Finite Group Databasebeta

← C7×#16477 #13193693

Subgroups — C7×#16477 #13193693

Order 1792.

1374 conjugacy classes of subgroups.

The subgroup lattice has 998 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C7×#398C211yesmaximal, characteristic, complemented
2C2×C7×#398C211yesmaximal, characteristic, complemented
3C2×C7×#396C211yesmaximal, characteristic
4C2×C7×#388C211yesmaximal, characteristic
5C7×#1444C211yesmaximal, characteristic, complemented
6C7×#1442C211yesmaximal, characteristic, complemented
7C7×#1442C211yesmaximal, characteristic, complemented
8C7×#1441C211yesmaximal, characteristic, complemented
9C7×#1439C211yesmaximal, characteristic
10C7×#1439C211yesmaximal, characteristic
11C7×#1439C211yesmaximal, characteristic
12C7×#1439C211yesmaximal, characteristic
13C7×#1439C211yesmaximal, 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×C4⋊C4C2211yescharacteristic
22C22×C7×C4⋊C4C2211yescharacteristic
23C22×C7×C4⋊C4C2211yescharacteristic
24C22×C7×C4⋊C4C2211yescharacteristic
25C22×C7×C22⋊C4C2211yescharacteristic
26C22×C7×C22⋊C4C2211yescharacteristic
27C22×C7×C22⋊C4C2211yescharacteristic
28C22×C7×C22⋊C4C2211yescharacteristic
29C22×C7×C22⋊C4C2211yescharacteristic
30C22×C7×C22⋊C4C2211yescharacteristic
31C22×C7×C22⋊C4C2211yescharacteristic
32C22×C42×C7C2211yescharacteristic
33C7×#398—24no—
34C7×#398—24no—
35C7×#396—24no—
36C7×#388—24no—
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#16477C711yesmaximal, 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—22no—
83C2×C7×C4⋊C4—22no—
84C2×C7×C4⋊C4—41no—
85C2×C7×C4⋊C4—41no—
86C2×C7×C4⋊C4—41no—
87C2×C7×C4⋊C4—41no—
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×C4⋊C4—41no—
94C2×C7×C4⋊C4—41no—
95C2×C7×C4⋊C4—41no—
96C2×C7×C4⋊C4—41no—
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—41no—
109C2×C7×C22⋊C4—41no—
110C2×C7×C22⋊C4—41no—
111C2×C7×C22⋊C4—41no—
112C2×C7×C22⋊C4—41no—
113C2×C7×C22⋊C4—41no—
114C2×C7×C22⋊C4—41no—
115C2×C7×C22⋊C4—41no—
116C2×C7×C22⋊C4—41no—
117C2×C7×C22⋊C4—41no—
118C2×C7×C22⋊C4Q814yes—
119C2×C42×C7—22no—
120C2×C42×C7—22no—
121C2×C42×C7—41no—
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—22no—
133C7×#95—41no—
134C7×#95—41no—
135C7×#95—41no—
136C7×#95—41no—
137C7×#95—41no—
138C7×#95—41no—
139C7×#95D414yes—
140C2×#398C2×C711yescharacteristic, complemented
141C2×#398C2×C711yescharacteristic, complemented
142C2×#396C2×C711yescharacteristic
143C2×#388C2×C711yescharacteristic
144#1444C2×C711yescharacteristic, complemented
145#1442C2×C711yescharacteristic, complemented
146#1442C2×C711yescharacteristic, complemented
147#1441C2×C711yescharacteristic, complemented
148#1439C2×C711yescharacteristic
149#1439C2×C711yescharacteristic
150#1439C2×C711yescharacteristic
151#1439C2×C711yescharacteristic
152#1439C2×C711yescharacteristic
153#1436C2×C711yescharacteristic, complemented
154C4⋊#95C2×C711yescharacteristic, complemented
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—21no—
166C24×C7—21no—
167C24×C7—21no—
168C24×C7—21no—
169C24×C7C2×Q812yes—
170C24×C7C2411yescharacteristic
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—21no—
257C22×C4×C7C2×D412yes—
258C22×C4×C7C2×D412yes—
259C22×C4×C7C2×D412yes—
260C22×C4×C7C2×D412yes—
261C22×C4×C7C2×D412yes—
262C22×C4×C7C2×D412yes—
263C22×C4×C7C2×Q812yes—
264C22×C4×C7C2×Q812yes—
265C22×C4×C7#4112yes—
266C22×C4×C7#4112yes—
267C22×C4×C7#4112yes—
268C22×C4×C7#4112yes—
269C7×C4⋊C4—44no—
270C7×C4⋊C4—44no—
271C7×C4⋊C4—44no—
272C7×C4⋊C4—44no—
273C7×C4⋊C4—44no—
274C7×C4⋊C4—44no—
275C7×C4⋊C4—44no—
276C7×C4⋊C4—44no—
277C7×C4⋊C4—44no—
278C7×C22⋊C4—28no—
279C7×C22⋊C4—44no—
280C7×C22⋊C4—44no—
281C7×C22⋊C4—44no—
282C7×C22⋊C4—44no—
283C7×C22⋊C4—44no—
284C7×C22⋊C4—44no—
285C42×C7—44no—
286C22×C4⋊C4C22×C711yescharacteristic
287C22×C4⋊C4C22×C711yescharacteristic
288C22×C4⋊C4C22×C711yescharacteristic
289C22×C4⋊C4C22×C711yescharacteristic
290C22×C4⋊C4C22×C711yescharacteristic
291C22×C4⋊C4C22×C711yescharacteristic
292C22×C4⋊C4C22×C711yescharacteristic
293C22×C4⋊C4C22×C711yescharacteristic
294C22×C4⋊C4C22×C711yescharacteristic
295C22×C22⋊C4C22×C711yescharacteristic
296C22×C22⋊C4C22×C711yescharacteristic
297C22×C22⋊C4C22×C711yescharacteristic
298C22×C22⋊C4C22×C711yescharacteristic
299C22×C22⋊C4C22×C711yescharacteristic
300C22×C22⋊C4C22×C711yescharacteristic
301C22×C22⋊C4C22×C711yescharacteristic
302C22×C42C22×C711yescharacteristic
303#398—24no—
304#398—24no—
305#396—24no—
306#388—24no—
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
323C2×#95C22×C711yescharacteristic
324C2×#95C22×C711yescharacteristic
325C23×C7—22no—
326C23×C7—22no—
327C23×C7—22no—
328C23×C7—22no—
329C23×C7—22no—
330C23×C7—22no—
331C23×C7—22no—
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×C7—41no—
355C23×C7—41no—
356C23×C7—41no—
357C23×C7—41no—
358C23×C7—41no—
359C23×C7—41no—
360C23×C7C22×D411yescharacteristic
361C23×C7C22×D411yescharacteristic
362C23×C7C22×Q811yescharacteristic
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×C7H(5,𝔽2)11yescharacteristic
371C23×C7H(5,𝔽2)11yescharacteristic
372C23×C72−1+411yescharacteristic
373C23×C72−1+411yescharacteristic
374C23×C72−1+411yescharacteristic
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—22no—
406C2×C4×C7—22no—
407C2×C4×C7—22no—
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—
472C2×C4×C7C22⋊Q814yes—
473C25C23×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
484C23×C4C23×C711yescharacteristic
485C23×C4C23×C711yescharacteristic
486C23×C4C23×C711yescharacteristic
487C23×C4C23×C711yescharacteristic
488C2×C4⋊C4—22no—
489C2×C4⋊C4—22no—
490C2×C4⋊C4—22no—
491C2×C4⋊C4—22no—
492C2×C4⋊C4—22no—
493C2×C4⋊C4—22no—
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—41no—
502C2×C4⋊C4—41no—
503C2×C4⋊C4—41no—
504C2×C4⋊C4—41no—
505C2×C4⋊C4—41no—
506C2×C4⋊C4—41no—
507C2×C4⋊C4—41no—
508C2×C4⋊C4—41no—
509C2×C4⋊C4—41no—
510C2×C4⋊C4—41no—
511C2×C4⋊C4—41no—
512C2×C4⋊C4—41no—
513C2×C4⋊C4—41no—
514C2×C4⋊C4C7×D414yes—
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—22no—
523C2×C22⋊C4—22no—
524C2×C22⋊C4—22no—
525C2×C22⋊C4—41no—
526C2×C22⋊C4—41no—
527C2×C22⋊C4—41no—
528C2×C22⋊C4—41no—
529C2×C22⋊C4—41no—
530C2×C22⋊C4—41no—
531C2×C22⋊C4—41no—
532C2×C22⋊C4—41no—
533C2×C22⋊C4—41no—
534C2×C22⋊C4—41no—
535C2×C22⋊C4C7×Q814yes—
536C2×C42—22no—
537C2×C42—22no—
538C2×C42—41no—
539#95—22no—
540#95—22no—
541#95—22no—
542#95—22no—
543#95—22no—
544#95—22no—
545#95—22no—
546#95—22no—
547#95—22no—
548#95—22no—
549#95—22no—
550#95—41no—
551#95—41no—
552#95—41no—
553#95—41no—
554#95—41no—
555#95—41no—
556#95C7×D414yes—
557C22×C7—42no—
558C22×C7—42no—
559C22×C7—42no—
560C22×C7—42no—
561C22×C7—42no—
562C22×C7—42no—
563C22×C7—42no—
564C22×C7—81no—
565C22×C7—81no—
566C22×C7—81no—
567C22×C7—81no—
568C22×C7—81no—
569C22×C7—81no—
570C22×C7—81no—
571C22×C7—81no—
572C22×C7C2×C22⋊Q811yescharacteristic
573C22×C7#52911yescharacteristic
574C22×C7#53211yescharacteristic
575C22×C7#53411yescharacteristic
576C22×C7#53511yescharacteristic
577C22×C7#53711yescharacteristic
578C22×C7#53711yescharacteristic
579C22×C7#53811yescharacteristic
580C22×C7#53811yescharacteristic
581C22×C7#53811yescharacteristic
582C22×C7#53911yescharacteristic
583C22×C7#54011yescharacteristic
584C22×C7#54011yescharacteristic
585C22×C7#54011yescharacteristic
586C22×C7#54111yescharacteristic
587C22×C7#54211yescharacteristic
588C22×C7#54211yescharacteristic
589C22×C7#54411yescharacteristic
590C22×C7#54411yescharacteristic
591C22×C7D4211yescharacteristic
592C22×C7#54611yescharacteristic
593C22×C7#54611yescharacteristic
594C22×C7#54711yescharacteristic
595C22×C7#54811yescharacteristic
596C22×C7#54811yescharacteristic
597C22×C7D4×Q811yescharacteristic
598C22×C7#55211yescharacteristic
599C22×C7#55211yescharacteristic
600C22×C7#55411yescharacteristic
601C22×C7#55411yescharacteristic
602C22×C7#55411yescharacteristic
603C22×C7#56211yescharacteristic
604C22×C7#56211yescharacteristic
605C22×C7#56311yescharacteristic
606C22×C7#56311yescharacteristic
607C4×C7—24no—
608C4×C7—42no—
609C4×C7—42no—
610C4×C7—42no—
611C4×C7—42no—
612C4×C7—42no—
613C4×C7—42no—
614C4×C7—42no—
615C4×C7—42no—
616C4×C7—42no—
617C4×C7—81no—
618C4×C7—81no—
619C4×C7—81no—
620C4×C7—81no—
621C24—21no—
622C24—21no—
623C24—21no—
624C24—21no—
625C24—21no—
626C24—21no—
627C24—21no—
628C24—21no—
629C24—21no—
630C24—21no—
631C24—21no—
632C24—21no—
633C24—21no—
634C24—21no—
635C24C2×C7×Q812yes—
636C24C24×C711yescharacteristic
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—21no—
722C22×C4—21no—
723C22×C4C2×C7×D412yes—
724C22×C4C2×C7×D412yes—
725C22×C4C2×C7×D412yes—
726C22×C4C2×C7×D412yes—
727C22×C4C2×C7×D412yes—
728C22×C4C2×C7×D412yes—
729C22×C4C2×C7×Q812yes—
730C22×C4C2×C7×Q812yes—
731C22×C4C7×#4112yes—
732C22×C4C7×#4112yes—
733C22×C4C7×#4112yes—
734C22×C4C7×#4112yes—
735C4⋊C4—44no—
736C4⋊C4—44no—
737C4⋊C4—44no—
738C4⋊C4—44no—
739C4⋊C4—44no—
740C4⋊C4—44no—
741C4⋊C4—44no—
742C4⋊C4—44no—
743C4⋊C4—44no—
744C22⋊C4—28no—
745C22⋊C4—44no—
746C22⋊C4—44no—
747C22⋊C4—44no—
748C22⋊C4—44no—
749C22⋊C4—44no—
750C22⋊C4—44no—
751C42—44no—
752C2×C7—82no—
753C2×C7#245011yescharacteristic
754C2×C7#245211yescharacteristic
755C2×C7#251911yescharacteristic
756C2×C7#262911yescharacteristic
757C2×C7#265111yescharacteristic
758C2×C7#266111yescharacteristic
759C2×C7#267111yescharacteristic
760C2×C7#267611yescharacteristic
761C2×C7#270211yescharacteristic
762C2×C7#270711yescharacteristic
763C2×C7#272011yescharacteristic
764C2×C7#272911yescharacteristic
765C2×C7#276811yescharacteristic
766C2×C7#276811yescharacteristic
767C2×C7#283111yescharacteristic
768C23—22no—
769C23—22no—
770C23—22no—
771C23—22no—
772C23—22no—
773C23—22no—
774C23—22no—
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—
791C23—41no—
792C23—41no—
793C23—41no—
794C23—41no—
795C23—41no—
796C23—41no—
797C23—41no—
798C23—41no—
799C23—41no—
800C23—41no—
801C23—41no—
802C23—41no—
803C23C22×C7×D411yescharacteristic
804C23C22×C7×D411yescharacteristic
805C23C22×C7×Q811yescharacteristic
806C23C2×C7×#4111yescharacteristic
807C23C2×C7×#4111yescharacteristic
808C23C2×C7×#4111yescharacteristic
809C23C2×C7×#4111yescharacteristic
810C23C7×H(5,𝔽2)11yescharacteristic
811C23C7×H(5,𝔽2)11yescharacteristic
812C23C7×H(5,𝔽2)11yescharacteristic
813C23C7×H(5,𝔽2)11yescharacteristic
814C23C7×H(5,𝔽2)11yescharacteristic
815C23C7×2−1+411yescharacteristic
816C23C7×2−1+411yescharacteristic
817C23C7×2−1+411yescharacteristic
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—22no—
846C2×C4—22no—
847C2×C4—22no—
848C2×C4—22no—
849C2×C4—22no—
850C2×C4—22no—
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—
914C2×C4—41no—
915C2×C4C7×C22⋊Q814yes—
916C7#1647711yescharacteristic, direct product factor, Sylow
917C22—42no—
918C22—42no—
919C22—42no—
920C22—42no—
921C22—42no—
922C22—42no—
923C22—42no—
924C22—81no—
925C22—81no—
926C22—81no—
927C22—81no—
928C22—81no—
929C22—81no—
930C22—81no—
931C22—81no—
932C22C2×C7×C22⋊Q811yescharacteristic
933C22C7×#52911yescharacteristic
934C22C7×#53211yescharacteristic
935C22C7×#53411yescharacteristic
936C22C7×#53511yescharacteristic
937C22C7×#53711yescharacteristic
938C22C7×#53711yescharacteristic
939C22C7×#53811yescharacteristic
940C22C7×#53811yescharacteristic
941C22C7×#53811yescharacteristic
942C22C7×#53911yescharacteristic
943C22C7×#54011yescharacteristic
944C22C7×#54011yescharacteristic
945C22C7×#54011yescharacteristic
946C22C7×#54111yescharacteristic
947C22C7×#54211yescharacteristic
948C22C7×#54211yescharacteristic
949C22C7×#54411yescharacteristic
950C22C7×#54411yescharacteristic
951C22C7×D4211yescharacteristic
952C22C7×#54611yescharacteristic
953C22C7×#54611yescharacteristic
954C22C7×#54711yescharacteristic
955C22C7×#54811yescharacteristic
956C22C7×#54811yescharacteristic
957C22C7×D4×Q811yescharacteristic
958C22C7×#55211yescharacteristic
959C22C7×#55211yescharacteristic
960C22C7×#55411yescharacteristic
961C22C7×#55411yescharacteristic
962C22C7×#55411yescharacteristic
963C22C7×#56211yescharacteristic
964C22C7×#56211yescharacteristic
965C22C7×#56311yescharacteristic
966C22C7×#56311yescharacteristic
967C4—24no—
968C4—42no—
969C4—42no—
970C4—42no—
971C4—42no—
972C4—42no—
973C4—42no—
974C4—42no—
975C4—42no—
976C4—42no—
977C4—81no—
978C4—81no—
979C4—81no—
980C4—81no—
981C2—82no—
982C2C7×#245011yescharacteristic
983C2C7×#245211yescharacteristic
984C2C7×#251911yescharacteristic
985C2C7×#262911yescharacteristic
986C2C7×#265111yescharacteristic
987C2C7×#266111yescharacteristic
988C2C7×#267111yescharacteristic
989C2C7×#267611yescharacteristic
990C2C7×#270211yescharacteristic
991C2C7×#270711yescharacteristic
992C2C7×#272011yescharacteristic
993C2C7×#272911yescharacteristic
994C2C7×#276811yescharacteristic
995C2C7×#276811yescharacteristic
996C2C7×#283111yescharacteristic
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×#398C2semidirect
2. C2×C7×#398C2semidirect
5. C7×#1444C2semidirect
6. C7×#1442C2semidirect
7. C7×#1442C2semidirect
8. C7×#1441C2semidirect
14. C7×#1436C2semidirect
15. C7×C4⋊#95C2semidirect
55. #16477C7direct (N × H)
140. C2×#398C2×C7semidirect
141. C2×#398C2×C7semidirect
144. #1444C2×C7semidirect
145. #1442C2×C7semidirect
146. #1442C2×C7semidirect
147. #1441C2×C7semidirect
153. #1436C2×C7semidirect
154. C4⋊#95C2×C7semidirect
916. C7#16477direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C7×#3982
C2×C7×#3962
C2×C7×#3882
C7×#14442
C7×#14422
C7×#14412
C7×#14392
C7×#14362
C7×C4⋊#952
#164777