Finite Group Databasebeta

← C7×#14101 #13191317

Subgroups — C7×#14101 #13191317

Order 1792.

1674 conjugacy classes of subgroups.

The subgroup lattice has 1002 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C7×#126C211yesmaximal, characteristic
2C2×C7×#387C211yesmaximal, characteristic, complemented
3C2×C4×C7×C4⋊C4C211yesmaximal, characteristic, complemented
4C7×#1445C211yesmaximal, characteristic, complemented
5C7×#1441C211yesmaximal, characteristic, complemented
6C7×#1439C211yesmaximal, characteristic
7C7×#1439C211yesmaximal, characteristic
8C7×#1437C211yesmaximal, characteristic
9C7×#1437C211yesmaximal, characteristic
10C7×#1437C211yesmaximal, characteristic
11C7×#1437C211yesmaximal, characteristic
12C7×#1436C211yesmaximal, characteristic, complemented
13C7×C4⋊#95C211yesmaximal, characteristic, complemented
14C7×#1434C211yesmaximal, characteristic, complemented
15C4×C7×#95C211yesmaximal, characteristic, complemented
16C2×C7×#126—24no—
17C2×C7×#126—24no—
18C2×C7×#126C418yescomplemented
19C22×C7×C4⋊C4C2211yescharacteristic
20C22×C7×C4⋊C4C2211yescharacteristic
21C22×C7×C4⋊C4C2211yescharacteristic
22C22×C7×C4⋊C4C2211yescharacteristic
23C22×C7×C4⋊C4C2211yescharacteristic
24C22×C7×C22⋊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×C42×C7C2211yescharacteristic
32C22×C42×C7C2211yescharacteristic
33C22×C42×C7C2211yescharacteristic
34C22×C42×C7C2211yescharacteristic
35C22×C42×C7C2211yescharacteristic
36C7×#387—24no—
37C4×C7×C4⋊C4—24no—
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#14101C711yesmaximal, characteristic, direct product factor, Sylow
57C25×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
71C23×C4×C7C2311yescharacteristic
72C7×#126—232no—
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—41no—
83C2×C7×C4⋊C4C2×C414yes—
84C2×C7×C4⋊C4C2×C414yes—
85C2×C7×C4⋊C4C2×C414yes—
86C2×C7×C4⋊C4D414yes—
87C2×C7×C4⋊C4D414yes—
88C2×C7×C22⋊C4—22no—
89C2×C7×C22⋊C4—22no—
90C2×C7×C22⋊C4—22no—
91C2×C7×C22⋊C4—22no—
92C2×C7×C22⋊C4—22no—
93C2×C7×C22⋊C4—22no—
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—41no—
103C2×C7×C22⋊C4—41no—
104C2×C7×C22⋊C4—41no—
105C2×C7×C22⋊C4—41no—
106C2×C7×C22⋊C4C2×C414yes—
107C2×C7×C22⋊C4C2×C414yes—
108C2×C7×C22⋊C4C2×C414yes—
109C2×C42×C7—22no—
110C2×C42×C7—22no—
111C2×C42×C7—22no—
112C2×C42×C7—22no—
113C2×C42×C7—22no—
114C2×C42×C7—22no—
115C2×C42×C7—22no—
116C2×C42×C7—22no—
117C2×C42×C7—22no—
118C2×C42×C7—22no—
119C2×C42×C7—22no—
120C2×C42×C7—41no—
121C2×C42×C7—41no—
122C2×C42×C7—41no—
123C2×C42×C7C2×C414yes—
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—22no—
137C7×#95—22no—
138C7×#95—41no—
139C7×#95—41no—
140C7×#95—41no—
141C7×#95—41no—
142C22×#126C2×C711yescharacteristic
143C2×#387C2×C711yescharacteristic, complemented
144C2×C4×C4⋊C4C2×C711yescharacteristic, complemented
145#1445C2×C711yescharacteristic, complemented
146#1441C2×C711yescharacteristic, complemented
147#1439C2×C711yescharacteristic
148#1439C2×C711yescharacteristic
149#1437C2×C711yescharacteristic
150#1437C2×C711yescharacteristic
151#1437C2×C711yescharacteristic
152#1437C2×C711yescharacteristic
153#1436C2×C711yescharacteristic, complemented
154C4⋊#95C2×C711yescharacteristic, complemented
155#1434C2×C711yescharacteristic, complemented
156C4×#95C2×C711yescharacteristic, complemented
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×C7—21no—
170C24×C7—21no—
171C24×C7C22×C412yes—
172C24×C7C2411yescharacteristic
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×C7C22×C412yes—
252C22×C4×C7C22×C412yes—
253C22×C4×C7C22×C412yes—
254C22×C4×C7C22×C412yes—
255C22×C4×C7C22×C412yes—
256C22×C4×C7C22×C412yes—
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×C7#4112yes—
264C22×C4×C7#4112yes—
265C22×C4×C7#4112yes—
266C22×C4×C7#4112yes—
267C22×C4×C7#4112yes—
268C22×C4×C7#4112yes—
269C22×C4×C7#4112yes—
270C22×C4×C7#4112yes—
271C7×C4⋊C4—28no—
272C7×C4⋊C4—28no—
273C7×C4⋊C4—28no—
274C7×C4⋊C4—44no—
275C7×C4⋊C4C22⋊C4116yescomplemented
276C7×C22⋊C4—28no—
277C7×C22⋊C4—28no—
278C7×C22⋊C4—28no—
279C7×C22⋊C4—44no—
280C7×C22⋊C4—44no—
281C7×C22⋊C4—44no—
282C7×C22⋊C4—44no—
283C42×C7—28no—
284C42×C7—28no—
285C42×C7—44no—
286C42×C7—44no—
287C42×C7—44no—
288C2×#126—24no—
289C2×#126—24no—
290C2×#126C4×C718yescomplemented
291C22×C4⋊C4C22×C711yescharacteristic
292C22×C4⋊C4C22×C711yescharacteristic
293C22×C4⋊C4C22×C711yescharacteristic
294C22×C4⋊C4C22×C711yescharacteristic
295C22×C4⋊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×C22⋊C4C22×C711yescharacteristic
303C22×C42C22×C711yescharacteristic
304C22×C42C22×C711yescharacteristic
305C22×C42C22×C711yescharacteristic
306C22×C42C22×C711yescharacteristic
307C22×C42C22×C711yescharacteristic
308#387—24no—
309C4×C4⋊C4—24no—
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
325C2×#95C22×C711yescharacteristic
326C2×#95C22×C711yescharacteristic
327C2×#95C22×C711yescharacteristic
328C23×C7—22no—
329C23×C7—22no—
330C23×C7—22no—
331C23×C7—22no—
332C23×C7—22no—
333C23×C7—22no—
334C23×C7—22no—
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×C7—41no—
361C23×C7—41no—
362C23×C7—41no—
363C23×C7C23×C411yescharacteristic
364C23×C7C22×D411yescharacteristic
365C23×C7C22×D411yescharacteristic
366C23×C7C2×#4111yescharacteristic
367C23×C7C2×#4111yescharacteristic
368C23×C7C2×#4111yescharacteristic
369C23×C7C2×#4111yescharacteristic
370C23×C7C2×#4111yescharacteristic
371C23×C7C2×#4111yescharacteristic
372C23×C7C2×#4111yescharacteristic
373C23×C7C2×#4111yescharacteristic
374C23×C7H(5,𝔽2)11yescharacteristic
375C23×C7H(5,𝔽2)11yescharacteristic
376C23×C72−1+411yescharacteristic
377C23×C72−1+411yescharacteristic
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—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—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×C7C2×C22⋊C414yes—
473C2×C4×C7C2×C22⋊C414yes—
474C2×C4×C7C2×C22⋊C414yes—
475C2×C4×C7#12614yescomplemented
476C25C23×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
490C23×C4C23×C711yescharacteristic
491#126—232no—
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⋊C4C2×C4×C714yes—
503C2×C4⋊C4C2×C4×C714yes—
504C2×C4⋊C4C2×C4×C714yes—
505C2×C4⋊C4C7×D414yes—
506C2×C4⋊C4C7×D414yes—
507C2×C22⋊C4—22no—
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—22no—
519C2×C22⋊C4—22no—
520C2×C22⋊C4—22no—
521C2×C22⋊C4—41no—
522C2×C22⋊C4—41no—
523C2×C22⋊C4—41no—
524C2×C22⋊C4—41no—
525C2×C22⋊C4C2×C4×C714yes—
526C2×C22⋊C4C2×C4×C714yes—
527C2×C22⋊C4C2×C4×C714yes—
528C2×C42—22no—
529C2×C42—22no—
530C2×C42—22no—
531C2×C42—22no—
532C2×C42—22no—
533C2×C42—22no—
534C2×C42—22no—
535C2×C42—22no—
536C2×C42—22no—
537C2×C42—22no—
538C2×C42—22no—
539C2×C42—41no—
540C2×C42—41no—
541C2×C42—41no—
542C2×C42C2×C4×C714yes—
543#95—22no—
544#95—22no—
545#95—22no—
546#95—22no—
547#95—22no—
548#95—22no—
549#95—22no—
550#95—22no—
551#95—22no—
552#95—22no—
553#95—22no—
554#95—22no—
555#95—22no—
556#95—22no—
557#95—41no—
558#95—41no—
559#95—41no—
560#95—41no—
561C22×C7—42no—
562C22×C7—42no—
563C22×C7—42no—
564C22×C7—42no—
565C22×C7—42no—
566C22×C7—42no—
567C22×C7—42no—
568C22×C7—81no—
569C22×C7—81no—
570C22×C7—81no—
571C22×C7—81no—
572C22×C7—81no—
573C22×C7—81no—
574C22×C7—81no—
575C22×C7—81no—
576C22×C7C22×C22⋊C411yescharacteristic
577C22×C7C4×#4111yescharacteristic
578C22×C7C4×#4111yescharacteristic
579C22×C7C4×#4111yescharacteristic
580C22×C7C4×#4111yescharacteristic
581C22×C7#52011yescharacteristic
582C22×C7#52011yescharacteristic
583C22×C7#52511yescharacteristic
584C22×C7#52511yescharacteristic
585C22×C7C2×#12611yescharacteristic
586C22×C7#52911yescharacteristic
587C22×C7#52911yescharacteristic
588C22×C7#52911yescharacteristic
589C22×C7#53211yescharacteristic
590C22×C7#53211yescharacteristic
591C22×C7#53811yescharacteristic
592C22×C7#53911yescharacteristic
593C22×C7#54111yescharacteristic
594C22×C7#54211yescharacteristic
595C22×C7#54611yescharacteristic
596C22×C7#54611yescharacteristic
597C22×C7#54711yescharacteristic
598C22×C7#54711yescharacteristic
599C22×C7#54811yescharacteristic
600C22×C7#54811yescharacteristic
601C22×C7#55011yescharacteristic
602C22×C7#55011yescharacteristic
603C22×C7#55111yescharacteristic
604C22×C7#55111yescharacteristic
605C22×C7#55211yescharacteristic
606C22×C7#55211yescharacteristic
607C22×C7#55311yescharacteristic
608C22×C7#55311yescharacteristic
609C22×C7#55611yescharacteristic
610C22×C7#55611yescharacteristic
611C4×C7—24no—
612C4×C7—24no—
613C4×C7—24no—
614C4×C7—24no—
615C4×C7—42no—
616C4×C7—42no—
617C4×C7—42no—
618C4×C7—42no—
619C4×C7—42no—
620C4×C7—42no—
621C4×C7—42no—
622C4×C7—42no—
623C4×C7—81no—
624C4×C7—81no—
625C24—21no—
626C24—21no—
627C24—21no—
628C24—21no—
629C24—21no—
630C24—21no—
631C24—21no—
632C24—21no—
633C24—21no—
634C24—21no—
635C24—21no—
636C24—21no—
637C24—21no—
638C24—21no—
639C24C22×C4×C712yes—
640C24C24×C711yescharacteristic
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×C4C22×C4×C712yes—
720C22×C4C22×C4×C712yes—
721C22×C4C22×C4×C712yes—
722C22×C4C22×C4×C712yes—
723C22×C4C22×C4×C712yes—
724C22×C4C22×C4×C712yes—
725C22×C4C2×C7×D412yes—
726C22×C4C2×C7×D412yes—
727C22×C4C2×C7×D412yes—
728C22×C4C2×C7×D412yes—
729C22×C4C2×C7×D412yes—
730C22×C4C2×C7×D412yes—
731C22×C4C7×#4112yes—
732C22×C4C7×#4112yes—
733C22×C4C7×#4112yes—
734C22×C4C7×#4112yes—
735C22×C4C7×#4112yes—
736C22×C4C7×#4112yes—
737C22×C4C7×#4112yes—
738C22×C4C7×#4112yes—
739C4⋊C4—28no—
740C4⋊C4—28no—
741C4⋊C4—28no—
742C4⋊C4—44no—
743C4⋊C4C7×C22⋊C4116yescomplemented
744C22⋊C4—28no—
745C22⋊C4—28no—
746C22⋊C4—28no—
747C22⋊C4—44no—
748C22⋊C4—44no—
749C22⋊C4—44no—
750C22⋊C4—44no—
751C42—28no—
752C42—28no—
753C42—44no—
754C42—44no—
755C42—44no—
756C2×C7—82no—
757C2×C7#229711yescharacteristic
758C2×C7C4×#12611yescharacteristic
759C2×C7#233411yescharacteristic
760C2×C7#233911yescharacteristic
761C2×C7#234111yescharacteristic
762C2×C7#237311yescharacteristic
763C2×C7#237311yescharacteristic
764C2×C7#246711yescharacteristic
765C2×C7#246911yescharacteristic
766C2×C7#247911yescharacteristic
767C2×C7#248111yescharacteristic
768C2×C7#251211yescharacteristic
769C2×C7#251911yescharacteristic
770C2×C7#255411yescharacteristic
771C2×C7#256011yescharacteristic
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—
795C23—41no—
796C23—41no—
797C23—41no—
798C23—41no—
799C23—41no—
800C23—41no—
801C23—41no—
802C23—41no—
803C23—41no—
804C23—41no—
805C23—41no—
806C23—41no—
807C23C23×C4×C711yescharacteristic
808C23C22×C7×D411yescharacteristic
809C23C22×C7×D411yescharacteristic
810C23C2×C7×#4111yescharacteristic
811C23C2×C7×#4111yescharacteristic
812C23C2×C7×#4111yescharacteristic
813C23C2×C7×#4111yescharacteristic
814C23C2×C7×#4111yescharacteristic
815C23C2×C7×#4111yescharacteristic
816C23C2×C7×#4111yescharacteristic
817C23C2×C7×#4111yescharacteristic
818C23C7×H(5,𝔽2)11yescharacteristic
819C23C7×H(5,𝔽2)11yescharacteristic
820C23C7×2−1+411yescharacteristic
821C23C7×2−1+411yescharacteristic
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—22no—
852C2×C4—22no—
853C2×C4—22no—
854C2×C4—22no—
855C2×C4—22no—
856C2×C4—22no—
857C2×C4—22no—
858C2×C4—22no—
859C2×C4—22no—
860C2×C4—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—41no—
871C2×C4—41no—
872C2×C4—41no—
873C2×C4—41no—
874C2×C4—41no—
875C2×C4—41no—
876C2×C4—41no—
877C2×C4—41no—
878C2×C4—41no—
879C2×C4—41no—
880C2×C4—41no—
881C2×C4—41no—
882C2×C4—41no—
883C2×C4—41no—
884C2×C4—41no—
885C2×C4—41no—
886C2×C4—41no—
887C2×C4—41no—
888C2×C4—41no—
889C2×C4—41no—
890C2×C4—41no—
891C2×C4—41no—
892C2×C4—41no—
893C2×C4—41no—
894C2×C4—41no—
895C2×C4—41no—
896C2×C4—41no—
897C2×C4—41no—
898C2×C4—41no—
899C2×C4—41no—
900C2×C4—41no—
901C2×C4—41no—
902C2×C4—41no—
903C2×C4—41no—
904C2×C4—41no—
905C2×C4—41no—
906C2×C4—41no—
907C2×C4—41no—
908C2×C4—41no—
909C2×C4—41no—
910C2×C4—41no—
911C2×C4—41no—
912C2×C4—41no—
913C2×C4—41no—
914C2×C4—41no—
915C2×C4—41no—
916C2×C4C2×C7×C22⋊C414yes—
917C2×C4C2×C7×C22⋊C414yes—
918C2×C4C2×C7×C22⋊C414yes—
919C2×C4C7×#12614yescomplemented
920C7#1410111yescharacteristic, direct product factor, Sylow
921C22—42no—
922C22—42no—
923C22—42no—
924C22—42no—
925C22—42no—
926C22—42no—
927C22—42no—
928C22—81no—
929C22—81no—
930C22—81no—
931C22—81no—
932C22—81no—
933C22—81no—
934C22—81no—
935C22—81no—
936C22C22×C7×C22⋊C411yescharacteristic
937C22C4×C7×#4111yescharacteristic
938C22C4×C7×#4111yescharacteristic
939C22C4×C7×#4111yescharacteristic
940C22C4×C7×#4111yescharacteristic
941C22C7×#52011yescharacteristic
942C22C7×#52011yescharacteristic
943C22C7×#52511yescharacteristic
944C22C7×#52511yescharacteristic
945C22C2×C7×#12611yescharacteristic
946C22C7×#52911yescharacteristic
947C22C7×#52911yescharacteristic
948C22C7×#52911yescharacteristic
949C22C7×#53211yescharacteristic
950C22C7×#53211yescharacteristic
951C22C7×#53811yescharacteristic
952C22C7×#53911yescharacteristic
953C22C7×#54111yescharacteristic
954C22C7×#54211yescharacteristic
955C22C7×#54611yescharacteristic
956C22C7×#54611yescharacteristic
957C22C7×#54711yescharacteristic
958C22C7×#54711yescharacteristic
959C22C7×#54811yescharacteristic
960C22C7×#54811yescharacteristic
961C22C7×#55011yescharacteristic
962C22C7×#55011yescharacteristic
963C22C7×#55111yescharacteristic
964C22C7×#55111yescharacteristic
965C22C7×#55211yescharacteristic
966C22C7×#55211yescharacteristic
967C22C7×#55311yescharacteristic
968C22C7×#55311yescharacteristic
969C22C7×#55611yescharacteristic
970C22C7×#55611yescharacteristic
971C4—24no—
972C4—24no—
973C4—24no—
974C4—24no—
975C4—42no—
976C4—42no—
977C4—42no—
978C4—42no—
979C4—42no—
980C4—42no—
981C4—42no—
982C4—42no—
983C4—81no—
984C4—81no—
985C2—82no—
986C2C7×#229711yescharacteristic
987C2C4×C7×#12611yescharacteristic
988C2C7×#233411yescharacteristic
989C2C7×#233911yescharacteristic
990C2C7×#234111yescharacteristic
991C2C7×#237311yescharacteristic
992C2C7×#237311yescharacteristic
993C2C7×#246711yescharacteristic
994C2C7×#246911yescharacteristic
995C2C7×#247911yescharacteristic
996C2C7×#248111yescharacteristic
997C2C7×#251211yescharacteristic
998C2C7×#251911yescharacteristic
999C2C7×#255411yescharacteristic
1000C2C7×#256011yescharacteristic
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
2. C2×C7×#387C2semidirect
3. C2×C4×C7×C4⋊C4C2semidirect
4. C7×#1445C2semidirect
5. C7×#1441C2semidirect
12. C7×#1436C2semidirect
13. C7×C4⋊#95C2semidirect
14. C7×#1434C2semidirect
15. C4×C7×#95C2semidirect
18. C2×C7×#126C4semidirect
56. #14101C7direct (N × H)
143. C2×#387C2×C7semidirect
144. C2×C4×C4⋊C4C2×C7semidirect
145. #1445C2×C7semidirect
146. #1441C2×C7semidirect
153. #1436C2×C7semidirect
154. C4⋊#95C2×C7semidirect
155. #1434C2×C7semidirect
156. C4×#95C2×C7semidirect
275. C7×C4⋊C4C22⋊C4semidirect
290. C2×#126C4×C7semidirect
475. C2×C4×C7#126semidirect
743. C4⋊C4C7×C22⋊C4semidirect
919. C2×C4C7×#126semidirect
920. C7#14101direct (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×#3872
C2×C4×C7×C4⋊C42
C7×#14452
C7×#14412
C7×#14392
C7×#14372
C7×#14362
C7×C4⋊#952
C7×#14342
C4×C7×#952
#141017