Finite Group Databasebeta

← C7×#13980 #13191196

Subgroups — C7×#13980 #13191196

Order 1792.

1962 conjugacy classes of subgroups.

The subgroup lattice has 1042 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C7×#387C211yesmaximal, characteristic, complemented
2C2×C7×#385C211yesmaximal, characteristic
3C2×C7×#380C211yesmaximal, characteristic
4C2×C4×C7×C22⋊C4C211yesmaximal, characteristic
5C22×C7×#95C211yesmaximal, characteristic
6C7×#1445C211yesmaximal, characteristic, complemented
7C7×#1443C211yesmaximal, characteristic, complemented
8C7×#1442C211yesmaximal, characteristic, complemented
9C7×#1441C211yesmaximal, characteristic, complemented
10C7×#1436C211yesmaximal, characteristic, complemented
11C7×#1436C211yesmaximal, characteristic, complemented
12C7×#1434C211yesmaximal, characteristic, complemented
13C7×C22⋊#95C211yesmaximal, characteristic
14C7×C22⋊#95C211yesmaximal, characteristic
15C7×C22⋊#95C211yesmaximal, characteristic
16C24×C4×C7C2211yescharacteristic
17C24×C4×C7C2211yescharacteristic
18C24×C4×C7C2211yescharacteristic
19C22×C7×C4⋊C4C2211yescharacteristic
20C22×C7×C4⋊C4C2211yescharacteristic
21C22×C7×C4⋊C4C2211yescharacteristic
22C22×C7×C4⋊C4C2211yescharacteristic
23C22×C7×C22⋊C4C2211yescharacteristic
24C22×C7×C22⋊C4C2211yescharacteristic
25C22×C7×C22⋊C4C2211yescharacteristic
26C22×C7×C22⋊C4C2211yescharacteristic
27C22×C42×C7C2211yescharacteristic
28C22×C42×C7C2211yescharacteristic
29C7×#387—24no—
30C7×#385C418yescomplemented
31C7×#380—24no—
32C4×C7×C22⋊C4—24no—
33C2×C7×#95—24no—
34C2×C7×#95C2211yescharacteristic
35C2×C7×#95C2211yescharacteristic
36C2×C7×#95C2211yescharacteristic
37C2×C7×#95C2211yescharacteristic
38C2×C7×#95C2211yescharacteristic
39C2×C7×#95C2211yescharacteristic
40C2×C7×#95C2211yescharacteristic
41C2×C7×#95C2211yescharacteristic
42C2×C7×#95C2211yescharacteristic
43C2×C7×#95C2211yescharacteristic
44C2×C7×#95C2211yescharacteristic
45C2×C7×#95C2211yescharacteristic
46C2×C7×#95C2211yescharacteristic
47C2×C7×#95C2211yescharacteristic
48C2×C7×#95C2211yescharacteristic
49C2×C7×#95C2211yescharacteristic
50C2×C7×#95C2211yescharacteristic
51C2×C7×#95C2211yescharacteristic
52C2×C7×#95C2211yescharacteristic
53C2×C7×#95C2211yescharacteristic
54C2×C7×#95C2211yescharacteristic
55C2×C7×#95C2211yescharacteristic
56#13980C711yesmaximal, characteristic, direct product factor, Sylow
57C25×C7C2311yescharacteristic
58C23×C4×C7—22no—
59C23×C4×C7—22no—
60C23×C4×C7—22no—
61C23×C4×C7—22no—
62C23×C4×C7—22no—
63C23×C4×C7—22no—
64C23×C4×C7—22no—
65C23×C4×C7—22no—
66C23×C4×C7—22no—
67C23×C4×C7—22no—
68C23×C4×C7—22no—
69C23×C4×C7—22no—
70C23×C4×C7—22no—
71C23×C4×C7—41no—
72C23×C4×C7—41no—
73C23×C4×C7—41no—
74C23×C4×C7—41no—
75C23×C4×C7—41no—
76C23×C4×C7—41no—
77C23×C4×C7C2×C414yes—
78C23×C4×C7Q814yes—
79C23×C4×C7C2311yescharacteristic
80C23×C4×C7C2311yescharacteristic
81C23×C4×C7C2311yescharacteristic
82C23×C4×C7C2311yescharacteristic
83C23×C4×C7C2311yescharacteristic
84C23×C4×C7C2311yescharacteristic
85C23×C4×C7C2311yescharacteristic
86C23×C4×C7C2311yescharacteristic
87C23×C4×C7C2311yescharacteristic
88C23×C4×C7C2311yescharacteristic
89C23×C4×C7C2311yescharacteristic
90C23×C4×C7C2311yescharacteristic
91C23×C4×C7C2311yescharacteristic
92C23×C4×C7C2311yescharacteristic
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—41no—
100C2×C7×C4⋊C4—41no—
101C2×C7×C4⋊C4—41no—
102C2×C7×C4⋊C4—41no—
103C2×C7×C4⋊C4C2×C414yescomplemented
104C2×C7×C4⋊C4C2×C414yescomplemented
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⋊C4C2×C414yes—
115C2×C7×C22⋊C4C2×C414yes—
116C2×C7×C22⋊C4D414yes—
117C2×C42×C7—22no—
118C2×C42×C7—22no—
119C2×C42×C7—22no—
120C2×C42×C7—22no—
121C2×C42×C7—41no—
122C2×C42×C7—41no—
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—22no—
134C7×#95—22no—
135C7×#95—22no—
136C7×#95—41no—
137C7×#95—41no—
138C7×#95—41no—
139C7×#95—41no—
140C7×#95—41no—
141C7×#95—41no—
142C7×#95C2×C414yescomplemented
143C7×#95C2×C414yescomplemented
144C7×#95D414yes—
145C2×#387C2×C711yescharacteristic, complemented
146C2×#385C2×C711yescharacteristic
147C2×#380C2×C711yescharacteristic
148C2×C4×C22⋊C4C2×C711yescharacteristic
149C22×#95C2×C711yescharacteristic
150#1445C2×C711yescharacteristic, complemented
151#1443C2×C711yescharacteristic, complemented
152#1442C2×C711yescharacteristic, complemented
153#1441C2×C711yescharacteristic, complemented
154#1436C2×C711yescharacteristic, complemented
155#1436C2×C711yescharacteristic, complemented
156#1434C2×C711yescharacteristic, complemented
157C22⋊#95C2×C711yescharacteristic
158C22⋊#95C2×C711yescharacteristic
159C22⋊#95C2×C711yescharacteristic
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×C7C22×C412yes—
169C24×C7C2×D412yes—
170C24×C7C2×Q812yes—
171C24×C7#4112yes—
172C24×C7#4112yes—
173C24×C7#4112yes—
174C24×C7#4112yes—
175C24×C7C2411yescharacteristic
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—28no—
185C22×C4×C7—28no—
186C22×C4×C7—28no—
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—28no—
248C22×C4×C7—28no—
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—44no—
264C22×C4×C7—44no—
265C22×C4×C7—44no—
266C22×C4×C7—44no—
267C22×C4×C7—44no—
268C22×C4×C7—44no—
269C22×C4×C7—44no—
270C22×C4×C7—44no—
271C22×C4×C7—44no—
272C22×C4×C7—44no—
273C22×C4×C7—44no—
274C22×C4×C7—44no—
275C22×C4×C7—44no—
276C22×C4×C7—44no—
277C22×C4×C7—44no—
278C22×C4×C7—44no—
279C22×C4×C7C22×C412yes—
280C22×C4×C7C22×C412yes—
281C22×C4×C7C22×C412yes—
282C22×C4×C7C22×C412yes—
283C22×C4×C7C22×C412yes—
284C22×C4×C7C22×C412yes—
285C22×C4×C7C2×D412yes—
286C22×C4×C7C2×D412yes—
287C22×C4×C7C2×D412yes—
288C22×C4×C7C2×D412yes—
289C22×C4×C7C2×D412yes—
290C22×C4×C7C2×Q812yes—
291C22×C4×C7C2×Q812yes—
292C22×C4×C7#4112yes—
293C22×C4×C7#4112yes—
294C22×C4×C7#4112yes—
295C7×C4⋊C4—28no—
296C7×C4⋊C4—44no—
297C7×C4⋊C4—44no—
298C7×C4⋊C4—44no—
299C7×C22⋊C4—28no—
300C7×C22⋊C4—28no—
301C7×C22⋊C4—28no—
302C7×C22⋊C4—44no—
303C42×C7—44no—
304C42×C7—44no—
305C24×C4C22×C711yescharacteristic
306C24×C4C22×C711yescharacteristic
307C24×C4C22×C711yescharacteristic
308C22×C4⋊C4C22×C711yescharacteristic
309C22×C4⋊C4C22×C711yescharacteristic
310C22×C4⋊C4C22×C711yescharacteristic
311C22×C4⋊C4C22×C711yescharacteristic
312C22×C22⋊C4C22×C711yescharacteristic
313C22×C22⋊C4C22×C711yescharacteristic
314C22×C22⋊C4C22×C711yescharacteristic
315C22×C22⋊C4C22×C711yescharacteristic
316C22×C42C22×C711yescharacteristic
317C22×C42C22×C711yescharacteristic
318#387—24no—
319#385C4×C718yescomplemented
320#380—24no—
321C4×C22⋊C4—24no—
322C2×#95—24no—
323C2×#95C22×C711yescharacteristic
324C2×#95C22×C711yescharacteristic
325C2×#95C22×C711yescharacteristic
326C2×#95C22×C711yescharacteristic
327C2×#95C22×C711yescharacteristic
328C2×#95C22×C711yescharacteristic
329C2×#95C22×C711yescharacteristic
330C2×#95C22×C711yescharacteristic
331C2×#95C22×C711yescharacteristic
332C2×#95C22×C711yescharacteristic
333C2×#95C22×C711yescharacteristic
334C2×#95C22×C711yescharacteristic
335C2×#95C22×C711yescharacteristic
336C2×#95C22×C711yescharacteristic
337C2×#95C22×C711yescharacteristic
338C2×#95C22×C711yescharacteristic
339C2×#95C22×C711yescharacteristic
340C2×#95C22×C711yescharacteristic
341C2×#95C22×C711yescharacteristic
342C2×#95C22×C711yescharacteristic
343C2×#95C22×C711yescharacteristic
344C2×#95C22×C711yescharacteristic
345C23×C7—22no—
346C23×C7—22no—
347C23×C7—22no—
348C23×C7—22no—
349C23×C7—22no—
350C23×C7—22no—
351C23×C7—22no—
352C23×C7—22no—
353C23×C7—22no—
354C23×C7—22no—
355C23×C7—22no—
356C23×C7—22no—
357C23×C7—22no—
358C23×C7—22no—
359C23×C7—22no—
360C23×C7—22no—
361C23×C7—22no—
362C23×C7—22no—
363C23×C7—22no—
364C23×C7—22no—
365C23×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#11714yes—
374C23×C7C4×D414yes—
375C23×C7C4×Q814yes—
376C23×C7C22⋊Q814yes—
377C23×C7#12314yes—
378C23×C7#12514yes—
379C23×C7#12614yes—
380C23×C7C23×C411yescharacteristic
381C23×C7C22×D411yescharacteristic
382C23×C7C22×D411yescharacteristic
383C23×C7C22×Q811yescharacteristic
384C23×C7C2×#4111yescharacteristic
385C23×C7C2×#4111yescharacteristic
386C23×C7C2×#4111yescharacteristic
387C23×C7C2×#4111yescharacteristic
388C23×C7C2×#4111yescharacteristic
389C23×C7C2×#4111yescharacteristic
390C23×C7C2×#4111yescharacteristic
391C23×C7H(5,𝔽2)11yescharacteristic
392C23×C7H(5,𝔽2)11yescharacteristic
393C23×C7H(5,𝔽2)11yescharacteristic
394C23×C72−1+411yescharacteristic
395C2×C4×C7—22no—
396C2×C4×C7—22no—
397C2×C4×C7—22no—
398C2×C4×C7—22no—
399C2×C4×C7—22no—
400C2×C4×C7—22no—
401C2×C4×C7—22no—
402C2×C4×C7—22no—
403C2×C4×C7—22no—
404C2×C4×C7—22no—
405C2×C4×C7—22no—
406C2×C4×C7—22no—
407C2×C4×C7—22no—
408C2×C4×C7—22no—
409C2×C4×C7—22no—
410C2×C4×C7—22no—
411C2×C4×C7—22no—
412C2×C4×C7—22no—
413C2×C4×C7—22no—
414C2×C4×C7—22no—
415C2×C4×C7—22no—
416C2×C4×C7—22no—
417C2×C4×C7—22no—
418C2×C4×C7—22no—
419C2×C4×C7—22no—
420C2×C4×C7—22no—
421C2×C4×C7—22no—
422C2×C4×C7—22no—
423C2×C4×C7—22no—
424C2×C4×C7—22no—
425C2×C4×C7—22no—
426C2×C4×C7—22no—
427C2×C4×C7—22no—
428C2×C4×C7—22no—
429C2×C4×C7—22no—
430C2×C4×C7—22no—
431C2×C4×C7—22no—
432C2×C4×C7—22no—
433C2×C4×C7—22no—
434C2×C4×C7—22no—
435C2×C4×C7—22no—
436C2×C4×C7—22no—
437C2×C4×C7—416no—
438C2×C4×C7—416no—
439C2×C4×C7—416no—
440C2×C4×C7—41no—
441C2×C4×C7—41no—
442C2×C4×C7—41no—
443C2×C4×C7—41no—
444C2×C4×C7—41no—
445C2×C4×C7—41no—
446C2×C4×C7—41no—
447C2×C4×C7—41no—
448C2×C4×C7—41no—
449C2×C4×C7—41no—
450C2×C4×C7—41no—
451C2×C4×C7—41no—
452C2×C4×C7—41no—
453C2×C4×C7—41no—
454C2×C4×C7—41no—
455C2×C4×C7—41no—
456C2×C4×C7—41no—
457C2×C4×C7—41no—
458C2×C4×C7—41no—
459C2×C4×C7—41no—
460C2×C4×C7—41no—
461C2×C4×C7—41no—
462C2×C4×C7—41no—
463C2×C4×C7—41no—
464C2×C4×C7—41no—
465C2×C4×C7—41no—
466C2×C4×C7—41no—
467C2×C4×C7—41no—
468C2×C4×C7—41no—
469C2×C4×C7—41no—
470C2×C4×C7—41no—
471C2×C4×C7—41no—
472C2×C4×C7—41no—
473C2×C4×C7—41no—
474C2×C4×C7—41no—
475C2×C4×C7—41no—
476C2×C4×C7—41no—
477C2×C4×C7—41no—
478C2×C4×C7—41no—
479C2×C4×C7—41no—
480C2×C4×C7—41no—
481C2×C4×C7—41no—
482C2×C4×C7—41no—
483C2×C4×C7—41no—
484C2×C4×C7—41no—
485C2×C4×C7—41no—
486C2×C4×C7—41no—
487C2×C4×C7—41no—
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×C7C4×D414yes—
495C2×C4×C7C22⋊Q814yes—
496C25C23×C711yescharacteristic
497C23×C4—22no—
498C23×C4—22no—
499C23×C4—22no—
500C23×C4—22no—
501C23×C4—22no—
502C23×C4—22no—
503C23×C4—22no—
504C23×C4—22no—
505C23×C4—22no—
506C23×C4—22no—
507C23×C4—22no—
508C23×C4—22no—
509C23×C4—22no—
510C23×C4—41no—
511C23×C4—41no—
512C23×C4—41no—
513C23×C4—41no—
514C23×C4—41no—
515C23×C4—41no—
516C23×C4C2×C4×C714yes—
517C23×C4C7×Q814yes—
518C23×C4C23×C711yescharacteristic
519C23×C4C23×C711yescharacteristic
520C23×C4C23×C711yescharacteristic
521C23×C4C23×C711yescharacteristic
522C23×C4C23×C711yescharacteristic
523C23×C4C23×C711yescharacteristic
524C23×C4C23×C711yescharacteristic
525C23×C4C23×C711yescharacteristic
526C23×C4C23×C711yescharacteristic
527C23×C4C23×C711yescharacteristic
528C23×C4C23×C711yescharacteristic
529C23×C4C23×C711yescharacteristic
530C23×C4C23×C711yescharacteristic
531C23×C4C23×C711yescharacteristic
532C2×C4⋊C4—22no—
533C2×C4⋊C4—22no—
534C2×C4⋊C4—22no—
535C2×C4⋊C4—22no—
536C2×C4⋊C4—22no—
537C2×C4⋊C4—22no—
538C2×C4⋊C4—41no—
539C2×C4⋊C4—41no—
540C2×C4⋊C4—41no—
541C2×C4⋊C4—41no—
542C2×C4⋊C4C2×C4×C714yescomplemented
543C2×C4⋊C4C2×C4×C714yescomplemented
544C2×C22⋊C4—22no—
545C2×C22⋊C4—22no—
546C2×C22⋊C4—22no—
547C2×C22⋊C4—22no—
548C2×C22⋊C4—22no—
549C2×C22⋊C4—22no—
550C2×C22⋊C4—22no—
551C2×C22⋊C4—22no—
552C2×C22⋊C4—22no—
553C2×C22⋊C4C2×C4×C714yes—
554C2×C22⋊C4C2×C4×C714yes—
555C2×C22⋊C4C7×D414yes—
556C2×C42—22no—
557C2×C42—22no—
558C2×C42—22no—
559C2×C42—22no—
560C2×C42—41no—
561C2×C42—41no—
562#95—22no—
563#95—22no—
564#95—22no—
565#95—22no—
566#95—22no—
567#95—22no—
568#95—22no—
569#95—22no—
570#95—22no—
571#95—22no—
572#95—22no—
573#95—22no—
574#95—22no—
575#95—41no—
576#95—41no—
577#95—41no—
578#95—41no—
579#95—41no—
580#95—41no—
581#95C2×C4×C714yescomplemented
582#95C2×C4×C714yescomplemented
583#95C7×D414yes—
584C22×C7—24no—
585C22×C7—24no—
586C22×C7—24no—
587C22×C7—24no—
588C22×C7—24no—
589C22×C7—24no—
590C22×C7—24no—
591C22×C7—24no—
592C22×C7—24no—
593C22×C7—24no—
594C22×C7—24no—
595C22×C7—24no—
596C22×C7—24no—
597C22×C7—24no—
598C22×C7#38718yescomplemented
599C22×C7C2×#11711yescharacteristic
600C22×C7C2×C4×D411yescharacteristic
601C22×C7C2×C4×D411yescharacteristic
602C22×C7C2×C4×Q811yescharacteristic
603C22×C7C4×#4111yescharacteristic
604C22×C7#51811yescharacteristic
605C22×C7#52011yescharacteristic
606C22×C7C2×C22⋊Q811yescharacteristic
607C22×C7C2×C22⋊Q811yescharacteristic
608C22×C7C2×#12311yescharacteristic
609C22×C7#52511yescharacteristic
610C22×C7C2×#12511yescharacteristic
611C22×C7C2×#12611yescharacteristic
612C22×C7#52911yescharacteristic
613C22×C7#53311yescharacteristic
614C22×C7#53811yescharacteristic
615C22×C7#53911yescharacteristic
616C22×C7#54311yescharacteristic
617C22×C7#54411yescharacteristic
618C22×C7D4211yescharacteristic
619C22×C7#54611yescharacteristic
620C22×C7#54611yescharacteristic
621C22×C7#54611yescharacteristic
622C22×C7#54611yescharacteristic
623C22×C7#54711yescharacteristic
624C22×C7#54811yescharacteristic
625C22×C7#55111yescharacteristic
626C22×C7#55111yescharacteristic
627C22×C7#55111yescharacteristic
628C22×C7#55111yescharacteristic
629C22×C7#55211yescharacteristic
630C22×C7#55211yescharacteristic
631C22×C7#55311yescharacteristic
632C22×C7#55311yescharacteristic
633C22×C7#55311yescharacteristic
634C4×C7—24no—
635C4×C7—24no—
636C4×C7—42no—
637C4×C7—42no—
638C4×C7—42no—
639C4×C7—42no—
640C4×C7—42no—
641C4×C7—42no—
642C4×C7—42no—
643C4×C7—42no—
644C4×C7—42no—
645C4×C7—42no—
646C4×C7—81no—
647C4×C7—81no—
648C24—21no—
649C24—21no—
650C24—21no—
651C24—21no—
652C24—21no—
653C24—21no—
654C24—21no—
655C24—21no—
656C24C22×C4×C712yes—
657C24C2×C7×D412yes—
658C24C2×C7×Q812yes—
659C24C7×#4112yes—
660C24C7×#4112yes—
661C24C7×#4112yes—
662C24C7×#4112yes—
663C24C24×C711yescharacteristic
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—28no—
673C22×C4—28no—
674C22×C4—28no—
675C22×C4—21no—
676C22×C4—21no—
677C22×C4—21no—
678C22×C4—21no—
679C22×C4—21no—
680C22×C4—21no—
681C22×C4—21no—
682C22×C4—21no—
683C22×C4—21no—
684C22×C4—21no—
685C22×C4—21no—
686C22×C4—21no—
687C22×C4—21no—
688C22×C4—21no—
689C22×C4—21no—
690C22×C4—21no—
691C22×C4—21no—
692C22×C4—21no—
693C22×C4—21no—
694C22×C4—21no—
695C22×C4—21no—
696C22×C4—21no—
697C22×C4—21no—
698C22×C4—21no—
699C22×C4—21no—
700C22×C4—21no—
701C22×C4—21no—
702C22×C4—21no—
703C22×C4—21no—
704C22×C4—21no—
705C22×C4—21no—
706C22×C4—21no—
707C22×C4—21no—
708C22×C4—21no—
709C22×C4—21no—
710C22×C4—21no—
711C22×C4—21no—
712C22×C4—21no—
713C22×C4—21no—
714C22×C4—21no—
715C22×C4—21no—
716C22×C4—21no—
717C22×C4—21no—
718C22×C4—21no—
719C22×C4—21no—
720C22×C4—21no—
721C22×C4—21no—
722C22×C4—21no—
723C22×C4—21no—
724C22×C4—21no—
725C22×C4—21no—
726C22×C4—21no—
727C22×C4—21no—
728C22×C4—21no—
729C22×C4—21no—
730C22×C4—21no—
731C22×C4—21no—
732C22×C4—21no—
733C22×C4—21no—
734C22×C4—21no—
735C22×C4—28no—
736C22×C4—28no—
737C22×C4—21no—
738C22×C4—21no—
739C22×C4—21no—
740C22×C4—21no—
741C22×C4—21no—
742C22×C4—21no—
743C22×C4—21no—
744C22×C4—21no—
745C22×C4—21no—
746C22×C4—21no—
747C22×C4—21no—
748C22×C4—21no—
749C22×C4—21no—
750C22×C4—21no—
751C22×C4—44no—
752C22×C4—44no—
753C22×C4—44no—
754C22×C4—44no—
755C22×C4—44no—
756C22×C4—44no—
757C22×C4—44no—
758C22×C4—44no—
759C22×C4—44no—
760C22×C4—44no—
761C22×C4—44no—
762C22×C4—44no—
763C22×C4—44no—
764C22×C4—44no—
765C22×C4—44no—
766C22×C4—44no—
767C22×C4C22×C4×C712yes—
768C22×C4C22×C4×C712yes—
769C22×C4C22×C4×C712yes—
770C22×C4C22×C4×C712yes—
771C22×C4C22×C4×C712yes—
772C22×C4C22×C4×C712yes—
773C22×C4C2×C7×D412yes—
774C22×C4C2×C7×D412yes—
775C22×C4C2×C7×D412yes—
776C22×C4C2×C7×D412yes—
777C22×C4C2×C7×D412yes—
778C22×C4C2×C7×Q812yes—
779C22×C4C2×C7×Q812yes—
780C22×C4C7×#4112yes—
781C22×C4C7×#4112yes—
782C22×C4C7×#4112yes—
783C4⋊C4—28no—
784C4⋊C4—44no—
785C4⋊C4—44no—
786C4⋊C4—44no—
787C22⋊C4—28no—
788C22⋊C4—28no—
789C22⋊C4—28no—
790C22⋊C4—44no—
791C42—44no—
792C42—44no—
793C2×C7—28no—
794C2×C7C2×#38711yescharacteristic
795C2×C7C4×C22⋊Q811yescharacteristic
796C2×C7#232911yescharacteristic
797C2×C7#235211yescharacteristic
798C2×C7#235311yescharacteristic
799C2×C7#235811yescharacteristic
800C2×C7#235911yescharacteristic
801C2×C7#243711yescharacteristic
802C2×C7#243811yescharacteristic
803C2×C7#244211yescharacteristic
804C2×C7#244311yescharacteristic
805C2×C7#244411yescharacteristic
806C2×C7#248011yescharacteristic
807C2×C7#249311yescharacteristic
808C2×C7#256911yescharacteristic
809C23—22no—
810C23—22no—
811C23—22no—
812C23—22no—
813C23—22no—
814C23—22no—
815C23—22no—
816C23—22no—
817C23—22no—
818C23—22no—
819C23—22no—
820C23—22no—
821C23—22no—
822C23—22no—
823C23—22no—
824C23—22no—
825C23—22no—
826C23—22no—
827C23—22no—
828C23—22no—
829C23—22no—
830C23—22no—
831C23—22no—
832C23—22no—
833C23—22no—
834C23—22no—
835C23—22no—
836C23—22no—
837C23C7×#11714yes—
838C23C4×C7×D414yes—
839C23C4×C7×Q814yes—
840C23C7×C22⋊Q814yes—
841C23C7×#12314yes—
842C23C7×#12514yes—
843C23C7×#12614yes—
844C23C23×C4×C711yescharacteristic
845C23C22×C7×D411yescharacteristic
846C23C22×C7×D411yescharacteristic
847C23C22×C7×Q811yescharacteristic
848C23C2×C7×#4111yescharacteristic
849C23C2×C7×#4111yescharacteristic
850C23C2×C7×#4111yescharacteristic
851C23C2×C7×#4111yescharacteristic
852C23C2×C7×#4111yescharacteristic
853C23C2×C7×#4111yescharacteristic
854C23C2×C7×#4111yescharacteristic
855C23C7×H(5,𝔽2)11yescharacteristic
856C23C7×H(5,𝔽2)11yescharacteristic
857C23C7×H(5,𝔽2)11yescharacteristic
858C23C7×2−1+411yescharacteristic
859C2×C4—22no—
860C2×C4—22no—
861C2×C4—22no—
862C2×C4—22no—
863C2×C4—22no—
864C2×C4—22no—
865C2×C4—22no—
866C2×C4—22no—
867C2×C4—22no—
868C2×C4—22no—
869C2×C4—22no—
870C2×C4—22no—
871C2×C4—22no—
872C2×C4—22no—
873C2×C4—22no—
874C2×C4—22no—
875C2×C4—22no—
876C2×C4—22no—
877C2×C4—22no—
878C2×C4—22no—
879C2×C4—22no—
880C2×C4—22no—
881C2×C4—22no—
882C2×C4—22no—
883C2×C4—22no—
884C2×C4—22no—
885C2×C4—22no—
886C2×C4—22no—
887C2×C4—22no—
888C2×C4—22no—
889C2×C4—22no—
890C2×C4—22no—
891C2×C4—22no—
892C2×C4—22no—
893C2×C4—22no—
894C2×C4—22no—
895C2×C4—22no—
896C2×C4—22no—
897C2×C4—22no—
898C2×C4—22no—
899C2×C4—22no—
900C2×C4—22no—
901C2×C4—416no—
902C2×C4—416no—
903C2×C4—416no—
904C2×C4—41no—
905C2×C4—41no—
906C2×C4—41no—
907C2×C4—41no—
908C2×C4—41no—
909C2×C4—41no—
910C2×C4—41no—
911C2×C4—41no—
912C2×C4—41no—
913C2×C4—41no—
914C2×C4—41no—
915C2×C4—41no—
916C2×C4—41no—
917C2×C4—41no—
918C2×C4—41no—
919C2×C4—41no—
920C2×C4—41no—
921C2×C4—41no—
922C2×C4—41no—
923C2×C4—41no—
924C2×C4—41no—
925C2×C4—41no—
926C2×C4—41no—
927C2×C4—41no—
928C2×C4—41no—
929C2×C4—41no—
930C2×C4—41no—
931C2×C4—41no—
932C2×C4—41no—
933C2×C4—41no—
934C2×C4—41no—
935C2×C4—41no—
936C2×C4—41no—
937C2×C4—41no—
938C2×C4—41no—
939C2×C4—41no—
940C2×C4—41no—
941C2×C4—41no—
942C2×C4—41no—
943C2×C4—41no—
944C2×C4—41no—
945C2×C4—41no—
946C2×C4—41no—
947C2×C4—41no—
948C2×C4—41no—
949C2×C4—41no—
950C2×C4—41no—
951C2×C4—41no—
952C2×C4—41no—
953C2×C4—41no—
954C2×C4—41no—
955C2×C4—41no—
956C2×C4—41no—
957C2×C4—41no—
958C2×C4C4×C7×D414yes—
959C2×C4C7×C22⋊Q814yes—
960C7#1398011yescharacteristic, direct product factor, Sylow
961C22—24no—
962C22—24no—
963C22—24no—
964C22—24no—
965C22—24no—
966C22—24no—
967C22—24no—
968C22—24no—
969C22—24no—
970C22—24no—
971C22—24no—
972C22—24no—
973C22—24no—
974C22—24no—
975C22C7×#38718yescomplemented
976C22C2×C7×#11711yescharacteristic
977C22C2×C4×C7×D411yescharacteristic
978C22C2×C4×C7×D411yescharacteristic
979C22C2×C4×C7×Q811yescharacteristic
980C22C4×C7×#4111yescharacteristic
981C22C7×#51811yescharacteristic
982C22C7×#52011yescharacteristic
983C22C2×C7×C22⋊Q811yescharacteristic
984C22C2×C7×C22⋊Q811yescharacteristic
985C22C2×C7×#12311yescharacteristic
986C22C7×#52511yescharacteristic
987C22C2×C7×#12511yescharacteristic
988C22C2×C7×#12611yescharacteristic
989C22C7×#52911yescharacteristic
990C22C7×#53311yescharacteristic
991C22C7×#53811yescharacteristic
992C22C7×#53911yescharacteristic
993C22C7×#54311yescharacteristic
994C22C7×#54411yescharacteristic
995C22C7×D4211yescharacteristic
996C22C7×#54611yescharacteristic
997C22C7×#54611yescharacteristic
998C22C7×#54611yescharacteristic
999C22C7×#54611yescharacteristic
1000C22C7×#54711yescharacteristic
1001C22C7×#54811yescharacteristic
1002C22C7×#55111yescharacteristic
1003C22C7×#55111yescharacteristic
1004C22C7×#55111yescharacteristic
1005C22C7×#55111yescharacteristic
1006C22C7×#55211yescharacteristic
1007C22C7×#55211yescharacteristic
1008C22C7×#55311yescharacteristic
1009C22C7×#55311yescharacteristic
1010C22C7×#55311yescharacteristic
1011C4—24no—
1012C4—24no—
1013C4—42no—
1014C4—42no—
1015C4—42no—
1016C4—42no—
1017C4—42no—
1018C4—42no—
1019C4—42no—
1020C4—42no—
1021C4—42no—
1022C4—42no—
1023C4—81no—
1024C4—81no—
1025C2—28no—
1026C2C2×C7×#38711yescharacteristic
1027C2C4×C7×C22⋊Q811yescharacteristic
1028C2C7×#232911yescharacteristic
1029C2C7×#235211yescharacteristic
1030C2C7×#235311yescharacteristic
1031C2C7×#235811yescharacteristic
1032C2C7×#235911yescharacteristic
1033C2C7×#243711yescharacteristic
1034C2C7×#243811yescharacteristic
1035C2C7×#244211yescharacteristic
1036C2C7×#244311yescharacteristic
1037C2C7×#244411yescharacteristic
1038C2C7×#248011yescharacteristic
1039C2C7×#249311yescharacteristic
1040C2C7×#256911yescharacteristic
subgroupG/H
center, socleC24×C7C24
commutatorC23C23×C4×C7
Frattini, cosocleC24C24×C7
prime radicalC25×C7C23
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C24×C7 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C7×#387C2semidirect
6. C7×#1445C2semidirect
7. C7×#1443C2semidirect
8. C7×#1442C2semidirect
9. C7×#1441C2semidirect
10. C7×#1436C2semidirect
11. C7×#1436C2semidirect
12. C7×#1434C2semidirect
30. C7×#385C4semidirect
56. #13980C7direct (N × H)
103. C2×C7×C4⋊C4C2×C4semidirect
104. C2×C7×C4⋊C4C2×C4semidirect
142. C7×#95C2×C4semidirect
143. C7×#95C2×C4semidirect
145. C2×#387C2×C7semidirect
150. #1445C2×C7semidirect
151. #1443C2×C7semidirect
152. #1442C2×C7semidirect
153. #1441C2×C7semidirect
154. #1436C2×C7semidirect
155. #1436C2×C7semidirect
156. #1434C2×C7semidirect
319. #385C4×C7semidirect
542. C2×C4⋊C4C2×C4×C7semidirect
543. C2×C4⋊C4C2×C4×C7semidirect
581. #95C2×C4×C7semidirect
582. #95C2×C4×C7semidirect
598. C22×C7#387semidirect
960. C7#13980direct (N × H)
975. C22C7×#387semidirect

Maximal subgroups

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

subgroupindex
C2×C7×#3872
C2×C7×#3852
C2×C7×#3802
C2×C4×C7×C22⋊C42
C22×C7×#952
C7×#14452
C7×#14432
C7×#14422
C7×#14412
C7×#14362
C7×#14342
C7×C22⋊#952
#139807