Finite Group Databasebeta

← C7×#21420 #13198636

Subgroups — C7×#21420 #13198636

Order 1792.

1678 conjugacy classes of subgroups.

The subgroup lattice has 798 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C7×#525C211yesmaximal, characteristic
2C7×#2280C211yesmaximal, characteristic, complemented
3C2×C4×C7×C22⋊C4C211yesmaximal, characteristic, complemented
4C7×#1996C212yesmaximal, complemented
5C7×#1964C212yesmaximal, complemented
6C7×#1898C214yesmaximal, complemented
7C4×C7×#99C214yesmaximal, complemented
8C22×C7×#41C411yescharacteristic, complemented
9C24×C4×C7C2211yescharacteristic
10C7×#525—21no—
11C7×#525—21no—
12C7×#525—21no—
13C7×#525—21no—
14C7×#525—21no—
15C7×#525—21no—
16C7×#525—21no—
17C7×#525—21no—
18C2×C7×#123C412yescomplemented
19C2×C7×C22⋊Q8C411yescharacteristic, complemented
20C2×C7×C22⋊Q8C2211yescharacteristic
21C2×C7×#121C411yescharacteristic, complemented
22C2×C7×#121C2211yescharacteristic
23C2×C7×#120C2212yes—
24C2×C4×C7×D4C412yescomplemented
25C2×C4×C7×D4C2212yes—
26C2×C7×#117—21no—
27C2×C7×#117C411yescharacteristic, complemented
28C22×C7×C22⋊C4C2212yes—
29C22×C42×C7—21no—
30C2×C7×#99C2218yes—
31C7×#381—21no—
32C7×#380—21no—
33C7×#380C2212yes—
34C7×#379C2212yes—
35C4×C7×C22⋊C4—21no—
36C4×C7×C22⋊C4—21no—
37C4×C7×C22⋊C4—21no—
38C4×C7×C22⋊C4C2212yes—
39C4×C7×C22⋊C4C2212yes—
40C4×C7×C22⋊C4C2212yes—
41C2×C7×#95—21no—
42C7×#342C2218yes—
43#21420C711yesmaximal, characteristic, direct product factor, Sylow
44C25×C7C2311yescharacteristic
45C2×C7×#41—21no—
46C2×C7×#41—21no—
47C2×C7×#41—21no—
48C2×C7×#41—21no—
49C2×C7×#41—44no—
50C22×C7×Q8C2×C411yescharacteristic, complemented
51C22×C7×D4C2×C412yes—
52C22×C7×D4C2×C412yes—
53C22×C7×D4C2×C411yescharacteristic, complemented
54C22×C7×D4C2312yes—
55C23×C4×C7—22no—
56C23×C4×C7—44no—
57C23×C4×C7C2×C411yescharacteristic
58C23×C4×C7C2×C411yescharacteristic
59C23×C4×C7C2×C411yescharacteristic
60C23×C4×C7C2×C411yescharacteristic
61C23×C4×C7C2×C412yescomplemented
62C23×C4×C7D411yescharacteristic
63C23×C4×C7D411yescharacteristic
64C23×C4×C7D411yescharacteristic
65C23×C4×C7D411yescharacteristic
66C23×C4×C7D411yescharacteristic
67C23×C4×C7D411yescharacteristic
68C23×C4×C7D411yescharacteristic
69C23×C4×C7D411yescharacteristic
70C23×C4×C7C2311yescharacteristic
71C23×C4×C7C2311yescharacteristic
72C7×#123—22no—
73C7×#123—22no—
74C7×#123—22no—
75C7×#123—22no—
76C7×C22⋊Q8—21no—
77C7×C22⋊Q8—21no—
78C7×C22⋊Q8—21no—
79C7×C22⋊Q8—21no—
80C7×C22⋊Q8—21no—
81C7×C22⋊Q8—21no—
82C7×C22⋊Q8—21no—
83C7×C22⋊Q8—21no—
84C7×#121—21no—
85C7×#121—21no—
86C7×#121—21no—
87C7×#121—21no—
88C7×#121—21no—
89C7×#121—21no—
90C7×#121—21no—
91C7×#121—21no—
92C7×#120—22no—
93C7×#120—22no—
94C7×#120—22no—
95C7×#120—22no—
96C4×C7×D4—22no—
97C4×C7×D4—22no—
98C4×C7×D4—22no—
99C4×C7×D4—22no—
100C4×C7×D4—22no—
101C4×C7×D4—22no—
102C4×C7×D4—22no—
103C4×C7×D4—22no—
104C7×#117—21no—
105C7×#117—21no—
106C7×#117—21no—
107C7×#117—21no—
108C7×#117—44no—
109C2×C7×C4⋊C4—22no—
110C2×C7×C4⋊C4C2×C411yescharacteristic, complemented
111C2×C7×C4⋊C4C2×C411yescharacteristic, complemented
112C2×C7×C4⋊C4C2×C412yescomplemented
113C2×C7×C4⋊C4C2×C412yescomplemented
114C2×C7×C22⋊C4—22no—
115C2×C7×C22⋊C4—28no—
116C2×C7×C22⋊C4—22no—
117C2×C7×C22⋊C4—22no—
118C2×C7×C22⋊C4C2×C412yes—
119C2×C7×C22⋊C4C2×C412yes—
120C2×C7×C22⋊C4C2×C412yescomplemented
121C2×C7×C22⋊C4C2×C412yescomplemented
122C2×C7×C22⋊C4C2314yes—
123C2×C7×C22⋊C4C2312yes—
124C2×C7×C22⋊C4C2314yes—
125C2×C42×C7—22no—
126C2×C42×C7—22no—
127C2×C42×C7—22no—
128C2×C42×C7—44no—
129C2×C42×C7C2×C412yescomplemented
130C7×#99—216no—
131C7×#95—22no—
132C7×#95—22no—
133C7×#95—22no—
134C7×#95—22no—
135C2×#525C2×C711yescharacteristic
136#2280C2×C711yescharacteristic, complemented
137C2×C4×C22⋊C4C2×C711yescharacteristic, complemented
138#1996C2×C712yescomplemented
139#1964C2×C712yescomplemented
140#1898C2×C714yescomplemented
141C4×#99C2×C714yescomplemented
142C24×C7—24no—
143C24×C7—42no—
144C24×C7—42no—
145C24×C7C22×C411yescharacteristic
146C24×C7C22×C411yescharacteristic
147C24×C7C22×C412yes—
148C24×C7C2×D411yescharacteristic
149C24×C7C2×D411yescharacteristic
150C24×C7C2×D411yescharacteristic
151C24×C7C2×D411yescharacteristic
152C24×C7C2411yescharacteristic
153C7×#41—44no—
154C7×#41—44no—
155C7×#41—44no—
156C7×#41—44no—
157C2×C7×Q8—21no—
158C2×C7×Q8—21no—
159C2×C7×Q8—42no—
160C2×C7×D4—22no—
161C2×C7×D4—22no—
162C2×C7×D4—22no—
163C2×C7×D4—22no—
164C2×C7×D4—22no—
165C2×C7×D4—22no—
166C2×C7×D4—28no—
167C2×C7×D4—21no—
168C2×C7×D4—21no—
169C2×C7×D4—42no—
170C2×C7×D4—44no—
171C2×C7×D4—44no—
172C22×C4×C7—24no—
173C22×C4×C7—24no—
174C22×C4×C7—24no—
175C22×C4×C7—28no—
176C22×C4×C7—24no—
177C22×C4×C7—22no—
178C22×C4×C7—22no—
179C22×C4×C7—24no—
180C22×C4×C7—42no—
181C22×C4×C7—42no—
182C22×C4×C7—42no—
183C22×C4×C7—42no—
184C22×C4×C7—42no—
185C22×C4×C7—42no—
186C22×C4×C7—42no—
187C22×C4×C7—42no—
188C22×C4×C7—42no—
189C22×C4×C7—42no—
190C22×C4×C7—42no—
191C22×C4×C7—44no—
192C22×C4×C7—44no—
193C22×C4×C7—44no—
194C22×C4×C7C22⋊C411yescharacteristic
195C22×C4×C7C22⋊C411yescharacteristic
196C22×C4×C7C22⋊C411yescharacteristic
197C22×C4×C7C22⋊C411yescharacteristic
198C22×C4×C7C22⋊C411yescharacteristic
199C22×C4×C7C22⋊C411yescharacteristic
200C22×C4×C7C22⋊C411yescharacteristic
201C22×C4×C7C22⋊C411yescharacteristic
202C22×C4×C7C22⋊C411yescharacteristic
203C22×C4×C7C22⋊C411yescharacteristic
204C22×C4×C7C22⋊C411yescharacteristic
205C22×C4×C7C22⋊C411yescharacteristic
206C22×C4×C7C22⋊C411yescharacteristic
207C22×C4×C7C22⋊C411yescharacteristic
208C22×C4×C7C22⋊C411yescharacteristic
209C22×C4×C7C22⋊C411yescharacteristic
210C22×C4×C7C22×C412yes—
211C22×C4×C7C22×C411yescharacteristic
212C22×C4×C7C22×C411yescharacteristic
213C22×C4×C7C22×C412yes—
214C22×C4×C7C22×C412yes—
215C22×C4×C7C22×C411yescharacteristic
216C22×C4×C7C22×C411yescharacteristic
217C22×C4×C7C2×D411yescharacteristic
218C22×C4×C7C2×D411yescharacteristic
219C22×C4×C7C2×D411yescharacteristic
220C22×C4×C7C2×D411yescharacteristic
221C22×C4×C7C2×D411yescharacteristic
222C22×C4×C7C2×D411yescharacteristic
223C22×C4×C7C2×D411yescharacteristic
224C22×C4×C7C2×D411yescharacteristic
225C7×C4⋊C4—21no—
226C7×C4⋊C4—21no—
227C7×C4⋊C4—21no—
228C7×C4⋊C4—21no—
229C7×C4⋊C4—22no—
230C7×C4⋊C4—22no—
231C7×C4⋊C4—22no—
232C7×C4⋊C4—22no—
233C7×C4⋊C4—44no—
234C7×C22⋊C4—28no—
235C7×C22⋊C4—22no—
236C7×C22⋊C4—22no—
237C7×C22⋊C4—22no—
238C7×C22⋊C4—22no—
239C7×C22⋊C4—22no—
240C7×C22⋊C4—22no—
241C7×C22⋊C4—24no—
242C7×C22⋊C4—22no—
243C7×C22⋊C4—22no—
244C7×C22⋊C4—22no—
245C7×C22⋊C4—22no—
246C7×C22⋊C4—28no—
247C7×C22⋊C4—44no—
248C7×C22⋊C4—44no—
249C7×C22⋊C4#4118yescomplemented
250C42×C7—22no—
251C42×C7—22no—
252C42×C7—44no—
253C42×C7—44no—
254C42×C7—44no—
255C22×#41C4×C711yescharacteristic, complemented
256C24×C4C22×C711yescharacteristic
257#525—21no—
258#525—21no—
259#525—21no—
260#525—21no—
261#525—21no—
262#525—21no—
263#525—21no—
264#525—21no—
265C2×#123C4×C712yescomplemented
266C2×C22⋊Q8C4×C711yescharacteristic, complemented
267C2×C22⋊Q8C22×C711yescharacteristic
268C2×#121C4×C711yescharacteristic, complemented
269C2×#121C22×C711yescharacteristic
270C2×#120C22×C712yes—
271C2×C4×D4C4×C712yescomplemented
272C2×C4×D4C22×C712yes—
273C2×#117—21no—
274C2×#117C4×C711yescharacteristic, complemented
275C22×C22⋊C4C22×C712yes—
276C22×C42—21no—
277C2×#99C22×C718yes—
278#381—21no—
279#380—21no—
280#380C22×C712yes—
281#379C22×C712yes—
282C4×C22⋊C4—21no—
283C4×C22⋊C4—21no—
284C4×C22⋊C4—21no—
285C4×C22⋊C4C22×C712yes—
286C4×C22⋊C4C22×C712yes—
287C4×C22⋊C4C22×C712yes—
288C2×#95—21no—
289#342C22×C718yes—
290C23×C7—22no—
291C23×C7—22no—
292C23×C7—22no—
293C23×C7—22no—
294C23×C7—22no—
295C23×C7—22no—
296C23×C7—22no—
297C23×C7—22no—
298C23×C7—22no—
299C23×C7—22no—
300C23×C7—22no—
301C23×C7—22no—
302C23×C7—22no—
303C23×C7—24no—
304C23×C7—41no—
305C23×C7—41no—
306C23×C7—41no—
307C23×C7—41no—
308C23×C7—41no—
309C23×C7—41no—
310C23×C7—41no—
311C23×C7—41no—
312C23×C7—416no—
313C23×C7—42no—
314C23×C7—42no—
315C23×C7C2×C22⋊C411yescharacteristic
316C23×C7C2×C22⋊C411yescharacteristic
317C23×C7C2×C22⋊C411yescharacteristic
318C23×C7C2×C22⋊C411yescharacteristic
319C23×C7C23×C411yescharacteristic
320C23×C7C22×D411yescharacteristic
321C23×C7C22×D411yescharacteristic
322C23×C7C2×#4114yes—
323C7×Q8—42no—
324C7×Q8—42no—
325C7×D4—42no—
326C7×D4—44no—
327C7×D4—44no—
328C7×D4—44no—
329C7×D4—44no—
330C7×D4—44no—
331C7×D4—44no—
332C7×D4—42no—
333C2×C4×C7—22no—
334C2×C4×C7—22no—
335C2×C4×C7—22no—
336C2×C4×C7—22no—
337C2×C4×C7—22no—
338C2×C4×C7—22no—
339C2×C4×C7—22no—
340C2×C4×C7—22no—
341C2×C4×C7—22no—
342C2×C4×C7—22no—
343C2×C4×C7—22no—
344C2×C4×C7—22no—
345C2×C4×C7—22no—
346C2×C4×C7—22no—
347C2×C4×C7—22no—
348C2×C4×C7—22no—
349C2×C4×C7—22no—
350C2×C4×C7—22no—
351C2×C4×C7—24no—
352C2×C4×C7—28no—
353C2×C4×C7—41no—
354C2×C4×C7—41no—
355C2×C4×C7—41no—
356C2×C4×C7—41no—
357C2×C4×C7—41no—
358C2×C4×C7—41no—
359C2×C4×C7—41no—
360C2×C4×C7—41no—
361C2×C4×C7—41no—
362C2×C4×C7—41no—
363C2×C4×C7—41no—
364C2×C4×C7—41no—
365C2×C4×C7—44no—
366C2×C4×C7—44no—
367C2×C4×C7—416no—
368C2×C4×C7—44no—
369C2×C4×C7—44no—
370C2×C4×C7—42no—
371C2×C4×C7—42no—
372C2×C4×C7—44no—
373C2×C4×C7—44no—
374C2×C4×C7—44no—
375C2×C4×C7#9914yescomplemented
376C2×C4×C7C2×C22⋊C411yescharacteristic
377C2×C4×C7C2×C22⋊C411yescharacteristic
378C2×C4×C7C2×C22⋊C411yescharacteristic
379C2×C4×C7C2×C22⋊C411yescharacteristic
380C2×C4×C7C2×C22⋊C411yescharacteristic
381C2×C4×C7C2×C22⋊C411yescharacteristic
382C2×C4×C7C2×C22⋊C411yescharacteristic
383C2×C4×C7C2×C22⋊C411yescharacteristic
384C25C23×C711yescharacteristic
385C2×#41—21no—
386C2×#41—21no—
387C2×#41—21no—
388C2×#41—21no—
389C2×#41—44no—
390C22×Q8C2×C4×C711yescharacteristic, complemented
391C22×D4C2×C4×C712yes—
392C22×D4C2×C4×C712yes—
393C22×D4C2×C4×C711yescharacteristic, complemented
394C22×D4C23×C712yes—
395C23×C4—22no—
396C23×C4—44no—
397C23×C4C2×C4×C711yescharacteristic
398C23×C4C2×C4×C711yescharacteristic
399C23×C4C2×C4×C711yescharacteristic
400C23×C4C2×C4×C711yescharacteristic
401C23×C4C2×C4×C712yescomplemented
402C23×C4C7×D411yescharacteristic
403C23×C4C7×D411yescharacteristic
404C23×C4C7×D411yescharacteristic
405C23×C4C7×D411yescharacteristic
406C23×C4C7×D411yescharacteristic
407C23×C4C7×D411yescharacteristic
408C23×C4C7×D411yescharacteristic
409C23×C4C7×D411yescharacteristic
410C23×C4C23×C711yescharacteristic
411C23×C4C23×C711yescharacteristic
412#123—22no—
413#123—22no—
414#123—22no—
415#123—22no—
416C22⋊Q8—21no—
417C22⋊Q8—21no—
418C22⋊Q8—21no—
419C22⋊Q8—21no—
420C22⋊Q8—21no—
421C22⋊Q8—21no—
422C22⋊Q8—21no—
423C22⋊Q8—21no—
424#121—21no—
425#121—21no—
426#121—21no—
427#121—21no—
428#121—21no—
429#121—21no—
430#121—21no—
431#121—21no—
432#120—22no—
433#120—22no—
434#120—22no—
435#120—22no—
436C4×D4—22no—
437C4×D4—22no—
438C4×D4—22no—
439C4×D4—22no—
440C4×D4—22no—
441C4×D4—22no—
442C4×D4—22no—
443C4×D4—22no—
444#117—21no—
445#117—21no—
446#117—21no—
447#117—21no—
448#117—44no—
449C2×C4⋊C4—22no—
450C2×C4⋊C4C2×C4×C711yescharacteristic, complemented
451C2×C4⋊C4C2×C4×C711yescharacteristic, complemented
452C2×C4⋊C4C2×C4×C712yescomplemented
453C2×C4⋊C4C2×C4×C712yescomplemented
454C2×C22⋊C4—22no—
455C2×C22⋊C4—28no—
456C2×C22⋊C4—22no—
457C2×C22⋊C4—22no—
458C2×C22⋊C4C2×C4×C712yes—
459C2×C22⋊C4C2×C4×C712yes—
460C2×C22⋊C4C2×C4×C712yescomplemented
461C2×C22⋊C4C2×C4×C712yescomplemented
462C2×C22⋊C4C23×C714yes—
463C2×C22⋊C4C23×C712yes—
464C2×C22⋊C4C23×C714yes—
465C2×C42—22no—
466C2×C42—22no—
467C2×C42—22no—
468C2×C42—44no—
469C2×C42C2×C4×C712yescomplemented
470#99—216no—
471#95—22no—
472#95—22no—
473#95—22no—
474#95—22no—
475C22×C7—28no—
476C22×C7—21no—
477C22×C7—21no—
478C22×C7—21no—
479C22×C7—21no—
480C22×C7—21no—
481C22×C7—21no—
482C22×C7—21no—
483C22×C7—21no—
484C22×C7—21no—
485C22×C7—21no—
486C22×C7—21no—
487C22×C7—21no—
488C22×C7—21no—
489C22×C7—21no—
490C22×C7—21no—
491C22×C7—21no—
492C22×C7—44no—
493C22×C7—44no—
494C22×C7—44no—
495C22×C7—44no—
496C22×C7—44no—
497C22×C7—44no—
498C22×C7—42no—
499C22×C7—42no—
500C22×C7—42no—
501C22×C7—84no—
502C22×C7C2×#9912yes—
503C22×C7#41012yes—
504C22×C7C22×C22⋊C411yescharacteristic
505C22×C7C4×#4112yes—
506C22×C7#52512yes—
507C22×C7#53212yes—
508C4×C7—21no—
509C4×C7—21no—
510C4×C7—21no—
511C4×C7—21no—
512C4×C7—21no—
513C4×C7—21no—
514C4×C7—48no—
515C4×C7—42no—
516C4×C7—42no—
517C4×C7—42no—
518C4×C7—84no—
519C4×C7C2×#9912yes—
520C4×C7C2×#9912yes—
521C24—24no—
522C24—42no—
523C24—42no—
524C24C22×C4×C711yescharacteristic
525C24C22×C4×C711yescharacteristic
526C24C22×C4×C712yes—
527C24C2×C7×D411yescharacteristic
528C24C2×C7×D411yescharacteristic
529C24C2×C7×D411yescharacteristic
530C24C2×C7×D411yescharacteristic
531C24C24×C711yescharacteristic
532#41—44no—
533#41—44no—
534#41—44no—
535#41—44no—
536C2×Q8—21no—
537C2×Q8—21no—
538C2×Q8—42no—
539C2×D4—22no—
540C2×D4—22no—
541C2×D4—22no—
542C2×D4—22no—
543C2×D4—22no—
544C2×D4—22no—
545C2×D4—28no—
546C2×D4—21no—
547C2×D4—21no—
548C2×D4—42no—
549C2×D4—44no—
550C2×D4—44no—
551C22×C4—24no—
552C22×C4—24no—
553C22×C4—24no—
554C22×C4—28no—
555C22×C4—24no—
556C22×C4—22no—
557C22×C4—22no—
558C22×C4—24no—
559C22×C4—42no—
560C22×C4—42no—
561C22×C4—42no—
562C22×C4—42no—
563C22×C4—42no—
564C22×C4—42no—
565C22×C4—42no—
566C22×C4—42no—
567C22×C4—42no—
568C22×C4—42no—
569C22×C4—42no—
570C22×C4—44no—
571C22×C4—44no—
572C22×C4—44no—
573C22×C4C7×C22⋊C411yescharacteristic
574C22×C4C7×C22⋊C411yescharacteristic
575C22×C4C7×C22⋊C411yescharacteristic
576C22×C4C7×C22⋊C411yescharacteristic
577C22×C4C7×C22⋊C411yescharacteristic
578C22×C4C7×C22⋊C411yescharacteristic
579C22×C4C7×C22⋊C411yescharacteristic
580C22×C4C7×C22⋊C411yescharacteristic
581C22×C4C7×C22⋊C411yescharacteristic
582C22×C4C7×C22⋊C411yescharacteristic
583C22×C4C7×C22⋊C411yescharacteristic
584C22×C4C7×C22⋊C411yescharacteristic
585C22×C4C7×C22⋊C411yescharacteristic
586C22×C4C7×C22⋊C411yescharacteristic
587C22×C4C7×C22⋊C411yescharacteristic
588C22×C4C7×C22⋊C411yescharacteristic
589C22×C4C22×C4×C712yes—
590C22×C4C22×C4×C711yescharacteristic
591C22×C4C22×C4×C711yescharacteristic
592C22×C4C22×C4×C712yes—
593C22×C4C22×C4×C712yes—
594C22×C4C22×C4×C711yescharacteristic
595C22×C4C22×C4×C711yescharacteristic
596C22×C4C2×C7×D411yescharacteristic
597C22×C4C2×C7×D411yescharacteristic
598C22×C4C2×C7×D411yescharacteristic
599C22×C4C2×C7×D411yescharacteristic
600C22×C4C2×C7×D411yescharacteristic
601C22×C4C2×C7×D411yescharacteristic
602C22×C4C2×C7×D411yescharacteristic
603C22×C4C2×C7×D411yescharacteristic
604C4⋊C4—21no—
605C4⋊C4—21no—
606C4⋊C4—21no—
607C4⋊C4—21no—
608C4⋊C4—22no—
609C4⋊C4—22no—
610C4⋊C4—22no—
611C4⋊C4—22no—
612C4⋊C4—44no—
613C22⋊C4—28no—
614C22⋊C4—22no—
615C22⋊C4—22no—
616C22⋊C4—22no—
617C22⋊C4—22no—
618C22⋊C4—22no—
619C22⋊C4—22no—
620C22⋊C4—24no—
621C22⋊C4—22no—
622C22⋊C4—22no—
623C22⋊C4—22no—
624C22⋊C4—22no—
625C22⋊C4—28no—
626C22⋊C4—44no—
627C22⋊C4—44no—
628C22⋊C4C7×#4118yescomplemented
629C42—22no—
630C42—22no—
631C42—44no—
632C42—44no—
633C42—44no—
634C2×C7—22no—
635C2×C7—22no—
636C2×C7—22no—
637C2×C7—22no—
638C2×C7—22no—
639C2×C7—41no—
640C2×C7—41no—
641C2×C7—82no—
642C2×C7#229711yescharacteristic
643C2×C7C22×#9911yescharacteristic
644C2×C7C2×#41011yescharacteristic
645C23—22no—
646C23—22no—
647C23—22no—
648C23—22no—
649C23—22no—
650C23—22no—
651C23—22no—
652C23—22no—
653C23—22no—
654C23—22no—
655C23—22no—
656C23—22no—
657C23—22no—
658C23—24no—
659C23—41no—
660C23—41no—
661C23—41no—
662C23—41no—
663C23—41no—
664C23—41no—
665C23—41no—
666C23—41no—
667C23—416no—
668C23—42no—
669C23—42no—
670C23C2×C7×C22⋊C411yescharacteristic
671C23C2×C7×C22⋊C411yescharacteristic
672C23C2×C7×C22⋊C411yescharacteristic
673C23C2×C7×C22⋊C411yescharacteristic
674C23C23×C4×C711yescharacteristic
675C23C22×C7×D411yescharacteristic
676C23C22×C7×D411yescharacteristic
677C23C2×C7×#4114yes—
678Q8—42no—
679Q8—42no—
680D4—42no—
681D4—44no—
682D4—44no—
683D4—44no—
684D4—44no—
685D4—44no—
686D4—44no—
687D4—42no—
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—22no—
698C2×C4—22no—
699C2×C4—22no—
700C2×C4—22no—
701C2×C4—22no—
702C2×C4—22no—
703C2×C4—22no—
704C2×C4—22no—
705C2×C4—22no—
706C2×C4—24no—
707C2×C4—28no—
708C2×C4—41no—
709C2×C4—41no—
710C2×C4—41no—
711C2×C4—41no—
712C2×C4—41no—
713C2×C4—41no—
714C2×C4—41no—
715C2×C4—41no—
716C2×C4—41no—
717C2×C4—41no—
718C2×C4—41no—
719C2×C4—41no—
720C2×C4—44no—
721C2×C4—44no—
722C2×C4—416no—
723C2×C4—44no—
724C2×C4—44no—
725C2×C4—42no—
726C2×C4—42no—
727C2×C4—44no—
728C2×C4—44no—
729C2×C4—44no—
730C2×C4C7×#9914yescomplemented
731C2×C4C2×C7×C22⋊C411yescharacteristic
732C2×C4C2×C7×C22⋊C411yescharacteristic
733C2×C4C2×C7×C22⋊C411yescharacteristic
734C2×C4C2×C7×C22⋊C411yescharacteristic
735C2×C4C2×C7×C22⋊C411yescharacteristic
736C2×C4C2×C7×C22⋊C411yescharacteristic
737C2×C4C2×C7×C22⋊C411yescharacteristic
738C2×C4C2×C7×C22⋊C411yescharacteristic
739C7#2142011yescharacteristic, direct product factor, Sylow
740C22—28no—
741C22—21no—
742C22—21no—
743C22—21no—
744C22—21no—
745C22—21no—
746C22—21no—
747C22—21no—
748C22—21no—
749C22—21no—
750C22—21no—
751C22—21no—
752C22—21no—
753C22—21no—
754C22—21no—
755C22—21no—
756C22—21no—
757C22—44no—
758C22—44no—
759C22—44no—
760C22—44no—
761C22—44no—
762C22—44no—
763C22—42no—
764C22—42no—
765C22—42no—
766C22—84no—
767C22C2×C7×#9912yes—
768C22C7×#41012yes—
769C22C22×C7×C22⋊C411yescharacteristic
770C22C4×C7×#4112yes—
771C22C7×#52512yes—
772C22C7×#53212yes—
773C4—21no—
774C4—21no—
775C4—21no—
776C4—21no—
777C4—21no—
778C4—21no—
779C4—48no—
780C4—42no—
781C4—42no—
782C4—42no—
783C4—84no—
784C4C2×C7×#9912yes—
785C4C2×C7×#9912yes—
786C2—22no—
787C2—22no—
788C2—22no—
789C2—22no—
790C2—22no—
791C2—41no—
792C2—41no—
793C2—82no—
794C2C7×#229711yescharacteristic
795C2C22×C7×#9911yescharacteristic
796C2C2×C7×#41011yescharacteristic
subgroupG/H
centerC2×C4×C7C2×C22⋊C4
commutatorC23C23×C4×C7
Frattini, cosocleC24C24×C7
socleC22×C7C22×C22⋊C4
prime radicalC2×C7×#525C2
LCSG ▷ C23 ▷ C2 ▷ C1
UCSC1 ◁ C2×C4×C7 ◁ C24×C4×C7 ◁ G

Complements

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

NH ≅ G/Ntype
2. C7×#2280C2semidirect
3. C2×C4×C7×C22⋊C4C2semidirect
4. C7×#1996C2semidirect
5. C7×#1964C2semidirect
6. C7×#1898C2semidirect
7. C4×C7×#99C2semidirect
8. C22×C7×#41C4semidirect
18. C2×C7×#123C4semidirect
19. C2×C7×C22⋊Q8C4semidirect
21. C2×C7×#121C4semidirect
24. C2×C4×C7×D4C4semidirect
27. C2×C7×#117C4semidirect
43. #21420C7direct (N × H)
50. C22×C7×Q8C2×C4semidirect
53. C22×C7×D4C2×C4semidirect
61. C23×C4×C7C2×C4semidirect
110. C2×C7×C4⋊C4C2×C4semidirect
111. C2×C7×C4⋊C4C2×C4semidirect
112. C2×C7×C4⋊C4C2×C4semidirect
113. C2×C7×C4⋊C4C2×C4semidirect
120. C2×C7×C22⋊C4C2×C4semidirect
121. C2×C7×C22⋊C4C2×C4semidirect
129. C2×C42×C7C2×C4semidirect
136. #2280C2×C7semidirect
137. C2×C4×C22⋊C4C2×C7semidirect
138. #1996C2×C7semidirect
139. #1964C2×C7semidirect
140. #1898C2×C7semidirect
141. C4×#99C2×C7semidirect
249. C7×C22⋊C4#41semidirect
255. C22×#41C4×C7semidirect
265. C2×#123C4×C7semidirect
266. C2×C22⋊Q8C4×C7semidirect
268. C2×#121C4×C7semidirect
271. C2×C4×D4C4×C7semidirect
274. C2×#117C4×C7semidirect
375. C2×C4×C7#99semidirect
390. C22×Q8C2×C4×C7semidirect
393. C22×D4C2×C4×C7semidirect
401. C23×C4C2×C4×C7semidirect
450. C2×C4⋊C4C2×C4×C7semidirect
451. C2×C4⋊C4C2×C4×C7semidirect
452. C2×C4⋊C4C2×C4×C7semidirect
453. C2×C4⋊C4C2×C4×C7semidirect
460. C2×C22⋊C4C2×C4×C7semidirect
461. C2×C22⋊C4C2×C4×C7semidirect
469. C2×C42C2×C4×C7semidirect
628. C22⋊C4C7×#41semidirect
730. C2×C4C7×#99semidirect
739. C7#21420direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C7×#5252
C7×#22802
C2×C4×C7×C22⋊C42
C7×#19962
C7×#19642
C7×#18982
C4×C7×#992
#214207