Finite Group Databasebeta

← C7×#16550 #13193766

Subgroups — C7×#16550 #13193766

Order 1792.

1458 conjugacy classes of subgroups.

The subgroup lattice has 1014 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C7×#399C211yesmaximal, characteristic
2C2×C7×#398C211yesmaximal, characteristic, complemented
3C2×C7×#398C211yesmaximal, characteristic, complemented
4C2×C7×#396C211yesmaximal, characteristic
5C2×C7×#396C211yesmaximal, characteristic
6C2×C7×#389C211yesmaximal, characteristic, complemented
7C7×#1444C211yesmaximal, characteristic, complemented
8C7×#1441C211yesmaximal, characteristic, complemented
9C7×#1441C211yesmaximal, characteristic, complemented
10C7×#1441C211yesmaximal, characteristic, complemented
11C7×#1440C211yesmaximal, characteristic
12C7×#1439C211yesmaximal, characteristic
13C7×#1439C211yesmaximal, characteristic
14C7×#1437C211yesmaximal, characteristic
15C7×#1436C211yesmaximal, characteristic, complemented
16C22×C7×C4⋊C4C2211yescharacteristic
17C22×C7×C4⋊C4C2211yescharacteristic
18C22×C7×C4⋊C4C2211yescharacteristic
19C22×C7×C4⋊C4C2211yescharacteristic
20C22×C7×C4⋊C4C2211yescharacteristic
21C22×C7×C4⋊C4C2211yescharacteristic
22C22×C7×C4⋊C4C2211yescharacteristic
23C22×C7×C4⋊C4C2211yescharacteristic
24C22×C7×C4⋊C4C2211yescharacteristic
25C22×C7×C4⋊C4C2211yescharacteristic
26C22×C7×C4⋊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×C42×C7C2211yescharacteristic
35C7×#399—24no—
36C7×#398—24no—
37C7×#398—24no—
38C7×#396—24no—
39C7×#396—24no—
40C7×#389—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#16550C711yesmaximal, characteristic, direct product factor, Sylow
58C25×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
72C23×C4×C7C2311yescharacteristic
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—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—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—41no—
95C2×C7×C4⋊C4—41no—
96C2×C7×C4⋊C4—41no—
97C2×C7×C4⋊C4—41no—
98C2×C7×C4⋊C4—41no—
99C2×C7×C4⋊C4—41no—
100C2×C7×C4⋊C4—41no—
101C2×C7×C4⋊C4—41no—
102C2×C7×C4⋊C4—41no—
103C2×C7×C4⋊C4—41no—
104C2×C7×C4⋊C4D414yes—
105C2×C7×C4⋊C4D414yes—
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—41no—
119C2×C7×C22⋊C4—41no—
120C2×C7×C22⋊C4—41no—
121C2×C7×C22⋊C4—41no—
122C2×C7×C22⋊C4—41no—
123C2×C7×C22⋊C4—41no—
124C2×C7×C22⋊C4—41no—
125C2×C7×C22⋊C4—41no—
126C2×C7×C22⋊C4Q814yes—
127C2×C42×C7—22no—
128C2×C42×C7—41no—
129C2×C42×C7—41no—
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—22no—
139C7×#95—22no—
140C7×#95—22no—
141C7×#95—41no—
142C7×#95—41no—
143C7×#95—41no—
144C7×#95—41no—
145C7×#95D414yes—
146C2×#399C2×C711yescharacteristic
147C2×#398C2×C711yescharacteristic, complemented
148C2×#398C2×C711yescharacteristic, complemented
149C2×#396C2×C711yescharacteristic
150C2×#396C2×C711yescharacteristic
151C2×#389C2×C711yescharacteristic, complemented
152#1444C2×C711yescharacteristic, complemented
153#1441C2×C711yescharacteristic, complemented
154#1441C2×C711yescharacteristic, complemented
155#1441C2×C711yescharacteristic, complemented
156#1440C2×C711yescharacteristic
157#1439C2×C711yescharacteristic
158#1439C2×C711yescharacteristic
159#1437C2×C711yescharacteristic
160#1436C2×C711yescharacteristic, complemented
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×C7—21no—
172C24×C7—21no—
173C24×C7—21no—
174C24×C7—21no—
175C24×C7C2×Q812yes—
176C24×C7C2411yescharacteristic
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×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×C7C2×D412yes—
262C22×C4×C7C2×D412yes—
263C22×C4×C7C2×D412yes—
264C22×C4×C7C2×D412yes—
265C22×C4×C7C2×D412yes—
266C22×C4×C7C2×D412yes—
267C22×C4×C7C2×D412yes—
268C22×C4×C7C2×D412yes—
269C22×C4×C7C2×D412yes—
270C22×C4×C7C2×Q812yes—
271C22×C4×C7C2×Q812yes—
272C22×C4×C7#4112yes—
273C22×C4×C7#4112yes—
274C22×C4×C7#4112yes—
275C7×C4⋊C4—28no—
276C7×C4⋊C4—44no—
277C7×C4⋊C4—44no—
278C7×C4⋊C4—44no—
279C7×C4⋊C4—44no—
280C7×C4⋊C4—44no—
281C7×C4⋊C4—44no—
282C7×C4⋊C4—44no—
283C7×C4⋊C4—44no—
284C7×C4⋊C4—44no—
285C7×C4⋊C4—44no—
286C7×C22⋊C4—44no—
287C7×C22⋊C4—44no—
288C7×C22⋊C4—44no—
289C7×C22⋊C4—44no—
290C7×C22⋊C4—44no—
291C7×C22⋊C4—44no—
292C7×C22⋊C4—44no—
293C42×C7—44no—
294C22×C4⋊C4C22×C711yescharacteristic
295C22×C4⋊C4C22×C711yescharacteristic
296C22×C4⋊C4C22×C711yescharacteristic
297C22×C4⋊C4C22×C711yescharacteristic
298C22×C4⋊C4C22×C711yescharacteristic
299C22×C4⋊C4C22×C711yescharacteristic
300C22×C4⋊C4C22×C711yescharacteristic
301C22×C4⋊C4C22×C711yescharacteristic
302C22×C4⋊C4C22×C711yescharacteristic
303C22×C4⋊C4C22×C711yescharacteristic
304C22×C4⋊C4C22×C711yescharacteristic
305C22×C22⋊C4C22×C711yescharacteristic
306C22×C22⋊C4C22×C711yescharacteristic
307C22×C22⋊C4C22×C711yescharacteristic
308C22×C22⋊C4C22×C711yescharacteristic
309C22×C22⋊C4C22×C711yescharacteristic
310C22×C22⋊C4C22×C711yescharacteristic
311C22×C22⋊C4C22×C711yescharacteristic
312C22×C42C22×C711yescharacteristic
313#399—24no—
314#398—24no—
315#398—24no—
316#396—24no—
317#396—24no—
318#389—24no—
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
332C2×#95C22×C711yescharacteristic
333C2×#95C22×C711yescharacteristic
334C2×#95C22×C711yescharacteristic
335C23×C7—22no—
336C23×C7—22no—
337C23×C7—22no—
338C23×C7—22no—
339C23×C7—22no—
340C23×C7—22no—
341C23×C7—22no—
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×C7—41no—
364C23×C7—41no—
365C23×C7—41no—
366C23×C7—41no—
367C23×C7—41no—
368C23×C7—41no—
369C23×C7—41no—
370C23×C7C22×D411yescharacteristic
371C23×C7C22×D411yescharacteristic
372C23×C7C22×D411yescharacteristic
373C23×C7C22×Q811yescharacteristic
374C23×C7C2×#4111yescharacteristic
375C23×C7C2×#4111yescharacteristic
376C23×C7C2×#4111yescharacteristic
377C23×C7H(5,𝔽2)11yescharacteristic
378C23×C7H(5,𝔽2)11yescharacteristic
379C23×C7H(5,𝔽2)11yescharacteristic
380C23×C7H(5,𝔽2)11yescharacteristic
381C23×C72−1+411yescharacteristic
382C23×C72−1+411yescharacteristic
383C23×C72−1+411yescharacteristic
384C23×C72−1+411yescharacteristic
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—41no—
425C2×C4×C7—41no—
426C2×C4×C7—41no—
427C2×C4×C7—41no—
428C2×C4×C7—41no—
429C2×C4×C7—41no—
430C2×C4×C7—41no—
431C2×C4×C7—41no—
432C2×C4×C7—41no—
433C2×C4×C7—41no—
434C2×C4×C7—41no—
435C2×C4×C7—41no—
436C2×C4×C7—41no—
437C2×C4×C7—41no—
438C2×C4×C7—41no—
439C2×C4×C7—41no—
440C2×C4×C7—41no—
441C2×C4×C7—41no—
442C2×C4×C7—41no—
443C2×C4×C7—41no—
444C2×C4×C7—41no—
445C2×C4×C7—41no—
446C2×C4×C7—41no—
447C2×C4×C7—41no—
448C2×C4×C7—41no—
449C2×C4×C7—41no—
450C2×C4×C7—41no—
451C2×C4×C7—41no—
452C2×C4×C7—41no—
453C2×C4×C7—41no—
454C2×C4×C7—41no—
455C2×C4×C7—41no—
456C2×C4×C7—41no—
457C2×C4×C7—41no—
458C2×C4×C7—41no—
459C2×C4×C7—41no—
460C2×C4×C7—41no—
461C2×C4×C7—41no—
462C2×C4×C7—41no—
463C2×C4×C7—41no—
464C2×C4×C7—41no—
465C2×C4×C7—41no—
466C2×C4×C7—41no—
467C2×C4×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#12114yes—
483C25C23×C711yescharacteristic
484C23×C4C23×C711yescharacteristic
485C23×C4C23×C711yescharacteristic
486C23×C4C23×C711yescharacteristic
487C23×C4C23×C711yescharacteristic
488C23×C4C23×C711yescharacteristic
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
498C2×C4⋊C4—22no—
499C2×C4⋊C4—22no—
500C2×C4⋊C4—22no—
501C2×C4⋊C4—22no—
502C2×C4⋊C4—22no—
503C2×C4⋊C4—22no—
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—22no—
513C2×C4⋊C4—22no—
514C2×C4⋊C4—22no—
515C2×C4⋊C4—22no—
516C2×C4⋊C4—22no—
517C2×C4⋊C4—22no—
518C2×C4⋊C4—22no—
519C2×C4⋊C4—41no—
520C2×C4⋊C4—41no—
521C2×C4⋊C4—41no—
522C2×C4⋊C4—41no—
523C2×C4⋊C4—41no—
524C2×C4⋊C4—41no—
525C2×C4⋊C4—41no—
526C2×C4⋊C4—41no—
527C2×C4⋊C4—41no—
528C2×C4⋊C4—41no—
529C2×C4⋊C4C7×D414yes—
530C2×C4⋊C4C7×D414yes—
531C2×C22⋊C4—22no—
532C2×C22⋊C4—22no—
533C2×C22⋊C4—22no—
534C2×C22⋊C4—22no—
535C2×C22⋊C4—22no—
536C2×C22⋊C4—22no—
537C2×C22⋊C4—22no—
538C2×C22⋊C4—22no—
539C2×C22⋊C4—22no—
540C2×C22⋊C4—22no—
541C2×C22⋊C4—22no—
542C2×C22⋊C4—22no—
543C2×C22⋊C4—41no—
544C2×C22⋊C4—41no—
545C2×C22⋊C4—41no—
546C2×C22⋊C4—41no—
547C2×C22⋊C4—41no—
548C2×C22⋊C4—41no—
549C2×C22⋊C4—41no—
550C2×C22⋊C4—41no—
551C2×C22⋊C4C7×Q814yes—
552C2×C42—22no—
553C2×C42—41no—
554C2×C42—41no—
555#95—22no—
556#95—22no—
557#95—22no—
558#95—22no—
559#95—22no—
560#95—22no—
561#95—22no—
562#95—22no—
563#95—22no—
564#95—22no—
565#95—22no—
566#95—41no—
567#95—41no—
568#95—41no—
569#95—41no—
570#95C7×D414yes—
571C22×C7—42no—
572C22×C7—42no—
573C22×C7—42no—
574C22×C7—42no—
575C22×C7—42no—
576C22×C7—42no—
577C22×C7—42no—
578C22×C7—81no—
579C22×C7—81no—
580C22×C7—81no—
581C22×C7—81no—
582C22×C7—81no—
583C22×C7—81no—
584C22×C7—81no—
585C22×C7—81no—
586C22×C7C2×#12111yescharacteristic
587C22×C7#53211yescharacteristic
588C22×C7#53311yescharacteristic
589C22×C7#53411yescharacteristic
590C22×C7#53611yescharacteristic
591C22×C7#53611yescharacteristic
592C22×C7#53711yescharacteristic
593C22×C7#53711yescharacteristic
594C22×C7#53711yescharacteristic
595C22×C7#53911yescharacteristic
596C22×C7#53911yescharacteristic
597C22×C7#53911yescharacteristic
598C22×C7#53911yescharacteristic
599C22×C7#54011yescharacteristic
600C22×C7#54011yescharacteristic
601C22×C7#54111yescharacteristic
602C22×C7#54111yescharacteristic
603C22×C7#54311yescharacteristic
604C22×C7#54411yescharacteristic
605C22×C7D4211yescharacteristic
606C22×C7D4211yescharacteristic
607C22×C7#54611yescharacteristic
608C22×C7#54611yescharacteristic
609C22×C7#54711yescharacteristic
610C22×C7#54811yescharacteristic
611C22×C7D4×Q811yescharacteristic
612C22×C7D4×Q811yescharacteristic
613C22×C7D4×Q811yescharacteristic
614C22×C7#55011yescharacteristic
615C22×C7#55211yescharacteristic
616C22×C7#55411yescharacteristic
617C22×C7#56211yescharacteristic
618C22×C7#56211yescharacteristic
619C22×C7#56311yescharacteristic
620C22×C7#56311yescharacteristic
621C4×C7—24no—
622C4×C7—42no—
623C4×C7—42no—
624C4×C7—42no—
625C4×C7—42no—
626C4×C7—42no—
627C4×C7—42no—
628C4×C7—42no—
629C4×C7—42no—
630C4×C7—42no—
631C4×C7—42no—
632C4×C7—42no—
633C4×C7—81no—
634C4×C7—81no—
635C24—21no—
636C24—21no—
637C24—21no—
638C24—21no—
639C24—21no—
640C24—21no—
641C24—21no—
642C24—21no—
643C24—21no—
644C24—21no—
645C24—21no—
646C24—21no—
647C24—21no—
648C24—21no—
649C24C2×C7×Q812yes—
650C24C24×C711yescharacteristic
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×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×C4C2×C7×D412yes—
736C22×C4C2×C7×D412yes—
737C22×C4C2×C7×D412yes—
738C22×C4C2×C7×D412yes—
739C22×C4C2×C7×D412yes—
740C22×C4C2×C7×D412yes—
741C22×C4C2×C7×D412yes—
742C22×C4C2×C7×D412yes—
743C22×C4C2×C7×D412yes—
744C22×C4C2×C7×Q812yes—
745C22×C4C2×C7×Q812yes—
746C22×C4C7×#4112yes—
747C22×C4C7×#4112yes—
748C22×C4C7×#4112yes—
749C4⋊C4—28no—
750C4⋊C4—44no—
751C4⋊C4—44no—
752C4⋊C4—44no—
753C4⋊C4—44no—
754C4⋊C4—44no—
755C4⋊C4—44no—
756C4⋊C4—44no—
757C4⋊C4—44no—
758C4⋊C4—44no—
759C4⋊C4—44no—
760C22⋊C4—44no—
761C22⋊C4—44no—
762C22⋊C4—44no—
763C22⋊C4—44no—
764C22⋊C4—44no—
765C22⋊C4—44no—
766C22⋊C4—44no—
767C42—44no—
768C2×C7—82no—
769C2×C7#242811yescharacteristic
770C2×C7#242911yescharacteristic
771C2×C7#255611yescharacteristic
772C2×C7#261811yescharacteristic
773C2×C7#266411yescharacteristic
774C2×C7#266711yescharacteristic
775C2×C7#267111yescharacteristic
776C2×C7#267711yescharacteristic
777C2×C7#268111yescharacteristic
778C2×C7#268311yescharacteristic
779C2×C7#270411yescharacteristic
780C2×C7#270711yescharacteristic
781C2×C7#272111yescharacteristic
782C2×C7#273211yescharacteristic
783C2×C7#283611yescharacteristic
784C23—22no—
785C23—22no—
786C23—22no—
787C23—22no—
788C23—22no—
789C23—22no—
790C23—22no—
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—
807C23—41no—
808C23—41no—
809C23—41no—
810C23—41no—
811C23—41no—
812C23—41no—
813C23—41no—
814C23—41no—
815C23—41no—
816C23—41no—
817C23—41no—
818C23—41no—
819C23C22×C7×D411yescharacteristic
820C23C22×C7×D411yescharacteristic
821C23C22×C7×D411yescharacteristic
822C23C22×C7×Q811yescharacteristic
823C23C2×C7×#4111yescharacteristic
824C23C2×C7×#4111yescharacteristic
825C23C2×C7×#4111yescharacteristic
826C23C7×H(5,𝔽2)11yescharacteristic
827C23C7×H(5,𝔽2)11yescharacteristic
828C23C7×H(5,𝔽2)11yescharacteristic
829C23C7×H(5,𝔽2)11yescharacteristic
830C23C7×2−1+411yescharacteristic
831C23C7×2−1+411yescharacteristic
832C23C7×2−1+411yescharacteristic
833C23C7×2−1+411yescharacteristic
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—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×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×C4C7×#12114yes—
932C7#1655011yescharacteristic, direct product factor, Sylow
933C22—42no—
934C22—42no—
935C22—42no—
936C22—42no—
937C22—42no—
938C22—42no—
939C22—42no—
940C22—81no—
941C22—81no—
942C22—81no—
943C22—81no—
944C22—81no—
945C22—81no—
946C22—81no—
947C22—81no—
948C22C2×C7×#12111yescharacteristic
949C22C7×#53211yescharacteristic
950C22C7×#53311yescharacteristic
951C22C7×#53411yescharacteristic
952C22C7×#53611yescharacteristic
953C22C7×#53611yescharacteristic
954C22C7×#53711yescharacteristic
955C22C7×#53711yescharacteristic
956C22C7×#53711yescharacteristic
957C22C7×#53911yescharacteristic
958C22C7×#53911yescharacteristic
959C22C7×#53911yescharacteristic
960C22C7×#53911yescharacteristic
961C22C7×#54011yescharacteristic
962C22C7×#54011yescharacteristic
963C22C7×#54111yescharacteristic
964C22C7×#54111yescharacteristic
965C22C7×#54311yescharacteristic
966C22C7×#54411yescharacteristic
967C22C7×D4211yescharacteristic
968C22C7×D4211yescharacteristic
969C22C7×#54611yescharacteristic
970C22C7×#54611yescharacteristic
971C22C7×#54711yescharacteristic
972C22C7×#54811yescharacteristic
973C22C7×D4×Q811yescharacteristic
974C22C7×D4×Q811yescharacteristic
975C22C7×D4×Q811yescharacteristic
976C22C7×#55011yescharacteristic
977C22C7×#55211yescharacteristic
978C22C7×#55411yescharacteristic
979C22C7×#56211yescharacteristic
980C22C7×#56211yescharacteristic
981C22C7×#56311yescharacteristic
982C22C7×#56311yescharacteristic
983C4—24no—
984C4—42no—
985C4—42no—
986C4—42no—
987C4—42no—
988C4—42no—
989C4—42no—
990C4—42no—
991C4—42no—
992C4—42no—
993C4—42no—
994C4—42no—
995C4—81no—
996C4—81no—
997C2—82no—
998C2C7×#242811yescharacteristic
999C2C7×#242911yescharacteristic
1000C2C7×#255611yescharacteristic
1001C2C7×#261811yescharacteristic
1002C2C7×#266411yescharacteristic
1003C2C7×#266711yescharacteristic
1004C2C7×#267111yescharacteristic
1005C2C7×#267711yescharacteristic
1006C2C7×#268111yescharacteristic
1007C2C7×#268311yescharacteristic
1008C2C7×#270411yescharacteristic
1009C2C7×#270711yescharacteristic
1010C2C7×#272111yescharacteristic
1011C2C7×#273211yescharacteristic
1012C2C7×#283611yescharacteristic
subgroupG/H
center, socleC24×C7C24
commutator, Frattini, cosocleC24C24×C7
prime radicalC25×C7C23
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C24×C7 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C7×#398C2semidirect
3. C2×C7×#398C2semidirect
6. C2×C7×#389C2semidirect
7. C7×#1444C2semidirect
8. C7×#1441C2semidirect
9. C7×#1441C2semidirect
10. C7×#1441C2semidirect
15. C7×#1436C2semidirect
57. #16550C7direct (N × H)
147. C2×#398C2×C7semidirect
148. C2×#398C2×C7semidirect
151. C2×#389C2×C7semidirect
152. #1444C2×C7semidirect
153. #1441C2×C7semidirect
154. #1441C2×C7semidirect
155. #1441C2×C7semidirect
160. #1436C2×C7semidirect
932. C7#16550direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C7×#3992
C2×C7×#3982
C2×C7×#3962
C2×C7×#3892
C7×#14442
C7×#14412
C7×#14402
C7×#14392
C7×#14372
C7×#14362
#165507