Finite Group Databasebeta

← C7×#22526 #13199742

Subgroups — C7×#22526 #13199742

Order 1792.

1066 conjugacy classes of subgroups.

The subgroup lattice has 646 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C7×#554C211yesmaximal, characteristic
2C2×C7×#446C211yesmaximal, characteristic, complemented
3C7×#2355C211yesmaximal, characteristic, complemented
4C7×#1993C211yesmaximal, characteristic, complemented
5C7×#1992C211yesmaximal, characteristic, complemented
6C7×#1991C211yesmaximal, characteristic, complemented
7C7×#1989C211yesmaximal, characteristic, complemented
8C7×#1989C211yesmaximal, characteristic, complemented
9C7×#1988C211yesmaximal, characteristic, complemented
10C7×#1804C211yesmaximal, characteristic
11C7×#1804C211yesmaximal, characteristic
12C7×#1802C211yesmaximal, characteristic
13C7×#1762C211yesmaximal, characteristic
14C7×#1762C211yesmaximal, characteristic
15C4×C7×#102C211yesmaximal, characteristic
16C7×#554—24no—
17C7×#554C418yescomplemented
18C2×C7×C4⋊Q8C2211yescharacteristic
19C2×C7×#125C2211yescharacteristic
20C2×C7×#125C2211yescharacteristic
21C2×C7×C22⋊Q8—21no—
22C2×C7×C22⋊Q8—21no—
23C2×C7×C22⋊Q8—21no—
24C2×C4×C7×Q8C2211yescharacteristic
25C2×C4×C7×D4C2211yescharacteristic
26C2×C4×C7×D4C2211yescharacteristic
27C2×C4×C7×D4C2211yescharacteristic
28C22×C7×C4⋊C4—21no—
29C7×#446—24no—
30C2×C7×C4⋊C8C2211yescharacteristic
31C2×C7×C4⋊C8C2211yescharacteristic
32C2×C7×C4⋊C8C2211yescharacteristic
33C2×C7×#102C2211yescharacteristic
34C2×C7×#102C2211yescharacteristic
35C2×C7×#102C2211yescharacteristic
36C2×C7×#102C2211yescharacteristic
37C2×C7×#97C2211yescharacteristic
38C2×C7×#97C2211yescharacteristic
39C2×C4×C7×C8C2211yescharacteristic
40C7×#391—21no—
41C7×#387—21no—
42C7×#387—21no—
43C7×#384C2211yescharacteristic
44C7×#382C2211yescharacteristic
45C7×#382C2211yescharacteristic
46C4×C7×C4⋊C4—21no—
47C4×C7×C4⋊C4C2211yescharacteristic
48C4×C7×C4⋊C4C2211yescharacteristic
49C4×C7×C4⋊C4C2211yescharacteristic
50C7×#340C2211yescharacteristic
51C7×#340C2211yescharacteristic
52C7×#340C2211yescharacteristic
53C7×#340C2211yescharacteristic
54C7×#340C2211yescharacteristic
55C7×#340C2211yescharacteristic
56C7×#340C2211yescharacteristic
57C7×#340C2211yescharacteristic
58C7×#340C2211yescharacteristic
59C7×#340C2211yescharacteristic
60C7×#340C2211yescharacteristic
61C7×#340C2211yescharacteristic
62#22526C711yesmaximal, characteristic, direct product factor, Sylow
63C22×C7×Q8—21no—
64C22×C7×Q8D411yescharacteristic
65C22×C7×D4C2311yescharacteristic
66C23×C4×C7—21no—
67C23×C4×C7—21no—
68C23×C4×C7—21no—
69C22×C7×C8C2311yescharacteristic
70C22×C7×C8C2311yescharacteristic
71C22×C7×C8C2311yescharacteristic
72C22×C7×C8C2311yescharacteristic
73C7×C4⋊Q8—22no—
74C7×C4⋊Q8C2×C414yes—
75C7×#125—22no—
76C7×#125—22no—
77C7×#125C2×C414yes—
78C7×#125C2×C414yes—
79C7×C22⋊Q8—28no—
80C7×C22⋊Q8—28no—
81C7×C22⋊Q8—28no—
82C4×C7×Q8C2×C414yes—
83C4×C7×Q8D414yes—
84C4×C7×D4—22no—
85C4×C7×D4—22no—
86C4×C7×D4—22no—
87C4×C7×D4C2×C414yes—
88C4×C7×D4C2×C414yes—
89C4×C7×D4C2×C414yes—
90C2×C7×C4⋊C4—21no—
91C2×C7×C4⋊C4—21no—
92C2×C7×C4⋊C4—21no—
93C2×C7×C4⋊C4—21no—
94C2×C7×C4⋊C4—21no—
95C2×C7×C4⋊C4—28no—
96C2×C7×C4⋊C4—21no—
97C2×C7×C4⋊C4—21no—
98C2×C7×C4⋊C4D411yescharacteristic
99C2×C7×C4⋊C4D411yescharacteristic
100C2×C7×C4⋊C4D411yescharacteristic
101C2×C7×C4⋊C4C2311yescharacteristic
102C2×C7×C4⋊C4C2311yescharacteristic
103C2×C7×C4⋊C4C2311yescharacteristic
104C2×C7×C4⋊C4C2311yescharacteristic
105C2×C7×C4⋊C4C2311yescharacteristic
106C2×C7×C4⋊C4C2311yescharacteristic
107C2×C7×C4⋊C4C2311yescharacteristic
108C2×C7×C22⋊C4—21no—
109C2×C7×C22⋊C4—21no—
110C2×C7×C22⋊C4—21no—
111C2×C42×C7—21no—
112C2×C42×C7—21no—
113C2×C42×C7—21no—
114C2×C42×C7C2311yescharacteristic
115C2×C42×C7C2311yescharacteristic
116C2×C42×C7C2311yescharacteristic
117C7×C4⋊C8—22no—
118C7×C4⋊C8—22no—
119C7×C4⋊C8—22no—
120C7×#102—22no—
121C7×#102—22no—
122C7×#102—22no—
123C7×#102Q814yescomplemented
124C7×#97—22no—
125C7×#97—22no—
126C4×C7×C8—22no—
127C7×#95—21no—
128C7×#95—21no—
129C7×#95—21no—
130C7×#95—21no—
131C7×#95—21no—
132C7×#95—21no—
133C7×#95—21no—
134C2×#554C2×C711yescharacteristic
135C2×#446C2×C711yescharacteristic, complemented
136#2355C2×C711yescharacteristic, complemented
137#1993C2×C711yescharacteristic, complemented
138#1992C2×C711yescharacteristic, complemented
139#1991C2×C711yescharacteristic, complemented
140#1989C2×C711yescharacteristic, complemented
141#1989C2×C711yescharacteristic, complemented
142#1988C2×C711yescharacteristic, complemented
143#1804C2×C711yescharacteristic
144#1804C2×C711yescharacteristic
145#1802C2×C711yescharacteristic
146#1762C2×C711yescharacteristic
147#1762C2×C711yescharacteristic
148C4×#102C2×C711yescharacteristic
149C24×C7—21no—
150C2×C7×Q8—24no—
151C2×C7×Q8—41no—
152C2×C7×Q8—41no—
153C2×C7×Q8—81no—
154C2×C7×Q8—81no—
155C2×C7×Q8C22⋊C414yes—
156C2×C7×D4—21no—
157C2×C7×D4—21no—
158C2×C7×D4—21no—
159C2×C7×D4C22×C412yes—
160C2×C7×D4C2×Q812yes—
161C2×C7×D4#4112yes—
162C22×C4×C7—21no—
163C22×C4×C7—21no—
164C22×C4×C7—21no—
165C22×C4×C7—21no—
166C22×C4×C7—24no—
167C22×C4×C7—24no—
168C22×C4×C7—24no—
169C22×C4×C7—21no—
170C22×C4×C7—21no—
171C22×C4×C7—21no—
172C22×C4×C7—42no—
173C22×C4×C7—42no—
174C22×C4×C7—81no—
175C22×C4×C7—81no—
176C22×C4×C7—81no—
177C22×C4×C7—81no—
178C22×C4×C7C2×D411yescharacteristic
179C22×C4×C7C2×D411yescharacteristic
180C22×C4×C7C2×D411yescharacteristic
181C22×C4×C7C2×D411yescharacteristic
182C22×C4×C7C2×D411yescharacteristic
183C22×C4×C7C2×D411yescharacteristic
184C22×C4×C7C2411yescharacteristic
185C2×C7×C8—21no—
186C2×C7×C8—21no—
187C2×C7×C8—21no—
188C2×C7×C8—21no—
189C2×C7×C8—21no—
190C2×C7×C8—21no—
191C2×C7×C8—21no—
192C2×C7×C8—21no—
193C2×C7×C8—21no—
194C2×C7×C8—21no—
195C2×C7×C8—21no—
196C2×C7×C8C2×Q812yes—
197C7×C4⋊C4—24no—
198C7×C4⋊C4—24no—
199C7×C4⋊C4—24no—
200C7×C4⋊C4—24no—
201C7×C4⋊C4—24no—
202C7×C4⋊C4—21no—
203C7×C4⋊C4—21no—
204C7×C4⋊C4—21no—
205C7×C4⋊C4—21no—
206C7×C4⋊C4—21no—
207C7×C4⋊C4—21no—
208C7×C4⋊C4—21no—
209C7×C4⋊C4—21no—
210C7×C4⋊C4—21no—
211C7×C4⋊C4—21no—
212C7×C4⋊C4—42no—
213C7×C4⋊C4—81no—
214C7×C4⋊C4C22⋊C414yes—
215C7×C4⋊C4C22⋊C414yes—
216C7×C4⋊C4C22⋊C414yes—
217C7×C4⋊C4C22×C412yes—
218C7×C4⋊C4C22×C412yes—
219C7×C4⋊C4C22×C412yes—
220C7×C4⋊C4C2×Q812yes—
221C7×C22⋊C4—24no—
222C7×C22⋊C4—24no—
223C7×C22⋊C4—24no—
224C42×C7—42no—
225C42×C7—81no—
226C42×C7—81no—
227C42×C7C22×C412yes—
228C42×C7C22×C412yes—
229C42×C7C22×C412yes—
230C42×C7C2×D412yes—
231C42×C7C2×D412yes—
232C42×C7C2×D412yes—
233#554—24no—
234#554C4×C718yescomplemented
235C2×C4⋊Q8C22×C711yescharacteristic
236C2×#125C22×C711yescharacteristic
237C2×#125C22×C711yescharacteristic
238C2×C22⋊Q8—21no—
239C2×C22⋊Q8—21no—
240C2×C22⋊Q8—21no—
241C2×C4×Q8C22×C711yescharacteristic
242C2×C4×D4C22×C711yescharacteristic
243C2×C4×D4C22×C711yescharacteristic
244C2×C4×D4C22×C711yescharacteristic
245C22×C4⋊C4—21no—
246#446—24no—
247C2×C4⋊C8C22×C711yescharacteristic
248C2×C4⋊C8C22×C711yescharacteristic
249C2×C4⋊C8C22×C711yescharacteristic
250C2×#102C22×C711yescharacteristic
251C2×#102C22×C711yescharacteristic
252C2×#102C22×C711yescharacteristic
253C2×#102C22×C711yescharacteristic
254C2×#97C22×C711yescharacteristic
255C2×#97C22×C711yescharacteristic
256C2×C4×C8C22×C711yescharacteristic
257#391—21no—
258#387—21no—
259#387—21no—
260#384C22×C711yescharacteristic
261#382C22×C711yescharacteristic
262#382C22×C711yescharacteristic
263C4×C4⋊C4—21no—
264C4×C4⋊C4C22×C711yescharacteristic
265C4×C4⋊C4C22×C711yescharacteristic
266C4×C4⋊C4C22×C711yescharacteristic
267#340C22×C711yescharacteristic
268#340C22×C711yescharacteristic
269#340C22×C711yescharacteristic
270#340C22×C711yescharacteristic
271#340C22×C711yescharacteristic
272#340C22×C711yescharacteristic
273#340C22×C711yescharacteristic
274#340C22×C711yescharacteristic
275#340C22×C711yescharacteristic
276#340C22×C711yescharacteristic
277#340C22×C711yescharacteristic
278#340C22×C711yescharacteristic
279C23×C7—22no—
280C23×C7—22no—
281C23×C7—22no—
282C23×C7—41no—
283C23×C7—41no—
284C23×C7—41no—
285C23×C7—41no—
286C23×C7C22×D411yescharacteristic
287C7×Q8—44no—
288C7×Q8—84no—
289C7×D4—22no—
290C7×D4—22no—
291C7×D4—22no—
292C7×D4C4×Q814yes—
293C2×C4×C7—21no—
294C2×C4×C7—21no—
295C2×C4×C7—21no—
296C2×C4×C7—21no—
297C2×C4×C7—21no—
298C2×C4×C7—21no—
299C2×C4×C7—21no—
300C2×C4×C7—21no—
301C2×C4×C7—21no—
302C2×C4×C7—21no—
303C2×C4×C7—21no—
304C2×C4×C7—21no—
305C2×C4×C7—22no—
306C2×C4×C7—22no—
307C2×C4×C7—22no—
308C2×C4×C7—22no—
309C2×C4×C7—48no—
310C2×C4×C7—41no—
311C2×C4×C7—41no—
312C2×C4×C7—41no—
313C2×C4×C7—41no—
314C2×C4×C7—41no—
315C2×C4×C7—41no—
316C2×C4×C7—41no—
317C2×C4×C7—41no—
318C2×C4×C7—41no—
319C2×C4×C7—41no—
320C2×C4×C7—41no—
321C2×C4×C7—41no—
322C2×C4×C7—41no—
323C2×C4×C7—41no—
324C2×C4×C7—41no—
325C2×C4×C7—41no—
326C2×C4×C7—41no—
327C2×C4×C7—84no—
328C2×C4×C7—84no—
329C2×C4×C7C2×C22⋊C412yes—
330C2×C4×C7C2×C22⋊C412yes—
331C2×C4×C7C2×C22⋊C412yes—
332C2×C4×C7C2×C22⋊C412yes—
333C2×C4×C7C2×C22⋊C412yes—
334C2×C4×C7C2×C22⋊C412yes—
335C2×C4×C7C23×C411yescharacteristic
336C2×C4×C7C22×D411yescharacteristic
337C2×C4×C7C22×Q811yescharacteristic
338C2×C4×C7C2×#4111yescharacteristic
339C2×C4×C72−1+411yescharacteristic
340C2×C4×C72−1+411yescharacteristic
341C7×C8—22no—
342C7×C8—41no—
343C7×C8—41no—
344C7×C8—41no—
345C22×Q8—21no—
346C22×Q8C7×D411yescharacteristic
347C22×D4C23×C711yescharacteristic
348C23×C4—21no—
349C23×C4—21no—
350C23×C4—21no—
351C22×C8C23×C711yescharacteristic
352C22×C8C23×C711yescharacteristic
353C22×C8C23×C711yescharacteristic
354C22×C8C23×C711yescharacteristic
355C4⋊Q8—22no—
356C4⋊Q8C2×C4×C714yes—
357#125—22no—
358#125—22no—
359#125C2×C4×C714yes—
360#125C2×C4×C714yes—
361C22⋊Q8—28no—
362C22⋊Q8—28no—
363C22⋊Q8—28no—
364C4×Q8C2×C4×C714yes—
365C4×Q8C7×D414yes—
366C4×D4—22no—
367C4×D4—22no—
368C4×D4—22no—
369C4×D4C2×C4×C714yes—
370C4×D4C2×C4×C714yes—
371C4×D4C2×C4×C714yes—
372C2×C4⋊C4—21no—
373C2×C4⋊C4—21no—
374C2×C4⋊C4—21no—
375C2×C4⋊C4—21no—
376C2×C4⋊C4—21no—
377C2×C4⋊C4—28no—
378C2×C4⋊C4—21no—
379C2×C4⋊C4—21no—
380C2×C4⋊C4C7×D411yescharacteristic
381C2×C4⋊C4C7×D411yescharacteristic
382C2×C4⋊C4C7×D411yescharacteristic
383C2×C4⋊C4C23×C711yescharacteristic
384C2×C4⋊C4C23×C711yescharacteristic
385C2×C4⋊C4C23×C711yescharacteristic
386C2×C4⋊C4C23×C711yescharacteristic
387C2×C4⋊C4C23×C711yescharacteristic
388C2×C4⋊C4C23×C711yescharacteristic
389C2×C4⋊C4C23×C711yescharacteristic
390C2×C22⋊C4—21no—
391C2×C22⋊C4—21no—
392C2×C22⋊C4—21no—
393C2×C42—21no—
394C2×C42—21no—
395C2×C42—21no—
396C2×C42C23×C711yescharacteristic
397C2×C42C23×C711yescharacteristic
398C2×C42C23×C711yescharacteristic
399C4⋊C8—22no—
400C4⋊C8—22no—
401C4⋊C8—22no—
402#102—22no—
403#102—22no—
404#102—22no—
405#102C7×Q814yescomplemented
406#97—22no—
407#97—22no—
408C4×C8—22no—
409#95—21no—
410#95—21no—
411#95—21no—
412#95—21no—
413#95—21no—
414#95—21no—
415#95—21no—
416C22×C7—24no—
417C22×C7—42no—
418C22×C7—42no—
419C22×C7—42no—
420C22×C7—42no—
421C22×C7—42no—
422C22×C7—42no—
423C22×C7C22×C22⋊C411yescharacteristic
424C22×C7#54811yescharacteristic
425C22×C7D4×Q811yescharacteristic
426C22×C7#57511yescharacteristic
427C22×C7#57511yescharacteristic
428C22×C7#57611yescharacteristic
429C22×C7#57711yescharacteristic
430C4×C7—22no—
431C4×C7—22no—
432C4×C7—22no—
433C4×C7—22no—
434C4×C7—22no—
435C4×C7—22no—
436C4×C7—42no—
437C4×C7—42no—
438C4×C7—42no—
439C4×C7—42no—
440C4×C7—81no—
441C4×C7—81no—
442C4×C7—81no—
443C4×C7C2×C4×Q811yescharacteristic
444C4×C7#51911yescharacteristic
445C4×C7#54811yescharacteristic
446C4×C7D4×Q811yescharacteristic
447C24—21no—
448C2×Q8—24no—
449C2×Q8—41no—
450C2×Q8—41no—
451C2×Q8—81no—
452C2×Q8—81no—
453C2×Q8C7×C22⋊C414yes—
454C2×D4—21no—
455C2×D4—21no—
456C2×D4—21no—
457C2×D4C22×C4×C712yes—
458C2×D4C2×C7×Q812yes—
459C2×D4C7×#4112yes—
460C22×C4—21no—
461C22×C4—21no—
462C22×C4—21no—
463C22×C4—21no—
464C22×C4—24no—
465C22×C4—24no—
466C22×C4—24no—
467C22×C4—21no—
468C22×C4—21no—
469C22×C4—21no—
470C22×C4—42no—
471C22×C4—42no—
472C22×C4—81no—
473C22×C4—81no—
474C22×C4—81no—
475C22×C4—81no—
476C22×C4C2×C7×D411yescharacteristic
477C22×C4C2×C7×D411yescharacteristic
478C22×C4C2×C7×D411yescharacteristic
479C22×C4C2×C7×D411yescharacteristic
480C22×C4C2×C7×D411yescharacteristic
481C22×C4C2×C7×D411yescharacteristic
482C22×C4C24×C711yescharacteristic
483C2×C8—21no—
484C2×C8—21no—
485C2×C8—21no—
486C2×C8—21no—
487C2×C8—21no—
488C2×C8—21no—
489C2×C8—21no—
490C2×C8—21no—
491C2×C8—21no—
492C2×C8—21no—
493C2×C8—21no—
494C2×C8C2×C7×Q812yes—
495C4⋊C4—24no—
496C4⋊C4—24no—
497C4⋊C4—24no—
498C4⋊C4—24no—
499C4⋊C4—24no—
500C4⋊C4—21no—
501C4⋊C4—21no—
502C4⋊C4—21no—
503C4⋊C4—21no—
504C4⋊C4—21no—
505C4⋊C4—21no—
506C4⋊C4—21no—
507C4⋊C4—21no—
508C4⋊C4—21no—
509C4⋊C4—21no—
510C4⋊C4—42no—
511C4⋊C4—81no—
512C4⋊C4C7×C22⋊C414yes—
513C4⋊C4C7×C22⋊C414yes—
514C4⋊C4C7×C22⋊C414yes—
515C4⋊C4C22×C4×C712yes—
516C4⋊C4C22×C4×C712yes—
517C4⋊C4C22×C4×C712yes—
518C4⋊C4C2×C7×Q812yes—
519C22⋊C4—24no—
520C22⋊C4—24no—
521C22⋊C4—24no—
522C42—42no—
523C42—81no—
524C42—81no—
525C42C22×C4×C712yes—
526C42C22×C4×C712yes—
527C42C22×C4×C712yes—
528C42C2×C7×D412yes—
529C42C2×C7×D412yes—
530C42C2×C7×D412yes—
531C2×C7—44no—
532C2×C7Q8×C22⋊C411yescharacteristic
533C2×C7#289611yescharacteristic
534C2×C7#289711yescharacteristic
535C2×C7#337011yescharacteristic
536C2×C7#337611yescharacteristic
537C2×C7#338811yescharacteristic
538C2×C7#338911yescharacteristic
539C23—22no—
540C23—22no—
541C23—22no—
542C23—41no—
543C23—41no—
544C23—41no—
545C23—41no—
546C23C22×C7×D411yescharacteristic
547Q8—44no—
548Q8—84no—
549D4—22no—
550D4—22no—
551D4—22no—
552D4C4×C7×Q814yes—
553C2×C4—21no—
554C2×C4—21no—
555C2×C4—21no—
556C2×C4—21no—
557C2×C4—21no—
558C2×C4—21no—
559C2×C4—21no—
560C2×C4—21no—
561C2×C4—21no—
562C2×C4—21no—
563C2×C4—21no—
564C2×C4—21no—
565C2×C4—22no—
566C2×C4—22no—
567C2×C4—22no—
568C2×C4—22no—
569C2×C4—48no—
570C2×C4—41no—
571C2×C4—41no—
572C2×C4—41no—
573C2×C4—41no—
574C2×C4—41no—
575C2×C4—41no—
576C2×C4—41no—
577C2×C4—41no—
578C2×C4—41no—
579C2×C4—41no—
580C2×C4—41no—
581C2×C4—41no—
582C2×C4—41no—
583C2×C4—41no—
584C2×C4—41no—
585C2×C4—41no—
586C2×C4—41no—
587C2×C4—84no—
588C2×C4—84no—
589C2×C4C2×C7×C22⋊C412yes—
590C2×C4C2×C7×C22⋊C412yes—
591C2×C4C2×C7×C22⋊C412yes—
592C2×C4C2×C7×C22⋊C412yes—
593C2×C4C2×C7×C22⋊C412yes—
594C2×C4C2×C7×C22⋊C412yes—
595C2×C4C23×C4×C711yescharacteristic
596C2×C4C22×C7×D411yescharacteristic
597C2×C4C22×C7×Q811yescharacteristic
598C2×C4C2×C7×#4111yescharacteristic
599C2×C4C7×2−1+411yescharacteristic
600C2×C4C7×2−1+411yescharacteristic
601C8—22no—
602C8—41no—
603C8—41no—
604C8—41no—
605C7#2252611yescharacteristic, direct product factor, Sylow
606C22—24no—
607C22—42no—
608C22—42no—
609C22—42no—
610C22—42no—
611C22—42no—
612C22—42no—
613C22C22×C7×C22⋊C411yescharacteristic
614C22C7×#54811yescharacteristic
615C22C7×D4×Q811yescharacteristic
616C22C7×#57511yescharacteristic
617C22C7×#57511yescharacteristic
618C22C7×#57611yescharacteristic
619C22C7×#57711yescharacteristic
620C4—22no—
621C4—22no—
622C4—22no—
623C4—22no—
624C4—22no—
625C4—22no—
626C4—42no—
627C4—42no—
628C4—42no—
629C4—42no—
630C4—81no—
631C4—81no—
632C4—81no—
633C4C2×C4×C7×Q811yescharacteristic
634C4C7×#51911yescharacteristic
635C4C7×#54811yescharacteristic
636C4C7×D4×Q811yescharacteristic
637C2—44no—
638C2C7×Q8×C22⋊C411yescharacteristic
639C2C7×#289611yescharacteristic
640C2C7×#289711yescharacteristic
641C2C7×#337011yescharacteristic
642C2C7×#337611yescharacteristic
643C2C7×#338811yescharacteristic
644C2C7×#338911yescharacteristic
subgroupG/H
center, socleC23×C7C22×D4
commutatorC2×C4C23×C4×C7
Frattini, cosocleC22×C4C24×C7
prime radicalC22×C7×D4C23
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C7 ◁ C2×C4×C7×Q8 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C7×#446C2semidirect
3. C7×#2355C2semidirect
4. C7×#1993C2semidirect
5. C7×#1992C2semidirect
6. C7×#1991C2semidirect
7. C7×#1989C2semidirect
8. C7×#1989C2semidirect
9. C7×#1988C2semidirect
17. C7×#554C4semidirect
62. #22526C7direct (N × H)
123. C7×#102Q8semidirect
135. C2×#446C2×C7semidirect
136. #2355C2×C7semidirect
137. #1993C2×C7semidirect
138. #1992C2×C7semidirect
139. #1991C2×C7semidirect
140. #1989C2×C7semidirect
141. #1989C2×C7semidirect
142. #1988C2×C7semidirect
234. #554C4×C7semidirect
405. #102C7×Q8semidirect
605. C7#22526direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C7×#5542
C2×C7×#4462
C7×#23552
C7×#19932
C7×#19922
C7×#19912
C7×#19892
C7×#19882
C7×#18042
C7×#18022
C7×#17622
C4×C7×#1022
#225267