Finite Group Databasebeta

← C7×#14102 #13191318

Subgroups — C7×#14102 #13191318

Order 1792.

1782 conjugacy classes of subgroups.

The subgroup lattice has 1012 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C7×#126C211yesmaximal, characteristic
2C2×C7×#388C211yesmaximal, characteristic
3C2×C4×C7×C22⋊C4C211yesmaximal, characteristic
4C7×#1445C211yesmaximal, characteristic, complemented
5C7×#1441C211yesmaximal, characteristic, complemented
6C7×#1440C211yesmaximal, characteristic
7C7×#1440C211yesmaximal, characteristic
8C7×#1436C211yesmaximal, characteristic, complemented
9C7×#1436C211yesmaximal, characteristic, complemented
10C7×#1436C211yesmaximal, characteristic, complemented
11C7×C4⋊#95C211yesmaximal, characteristic, complemented
12C7×#1434C211yesmaximal, characteristic, complemented
13C7×C22⋊#95C211yesmaximal, characteristic
14C7×C22⋊#95C211yesmaximal, characteristic
15C4×C7×#95C211yesmaximal, characteristic, complemented
16C24×C4×C7C2211yescharacteristic
17C2×C7×#126—24no—
18C2×C7×#126—24no—
19C2×C7×#126C418yescomplemented
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×C42×C7C2211yescharacteristic
31C22×C42×C7C2211yescharacteristic
32C22×C42×C7C2211yescharacteristic
33C22×C42×C7C2211yescharacteristic
34C7×#388—24no—
35C4×C7×C22⋊C4—24no—
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#14102C711yesmaximal, 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—41no—
64C23×C4×C7—41no—
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
76C23×C4×C7C2311yescharacteristic
77C23×C4×C7C2311yescharacteristic
78C23×C4×C7C2311yescharacteristic
79C7×#126—232no—
80C2×C7×C4⋊C4—22no—
81C2×C7×C4⋊C4—22no—
82C2×C7×C4⋊C4—22no—
83C2×C7×C4⋊C4—22no—
84C2×C7×C4⋊C4—22no—
85C2×C7×C4⋊C4—22no—
86C2×C7×C4⋊C4—22no—
87C2×C7×C4⋊C4—22no—
88C2×C7×C4⋊C4—41no—
89C2×C7×C4⋊C4C2×C414yescomplemented
90C2×C7×C4⋊C4C2×C414yescomplemented
91C2×C7×C4⋊C4C2×C414yescomplemented
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—22no—
103C2×C7×C22⋊C4—41no—
104C2×C7×C22⋊C4—41no—
105C2×C7×C22⋊C4C2×C414yes—
106C2×C7×C22⋊C4C2×C414yes—
107C2×C7×C22⋊C4C2×C414yes—
108C2×C7×C22⋊C4D414yes—
109C2×C7×C22⋊C4D414yes—
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—41no—
119C2×C42×C7—41no—
120C2×C42×C7—41no—
121C2×C42×C7C2×C414yescomplemented
122C7×#95—22no—
123C7×#95—22no—
124C7×#95—22no—
125C7×#95—22no—
126C7×#95—22no—
127C7×#95—22no—
128C7×#95—22no—
129C7×#95—22no—
130C7×#95—22no—
131C7×#95—22no—
132C7×#95—22no—
133C7×#95—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×#388C2×C711yescharacteristic
144C2×C4×C22⋊C4C2×C711yescharacteristic
145#1445C2×C711yescharacteristic, complemented
146#1441C2×C711yescharacteristic, complemented
147#1440C2×C711yescharacteristic
148#1440C2×C711yescharacteristic
149#1436C2×C711yescharacteristic, complemented
150#1436C2×C711yescharacteristic, complemented
151#1436C2×C711yescharacteristic, complemented
152C4⋊#95C2×C711yescharacteristic, complemented
153#1434C2×C711yescharacteristic, complemented
154C22⋊#95C2×C711yescharacteristic
155C22⋊#95C2×C711yescharacteristic
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×C7C22×C412yes—
170C24×C7C2×D412yes—
171C24×C7C2×D412yes—
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—28no—
186C22×C4×C7—21no—
187C22×C4×C7—21no—
188C22×C4×C7—21no—
189C22×C4×C7—21no—
190C22×C4×C7—21no—
191C22×C4×C7—21no—
192C22×C4×C7—21no—
193C22×C4×C7—21no—
194C22×C4×C7—21no—
195C22×C4×C7—21no—
196C22×C4×C7—21no—
197C22×C4×C7—21no—
198C22×C4×C7—21no—
199C22×C4×C7—21no—
200C22×C4×C7—21no—
201C22×C4×C7—21no—
202C22×C4×C7—21no—
203C22×C4×C7—21no—
204C22×C4×C7—21no—
205C22×C4×C7—21no—
206C22×C4×C7—21no—
207C22×C4×C7—21no—
208C22×C4×C7—21no—
209C22×C4×C7—21no—
210C22×C4×C7—21no—
211C22×C4×C7—21no—
212C22×C4×C7—21no—
213C22×C4×C7—21no—
214C22×C4×C7—21no—
215C22×C4×C7—21no—
216C22×C4×C7—21no—
217C22×C4×C7—21no—
218C22×C4×C7—21no—
219C22×C4×C7—21no—
220C22×C4×C7—21no—
221C22×C4×C7—21no—
222C22×C4×C7—21no—
223C22×C4×C7—21no—
224C22×C4×C7—21no—
225C22×C4×C7—21no—
226C22×C4×C7—21no—
227C22×C4×C7—21no—
228C22×C4×C7—21no—
229C22×C4×C7—21no—
230C22×C4×C7—21no—
231C22×C4×C7—21no—
232C22×C4×C7—21no—
233C22×C4×C7—21no—
234C22×C4×C7—21no—
235C22×C4×C7—21no—
236C22×C4×C7—21no—
237C22×C4×C7—21no—
238C22×C4×C7—21no—
239C22×C4×C7—21no—
240C22×C4×C7—21no—
241C22×C4×C7—21no—
242C22×C4×C7—21no—
243C22×C4×C7—21no—
244C22×C4×C7—21no—
245C22×C4×C7—21no—
246C22×C4×C7—21no—
247C22×C4×C7—21no—
248C22×C4×C7—21no—
249C22×C4×C7—21no—
250C22×C4×C7—21no—
251C22×C4×C7—21no—
252C22×C4×C7—21no—
253C22×C4×C7—21no—
254C22×C4×C7—44no—
255C22×C4×C7—44no—
256C22×C4×C7—44no—
257C22×C4×C7—44no—
258C22×C4×C7—44no—
259C22×C4×C7—44no—
260C22×C4×C7C22×C412yes—
261C22×C4×C7C22×C412yes—
262C22×C4×C7C22×C412yes—
263C22×C4×C7C22×C412yes—
264C22×C4×C7C22×C412yes—
265C22×C4×C7C22×C412yes—
266C22×C4×C7C2×D412yes—
267C22×C4×C7C2×D412yes—
268C22×C4×C7C2×D412yes—
269C22×C4×C7C2×D412yes—
270C22×C4×C7#4112yes—
271C22×C4×C7#4112yes—
272C22×C4×C7#4112yes—
273C22×C4×C7#4112yes—
274C22×C4×C7#4112yes—
275C22×C4×C7#4112yes—
276C22×C4×C7#4112yes—
277C22×C4×C7#4112yes—
278C7×C4⋊C4—28no—
279C7×C4⋊C4—28no—
280C7×C4⋊C4—28no—
281C7×C4⋊C4—44no—
282C7×C22⋊C4—28no—
283C7×C22⋊C4—28no—
284C7×C22⋊C4—28no—
285C7×C22⋊C4—44no—
286C7×C22⋊C4—44no—
287C7×C22⋊C4C22⋊C4116yes—
288C42×C7—28no—
289C42×C7—44no—
290C42×C7—44no—
291C42×C7—44no—
292C24×C4C22×C711yescharacteristic
293C2×#126—24no—
294C2×#126—24no—
295C2×#126C4×C718yescomplemented
296C22×C4⋊C4C22×C711yescharacteristic
297C22×C4⋊C4C22×C711yescharacteristic
298C22×C4⋊C4C22×C711yescharacteristic
299C22×C4⋊C4C22×C711yescharacteristic
300C22×C22⋊C4C22×C711yescharacteristic
301C22×C22⋊C4C22×C711yescharacteristic
302C22×C22⋊C4C22×C711yescharacteristic
303C22×C22⋊C4C22×C711yescharacteristic
304C22×C22⋊C4C22×C711yescharacteristic
305C22×C22⋊C4C22×C711yescharacteristic
306C22×C42C22×C711yescharacteristic
307C22×C42C22×C711yescharacteristic
308C22×C42C22×C711yescharacteristic
309C22×C42C22×C711yescharacteristic
310#388—24no—
311C4×C22⋊C4—24no—
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
328C2×#95C22×C711yescharacteristic
329C2×#95C22×C711yescharacteristic
330C2×#95C22×C711yescharacteristic
331C2×#95C22×C711yescharacteristic
332C23×C7—22no—
333C23×C7—22no—
334C23×C7—22no—
335C23×C7—22no—
336C23×C7—22no—
337C23×C7—22no—
338C23×C7—22no—
339C23×C7—22no—
340C23×C7—22no—
341C23×C7—22no—
342C23×C7—22no—
343C23×C7—22no—
344C23×C7—22no—
345C23×C7—22no—
346C23×C7—22no—
347C23×C7—22no—
348C23×C7—22no—
349C23×C7—22no—
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×C7—41no—
364C23×C7—41no—
365C23×C7—41no—
366C23×C7C2×C22⋊C414yes—
367C23×C7C23×C411yescharacteristic
368C23×C7C22×D411yescharacteristic
369C23×C7C22×D411yescharacteristic
370C23×C7C2×#4111yescharacteristic
371C23×C7C2×#4111yescharacteristic
372C23×C7C2×#4111yescharacteristic
373C23×C7C2×#4111yescharacteristic
374C23×C7C2×#4111yescharacteristic
375C23×C7C2×#4111yescharacteristic
376C23×C7C2×#4111yescharacteristic
377C23×C7C2×#4111yescharacteristic
378C23×C7H(5,𝔽2)11yescharacteristic
379C23×C7H(5,𝔽2)11yescharacteristic
380C23×C72−1+411yescharacteristic
381C23×C72−1+411yescharacteristic
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—22no—
427C2×C4×C7—416no—
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×C7—41no—
473C2×C4×C7—41no—
474C2×C4×C7—41no—
475C2×C4×C7—41no—
476C2×C4×C7—41no—
477C2×C4×C7—41no—
478C2×C4×C7C2×C22⋊C414yes—
479C2×C4×C7C2×C22⋊C414yes—
480C2×C4×C7#12614yescomplemented
481C25C23×C711yescharacteristic
482C23×C4—22no—
483C23×C4—22no—
484C23×C4—22no—
485C23×C4—22no—
486C23×C4—22no—
487C23×C4—41no—
488C23×C4—41no—
489C23×C4C23×C711yescharacteristic
490C23×C4C23×C711yescharacteristic
491C23×C4C23×C711yescharacteristic
492C23×C4C23×C711yescharacteristic
493C23×C4C23×C711yescharacteristic
494C23×C4C23×C711yescharacteristic
495C23×C4C23×C711yescharacteristic
496C23×C4C23×C711yescharacteristic
497C23×C4C23×C711yescharacteristic
498C23×C4C23×C711yescharacteristic
499C23×C4C23×C711yescharacteristic
500C23×C4C23×C711yescharacteristic
501C23×C4C23×C711yescharacteristic
502C23×C4C23×C711yescharacteristic
503#126—232no—
504C2×C4⋊C4—22no—
505C2×C4⋊C4—22no—
506C2×C4⋊C4—22no—
507C2×C4⋊C4—22no—
508C2×C4⋊C4—22no—
509C2×C4⋊C4—22no—
510C2×C4⋊C4—22no—
511C2×C4⋊C4—22no—
512C2×C4⋊C4—41no—
513C2×C4⋊C4C2×C4×C714yescomplemented
514C2×C4⋊C4C2×C4×C714yescomplemented
515C2×C4⋊C4C2×C4×C714yescomplemented
516C2×C22⋊C4—22no—
517C2×C22⋊C4—22no—
518C2×C22⋊C4—22no—
519C2×C22⋊C4—22no—
520C2×C22⋊C4—22no—
521C2×C22⋊C4—22no—
522C2×C22⋊C4—22no—
523C2×C22⋊C4—22no—
524C2×C22⋊C4—22no—
525C2×C22⋊C4—22no—
526C2×C22⋊C4—22no—
527C2×C22⋊C4—41no—
528C2×C22⋊C4—41no—
529C2×C22⋊C4C2×C4×C714yes—
530C2×C22⋊C4C2×C4×C714yes—
531C2×C22⋊C4C2×C4×C714yes—
532C2×C22⋊C4C7×D414yes—
533C2×C22⋊C4C7×D414yes—
534C2×C42—22no—
535C2×C42—22no—
536C2×C42—22no—
537C2×C42—22no—
538C2×C42—22no—
539C2×C42—22no—
540C2×C42—22no—
541C2×C42—22no—
542C2×C42—41no—
543C2×C42—41no—
544C2×C42—41no—
545C2×C42C2×C4×C714yescomplemented
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—22no—
558#95—22no—
559#95—22no—
560#95—22no—
561#95—22no—
562#95—41no—
563#95—41no—
564#95—41no—
565#95—41no—
566C22×C7—24no—
567C22×C7—24no—
568C22×C7—24no—
569C22×C7—42no—
570C22×C7—42no—
571C22×C7—42no—
572C22×C7—42no—
573C22×C7—42no—
574C22×C7—42no—
575C22×C7—42no—
576C22×C7—42no—
577C22×C7—42no—
578C22×C7—42no—
579C22×C7—42no—
580C22×C7—42no—
581C22×C7C22×C22⋊C411yescharacteristic
582C22×C7C4×#4111yescharacteristic
583C22×C7C4×#4111yescharacteristic
584C22×C7C4×#4111yescharacteristic
585C22×C7C4×#4111yescharacteristic
586C22×C7#52011yescharacteristic
587C22×C7#52011yescharacteristic
588C22×C7#52511yescharacteristic
589C22×C7#52511yescharacteristic
590C22×C7C2×#12611yescharacteristic
591C22×C7#52911yescharacteristic
592C22×C7#52911yescharacteristic
593C22×C7#52911yescharacteristic
594C22×C7#53211yescharacteristic
595C22×C7#53211yescharacteristic
596C22×C7#53811yescharacteristic
597C22×C7#53911yescharacteristic
598C22×C7#54111yescharacteristic
599C22×C7#54211yescharacteristic
600C22×C7#54611yescharacteristic
601C22×C7#54611yescharacteristic
602C22×C7#54611yescharacteristic
603C22×C7#54611yescharacteristic
604C22×C7#54711yescharacteristic
605C22×C7#54711yescharacteristic
606C22×C7#54711yescharacteristic
607C22×C7#54711yescharacteristic
608C22×C7#55111yescharacteristic
609C22×C7#55111yescharacteristic
610C22×C7#55211yescharacteristic
611C22×C7#55211yescharacteristic
612C22×C7#55311yescharacteristic
613C22×C7#55311yescharacteristic
614C22×C7#55611yescharacteristic
615C22×C7#55611yescharacteristic
616C4×C7—24no—
617C4×C7—24no—
618C4×C7—24no—
619C4×C7—42no—
620C4×C7—42no—
621C4×C7—42no—
622C4×C7—42no—
623C4×C7—42no—
624C4×C7—42no—
625C4×C7—42no—
626C4×C7—42no—
627C4×C7—42no—
628C4×C7—81no—
629C4×C7—81no—
630C24—21no—
631C24—21no—
632C24—21no—
633C24—21no—
634C24—21no—
635C24—21no—
636C24—21no—
637C24—21no—
638C24—21no—
639C24—21no—
640C24—21no—
641C24—21no—
642C24C22×C4×C712yes—
643C24C2×C7×D412yes—
644C24C2×C7×D412yes—
645C24C24×C711yescharacteristic
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—28no—
659C22×C4—21no—
660C22×C4—21no—
661C22×C4—21no—
662C22×C4—21no—
663C22×C4—21no—
664C22×C4—21no—
665C22×C4—21no—
666C22×C4—21no—
667C22×C4—21no—
668C22×C4—21no—
669C22×C4—21no—
670C22×C4—21no—
671C22×C4—21no—
672C22×C4—21no—
673C22×C4—21no—
674C22×C4—21no—
675C22×C4—21no—
676C22×C4—21no—
677C22×C4—21no—
678C22×C4—21no—
679C22×C4—21no—
680C22×C4—21no—
681C22×C4—21no—
682C22×C4—21no—
683C22×C4—21no—
684C22×C4—21no—
685C22×C4—21no—
686C22×C4—21no—
687C22×C4—21no—
688C22×C4—21no—
689C22×C4—21no—
690C22×C4—21no—
691C22×C4—21no—
692C22×C4—21no—
693C22×C4—21no—
694C22×C4—21no—
695C22×C4—21no—
696C22×C4—21no—
697C22×C4—21no—
698C22×C4—21no—
699C22×C4—21no—
700C22×C4—21no—
701C22×C4—21no—
702C22×C4—21no—
703C22×C4—21no—
704C22×C4—21no—
705C22×C4—21no—
706C22×C4—21no—
707C22×C4—21no—
708C22×C4—21no—
709C22×C4—21no—
710C22×C4—21no—
711C22×C4—21no—
712C22×C4—21no—
713C22×C4—21no—
714C22×C4—21no—
715C22×C4—21no—
716C22×C4—21no—
717C22×C4—21no—
718C22×C4—21no—
719C22×C4—21no—
720C22×C4—21no—
721C22×C4—21no—
722C22×C4—21no—
723C22×C4—21no—
724C22×C4—21no—
725C22×C4—21no—
726C22×C4—21no—
727C22×C4—44no—
728C22×C4—44no—
729C22×C4—44no—
730C22×C4—44no—
731C22×C4—44no—
732C22×C4—44no—
733C22×C4C22×C4×C712yes—
734C22×C4C22×C4×C712yes—
735C22×C4C22×C4×C712yes—
736C22×C4C22×C4×C712yes—
737C22×C4C22×C4×C712yes—
738C22×C4C22×C4×C712yes—
739C22×C4C2×C7×D412yes—
740C22×C4C2×C7×D412yes—
741C22×C4C2×C7×D412yes—
742C22×C4C2×C7×D412yes—
743C22×C4C7×#4112yes—
744C22×C4C7×#4112yes—
745C22×C4C7×#4112yes—
746C22×C4C7×#4112yes—
747C22×C4C7×#4112yes—
748C22×C4C7×#4112yes—
749C22×C4C7×#4112yes—
750C22×C4C7×#4112yes—
751C4⋊C4—28no—
752C4⋊C4—28no—
753C4⋊C4—28no—
754C4⋊C4—44no—
755C22⋊C4—28no—
756C22⋊C4—28no—
757C22⋊C4—28no—
758C22⋊C4—44no—
759C22⋊C4—44no—
760C22⋊C4C7×C22⋊C4116yes—
761C42—28no—
762C42—44no—
763C42—44no—
764C42—44no—
765C2×C7—44no—
766C2×C7#229711yescharacteristic
767C2×C7C4×#12611yescharacteristic
768C2×C7#233411yescharacteristic
769C2×C7#233911yescharacteristic
770C2×C7#233911yescharacteristic
771C2×C7#237311yescharacteristic
772C2×C7#237311yescharacteristic
773C2×C7#246611yescharacteristic
774C2×C7#246811yescharacteristic
775C2×C7#247811yescharacteristic
776C2×C7#248011yescharacteristic
777C2×C7#249611yescharacteristic
778C2×C7#252111yescharacteristic
779C2×C7#255311yescharacteristic
780C2×C7#255911yescharacteristic
781C23—22no—
782C23—22no—
783C23—22no—
784C23—22no—
785C23—22no—
786C23—22no—
787C23—22no—
788C23—22no—
789C23—22no—
790C23—22no—
791C23—22no—
792C23—22no—
793C23—22no—
794C23—22no—
795C23—22no—
796C23—22no—
797C23—22no—
798C23—22no—
799C23—41no—
800C23—41no—
801C23—41no—
802C23—41no—
803C23—41no—
804C23—41no—
805C23—41no—
806C23—41no—
807C23—41no—
808C23—41no—
809C23—41no—
810C23—41no—
811C23—41no—
812C23—41no—
813C23—41no—
814C23—41no—
815C23C2×C7×C22⋊C414yes—
816C23C23×C4×C711yescharacteristic
817C23C22×C7×D411yescharacteristic
818C23C22×C7×D411yescharacteristic
819C23C2×C7×#4111yescharacteristic
820C23C2×C7×#4111yescharacteristic
821C23C2×C7×#4111yescharacteristic
822C23C2×C7×#4111yescharacteristic
823C23C2×C7×#4111yescharacteristic
824C23C2×C7×#4111yescharacteristic
825C23C2×C7×#4111yescharacteristic
826C23C2×C7×#4111yescharacteristic
827C23C7×H(5,𝔽2)11yescharacteristic
828C23C7×H(5,𝔽2)11yescharacteristic
829C23C7×2−1+411yescharacteristic
830C23C7×2−1+411yescharacteristic
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—22no—
871C2×C4—22no—
872C2×C4—22no—
873C2×C4—22no—
874C2×C4—22no—
875C2×C4—22no—
876C2×C4—416no—
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×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×C4C2×C7×C22⋊C414yes—
928C2×C4C2×C7×C22⋊C414yes—
929C2×C4C7×#12614yescomplemented
930C7#1410211yescharacteristic, direct product factor, Sylow
931C22—24no—
932C22—24no—
933C22—24no—
934C22—42no—
935C22—42no—
936C22—42no—
937C22—42no—
938C22—42no—
939C22—42no—
940C22—42no—
941C22—42no—
942C22—42no—
943C22—42no—
944C22—42no—
945C22—42no—
946C22C22×C7×C22⋊C411yescharacteristic
947C22C4×C7×#4111yescharacteristic
948C22C4×C7×#4111yescharacteristic
949C22C4×C7×#4111yescharacteristic
950C22C4×C7×#4111yescharacteristic
951C22C7×#52011yescharacteristic
952C22C7×#52011yescharacteristic
953C22C7×#52511yescharacteristic
954C22C7×#52511yescharacteristic
955C22C2×C7×#12611yescharacteristic
956C22C7×#52911yescharacteristic
957C22C7×#52911yescharacteristic
958C22C7×#52911yescharacteristic
959C22C7×#53211yescharacteristic
960C22C7×#53211yescharacteristic
961C22C7×#53811yescharacteristic
962C22C7×#53911yescharacteristic
963C22C7×#54111yescharacteristic
964C22C7×#54211yescharacteristic
965C22C7×#54611yescharacteristic
966C22C7×#54611yescharacteristic
967C22C7×#54611yescharacteristic
968C22C7×#54611yescharacteristic
969C22C7×#54711yescharacteristic
970C22C7×#54711yescharacteristic
971C22C7×#54711yescharacteristic
972C22C7×#54711yescharacteristic
973C22C7×#55111yescharacteristic
974C22C7×#55111yescharacteristic
975C22C7×#55211yescharacteristic
976C22C7×#55211yescharacteristic
977C22C7×#55311yescharacteristic
978C22C7×#55311yescharacteristic
979C22C7×#55611yescharacteristic
980C22C7×#55611yescharacteristic
981C4—24no—
982C4—24no—
983C4—24no—
984C4—42no—
985C4—42no—
986C4—42no—
987C4—42no—
988C4—42no—
989C4—42no—
990C4—42no—
991C4—42no—
992C4—42no—
993C4—81no—
994C4—81no—
995C2—44no—
996C2C7×#229711yescharacteristic
997C2C4×C7×#12611yescharacteristic
998C2C7×#233411yescharacteristic
999C2C7×#233911yescharacteristic
1000C2C7×#233911yescharacteristic
1001C2C7×#237311yescharacteristic
1002C2C7×#237311yescharacteristic
1003C2C7×#246611yescharacteristic
1004C2C7×#246811yescharacteristic
1005C2C7×#247811yescharacteristic
1006C2C7×#248011yescharacteristic
1007C2C7×#249611yescharacteristic
1008C2C7×#252111yescharacteristic
1009C2C7×#255311yescharacteristic
1010C2C7×#255911yescharacteristic
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
4. C7×#1445C2semidirect
5. C7×#1441C2semidirect
8. C7×#1436C2semidirect
9. C7×#1436C2semidirect
10. C7×#1436C2semidirect
11. C7×C4⋊#95C2semidirect
12. C7×#1434C2semidirect
15. C4×C7×#95C2semidirect
19. C2×C7×#126C4semidirect
56. #14102C7direct (N × H)
89. C2×C7×C4⋊C4C2×C4semidirect
90. C2×C7×C4⋊C4C2×C4semidirect
91. C2×C7×C4⋊C4C2×C4semidirect
121. C2×C42×C7C2×C4semidirect
145. #1445C2×C7semidirect
146. #1441C2×C7semidirect
149. #1436C2×C7semidirect
150. #1436C2×C7semidirect
151. #1436C2×C7semidirect
152. C4⋊#95C2×C7semidirect
153. #1434C2×C7semidirect
156. C4×#95C2×C7semidirect
295. C2×#126C4×C7semidirect
480. C2×C4×C7#126semidirect
513. C2×C4⋊C4C2×C4×C7semidirect
514. C2×C4⋊C4C2×C4×C7semidirect
515. C2×C4⋊C4C2×C4×C7semidirect
545. C2×C42C2×C4×C7semidirect
929. C2×C4C7×#126semidirect
930. C7#14102direct (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×#3882
C2×C4×C7×C22⋊C42
C7×#14452
C7×#14412
C7×#14402
C7×#14362
C7×C4⋊#952
C7×#14342
C7×C22⋊#952
C4×C7×#952
#141027