Finite Group Databasebeta

← C7×#15940 #13193156

Subgroups — C7×#15940 #13193156

Order 1792.

1566 conjugacy classes of subgroups.

The subgroup lattice has 1004 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C7×#126C211yesmaximal, characteristic
2C2×C7×#400C211yesmaximal, characteristic, complemented
3C2×C7×#396C211yesmaximal, characteristic
4C2×C7×#389C211yesmaximal, characteristic, complemented
5C7×#1444C211yesmaximal, characteristic, complemented
6C7×#1442C211yesmaximal, characteristic, complemented
7C7×#1441C211yesmaximal, characteristic, complemented
8C7×#1440C211yesmaximal, characteristic
9C7×#1440C211yesmaximal, characteristic
10C7×#1439C211yesmaximal, characteristic
11C7×#1439C211yesmaximal, characteristic
12C7×#1437C211yesmaximal, characteristic
13C7×#1436C211yesmaximal, characteristic, complemented
14C7×#1436C211yesmaximal, characteristic, complemented
15C7×C4⋊#95C211yesmaximal, characteristic, complemented
16C2×C7×#126—24no—
17C2×C7×#126—24no—
18C2×C7×#126—24no—
19C22×C7×C4⋊C4C2211yescharacteristic
20C22×C7×C4⋊C4C2211yescharacteristic
21C22×C7×C4⋊C4C2211yescharacteristic
22C22×C7×C4⋊C4C2211yescharacteristic
23C22×C7×C4⋊C4C2211yescharacteristic
24C22×C7×C4⋊C4C2211yescharacteristic
25C22×C7×C4⋊C4C2211yescharacteristic
26C22×C7×C4⋊C4C2211yescharacteristic
27C22×C7×C22⋊C4C2211yescharacteristic
28C22×C7×C22⋊C4C2211yescharacteristic
29C22×C7×C22⋊C4C2211yescharacteristic
30C22×C7×C22⋊C4C2211yescharacteristic
31C22×C7×C22⋊C4C2211yescharacteristic
32C22×C7×C22⋊C4C2211yescharacteristic
33C22×C7×C22⋊C4C2211yescharacteristic
34C22×C42×C7C2211yescharacteristic
35C22×C42×C7C2211yescharacteristic
36C7×#400—24no—
37C7×#396—24no—
38C7×#389—24no—
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
55C2×C7×#95C2211yescharacteristic
56C2×C7×#95C2211yescharacteristic
57#15940C711yesmaximal, characteristic, direct product factor, Sylow
58C25×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
71C23×C4×C7C2311yescharacteristic
72C23×C4×C7C2311yescharacteristic
73C7×#126—232no—
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—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—22no—
89C2×C7×C4⋊C4—22no—
90C2×C7×C4⋊C4—22no—
91C2×C7×C4⋊C4—22no—
92C2×C7×C4⋊C4—22no—
93C2×C7×C4⋊C4—41no—
94C2×C7×C4⋊C4—41no—
95C2×C7×C4⋊C4—41no—
96C2×C7×C4⋊C4D414yes—
97C2×C7×C4⋊C4D414yes—
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—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⋊C4—41no—
115C2×C7×C22⋊C4—41no—
116C2×C7×C22⋊C4—41no—
117C2×C7×C22⋊C4—41no—
118C2×C7×C22⋊C4D414yes—
119C2×C42×C7—22no—
120C2×C42×C7—22no—
121C2×C42×C7—22no—
122C2×C42×C7—22no—
123C2×C42×C7—22no—
124C2×C42×C7—41no—
125C7×#95—22no—
126C7×#95—22no—
127C7×#95—22no—
128C7×#95—22no—
129C7×#95—22no—
130C7×#95—22no—
131C7×#95—22no—
132C7×#95—22no—
133C7×#95—22no—
134C7×#95—22no—
135C7×#95—22no—
136C7×#95—22no—
137C7×#95—22no—
138C7×#95—22no—
139C7×#95—41no—
140C7×#95—41no—
141C7×#95—41no—
142C7×#95—41no—
143C22×#126C2×C711yescharacteristic
144C2×#400C2×C711yescharacteristic, complemented
145C2×#396C2×C711yescharacteristic
146C2×#389C2×C711yescharacteristic, complemented
147#1444C2×C711yescharacteristic, complemented
148#1442C2×C711yescharacteristic, complemented
149#1441C2×C711yescharacteristic, complemented
150#1440C2×C711yescharacteristic
151#1440C2×C711yescharacteristic
152#1439C2×C711yescharacteristic
153#1439C2×C711yescharacteristic
154#1437C2×C711yescharacteristic
155#1436C2×C711yescharacteristic, complemented
156#1436C2×C711yescharacteristic, complemented
157C4⋊#95C2×C711yescharacteristic, complemented
158C24×C7—21no—
159C24×C7—21no—
160C24×C7—21no—
161C24×C7—21no—
162C24×C7—21no—
163C24×C7—21no—
164C24×C7—21no—
165C24×C7—21no—
166C24×C7—21no—
167C24×C7—21no—
168C24×C7—21no—
169C24×C7—21no—
170C24×C7—21no—
171C24×C7—21no—
172C24×C7C2×D412yes—
173C24×C7C2411yescharacteristic
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×C7C2×D412yes—
259C22×C4×C7C2×D412yes—
260C22×C4×C7C2×D412yes—
261C22×C4×C7C2×D412yes—
262C22×C4×C7C2×D412yes—
263C22×C4×C7C2×D412yes—
264C22×C4×C7C2×D412yes—
265C22×C4×C7C2×D412yes—
266C22×C4×C7#4112yes—
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—28no—
274C7×C4⋊C4—28no—
275C7×C4⋊C4—28no—
276C7×C4⋊C4—44no—
277C7×C4⋊C4—44no—
278C7×C4⋊C4—44no—
279C7×C4⋊C4—44no—
280C7×C22⋊C4—28no—
281C7×C22⋊C4—28no—
282C7×C22⋊C4—28no—
283C7×C22⋊C4—44no—
284C7×C22⋊C4—44no—
285C7×C22⋊C4—44no—
286C7×C22⋊C4—44no—
287C42×C7—28no—
288C42×C7—44no—
289C2×#126—24no—
290C2×#126—24no—
291C2×#126—24no—
292C22×C4⋊C4C22×C711yescharacteristic
293C22×C4⋊C4C22×C711yescharacteristic
294C22×C4⋊C4C22×C711yescharacteristic
295C22×C4⋊C4C22×C711yescharacteristic
296C22×C4⋊C4C22×C711yescharacteristic
297C22×C4⋊C4C22×C711yescharacteristic
298C22×C4⋊C4C22×C711yescharacteristic
299C22×C4⋊C4C22×C711yescharacteristic
300C22×C22⋊C4C22×C711yescharacteristic
301C22×C22⋊C4C22×C711yescharacteristic
302C22×C22⋊C4C22×C711yescharacteristic
303C22×C22⋊C4C22×C711yescharacteristic
304C22×C22⋊C4C22×C711yescharacteristic
305C22×C22⋊C4C22×C711yescharacteristic
306C22×C22⋊C4C22×C711yescharacteristic
307C22×C42C22×C711yescharacteristic
308C22×C42C22×C711yescharacteristic
309#400—24no—
310#396—24no—
311#389—24no—
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
323C2×#95C22×C711yescharacteristic
324C2×#95C22×C711yescharacteristic
325C2×#95C22×C711yescharacteristic
326C2×#95C22×C711yescharacteristic
327C2×#95C22×C711yescharacteristic
328C2×#95C22×C711yescharacteristic
329C2×#95C22×C711yescharacteristic
330C23×C7—22no—
331C23×C7—22no—
332C23×C7—22no—
333C23×C7—22no—
334C23×C7—22no—
335C23×C7—22no—
336C23×C7—22no—
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×C7—41no—
355C23×C7—41no—
356C23×C7—41no—
357C23×C7—41no—
358C23×C7—41no—
359C23×C7—41no—
360C23×C7—41no—
361C23×C7—41no—
362C23×C7—41no—
363C23×C7—41no—
364C23×C7—41no—
365C23×C7C22×D411yescharacteristic
366C23×C7C22×D411yescharacteristic
367C23×C7C22×D411yescharacteristic
368C23×C7C2×#4111yescharacteristic
369C23×C7C2×#4111yescharacteristic
370C23×C7C2×#4111yescharacteristic
371C23×C7C2×#4111yescharacteristic
372C23×C7C2×#4111yescharacteristic
373C23×C7C2×#4111yescharacteristic
374C23×C7H(5,𝔽2)11yescharacteristic
375C23×C7H(5,𝔽2)11yescharacteristic
376C23×C72−1+411yescharacteristic
377C23×C72−1+411yescharacteristic
378C23×C72−1+411yescharacteristic
379C23×C72−1+411yescharacteristic
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—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—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—
472C2×C4×C7—41no—
473C2×C4×C7—41no—
474C2×C4×C7—41no—
475C2×C4×C7—41no—
476C2×C4×C7#12014yes—
477C2×C4×C7#12614yescomplemented
478C25C23×C711yescharacteristic
479C23×C4C23×C711yescharacteristic
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
493#126—232no—
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—22no—
505C2×C4⋊C4—22no—
506C2×C4⋊C4—22no—
507C2×C4⋊C4—22no—
508C2×C4⋊C4—22no—
509C2×C4⋊C4—22no—
510C2×C4⋊C4—22no—
511C2×C4⋊C4—22no—
512C2×C4⋊C4—22no—
513C2×C4⋊C4—41no—
514C2×C4⋊C4—41no—
515C2×C4⋊C4—41no—
516C2×C4⋊C4C7×D414yes—
517C2×C4⋊C4C7×D414yes—
518C2×C22⋊C4—22no—
519C2×C22⋊C4—22no—
520C2×C22⋊C4—22no—
521C2×C22⋊C4—22no—
522C2×C22⋊C4—22no—
523C2×C22⋊C4—22no—
524C2×C22⋊C4—22no—
525C2×C22⋊C4—22no—
526C2×C22⋊C4—22no—
527C2×C22⋊C4—22no—
528C2×C22⋊C4—22no—
529C2×C22⋊C4—22no—
530C2×C22⋊C4—22no—
531C2×C22⋊C4—22no—
532C2×C22⋊C4—22no—
533C2×C22⋊C4—22no—
534C2×C22⋊C4—41no—
535C2×C22⋊C4—41no—
536C2×C22⋊C4—41no—
537C2×C22⋊C4—41no—
538C2×C22⋊C4C7×D414yes—
539C2×C42—22no—
540C2×C42—22no—
541C2×C42—22no—
542C2×C42—22no—
543C2×C42—22no—
544C2×C42—41no—
545#95—22no—
546#95—22no—
547#95—22no—
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—41no—
560#95—41no—
561#95—41no—
562#95—41no—
563C22×C7—42no—
564C22×C7—42no—
565C22×C7—42no—
566C22×C7—42no—
567C22×C7—42no—
568C22×C7—42no—
569C22×C7—42no—
570C22×C7—81no—
571C22×C7—81no—
572C22×C7—81no—
573C22×C7—81no—
574C22×C7—81no—
575C22×C7—81no—
576C22×C7—81no—
577C22×C7—81no—
578C22×C7C2×#12011yescharacteristic
579C22×C7#52511yescharacteristic
580C22×C7C2×#12611yescharacteristic
581C22×C7#52911yescharacteristic
582C22×C7#53211yescharacteristic
583C22×C7#53211yescharacteristic
584C22×C7#53611yescharacteristic
585C22×C7#53711yescharacteristic
586C22×C7#53711yescharacteristic
587C22×C7#53811yescharacteristic
588C22×C7#53911yescharacteristic
589C22×C7#54111yescharacteristic
590C22×C7#54111yescharacteristic
591C22×C7#54111yescharacteristic
592C22×C7#54211yescharacteristic
593C22×C7#54611yescharacteristic
594C22×C7#54611yescharacteristic
595C22×C7#54611yescharacteristic
596C22×C7#54711yescharacteristic
597C22×C7#54711yescharacteristic
598C22×C7#54711yescharacteristic
599C22×C7#54711yescharacteristic
600C22×C7#54711yescharacteristic
601C22×C7#54811yescharacteristic
602C22×C7#54811yescharacteristic
603C22×C7#54811yescharacteristic
604C22×C7#55011yescharacteristic
605C22×C7#55211yescharacteristic
606C22×C7#55211yescharacteristic
607C22×C7#55311yescharacteristic
608C22×C7#55311yescharacteristic
609C22×C7#55611yescharacteristic
610C22×C7#55611yescharacteristic
611C22×C7#56311yescharacteristic
612C22×C7#56311yescharacteristic
613C4×C7—24no—
614C4×C7—24no—
615C4×C7—42no—
616C4×C7—42no—
617C4×C7—42no—
618C4×C7—42no—
619C4×C7—42no—
620C4×C7—42no—
621C4×C7—42no—
622C4×C7—42no—
623C4×C7—81no—
624C4×C7—81no—
625C4×C7—81no—
626C4×C7—81no—
627C24—21no—
628C24—21no—
629C24—21no—
630C24—21no—
631C24—21no—
632C24—21no—
633C24—21no—
634C24—21no—
635C24—21no—
636C24—21no—
637C24—21no—
638C24—21no—
639C24—21no—
640C24—21no—
641C24C2×C7×D412yes—
642C24C24×C711yescharacteristic
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—21no—
722C22×C4—21no—
723C22×C4—21no—
724C22×C4—21no—
725C22×C4—21no—
726C22×C4—21no—
727C22×C4C2×C7×D412yes—
728C22×C4C2×C7×D412yes—
729C22×C4C2×C7×D412yes—
730C22×C4C2×C7×D412yes—
731C22×C4C2×C7×D412yes—
732C22×C4C2×C7×D412yes—
733C22×C4C2×C7×D412yes—
734C22×C4C2×C7×D412yes—
735C22×C4C7×#4112yes—
736C22×C4C7×#4112yes—
737C22×C4C7×#4112yes—
738C22×C4C7×#4112yes—
739C22×C4C7×#4112yes—
740C22×C4C7×#4112yes—
741C4⋊C4—28no—
742C4⋊C4—28no—
743C4⋊C4—28no—
744C4⋊C4—28no—
745C4⋊C4—44no—
746C4⋊C4—44no—
747C4⋊C4—44no—
748C4⋊C4—44no—
749C22⋊C4—28no—
750C22⋊C4—28no—
751C22⋊C4—28no—
752C22⋊C4—44no—
753C22⋊C4—44no—
754C22⋊C4—44no—
755C22⋊C4—44no—
756C42—28no—
757C42—44no—
758C2×C7—82no—
759C2×C7#240711yescharacteristic
760C2×C7#243011yescharacteristic
761C2×C7#243211yescharacteristic
762C2×C7#246911yescharacteristic
763C2×C7#248111yescharacteristic
764C2×C7#249611yescharacteristic
765C2×C7#251211yescharacteristic
766C2×C7#251911yescharacteristic
767C2×C7#255911yescharacteristic
768C2×C7#268911yescharacteristic
769C2×C7#269811yescharacteristic
770C2×C7#270211yescharacteristic
771C2×C7#272511yescharacteristic
772C2×C7#272511yescharacteristic
773C2×C7#272711yescharacteristic
774C23—22no—
775C23—22no—
776C23—22no—
777C23—22no—
778C23—22no—
779C23—22no—
780C23—22no—
781C23—41no—
782C23—41no—
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—
799C23—41no—
800C23—41no—
801C23—41no—
802C23—41no—
803C23—41no—
804C23—41no—
805C23—41no—
806C23—41no—
807C23—41no—
808C23—41no—
809C23C22×C7×D411yescharacteristic
810C23C22×C7×D411yescharacteristic
811C23C22×C7×D411yescharacteristic
812C23C2×C7×#4111yescharacteristic
813C23C2×C7×#4111yescharacteristic
814C23C2×C7×#4111yescharacteristic
815C23C2×C7×#4111yescharacteristic
816C23C2×C7×#4111yescharacteristic
817C23C2×C7×#4111yescharacteristic
818C23C7×H(5,𝔽2)11yescharacteristic
819C23C7×H(5,𝔽2)11yescharacteristic
820C23C7×2−1+411yescharacteristic
821C23C7×2−1+411yescharacteristic
822C23C7×2−1+411yescharacteristic
823C23C7×2−1+411yescharacteristic
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—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—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—
914C2×C4—41no—
915C2×C4—41no—
916C2×C4—41no—
917C2×C4—41no—
918C2×C4—41no—
919C2×C4—41no—
920C2×C4C7×#12014yes—
921C2×C4C7×#12614yescomplemented
922C7#1594011yescharacteristic, direct product factor, Sylow
923C22—42no—
924C22—42no—
925C22—42no—
926C22—42no—
927C22—42no—
928C22—42no—
929C22—42no—
930C22—81no—
931C22—81no—
932C22—81no—
933C22—81no—
934C22—81no—
935C22—81no—
936C22—81no—
937C22—81no—
938C22C2×C7×#12011yescharacteristic
939C22C7×#52511yescharacteristic
940C22C2×C7×#12611yescharacteristic
941C22C7×#52911yescharacteristic
942C22C7×#53211yescharacteristic
943C22C7×#53211yescharacteristic
944C22C7×#53611yescharacteristic
945C22C7×#53711yescharacteristic
946C22C7×#53711yescharacteristic
947C22C7×#53811yescharacteristic
948C22C7×#53911yescharacteristic
949C22C7×#54111yescharacteristic
950C22C7×#54111yescharacteristic
951C22C7×#54111yescharacteristic
952C22C7×#54211yescharacteristic
953C22C7×#54611yescharacteristic
954C22C7×#54611yescharacteristic
955C22C7×#54611yescharacteristic
956C22C7×#54711yescharacteristic
957C22C7×#54711yescharacteristic
958C22C7×#54711yescharacteristic
959C22C7×#54711yescharacteristic
960C22C7×#54711yescharacteristic
961C22C7×#54811yescharacteristic
962C22C7×#54811yescharacteristic
963C22C7×#54811yescharacteristic
964C22C7×#55011yescharacteristic
965C22C7×#55211yescharacteristic
966C22C7×#55211yescharacteristic
967C22C7×#55311yescharacteristic
968C22C7×#55311yescharacteristic
969C22C7×#55611yescharacteristic
970C22C7×#55611yescharacteristic
971C22C7×#56311yescharacteristic
972C22C7×#56311yescharacteristic
973C4—24no—
974C4—24no—
975C4—42no—
976C4—42no—
977C4—42no—
978C4—42no—
979C4—42no—
980C4—42no—
981C4—42no—
982C4—42no—
983C4—81no—
984C4—81no—
985C4—81no—
986C4—81no—
987C2—82no—
988C2C7×#240711yescharacteristic
989C2C7×#243011yescharacteristic
990C2C7×#243211yescharacteristic
991C2C7×#246911yescharacteristic
992C2C7×#248111yescharacteristic
993C2C7×#249611yescharacteristic
994C2C7×#251211yescharacteristic
995C2C7×#251911yescharacteristic
996C2C7×#255911yescharacteristic
997C2C7×#268911yescharacteristic
998C2C7×#269811yescharacteristic
999C2C7×#270211yescharacteristic
1000C2C7×#272511yescharacteristic
1001C2C7×#272511yescharacteristic
1002C2C7×#272711yescharacteristic
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×#400C2semidirect
4. C2×C7×#389C2semidirect
5. C7×#1444C2semidirect
6. C7×#1442C2semidirect
7. C7×#1441C2semidirect
13. C7×#1436C2semidirect
14. C7×#1436C2semidirect
15. C7×C4⋊#95C2semidirect
57. #15940C7direct (N × H)
144. C2×#400C2×C7semidirect
146. C2×#389C2×C7semidirect
147. #1444C2×C7semidirect
148. #1442C2×C7semidirect
149. #1441C2×C7semidirect
155. #1436C2×C7semidirect
156. #1436C2×C7semidirect
157. C4⋊#95C2×C7semidirect
477. C2×C4×C7#126semidirect
921. C2×C4C7×#126semidirect
922. C7#15940direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C7×#1262
C2×C7×#4002
C2×C7×#3962
C2×C7×#3892
C7×#14442
C7×#14422
C7×#14412
C7×#14402
C7×#14392
C7×#14372
C7×#14362
C7×C4⋊#952
#159407