Finite Group Databasebeta

← C7×#13876 #13191092

Subgroups — C7×#13876 #13191092

Order 1792.

1846 conjugacy classes of subgroups.

The subgroup lattice has 822 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C7×#388C212yesmaximal
2C2×C7×#384C211yesmaximal, characteristic, complemented
3C2×C7×#380C211yesmaximal, characteristic
4C2×C7×#380C211yesmaximal, characteristic
5C2×C4×C7×C4⋊C4C211yesmaximal, characteristic, complemented
6C2×C4×C7×C22⋊C4C211yesmaximal, characteristic
7C7×#1442C212yesmaximal, complemented
8C7×#1439C212yesmaximal
9C7×#1436C212yesmaximal, complemented
10C7×C4⋊#95C211yesmaximal, characteristic, complemented
11C7×C4⋊#95C211yesmaximal, characteristic, complemented
12C24×C4×C7C2211yescharacteristic
13C22×C7×C4⋊C4C2211yescharacteristic
14C22×C7×C4⋊C4C2211yescharacteristic
15C22×C7×C4⋊C4C2212yes—
16C22×C7×C4⋊C4C2212yes—
17C22×C7×C4⋊C4C2211yescharacteristic
18C22×C7×C4⋊C4C2211yescharacteristic
19C22×C7×C22⋊C4C2212yes—
20C22×C7×C22⋊C4C2212yes—
21C22×C7×C22⋊C4C2211yescharacteristic
22C22×C7×C22⋊C4C2211yescharacteristic
23C22×C42×C7C2212yes—
24C22×C42×C7C2211yescharacteristic
25C22×C42×C7C2211yescharacteristic
26C7×#388—28no—
27C7×#384—24no—
28C7×#380—24no—
29C7×#380—24no—
30C4×C7×C4⋊C4—24no—
31C4×C7×C22⋊C4C418yescomplemented
32C2×C7×#95C2212yes—
33C2×C7×#95C2212yes—
34C2×C7×#95C2212yes—
35C2×C7×#95C2212yes—
36C2×C7×#95C2212yes—
37C2×C7×#95C2212yes—
38C2×C7×#95C2212yes—
39C2×C7×#95C2211yescharacteristic
40C2×C7×#95C2211yescharacteristic
41#13876C711yesmaximal, characteristic, direct product factor, Sylow
42C25×C7C2311yescharacteristic
43C23×C4×C7—22no—
44C23×C4×C7—22no—
45C23×C4×C7—22no—
46C23×C4×C7—22no—
47C23×C4×C7—22no—
48C23×C4×C7—22no—
49C23×C4×C7C2×C414yes—
50C23×C4×C7C2312yes—
51C23×C4×C7C2312yes—
52C23×C4×C7C2311yescharacteristic
53C23×C4×C7C2311yescharacteristic
54C23×C4×C7C2312yes—
55C23×C4×C7C2312yes—
56C23×C4×C7C2311yescharacteristic
57C23×C4×C7C2311yescharacteristic
58C23×C4×C7C2311yescharacteristic
59C23×C4×C7C2311yescharacteristic
60C2×C7×C4⋊C4—22no—
61C2×C7×C4⋊C4—22no—
62C2×C7×C4⋊C4—22no—
63C2×C7×C4⋊C4—22no—
64C2×C7×C4⋊C4—22no—
65C2×C7×C4⋊C4—22no—
66C2×C7×C4⋊C4—24no—
67C2×C7×C4⋊C4—24no—
68C2×C7×C4⋊C4—22no—
69C2×C7×C4⋊C4—24no—
70C2×C7×C4⋊C4—24no—
71C2×C7×C4⋊C4—22no—
72C2×C7×C4⋊C4—22no—
73C2×C7×C4⋊C4—22no—
74C2×C7×C4⋊C4—42no—
75C2×C7×C4⋊C4—42no—
76C2×C7×C4⋊C4D414yes—
77C2×C7×C4⋊C4D414yes—
78C2×C7×C22⋊C4—22no—
79C2×C7×C22⋊C4—22no—
80C2×C7×C22⋊C4—24no—
81C2×C7×C22⋊C4—24no—
82C2×C7×C22⋊C4—24no—
83C2×C7×C22⋊C4—24no—
84C2×C7×C22⋊C4—42no—
85C2×C7×C22⋊C4—42no—
86C2×C7×C22⋊C4C2×C414yes—
87C2×C7×C22⋊C4C2×C414yes—
88C2×C7×C22⋊C4D414yes—
89C2×C7×C22⋊C4Q814yes—
90C2×C42×C7—22no—
91C2×C42×C7—22no—
92C2×C42×C7—22no—
93C2×C42×C7—22no—
94C2×C42×C7—24no—
95C2×C42×C7—24no—
96C2×C42×C7—42no—
97C2×C42×C7C2×C414yes—
98C2×C42×C7C2×C414yes—
99C7×#95—24no—
100C7×#95—24no—
101C7×#95—24no—
102C7×#95—24no—
103C7×#95—24no—
104C7×#95—24no—
105C7×#95—42no—
106C7×#95C2×C414yes—
107C7×#95C2×C414yes—
108C2×#388C2×C712yes—
109C2×#384C2×C711yescharacteristic, complemented
110C2×#380C2×C711yescharacteristic
111C2×#380C2×C711yescharacteristic
112C2×C4×C4⋊C4C2×C711yescharacteristic, complemented
113C2×C4×C22⋊C4C2×C711yescharacteristic
114#1442C2×C712yescomplemented
115#1439C2×C712yes—
116#1436C2×C712yescomplemented
117C4⋊#95C2×C711yescharacteristic, complemented
118C4⋊#95C2×C711yescharacteristic, complemented
119C24×C7—21no—
120C24×C7—21no—
121C24×C7—21no—
122C24×C7—21no—
123C24×C7—21no—
124C24×C7—21no—
125C24×C7—21no—
126C24×C7—21no—
127C24×C7—21no—
128C24×C7—21no—
129C24×C7—21no—
130C24×C7—21no—
131C24×C7C22×C412yes—
132C24×C7C2×D412yes—
133C24×C7C2×Q812yes—
134C24×C7C2411yescharacteristic
135C22×C4×C7—21no—
136C22×C4×C7—21no—
137C22×C4×C7—21no—
138C22×C4×C7—21no—
139C22×C4×C7—21no—
140C22×C4×C7—21no—
141C22×C4×C7—21no—
142C22×C4×C7—21no—
143C22×C4×C7—21no—
144C22×C4×C7—21no—
145C22×C4×C7—21no—
146C22×C4×C7—21no—
147C22×C4×C7—21no—
148C22×C4×C7—21no—
149C22×C4×C7—21no—
150C22×C4×C7—22no—
151C22×C4×C7—22no—
152C22×C4×C7—22no—
153C22×C4×C7—22no—
154C22×C4×C7—21no—
155C22×C4×C7—21no—
156C22×C4×C7—21no—
157C22×C4×C7—22no—
158C22×C4×C7—22no—
159C22×C4×C7—22no—
160C22×C4×C7—22no—
161C22×C4×C7—21no—
162C22×C4×C7—21no—
163C22×C4×C7—21no—
164C22×C4×C7—21no—
165C22×C4×C7—21no—
166C22×C4×C7—22no—
167C22×C4×C7—22no—
168C22×C4×C7—22no—
169C22×C4×C7—21no—
170C22×C4×C7—22no—
171C22×C4×C7—28no—
172C22×C4×C7—28no—
173C22×C4×C7—28no—
174C22×C4×C7—22no—
175C22×C4×C7—22no—
176C22×C4×C7—22no—
177C22×C4×C7—22no—
178C22×C4×C7—22no—
179C22×C4×C7—22no—
180C22×C4×C7—22no—
181C22×C4×C7—22no—
182C22×C4×C7—22no—
183C22×C4×C7—22no—
184C22×C4×C7—22no—
185C22×C4×C7—22no—
186C22×C4×C7—22no—
187C22×C4×C7—22no—
188C22×C4×C7—44no—
189C22×C4×C7—44no—
190C22×C4×C7—44no—
191C22×C4×C7—44no—
192C22×C4×C7C22×C412yes—
193C22×C4×C7C22×C412yes—
194C22×C4×C7C22×C412yes—
195C22×C4×C7C22×C412yes—
196C22×C4×C7C22×C412yes—
197C22×C4×C7C22×C412yes—
198C22×C4×C7C2×D414yes—
199C22×C4×C7C2×D414yes—
200C22×C4×C7C2×D412yes—
201C22×C4×C7C2×D412yes—
202C22×C4×C7C2×D412yes—
203C22×C4×C7C2×D412yes—
204C22×C4×C7C2×Q812yes—
205C22×C4×C7C2×Q812yes—
206C22×C4×C7#4112yes—
207C22×C4×C7#4112yes—
208C22×C4×C7#4112yes—
209C22×C4×C7#4112yes—
210C22×C4×C7#4112yes—
211C22×C4×C7#4112yes—
212C7×C4⋊C4—28no—
213C7×C4⋊C4—28no—
214C7×C4⋊C4—48no—
215C7×C4⋊C4—48no—
216C7×C4⋊C4—44no—
217C7×C4⋊C4—44no—
218C7×C22⋊C4—28no—
219C7×C22⋊C4—48no—
220C7×C22⋊C4—48no—
221C7×C22⋊C4C4⋊C4116yescomplemented
222C42×C7—28no—
223C42×C7—28no—
224C42×C7—48no—
225C24×C4C22×C711yescharacteristic
226C22×C4⋊C4C22×C711yescharacteristic
227C22×C4⋊C4C22×C711yescharacteristic
228C22×C4⋊C4C22×C712yes—
229C22×C4⋊C4C22×C712yes—
230C22×C4⋊C4C22×C711yescharacteristic
231C22×C4⋊C4C22×C711yescharacteristic
232C22×C22⋊C4C22×C712yes—
233C22×C22⋊C4C22×C712yes—
234C22×C22⋊C4C22×C711yescharacteristic
235C22×C22⋊C4C22×C711yescharacteristic
236C22×C42C22×C712yes—
237C22×C42C22×C711yescharacteristic
238C22×C42C22×C711yescharacteristic
239#388—28no—
240#384—24no—
241#380—24no—
242#380—24no—
243C4×C4⋊C4—24no—
244C4×C22⋊C4C4×C718yescomplemented
245C2×#95C22×C712yes—
246C2×#95C22×C712yes—
247C2×#95C22×C712yes—
248C2×#95C22×C712yes—
249C2×#95C22×C712yes—
250C2×#95C22×C712yes—
251C2×#95C22×C712yes—
252C2×#95C22×C711yescharacteristic
253C2×#95C22×C711yescharacteristic
254C23×C7—22no—
255C23×C7—22no—
256C23×C7—22no—
257C23×C7—22no—
258C23×C7—22no—
259C23×C7—22no—
260C23×C7—22no—
261C23×C7—22no—
262C23×C7—22no—
263C23×C7—22no—
264C23×C7—22no—
265C23×C7—22no—
266C23×C7—22no—
267C23×C7—22no—
268C23×C7—22no—
269C23×C7—22no—
270C23×C7—22no—
271C23×C7—22no—
272C23×C7—41no—
273C23×C7—41no—
274C23×C7—41no—
275C23×C7—41no—
276C23×C7—41no—
277C23×C7—41no—
278C23×C7—41no—
279C23×C7—41no—
280C23×C7—41no—
281C23×C7—41no—
282C23×C7—41no—
283C23×C7—41no—
284C23×C7—41no—
285C23×C7—41no—
286C23×C7—41no—
287C23×C7—41no—
288C23×C7C2×C4⋊C414yes—
289C23×C7C23×C411yescharacteristic
290C23×C7C22×D411yescharacteristic
291C23×C7C22×D411yescharacteristic
292C23×C7C22×D411yescharacteristic
293C23×C7C22×Q811yescharacteristic
294C23×C7C2×#4111yescharacteristic
295C23×C7C2×#4111yescharacteristic
296C23×C7C2×#4111yescharacteristic
297C23×C7C2×#4111yescharacteristic
298C23×C7C2×#4111yescharacteristic
299C23×C7C2×#4111yescharacteristic
300C23×C7H(5,𝔽2)11yescharacteristic
301C23×C7H(5,𝔽2)11yescharacteristic
302C23×C72−1+411yescharacteristic
303C23×C72−1+411yescharacteristic
304C2×C4×C7—22no—
305C2×C4×C7—22no—
306C2×C4×C7—22no—
307C2×C4×C7—22no—
308C2×C4×C7—22no—
309C2×C4×C7—22no—
310C2×C4×C7—22no—
311C2×C4×C7—22no—
312C2×C4×C7—22no—
313C2×C4×C7—22no—
314C2×C4×C7—22no—
315C2×C4×C7—22no—
316C2×C4×C7—22no—
317C2×C4×C7—22no—
318C2×C4×C7—22no—
319C2×C4×C7—22no—
320C2×C4×C7—22no—
321C2×C4×C7—22no—
322C2×C4×C7—22no—
323C2×C4×C7—22no—
324C2×C4×C7—22no—
325C2×C4×C7—22no—
326C2×C4×C7—22no—
327C2×C4×C7—22no—
328C2×C4×C7—24no—
329C2×C4×C7—24no—
330C2×C4×C7—24no—
331C2×C4×C7—24no—
332C2×C4×C7—24no—
333C2×C4×C7—24no—
334C2×C4×C7—41no—
335C2×C4×C7—41no—
336C2×C4×C7—41no—
337C2×C4×C7—41no—
338C2×C4×C7—42no—
339C2×C4×C7—42no—
340C2×C4×C7—42no—
341C2×C4×C7—42no—
342C2×C4×C7—42no—
343C2×C4×C7—41no—
344C2×C4×C7—42no—
345C2×C4×C7—41no—
346C2×C4×C7—42no—
347C2×C4×C7—42no—
348C2×C4×C7—41no—
349C2×C4×C7—41no—
350C2×C4×C7—416no—
351C2×C4×C7—42no—
352C2×C4×C7—42no—
353C2×C4×C7—42no—
354C2×C4×C7—42no—
355C2×C4×C7—42no—
356C2×C4×C7—42no—
357C2×C4×C7—42no—
358C2×C4×C7—42no—
359C2×C4×C7—42no—
360C2×C4×C7—42no—
361C2×C4×C7—42no—
362C2×C4×C7—42no—
363C2×C4×C7—42no—
364C2×C4×C7—42no—
365C2×C4×C7C2×C4⋊C414yes—
366C2×C4×C7C2×C4⋊C414yes—
367C2×C4×C7#11714yes—
368C2×C4×C7#11714yes—
369C2×C4×C7C4×D414yes—
370C2×C4×C7C4×D414yes—
371C2×C4×C7#12114yes—
372C2×C4×C7#12314yes—
373C2×C4×C7#12414yes—
374C2×C4×C7#12614yes—
375C25C23×C711yescharacteristic
376C23×C4—22no—
377C23×C4—22no—
378C23×C4—22no—
379C23×C4—22no—
380C23×C4—22no—
381C23×C4—22no—
382C23×C4C2×C4×C714yes—
383C23×C4C23×C712yes—
384C23×C4C23×C712yes—
385C23×C4C23×C711yescharacteristic
386C23×C4C23×C711yescharacteristic
387C23×C4C23×C712yes—
388C23×C4C23×C712yes—
389C23×C4C23×C711yescharacteristic
390C23×C4C23×C711yescharacteristic
391C23×C4C23×C711yescharacteristic
392C23×C4C23×C711yescharacteristic
393C2×C4⋊C4—22no—
394C2×C4⋊C4—22no—
395C2×C4⋊C4—22no—
396C2×C4⋊C4—22no—
397C2×C4⋊C4—22no—
398C2×C4⋊C4—22no—
399C2×C4⋊C4—24no—
400C2×C4⋊C4—24no—
401C2×C4⋊C4—22no—
402C2×C4⋊C4—24no—
403C2×C4⋊C4—24no—
404C2×C4⋊C4—22no—
405C2×C4⋊C4—22no—
406C2×C4⋊C4—22no—
407C2×C4⋊C4—42no—
408C2×C4⋊C4—42no—
409C2×C4⋊C4C7×D414yes—
410C2×C4⋊C4C7×D414yes—
411C2×C22⋊C4—22no—
412C2×C22⋊C4—22no—
413C2×C22⋊C4—24no—
414C2×C22⋊C4—24no—
415C2×C22⋊C4—24no—
416C2×C22⋊C4—24no—
417C2×C22⋊C4—42no—
418C2×C22⋊C4—42no—
419C2×C22⋊C4C2×C4×C714yes—
420C2×C22⋊C4C2×C4×C714yes—
421C2×C22⋊C4C7×D414yes—
422C2×C22⋊C4C7×Q814yes—
423C2×C42—22no—
424C2×C42—22no—
425C2×C42—22no—
426C2×C42—22no—
427C2×C42—24no—
428C2×C42—24no—
429C2×C42—42no—
430C2×C42C2×C4×C714yes—
431C2×C42C2×C4×C714yes—
432#95—24no—
433#95—24no—
434#95—24no—
435#95—24no—
436#95—24no—
437#95—24no—
438#95—42no—
439#95C2×C4×C714yes—
440#95C2×C4×C714yes—
441C22×C7—24no—
442C22×C7—24no—
443C22×C7—24no—
444C22×C7—42no—
445C22×C7—42no—
446C22×C7—42no—
447C22×C7—42no—
448C22×C7—42no—
449C22×C7—42no—
450C22×C7—42no—
451C22×C7—42no—
452C22×C7—42no—
453C22×C7—42no—
454C22×C7—42no—
455C22×C7—42no—
456C22×C7C22×C4⋊C411yescharacteristic
457C22×C7C2×#11711yescharacteristic
458C22×C7C2×#11711yescharacteristic
459C22×C7C2×C4×D411yescharacteristic
460C22×C7C2×C4×D411yescharacteristic
461C22×C7#52011yescharacteristic
462C22×C7#52011yescharacteristic
463C22×C7C2×#12111yescharacteristic
464C22×C7C2×#12311yescharacteristic
465C22×C7C2×#12411yescharacteristic
466C22×C7C2×#12611yescharacteristic
467C22×C7#53211yescharacteristic
468C22×C7#53211yescharacteristic
469C22×C7#53311yescharacteristic
470C22×C7#53311yescharacteristic
471C22×C7#54011yescharacteristic
472C22×C7#54111yescharacteristic
473C22×C7#54211yescharacteristic
474C22×C7#54211yescharacteristic
475C22×C7D4211yescharacteristic
476C22×C7D4211yescharacteristic
477C22×C7#54611yescharacteristic
478C22×C7#54711yescharacteristic
479C22×C7#54711yescharacteristic
480C22×C7#54711yescharacteristic
481C22×C7#54811yescharacteristic
482C22×C7D4×Q811yescharacteristic
483C22×C7D4×Q811yescharacteristic
484C22×C7#55011yescharacteristic
485C22×C7#55211yescharacteristic
486C22×C7#55311yescharacteristic
487C22×C7#55411yescharacteristic
488C22×C7#55411yescharacteristic
489C22×C7#55511yescharacteristic
490C22×C7#55611yescharacteristic
491C4×C7—24no—
492C4×C7—24no—
493C4×C7—24no—
494C4×C7—42no—
495C4×C7—44no—
496C4×C7—44no—
497C4×C7—42no—
498C4×C7—82no—
499C4×C7—82no—
500C4×C7#38818yescomplemented
501C24—21no—
502C24—21no—
503C24—21no—
504C24—21no—
505C24—21no—
506C24—21no—
507C24—21no—
508C24—21no—
509C24—21no—
510C24—21no—
511C24—21no—
512C24—21no—
513C24C22×C4×C712yes—
514C24C2×C7×D412yes—
515C24C2×C7×Q812yes—
516C24C24×C711yescharacteristic
517C22×C4—21no—
518C22×C4—21no—
519C22×C4—21no—
520C22×C4—21no—
521C22×C4—21no—
522C22×C4—21no—
523C22×C4—21no—
524C22×C4—21no—
525C22×C4—21no—
526C22×C4—21no—
527C22×C4—21no—
528C22×C4—21no—
529C22×C4—21no—
530C22×C4—21no—
531C22×C4—21no—
532C22×C4—22no—
533C22×C4—22no—
534C22×C4—22no—
535C22×C4—22no—
536C22×C4—21no—
537C22×C4—21no—
538C22×C4—21no—
539C22×C4—22no—
540C22×C4—22no—
541C22×C4—22no—
542C22×C4—22no—
543C22×C4—21no—
544C22×C4—21no—
545C22×C4—21no—
546C22×C4—21no—
547C22×C4—21no—
548C22×C4—22no—
549C22×C4—22no—
550C22×C4—22no—
551C22×C4—21no—
552C22×C4—22no—
553C22×C4—28no—
554C22×C4—28no—
555C22×C4—28no—
556C22×C4—22no—
557C22×C4—22no—
558C22×C4—22no—
559C22×C4—22no—
560C22×C4—22no—
561C22×C4—22no—
562C22×C4—22no—
563C22×C4—22no—
564C22×C4—22no—
565C22×C4—22no—
566C22×C4—22no—
567C22×C4—22no—
568C22×C4—22no—
569C22×C4—22no—
570C22×C4—44no—
571C22×C4—44no—
572C22×C4—44no—
573C22×C4—44no—
574C22×C4C22×C4×C712yes—
575C22×C4C22×C4×C712yes—
576C22×C4C22×C4×C712yes—
577C22×C4C22×C4×C712yes—
578C22×C4C22×C4×C712yes—
579C22×C4C22×C4×C712yes—
580C22×C4C2×C7×D414yes—
581C22×C4C2×C7×D414yes—
582C22×C4C2×C7×D412yes—
583C22×C4C2×C7×D412yes—
584C22×C4C2×C7×D412yes—
585C22×C4C2×C7×D412yes—
586C22×C4C2×C7×Q812yes—
587C22×C4C2×C7×Q812yes—
588C22×C4C7×#4112yes—
589C22×C4C7×#4112yes—
590C22×C4C7×#4112yes—
591C22×C4C7×#4112yes—
592C22×C4C7×#4112yes—
593C22×C4C7×#4112yes—
594C4⋊C4—28no—
595C4⋊C4—28no—
596C4⋊C4—48no—
597C4⋊C4—48no—
598C4⋊C4—44no—
599C4⋊C4—44no—
600C22⋊C4—28no—
601C22⋊C4—48no—
602C22⋊C4—48no—
603C22⋊C4C7×C4⋊C4116yescomplemented
604C42—28no—
605C42—28no—
606C42—48no—
607C2×C7—44no—
608C2×C7#228511yescharacteristic
609C2×C7C2×#38811yescharacteristic
610C2×C7#231411yescharacteristic
611C2×C7D4×C4⋊C411yescharacteristic
612C2×C7D4×C4⋊C411yescharacteristic
613C2×C7#235211yescharacteristic
614C2×C7#235411yescharacteristic
615C2×C7#242211yescharacteristic
616C2×C7#242311yescharacteristic
617C2×C7#242811yescharacteristic
618C2×C7#242911yescharacteristic
619C2×C7#249111yescharacteristic
620C2×C7#249211yescharacteristic
621C2×C7#249611yescharacteristic
622C2×C7#249711yescharacteristic
623C23—22no—
624C23—22no—
625C23—22no—
626C23—22no—
627C23—22no—
628C23—22no—
629C23—22no—
630C23—22no—
631C23—22no—
632C23—22no—
633C23—22no—
634C23—22no—
635C23—22no—
636C23—22no—
637C23—22no—
638C23—22no—
639C23—22no—
640C23—22no—
641C23—41no—
642C23—41no—
643C23—41no—
644C23—41no—
645C23—41no—
646C23—41no—
647C23—41no—
648C23—41no—
649C23—41no—
650C23—41no—
651C23—41no—
652C23—41no—
653C23—41no—
654C23—41no—
655C23—41no—
656C23—41no—
657C23C2×C7×C4⋊C414yes—
658C23C23×C4×C711yescharacteristic
659C23C22×C7×D411yescharacteristic
660C23C22×C7×D411yescharacteristic
661C23C22×C7×D411yescharacteristic
662C23C22×C7×Q811yescharacteristic
663C23C2×C7×#4111yescharacteristic
664C23C2×C7×#4111yescharacteristic
665C23C2×C7×#4111yescharacteristic
666C23C2×C7×#4111yescharacteristic
667C23C2×C7×#4111yescharacteristic
668C23C2×C7×#4111yescharacteristic
669C23C7×H(5,𝔽2)11yescharacteristic
670C23C7×H(5,𝔽2)11yescharacteristic
671C23C7×2−1+411yescharacteristic
672C23C7×2−1+411yescharacteristic
673C2×C4—22no—
674C2×C4—22no—
675C2×C4—22no—
676C2×C4—22no—
677C2×C4—22no—
678C2×C4—22no—
679C2×C4—22no—
680C2×C4—22no—
681C2×C4—22no—
682C2×C4—22no—
683C2×C4—22no—
684C2×C4—22no—
685C2×C4—22no—
686C2×C4—22no—
687C2×C4—22no—
688C2×C4—22no—
689C2×C4—22no—
690C2×C4—22no—
691C2×C4—22no—
692C2×C4—22no—
693C2×C4—22no—
694C2×C4—22no—
695C2×C4—22no—
696C2×C4—22no—
697C2×C4—24no—
698C2×C4—24no—
699C2×C4—24no—
700C2×C4—24no—
701C2×C4—24no—
702C2×C4—24no—
703C2×C4—41no—
704C2×C4—41no—
705C2×C4—41no—
706C2×C4—41no—
707C2×C4—42no—
708C2×C4—42no—
709C2×C4—42no—
710C2×C4—42no—
711C2×C4—42no—
712C2×C4—42no—
713C2×C4—41no—
714C2×C4—42no—
715C2×C4—41no—
716C2×C4—42no—
717C2×C4—41no—
718C2×C4—41no—
719C2×C4—416no—
720C2×C4—42no—
721C2×C4—42no—
722C2×C4—42no—
723C2×C4—42no—
724C2×C4—42no—
725C2×C4—42no—
726C2×C4—42no—
727C2×C4—42no—
728C2×C4—42no—
729C2×C4—42no—
730C2×C4—42no—
731C2×C4—42no—
732C2×C4—42no—
733C2×C4—42no—
734C2×C4C2×C7×C4⋊C414yes—
735C2×C4C2×C7×C4⋊C414yes—
736C2×C4C7×#11714yes—
737C2×C4C7×#11714yes—
738C2×C4C4×C7×D414yes—
739C2×C4C4×C7×D414yes—
740C2×C4C7×#12114yes—
741C2×C4C7×#12314yes—
742C2×C4C7×#12414yes—
743C2×C4C7×#12614yes—
744C7#1387611yescharacteristic, direct product factor, Sylow
745C22—24no—
746C22—24no—
747C22—24no—
748C22—42no—
749C22—42no—
750C22—42no—
751C22—42no—
752C22—42no—
753C22—42no—
754C22—42no—
755C22—42no—
756C22—42no—
757C22—42no—
758C22—42no—
759C22—42no—
760C22C22×C7×C4⋊C411yescharacteristic
761C22C2×C7×#11711yescharacteristic
762C22C2×C7×#11711yescharacteristic
763C22C2×C4×C7×D411yescharacteristic
764C22C2×C4×C7×D411yescharacteristic
765C22C7×#52011yescharacteristic
766C22C7×#52011yescharacteristic
767C22C2×C7×#12111yescharacteristic
768C22C2×C7×#12311yescharacteristic
769C22C2×C7×#12411yescharacteristic
770C22C2×C7×#12611yescharacteristic
771C22C7×#53211yescharacteristic
772C22C7×#53211yescharacteristic
773C22C7×#53311yescharacteristic
774C22C7×#53311yescharacteristic
775C22C7×#54011yescharacteristic
776C22C7×#54111yescharacteristic
777C22C7×#54211yescharacteristic
778C22C7×#54211yescharacteristic
779C22C7×D4211yescharacteristic
780C22C7×D4211yescharacteristic
781C22C7×#54611yescharacteristic
782C22C7×#54711yescharacteristic
783C22C7×#54711yescharacteristic
784C22C7×#54711yescharacteristic
785C22C7×#54811yescharacteristic
786C22C7×D4×Q811yescharacteristic
787C22C7×D4×Q811yescharacteristic
788C22C7×#55011yescharacteristic
789C22C7×#55211yescharacteristic
790C22C7×#55311yescharacteristic
791C22C7×#55411yescharacteristic
792C22C7×#55411yescharacteristic
793C22C7×#55511yescharacteristic
794C22C7×#55611yescharacteristic
795C4—24no—
796C4—24no—
797C4—24no—
798C4—44no—
799C4—44no—
800C4—42no—
801C4—42no—
802C4—82no—
803C4—82no—
804C4C7×#38818yescomplemented
805C2—44no—
806C2C7×#228511yescharacteristic
807C2C2×C7×#38811yescharacteristic
808C2C7×#231411yescharacteristic
809C2C7×D4×C4⋊C411yescharacteristic
810C2C7×D4×C4⋊C411yescharacteristic
811C2C7×#235211yescharacteristic
812C2C7×#235411yescharacteristic
813C2C7×#242211yescharacteristic
814C2C7×#242311yescharacteristic
815C2C7×#242811yescharacteristic
816C2C7×#242911yescharacteristic
817C2C7×#249111yescharacteristic
818C2C7×#249211yescharacteristic
819C2C7×#249611yescharacteristic
820C2C7×#249711yescharacteristic
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×#384C2semidirect
5. C2×C4×C7×C4⋊C4C2semidirect
7. C7×#1442C2semidirect
9. C7×#1436C2semidirect
10. C7×C4⋊#95C2semidirect
11. C7×C4⋊#95C2semidirect
31. C4×C7×C22⋊C4C4semidirect
41. #13876C7direct (N × H)
109. C2×#384C2×C7semidirect
112. C2×C4×C4⋊C4C2×C7semidirect
114. #1442C2×C7semidirect
116. #1436C2×C7semidirect
117. C4⋊#95C2×C7semidirect
118. C4⋊#95C2×C7semidirect
221. C7×C22⋊C4C4⋊C4semidirect
244. C4×C22⋊C4C4×C7semidirect
500. C4×C7#388semidirect
603. C22⋊C4C7×C4⋊C4semidirect
744. C7#13876direct (N × H)
804. C4C7×#388semidirect

Maximal subgroups

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

subgroupindex
C2×C7×#3882
C2×C7×#3842
C2×C7×#3802
C2×C4×C7×C4⋊C42
C2×C4×C7×C22⋊C42
C7×#14422
C7×#14392
C7×#14362
C7×C4⋊#952
#138767