429C2×C4⋊C4C23×C711yescharacteristic
430C2×C4⋊C4C23×C711yescharacteristic
431C2×C4⋊C4C23×C711yescharacteristic
432C2×C4⋊C4C23×C711yescharacteristic
433C2×C22⋊C4—21no—
434C2×C22⋊C4—21no—
435C2×C22⋊C4—21no—
436C2×C22⋊C4—21no—
437C2×C22⋊C4C7×D411yescharacteristic
438C2×C22⋊C4C7×D411yescharacteristic
439C2×C42—21no—
440C2×C42—21no—
441C2×C42C23×C711yescharacteristic
442C2×C42C23×C711yescharacteristic
443#107—22no—
444#107—41no—
445#103—22no—
446#103—22no—
447#103—22no—
448#103—41no—
449#103C2×C4×C714yescomplemented
450#102—22no—
451#102C2×C4×C714yescomplemented
452#102C7×D414yes—
453C22⋊C8C2×C4×C714yescomplemented
454#97—22no—
455C4×C8—41no—
456#95—21no—
457#95—21no—
458#95—21no—
459#95—21no—
460#95—21no—
461#95—21no—
462#95—21no—
463#95—21no—
464#95—21no—
465#95C7×D411yescharacteristic
466#95C7×D411yescharacteristic
467C22×C7—22no—
468C22×C7—24no—
469C22×C7—22no—
470C22×C7—22no—
471C22×C7—42no—
472C22×C7—42no—
473C22×C7—41no—
474C22×C7—42no—
475C22×C7—41no—
476C22×C7—42no—
477C22×C7—42no—
478C22×C7—41no—
479C22×C7—41no—
480C22×C7—42no—
481C22×C7C2×C4×D411yescharacteristic
482C22×C7D4211yescharacteristic
483C22×C7#54611yescharacteristic
484C22×C7C2×#13711yescharacteristic
485C22×C7#57511yescharacteristic
486C22×C7#57611yescharacteristic
487C22×C7#57811yescharacteristic
488C4×C7—22no—
489C4×C7—22no—
490C4×C7—42no—
491C4×C7—42no—
492C4×C7—42no—
493C4×C7—41no—
494C4×C7—42no—
495C4×C7—41no—
496C4×C7—41no—
497C4×C7—81no—
498C4×C7—81no—
499C4×C7—81no—
500C4×C7C2×C4×D411yescharacteristic
501C4×C7#51811yescharacteristic
502C4×C7#54611yescharacteristic
503C4×C7#55111yescharacteristic
504C24—21no—
505C24C2×C7×D411yescharacteristic
506#41—28no—
507#41—44no—
508#41—44no—
509#41—44no—
510C2×Q8—21no—
511C2×Q8—21no—
512C2×Q8—21no—
513C2×Q8—21no—
514C2×Q8—21no—
515C2×Q8—21no—
516C2×Q8—21no—
517C2×Q8—21no—
518C2×Q8—21no—
519C2×Q8—21no—
520C2×Q8C22×C4×C712yes—
521C2×Q8C22×C4×C712yes—
522C2×D4—24no—
523C2×D4—21no—
524C2×D4—21no—
525C2×D4—21no—
526C2×D4—42no—
527C2×D4—42no—
528C2×D4C22×C4×C712yes—
529C2×D4C2×C7×D412yes—
530C2×D4C7×#4112yes—
531C22×C4—21no—
532C22×C4—21no—
533C22×C4—21no—
534C22×C4—21no—
535C22×C4—21no—
536C22×C4—21no—
537C22×C4—21no—
538C22×C4—21no—
539C22×C4—24no—
540C22×C4—21no—
541C22×C4—21no—
542C22×C4—21no—
543C22×C4—42no—
544C22×C4—42no—
545C22×C4—42no—
546C22×C4—42no—
547C22×C4—42no—
548C22×C4—42no—
549C22×C4—42no—
550C22×C4—42no—
551C22×C4—81no—
552C22×C4—81no—
553C22×C4—81no—
554C22×C4C22×C4×C712yes—
555C22×C4C2×C7×D411yescharacteristic
556C22×C4C2×C7×D411yescharacteristic
557C22×C4C2×C7×D411yescharacteristic
558C22×C4C2×C7×D411yescharacteristic
559C22×C4C2×C7×D411yescharacteristic
560C22×C4C7×#4112yes—
561C22×C4C24×C711yescharacteristic
562Q16—44no—
563SD16—28no—
564M16—44no—
565C2×C8—21no—
566C2×C8—21no—
567C2×C8—21no—
568C2×C8—21no—
569C2×C8—21no—
570C2×C8—21no—
571C2×C8—21no—
572C2×C8—21no—
573C2×C8—21no—
574C2×C8C22×C4×C712yes—
575C2×C8C22×C4×C712yes—
576C2×C8C2×C7×D412yes—
577C4⋊C4—24no—
578C4⋊C4—21no—
579C4⋊C4—21no—
580C4⋊C4—21no—
581C4⋊C4—21no—
582C4⋊C4—21no—
583C4⋊C4—21no—
584C4⋊C4—21no—
585C4⋊C4—21no—
586C4⋊C4—42no—
587C4⋊C4—42no—
588C4⋊C4—81no—
589C4⋊C4C22×C4×C712yes—
590C4⋊C4C2×C7×D412yes—
591C22⋊C4—24no—
592C22⋊C4—22no—
593C22⋊C4—41no—
594C22⋊C4—42no—
595C22⋊C4—42no—
596C22⋊C4—81no—
597C42—21no—
598C42—21no—
599C42—21no—
600C42—21no—
601C42—42no—
602C42—81no—
603C2×C7—42no—
604C2×C7—44no—
605C2×C7#235811yescharacteristic
606C2×C7C4×#13711yescharacteristic
607C2×C7#295111yescharacteristic
608C2×C7#327311yescharacteristic
609C2×C7#327611yescharacteristic
610C2×C7#331411yescharacteristic
611C2×C7#331511yescharacteristic
612C23—22no—
613C23—22no—
614C23—21no—
615C23—22no—
616C23—21no—
617C23—21no—
618C23—21no—
619C23—21no—
620C23—21no—
621C23—41no—
622C23—41no—
623C23—41no—
624C23—41no—
625C23C4×C7×D412yes—
626C23C22×C7×D411yescharacteristic
627Q8—22no—
628Q8—22no—
629Q8—22no—
630Q8—22no—
631Q8—41no—
632Q8—41no—
633Q8—41no—
634Q8—41no—
635D4—22no—
636D4—22no—
637D4—22no—
638D4—48no—
639D4C4×C7×D414yes—
640C2×C4—21no—
641C2×C4—21no—
642C2×C4—21no—
643C2×C4—21no—
644C2×C4—22no—
645C2×C4—22no—
646C2×C4—22no—
647C2×C4—22no—
648C2×C4—22no—
649C2×C4—22no—
650C2×C4—22no—
651C2×C4—21no—
652C2×C4—21no—
653C2×C4—22no—
654C2×C4—21no—
655C2×C4—21no—
656C2×C4—21no—
657C2×C4—21no—
658C2×C4—21no—
659C2×C4—21no—
660C2×C4—21no—
661C2×C4—48no—
662C2×C4—41no—
663C2×C4—41no—
664C2×C4—41no—
665C2×C4—41no—
666C2×C4—41no—
667C2×C4—41no—
668C2×C4—41no—
669C2×C4—41no—
670C2×C4—41no—
671C2×C4—41no—
672C2×C4—41no—
673C2×C4—41no—
674C2×C4—41no—
675C2×C4—41no—
676C2×C4—41no—
677C2×C4—41no—
678C2×C4—41no—
679C2×C4—84no—
680C2×C4—84no—
681C2×C4—84no—
682C2×C4C4×C7×D412yes—
683C2×C4C7×#13712yes—
684C2×C4C23×C4×C711yescharacteristic
685C2×C4C22×C7×D411yescharacteristic
686C2×C4C2×C7×#4111yescharacteristic
687C2×C4C2×C7×#4111yescharacteristic
688C2×C4C7×H(5,𝔽2)11yescharacteristic
689C2×C4C7×H(5,𝔽2)11yescharacteristic
690C8—22no—
691C8—22no—
692C8—22no—
693C8—41no—
694C7#2286211yescharacteristic, direct product factor, Sylow
695C22—22no—
696C22—22no—
697C22—22no—
698C22—24no—
699C22—42no—
700C22—42no—
701C22—41no—
702C22—42no—
703C22—41no—
704C22—42no—
705C22—42no—
706C22—41no—
707C22—41no—
708C22—42no—
709C22C2×C4×C7×D411yescharacteristic
710C22C7×D4211yescharacteristic
711C22C7×#54611yescharacteristic
712C22C2×C7×#13711yescharacteristic
713C22C7×#57511yescharacteristic
714C22C7×#57611yescharacteristic
715C22C7×#57811yescharacteristic
716C4—22no—
717C4—22no—
718C4—42no—
719C4—41no—
720C4—42no—
721C4—41no—
722C4—41no—
723C4—42no—
724C4—42no—
725C4—81no—
726C4—81no—
727C4—81no—
728C4C2×C4×C7×D411yescharacteristic
729C4C7×#51811yescharacteristic
730C4C7×#54611yescharacteristic
731C4C7×#55111yescharacteristic
732C2—42no—
733C2—44no—
734C2C7×#235811yescharacteristic
735C2C4×C7×#13711yescharacteristic
736C2C7×#295111yescharacteristic
737C2C7×#327311yescharacteristic
738C2C7×#327611yescharacteristic
739C2C7×#331411yescharacteristic
740C2C7×#331511yescharacteristic
subgroupG/H
center, socleC23×C7C22×D4
commutatorC2×C4C23×C4×C7
Frattini, cosocleC22×C4C24×C7
prime radicalC22×C7×#41C22
LCSG ▷ C2×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. C2×C7×#440C2semidirect
4. C7×#2360C2semidirect
6. C7×#1969C2semidirect
7. C7×#1935C2semidirect
8. C7×#1928C2semidirect
9. C7×#1894C2semidirect
10. C7×#1878C2semidirect
11. C7×#1877C2semidirect
12. C7×#1862C2semidirect
13. C7×#1852C2semidirect
14. C4×C7×#102C2semidirect
15. C7×#1753C2semidirect
25. C7×#452C4semidirect
62. #22862C7direct (N × H)
80. C2×C7×Q16C2×C4semidirect
83. C2×C7×SD16C2×C4semidirect
92. C7×C22⋊Q8C2×C4semidirect
126. C7×#103C2×C4semidirect
128. C7×#102C2×C4semidirect
130. C7×C22⋊C8C2×C4semidirect
145. C2×#440C2×C7semidirect
147. #2360C2×C7semidirect
149. #1969C2×C7semidirect
150. #1935C2×C7semidirect
151. #1928C2×C7semidirect
152. #1894C2×C7semidirect
153. #1878C2×C7semidirect
154. #1877C2×C7semidirect
155. #1862C2×C7semidirect
156. #1852C2×C7semidirect
157. C4×#102C2×C7semidirect
158. #1753C2×C7semidirect
267. #452C4×C7semidirect
403. C2×Q16C2×C4×C7semidirect
406. C2×SD16C2×C4×C7semidirect
415. C22⋊Q8C2×C4×C7semidirect
449. #103C2×C4×C7semidirect
451. #102C2×C4×C7semidirect
453. C22⋊C8C2×C4×C7semidirect
694. C7#22862direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C7×#4522
C2×C7×#4402
C2×C7×#4172
C7×#23602
C7×#23392
C7×#19692
C7×#19352
C7×#19282
C7×#18942
C7×#18782
C7×#18772
C7×#18622
C7×#18522
C4×C7×#1022
C7×#17532
#228627