Finite Group Databasebeta

← C7×#15931 #13193147

Subgroups — C7×#15931 #13193147

Order 1792.

1342 conjugacy classes of subgroups.

The subgroup lattice has 980 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C7×#393C211yesmaximal, characteristic
2C2×C7×#383C211yesmaximal, characteristic, complemented
3C7×#1446C211yesmaximal, characteristic, complemented
4C7×#1446C211yesmaximal, characteristic, complemented
5C7×#1445C211yesmaximal, characteristic, complemented
6C7×#1443C211yesmaximal, characteristic, complemented
7C7×#1440C211yesmaximal, characteristic
8C7×#1440C211yesmaximal, characteristic
9C7×#1440C211yesmaximal, characteristic
10C7×#1439C211yesmaximal, characteristic
11C7×#1437C211yesmaximal, characteristic
12C7×#1437C211yesmaximal, characteristic
13C7×#1436C211yesmaximal, characteristic, complemented
14C7×#1434C211yesmaximal, characteristic, complemented
15C7×#1434C211yesmaximal, characteristic, complemented
16C23×C7×Q8C2211yescharacteristic
17C22×C7×C4⋊C4C2211yescharacteristic
18C22×C7×C22⋊C4C2211yescharacteristic
19C22×C7×C22⋊C4C2211yescharacteristic
20C22×C7×C22⋊C4C2211yescharacteristic
21C22×C7×C22⋊C4C2211yescharacteristic
22C22×C7×C22⋊C4C2211yescharacteristic
23C22×C7×C22⋊C4C2211yescharacteristic
24C22×C7×C22⋊C4C2211yescharacteristic
25C22×C42×C7C2211yescharacteristic
26C22×C42×C7C2211yescharacteristic
27C7×#393—24no—
28C7×#383—24no—
29C2×C7×#95C2211yescharacteristic
30C2×C7×#95C2211yescharacteristic
31C2×C7×#95C2211yescharacteristic
32C2×C7×#95C2211yescharacteristic
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
53#15931C711yesmaximal, characteristic, direct product factor, Sylow
54C25×C7C2311yescharacteristic
55C22×C7×Q8—22no—
56C22×C7×Q8—22no—
57C22×C7×Q8—22no—
58C22×C7×Q8—41no—
59C22×C7×Q8—41no—
60C22×C7×Q8—41no—
61C22×C7×Q8—41no—
62C23×C4×C7C2311yescharacteristic
63C23×C4×C7C2311yescharacteristic
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
76C2×C7×C4⋊C4—22no—
77C2×C7×C4⋊C4—22no—
78C2×C7×C4⋊C4—41no—
79C2×C7×C22⋊C4—22no—
80C2×C7×C22⋊C4—22no—
81C2×C7×C22⋊C4—22no—
82C2×C7×C22⋊C4—22no—
83C2×C7×C22⋊C4—22no—
84C2×C7×C22⋊C4—22no—
85C2×C7×C22⋊C4—22no—
86C2×C7×C22⋊C4—22no—
87C2×C7×C22⋊C4—22no—
88C2×C7×C22⋊C4—22no—
89C2×C7×C22⋊C4—22no—
90C2×C7×C22⋊C4—22no—
91C2×C7×C22⋊C4—22no—
92C2×C7×C22⋊C4—41no—
93C2×C7×C22⋊C4—41no—
94C2×C7×C22⋊C4—41no—
95C2×C7×C22⋊C4—41no—
96C2×C7×C22⋊C4—41no—
97C2×C7×C22⋊C4—41no—
98C2×C7×C22⋊C4—41no—
99C2×C7×C22⋊C4—41no—
100C2×C42×C7—22no—
101C2×C42×C7—22no—
102C2×C42×C7—22no—
103C2×C42×C7—22no—
104C2×C42×C7—22no—
105C2×C42×C7—41no—
106C7×#95—22no—
107C7×#95—22no—
108C7×#95—22no—
109C7×#95—22no—
110C7×#95—22no—
111C7×#95—22no—
112C7×#95—22no—
113C7×#95—22no—
114C7×#95—22no—
115C7×#95—22no—
116C7×#95—22no—
117C7×#95—22no—
118C7×#95—22no—
119C7×#95—41no—
120C7×#95—41no—
121C7×#95—41no—
122C7×#95—41no—
123C7×#95—41no—
124C7×#95—41no—
125C7×#95—41no—
126C7×#95—41no—
127C7×#95—41no—
128C7×#95—41no—
129C7×#95D414yes—
130C2×#393C2×C711yescharacteristic
131C2×#383C2×C711yescharacteristic, complemented
132#1446C2×C711yescharacteristic, complemented
133#1446C2×C711yescharacteristic, complemented
134#1445C2×C711yescharacteristic, complemented
135#1443C2×C711yescharacteristic, complemented
136#1440C2×C711yescharacteristic
137#1440C2×C711yescharacteristic
138#1440C2×C711yescharacteristic
139#1439C2×C711yescharacteristic
140#1437C2×C711yescharacteristic
141#1437C2×C711yescharacteristic
142#1436C2×C711yescharacteristic, complemented
143#1434C2×C711yescharacteristic, complemented
144#1434C2×C711yescharacteristic, complemented
145C24×C7—21no—
146C24×C7—21no—
147C24×C7—21no—
148C24×C7—21no—
149C24×C7—21no—
150C24×C7—21no—
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#4112yes—
160C24×C7C2411yescharacteristic
161C2×C7×Q8—44no—
162C2×C7×Q8—44no—
163C2×C7×Q8—44no—
164C2×C7×Q8—44no—
165C2×C7×Q8—44no—
166C2×C7×Q8—44no—
167C2×C7×Q8—44no—
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×C7C2×D412yes—
257C22×C4×C7C2×D412yes—
258C22×C4×C7C2×D412yes—
259C22×C4×C7#4112yes—
260C22×C4×C7#4112yes—
261C22×C4×C7#4112yes—
262C22×C4×C7#4112yes—
263C22×C4×C7#4112yes—
264C22×C4×C7#4112yes—
265C22×C4×C7#4112yes—
266C7×C4⋊C4—44no—
267C7×C22⋊C4—44no—
268C7×C22⋊C4—44no—
269C7×C22⋊C4—44no—
270C7×C22⋊C4—44no—
271C7×C22⋊C4—44no—
272C7×C22⋊C4—44no—
273C7×C22⋊C4—44no—
274C42×C7—28no—
275C42×C7—44no—
276C23×Q8C22×C711yescharacteristic
277C22×C4⋊C4C22×C711yescharacteristic
278C22×C22⋊C4C22×C711yescharacteristic
279C22×C22⋊C4C22×C711yescharacteristic
280C22×C22⋊C4C22×C711yescharacteristic
281C22×C22⋊C4C22×C711yescharacteristic
282C22×C22⋊C4C22×C711yescharacteristic
283C22×C22⋊C4C22×C711yescharacteristic
284C22×C22⋊C4C22×C711yescharacteristic
285C22×C42C22×C711yescharacteristic
286C22×C42C22×C711yescharacteristic
287#393—24no—
288#383—24no—
289C2×#95C22×C711yescharacteristic
290C2×#95C22×C711yescharacteristic
291C2×#95C22×C711yescharacteristic
292C2×#95C22×C711yescharacteristic
293C2×#95C22×C711yescharacteristic
294C2×#95C22×C711yescharacteristic
295C2×#95C22×C711yescharacteristic
296C2×#95C22×C711yescharacteristic
297C2×#95C22×C711yescharacteristic
298C2×#95C22×C711yescharacteristic
299C2×#95C22×C711yescharacteristic
300C2×#95C22×C711yescharacteristic
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
313C23×C7—22no—
314C23×C7—22no—
315C23×C7—22no—
316C23×C7—22no—
317C23×C7—22no—
318C23×C7—22no—
319C23×C7—22no—
320C23×C7—41no—
321C23×C7—41no—
322C23×C7—41no—
323C23×C7—41no—
324C23×C7—41no—
325C23×C7—41no—
326C23×C7—41no—
327C23×C7—41no—
328C23×C7—41no—
329C23×C7—41no—
330C23×C7—41no—
331C23×C7—41no—
332C23×C7—41no—
333C23×C7—41no—
334C23×C7—41no—
335C23×C7—41no—
336C23×C7—41no—
337C23×C7—41no—
338C23×C7—41no—
339C23×C7—41no—
340C23×C7—41no—
341C23×C7—41no—
342C23×C7—41no—
343C23×C7—41no—
344C23×C7—41no—
345C23×C7—41no—
346C23×C7—41no—
347C23×C7—41no—
348C23×C7C22×D411yescharacteristic
349C23×C7C2×#4111yescharacteristic
350C23×C7C2×#4111yescharacteristic
351C23×C7C2×#4111yescharacteristic
352C23×C7C2×#4111yescharacteristic
353C23×C7C2×#4111yescharacteristic
354C23×C7C2×#4111yescharacteristic
355C23×C7C2×#4111yescharacteristic
356C23×C7C2×#4111yescharacteristic
357C23×C7H(5,𝔽2)11yescharacteristic
358C23×C7H(5,𝔽2)11yescharacteristic
359C23×C7H(5,𝔽2)11yescharacteristic
360C23×C7H(5,𝔽2)11yescharacteristic
361C23×C72−1+411yescharacteristic
362C23×C72−1+411yescharacteristic
363C7×Q8—416no—
364C2×C4×C7—22no—
365C2×C4×C7—22no—
366C2×C4×C7—22no—
367C2×C4×C7—22no—
368C2×C4×C7—22no—
369C2×C4×C7—22no—
370C2×C4×C7—22no—
371C2×C4×C7—22no—
372C2×C4×C7—22no—
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—41no—
395C2×C4×C7—41no—
396C2×C4×C7—41no—
397C2×C4×C7—41no—
398C2×C4×C7—41no—
399C2×C4×C7—41no—
400C2×C4×C7—41no—
401C2×C4×C7—41no—
402C2×C4×C7—41no—
403C2×C4×C7—41no—
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—
462C25C23×C711yescharacteristic
463C22×Q8—22no—
464C22×Q8—22no—
465C22×Q8—22no—
466C22×Q8—41no—
467C22×Q8—41no—
468C22×Q8—41no—
469C22×Q8—41no—
470C23×C4C23×C711yescharacteristic
471C23×C4C23×C711yescharacteristic
472C23×C4C23×C711yescharacteristic
473C23×C4C23×C711yescharacteristic
474C23×C4C23×C711yescharacteristic
475C23×C4C23×C711yescharacteristic
476C23×C4C23×C711yescharacteristic
477C23×C4C23×C711yescharacteristic
478C23×C4C23×C711yescharacteristic
479C23×C4C23×C711yescharacteristic
480C23×C4C23×C711yescharacteristic
481C23×C4C23×C711yescharacteristic
482C23×C4C23×C711yescharacteristic
483C23×C4C23×C711yescharacteristic
484C2×C4⋊C4—22no—
485C2×C4⋊C4—22no—
486C2×C4⋊C4—41no—
487C2×C22⋊C4—22no—
488C2×C22⋊C4—22no—
489C2×C22⋊C4—22no—
490C2×C22⋊C4—22no—
491C2×C22⋊C4—22no—
492C2×C22⋊C4—22no—
493C2×C22⋊C4—22no—
494C2×C22⋊C4—22no—
495C2×C22⋊C4—22no—
496C2×C22⋊C4—22no—
497C2×C22⋊C4—22no—
498C2×C22⋊C4—22no—
499C2×C22⋊C4—22no—
500C2×C22⋊C4—41no—
501C2×C22⋊C4—41no—
502C2×C22⋊C4—41no—
503C2×C22⋊C4—41no—
504C2×C22⋊C4—41no—
505C2×C22⋊C4—41no—
506C2×C22⋊C4—41no—
507C2×C22⋊C4—41no—
508C2×C42—22no—
509C2×C42—22no—
510C2×C42—22no—
511C2×C42—22no—
512C2×C42—22no—
513C2×C42—41no—
514#95—22no—
515#95—22no—
516#95—22no—
517#95—22no—
518#95—22no—
519#95—22no—
520#95—22no—
521#95—22no—
522#95—22no—
523#95—22no—
524#95—22no—
525#95—22no—
526#95—22no—
527#95—41no—
528#95—41no—
529#95—41no—
530#95—41no—
531#95—41no—
532#95—41no—
533#95—41no—
534#95—41no—
535#95—41no—
536#95—41no—
537#95C7×D414yes—
538C22×C7—42no—
539C22×C7—42no—
540C22×C7—42no—
541C22×C7—42no—
542C22×C7—42no—
543C22×C7—42no—
544C22×C7—42no—
545C22×C7—81no—
546C22×C7—81no—
547C22×C7—81no—
548C22×C7—81no—
549C22×C7—81no—
550C22×C7—81no—
551C22×C7—81no—
552C22×C7—81no—
553C22×C7#52511yescharacteristic
554C22×C7#52911yescharacteristic
555C22×C7#52911yescharacteristic
556C22×C7#52911yescharacteristic
557C22×C7#52911yescharacteristic
558C22×C7#53211yescharacteristic
559C22×C7#53511yescharacteristic
560C22×C7#53811yescharacteristic
561C22×C7#53811yescharacteristic
562C22×C7#53911yescharacteristic
563C22×C7#53911yescharacteristic
564C22×C7#54211yescharacteristic
565C22×C7#54211yescharacteristic
566C22×C7#54211yescharacteristic
567C22×C7#54211yescharacteristic
568C22×C7#54611yescharacteristic
569C22×C7#54611yescharacteristic
570C22×C7#54711yescharacteristic
571C22×C7#54811yescharacteristic
572C22×C7#55111yescharacteristic
573C22×C7#55111yescharacteristic
574C22×C7#55111yescharacteristic
575C22×C7#55111yescharacteristic
576C22×C7#55111yescharacteristic
577C22×C7#55111yescharacteristic
578C22×C7#55111yescharacteristic
579C22×C7#55211yescharacteristic
580C22×C7#55511yescharacteristic
581C22×C7#55511yescharacteristic
582C22×C7#55511yescharacteristic
583C22×C7#55611yescharacteristic
584C22×C7#55611yescharacteristic
585C22×C7#55611yescharacteristic
586C22×C7#56011yescharacteristic
587C22×C7#56311yescharacteristic
588C4×C7—42no—
589C4×C7—42no—
590C4×C7—42no—
591C4×C7—42no—
592C4×C7—42no—
593C4×C7—42no—
594C4×C7—42no—
595C4×C7—42no—
596C4×C7—42no—
597C4×C7—42no—
598C4×C7—81no—
599C4×C7—81no—
600C4×C7—81no—
601C4×C7—81no—
602C24—21no—
603C24—21no—
604C24—21no—
605C24—21no—
606C24—21no—
607C24—21no—
608C24—21no—
609C24—21no—
610C24—21no—
611C24—21no—
612C24—21no—
613C24—21no—
614C24—21no—
615C24—21no—
616C24C7×#4112yes—
617C24C24×C711yescharacteristic
618C2×Q8—44no—
619C2×Q8—44no—
620C2×Q8—44no—
621C2×Q8—44no—
622C2×Q8—44no—
623C2×Q8—44no—
624C2×Q8—44no—
625C22×C4—21no—
626C22×C4—21no—
627C22×C4—21no—
628C22×C4—21no—
629C22×C4—21no—
630C22×C4—21no—
631C22×C4—21no—
632C22×C4—21no—
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×C4C2×C7×D412yes—
714C22×C4C2×C7×D412yes—
715C22×C4C2×C7×D412yes—
716C22×C4C7×#4112yes—
717C22×C4C7×#4112yes—
718C22×C4C7×#4112yes—
719C22×C4C7×#4112yes—
720C22×C4C7×#4112yes—
721C22×C4C7×#4112yes—
722C22×C4C7×#4112yes—
723C4⋊C4—44no—
724C22⋊C4—44no—
725C22⋊C4—44no—
726C22⋊C4—44no—
727C22⋊C4—44no—
728C22⋊C4—44no—
729C22⋊C4—44no—
730C22⋊C4—44no—
731C42—28no—
732C42—44no—
733C2×C7—82no—
734C2×C7#247411yescharacteristic
735C2×C7#247711yescharacteristic
736C2×C7#252111yescharacteristic
737C2×C7#252311yescharacteristic
738C2×C7#253211yescharacteristic
739C2×C7#256011yescharacteristic
740C2×C7#257211yescharacteristic
741C2×C7#257211yescharacteristic
742C2×C7#261011yescharacteristic
743C2×C7#268511yescharacteristic
744C2×C7#272311yescharacteristic
745C2×C7#273711yescharacteristic
746C2×C7#273711yescharacteristic
747C2×C7#275911yescharacteristic
748C2×C7#277511yescharacteristic
749C23—22no—
750C23—22no—
751C23—22no—
752C23—22no—
753C23—22no—
754C23—22no—
755C23—22no—
756C23—41no—
757C23—41no—
758C23—41no—
759C23—41no—
760C23—41no—
761C23—41no—
762C23—41no—
763C23—41no—
764C23—41no—
765C23—41no—
766C23—41no—
767C23—41no—
768C23—41no—
769C23—41no—
770C23—41no—
771C23—41no—
772C23—41no—
773C23—41no—
774C23—41no—
775C23—41no—
776C23—41no—
777C23—41no—
778C23—41no—
779C23—41no—
780C23—41no—
781C23—41no—
782C23—41no—
783C23—41no—
784C23C22×C7×D411yescharacteristic
785C23C2×C7×#4111yescharacteristic
786C23C2×C7×#4111yescharacteristic
787C23C2×C7×#4111yescharacteristic
788C23C2×C7×#4111yescharacteristic
789C23C2×C7×#4111yescharacteristic
790C23C2×C7×#4111yescharacteristic
791C23C2×C7×#4111yescharacteristic
792C23C2×C7×#4111yescharacteristic
793C23C7×H(5,𝔽2)11yescharacteristic
794C23C7×H(5,𝔽2)11yescharacteristic
795C23C7×H(5,𝔽2)11yescharacteristic
796C23C7×H(5,𝔽2)11yescharacteristic
797C23C7×2−1+411yescharacteristic
798C23C7×2−1+411yescharacteristic
799Q8—416no—
800C2×C4—22no—
801C2×C4—22no—
802C2×C4—22no—
803C2×C4—22no—
804C2×C4—22no—
805C2×C4—22no—
806C2×C4—22no—
807C2×C4—22no—
808C2×C4—22no—
809C2×C4—22no—
810C2×C4—22no—
811C2×C4—22no—
812C2×C4—22no—
813C2×C4—22no—
814C2×C4—22no—
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—41no—
831C2×C4—41no—
832C2×C4—41no—
833C2×C4—41no—
834C2×C4—41no—
835C2×C4—41no—
836C2×C4—41no—
837C2×C4—41no—
838C2×C4—41no—
839C2×C4—41no—
840C2×C4—41no—
841C2×C4—41no—
842C2×C4—41no—
843C2×C4—41no—
844C2×C4—41no—
845C2×C4—41no—
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—
898C7#1593111yescharacteristic, direct product factor, Sylow
899C22—42no—
900C22—42no—
901C22—42no—
902C22—42no—
903C22—42no—
904C22—42no—
905C22—42no—
906C22—81no—
907C22—81no—
908C22—81no—
909C22—81no—
910C22—81no—
911C22—81no—
912C22—81no—
913C22—81no—
914C22C7×#52511yescharacteristic
915C22C7×#52911yescharacteristic
916C22C7×#52911yescharacteristic
917C22C7×#52911yescharacteristic
918C22C7×#52911yescharacteristic
919C22C7×#53211yescharacteristic
920C22C7×#53511yescharacteristic
921C22C7×#53811yescharacteristic
922C22C7×#53811yescharacteristic
923C22C7×#53911yescharacteristic
924C22C7×#53911yescharacteristic
925C22C7×#54211yescharacteristic
926C22C7×#54211yescharacteristic
927C22C7×#54211yescharacteristic
928C22C7×#54211yescharacteristic
929C22C7×#54611yescharacteristic
930C22C7×#54611yescharacteristic
931C22C7×#54711yescharacteristic
932C22C7×#54811yescharacteristic
933C22C7×#55111yescharacteristic
934C22C7×#55111yescharacteristic
935C22C7×#55111yescharacteristic
936C22C7×#55111yescharacteristic
937C22C7×#55111yescharacteristic
938C22C7×#55111yescharacteristic
939C22C7×#55111yescharacteristic
940C22C7×#55211yescharacteristic
941C22C7×#55511yescharacteristic
942C22C7×#55511yescharacteristic
943C22C7×#55511yescharacteristic
944C22C7×#55611yescharacteristic
945C22C7×#55611yescharacteristic
946C22C7×#55611yescharacteristic
947C22C7×#56011yescharacteristic
948C22C7×#56311yescharacteristic
949C4—42no—
950C4—42no—
951C4—42no—
952C4—42no—
953C4—42no—
954C4—42no—
955C4—42no—
956C4—42no—
957C4—42no—
958C4—42no—
959C4—81no—
960C4—81no—
961C4—81no—
962C4—81no—
963C2—82no—
964C2C7×#247411yescharacteristic
965C2C7×#247711yescharacteristic
966C2C7×#252111yescharacteristic
967C2C7×#252311yescharacteristic
968C2C7×#253211yescharacteristic
969C2C7×#256011yescharacteristic
970C2C7×#257211yescharacteristic
971C2C7×#257211yescharacteristic
972C2C7×#261011yescharacteristic
973C2C7×#268511yescharacteristic
974C2C7×#272311yescharacteristic
975C2C7×#273711yescharacteristic
976C2C7×#273711yescharacteristic
977C2C7×#275911yescharacteristic
978C2C7×#277511yescharacteristic
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×#383C2semidirect
3. C7×#1446C2semidirect
4. C7×#1446C2semidirect
5. C7×#1445C2semidirect
6. C7×#1443C2semidirect
13. C7×#1436C2semidirect
14. C7×#1434C2semidirect
15. C7×#1434C2semidirect
53. #15931C7direct (N × H)
131. C2×#383C2×C7semidirect
132. #1446C2×C7semidirect
133. #1446C2×C7semidirect
134. #1445C2×C7semidirect
135. #1443C2×C7semidirect
142. #1436C2×C7semidirect
143. #1434C2×C7semidirect
144. #1434C2×C7semidirect
898. C7#15931direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C7×#3932
C2×C7×#3832
C7×#14462
C7×#14452
C7×#14432
C7×#14402
C7×#14392
C7×#14372
C7×#14362
C7×#14342
#159317