Finite Group Databasebeta

← C7×#15117 #13192333

Subgroups — C7×#15117 #13192333

Order 1792.

1434 conjugacy classes of subgroups.

The subgroup lattice has 986 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C7×#388C211yesmaximal, characteristic
2C2×C7×#388C211yesmaximal, characteristic
3C2×C7×#387C211yesmaximal, characteristic, complemented
4C2×C7×#376C211yesmaximal, characteristic, complemented
5C7×#1443C211yesmaximal, characteristic, complemented
6C7×#1442C211yesmaximal, characteristic, complemented
7C7×#1441C211yesmaximal, characteristic, complemented
8C7×#1441C211yesmaximal, characteristic, complemented
9C7×#1440C211yesmaximal, characteristic
10C7×#1439C211yesmaximal, characteristic
11C7×#1439C211yesmaximal, characteristic
12C7×#1439C211yesmaximal, characteristic
13C7×#1437C211yesmaximal, characteristic
14C7×#1436C211yesmaximal, characteristic, complemented
15C7×C4⋊#95C211yesmaximal, characteristic, complemented
16C22×C7×C4⋊C4C2211yescharacteristic
17C22×C7×C4⋊C4C2211yescharacteristic
18C22×C7×C4⋊C4C2211yescharacteristic
19C22×C7×C4⋊C4C2211yescharacteristic
20C22×C7×C4⋊C4C2211yescharacteristic
21C22×C7×C22⋊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
29C22×C42×C7C2211yescharacteristic
30C22×C42×C7C2211yescharacteristic
31C7×#388—24no—
32C7×#388—24no—
33C7×#387—24no—
34C7×#376—24no—
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#15117C711yesmaximal, characteristic, direct product factor, Sylow
56C25×C7C2311yescharacteristic
57C23×C4×C7C2311yescharacteristic
58C23×C4×C7C2311yescharacteristic
59C23×C4×C7C2311yescharacteristic
60C23×C4×C7C2311yescharacteristic
61C23×C4×C7C2311yescharacteristic
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
71C2×C7×C4⋊C4—22no—
72C2×C7×C4⋊C4—22no—
73C2×C7×C4⋊C4—22no—
74C2×C7×C4⋊C4—22no—
75C2×C7×C4⋊C4—22no—
76C2×C7×C4⋊C4—22no—
77C2×C7×C4⋊C4—22no—
78C2×C7×C4⋊C4—22no—
79C2×C7×C4⋊C4—22no—
80C2×C7×C4⋊C4—22no—
81C2×C7×C4⋊C4—22no—
82C2×C7×C4⋊C4—41no—
83C2×C7×C4⋊C4—41no—
84C2×C7×C4⋊C4—41no—
85C2×C7×C4⋊C4—41no—
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—22no—
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—41no—
104C2×C7×C22⋊C4—41no—
105C2×C7×C22⋊C4—41no—
106C2×C7×C22⋊C4—41no—
107C2×C42×C7—22no—
108C2×C42×C7—22no—
109C2×C42×C7—22no—
110C2×C42×C7—22no—
111C2×C42×C7—22no—
112C2×C42×C7—22no—
113C2×C42×C7—22no—
114C2×C42×C7D414yes—
115C2×C42×C7D414yes—
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—22no—
130C7×#95—22no—
131C7×#95—22no—
132C7×#95—41no—
133C7×#95—41no—
134C7×#95—41no—
135C7×#95—41no—
136C2×#388C2×C711yescharacteristic
137C2×#388C2×C711yescharacteristic
138C2×#387C2×C711yescharacteristic, complemented
139C2×#376C2×C711yescharacteristic, complemented
140#1443C2×C711yescharacteristic, complemented
141#1442C2×C711yescharacteristic, complemented
142#1441C2×C711yescharacteristic, complemented
143#1441C2×C711yescharacteristic, complemented
144#1440C2×C711yescharacteristic
145#1439C2×C711yescharacteristic
146#1439C2×C711yescharacteristic
147#1439C2×C711yescharacteristic
148#1437C2×C711yescharacteristic
149#1436C2×C711yescharacteristic, complemented
150C4⋊#95C2×C711yescharacteristic, complemented
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×C7—21no—
164C24×C7—21no—
165C24×C7#4112yes—
166C24×C7C2411yescharacteristic
167C22×C4×C7—21no—
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×C7C2×D412yes—
252C22×C4×C7C2×D412yes—
253C22×C4×C7C2×D412yes—
254C22×C4×C7C2×D412yes—
255C22×C4×C7C2×D412yes—
256C22×C4×C7C2×D412yes—
257C22×C4×C7#4112yes—
258C22×C4×C7#4112yes—
259C22×C4×C7#4112yes—
260C22×C4×C7#4112yes—
261C22×C4×C7#4112yes—
262C22×C4×C7#4112yes—
263C22×C4×C7#4112yes—
264C22×C4×C7#4112yes—
265C7×C4⋊C4—28no—
266C7×C4⋊C4—44no—
267C7×C4⋊C4—44no—
268C7×C4⋊C4—44no—
269C7×C4⋊C4—44no—
270C7×C22⋊C4—28no—
271C7×C22⋊C4—28no—
272C7×C22⋊C4—44no—
273C7×C22⋊C4—44no—
274C7×C22⋊C4—44no—
275C7×C22⋊C4—44no—
276C7×C22⋊C4—44no—
277C42×C7—28no—
278C42×C7—28no—
279C42×C7—28no—
280C22×C4⋊C4C22×C711yescharacteristic
281C22×C4⋊C4C22×C711yescharacteristic
282C22×C4⋊C4C22×C711yescharacteristic
283C22×C4⋊C4C22×C711yescharacteristic
284C22×C4⋊C4C22×C711yescharacteristic
285C22×C22⋊C4C22×C711yescharacteristic
286C22×C22⋊C4C22×C711yescharacteristic
287C22×C22⋊C4C22×C711yescharacteristic
288C22×C22⋊C4C22×C711yescharacteristic
289C22×C22⋊C4C22×C711yescharacteristic
290C22×C22⋊C4C22×C711yescharacteristic
291C22×C22⋊C4C22×C711yescharacteristic
292C22×C42C22×C711yescharacteristic
293C22×C42C22×C711yescharacteristic
294C22×C42C22×C711yescharacteristic
295#388—24no—
296#388—24no—
297#387—24no—
298#376—24no—
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
313C2×#95C22×C711yescharacteristic
314C2×#95C22×C711yescharacteristic
315C2×#95C22×C711yescharacteristic
316C2×#95C22×C711yescharacteristic
317C2×#95C22×C711yescharacteristic
318C2×#95C22×C711yescharacteristic
319C23×C7—22no—
320C23×C7—22no—
321C23×C7—22no—
322C23×C7—22no—
323C23×C7—22no—
324C23×C7—22no—
325C23×C7—22no—
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×C7—41no—
349C23×C7—41no—
350C23×C7—41no—
351C23×C7—41no—
352C23×C7—41no—
353C23×C7—41no—
354C23×C7C22×D411yescharacteristic
355C23×C7C22×D411yescharacteristic
356C23×C7C2×#4111yescharacteristic
357C23×C7C2×#4111yescharacteristic
358C23×C7C2×#4111yescharacteristic
359C23×C7C2×#4111yescharacteristic
360C23×C7C2×#4111yescharacteristic
361C23×C7C2×#4111yescharacteristic
362C23×C7C2×#4111yescharacteristic
363C23×C7C2×#4111yescharacteristic
364C23×C7C2×#4111yescharacteristic
365C23×C7H(5,𝔽2)11yescharacteristic
366C23×C7H(5,𝔽2)11yescharacteristic
367C23×C72−1+411yescharacteristic
368C23×C72−1+411yescharacteristic
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—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—22no—
404C2×C4×C7—22no—
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#12114yes—
466C2×C4×C7#12314yes—
467C25C23×C711yescharacteristic
468C23×C4C23×C711yescharacteristic
469C23×C4C23×C711yescharacteristic
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
482C2×C4⋊C4—22no—
483C2×C4⋊C4—22no—
484C2×C4⋊C4—22no—
485C2×C4⋊C4—22no—
486C2×C4⋊C4—22no—
487C2×C4⋊C4—22no—
488C2×C4⋊C4—22no—
489C2×C4⋊C4—22no—
490C2×C4⋊C4—22no—
491C2×C4⋊C4—22no—
492C2×C4⋊C4—22no—
493C2×C4⋊C4—41no—
494C2×C4⋊C4—41no—
495C2×C4⋊C4—41no—
496C2×C4⋊C4—41no—
497C2×C22⋊C4—22no—
498C2×C22⋊C4—22no—
499C2×C22⋊C4—22no—
500C2×C22⋊C4—22no—
501C2×C22⋊C4—22no—
502C2×C22⋊C4—22no—
503C2×C22⋊C4—22no—
504C2×C22⋊C4—22no—
505C2×C22⋊C4—22no—
506C2×C22⋊C4—22no—
507C2×C22⋊C4—22no—
508C2×C22⋊C4—22no—
509C2×C22⋊C4—22no—
510C2×C22⋊C4—22no—
511C2×C22⋊C4—22no—
512C2×C22⋊C4—22no—
513C2×C22⋊C4—22no—
514C2×C22⋊C4—41no—
515C2×C22⋊C4—41no—
516C2×C22⋊C4—41no—
517C2×C22⋊C4—41no—
518C2×C42—22no—
519C2×C42—22no—
520C2×C42—22no—
521C2×C42—22no—
522C2×C42—22no—
523C2×C42—22no—
524C2×C42—22no—
525C2×C42C7×D414yes—
526C2×C42C7×D414yes—
527#95—22no—
528#95—22no—
529#95—22no—
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—41no—
544#95—41no—
545#95—41no—
546#95—41no—
547C22×C7—42no—
548C22×C7—42no—
549C22×C7—42no—
550C22×C7—42no—
551C22×C7—42no—
552C22×C7—42no—
553C22×C7—42no—
554C22×C7—81no—
555C22×C7—81no—
556C22×C7—81no—
557C22×C7—81no—
558C22×C7—81no—
559C22×C7—81no—
560C22×C7—81no—
561C22×C7—81no—
562C22×C7C2×#12111yescharacteristic
563C22×C7C2×#12311yescharacteristic
564C22×C7#52511yescharacteristic
565C22×C7#52511yescharacteristic
566C22×C7#52511yescharacteristic
567C22×C7#52511yescharacteristic
568C22×C7#52911yescharacteristic
569C22×C7#52911yescharacteristic
570C22×C7#52911yescharacteristic
571C22×C7#52911yescharacteristic
572C22×C7#53211yescharacteristic
573C22×C7#53211yescharacteristic
574C22×C7#53211yescharacteristic
575C22×C7#53511yescharacteristic
576C22×C7#53611yescharacteristic
577C22×C7#53711yescharacteristic
578C22×C7#53711yescharacteristic
579C22×C7#54211yescharacteristic
580C22×C7#54211yescharacteristic
581C22×C7#55111yescharacteristic
582C22×C7#55111yescharacteristic
583C22×C7#55111yescharacteristic
584C22×C7#55111yescharacteristic
585C22×C7#55211yescharacteristic
586C22×C7#55211yescharacteristic
587C22×C7#55211yescharacteristic
588C22×C7#55211yescharacteristic
589C22×C7#55211yescharacteristic
590C22×C7#55211yescharacteristic
591C22×C7#55311yescharacteristic
592C22×C7#55311yescharacteristic
593C22×C7#55511yescharacteristic
594C22×C7#55511yescharacteristic
595C22×C7#55611yescharacteristic
596C22×C7#55611yescharacteristic
597C4×C7—24no—
598C4×C7—24no—
599C4×C7—42no—
600C4×C7—42no—
601C4×C7—42no—
602C4×C7—42no—
603C4×C7—42no—
604C4×C7—42no—
605C4×C7—42no—
606C4×C7—42no—
607C4×C7—81no—
608C4×C7—81no—
609C4×C7—81no—
610C4×C7—81no—
611C24—21no—
612C24—21no—
613C24—21no—
614C24—21no—
615C24—21no—
616C24—21no—
617C24—21no—
618C24—21no—
619C24—21no—
620C24—21no—
621C24—21no—
622C24—21no—
623C24—21no—
624C24—21no—
625C24C7×#4112yes—
626C24C24×C711yescharacteristic
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×C4C2×C7×D412yes—
712C22×C4C2×C7×D412yes—
713C22×C4C2×C7×D412yes—
714C22×C4C2×C7×D412yes—
715C22×C4C2×C7×D412yes—
716C22×C4C2×C7×D412yes—
717C22×C4C7×#4112yes—
718C22×C4C7×#4112yes—
719C22×C4C7×#4112yes—
720C22×C4C7×#4112yes—
721C22×C4C7×#4112yes—
722C22×C4C7×#4112yes—
723C22×C4C7×#4112yes—
724C22×C4C7×#4112yes—
725C4⋊C4—28no—
726C4⋊C4—44no—
727C4⋊C4—44no—
728C4⋊C4—44no—
729C4⋊C4—44no—
730C22⋊C4—28no—
731C22⋊C4—28no—
732C22⋊C4—44no—
733C22⋊C4—44no—
734C22⋊C4—44no—
735C22⋊C4—44no—
736C22⋊C4—44no—
737C42—28no—
738C42—28no—
739C42—28no—
740C2×C7—82no—
741C2×C7#239211yescharacteristic
742C2×C7#248511yescharacteristic
743C2×C7#249811yescharacteristic
744C2×C7#252711yescharacteristic
745C2×C7#252911yescharacteristic
746C2×C7#253011yescharacteristic
747C2×C7#253211yescharacteristic
748C2×C7#260111yescharacteristic
749C2×C7#260311yescharacteristic
750C2×C7#260411yescharacteristic
751C2×C7#260911yescharacteristic
752C2×C7#261011yescharacteristic
753C2×C7#261111yescharacteristic
754C2×C7#262011yescharacteristic
755C2×C7#285411yescharacteristic
756C23—22no—
757C23—22no—
758C23—22no—
759C23—22no—
760C23—22no—
761C23—22no—
762C23—22no—
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—
784C23—41no—
785C23—41no—
786C23—41no—
787C23—41no—
788C23—41no—
789C23—41no—
790C23—41no—
791C23C22×C7×D411yescharacteristic
792C23C22×C7×D411yescharacteristic
793C23C2×C7×#4111yescharacteristic
794C23C2×C7×#4111yescharacteristic
795C23C2×C7×#4111yescharacteristic
796C23C2×C7×#4111yescharacteristic
797C23C2×C7×#4111yescharacteristic
798C23C2×C7×#4111yescharacteristic
799C23C2×C7×#4111yescharacteristic
800C23C2×C7×#4111yescharacteristic
801C23C2×C7×#4111yescharacteristic
802C23C7×H(5,𝔽2)11yescharacteristic
803C23C7×H(5,𝔽2)11yescharacteristic
804C23C7×2−1+411yescharacteristic
805C23C7×2−1+411yescharacteristic
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—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—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—
898C2×C4—41no—
899C2×C4—41no—
900C2×C4—41no—
901C2×C4—41no—
902C2×C4C7×#12114yes—
903C2×C4C7×#12314yes—
904C7#1511711yescharacteristic, direct product factor, Sylow
905C22—42no—
906C22—42no—
907C22—42no—
908C22—42no—
909C22—42no—
910C22—42no—
911C22—42no—
912C22—81no—
913C22—81no—
914C22—81no—
915C22—81no—
916C22—81no—
917C22—81no—
918C22—81no—
919C22—81no—
920C22C2×C7×#12111yescharacteristic
921C22C2×C7×#12311yescharacteristic
922C22C7×#52511yescharacteristic
923C22C7×#52511yescharacteristic
924C22C7×#52511yescharacteristic
925C22C7×#52511yescharacteristic
926C22C7×#52911yescharacteristic
927C22C7×#52911yescharacteristic
928C22C7×#52911yescharacteristic
929C22C7×#52911yescharacteristic
930C22C7×#53211yescharacteristic
931C22C7×#53211yescharacteristic
932C22C7×#53211yescharacteristic
933C22C7×#53511yescharacteristic
934C22C7×#53611yescharacteristic
935C22C7×#53711yescharacteristic
936C22C7×#53711yescharacteristic
937C22C7×#54211yescharacteristic
938C22C7×#54211yescharacteristic
939C22C7×#55111yescharacteristic
940C22C7×#55111yescharacteristic
941C22C7×#55111yescharacteristic
942C22C7×#55111yescharacteristic
943C22C7×#55211yescharacteristic
944C22C7×#55211yescharacteristic
945C22C7×#55211yescharacteristic
946C22C7×#55211yescharacteristic
947C22C7×#55211yescharacteristic
948C22C7×#55211yescharacteristic
949C22C7×#55311yescharacteristic
950C22C7×#55311yescharacteristic
951C22C7×#55511yescharacteristic
952C22C7×#55511yescharacteristic
953C22C7×#55611yescharacteristic
954C22C7×#55611yescharacteristic
955C4—24no—
956C4—24no—
957C4—42no—
958C4—42no—
959C4—42no—
960C4—42no—
961C4—42no—
962C4—42no—
963C4—42no—
964C4—42no—
965C4—81no—
966C4—81no—
967C4—81no—
968C4—81no—
969C2—82no—
970C2C7×#239211yescharacteristic
971C2C7×#248511yescharacteristic
972C2C7×#249811yescharacteristic
973C2C7×#252711yescharacteristic
974C2C7×#252911yescharacteristic
975C2C7×#253011yescharacteristic
976C2C7×#253211yescharacteristic
977C2C7×#260111yescharacteristic
978C2C7×#260311yescharacteristic
979C2C7×#260411yescharacteristic
980C2C7×#260911yescharacteristic
981C2C7×#261011yescharacteristic
982C2C7×#261111yescharacteristic
983C2C7×#262011yescharacteristic
984C2C7×#285411yescharacteristic
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
3. C2×C7×#387C2semidirect
4. C2×C7×#376C2semidirect
5. C7×#1443C2semidirect
6. C7×#1442C2semidirect
7. C7×#1441C2semidirect
8. C7×#1441C2semidirect
14. C7×#1436C2semidirect
15. C7×C4⋊#95C2semidirect
55. #15117C7direct (N × H)
138. C2×#387C2×C7semidirect
139. C2×#376C2×C7semidirect
140. #1443C2×C7semidirect
141. #1442C2×C7semidirect
142. #1441C2×C7semidirect
143. #1441C2×C7semidirect
149. #1436C2×C7semidirect
150. C4⋊#95C2×C7semidirect
904. C7#15117direct (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×#3762
C7×#14432
C7×#14422
C7×#14412
C7×#14402
C7×#14392
C7×#14372
C7×#14362
C7×C4⋊#952
#151177