Finite Group Databasebeta

← C7×#16569 #13193785

Subgroups — C7×#16569 #13193785

Order 1792.

1398 conjugacy classes of subgroups.

The subgroup lattice has 992 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C7×#398C211yesmaximal, characteristic, complemented
2C2×C7×#380C211yesmaximal, characteristic
3C7×#1445C211yesmaximal, characteristic, complemented
4C7×#1443C211yesmaximal, characteristic, complemented
5C7×#1442C211yesmaximal, characteristic, complemented
6C7×#1442C211yesmaximal, characteristic, complemented
7C7×#1442C211yesmaximal, characteristic, complemented
8C7×#1441C211yesmaximal, characteristic, complemented
9C7×#1441C211yesmaximal, characteristic, complemented
10C7×#1439C211yesmaximal, characteristic
11C7×#1439C211yesmaximal, characteristic
12C7×#1439C211yesmaximal, characteristic
13C7×#1439C211yesmaximal, characteristic
14C7×C22⋊#95C211yesmaximal, characteristic
15C7×C22⋊#95C211yesmaximal, characteristic
16C24×C4×C7C2211yescharacteristic
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×C22⋊C4C2211yescharacteristic
24C22×C7×C22⋊C4C2211yescharacteristic
25C22×C7×C22⋊C4C2211yescharacteristic
26C22×C7×C22⋊C4C2211yescharacteristic
27C22×C7×C22⋊C4C2211yescharacteristic
28C22×C7×C22⋊C4C2211yescharacteristic
29C7×#398—24no—
30C7×#380—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
53#16569C711yesmaximal, characteristic, direct product factor, Sylow
54C25×C7C2311yescharacteristic
55C23×C4×C7—22no—
56C23×C4×C7—22no—
57C23×C4×C7—41no—
58C23×C4×C7—41no—
59C23×C4×C7—41no—
60C23×C4×C7—41no—
61C23×C4×C7Q814yes—
62C23×C4×C7C2311yescharacteristic
63C23×C4×C7C2311yescharacteristic
64C23×C4×C7C2311yescharacteristic
65C23×C4×C7C2311yescharacteristic
66C23×C4×C7C2311yescharacteristic
67C23×C4×C7C2311yescharacteristic
68C23×C4×C7C2311yescharacteristic
69C23×C4×C7C2311yescharacteristic
70C23×C4×C7C2311yescharacteristic
71C23×C4×C7C2311yescharacteristic
72C23×C4×C7C2311yescharacteristic
73C23×C4×C7C2311yescharacteristic
74C23×C4×C7C2311yescharacteristic
75C23×C4×C7C2311yescharacteristic
76C2×C7×C4⋊C4—22no—
77C2×C7×C4⋊C4—22no—
78C2×C7×C4⋊C4—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×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⋊C4D414yes—
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—22no—
104C2×C7×C22⋊C4—41no—
105C2×C7×C22⋊C4—41no—
106C2×C7×C22⋊C4—41no—
107C2×C7×C22⋊C4—41no—
108C2×C7×C22⋊C4—41no—
109C2×C7×C22⋊C4—41no—
110C2×C7×C22⋊C4—41no—
111C2×C7×C22⋊C4—41no—
112C7×#95—22no—
113C7×#95—22no—
114C7×#95—22no—
115C7×#95—22no—
116C7×#95—22no—
117C7×#95—22no—
118C7×#95—22no—
119C7×#95—22no—
120C7×#95—22no—
121C7×#95—41no—
122C7×#95—41no—
123C7×#95—41no—
124C7×#95—41no—
125C7×#95—41no—
126C7×#95—41no—
127C7×#95—41no—
128C7×#95—41no—
129C7×#95—41no—
130C7×#95—41no—
131C7×#95—41no—
132C7×#95—41no—
133C7×#95—41no—
134C2×#398C2×C711yescharacteristic, complemented
135C2×#380C2×C711yescharacteristic
136#1445C2×C711yescharacteristic, complemented
137#1443C2×C711yescharacteristic, complemented
138#1442C2×C711yescharacteristic, complemented
139#1442C2×C711yescharacteristic, complemented
140#1442C2×C711yescharacteristic, complemented
141#1441C2×C711yescharacteristic, complemented
142#1441C2×C711yescharacteristic, complemented
143#1439C2×C711yescharacteristic
144#1439C2×C711yescharacteristic
145#1439C2×C711yescharacteristic
146#1439C2×C711yescharacteristic
147C22⋊#95C2×C711yescharacteristic
148C22⋊#95C2×C711yescharacteristic
149C24×C7—21no—
150C24×C7—21no—
151C24×C7—21no—
152C24×C7—21no—
153C24×C7—21no—
154C24×C7—21no—
155C24×C7—21no—
156C24×C7—21no—
157C24×C7—21no—
158C24×C7—21no—
159C24×C7—21no—
160C24×C7—21no—
161C24×C7C2×Q812yes—
162C24×C7#4112yes—
163C24×C7#4112yes—
164C24×C7C2411yescharacteristic
165C22×C4×C7—21no—
166C22×C4×C7—21no—
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—28no—
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—44no—
257C22×C4×C7—44no—
258C22×C4×C7—44no—
259C22×C4×C7—44no—
260C22×C4×C7—44no—
261C22×C4×C7—44no—
262C22×C4×C7C2×D412yes—
263C22×C4×C7C2×D412yes—
264C22×C4×C7C2×D412yes—
265C22×C4×C7C2×Q812yes—
266C22×C4×C7C2×Q812yes—
267C22×C4×C7#4112yes—
268C22×C4×C7#4112yes—
269C22×C4×C7#4112yes—
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×C22⋊C4—44no—
277C7×C22⋊C4—44no—
278C7×C22⋊C4—44no—
279C7×C22⋊C4—44no—
280C7×C22⋊C4—44no—
281C7×C22⋊C4—44no—
282C24×C4C22×C711yescharacteristic
283C22×C4⋊C4C22×C711yescharacteristic
284C22×C4⋊C4C22×C711yescharacteristic
285C22×C4⋊C4C22×C711yescharacteristic
286C22×C4⋊C4C22×C711yescharacteristic
287C22×C4⋊C4C22×C711yescharacteristic
288C22×C4⋊C4C22×C711yescharacteristic
289C22×C22⋊C4C22×C711yescharacteristic
290C22×C22⋊C4C22×C711yescharacteristic
291C22×C22⋊C4C22×C711yescharacteristic
292C22×C22⋊C4C22×C711yescharacteristic
293C22×C22⋊C4C22×C711yescharacteristic
294C22×C22⋊C4C22×C711yescharacteristic
295#398—24no—
296#380—24no—
297C2×#95C22×C711yescharacteristic
298C2×#95C22×C711yescharacteristic
299C2×#95C22×C711yescharacteristic
300C2×#95C22×C711yescharacteristic
301C2×#95C22×C711yescharacteristic
302C2×#95C22×C711yescharacteristic
303C2×#95C22×C711yescharacteristic
304C2×#95C22×C711yescharacteristic
305C2×#95C22×C711yescharacteristic
306C2×#95C22×C711yescharacteristic
307C2×#95C22×C711yescharacteristic
308C2×#95C22×C711yescharacteristic
309C2×#95C22×C711yescharacteristic
310C2×#95C22×C711yescharacteristic
311C2×#95C22×C711yescharacteristic
312C2×#95C22×C711yescharacteristic
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—22no—
327C23×C7—22no—
328C23×C7—22no—
329C23×C7—22no—
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#12514yes—
354C23×C7C22×D411yescharacteristic
355C23×C7C22×Q811yescharacteristic
356C23×C7C2×#4111yescharacteristic
357C23×C7C2×#4111yescharacteristic
358C23×C7C2×#4111yescharacteristic
359C23×C7C2×#4111yescharacteristic
360C23×C7C2×#4111yescharacteristic
361C23×C7H(5,𝔽2)11yescharacteristic
362C23×C7H(5,𝔽2)11yescharacteristic
363C23×C7H(5,𝔽2)11yescharacteristic
364C23×C7H(5,𝔽2)11yescharacteristic
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—416no—
391C2×C4×C7—41no—
392C2×C4×C7—41no—
393C2×C4×C7—41no—
394C2×C4×C7—41no—
395C2×C4×C7—41no—
396C2×C4×C7—41no—
397C2×C4×C7—41no—
398C2×C4×C7—41no—
399C2×C4×C7—41no—
400C2×C4×C7—41no—
401C2×C4×C7—41no—
402C2×C4×C7—41no—
403C2×C4×C7—41no—
404C2×C4×C7—41no—
405C2×C4×C7—41no—
406C2×C4×C7—41no—
407C2×C4×C7—41no—
408C2×C4×C7—41no—
409C2×C4×C7—41no—
410C2×C4×C7—41no—
411C2×C4×C7—41no—
412C2×C4×C7—41no—
413C2×C4×C7—41no—
414C2×C4×C7—41no—
415C2×C4×C7—41no—
416C2×C4×C7—41no—
417C2×C4×C7—41no—
418C2×C4×C7—41no—
419C2×C4×C7—41no—
420C2×C4×C7—41no—
421C2×C4×C7—41no—
422C2×C4×C7—41no—
423C2×C4×C7—41no—
424C2×C4×C7—41no—
425C2×C4×C7—41no—
426C2×C4×C7—41no—
427C2×C4×C7—41no—
428C2×C4×C7—41no—
429C2×C4×C7—41no—
430C2×C4×C7—41no—
431C2×C4×C7—41no—
432C2×C4×C7—41no—
433C2×C4×C7—41no—
434C2×C4×C7—41no—
435C2×C4×C7—41no—
436C2×C4×C7—41no—
437C2×C4×C7—41no—
438C2×C4×C7—41no—
439C2×C4×C7—41no—
440C2×C4×C7—41no—
441C2×C4×C7—41no—
442C2×C4×C7—41no—
443C2×C4×C7—41no—
444C2×C4×C7—41no—
445C2×C4×C7—41no—
446C2×C4×C7—41no—
447C2×C4×C7—41no—
448C2×C4×C7—41no—
449C2×C4×C7—41no—
450C2×C4×C7—41no—
451C2×C4×C7—41no—
452C2×C4×C7—41no—
453C2×C4×C7—41no—
454C2×C4×C7—41no—
455C2×C4×C7—41no—
456C2×C4×C7—41no—
457C2×C4×C7—41no—
458C2×C4×C7—41no—
459C2×C4×C7—41no—
460C2×C4×C7—41no—
461C2×C4×C7—41no—
462C2×C4×C7—41no—
463C2×C4×C7—41no—
464C2×C4×C7—41no—
465C2×C4×C7—41no—
466C2×C4×C7—41no—
467C2×C4×C7C22⋊Q814yes—
468C25C23×C711yescharacteristic
469C23×C4—22no—
470C23×C4—22no—
471C23×C4—41no—
472C23×C4—41no—
473C23×C4—41no—
474C23×C4—41no—
475C23×C4C7×Q814yes—
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
488C23×C4C23×C711yescharacteristic
489C23×C4C23×C711yescharacteristic
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—41no—
497C2×C4⋊C4—41no—
498C2×C4⋊C4—41no—
499C2×C4⋊C4—41no—
500C2×C4⋊C4—41no—
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⋊C4C7×D414yes—
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—22no—
515C2×C22⋊C4—22no—
516C2×C22⋊C4—22no—
517C2×C22⋊C4—22no—
518C2×C22⋊C4—41no—
519C2×C22⋊C4—41no—
520C2×C22⋊C4—41no—
521C2×C22⋊C4—41no—
522C2×C22⋊C4—41no—
523C2×C22⋊C4—41no—
524C2×C22⋊C4—41no—
525C2×C22⋊C4—41no—
526#95—22no—
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—41no—
536#95—41no—
537#95—41no—
538#95—41no—
539#95—41no—
540#95—41no—
541#95—41no—
542#95—41no—
543#95—41no—
544#95—41no—
545#95—41no—
546#95—41no—
547#95—41no—
548C22×C7—24no—
549C22×C7—24no—
550C22×C7—24no—
551C22×C7—42no—
552C22×C7—42no—
553C22×C7—42no—
554C22×C7—42no—
555C22×C7—42no—
556C22×C7—42no—
557C22×C7—42no—
558C22×C7—42no—
559C22×C7—42no—
560C22×C7—42no—
561C22×C7—42no—
562C22×C7—42no—
563C22×C7C2×C22⋊Q811yescharacteristic
564C22×C7C2×#12511yescharacteristic
565C22×C7#53311yescharacteristic
566C22×C7#53411yescharacteristic
567C22×C7#53511yescharacteristic
568C22×C7#53811yescharacteristic
569C22×C7#53811yescharacteristic
570C22×C7#53811yescharacteristic
571C22×C7#53811yescharacteristic
572C22×C7#53911yescharacteristic
573C22×C7#53911yescharacteristic
574C22×C7#53911yescharacteristic
575C22×C7#53911yescharacteristic
576C22×C7#54011yescharacteristic
577C22×C7#54011yescharacteristic
578C22×C7#54311yescharacteristic
579C22×C7#54311yescharacteristic
580C22×C7#54411yescharacteristic
581C22×C7#54411yescharacteristic
582C22×C7#54611yescharacteristic
583C22×C7#54611yescharacteristic
584C22×C7#54811yescharacteristic
585C22×C7#54811yescharacteristic
586C22×C7#55111yescharacteristic
587C22×C7#55111yescharacteristic
588C22×C7#55211yescharacteristic
589C22×C7#55311yescharacteristic
590C22×C7#55311yescharacteristic
591C22×C7#55311yescharacteristic
592C22×C7#55511yescharacteristic
593C22×C7#55611yescharacteristic
594C22×C7#56011yescharacteristic
595C22×C7#56211yescharacteristic
596C22×C7#56211yescharacteristic
597C22×C7#56311yescharacteristic
598C4×C7—24no—
599C4×C7—42no—
600C4×C7—42no—
601C4×C7—42no—
602C4×C7—42no—
603C4×C7—42no—
604C4×C7—81no—
605C4×C7—81no—
606C4×C7—81no—
607C4×C7—81no—
608C4×C7—81no—
609C4×C7—81no—
610C4×C7—81no—
611C4×C7—81no—
612C24—21no—
613C24—21no—
614C24—21no—
615C24—21no—
616C24—21no—
617C24—21no—
618C24—21no—
619C24—21no—
620C24—21no—
621C24—21no—
622C24—21no—
623C24—21no—
624C24C2×C7×Q812yes—
625C24C7×#4112yes—
626C24C7×#4112yes—
627C24C24×C711yescharacteristic
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—28no—
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—44no—
720C22×C4—44no—
721C22×C4—44no—
722C22×C4—44no—
723C22×C4—44no—
724C22×C4—44no—
725C22×C4C2×C7×D412yes—
726C22×C4C2×C7×D412yes—
727C22×C4C2×C7×D412yes—
728C22×C4C2×C7×Q812yes—
729C22×C4C2×C7×Q812yes—
730C22×C4C7×#4112yes—
731C22×C4C7×#4112yes—
732C22×C4C7×#4112yes—
733C4⋊C4—44no—
734C4⋊C4—44no—
735C4⋊C4—44no—
736C4⋊C4—44no—
737C4⋊C4—44no—
738C4⋊C4—44no—
739C22⋊C4—44no—
740C22⋊C4—44no—
741C22⋊C4—44no—
742C22⋊C4—44no—
743C22⋊C4—44no—
744C22⋊C4—44no—
745C2×C7—44no—
746C2×C7#243911yescharacteristic
747C2×C7#244211yescharacteristic
748C2×C7#256911yescharacteristic
749C2×C7#262611yescharacteristic
750C2×C7#264611yescharacteristic
751C2×C7#266711yescharacteristic
752C2×C7#268811yescharacteristic
753C2×C7#269611yescharacteristic
754C2×C7#271111yescharacteristic
755C2×C7#272811yescharacteristic
756C2×C7#275611yescharacteristic
757C2×C7#278111yescharacteristic
758C2×C7#278611yescharacteristic
759C2×C7#278711yescharacteristic
760C2×C7#284111yescharacteristic
761C23—22no—
762C23—22no—
763C23—22no—
764C23—22no—
765C23—22no—
766C23—22no—
767C23—22no—
768C23—22no—
769C23—22no—
770C23—22no—
771C23—22no—
772C23—22no—
773C23—22no—
774C23—22no—
775C23—22no—
776C23—22no—
777C23—22no—
778C23—22no—
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—
795C23C7×#12514yes—
796C23C22×C7×D411yescharacteristic
797C23C22×C7×Q811yescharacteristic
798C23C2×C7×#4111yescharacteristic
799C23C2×C7×#4111yescharacteristic
800C23C2×C7×#4111yescharacteristic
801C23C2×C7×#4111yescharacteristic
802C23C2×C7×#4111yescharacteristic
803C23C7×H(5,𝔽2)11yescharacteristic
804C23C7×H(5,𝔽2)11yescharacteristic
805C23C7×H(5,𝔽2)11yescharacteristic
806C23C7×H(5,𝔽2)11yescharacteristic
807C23C7×H(5,𝔽2)11yescharacteristic
808C23C7×H(5,𝔽2)11yescharacteristic
809C23C7×2−1+411yescharacteristic
810C23C7×2−1+411yescharacteristic
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—416no—
833C2×C4—41no—
834C2×C4—41no—
835C2×C4—41no—
836C2×C4—41no—
837C2×C4—41no—
838C2×C4—41no—
839C2×C4—41no—
840C2×C4—41no—
841C2×C4—41no—
842C2×C4—41no—
843C2×C4—41no—
844C2×C4—41no—
845C2×C4—41no—
846C2×C4—41no—
847C2×C4—41no—
848C2×C4—41no—
849C2×C4—41no—
850C2×C4—41no—
851C2×C4—41no—
852C2×C4—41no—
853C2×C4—41no—
854C2×C4—41no—
855C2×C4—41no—
856C2×C4—41no—
857C2×C4—41no—
858C2×C4—41no—
859C2×C4—41no—
860C2×C4—41no—
861C2×C4—41no—
862C2×C4—41no—
863C2×C4—41no—
864C2×C4—41no—
865C2×C4—41no—
866C2×C4—41no—
867C2×C4—41no—
868C2×C4—41no—
869C2×C4—41no—
870C2×C4—41no—
871C2×C4—41no—
872C2×C4—41no—
873C2×C4—41no—
874C2×C4—41no—
875C2×C4—41no—
876C2×C4—41no—
877C2×C4—41no—
878C2×C4—41no—
879C2×C4—41no—
880C2×C4—41no—
881C2×C4—41no—
882C2×C4—41no—
883C2×C4—41no—
884C2×C4—41no—
885C2×C4—41no—
886C2×C4—41no—
887C2×C4—41no—
888C2×C4—41no—
889C2×C4—41no—
890C2×C4—41no—
891C2×C4—41no—
892C2×C4—41no—
893C2×C4—41no—
894C2×C4—41no—
895C2×C4—41no—
896C2×C4—41no—
897C2×C4—41no—
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×C4C7×C22⋊Q814yes—
910C7#1656911yescharacteristic, direct product factor, Sylow
911C22—24no—
912C22—24no—
913C22—24no—
914C22—42no—
915C22—42no—
916C22—42no—
917C22—42no—
918C22—42no—
919C22—42no—
920C22—42no—
921C22—42no—
922C22—42no—
923C22—42no—
924C22—42no—
925C22—42no—
926C22C2×C7×C22⋊Q811yescharacteristic
927C22C2×C7×#12511yescharacteristic
928C22C7×#53311yescharacteristic
929C22C7×#53411yescharacteristic
930C22C7×#53511yescharacteristic
931C22C7×#53811yescharacteristic
932C22C7×#53811yescharacteristic
933C22C7×#53811yescharacteristic
934C22C7×#53811yescharacteristic
935C22C7×#53911yescharacteristic
936C22C7×#53911yescharacteristic
937C22C7×#53911yescharacteristic
938C22C7×#53911yescharacteristic
939C22C7×#54011yescharacteristic
940C22C7×#54011yescharacteristic
941C22C7×#54311yescharacteristic
942C22C7×#54311yescharacteristic
943C22C7×#54411yescharacteristic
944C22C7×#54411yescharacteristic
945C22C7×#54611yescharacteristic
946C22C7×#54611yescharacteristic
947C22C7×#54811yescharacteristic
948C22C7×#54811yescharacteristic
949C22C7×#55111yescharacteristic
950C22C7×#55111yescharacteristic
951C22C7×#55211yescharacteristic
952C22C7×#55311yescharacteristic
953C22C7×#55311yescharacteristic
954C22C7×#55311yescharacteristic
955C22C7×#55511yescharacteristic
956C22C7×#55611yescharacteristic
957C22C7×#56011yescharacteristic
958C22C7×#56211yescharacteristic
959C22C7×#56211yescharacteristic
960C22C7×#56311yescharacteristic
961C4—24no—
962C4—42no—
963C4—42no—
964C4—42no—
965C4—42no—
966C4—42no—
967C4—81no—
968C4—81no—
969C4—81no—
970C4—81no—
971C4—81no—
972C4—81no—
973C4—81no—
974C4—81no—
975C2—44no—
976C2C7×#243911yescharacteristic
977C2C7×#244211yescharacteristic
978C2C7×#256911yescharacteristic
979C2C7×#262611yescharacteristic
980C2C7×#264611yescharacteristic
981C2C7×#266711yescharacteristic
982C2C7×#268811yescharacteristic
983C2C7×#269611yescharacteristic
984C2C7×#271111yescharacteristic
985C2C7×#272811yescharacteristic
986C2C7×#275611yescharacteristic
987C2C7×#278111yescharacteristic
988C2C7×#278611yescharacteristic
989C2C7×#278711yescharacteristic
990C2C7×#284111yescharacteristic
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
3. C7×#1445C2semidirect
4. C7×#1443C2semidirect
5. C7×#1442C2semidirect
6. C7×#1442C2semidirect
7. C7×#1442C2semidirect
8. C7×#1441C2semidirect
9. C7×#1441C2semidirect
53. #16569C7direct (N × H)
134. C2×#398C2×C7semidirect
136. #1445C2×C7semidirect
137. #1443C2×C7semidirect
138. #1442C2×C7semidirect
139. #1442C2×C7semidirect
140. #1442C2×C7semidirect
141. #1441C2×C7semidirect
142. #1441C2×C7semidirect
910. C7#16569direct (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×#3802
C7×#14452
C7×#14432
C7×#14422
C7×#14412
C7×#14392
C7×C22⋊#952
#165697