Finite Group Databasebeta

← C7×#15953 #13193169

Subgroups — C7×#15953 #13193169

Order 1792.

1494 conjugacy classes of subgroups.

The subgroup lattice has 996 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C7×#388C211yesmaximal, characteristic
2C2×C7×#387C211yesmaximal, characteristic, complemented
3C2×C7×#385C211yesmaximal, characteristic
4C2×C7×#381C211yesmaximal, characteristic
5C7×#1445C211yesmaximal, characteristic, complemented
6C7×#1442C211yesmaximal, characteristic, complemented
7C7×#1442C211yesmaximal, characteristic, complemented
8C7×#1442C211yesmaximal, characteristic, complemented
9C7×#1442C211yesmaximal, characteristic, complemented
10C7×#1441C211yesmaximal, characteristic, complemented
11C7×#1440C211yesmaximal, characteristic
12C7×#1439C211yesmaximal, characteristic
13C7×#1439C211yesmaximal, characteristic
14C7×#1436C211yesmaximal, characteristic, complemented
15C7×C22⋊#95C211yesmaximal, characteristic
16C24×C4×C7C2211yescharacteristic
17C22×C7×C4⋊C4C2211yescharacteristic
18C22×C7×C4⋊C4C2211yescharacteristic
19C22×C7×C4⋊C4C2211yescharacteristic
20C22×C7×C4⋊C4C2211yescharacteristic
21C22×C7×C4⋊C4C2211yescharacteristic
22C22×C7×C22⋊C4C2211yescharacteristic
23C22×C7×C22⋊C4C2211yescharacteristic
24C22×C7×C22⋊C4C2211yescharacteristic
25C22×C7×C22⋊C4C2211yescharacteristic
26C22×C7×C22⋊C4C2211yescharacteristic
27C22×C7×C22⋊C4C2211yescharacteristic
28C22×C42×C7C2211yescharacteristic
29C7×#388—24no—
30C7×#387—24no—
31C7×#385—24no—
32C7×#381—24no—
33C2×C7×#95C2211yescharacteristic
34C2×C7×#95C2211yescharacteristic
35C2×C7×#95C2211yescharacteristic
36C2×C7×#95C2211yescharacteristic
37C2×C7×#95C2211yescharacteristic
38C2×C7×#95C2211yescharacteristic
39C2×C7×#95C2211yescharacteristic
40C2×C7×#95C2211yescharacteristic
41C2×C7×#95C2211yescharacteristic
42C2×C7×#95C2211yescharacteristic
43C2×C7×#95C2211yescharacteristic
44C2×C7×#95C2211yescharacteristic
45C2×C7×#95C2211yescharacteristic
46C2×C7×#95C2211yescharacteristic
47C2×C7×#95C2211yescharacteristic
48C2×C7×#95C2211yescharacteristic
49C2×C7×#95C2211yescharacteristic
50C2×C7×#95C2211yescharacteristic
51C2×C7×#95C2211yescharacteristic
52C2×C7×#95C2211yescharacteristic
53C2×C7×#95C2211yescharacteristic
54C2×C7×#95C2211yescharacteristic
55#15953C711yesmaximal, characteristic, direct product factor, Sylow
56C25×C7C2311yescharacteristic
57C23×C4×C7—22no—
58C23×C4×C7—22no—
59C23×C4×C7—22no—
60C23×C4×C7—22no—
61C23×C4×C7—22no—
62C23×C4×C7—41no—
63C23×C4×C7—41no—
64C23×C4×C7C2311yescharacteristic
65C23×C4×C7C2311yescharacteristic
66C23×C4×C7C2311yescharacteristic
67C23×C4×C7C2311yescharacteristic
68C23×C4×C7C2311yescharacteristic
69C23×C4×C7C2311yescharacteristic
70C23×C4×C7C2311yescharacteristic
71C23×C4×C7C2311yescharacteristic
72C23×C4×C7C2311yescharacteristic
73C23×C4×C7C2311yescharacteristic
74C23×C4×C7C2311yescharacteristic
75C23×C4×C7C2311yescharacteristic
76C23×C4×C7C2311yescharacteristic
77C23×C4×C7C2311yescharacteristic
78C2×C7×C4⋊C4—22no—
79C2×C7×C4⋊C4—22no—
80C2×C7×C4⋊C4—22no—
81C2×C7×C4⋊C4—22no—
82C2×C7×C4⋊C4—22no—
83C2×C7×C4⋊C4—22no—
84C2×C7×C4⋊C4—22no—
85C2×C7×C4⋊C4—22no—
86C2×C7×C4⋊C4—22no—
87C2×C7×C4⋊C4—22no—
88C2×C7×C4⋊C4—41no—
89C2×C7×C4⋊C4—41no—
90C2×C7×C4⋊C4—41no—
91C2×C7×C4⋊C4—41no—
92C2×C7×C4⋊C4—41no—
93C2×C7×C22⋊C4—22no—
94C2×C7×C22⋊C4—22no—
95C2×C7×C22⋊C4—22no—
96C2×C7×C22⋊C4—22no—
97C2×C7×C22⋊C4—22no—
98C2×C7×C22⋊C4—22no—
99C2×C7×C22⋊C4—22no—
100C2×C7×C22⋊C4—22no—
101C2×C7×C22⋊C4—22no—
102C2×C7×C22⋊C4—22no—
103C2×C7×C22⋊C4—22no—
104C2×C7×C22⋊C4—22no—
105C2×C7×C22⋊C4—22no—
106C2×C7×C22⋊C4—41no—
107C2×C7×C22⋊C4—41no—
108C2×C7×C22⋊C4—41no—
109C2×C7×C22⋊C4—41no—
110C2×C7×C22⋊C4D414yes—
111C2×C42×C7—22no—
112C2×C42×C7—22no—
113C2×C42×C7—41no—
114C7×#95—22no—
115C7×#95—22no—
116C7×#95—22no—
117C7×#95—22no—
118C7×#95—22no—
119C7×#95—22no—
120C7×#95—22no—
121C7×#95—22no—
122C7×#95—22no—
123C7×#95—22no—
124C7×#95—22no—
125C7×#95—22no—
126C7×#95—22no—
127C7×#95—22no—
128C7×#95—22no—
129C7×#95—41no—
130C7×#95—41no—
131C7×#95—41no—
132C7×#95—41no—
133C7×#95—41no—
134C7×#95—41no—
135C7×#95D414yes—
136C2×#388C2×C711yescharacteristic
137C2×#387C2×C711yescharacteristic, complemented
138C2×#385C2×C711yescharacteristic
139C2×#381C2×C711yescharacteristic
140#1445C2×C711yescharacteristic, complemented
141#1442C2×C711yescharacteristic, complemented
142#1442C2×C711yescharacteristic, complemented
143#1442C2×C711yescharacteristic, complemented
144#1442C2×C711yescharacteristic, complemented
145#1441C2×C711yescharacteristic, complemented
146#1440C2×C711yescharacteristic
147#1439C2×C711yescharacteristic
148#1439C2×C711yescharacteristic
149#1436C2×C711yescharacteristic, complemented
150C22⋊#95C2×C711yescharacteristic
151C24×C7—21no—
152C24×C7—21no—
153C24×C7—21no—
154C24×C7—21no—
155C24×C7—21no—
156C24×C7—21no—
157C24×C7—21no—
158C24×C7—21no—
159C24×C7—21no—
160C24×C7—21no—
161C24×C7—21no—
162C24×C7—21no—
163C24×C7C2×D412yes—
164C24×C7#4112yes—
165C24×C7#4112yes—
166C24×C7C2411yescharacteristic
167C22×C4×C7—28no—
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—21no—
177C22×C4×C7—21no—
178C22×C4×C7—21no—
179C22×C4×C7—21no—
180C22×C4×C7—21no—
181C22×C4×C7—21no—
182C22×C4×C7—21no—
183C22×C4×C7—21no—
184C22×C4×C7—21no—
185C22×C4×C7—21no—
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—21no—
197C22×C4×C7—21no—
198C22×C4×C7—21no—
199C22×C4×C7—21no—
200C22×C4×C7—21no—
201C22×C4×C7—21no—
202C22×C4×C7—21no—
203C22×C4×C7—21no—
204C22×C4×C7—21no—
205C22×C4×C7—21no—
206C22×C4×C7—21no—
207C22×C4×C7—21no—
208C22×C4×C7—21no—
209C22×C4×C7—21no—
210C22×C4×C7—21no—
211C22×C4×C7—21no—
212C22×C4×C7—21no—
213C22×C4×C7—21no—
214C22×C4×C7—21no—
215C22×C4×C7—21no—
216C22×C4×C7—21no—
217C22×C4×C7—21no—
218C22×C4×C7—21no—
219C22×C4×C7—21no—
220C22×C4×C7—21no—
221C22×C4×C7—21no—
222C22×C4×C7—21no—
223C22×C4×C7—21no—
224C22×C4×C7—21no—
225C22×C4×C7—21no—
226C22×C4×C7—21no—
227C22×C4×C7—21no—
228C22×C4×C7—21no—
229C22×C4×C7—21no—
230C22×C4×C7—21no—
231C22×C4×C7—21no—
232C22×C4×C7—21no—
233C22×C4×C7—21no—
234C22×C4×C7—21no—
235C22×C4×C7—21no—
236C22×C4×C7—21no—
237C22×C4×C7—21no—
238C22×C4×C7—21no—
239C22×C4×C7—21no—
240C22×C4×C7—21no—
241C22×C4×C7—21no—
242C22×C4×C7—21no—
243C22×C4×C7—21no—
244C22×C4×C7—21no—
245C22×C4×C7—21no—
246C22×C4×C7—21no—
247C22×C4×C7—21no—
248C22×C4×C7—21no—
249C22×C4×C7—21no—
250C22×C4×C7—21no—
251C22×C4×C7—21no—
252C22×C4×C7—21no—
253C22×C4×C7—21no—
254C22×C4×C7—21no—
255C22×C4×C7—21no—
256C22×C4×C7—44no—
257C22×C4×C7—44no—
258C22×C4×C7—44no—
259C22×C4×C7—44no—
260C22×C4×C7—44no—
261C22×C4×C7—44no—
262C22×C4×C7C2×D412yes—
263C22×C4×C7C2×D412yes—
264C22×C4×C7C2×D412yes—
265C22×C4×C7C2×D412yes—
266C22×C4×C7C2×D412yes—
267C22×C4×C7#4112yes—
268C22×C4×C7#4112yes—
269C22×C4×C7#4112yes—
270C22×C4×C7#4112yes—
271C22×C4×C7#4112yes—
272C7×C4⋊C4—28no—
273C7×C4⋊C4—44no—
274C7×C4⋊C4—44no—
275C7×C4⋊C4—44no—
276C7×C4⋊C4—44no—
277C7×C22⋊C4—28no—
278C7×C22⋊C4—28no—
279C7×C22⋊C4—44no—
280C7×C22⋊C4—44no—
281C7×C22⋊C4—44no—
282C7×C22⋊C4—44no—
283C42×C7—44no—
284C24×C4C22×C711yescharacteristic
285C22×C4⋊C4C22×C711yescharacteristic
286C22×C4⋊C4C22×C711yescharacteristic
287C22×C4⋊C4C22×C711yescharacteristic
288C22×C4⋊C4C22×C711yescharacteristic
289C22×C4⋊C4C22×C711yescharacteristic
290C22×C22⋊C4C22×C711yescharacteristic
291C22×C22⋊C4C22×C711yescharacteristic
292C22×C22⋊C4C22×C711yescharacteristic
293C22×C22⋊C4C22×C711yescharacteristic
294C22×C22⋊C4C22×C711yescharacteristic
295C22×C22⋊C4C22×C711yescharacteristic
296C22×C42C22×C711yescharacteristic
297#388—24no—
298#387—24no—
299#385—24no—
300#381—24no—
301C2×#95C22×C711yescharacteristic
302C2×#95C22×C711yescharacteristic
303C2×#95C22×C711yescharacteristic
304C2×#95C22×C711yescharacteristic
305C2×#95C22×C711yescharacteristic
306C2×#95C22×C711yescharacteristic
307C2×#95C22×C711yescharacteristic
308C2×#95C22×C711yescharacteristic
309C2×#95C22×C711yescharacteristic
310C2×#95C22×C711yescharacteristic
311C2×#95C22×C711yescharacteristic
312C2×#95C22×C711yescharacteristic
313C2×#95C22×C711yescharacteristic
314C2×#95C22×C711yescharacteristic
315C2×#95C22×C711yescharacteristic
316C2×#95C22×C711yescharacteristic
317C2×#95C22×C711yescharacteristic
318C2×#95C22×C711yescharacteristic
319C2×#95C22×C711yescharacteristic
320C2×#95C22×C711yescharacteristic
321C2×#95C22×C711yescharacteristic
322C2×#95C22×C711yescharacteristic
323C23×C7—22no—
324C23×C7—22no—
325C23×C7—22no—
326C23×C7—22no—
327C23×C7—22no—
328C23×C7—22no—
329C23×C7—22no—
330C23×C7—22no—
331C23×C7—22no—
332C23×C7—22no—
333C23×C7—22no—
334C23×C7—22no—
335C23×C7—22no—
336C23×C7—22no—
337C23×C7—22no—
338C23×C7—22no—
339C23×C7—22no—
340C23×C7—22no—
341C23×C7—41no—
342C23×C7—41no—
343C23×C7—41no—
344C23×C7—41no—
345C23×C7—41no—
346C23×C7—41no—
347C23×C7—41no—
348C23×C7—41no—
349C23×C7—41no—
350C23×C7—41no—
351C23×C7—41no—
352C23×C7—41no—
353C23×C7—41no—
354C23×C7—41no—
355C23×C7—41no—
356C23×C7—41no—
357C23×C7#12314yes—
358C23×C7C22×D411yescharacteristic
359C23×C7C22×D411yescharacteristic
360C23×C7C2×#4111yescharacteristic
361C23×C7C2×#4111yescharacteristic
362C23×C7C2×#4111yescharacteristic
363C23×C7C2×#4111yescharacteristic
364C23×C7C2×#4111yescharacteristic
365C23×C7C2×#4111yescharacteristic
366C23×C7C2×#4111yescharacteristic
367C23×C7H(5,𝔽2)11yescharacteristic
368C23×C7H(5,𝔽2)11yescharacteristic
369C23×C7H(5,𝔽2)11yescharacteristic
370C23×C72−1+411yescharacteristic
371C23×C72−1+411yescharacteristic
372C23×C72−1+411yescharacteristic
373C2×C4×C7—22no—
374C2×C4×C7—22no—
375C2×C4×C7—22no—
376C2×C4×C7—22no—
377C2×C4×C7—22no—
378C2×C4×C7—22no—
379C2×C4×C7—22no—
380C2×C4×C7—22no—
381C2×C4×C7—22no—
382C2×C4×C7—22no—
383C2×C4×C7—22no—
384C2×C4×C7—22no—
385C2×C4×C7—22no—
386C2×C4×C7—22no—
387C2×C4×C7—22no—
388C2×C4×C7—22no—
389C2×C4×C7—22no—
390C2×C4×C7—22no—
391C2×C4×C7—22no—
392C2×C4×C7—22no—
393C2×C4×C7—22no—
394C2×C4×C7—22no—
395C2×C4×C7—22no—
396C2×C4×C7—22no—
397C2×C4×C7—22no—
398C2×C4×C7—22no—
399C2×C4×C7—22no—
400C2×C4×C7—22no—
401C2×C4×C7—22no—
402C2×C4×C7—22no—
403C2×C4×C7—416no—
404C2×C4×C7—41no—
405C2×C4×C7—41no—
406C2×C4×C7—41no—
407C2×C4×C7—41no—
408C2×C4×C7—41no—
409C2×C4×C7—41no—
410C2×C4×C7—41no—
411C2×C4×C7—41no—
412C2×C4×C7—41no—
413C2×C4×C7—41no—
414C2×C4×C7—41no—
415C2×C4×C7—41no—
416C2×C4×C7—41no—
417C2×C4×C7—41no—
418C2×C4×C7—41no—
419C2×C4×C7—41no—
420C2×C4×C7—41no—
421C2×C4×C7—41no—
422C2×C4×C7—41no—
423C2×C4×C7—41no—
424C2×C4×C7—41no—
425C2×C4×C7—41no—
426C2×C4×C7—41no—
427C2×C4×C7—41no—
428C2×C4×C7—41no—
429C2×C4×C7—41no—
430C2×C4×C7—41no—
431C2×C4×C7—41no—
432C2×C4×C7—41no—
433C2×C4×C7—41no—
434C2×C4×C7—41no—
435C2×C4×C7—41no—
436C2×C4×C7—41no—
437C2×C4×C7—41no—
438C2×C4×C7—41no—
439C2×C4×C7—41no—
440C2×C4×C7—41no—
441C2×C4×C7—41no—
442C2×C4×C7—41no—
443C2×C4×C7—41no—
444C2×C4×C7—41no—
445C2×C4×C7—41no—
446C2×C4×C7—41no—
447C2×C4×C7—41no—
448C2×C4×C7—41no—
449C2×C4×C7—41no—
450C2×C4×C7—41no—
451C2×C4×C7—41no—
452C2×C4×C7—41no—
453C2×C4×C7—41no—
454C2×C4×C7—41no—
455C2×C4×C7—41no—
456C2×C4×C7—41no—
457C2×C4×C7—41no—
458C2×C4×C7—41no—
459C2×C4×C7—41no—
460C2×C4×C7—41no—
461C2×C4×C7—41no—
462C2×C4×C7—41no—
463C2×C4×C7—41no—
464C2×C4×C7—41no—
465C2×C4×C7—41no—
466C2×C4×C7—41no—
467C2×C4×C7—41no—
468C2×C4×C7—41no—
469C2×C4×C7—41no—
470C2×C4×C7—41no—
471C2×C4×C7—41no—
472C25C23×C711yescharacteristic
473C23×C4—22no—
474C23×C4—22no—
475C23×C4—22no—
476C23×C4—22no—
477C23×C4—22no—
478C23×C4—41no—
479C23×C4—41no—
480C23×C4C23×C711yescharacteristic
481C23×C4C23×C711yescharacteristic
482C23×C4C23×C711yescharacteristic
483C23×C4C23×C711yescharacteristic
484C23×C4C23×C711yescharacteristic
485C23×C4C23×C711yescharacteristic
486C23×C4C23×C711yescharacteristic
487C23×C4C23×C711yescharacteristic
488C23×C4C23×C711yescharacteristic
489C23×C4C23×C711yescharacteristic
490C23×C4C23×C711yescharacteristic
491C23×C4C23×C711yescharacteristic
492C23×C4C23×C711yescharacteristic
493C23×C4C23×C711yescharacteristic
494C2×C4⋊C4—22no—
495C2×C4⋊C4—22no—
496C2×C4⋊C4—22no—
497C2×C4⋊C4—22no—
498C2×C4⋊C4—22no—
499C2×C4⋊C4—22no—
500C2×C4⋊C4—22no—
501C2×C4⋊C4—22no—
502C2×C4⋊C4—22no—
503C2×C4⋊C4—22no—
504C2×C4⋊C4—41no—
505C2×C4⋊C4—41no—
506C2×C4⋊C4—41no—
507C2×C4⋊C4—41no—
508C2×C4⋊C4—41no—
509C2×C22⋊C4—22no—
510C2×C22⋊C4—22no—
511C2×C22⋊C4—22no—
512C2×C22⋊C4—22no—
513C2×C22⋊C4—22no—
514C2×C22⋊C4—22no—
515C2×C22⋊C4—22no—
516C2×C22⋊C4—22no—
517C2×C22⋊C4—22no—
518C2×C22⋊C4—22no—
519C2×C22⋊C4—22no—
520C2×C22⋊C4—22no—
521C2×C22⋊C4—22no—
522C2×C22⋊C4—41no—
523C2×C22⋊C4—41no—
524C2×C22⋊C4—41no—
525C2×C22⋊C4—41no—
526C2×C22⋊C4C7×D414yes—
527C2×C42—22no—
528C2×C42—22no—
529C2×C42—41no—
530#95—22no—
531#95—22no—
532#95—22no—
533#95—22no—
534#95—22no—
535#95—22no—
536#95—22no—
537#95—22no—
538#95—22no—
539#95—22no—
540#95—22no—
541#95—22no—
542#95—22no—
543#95—22no—
544#95—22no—
545#95—41no—
546#95—41no—
547#95—41no—
548#95—41no—
549#95—41no—
550#95—41no—
551#95C7×D414yes—
552C22×C7—24no—
553C22×C7—24no—
554C22×C7—24no—
555C22×C7—42no—
556C22×C7—42no—
557C22×C7—42no—
558C22×C7—42no—
559C22×C7—42no—
560C22×C7—42no—
561C22×C7—42no—
562C22×C7—42no—
563C22×C7—42no—
564C22×C7—42no—
565C22×C7—42no—
566C22×C7—42no—
567C22×C7C2×#12311yescharacteristic
568C22×C7#52511yescharacteristic
569C22×C7#52511yescharacteristic
570C22×C7#52511yescharacteristic
571C22×C7#52911yescharacteristic
572C22×C7#52911yescharacteristic
573C22×C7#53611yescharacteristic
574C22×C7#53711yescharacteristic
575C22×C7#53811yescharacteristic
576C22×C7#53811yescharacteristic
577C22×C7#53911yescharacteristic
578C22×C7#53911yescharacteristic
579C22×C7#53911yescharacteristic
580C22×C7#54111yescharacteristic
581C22×C7#54211yescharacteristic
582C22×C7D4211yescharacteristic
583C22×C7#54611yescharacteristic
584C22×C7#54611yescharacteristic
585C22×C7#54611yescharacteristic
586C22×C7#54711yescharacteristic
587C22×C7#54711yescharacteristic
588C22×C7#54811yescharacteristic
589C22×C7#55111yescharacteristic
590C22×C7#55111yescharacteristic
591C22×C7#55211yescharacteristic
592C22×C7#55211yescharacteristic
593C22×C7#55211yescharacteristic
594C22×C7#55211yescharacteristic
595C22×C7#55211yescharacteristic
596C22×C7#55211yescharacteristic
597C22×C7#55511yescharacteristic
598C22×C7#55911yescharacteristic
599C22×C7#55911yescharacteristic
600C22×C7#56211yescharacteristic
601C22×C7#56311yescharacteristic
602C4×C7—42no—
603C4×C7—42no—
604C4×C7—42no—
605C4×C7—42no—
606C4×C7—42no—
607C4×C7—42no—
608C4×C7—42no—
609C4×C7—42no—
610C4×C7—42no—
611C4×C7—42no—
612C4×C7—81no—
613C4×C7—81no—
614C4×C7—81no—
615C4×C7—81no—
616C24—21no—
617C24—21no—
618C24—21no—
619C24—21no—
620C24—21no—
621C24—21no—
622C24—21no—
623C24—21no—
624C24—21no—
625C24—21no—
626C24—21no—
627C24—21no—
628C24C2×C7×D412yes—
629C24C7×#4112yes—
630C24C7×#4112yes—
631C24C24×C711yescharacteristic
632C22×C4—28no—
633C22×C4—21no—
634C22×C4—21no—
635C22×C4—21no—
636C22×C4—21no—
637C22×C4—21no—
638C22×C4—21no—
639C22×C4—21no—
640C22×C4—21no—
641C22×C4—21no—
642C22×C4—21no—
643C22×C4—21no—
644C22×C4—21no—
645C22×C4—21no—
646C22×C4—21no—
647C22×C4—21no—
648C22×C4—21no—
649C22×C4—21no—
650C22×C4—21no—
651C22×C4—21no—
652C22×C4—21no—
653C22×C4—21no—
654C22×C4—21no—
655C22×C4—21no—
656C22×C4—21no—
657C22×C4—21no—
658C22×C4—21no—
659C22×C4—21no—
660C22×C4—21no—
661C22×C4—21no—
662C22×C4—21no—
663C22×C4—21no—
664C22×C4—21no—
665C22×C4—21no—
666C22×C4—21no—
667C22×C4—21no—
668C22×C4—21no—
669C22×C4—21no—
670C22×C4—21no—
671C22×C4—21no—
672C22×C4—21no—
673C22×C4—21no—
674C22×C4—21no—
675C22×C4—21no—
676C22×C4—21no—
677C22×C4—21no—
678C22×C4—21no—
679C22×C4—21no—
680C22×C4—21no—
681C22×C4—21no—
682C22×C4—21no—
683C22×C4—21no—
684C22×C4—21no—
685C22×C4—21no—
686C22×C4—21no—
687C22×C4—21no—
688C22×C4—21no—
689C22×C4—21no—
690C22×C4—21no—
691C22×C4—21no—
692C22×C4—21no—
693C22×C4—21no—
694C22×C4—21no—
695C22×C4—21no—
696C22×C4—21no—
697C22×C4—21no—
698C22×C4—21no—
699C22×C4—21no—
700C22×C4—21no—
701C22×C4—21no—
702C22×C4—21no—
703C22×C4—21no—
704C22×C4—21no—
705C22×C4—21no—
706C22×C4—21no—
707C22×C4—21no—
708C22×C4—21no—
709C22×C4—21no—
710C22×C4—21no—
711C22×C4—21no—
712C22×C4—21no—
713C22×C4—21no—
714C22×C4—21no—
715C22×C4—21no—
716C22×C4—21no—
717C22×C4—21no—
718C22×C4—21no—
719C22×C4—21no—
720C22×C4—21no—
721C22×C4—44no—
722C22×C4—44no—
723C22×C4—44no—
724C22×C4—44no—
725C22×C4—44no—
726C22×C4—44no—
727C22×C4C2×C7×D412yes—
728C22×C4C2×C7×D412yes—
729C22×C4C2×C7×D412yes—
730C22×C4C2×C7×D412yes—
731C22×C4C2×C7×D412yes—
732C22×C4C7×#4112yes—
733C22×C4C7×#4112yes—
734C22×C4C7×#4112yes—
735C22×C4C7×#4112yes—
736C22×C4C7×#4112yes—
737C4⋊C4—28no—
738C4⋊C4—44no—
739C4⋊C4—44no—
740C4⋊C4—44no—
741C4⋊C4—44no—
742C22⋊C4—28no—
743C22⋊C4—28no—
744C22⋊C4—44no—
745C22⋊C4—44no—
746C22⋊C4—44no—
747C22⋊C4—44no—
748C42—44no—
749C2×C7—44no—
750C2×C7#241811yescharacteristic
751C2×C7#241911yescharacteristic
752C2×C7#245511yescharacteristic
753C2×C7#245811yescharacteristic
754C2×C7#245911yescharacteristic
755C2×C7#247511yescharacteristic
756C2×C7#248411yescharacteristic
757C2×C7#257511yescharacteristic
758C2×C7#260911yescharacteristic
759C2×C7#268111yescharacteristic
760C2×C7#269511yescharacteristic
761C2×C7#269811yescharacteristic
762C2×C7#274411yescharacteristic
763C2×C7#275111yescharacteristic
764C2×C7#277111yescharacteristic
765C23—22no—
766C23—22no—
767C23—22no—
768C23—22no—
769C23—22no—
770C23—22no—
771C23—22no—
772C23—22no—
773C23—22no—
774C23—22no—
775C23—22no—
776C23—22no—
777C23—22no—
778C23—22no—
779C23—22no—
780C23—22no—
781C23—22no—
782C23—22no—
783C23—41no—
784C23—41no—
785C23—41no—
786C23—41no—
787C23—41no—
788C23—41no—
789C23—41no—
790C23—41no—
791C23—41no—
792C23—41no—
793C23—41no—
794C23—41no—
795C23—41no—
796C23—41no—
797C23—41no—
798C23—41no—
799C23C7×#12314yes—
800C23C22×C7×D411yescharacteristic
801C23C22×C7×D411yescharacteristic
802C23C2×C7×#4111yescharacteristic
803C23C2×C7×#4111yescharacteristic
804C23C2×C7×#4111yescharacteristic
805C23C2×C7×#4111yescharacteristic
806C23C2×C7×#4111yescharacteristic
807C23C2×C7×#4111yescharacteristic
808C23C2×C7×#4111yescharacteristic
809C23C7×H(5,𝔽2)11yescharacteristic
810C23C7×H(5,𝔽2)11yescharacteristic
811C23C7×H(5,𝔽2)11yescharacteristic
812C23C7×2−1+411yescharacteristic
813C23C7×2−1+411yescharacteristic
814C23C7×2−1+411yescharacteristic
815C2×C4—22no—
816C2×C4—22no—
817C2×C4—22no—
818C2×C4—22no—
819C2×C4—22no—
820C2×C4—22no—
821C2×C4—22no—
822C2×C4—22no—
823C2×C4—22no—
824C2×C4—22no—
825C2×C4—22no—
826C2×C4—22no—
827C2×C4—22no—
828C2×C4—22no—
829C2×C4—22no—
830C2×C4—22no—
831C2×C4—22no—
832C2×C4—22no—
833C2×C4—22no—
834C2×C4—22no—
835C2×C4—22no—
836C2×C4—22no—
837C2×C4—22no—
838C2×C4—22no—
839C2×C4—22no—
840C2×C4—22no—
841C2×C4—22no—
842C2×C4—22no—
843C2×C4—22no—
844C2×C4—22no—
845C2×C4—416no—
846C2×C4—41no—
847C2×C4—41no—
848C2×C4—41no—
849C2×C4—41no—
850C2×C4—41no—
851C2×C4—41no—
852C2×C4—41no—
853C2×C4—41no—
854C2×C4—41no—
855C2×C4—41no—
856C2×C4—41no—
857C2×C4—41no—
858C2×C4—41no—
859C2×C4—41no—
860C2×C4—41no—
861C2×C4—41no—
862C2×C4—41no—
863C2×C4—41no—
864C2×C4—41no—
865C2×C4—41no—
866C2×C4—41no—
867C2×C4—41no—
868C2×C4—41no—
869C2×C4—41no—
870C2×C4—41no—
871C2×C4—41no—
872C2×C4—41no—
873C2×C4—41no—
874C2×C4—41no—
875C2×C4—41no—
876C2×C4—41no—
877C2×C4—41no—
878C2×C4—41no—
879C2×C4—41no—
880C2×C4—41no—
881C2×C4—41no—
882C2×C4—41no—
883C2×C4—41no—
884C2×C4—41no—
885C2×C4—41no—
886C2×C4—41no—
887C2×C4—41no—
888C2×C4—41no—
889C2×C4—41no—
890C2×C4—41no—
891C2×C4—41no—
892C2×C4—41no—
893C2×C4—41no—
894C2×C4—41no—
895C2×C4—41no—
896C2×C4—41no—
897C2×C4—41no—
898C2×C4—41no—
899C2×C4—41no—
900C2×C4—41no—
901C2×C4—41no—
902C2×C4—41no—
903C2×C4—41no—
904C2×C4—41no—
905C2×C4—41no—
906C2×C4—41no—
907C2×C4—41no—
908C2×C4—41no—
909C2×C4—41no—
910C2×C4—41no—
911C2×C4—41no—
912C2×C4—41no—
913C2×C4—41no—
914C7#1595311yescharacteristic, direct product factor, Sylow
915C22—24no—
916C22—24no—
917C22—24no—
918C22—42no—
919C22—42no—
920C22—42no—
921C22—42no—
922C22—42no—
923C22—42no—
924C22—42no—
925C22—42no—
926C22—42no—
927C22—42no—
928C22—42no—
929C22—42no—
930C22C2×C7×#12311yescharacteristic
931C22C7×#52511yescharacteristic
932C22C7×#52511yescharacteristic
933C22C7×#52511yescharacteristic
934C22C7×#52911yescharacteristic
935C22C7×#52911yescharacteristic
936C22C7×#53611yescharacteristic
937C22C7×#53711yescharacteristic
938C22C7×#53811yescharacteristic
939C22C7×#53811yescharacteristic
940C22C7×#53911yescharacteristic
941C22C7×#53911yescharacteristic
942C22C7×#53911yescharacteristic
943C22C7×#54111yescharacteristic
944C22C7×#54211yescharacteristic
945C22C7×D4211yescharacteristic
946C22C7×#54611yescharacteristic
947C22C7×#54611yescharacteristic
948C22C7×#54611yescharacteristic
949C22C7×#54711yescharacteristic
950C22C7×#54711yescharacteristic
951C22C7×#54811yescharacteristic
952C22C7×#55111yescharacteristic
953C22C7×#55111yescharacteristic
954C22C7×#55211yescharacteristic
955C22C7×#55211yescharacteristic
956C22C7×#55211yescharacteristic
957C22C7×#55211yescharacteristic
958C22C7×#55211yescharacteristic
959C22C7×#55211yescharacteristic
960C22C7×#55511yescharacteristic
961C22C7×#55911yescharacteristic
962C22C7×#55911yescharacteristic
963C22C7×#56211yescharacteristic
964C22C7×#56311yescharacteristic
965C4—42no—
966C4—42no—
967C4—42no—
968C4—42no—
969C4—42no—
970C4—42no—
971C4—42no—
972C4—42no—
973C4—42no—
974C4—42no—
975C4—81no—
976C4—81no—
977C4—81no—
978C4—81no—
979C2—44no—
980C2C7×#241811yescharacteristic
981C2C7×#241911yescharacteristic
982C2C7×#245511yescharacteristic
983C2C7×#245811yescharacteristic
984C2C7×#245911yescharacteristic
985C2C7×#247511yescharacteristic
986C2C7×#248411yescharacteristic
987C2C7×#257511yescharacteristic
988C2C7×#260911yescharacteristic
989C2C7×#268111yescharacteristic
990C2C7×#269511yescharacteristic
991C2C7×#269811yescharacteristic
992C2C7×#274411yescharacteristic
993C2C7×#275111yescharacteristic
994C2C7×#277111yescharacteristic
subgroupG/H
center, socleC24×C7C24
commutator, Frattini, cosocleC24C24×C7
prime radicalC25×C7C23
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C24×C7 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C7×#387C2semidirect
5. C7×#1445C2semidirect
6. C7×#1442C2semidirect
7. C7×#1442C2semidirect
8. C7×#1442C2semidirect
9. C7×#1442C2semidirect
10. C7×#1441C2semidirect
14. C7×#1436C2semidirect
55. #15953C7direct (N × H)
137. C2×#387C2×C7semidirect
140. #1445C2×C7semidirect
141. #1442C2×C7semidirect
142. #1442C2×C7semidirect
143. #1442C2×C7semidirect
144. #1442C2×C7semidirect
145. #1441C2×C7semidirect
149. #1436C2×C7semidirect
914. C7#15953direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C7×#3882
C2×C7×#3872
C2×C7×#3852
C2×C7×#3812
C7×#14452
C7×#14422
C7×#14412
C7×#14402
C7×#14392
C7×#14362
C7×C22⋊#952
#159537