Finite Group Databasebeta

← C7×#25958 #13203174

Subgroups — C7×#25958 #13203174

Order 1792.

1206 conjugacy classes of subgroups.

The subgroup lattice has 772 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C7×#476C211yesmaximal, characteristic, complemented
2C22×C7×#102C211yesmaximal, characteristic
3C7×#2440C211yesmaximal, characteristic, complemented
4C7×D4×C22⋊C4C211yesmaximal, characteristic
5C7×#2094C211yesmaximal, characteristic, complemented
6C7×#2065C211yesmaximal, characteristic, complemented
7C7×#2065C211yesmaximal, characteristic, complemented
8C7×#2023C211yesmaximal, characteristic, complemented
9C7×#1864C211yesmaximal, characteristic, complemented
10C7×#1864C211yesmaximal, characteristic, complemented
11C7×#1853C211yesmaximal, characteristic, complemented
12C7×#1850C211yesmaximal, characteristic, complemented
13C7×#1807C211yesmaximal, characteristic, complemented
14C7×#1802C211yesmaximal, characteristic, complemented
15C7×#1786C211yesmaximal, characteristic
16C23×C7×D4C2211yescharacteristic
17C23×C7×C8C2211yescharacteristic
18C2×C7×C4⋊Q8C2211yescharacteristic, complemented
19C2×C7×C22⋊Q8—21no—
20C2×C4×C7×D4C2211yescharacteristic
21C2×C4×C7×D4C2211yescharacteristic
22C22×C7×C4⋊C4C2211yescharacteristic
23C22×C7×C22⋊C4—21no—
24C7×#476—24no—
25C2×C7×#106C2211yescharacteristic, complemented
26C2×C7×#106C2211yescharacteristic, complemented
27C2×C7×#106C2211yescharacteristic, complemented
28C2×C7×#106C2211yescharacteristic, complemented
29C2×C7×C4⋊C8C2211yescharacteristic, complemented
30C2×C7×C4⋊C8C2211yescharacteristic, complemented
31C2×C7×#102—24no—
32C2×C7×#102C2211yescharacteristic
33C2×C7×#102C2211yescharacteristic
34C2×C7×#102C2211yescharacteristic
35C2×C7×#102C2211yescharacteristic
36C2×C7×#102C2211yescharacteristic
37C2×C7×#102C2211yescharacteristic
38C2×C7×#102C2211yescharacteristic
39C2×C7×#102C2211yescharacteristic
40C2×C7×C22⋊C8C2211yescharacteristic
41C7×#398—21no—
42C7×#395—21no—
43C7×#390C2211yescharacteristic
44C7×#390C2211yescharacteristic
45C7×#389C2211yescharacteristic, complemented
46C7×#389C2211yescharacteristic, complemented
47C7×#386—21no—
48C7×#386—21no—
49C7×#385—21no—
50C7×#384C2211yescharacteristic, complemented
51C7×#380C2211yescharacteristic
52C7×#380C2211yescharacteristic
53C7×#379—21no—
54C4×C7×C22⋊C4C2211yescharacteristic
55C7×#340C2211yescharacteristic, complemented
56C7×#340C2211yescharacteristic, complemented
57C7×#340C2211yescharacteristic, complemented
58C7×#340C2211yescharacteristic, complemented
59C7×#336C2211yescharacteristic, complemented
60C7×#336C2211yescharacteristic, complemented
61#25958C711yesmaximal, characteristic, direct product factor, Sylow
62C25×C7—21no—
63C22×C7×Q8—21no—
64C22×C7×D4—22no—
65C22×C7×D4—22no—
66C22×C7×D4—21no—
67C22×C7×D4—22no—
68C22×C7×D4—41no—
69C22×C7×D4—41no—
70C22×C7×D4Q814yescomplemented
71C22×C7×D4C2311yescharacteristic
72C22×C7×D4C2311yescharacteristic
73C23×C4×C7—21no—
74C23×C4×C7—21no—
75C23×C4×C7—21no—
76C23×C4×C7C2311yescharacteristic
77C22×C7×C8—22no—
78C22×C7×C8—22no—
79C22×C7×C8—41no—
80C22×C7×C8C2311yescharacteristic
81C22×C7×C8C2311yescharacteristic
82C22×C7×C8C2311yescharacteristic
83C22×C7×C8C2311yescharacteristic
84C7×C4⋊Q8—22no—
85C7×C4⋊Q8—41no—
86C7×C22⋊Q8—44no—
87C4×C7×D4—22no—
88C4×C7×D4—22no—
89C4×C7×D4—41no—
90C4×C7×D4—41no—
91C2×C7×C4⋊C4—22no—
92C2×C7×C4⋊C4—21no—
93C2×C7×C4⋊C4—21no—
94C2×C7×C4⋊C4—21no—
95C2×C7×C4⋊C4—21no—
96C2×C7×C4⋊C4—21no—
97C2×C7×C4⋊C4—21no—
98C2×C7×C4⋊C4—41no—
99C2×C7×C4⋊C4C2311yescharacteristic
100C2×C7×C4⋊C4C2311yescharacteristic
101C2×C7×C4⋊C4C2311yescharacteristic
102C2×C7×C4⋊C4C2311yescharacteristic
103C2×C7×C4⋊C4C2311yescharacteristic
104C2×C7×C4⋊C4C2311yescharacteristic
105C2×C7×C22⋊C4—21no—
106C2×C7×C22⋊C4—21no—
107C2×C7×C22⋊C4—21no—
108C2×C7×C22⋊C4—21no—
109C2×C7×C22⋊C4—21no—
110C2×C7×C22⋊C4—21no—
111C2×C7×C22⋊C4—21no—
112C2×C7×C22⋊C4—21no—
113C2×C7×C22⋊C4—44no—
114C2×C7×C22⋊C4D411yescharacteristic
115C2×C7×C22⋊C4D411yescharacteristic
116C2×C42×C7C2311yescharacteristic
117C2×C42×C7C2311yescharacteristic
118C7×#106—22no—
119C7×#106—22no—
120C7×#106—41no—
121C7×#106—41no—
122C7×C4⋊C8—22no—
123C7×C4⋊C8—41no—
124C7×#102—22no—
125C7×#102—22no—
126C7×#102—22no—
127C7×#102—22no—
128C7×#102—22no—
129C7×#102—41no—
130C7×#102—41no—
131C7×#102D414yes—
132C7×C22⋊C8—22no—
133C7×#95—21no—
134C7×#95—21no—
135C7×#95—21no—
136C7×#95—21no—
137C7×#95D411yescharacteristic
138C7×#95D411yescharacteristic
139C2×#476C2×C711yescharacteristic, complemented
140C22×#102C2×C711yescharacteristic
141#2440C2×C711yescharacteristic, complemented
142D4×C22⋊C4C2×C711yescharacteristic
143#2094C2×C711yescharacteristic, complemented
144#2065C2×C711yescharacteristic, complemented
145#2065C2×C711yescharacteristic, complemented
146#2023C2×C711yescharacteristic, complemented
147#1864C2×C711yescharacteristic, complemented
148#1864C2×C711yescharacteristic, complemented
149#1853C2×C711yescharacteristic, complemented
150#1850C2×C711yescharacteristic, complemented
151#1807C2×C711yescharacteristic, complemented
152#1802C2×C711yescharacteristic, complemented
153#1786C2×C711yescharacteristic
154C24×C7—21no—
155C24×C7—21no—
156C24×C7—24no—
157C24×C7—42no—
158C24×C7—42no—
159C24×C7—42no—
160C24×C7—42no—
161C24×C7—81no—
162C24×C7—81no—
163C24×C7C2×D411yescharacteristic
164C2×C7×Q8—42no—
165C2×C7×Q8—42no—
166C2×C7×Q8—81no—
167C2×C7×D4—28no—
168C2×C7×D4—24no—
169C2×C7×D4—21no—
170C2×C7×D4—21no—
171C2×C7×D4—21no—
172C2×C7×D4—21no—
173C2×C7×D4—21no—
174C2×C7×D4—21no—
175C2×C7×D4—21no—
176C2×C7×D4—21no—
177C2×C7×D4—44no—
178C2×C7×D4—44no—
179C2×C7×D4—44no—
180C2×C7×D4—42no—
181C2×C7×D4—42no—
182C2×C7×D4C2×D412yes—
183C2×C7×D4C2×Q812yes—
184C2×C7×D4C2×Q812yes—
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—21no—
195C22×C4×C7—21no—
196C22×C4×C7—42no—
197C22×C4×C7—42no—
198C22×C4×C7—42no—
199C22×C4×C7—42no—
200C22×C4×C7—42no—
201C22×C4×C7—42no—
202C22×C4×C7—81no—
203C22×C4×C7—81no—
204C22×C4×C7—81no—
205C22×C4×C7C2×D411yescharacteristic
206C22×C4×C7C2×D411yescharacteristic
207C22×C4×C7C2×D411yescharacteristic
208C22×C4×C7C2×D411yescharacteristic
209C22×C4×C7C2×D411yescharacteristic
210C22×C4×C7C2×Q812yes—
211C22×C4×C7#4112yes—
212C22×C4×C7C2411yescharacteristic
213C2×C7×C8—21no—
214C2×C7×C8—21no—
215C2×C7×C8—21no—
216C2×C7×C8—21no—
217C2×C7×C8—21no—
218C2×C7×C8—21no—
219C2×C7×C8—21no—
220C2×C7×C8—21no—
221C2×C7×C8—21no—
222C2×C7×C8—21no—
223C2×C7×C8—21no—
224C2×C7×C8—44no—
225C2×C7×C8C2×D412yes—
226C7×C4⋊C4—21no—
227C7×C4⋊C4—21no—
228C7×C4⋊C4—21no—
229C7×C4⋊C4—21no—
230C7×C4⋊C4—21no—
231C7×C4⋊C4—21no—
232C7×C4⋊C4—21no—
233C7×C4⋊C4—21no—
234C7×C4⋊C4—21no—
235C7×C4⋊C4—21no—
236C7×C4⋊C4—21no—
237C7×C4⋊C4—42no—
238C7×C4⋊C4—42no—
239C7×C4⋊C4—42no—
240C7×C4⋊C4—42no—
241C7×C4⋊C4—42no—
242C7×C4⋊C4—81no—
243C7×C4⋊C4C2×D412yes—
244C7×C22⋊C4—22no—
245C7×C22⋊C4—42no—
246C7×C22⋊C4—42no—
247C7×C22⋊C4—42no—
248C7×C22⋊C4—42no—
249C7×C22⋊C4—42no—
250C7×C22⋊C4—42no—
251C7×C22⋊C4—81no—
252C7×C22⋊C4—81no—
253C7×C22⋊C4SD1614yes—
254C42×C7—21no—
255C42×C7—21no—
256C42×C7—21no—
257C42×C7—21no—
258C23×D4C22×C711yescharacteristic
259C23×C8C22×C711yescharacteristic
260C2×C4⋊Q8C22×C711yescharacteristic, complemented
261C2×C22⋊Q8—21no—
262C2×C4×D4C22×C711yescharacteristic
263C2×C4×D4C22×C711yescharacteristic
264C22×C4⋊C4C22×C711yescharacteristic
265C22×C22⋊C4—21no—
266#476—24no—
267C2×#106C22×C711yescharacteristic, complemented
268C2×#106C22×C711yescharacteristic, complemented
269C2×#106C22×C711yescharacteristic, complemented
270C2×#106C22×C711yescharacteristic, complemented
271C2×C4⋊C8C22×C711yescharacteristic, complemented
272C2×C4⋊C8C22×C711yescharacteristic, complemented
273C2×#102—24no—
274C2×#102C22×C711yescharacteristic
275C2×#102C22×C711yescharacteristic
276C2×#102C22×C711yescharacteristic
277C2×#102C22×C711yescharacteristic
278C2×#102C22×C711yescharacteristic
279C2×#102C22×C711yescharacteristic
280C2×#102C22×C711yescharacteristic
281C2×#102C22×C711yescharacteristic
282C2×C22⋊C8C22×C711yescharacteristic
283#398—21no—
284#395—21no—
285#390C22×C711yescharacteristic
286#390C22×C711yescharacteristic
287#389C22×C711yescharacteristic, complemented
288#389C22×C711yescharacteristic, complemented
289#386—21no—
290#386—21no—
291#385—21no—
292#384C22×C711yescharacteristic, complemented
293#380C22×C711yescharacteristic
294#380C22×C711yescharacteristic
295#379—21no—
296C4×C22⋊C4C22×C711yescharacteristic
297#340C22×C711yescharacteristic, complemented
298#340C22×C711yescharacteristic, complemented
299#340C22×C711yescharacteristic, complemented
300#340C22×C711yescharacteristic, complemented
301#336C22×C711yescharacteristic, complemented
302#336C22×C711yescharacteristic, complemented
303C23×C7—21no—
304C23×C7—21no—
305C23×C7—21no—
306C23×C7—21no—
307C23×C7—22no—
308C23×C7—22no—
309C23×C7—22no—
310C23×C7—22no—
311C23×C7—48no—
312C23×C7—41no—
313C23×C7—41no—
314C23×C7—41no—
315C23×C7—41no—
316C23×C7—41no—
317C23×C7—41no—
318C23×C7—41no—
319C23×C7—41no—
320C23×C7—41no—
321C23×C7—41no—
322C23×C7—48no—
323C23×C7—84no—
324C23×C7—84no—
325C23×C7—84no—
326C23×C7—84no—
327C23×C7—84no—
328C23×C7C22⋊Q812yes—
329C23×C7C2×SD1612yes—
330C23×C7AGL(1,ℤ/8)12yes—
331C23×C7C22×D411yescharacteristic
332C7×Q8—84no—
333C7×D4—22no—
334C7×D4—22no—
335C7×D4—22no—
336C7×D4—22no—
337C7×D4—22no—
338C7×D4—48no—
339C7×D4—41no—
340C7×D4—41no—
341C7×D4C22⋊Q814yescomplemented
342C2×C4×C7—21no—
343C2×C4×C7—21no—
344C2×C4×C7—21no—
345C2×C4×C7—21no—
346C2×C4×C7—21no—
347C2×C4×C7—21no—
348C2×C4×C7—22no—
349C2×C4×C7—22no—
350C2×C4×C7—22no—
351C2×C4×C7—22no—
352C2×C4×C7—21no—
353C2×C4×C7—22no—
354C2×C4×C7—21no—
355C2×C4×C7—21no—
356C2×C4×C7—21no—
357C2×C4×C7—21no—
358C2×C4×C7—21no—
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—41no—
372C2×C4×C7—41no—
373C2×C4×C7—41no—
374C2×C4×C7—41no—
375C2×C4×C7—41no—
376C2×C4×C7—84no—
377C2×C4×C7—84no—
378C2×C4×C7—84no—
379C2×C4×C7C22⋊Q812yes—
380C2×C4×C7C2×SD1612yes—
381C2×C4×C7C2×SD1612yes—
382C2×C4×C7C22×D411yescharacteristic
383C2×C4×C7C22×Q811yescharacteristic
384C2×C4×C7C2×#4111yescharacteristic
385C2×C4×C7C2×#4111yescharacteristic
386C2×C4×C7H(5,𝔽2)11yescharacteristic
387C2×C4×C7H(5,𝔽2)11yescharacteristic
388C7×C8—22no—
389C7×C8—41no—
390C7×C8—41no—
391C7×C8—41no—
392C25—21no—
393C22×Q8—21no—
394C22×D4—22no—
395C22×D4—22no—
396C22×D4—21no—
397C22×D4—22no—
398C22×D4—41no—
399C22×D4—41no—
400C22×D4C7×Q814yescomplemented
401C22×D4C23×C711yescharacteristic
402C22×D4C23×C711yescharacteristic
403C23×C4—21no—
404C23×C4—21no—
405C23×C4—21no—
406C23×C4C23×C711yescharacteristic
407C22×C8—22no—
408C22×C8—22no—
409C22×C8—41no—
410C22×C8C23×C711yescharacteristic
411C22×C8C23×C711yescharacteristic
412C22×C8C23×C711yescharacteristic
413C22×C8C23×C711yescharacteristic
414C4⋊Q8—22no—
415C4⋊Q8—41no—
416C22⋊Q8—44no—
417C4×D4—22no—
418C4×D4—22no—
419C4×D4—41no—
420C4×D4—41no—
421C2×C4⋊C4—22no—
422C2×C4⋊C4—21no—
423C2×C4⋊C4—21no—
424C2×C4⋊C4—21no—
425C2×C4⋊C4—21no—
426C2×C4⋊C4—21no—
427C2×C4⋊C4—21no—
428C2×C4⋊C4—41no—
429C2×C4⋊C4C23×C711yescharacteristic
430C2×C4⋊C4C23×C711yescharacteristic
431C2×C4⋊C4C23×C711yescharacteristic
432C2×C4⋊C4C23×C711yescharacteristic
433C2×C4⋊C4C23×C711yescharacteristic
434C2×C4⋊C4C23×C711yescharacteristic
435C2×C22⋊C4—21no—
436C2×C22⋊C4—21no—
437C2×C22⋊C4—21no—
438C2×C22⋊C4—21no—
439C2×C22⋊C4—21no—
440C2×C22⋊C4—21no—
441C2×C22⋊C4—21no—
442C2×C22⋊C4—21no—
443C2×C22⋊C4—44no—
444C2×C22⋊C4C7×D411yescharacteristic
445C2×C22⋊C4C7×D411yescharacteristic
446C2×C42C23×C711yescharacteristic
447C2×C42C23×C711yescharacteristic
448#106—22no—
449#106—22no—
450#106—41no—
451#106—41no—
452C4⋊C8—22no—
453C4⋊C8—41no—
454#102—22no—
455#102—22no—
456#102—22no—
457#102—22no—
458#102—22no—
459#102—41no—
460#102—41no—
461#102C7×D414yes—
462C22⋊C8—22no—
463#95—21no—
464#95—21no—
465#95—21no—
466#95—21no—
467#95C7×D411yescharacteristic
468#95C7×D411yescharacteristic
469C22×C7—22no—
470C22×C7—22no—
471C22×C7—22no—
472C22×C7—22no—
473C22×C7—22no—
474C22×C7—22no—
475C22×C7—24no—
476C22×C7—42no—
477C22×C7—42no—
478C22×C7—42no—
479C22×C7—42no—
480C22×C7—42no—
481C22×C7—42no—
482C22×C7—42no—
483C22×C7—42no—
484C22×C7—42no—
485C22×C7—816no—
486C22×C7—81no—
487C22×C7—81no—
488C22×C7—81no—
489C22×C7—81no—
490C22×C7#47614yescomplemented
491C22×C7C2×C22⋊Q811yescharacteristic
492C22×C7D4211yescharacteristic
493C22×C7#54611yescharacteristic
494C22×C7C22×SD1611yescharacteristic
495C22×C7C2×AGL(1,ℤ/8)11yescharacteristic
496C22×C7#57611yescharacteristic
497C22×C7#57711yescharacteristic
498C4×C7—22no—
499C4×C7—22no—
500C4×C7—22no—
501C4×C7—41no—
502C4×C7—42no—
503C4×C7—41no—
504C4×C7—81no—
505C4×C7—81no—
506C4×C7—81no—
507C4×C7—81no—
508C4×C7—81no—
509C4×C7C2×C22⋊Q811yescharacteristic
510C4×C7#54311yescharacteristic
511C4×C7#54611yescharacteristic
512C4×C7#55111yescharacteristic
513C24—21no—
514C24—21no—
515C24—24no—
516C24—42no—
517C24—42no—
518C24—42no—
519C24—42no—
520C24—81no—
521C24—81no—
522C24C2×C7×D411yescharacteristic
523C2×Q8—42no—
524C2×Q8—42no—
525C2×Q8—81no—
526C2×D4—28no—
527C2×D4—24no—
528C2×D4—21no—
529C2×D4—21no—
530C2×D4—21no—
531C2×D4—21no—
532C2×D4—21no—
533C2×D4—21no—
534C2×D4—21no—
535C2×D4—21no—
536C2×D4—44no—
537C2×D4—44no—
538C2×D4—44no—
539C2×D4—42no—
540C2×D4—42no—
541C2×D4C2×C7×D412yes—
542C2×D4C2×C7×Q812yes—
543C2×D4C2×C7×Q812yes—
544C2×D4C7×#4112yes—
545C22×C4—21no—
546C22×C4—21no—
547C22×C4—21no—
548C22×C4—21no—
549C22×C4—21no—
550C22×C4—21no—
551C22×C4—21no—
552C22×C4—21no—
553C22×C4—21no—
554C22×C4—21no—
555C22×C4—42no—
556C22×C4—42no—
557C22×C4—42no—
558C22×C4—42no—
559C22×C4—42no—
560C22×C4—42no—
561C22×C4—81no—
562C22×C4—81no—
563C22×C4—81no—
564C22×C4C2×C7×D411yescharacteristic
565C22×C4C2×C7×D411yescharacteristic
566C22×C4C2×C7×D411yescharacteristic
567C22×C4C2×C7×D411yescharacteristic
568C22×C4C2×C7×D411yescharacteristic
569C22×C4C2×C7×Q812yes—
570C22×C4C7×#4112yes—
571C22×C4C24×C711yescharacteristic
572C2×C8—21no—
573C2×C8—21no—
574C2×C8—21no—
575C2×C8—21no—
576C2×C8—21no—
577C2×C8—21no—
578C2×C8—21no—
579C2×C8—21no—
580C2×C8—21no—
581C2×C8—21no—
582C2×C8—21no—
583C2×C8—44no—
584C2×C8C2×C7×D412yes—
585C4⋊C4—21no—
586C4⋊C4—21no—
587C4⋊C4—21no—
588C4⋊C4—21no—
589C4⋊C4—21no—
590C4⋊C4—21no—
591C4⋊C4—21no—
592C4⋊C4—21no—
593C4⋊C4—21no—
594C4⋊C4—21no—
595C4⋊C4—21no—
596C4⋊C4—42no—
597C4⋊C4—42no—
598C4⋊C4—42no—
599C4⋊C4—42no—
600C4⋊C4—42no—
601C4⋊C4—81no—
602C4⋊C4C2×C7×D412yes—
603C22⋊C4—22no—
604C22⋊C4—42no—
605C22⋊C4—42no—
606C22⋊C4—42no—
607C22⋊C4—42no—
608C22⋊C4—42no—
609C22⋊C4—42no—
610C22⋊C4—81no—
611C22⋊C4—81no—
612C22⋊C4C7×SD1614yes—
613C42—21no—
614C42—21no—
615C42—21no—
616C42—21no—
617C2×C7—24no—
618C2×C7—44no—
619C2×C7—82no—
620C2×C7#243711yescharacteristic
621C2×C7C2×#47611yescharacteristic
622C2×C7#308111yescharacteristic
623C2×C7#326411yescharacteristic
624C2×C7D4×SD1611yescharacteristic
625C2×C7#329511yescharacteristic
626C2×C7#330611yescharacteristic
627C23—21no—
628C23—21no—
629C23—21no—
630C23—21no—
631C23—22no—
632C23—22no—
633C23—22no—
634C23—22no—
635C23—48no—
636C23—41no—
637C23—41no—
638C23—41no—
639C23—41no—
640C23—48no—
641C23—41no—
642C23—41no—
643C23—41no—
644C23—41no—
645C23—41no—
646C23—41no—
647C23—84no—
648C23—84no—
649C23—84no—
650C23—84no—
651C23—84no—
652C23C7×C22⋊Q812yes—
653C23C2×C7×SD1612yes—
654C23C7×AGL(1,ℤ/8)12yes—
655C23C22×C7×D411yescharacteristic
656Q8—84no—
657D4—22no—
658D4—22no—
659D4—22no—
660D4—22no—
661D4—22no—
662D4—48no—
663D4—41no—
664D4—41no—
665D4C7×C22⋊Q814yescomplemented
666C2×C4—21no—
667C2×C4—21no—
668C2×C4—21no—
669C2×C4—21no—
670C2×C4—21no—
671C2×C4—21no—
672C2×C4—22no—
673C2×C4—22no—
674C2×C4—22no—
675C2×C4—22no—
676C2×C4—21no—
677C2×C4—22no—
678C2×C4—21no—
679C2×C4—21no—
680C2×C4—21no—
681C2×C4—21no—
682C2×C4—21no—
683C2×C4—41no—
684C2×C4—41no—
685C2×C4—41no—
686C2×C4—41no—
687C2×C4—41no—
688C2×C4—41no—
689C2×C4—41no—
690C2×C4—41no—
691C2×C4—41no—
692C2×C4—41no—
693C2×C4—41no—
694C2×C4—41no—
695C2×C4—41no—
696C2×C4—41no—
697C2×C4—41no—
698C2×C4—41no—
699C2×C4—41no—
700C2×C4—84no—
701C2×C4—84no—
702C2×C4—84no—
703C2×C4C7×C22⋊Q812yes—
704C2×C4C2×C7×SD1612yes—
705C2×C4C2×C7×SD1612yes—
706C2×C4C22×C7×D411yescharacteristic
707C2×C4C22×C7×Q811yescharacteristic
708C2×C4C2×C7×#4111yescharacteristic
709C2×C4C2×C7×#4111yescharacteristic
710C2×C4C7×H(5,𝔽2)11yescharacteristic
711C2×C4C7×H(5,𝔽2)11yescharacteristic
712C8—22no—
713C8—41no—
714C8—41no—
715C8—41no—
716C7#2595811yescharacteristic, direct product factor, Sylow
717C22—22no—
718C22—22no—
719C22—22no—
720C22—22no—
721C22—22no—
722C22—22no—
723C22—24no—
724C22—42no—
725C22—42no—
726C22—42no—
727C22—42no—
728C22—42no—
729C22—42no—
730C22—42no—
731C22—42no—
732C22—42no—
733C22—816no—
734C22—81no—
735C22—81no—
736C22—81no—
737C22—81no—
738C22C7×#47614yescomplemented
739C22C2×C7×C22⋊Q811yescharacteristic
740C22C7×D4211yescharacteristic
741C22C7×#54611yescharacteristic
742C22C22×C7×SD1611yescharacteristic
743C22C2×C7×AGL(1,ℤ/8)11yescharacteristic
744C22C7×#57611yescharacteristic
745C22C7×#57711yescharacteristic
746C4—22no—
747C4—22no—
748C4—22no—
749C4—41no—
750C4—42no—
751C4—41no—
752C4—81no—
753C4—81no—
754C4—81no—
755C4—81no—
756C4—81no—
757C4C2×C7×C22⋊Q811yescharacteristic
758C4C7×#54311yescharacteristic
759C4C7×#54611yescharacteristic
760C4C7×#55111yescharacteristic
761C2—24no—
762C2—44no—
763C2—82no—
764C2C7×#243711yescharacteristic
765C2C2×C7×#47611yescharacteristic
766C2C7×#308111yescharacteristic
767C2C7×#326411yescharacteristic
768C2C7×D4×SD1611yescharacteristic
769C2C7×#329511yescharacteristic
770C2C7×#330611yescharacteristic
subgroupG/H
center, socleC23×C7C22×D4
commutator, Frattini, cosocleC22×C4C24×C7
prime radicalC23×C7×D4C22
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
1. C2×C7×#476C2semidirect
3. C7×#2440C2semidirect
5. C7×#2094C2semidirect
6. C7×#2065C2semidirect
7. C7×#2065C2semidirect
8. C7×#2023C2semidirect
9. C7×#1864C2semidirect
10. C7×#1864C2semidirect
11. C7×#1853C2semidirect
12. C7×#1850C2semidirect
13. C7×#1807C2semidirect
14. C7×#1802C2semidirect
18. C2×C7×C4⋊Q8C22semidirect
25. C2×C7×#106C22semidirect
26. C2×C7×#106C22semidirect
27. C2×C7×#106C22semidirect
28. C2×C7×#106C22semidirect
29. C2×C7×C4⋊C8C22semidirect
30. C2×C7×C4⋊C8C22semidirect
45. C7×#389C22semidirect
46. C7×#389C22semidirect
50. C7×#384C22semidirect
55. C7×#340C22semidirect
56. C7×#340C22semidirect
57. C7×#340C22semidirect
58. C7×#340C22semidirect
59. C7×#336C22semidirect
60. C7×#336C22semidirect
61. #25958C7direct (N × H)
70. C22×C7×D4Q8semidirect
139. C2×#476C2×C7semidirect
141. #2440C2×C7semidirect
143. #2094C2×C7semidirect
144. #2065C2×C7semidirect
145. #2065C2×C7semidirect
146. #2023C2×C7semidirect
147. #1864C2×C7semidirect
148. #1864C2×C7semidirect
149. #1853C2×C7semidirect
150. #1850C2×C7semidirect
151. #1807C2×C7semidirect
152. #1802C2×C7semidirect
260. C2×C4⋊Q8C22×C7semidirect
267. C2×#106C22×C7semidirect
268. C2×#106C22×C7semidirect
269. C2×#106C22×C7semidirect
270. C2×#106C22×C7semidirect
271. C2×C4⋊C8C22×C7semidirect
272. C2×C4⋊C8C22×C7semidirect
287. #389C22×C7semidirect
288. #389C22×C7semidirect
292. #384C22×C7semidirect
297. #340C22×C7semidirect
298. #340C22×C7semidirect
299. #340C22×C7semidirect
300. #340C22×C7semidirect
301. #336C22×C7semidirect
302. #336C22×C7semidirect
341. C7×D4C22⋊Q8semidirect
400. C22×D4C7×Q8semidirect
490. C22×C7#476semidirect
665. D4C7×C22⋊Q8semidirect
716. C7#25958direct (N × H)
738. C22C7×#476semidirect

Maximal subgroups

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

subgroupindex
C2×C7×#4762
C22×C7×#1022
C7×#24402
C7×D4×C22⋊C42
C7×#20942
C7×#20652
C7×#20232
C7×#18642
C7×#18532
C7×#18502
C7×#18072
C7×#18022
C7×#17862
#259587