Finite Group Databasebeta

← C7×#14738 #13191954

Subgroups — C7×#14738 #13191954

Order 1792.

1794 conjugacy classes of subgroups.

The subgroup lattice has 1028 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C7×#400C211yesmaximal, characteristic, complemented
2C2×C7×#385C211yesmaximal, characteristic
3C2×C7×#385C211yesmaximal, characteristic
4C22×C7×#95C211yesmaximal, characteristic
5C7×#1445C211yesmaximal, characteristic, complemented
6C7×#1443C211yesmaximal, characteristic, complemented
7C7×#1443C211yesmaximal, characteristic, complemented
8C7×#1442C211yesmaximal, characteristic, complemented
9C7×#1442C211yesmaximal, characteristic, complemented
10C7×#1442C211yesmaximal, characteristic, complemented
11C7×#1441C211yesmaximal, characteristic, complemented
12C7×C22⋊#95C211yesmaximal, characteristic
13C7×C22⋊#95C211yesmaximal, characteristic
14C7×C22⋊#95C211yesmaximal, characteristic
15C7×C22⋊#95C211yesmaximal, characteristic
16C24×C4×C7C2211yescharacteristic
17C24×C4×C7C2211yescharacteristic
18C24×C4×C7C2211yescharacteristic
19C22×C7×C4⋊C4C2211yescharacteristic
20C22×C7×C4⋊C4C2211yescharacteristic
21C22×C7×C4⋊C4C2211yescharacteristic
22C22×C7×C4⋊C4C2211yescharacteristic
23C22×C7×C22⋊C4C2211yescharacteristic
24C22×C7×C22⋊C4C2211yescharacteristic
25C22×C7×C22⋊C4C2211yescharacteristic
26C22×C7×C22⋊C4C2211yescharacteristic
27C7×#400—24no—
28C7×#385—24no—
29C7×#385—24no—
30C2×C7×#95—24no—
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
53C2×C7×#95C2211yescharacteristic
54C2×C7×#95C2211yescharacteristic
55#14738C711yesmaximal, 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—22no—
63C23×C4×C7—22no—
64C23×C4×C7—22no—
65C23×C4×C7—22no—
66C23×C4×C7—22no—
67C23×C4×C7—22no—
68C23×C4×C7—22no—
69C23×C4×C7—22no—
70C23×C4×C7—22no—
71C23×C4×C7—22no—
72C23×C4×C7—41no—
73C23×C4×C7—41no—
74C23×C4×C7—41no—
75C23×C4×C7—41no—
76C23×C4×C7—41no—
77C23×C4×C7—41no—
78C23×C4×C7C2311yescharacteristic
79C23×C4×C7C2311yescharacteristic
80C23×C4×C7C2311yescharacteristic
81C23×C4×C7C2311yescharacteristic
82C23×C4×C7C2311yescharacteristic
83C23×C4×C7C2311yescharacteristic
84C23×C4×C7C2311yescharacteristic
85C23×C4×C7C2311yescharacteristic
86C23×C4×C7C2311yescharacteristic
87C23×C4×C7C2311yescharacteristic
88C23×C4×C7C2311yescharacteristic
89C23×C4×C7C2311yescharacteristic
90C23×C4×C7C2311yescharacteristic
91C23×C4×C7C2311yescharacteristic
92C2×C7×C4⋊C4—22no—
93C2×C7×C4⋊C4—22no—
94C2×C7×C4⋊C4—22no—
95C2×C7×C4⋊C4—22no—
96C2×C7×C4⋊C4—22no—
97C2×C7×C4⋊C4—22no—
98C2×C7×C4⋊C4—22no—
99C2×C7×C4⋊C4—22no—
100C2×C7×C4⋊C4—41no—
101C2×C7×C4⋊C4—41no—
102C2×C7×C4⋊C4—41no—
103C2×C7×C4⋊C4—41no—
104C2×C7×C22⋊C4—22no—
105C2×C7×C22⋊C4—22no—
106C2×C7×C22⋊C4—22no—
107C2×C7×C22⋊C4—22no—
108C2×C7×C22⋊C4—22no—
109C2×C7×C22⋊C4—22no—
110C2×C7×C22⋊C4—22no—
111C2×C7×C22⋊C4—22no—
112C2×C7×C22⋊C4—22no—
113C2×C7×C22⋊C4—22no—
114C2×C7×C22⋊C4D414yes—
115C2×C7×C22⋊C4Q814yes—
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—41no—
132C7×#95—41no—
133C7×#95—41no—
134C7×#95—41no—
135C7×#95—41no—
136C7×#95—41no—
137C7×#95—41no—
138C7×#95—41no—
139C7×#95D414yes—
140C2×#400C2×C711yescharacteristic, complemented
141C2×#385C2×C711yescharacteristic
142C2×#385C2×C711yescharacteristic
143C22×#95C2×C711yescharacteristic
144#1445C2×C711yescharacteristic, complemented
145#1443C2×C711yescharacteristic, complemented
146#1443C2×C711yescharacteristic, complemented
147#1442C2×C711yescharacteristic, complemented
148#1442C2×C711yescharacteristic, complemented
149#1442C2×C711yescharacteristic, complemented
150#1441C2×C711yescharacteristic, complemented
151C22⋊#95C2×C711yescharacteristic
152C22⋊#95C2×C711yescharacteristic
153C22⋊#95C2×C711yescharacteristic
154C22⋊#95C2×C711yescharacteristic
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×C7C2×Q812yes—
165C24×C7#4112yes—
166C24×C7#4112yes—
167C24×C7#4112yes—
168C24×C7#4112yes—
169C24×C7#4112yes—
170C24×C7C2411yescharacteristic
171C22×C4×C7—28no—
172C22×C4×C7—28no—
173C22×C4×C7—28no—
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—21no—
257C22×C4×C7—21no—
258C22×C4×C7—21no—
259C22×C4×C7—21no—
260C22×C4×C7—21no—
261C22×C4×C7—21no—
262C22×C4×C7—44no—
263C22×C4×C7—44no—
264C22×C4×C7—44no—
265C22×C4×C7—44no—
266C22×C4×C7—44no—
267C22×C4×C7—44no—
268C22×C4×C7—44no—
269C22×C4×C7—44no—
270C22×C4×C7—44no—
271C22×C4×C7—44no—
272C22×C4×C7—44no—
273C22×C4×C7—44no—
274C22×C4×C7—44no—
275C22×C4×C7—44no—
276C22×C4×C7—44no—
277C22×C4×C7—44no—
278C22×C4×C7—44no—
279C22×C4×C7—44no—
280C22×C4×C7C2×D412yes—
281C22×C4×C7C2×D412yes—
282C22×C4×C7C2×D412yes—
283C22×C4×C7C2×D412yes—
284C22×C4×C7C2×D412yes—
285C22×C4×C7C2×Q812yes—
286C22×C4×C7C2×Q812yes—
287C22×C4×C7#4112yes—
288C22×C4×C7#4112yes—
289C22×C4×C7#4112yes—
290C7×C4⋊C4—44no—
291C7×C4⋊C4—44no—
292C7×C4⋊C4—44no—
293C7×C4⋊C4—44no—
294C7×C22⋊C4—28no—
295C7×C22⋊C4—28no—
296C7×C22⋊C4—44no—
297C7×C22⋊C4—44no—
298C24×C4C22×C711yescharacteristic
299C24×C4C22×C711yescharacteristic
300C24×C4C22×C711yescharacteristic
301C22×C4⋊C4C22×C711yescharacteristic
302C22×C4⋊C4C22×C711yescharacteristic
303C22×C4⋊C4C22×C711yescharacteristic
304C22×C4⋊C4C22×C711yescharacteristic
305C22×C22⋊C4C22×C711yescharacteristic
306C22×C22⋊C4C22×C711yescharacteristic
307C22×C22⋊C4C22×C711yescharacteristic
308C22×C22⋊C4C22×C711yescharacteristic
309#400—24no—
310#385—24no—
311#385—24no—
312C2×#95—24no—
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
323C2×#95C22×C711yescharacteristic
324C2×#95C22×C711yescharacteristic
325C2×#95C22×C711yescharacteristic
326C2×#95C22×C711yescharacteristic
327C2×#95C22×C711yescharacteristic
328C2×#95C22×C711yescharacteristic
329C2×#95C22×C711yescharacteristic
330C2×#95C22×C711yescharacteristic
331C2×#95C22×C711yescharacteristic
332C2×#95C22×C711yescharacteristic
333C2×#95C22×C711yescharacteristic
334C2×#95C22×C711yescharacteristic
335C2×#95C22×C711yescharacteristic
336C2×#95C22×C711yescharacteristic
337C23×C7—22no—
338C23×C7—22no—
339C23×C7—22no—
340C23×C7—22no—
341C23×C7—22no—
342C23×C7—22no—
343C23×C7—22no—
344C23×C7—22no—
345C23×C7—22no—
346C23×C7—22no—
347C23×C7—22no—
348C23×C7—22no—
349C23×C7—22no—
350C23×C7—22no—
351C23×C7—22no—
352C23×C7—22no—
353C23×C7—22no—
354C23×C7—22no—
355C23×C7—22no—
356C23×C7—22no—
357C23×C7—22no—
358C23×C7—22no—
359C23×C7—22no—
360C23×C7—22no—
361C23×C7—22no—
362C23×C7—22no—
363C23×C7—22no—
364C23×C7—22no—
365C23×C7C22⋊Q814yes—
366C23×C7#12314yes—
367C23×C7#12414yes—
368C23×C7#12514yes—
369C23×C7#12514yes—
370C23×C7#12614yes—
371C23×C7#12614yes—
372C23×C7C22×D411yescharacteristic
373C23×C7C22×D411yescharacteristic
374C23×C7C22×Q811yescharacteristic
375C23×C7C2×#4111yescharacteristic
376C23×C7C2×#4111yescharacteristic
377C23×C7C2×#4111yescharacteristic
378C23×C7C2×#4111yescharacteristic
379C23×C7C2×#4111yescharacteristic
380C23×C7C2×#4111yescharacteristic
381C23×C7C2×#4111yescharacteristic
382C23×C7C2×#4111yescharacteristic
383C23×C7H(5,𝔽2)11yescharacteristic
384C23×C7H(5,𝔽2)11yescharacteristic
385C23×C7H(5,𝔽2)11yescharacteristic
386C23×C72−1+411yescharacteristic
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—22no—
406C2×C4×C7—22no—
407C2×C4×C7—22no—
408C2×C4×C7—22no—
409C2×C4×C7—22no—
410C2×C4×C7—22no—
411C2×C4×C7—22no—
412C2×C4×C7—22no—
413C2×C4×C7—22no—
414C2×C4×C7—22no—
415C2×C4×C7—22no—
416C2×C4×C7—22no—
417C2×C4×C7—416no—
418C2×C4×C7—416no—
419C2×C4×C7—416no—
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—
472C2×C4×C7—41no—
473C2×C4×C7—41no—
474C2×C4×C7—41no—
475C2×C4×C7—41no—
476C2×C4×C7—41no—
477C2×C4×C7—41no—
478C2×C4×C7—41no—
479C2×C4×C7—41no—
480C2×C4×C7—41no—
481C2×C4×C7—41no—
482C2×C4×C7—41no—
483C2×C4×C7—41no—
484C2×C4×C7—41no—
485C2×C4×C7—41no—
486C2×C4×C7—41no—
487C2×C4×C7—41no—
488C25C23×C711yescharacteristic
489C23×C4—22no—
490C23×C4—22no—
491C23×C4—22no—
492C23×C4—22no—
493C23×C4—22no—
494C23×C4—22no—
495C23×C4—22no—
496C23×C4—22no—
497C23×C4—22no—
498C23×C4—22no—
499C23×C4—22no—
500C23×C4—22no—
501C23×C4—22no—
502C23×C4—22no—
503C23×C4—22no—
504C23×C4—41no—
505C23×C4—41no—
506C23×C4—41no—
507C23×C4—41no—
508C23×C4—41no—
509C23×C4—41no—
510C23×C4C23×C711yescharacteristic
511C23×C4C23×C711yescharacteristic
512C23×C4C23×C711yescharacteristic
513C23×C4C23×C711yescharacteristic
514C23×C4C23×C711yescharacteristic
515C23×C4C23×C711yescharacteristic
516C23×C4C23×C711yescharacteristic
517C23×C4C23×C711yescharacteristic
518C23×C4C23×C711yescharacteristic
519C23×C4C23×C711yescharacteristic
520C23×C4C23×C711yescharacteristic
521C23×C4C23×C711yescharacteristic
522C23×C4C23×C711yescharacteristic
523C23×C4C23×C711yescharacteristic
524C2×C4⋊C4—22no—
525C2×C4⋊C4—22no—
526C2×C4⋊C4—22no—
527C2×C4⋊C4—22no—
528C2×C4⋊C4—22no—
529C2×C4⋊C4—22no—
530C2×C4⋊C4—22no—
531C2×C4⋊C4—22no—
532C2×C4⋊C4—41no—
533C2×C4⋊C4—41no—
534C2×C4⋊C4—41no—
535C2×C4⋊C4—41no—
536C2×C22⋊C4—22no—
537C2×C22⋊C4—22no—
538C2×C22⋊C4—22no—
539C2×C22⋊C4—22no—
540C2×C22⋊C4—22no—
541C2×C22⋊C4—22no—
542C2×C22⋊C4—22no—
543C2×C22⋊C4—22no—
544C2×C22⋊C4—22no—
545C2×C22⋊C4—22no—
546C2×C22⋊C4C7×D414yes—
547C2×C22⋊C4C7×Q814yes—
548#95—22no—
549#95—22no—
550#95—22no—
551#95—22no—
552#95—22no—
553#95—22no—
554#95—22no—
555#95—22no—
556#95—22no—
557#95—22no—
558#95—22no—
559#95—22no—
560#95—22no—
561#95—22no—
562#95—22no—
563#95—41no—
564#95—41no—
565#95—41no—
566#95—41no—
567#95—41no—
568#95—41no—
569#95—41no—
570#95—41no—
571#95C7×D414yes—
572C22×C7—24no—
573C22×C7—24no—
574C22×C7—24no—
575C22×C7—24no—
576C22×C7—24no—
577C22×C7—24no—
578C22×C7—24no—
579C22×C7—24no—
580C22×C7—24no—
581C22×C7—24no—
582C22×C7—24no—
583C22×C7—24no—
584C22×C7—24no—
585C22×C7—24no—
586C22×C7#40018yescomplemented
587C22×C7C2×C22⋊Q811yescharacteristic
588C22×C7C2×#12311yescharacteristic
589C22×C7#52511yescharacteristic
590C22×C7#52511yescharacteristic
591C22×C7#52511yescharacteristic
592C22×C7C2×#12411yescharacteristic
593C22×C7C2×#12511yescharacteristic
594C22×C7C2×#12511yescharacteristic
595C22×C7C2×#12611yescharacteristic
596C22×C7C2×#12611yescharacteristic
597C22×C7#52911yescharacteristic
598C22×C7#52911yescharacteristic
599C22×C7#52911yescharacteristic
600C22×C7#53811yescharacteristic
601C22×C7#53811yescharacteristic
602C22×C7#53811yescharacteristic
603C22×C7#53911yescharacteristic
604C22×C7#53911yescharacteristic
605C22×C7#53911yescharacteristic
606C22×C7D4211yescharacteristic
607C22×C7#54611yescharacteristic
608C22×C7#54611yescharacteristic
609C22×C7#54611yescharacteristic
610C22×C7#54611yescharacteristic
611C22×C7#54711yescharacteristic
612C22×C7D4×Q811yescharacteristic
613C22×C7#55111yescharacteristic
614C22×C7#55111yescharacteristic
615C22×C7#55111yescharacteristic
616C22×C7#55111yescharacteristic
617C22×C7#55211yescharacteristic
618C22×C7#55211yescharacteristic
619C22×C7#55411yescharacteristic
620C22×C7#55411yescharacteristic
621C22×C7#55411yescharacteristic
622C4×C7—42no—
623C4×C7—42no—
624C4×C7—42no—
625C4×C7—42no—
626C4×C7—42no—
627C4×C7—42no—
628C4×C7—42no—
629C4×C7—42no—
630C4×C7—42no—
631C4×C7—42no—
632C4×C7—81no—
633C4×C7—81no—
634C4×C7—81no—
635C4×C7—81no—
636C24—21no—
637C24—21no—
638C24—21no—
639C24—21no—
640C24—21no—
641C24—21no—
642C24—21no—
643C24—21no—
644C24C2×C7×D412yes—
645C24C2×C7×Q812yes—
646C24C7×#4112yes—
647C24C7×#4112yes—
648C24C7×#4112yes—
649C24C7×#4112yes—
650C24C7×#4112yes—
651C24C24×C711yescharacteristic
652C22×C4—28no—
653C22×C4—28no—
654C22×C4—28no—
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—21no—
722C22×C4—21no—
723C22×C4—21no—
724C22×C4—21no—
725C22×C4—21no—
726C22×C4—21no—
727C22×C4—21no—
728C22×C4—21no—
729C22×C4—21no—
730C22×C4—21no—
731C22×C4—21no—
732C22×C4—21no—
733C22×C4—21no—
734C22×C4—21no—
735C22×C4—21no—
736C22×C4—21no—
737C22×C4—21no—
738C22×C4—21no—
739C22×C4—21no—
740C22×C4—21no—
741C22×C4—21no—
742C22×C4—21no—
743C22×C4—44no—
744C22×C4—44no—
745C22×C4—44no—
746C22×C4—44no—
747C22×C4—44no—
748C22×C4—44no—
749C22×C4—44no—
750C22×C4—44no—
751C22×C4—44no—
752C22×C4—44no—
753C22×C4—44no—
754C22×C4—44no—
755C22×C4—44no—
756C22×C4—44no—
757C22×C4—44no—
758C22×C4—44no—
759C22×C4—44no—
760C22×C4—44no—
761C22×C4C2×C7×D412yes—
762C22×C4C2×C7×D412yes—
763C22×C4C2×C7×D412yes—
764C22×C4C2×C7×D412yes—
765C22×C4C2×C7×D412yes—
766C22×C4C2×C7×Q812yes—
767C22×C4C2×C7×Q812yes—
768C22×C4C7×#4112yes—
769C22×C4C7×#4112yes—
770C22×C4C7×#4112yes—
771C4⋊C4—44no—
772C4⋊C4—44no—
773C4⋊C4—44no—
774C4⋊C4—44no—
775C22⋊C4—28no—
776C22⋊C4—28no—
777C22⋊C4—44no—
778C22⋊C4—44no—
779C2×C7—28no—
780C2×C7C2×#40011yescharacteristic
781C2×C7#241811yescharacteristic
782C2×C7#241911yescharacteristic
783C2×C7#244911yescharacteristic
784C2×C7#245011yescharacteristic
785C2×C7#247211yescharacteristic
786C2×C7#247311yescharacteristic
787C2×C7#247311yescharacteristic
788C2×C7#248011yescharacteristic
789C2×C7#248811yescharacteristic
790C2×C7#249311yescharacteristic
791C2×C7#250511yescharacteristic
792C2×C7#250511yescharacteristic
793C2×C7#264311yescharacteristic
794C2×C7#285211yescharacteristic
795C23—22no—
796C23—22no—
797C23—22no—
798C23—22no—
799C23—22no—
800C23—22no—
801C23—22no—
802C23—22no—
803C23—22no—
804C23—22no—
805C23—22no—
806C23—22no—
807C23—22no—
808C23—22no—
809C23—22no—
810C23—22no—
811C23—22no—
812C23—22no—
813C23—22no—
814C23—22no—
815C23—22no—
816C23—22no—
817C23—22no—
818C23—22no—
819C23—22no—
820C23—22no—
821C23—22no—
822C23—22no—
823C23C7×C22⋊Q814yes—
824C23C7×#12314yes—
825C23C7×#12414yes—
826C23C7×#12514yes—
827C23C7×#12514yes—
828C23C7×#12614yes—
829C23C7×#12614yes—
830C23C22×C7×D411yescharacteristic
831C23C22×C7×D411yescharacteristic
832C23C22×C7×Q811yescharacteristic
833C23C2×C7×#4111yescharacteristic
834C23C2×C7×#4111yescharacteristic
835C23C2×C7×#4111yescharacteristic
836C23C2×C7×#4111yescharacteristic
837C23C2×C7×#4111yescharacteristic
838C23C2×C7×#4111yescharacteristic
839C23C2×C7×#4111yescharacteristic
840C23C2×C7×#4111yescharacteristic
841C23C7×H(5,𝔽2)11yescharacteristic
842C23C7×H(5,𝔽2)11yescharacteristic
843C23C7×H(5,𝔽2)11yescharacteristic
844C23C7×2−1+411yescharacteristic
845C2×C4—22no—
846C2×C4—22no—
847C2×C4—22no—
848C2×C4—22no—
849C2×C4—22no—
850C2×C4—22no—
851C2×C4—22no—
852C2×C4—22no—
853C2×C4—22no—
854C2×C4—22no—
855C2×C4—22no—
856C2×C4—22no—
857C2×C4—22no—
858C2×C4—22no—
859C2×C4—22no—
860C2×C4—22no—
861C2×C4—22no—
862C2×C4—22no—
863C2×C4—22no—
864C2×C4—22no—
865C2×C4—22no—
866C2×C4—22no—
867C2×C4—22no—
868C2×C4—22no—
869C2×C4—22no—
870C2×C4—22no—
871C2×C4—22no—
872C2×C4—22no—
873C2×C4—22no—
874C2×C4—22no—
875C2×C4—416no—
876C2×C4—416no—
877C2×C4—416no—
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—
914C2×C4—41no—
915C2×C4—41no—
916C2×C4—41no—
917C2×C4—41no—
918C2×C4—41no—
919C2×C4—41no—
920C2×C4—41no—
921C2×C4—41no—
922C2×C4—41no—
923C2×C4—41no—
924C2×C4—41no—
925C2×C4—41no—
926C2×C4—41no—
927C2×C4—41no—
928C2×C4—41no—
929C2×C4—41no—
930C2×C4—41no—
931C2×C4—41no—
932C2×C4—41no—
933C2×C4—41no—
934C2×C4—41no—
935C2×C4—41no—
936C2×C4—41no—
937C2×C4—41no—
938C2×C4—41no—
939C2×C4—41no—
940C2×C4—41no—
941C2×C4—41no—
942C2×C4—41no—
943C2×C4—41no—
944C2×C4—41no—
945C2×C4—41no—
946C7#1473811yescharacteristic, direct product factor, Sylow
947C22—24no—
948C22—24no—
949C22—24no—
950C22—24no—
951C22—24no—
952C22—24no—
953C22—24no—
954C22—24no—
955C22—24no—
956C22—24no—
957C22—24no—
958C22—24no—
959C22—24no—
960C22—24no—
961C22C7×#40018yescomplemented
962C22C2×C7×C22⋊Q811yescharacteristic
963C22C2×C7×#12311yescharacteristic
964C22C7×#52511yescharacteristic
965C22C7×#52511yescharacteristic
966C22C7×#52511yescharacteristic
967C22C2×C7×#12411yescharacteristic
968C22C2×C7×#12511yescharacteristic
969C22C2×C7×#12511yescharacteristic
970C22C2×C7×#12611yescharacteristic
971C22C2×C7×#12611yescharacteristic
972C22C7×#52911yescharacteristic
973C22C7×#52911yescharacteristic
974C22C7×#52911yescharacteristic
975C22C7×#53811yescharacteristic
976C22C7×#53811yescharacteristic
977C22C7×#53811yescharacteristic
978C22C7×#53911yescharacteristic
979C22C7×#53911yescharacteristic
980C22C7×#53911yescharacteristic
981C22C7×D4211yescharacteristic
982C22C7×#54611yescharacteristic
983C22C7×#54611yescharacteristic
984C22C7×#54611yescharacteristic
985C22C7×#54611yescharacteristic
986C22C7×#54711yescharacteristic
987C22C7×D4×Q811yescharacteristic
988C22C7×#55111yescharacteristic
989C22C7×#55111yescharacteristic
990C22C7×#55111yescharacteristic
991C22C7×#55111yescharacteristic
992C22C7×#55211yescharacteristic
993C22C7×#55211yescharacteristic
994C22C7×#55411yescharacteristic
995C22C7×#55411yescharacteristic
996C22C7×#55411yescharacteristic
997C4—42no—
998C4—42no—
999C4—42no—
1000C4—42no—
1001C4—42no—
1002C4—42no—
1003C4—42no—
1004C4—42no—
1005C4—42no—
1006C4—42no—
1007C4—81no—
1008C4—81no—
1009C4—81no—
1010C4—81no—
1011C2—28no—
1012C2C2×C7×#40011yescharacteristic
1013C2C7×#241811yescharacteristic
1014C2C7×#241911yescharacteristic
1015C2C7×#244911yescharacteristic
1016C2C7×#245011yescharacteristic
1017C2C7×#247211yescharacteristic
1018C2C7×#247311yescharacteristic
1019C2C7×#247311yescharacteristic
1020C2C7×#248011yescharacteristic
1021C2C7×#248811yescharacteristic
1022C2C7×#249311yescharacteristic
1023C2C7×#250511yescharacteristic
1024C2C7×#250511yescharacteristic
1025C2C7×#264311yescharacteristic
1026C2C7×#285211yescharacteristic
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
1. C2×C7×#400C2semidirect
5. C7×#1445C2semidirect
6. C7×#1443C2semidirect
7. C7×#1443C2semidirect
8. C7×#1442C2semidirect
9. C7×#1442C2semidirect
10. C7×#1442C2semidirect
11. C7×#1441C2semidirect
55. #14738C7direct (N × H)
140. C2×#400C2×C7semidirect
144. #1445C2×C7semidirect
145. #1443C2×C7semidirect
146. #1443C2×C7semidirect
147. #1442C2×C7semidirect
148. #1442C2×C7semidirect
149. #1442C2×C7semidirect
150. #1441C2×C7semidirect
586. C22×C7#400semidirect
946. C7#14738direct (N × H)
961. C22C7×#400semidirect

Maximal subgroups

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

subgroupindex
C2×C7×#4002
C2×C7×#3852
C22×C7×#952
C7×#14452
C7×#14432
C7×#14422
C7×#14412
C7×C22⋊#952
#147387