Finite Group Databasebeta

← C7×#15908 #13193124

Subgroups — C7×#15908 #13193124

Order 1792.

1934 conjugacy classes of subgroups.

The subgroup lattice has 1162 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C7×#126C211yesmaximal, characteristic, complemented
2C2×C7×#394C211yesmaximal, characteristic
3C2×C7×#394C211yesmaximal, characteristic
4C2×C7×#386C211yesmaximal, characteristic
5C7×#1444C211yesmaximal, characteristic, complemented
6C7×#1442C211yesmaximal, characteristic, complemented
7C7×#1441C211yesmaximal, characteristic, complemented
8C7×#1440C211yesmaximal, characteristic, complemented
9C7×#1439C211yesmaximal, characteristic, complemented
10C7×#1439C211yesmaximal, characteristic, complemented
11C7×#1439C211yesmaximal, characteristic, complemented
12C7×#1437C211yesmaximal, characteristic, complemented
13C7×#1436C211yesmaximal, characteristic, complemented
14C7×C22⋊#95C211yesmaximal, characteristic, complemented
15C7×C22⋊#95C211yesmaximal, characteristic, complemented
16C23×C7×D4C2211yescharacteristic
17C24×C4×C7C2211yescharacteristic
18C2×C7×#126—24no—
19C2×C7×#126—24no—
20C2×C7×#126—24no—
21C22×C7×C4⋊C4C2211yescharacteristic
22C22×C7×C4⋊C4C2211yescharacteristic
23C22×C7×C4⋊C4C2211yescharacteristic
24C22×C7×C4⋊C4C2211yescharacteristic
25C22×C7×C4⋊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×C7×C22⋊C4C2211yescharacteristic
33C22×C7×C22⋊C4C2211yescharacteristic
34C22×C7×C22⋊C4C2211yescharacteristic
35C22×C7×C22⋊C4C2211yescharacteristic
36C22×C7×C22⋊C4C2211yescharacteristic
37C22×C42×C7C2211yescharacteristic
38C7×#394—24no—
39C7×#394—24no—
40C7×#386—24no—
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#15908C711yesmaximal, characteristic, direct product factor, Sylow
58C25×C7C2311yescharacteristic
59C25×C7C2311yescharacteristic
60C22×C7×D4—22no—
61C22×C7×D4—22no—
62C22×C7×D4—22no—
63C22×C7×D4—22no—
64C22×C7×D4—22no—
65C22×C7×D4—41no—
66C22×C7×D4—41no—
67C23×C4×C7—22no—
68C23×C4×C7—22no—
69C23×C4×C7—22no—
70C23×C4×C7—41no—
71C23×C4×C7—41no—
72C23×C4×C7—41no—
73C23×C4×C7—41no—
74C23×C4×C7C2311yescharacteristic
75C23×C4×C7C2311yescharacteristic
76C23×C4×C7C2311yescharacteristic
77C23×C4×C7C2311yescharacteristic
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
87C7×#126—232no—
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—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—22no—
101C2×C7×C4⋊C4—41no—
102C2×C7×C4⋊C4—41no—
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—22no—
115C2×C7×C22⋊C4—22no—
116C2×C7×C22⋊C4—22no—
117C2×C7×C22⋊C4—22no—
118C2×C7×C22⋊C4—22no—
119C2×C7×C22⋊C4—22no—
120C2×C7×C22⋊C4—22no—
121C2×C7×C22⋊C4—22no—
122C2×C7×C22⋊C4—22no—
123C2×C7×C22⋊C4—22no—
124C2×C7×C22⋊C4—22no—
125C2×C7×C22⋊C4—41no—
126C2×C7×C22⋊C4—41no—
127C2×C7×C22⋊C4—41no—
128C2×C7×C22⋊C4—41no—
129C2×C7×C22⋊C4—41no—
130C2×C7×C22⋊C4—41no—
131C2×C7×C22⋊C4—41no—
132C2×C7×C22⋊C4—41no—
133C2×C7×C22⋊C4D414yes—
134C2×C7×C22⋊C4D414yes—
135C2×C7×C22⋊C4D414yes—
136C2×C42×C7—22no—
137C2×C42×C7—22no—
138C2×C42×C7—22no—
139C7×#95—22no—
140C7×#95—22no—
141C7×#95—22no—
142C7×#95—22no—
143C7×#95—22no—
144C7×#95—22no—
145C7×#95—22no—
146C7×#95—22no—
147C7×#95—41no—
148C7×#95—41no—
149C7×#95—41no—
150C7×#95—41no—
151C7×#95—41no—
152C7×#95—41no—
153C7×#95—41no—
154C7×#95—41no—
155C22×#126C2×C711yescharacteristic, complemented
156C2×#394C2×C711yescharacteristic
157C2×#394C2×C711yescharacteristic
158C2×#386C2×C711yescharacteristic
159#1444C2×C711yescharacteristic, complemented
160#1442C2×C711yescharacteristic, complemented
161#1441C2×C711yescharacteristic, complemented
162#1440C2×C711yescharacteristic, complemented
163#1439C2×C711yescharacteristic, complemented
164#1439C2×C711yescharacteristic, complemented
165#1439C2×C711yescharacteristic, complemented
166#1437C2×C711yescharacteristic, complemented
167#1436C2×C711yescharacteristic, complemented
168C22⋊#95C2×C711yescharacteristic, complemented
169C22⋊#95C2×C711yescharacteristic, complemented
170C24×C7—21no—
171C24×C7—21no—
172C24×C7—21no—
173C24×C7—21no—
174C24×C7—21no—
175C24×C7—21no—
176C24×C7—21no—
177C24×C7—21no—
178C24×C7—21no—
179C24×C7—21no—
180C24×C7—21no—
181C24×C7—21no—
182C24×C7—21no—
183C24×C7—21no—
184C24×C7—21no—
185C24×C7—21no—
186C24×C7—21no—
187C24×C7—21no—
188C24×C7—21no—
189C24×C7—21no—
190C24×C7—21no—
191C24×C7—21no—
192C24×C7—21no—
193C24×C7—21no—
194C24×C7—21no—
195C24×C7—21no—
196C24×C7C2×D412yes—
197C24×C7C2×D412yes—
198C24×C7C2×D412yes—
199C24×C7#4112yes—
200C24×C7C2411yescharacteristic
201C2×C7×D4—28no—
202C2×C7×D4—44no—
203C2×C7×D4—44no—
204C2×C7×D4—44no—
205C2×C7×D4—44no—
206C2×C7×D4—44no—
207C2×C7×D4—44no—
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—21no—
263C22×C4×C7—21no—
264C22×C4×C7—21no—
265C22×C4×C7—21no—
266C22×C4×C7—21no—
267C22×C4×C7—21no—
268C22×C4×C7—21no—
269C22×C4×C7—21no—
270C22×C4×C7—21no—
271C22×C4×C7—21no—
272C22×C4×C7—21no—
273C22×C4×C7—21no—
274C22×C4×C7—21no—
275C22×C4×C7—21no—
276C22×C4×C7—21no—
277C22×C4×C7—21no—
278C22×C4×C7—21no—
279C22×C4×C7—21no—
280C22×C4×C7—21no—
281C22×C4×C7—21no—
282C22×C4×C7—21no—
283C22×C4×C7—21no—
284C22×C4×C7—21no—
285C22×C4×C7—21no—
286C22×C4×C7—21no—
287C22×C4×C7—21no—
288C22×C4×C7—44no—
289C22×C4×C7—44no—
290C22×C4×C7—44no—
291C22×C4×C7—44no—
292C22×C4×C7—44no—
293C22×C4×C7—44no—
294C22×C4×C7—44no—
295C22×C4×C7C2×D412yes—
296C22×C4×C7C2×D412yes—
297C22×C4×C7C2×D412yes—
298C22×C4×C7C2×D412yes—
299C22×C4×C7C2×D412yes—
300C22×C4×C7C2×D412yes—
301C22×C4×C7#4112yes—
302C22×C4×C7#4112yes—
303C22×C4×C7#4112yes—
304C22×C4×C7#4112yes—
305C22×C4×C7#4112yes—
306C7×C4⋊C4—28no—
307C7×C4⋊C4—28no—
308C7×C4⋊C4—28no—
309C7×C4⋊C4—44no—
310C7×C4⋊C4—44no—
311C7×C22⋊C4—28no—
312C7×C22⋊C4—28no—
313C7×C22⋊C4—28no—
314C7×C22⋊C4—44no—
315C7×C22⋊C4—44no—
316C7×C22⋊C4—44no—
317C7×C22⋊C4—44no—
318C7×C22⋊C4—44no—
319C7×C22⋊C4—44no—
320C7×C22⋊C4—44no—
321C7×C22⋊C4—44no—
322C42×C7—28no—
323C23×D4C22×C711yescharacteristic
324C24×C4C22×C711yescharacteristic
325C2×#126—24no—
326C2×#126—24no—
327C2×#126—24no—
328C22×C4⋊C4C22×C711yescharacteristic
329C22×C4⋊C4C22×C711yescharacteristic
330C22×C4⋊C4C22×C711yescharacteristic
331C22×C4⋊C4C22×C711yescharacteristic
332C22×C4⋊C4C22×C711yescharacteristic
333C22×C22⋊C4C22×C711yescharacteristic
334C22×C22⋊C4C22×C711yescharacteristic
335C22×C22⋊C4C22×C711yescharacteristic
336C22×C22⋊C4C22×C711yescharacteristic
337C22×C22⋊C4C22×C711yescharacteristic
338C22×C22⋊C4C22×C711yescharacteristic
339C22×C22⋊C4C22×C711yescharacteristic
340C22×C22⋊C4C22×C711yescharacteristic
341C22×C22⋊C4C22×C711yescharacteristic
342C22×C22⋊C4C22×C711yescharacteristic
343C22×C22⋊C4C22×C711yescharacteristic
344C22×C42C22×C711yescharacteristic
345#394—24no—
346#394—24no—
347#386—24no—
348C2×#95C22×C711yescharacteristic
349C2×#95C22×C711yescharacteristic
350C2×#95C22×C711yescharacteristic
351C2×#95C22×C711yescharacteristic
352C2×#95C22×C711yescharacteristic
353C2×#95C22×C711yescharacteristic
354C2×#95C22×C711yescharacteristic
355C2×#95C22×C711yescharacteristic
356C2×#95C22×C711yescharacteristic
357C2×#95C22×C711yescharacteristic
358C2×#95C22×C711yescharacteristic
359C2×#95C22×C711yescharacteristic
360C2×#95C22×C711yescharacteristic
361C2×#95C22×C711yescharacteristic
362C2×#95C22×C711yescharacteristic
363C2×#95C22×C711yescharacteristic
364C23×C7—22no—
365C23×C7—22no—
366C23×C7—22no—
367C23×C7—22no—
368C23×C7—22no—
369C23×C7—22no—
370C23×C7—22no—
371C23×C7—22no—
372C23×C7—22no—
373C23×C7—22no—
374C23×C7—22no—
375C23×C7—22no—
376C23×C7—22no—
377C23×C7—22no—
378C23×C7—22no—
379C23×C7—22no—
380C23×C7—22no—
381C23×C7—22no—
382C23×C7—22no—
383C23×C7—22no—
384C23×C7—22no—
385C23×C7—22no—
386C23×C7—22no—
387C23×C7—22no—
388C23×C7—22no—
389C23×C7—41no—
390C23×C7—41no—
391C23×C7—41no—
392C23×C7—41no—
393C23×C7—41no—
394C23×C7—41no—
395C23×C7—41no—
396C23×C7—41no—
397C23×C7—41no—
398C23×C7—41no—
399C23×C7—41no—
400C23×C7—41no—
401C23×C7—41no—
402C23×C7—41no—
403C23×C7—41no—
404C23×C7—41no—
405C23×C7—41no—
406C23×C7—41no—
407C23×C7—41no—
408C23×C7—41no—
409C23×C7—41no—
410C23×C7—41no—
411C23×C7—41no—
412C23×C7—41no—
413C23×C7—41no—
414C23×C7—41no—
415C23×C7—41no—
416C23×C7—41no—
417C23×C7—41no—
418C23×C7—41no—
419C23×C7—41no—
420C23×C7—41no—
421C23×C7—41no—
422C23×C7—41no—
423C23×C7—41no—
424C23×C7—41no—
425C23×C7—41no—
426C23×C7—41no—
427C23×C7—41no—
428C23×C7—41no—
429C23×C7—41no—
430C23×C7—41no—
431C23×C7—41no—
432C23×C7—41no—
433C23×C7#12014yes—
434C23×C7C22×D411yescharacteristic
435C23×C7C22×D411yescharacteristic
436C23×C7C22×D411yescharacteristic
437C23×C7C2×#4111yescharacteristic
438C23×C7C2×#4111yescharacteristic
439C23×C7C2×#4111yescharacteristic
440C23×C7C2×#4111yescharacteristic
441C23×C7C2×#4111yescharacteristic
442C23×C7C2×#4111yescharacteristic
443C23×C7H(5,𝔽2)11yescharacteristic
444C23×C7H(5,𝔽2)11yescharacteristic
445C23×C7H(5,𝔽2)11yescharacteristic
446C23×C7H(5,𝔽2)11yescharacteristic
447C23×C72−1+411yescharacteristic
448C23×C72−1+411yescharacteristic
449C7×D4—416no—
450C2×C4×C7—22no—
451C2×C4×C7—22no—
452C2×C4×C7—22no—
453C2×C4×C7—22no—
454C2×C4×C7—22no—
455C2×C4×C7—22no—
456C2×C4×C7—22no—
457C2×C4×C7—22no—
458C2×C4×C7—22no—
459C2×C4×C7—22no—
460C2×C4×C7—22no—
461C2×C4×C7—22no—
462C2×C4×C7—22no—
463C2×C4×C7—22no—
464C2×C4×C7—22no—
465C2×C4×C7—22no—
466C2×C4×C7—22no—
467C2×C4×C7—22no—
468C2×C4×C7—22no—
469C2×C4×C7—22no—
470C2×C4×C7—22no—
471C2×C4×C7—22no—
472C2×C4×C7—22no—
473C2×C4×C7—22no—
474C2×C4×C7—22no—
475C2×C4×C7—22no—
476C2×C4×C7—22no—
477C2×C4×C7—22no—
478C2×C4×C7—22no—
479C2×C4×C7—22no—
480C2×C4×C7—22no—
481C2×C4×C7—22no—
482C2×C4×C7—22no—
483C2×C4×C7—416no—
484C2×C4×C7—41no—
485C2×C4×C7—41no—
486C2×C4×C7—41no—
487C2×C4×C7—41no—
488C2×C4×C7—41no—
489C2×C4×C7—41no—
490C2×C4×C7—41no—
491C2×C4×C7—41no—
492C2×C4×C7—41no—
493C2×C4×C7—41no—
494C2×C4×C7—41no—
495C2×C4×C7—41no—
496C2×C4×C7—41no—
497C2×C4×C7—41no—
498C2×C4×C7—41no—
499C2×C4×C7—41no—
500C2×C4×C7—41no—
501C2×C4×C7—41no—
502C2×C4×C7—41no—
503C2×C4×C7—41no—
504C2×C4×C7—41no—
505C2×C4×C7—41no—
506C2×C4×C7—41no—
507C2×C4×C7—41no—
508C2×C4×C7—41no—
509C2×C4×C7—41no—
510C2×C4×C7—41no—
511C2×C4×C7—41no—
512C2×C4×C7—41no—
513C2×C4×C7—41no—
514C2×C4×C7—41no—
515C2×C4×C7—41no—
516C2×C4×C7—41no—
517C2×C4×C7—41no—
518C2×C4×C7—41no—
519C2×C4×C7—41no—
520C2×C4×C7—41no—
521C2×C4×C7—41no—
522C2×C4×C7—41no—
523C2×C4×C7—41no—
524C2×C4×C7—41no—
525C2×C4×C7—41no—
526C2×C4×C7—41no—
527C2×C4×C7—41no—
528C2×C4×C7—41no—
529C2×C4×C7—41no—
530C2×C4×C7—41no—
531C2×C4×C7—41no—
532C2×C4×C7—41no—
533C2×C4×C7—41no—
534C2×C4×C7—41no—
535C2×C4×C7—41no—
536C2×C4×C7—41no—
537C2×C4×C7—41no—
538C2×C4×C7—41no—
539C2×C4×C7—41no—
540C2×C4×C7—41no—
541C2×C4×C7—41no—
542C25C23×C711yescharacteristic
543C25C23×C711yescharacteristic
544C22×D4—22no—
545C22×D4—22no—
546C22×D4—22no—
547C22×D4—22no—
548C22×D4—22no—
549C22×D4—41no—
550C22×D4—41no—
551C23×C4—22no—
552C23×C4—22no—
553C23×C4—22no—
554C23×C4—41no—
555C23×C4—41no—
556C23×C4—41no—
557C23×C4—41no—
558C23×C4C23×C711yescharacteristic
559C23×C4C23×C711yescharacteristic
560C23×C4C23×C711yescharacteristic
561C23×C4C23×C711yescharacteristic
562C23×C4C23×C711yescharacteristic
563C23×C4C23×C711yescharacteristic
564C23×C4C23×C711yescharacteristic
565C23×C4C23×C711yescharacteristic
566C23×C4C23×C711yescharacteristic
567C23×C4C23×C711yescharacteristic
568C23×C4C23×C711yescharacteristic
569C23×C4C23×C711yescharacteristic
570C23×C4C23×C711yescharacteristic
571#126—232no—
572C2×C4⋊C4—22no—
573C2×C4⋊C4—22no—
574C2×C4⋊C4—22no—
575C2×C4⋊C4—22no—
576C2×C4⋊C4—22no—
577C2×C4⋊C4—22no—
578C2×C4⋊C4—22no—
579C2×C4⋊C4—22no—
580C2×C4⋊C4—22no—
581C2×C4⋊C4—22no—
582C2×C4⋊C4—22no—
583C2×C4⋊C4—22no—
584C2×C4⋊C4—22no—
585C2×C4⋊C4—41no—
586C2×C4⋊C4—41no—
587C2×C22⋊C4—22no—
588C2×C22⋊C4—22no—
589C2×C22⋊C4—22no—
590C2×C22⋊C4—22no—
591C2×C22⋊C4—22no—
592C2×C22⋊C4—22no—
593C2×C22⋊C4—22no—
594C2×C22⋊C4—22no—
595C2×C22⋊C4—22no—
596C2×C22⋊C4—22no—
597C2×C22⋊C4—22no—
598C2×C22⋊C4—22no—
599C2×C22⋊C4—22no—
600C2×C22⋊C4—22no—
601C2×C22⋊C4—22no—
602C2×C22⋊C4—22no—
603C2×C22⋊C4—22no—
604C2×C22⋊C4—22no—
605C2×C22⋊C4—22no—
606C2×C22⋊C4—22no—
607C2×C22⋊C4—22no—
608C2×C22⋊C4—22no—
609C2×C22⋊C4—41no—
610C2×C22⋊C4—41no—
611C2×C22⋊C4—41no—
612C2×C22⋊C4—41no—
613C2×C22⋊C4—41no—
614C2×C22⋊C4—41no—
615C2×C22⋊C4—41no—
616C2×C22⋊C4—41no—
617C2×C22⋊C4C7×D414yes—
618C2×C22⋊C4C7×D414yes—
619C2×C22⋊C4C7×D414yes—
620C2×C42—22no—
621C2×C42—22no—
622C2×C42—22no—
623#95—22no—
624#95—22no—
625#95—22no—
626#95—22no—
627#95—22no—
628#95—22no—
629#95—22no—
630#95—22no—
631#95—41no—
632#95—41no—
633#95—41no—
634#95—41no—
635#95—41no—
636#95—41no—
637#95—41no—
638#95—41no—
639C22×C7—24no—
640C22×C7—24no—
641C22×C7—24no—
642C22×C7—42no—
643C22×C7—42no—
644C22×C7—42no—
645C22×C7—42no—
646C22×C7—42no—
647C22×C7—42no—
648C22×C7—42no—
649C22×C7—42no—
650C22×C7—42no—
651C22×C7—42no—
652C22×C7—42no—
653C22×C7—42no—
654C22×C7—42no—
655C22×C7—42no—
656C22×C7—42no—
657C22×C7—42no—
658C22×C7—42no—
659C22×C7—42no—
660C22×C7—42no—
661C22×C7—81no—
662C22×C7—81no—
663C22×C7—81no—
664C22×C7—81no—
665C22×C7—81no—
666C22×C7—81no—
667C22×C7—81no—
668C22×C7—81no—
669C22×C7C2×#12011yescharacteristic
670C22×C7#52511yescharacteristic
671C22×C7#52911yescharacteristic
672C22×C7#52911yescharacteristic
673C22×C7#53211yescharacteristic
674C22×C7#53211yescharacteristic
675C22×C7#53511yescharacteristic
676C22×C7#53711yescharacteristic
677C22×C7#53711yescharacteristic
678C22×C7#53811yescharacteristic
679C22×C7#53811yescharacteristic
680C22×C7#53911yescharacteristic
681C22×C7#53911yescharacteristic
682C22×C7#54211yescharacteristic
683C22×C7#54211yescharacteristic
684C22×C7#54611yescharacteristic
685C22×C7#54611yescharacteristic
686C22×C7#54611yescharacteristic
687C22×C7#54611yescharacteristic
688C22×C7#54611yescharacteristic
689C22×C7#54611yescharacteristic
690C22×C7#54611yescharacteristic
691C22×C7#54611yescharacteristic
692C22×C7#54711yescharacteristic
693C22×C7#54711yescharacteristic
694C22×C7#54711yescharacteristic
695C22×C7#54711yescharacteristic
696C22×C7#55111yescharacteristic
697C22×C7#55211yescharacteristic
698C22×C7#55311yescharacteristic
699C22×C7#55311yescharacteristic
700C22×C7#55311yescharacteristic
701C22×C7#55611yescharacteristic
702C22×C7#56011yescharacteristic
703C22×C7#56311yescharacteristic
704C4×C7—42no—
705C4×C7—42no—
706C4×C7—42no—
707C4×C7—42no—
708C4×C7—42no—
709C4×C7—42no—
710C4×C7—42no—
711C4×C7—42no—
712C4×C7—42no—
713C4×C7—42no—
714C4×C7—42no—
715C4×C7—81no—
716C4×C7—81no—
717C24—21no—
718C24—21no—
719C24—21no—
720C24—21no—
721C24—21no—
722C24—21no—
723C24—21no—
724C24—21no—
725C24—21no—
726C24—21no—
727C24—21no—
728C24—21no—
729C24—21no—
730C24—21no—
731C24—21no—
732C24—21no—
733C24—21no—
734C24—21no—
735C24—21no—
736C24—21no—
737C24—21no—
738C24—21no—
739C24—21no—
740C24—21no—
741C24—21no—
742C24—21no—
743C24C2×C7×D412yes—
744C24C2×C7×D412yes—
745C24C2×C7×D412yes—
746C24C7×#4112yes—
747C24C24×C711yescharacteristic
748C2×D4—28no—
749C2×D4—44no—
750C2×D4—44no—
751C2×D4—44no—
752C2×D4—44no—
753C2×D4—44no—
754C2×D4—44no—
755C22×C4—21no—
756C22×C4—21no—
757C22×C4—21no—
758C22×C4—21no—
759C22×C4—21no—
760C22×C4—21no—
761C22×C4—21no—
762C22×C4—21no—
763C22×C4—21no—
764C22×C4—21no—
765C22×C4—21no—
766C22×C4—21no—
767C22×C4—21no—
768C22×C4—21no—
769C22×C4—21no—
770C22×C4—21no—
771C22×C4—21no—
772C22×C4—21no—
773C22×C4—21no—
774C22×C4—21no—
775C22×C4—21no—
776C22×C4—21no—
777C22×C4—21no—
778C22×C4—21no—
779C22×C4—21no—
780C22×C4—21no—
781C22×C4—21no—
782C22×C4—21no—
783C22×C4—21no—
784C22×C4—21no—
785C22×C4—21no—
786C22×C4—21no—
787C22×C4—21no—
788C22×C4—21no—
789C22×C4—21no—
790C22×C4—21no—
791C22×C4—21no—
792C22×C4—21no—
793C22×C4—21no—
794C22×C4—21no—
795C22×C4—21no—
796C22×C4—21no—
797C22×C4—21no—
798C22×C4—21no—
799C22×C4—21no—
800C22×C4—21no—
801C22×C4—21no—
802C22×C4—21no—
803C22×C4—21no—
804C22×C4—21no—
805C22×C4—21no—
806C22×C4—21no—
807C22×C4—21no—
808C22×C4—21no—
809C22×C4—21no—
810C22×C4—21no—
811C22×C4—21no—
812C22×C4—21no—
813C22×C4—21no—
814C22×C4—21no—
815C22×C4—21no—
816C22×C4—21no—
817C22×C4—21no—
818C22×C4—21no—
819C22×C4—21no—
820C22×C4—21no—
821C22×C4—21no—
822C22×C4—21no—
823C22×C4—21no—
824C22×C4—21no—
825C22×C4—21no—
826C22×C4—21no—
827C22×C4—21no—
828C22×C4—21no—
829C22×C4—21no—
830C22×C4—21no—
831C22×C4—21no—
832C22×C4—21no—
833C22×C4—21no—
834C22×C4—21no—
835C22×C4—44no—
836C22×C4—44no—
837C22×C4—44no—
838C22×C4—44no—
839C22×C4—44no—
840C22×C4—44no—
841C22×C4—44no—
842C22×C4C2×C7×D412yes—
843C22×C4C2×C7×D412yes—
844C22×C4C2×C7×D412yes—
845C22×C4C2×C7×D412yes—
846C22×C4C2×C7×D412yes—
847C22×C4C2×C7×D412yes—
848C22×C4C7×#4112yes—
849C22×C4C7×#4112yes—
850C22×C4C7×#4112yes—
851C22×C4C7×#4112yes—
852C22×C4C7×#4112yes—
853C4⋊C4—28no—
854C4⋊C4—28no—
855C4⋊C4—28no—
856C4⋊C4—44no—
857C4⋊C4—44no—
858C22⋊C4—28no—
859C22⋊C4—28no—
860C22⋊C4—28no—
861C22⋊C4—44no—
862C22⋊C4—44no—
863C22⋊C4—44no—
864C22⋊C4—44no—
865C22⋊C4—44no—
866C22⋊C4—44no—
867C22⋊C4—44no—
868C22⋊C4—44no—
869C42—28no—
870C2×C7—44no—
871C2×C7—82no—
872C2×C7#240411yescharacteristic
873C2×C7#243011yescharacteristic
874C2×C7#243011yescharacteristic
875C2×C7#246611yescharacteristic
876C2×C7#246811yescharacteristic
877C2×C7#252111yescharacteristic
878C2×C7#255311yescharacteristic
879C2×C7#255911yescharacteristic
880C2×C7#255911yescharacteristic
881C2×C7#268511yescharacteristic
882C2×C7#269111yescharacteristic
883C2×C7#269111yescharacteristic
884C2×C7#269511yescharacteristic
885C2×C7#271511yescharacteristic
886C2×C7#271811yescharacteristic
887C23—22no—
888C23—22no—
889C23—22no—
890C23—22no—
891C23—22no—
892C23—22no—
893C23—22no—
894C23—22no—
895C23—22no—
896C23—22no—
897C23—22no—
898C23—22no—
899C23—22no—
900C23—22no—
901C23—22no—
902C23—22no—
903C23—22no—
904C23—22no—
905C23—22no—
906C23—22no—
907C23—22no—
908C23—22no—
909C23—22no—
910C23—22no—
911C23—22no—
912C23—41no—
913C23—41no—
914C23—41no—
915C23—41no—
916C23—41no—
917C23—41no—
918C23—41no—
919C23—41no—
920C23—41no—
921C23—41no—
922C23—41no—
923C23—41no—
924C23—41no—
925C23—41no—
926C23—41no—
927C23—41no—
928C23—41no—
929C23—41no—
930C23—41no—
931C23—41no—
932C23—41no—
933C23—41no—
934C23—41no—
935C23—41no—
936C23—41no—
937C23—41no—
938C23—41no—
939C23—41no—
940C23—41no—
941C23—41no—
942C23—41no—
943C23—41no—
944C23—41no—
945C23—41no—
946C23—41no—
947C23—41no—
948C23—41no—
949C23—41no—
950C23—41no—
951C23—41no—
952C23—41no—
953C23—41no—
954C23—41no—
955C23—41no—
956C23C7×#12014yes—
957C23C22×C7×D411yescharacteristic
958C23C22×C7×D411yescharacteristic
959C23C22×C7×D411yescharacteristic
960C23C2×C7×#4111yescharacteristic
961C23C2×C7×#4111yescharacteristic
962C23C2×C7×#4111yescharacteristic
963C23C2×C7×#4111yescharacteristic
964C23C2×C7×#4111yescharacteristic
965C23C2×C7×#4111yescharacteristic
966C23C7×H(5,𝔽2)11yescharacteristic
967C23C7×H(5,𝔽2)11yescharacteristic
968C23C7×H(5,𝔽2)11yescharacteristic
969C23C7×H(5,𝔽2)11yescharacteristic
970C23C7×2−1+411yescharacteristic
971C23C7×2−1+411yescharacteristic
972D4—416no—
973C2×C4—22no—
974C2×C4—22no—
975C2×C4—22no—
976C2×C4—22no—
977C2×C4—22no—
978C2×C4—22no—
979C2×C4—22no—
980C2×C4—22no—
981C2×C4—22no—
982C2×C4—22no—
983C2×C4—22no—
984C2×C4—22no—
985C2×C4—22no—
986C2×C4—22no—
987C2×C4—22no—
988C2×C4—22no—
989C2×C4—22no—
990C2×C4—22no—
991C2×C4—22no—
992C2×C4—22no—
993C2×C4—22no—
994C2×C4—22no—
995C2×C4—22no—
996C2×C4—22no—
997C2×C4—22no—
998C2×C4—22no—
999C2×C4—22no—
1000C2×C4—22no—
1001C2×C4—22no—
1002C2×C4—22no—
1003C2×C4—22no—
1004C2×C4—22no—
1005C2×C4—22no—
1006C2×C4—416no—
1007C2×C4—41no—
1008C2×C4—41no—
1009C2×C4—41no—
1010C2×C4—41no—
1011C2×C4—41no—
1012C2×C4—41no—
1013C2×C4—41no—
1014C2×C4—41no—
1015C2×C4—41no—
1016C2×C4—41no—
1017C2×C4—41no—
1018C2×C4—41no—
1019C2×C4—41no—
1020C2×C4—41no—
1021C2×C4—41no—
1022C2×C4—41no—
1023C2×C4—41no—
1024C2×C4—41no—
1025C2×C4—41no—
1026C2×C4—41no—
1027C2×C4—41no—
1028C2×C4—41no—
1029C2×C4—41no—
1030C2×C4—41no—
1031C2×C4—41no—
1032C2×C4—41no—
1033C2×C4—41no—
1034C2×C4—41no—
1035C2×C4—41no—
1036C2×C4—41no—
1037C2×C4—41no—
1038C2×C4—41no—
1039C2×C4—41no—
1040C2×C4—41no—
1041C2×C4—41no—
1042C2×C4—41no—
1043C2×C4—41no—
1044C2×C4—41no—
1045C2×C4—41no—
1046C2×C4—41no—
1047C2×C4—41no—
1048C2×C4—41no—
1049C2×C4—41no—
1050C2×C4—41no—
1051C2×C4—41no—
1052C2×C4—41no—
1053C2×C4—41no—
1054C2×C4—41no—
1055C2×C4—41no—
1056C2×C4—41no—
1057C2×C4—41no—
1058C2×C4—41no—
1059C2×C4—41no—
1060C2×C4—41no—
1061C2×C4—41no—
1062C2×C4—41no—
1063C2×C4—41no—
1064C2×C4—41no—
1065C7#1590811yescharacteristic, direct product factor, Sylow
1066C22—24no—
1067C22—24no—
1068C22—24no—
1069C22—42no—
1070C22—42no—
1071C22—42no—
1072C22—42no—
1073C22—42no—
1074C22—42no—
1075C22—42no—
1076C22—42no—
1077C22—42no—
1078C22—42no—
1079C22—42no—
1080C22—42no—
1081C22—42no—
1082C22—42no—
1083C22—42no—
1084C22—42no—
1085C22—42no—
1086C22—42no—
1087C22—42no—
1088C22—81no—
1089C22—81no—
1090C22—81no—
1091C22—81no—
1092C22—81no—
1093C22—81no—
1094C22—81no—
1095C22—81no—
1096C22C2×C7×#12011yescharacteristic
1097C22C7×#52511yescharacteristic
1098C22C7×#52911yescharacteristic
1099C22C7×#52911yescharacteristic
1100C22C7×#53211yescharacteristic
1101C22C7×#53211yescharacteristic
1102C22C7×#53511yescharacteristic
1103C22C7×#53711yescharacteristic
1104C22C7×#53711yescharacteristic
1105C22C7×#53811yescharacteristic
1106C22C7×#53811yescharacteristic
1107C22C7×#53911yescharacteristic
1108C22C7×#53911yescharacteristic
1109C22C7×#54211yescharacteristic
1110C22C7×#54211yescharacteristic
1111C22C7×#54611yescharacteristic
1112C22C7×#54611yescharacteristic
1113C22C7×#54611yescharacteristic
1114C22C7×#54611yescharacteristic
1115C22C7×#54611yescharacteristic
1116C22C7×#54611yescharacteristic
1117C22C7×#54611yescharacteristic
1118C22C7×#54611yescharacteristic
1119C22C7×#54711yescharacteristic
1120C22C7×#54711yescharacteristic
1121C22C7×#54711yescharacteristic
1122C22C7×#54711yescharacteristic
1123C22C7×#55111yescharacteristic
1124C22C7×#55211yescharacteristic
1125C22C7×#55311yescharacteristic
1126C22C7×#55311yescharacteristic
1127C22C7×#55311yescharacteristic
1128C22C7×#55611yescharacteristic
1129C22C7×#56011yescharacteristic
1130C22C7×#56311yescharacteristic
1131C4—42no—
1132C4—42no—
1133C4—42no—
1134C4—42no—
1135C4—42no—
1136C4—42no—
1137C4—42no—
1138C4—42no—
1139C4—42no—
1140C4—42no—
1141C4—42no—
1142C4—81no—
1143C4—81no—
1144C2—44no—
1145C2—82no—
1146C2C7×#240411yescharacteristic
1147C2C7×#243011yescharacteristic
1148C2C7×#243011yescharacteristic
1149C2C7×#246611yescharacteristic
1150C2C7×#246811yescharacteristic
1151C2C7×#252111yescharacteristic
1152C2C7×#255311yescharacteristic
1153C2C7×#255911yescharacteristic
1154C2C7×#255911yescharacteristic
1155C2C7×#268511yescharacteristic
1156C2C7×#269111yescharacteristic
1157C2C7×#269111yescharacteristic
1158C2C7×#269511yescharacteristic
1159C2C7×#271511yescharacteristic
1160C2C7×#271811yescharacteristic
subgroupG/H
center, socleC24×C7C24
commutator, Frattini, cosocleC24C24×C7
prime radicalC23×C7×D4C22
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C24×C7 ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. C22×C7×#126C2semidirect
5. C7×#1444C2semidirect
6. C7×#1442C2semidirect
7. C7×#1441C2semidirect
8. C7×#1440C2semidirect
9. C7×#1439C2semidirect
10. C7×#1439C2semidirect
11. C7×#1439C2semidirect
12. C7×#1437C2semidirect
13. C7×#1436C2semidirect
14. C7×C22⋊#95C2semidirect
15. C7×C22⋊#95C2semidirect
57. #15908C7direct (N × H)
155. C22×#126C2×C7semidirect
159. #1444C2×C7semidirect
160. #1442C2×C7semidirect
161. #1441C2×C7semidirect
162. #1440C2×C7semidirect
163. #1439C2×C7semidirect
164. #1439C2×C7semidirect
165. #1439C2×C7semidirect
166. #1437C2×C7semidirect
167. #1436C2×C7semidirect
168. C22⋊#95C2×C7semidirect
169. C22⋊#95C2×C7semidirect
1065. C7#15908direct (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×#3942
C2×C7×#3862
C7×#14442
C7×#14422
C7×#14412
C7×#14402
C7×#14392
C7×#14372
C7×#14362
C7×C22⋊#952
#159087