Finite Group Databasebeta

← #13370278

Subgroups — #13370278

Order 1792.

1262 conjugacy classes of subgroups.

The subgroup lattice has 726 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C7×#3475C211yesmaximal, characteristic
2C4×D4×Dic7C211yesmaximal, characteristic, complemented
3D4×#1136C211yesmaximal, characteristic, complemented
4#11729595C211yesmaximal, characteristic, complemented
5#11729593C211yesmaximal, characteristic, complemented
6#11729467C212yesmaximal, complemented
7#11729465C212yesmaximal, complemented
8#11729400C211yesmaximal, characteristic, complemented
9C4×#6411C211yesmaximal, characteristic, complemented
10#11729344C212yesmaximal, complemented
11C2×#89327C212yesmaximal, complemented
12C7×#556C411yescharacteristic, complemented
13C7×#555C411yescharacteristic, complemented
14C7×#554C411yescharacteristic, complemented
15C7×#553C412yescomplemented
16C7×#552—21no—
17C7×#552C412yescomplemented
18C7×#551—22no—
19C7×#547C411yescharacteristic, complemented
20C7×#546—21no—
21C7×#533C2211yescharacteristic
22C7×#529—22no—
23C7×#529—21no—
24C7×#525C2212yes—
25C4×C7×#41—21no—
26C4×C7×#41C2211yescharacteristic
27C2×C4×C7×D4C2211yescharacteristic
28C2×C7×#117C2212yes—
29C2×D4×Dic7—21no—
30C22×C4×Dic7C2212yes—
31C22×#1136C2212yes—
32C2×#6411C2211yescharacteristic
33C2×#6411C2211yescharacteristic
34C2×#6411C2212yes—
35C4×C22⋊Dic7C2212yes—
36#89979C2212yes—
37#89784—21no—
38#89783—22no—
39D4×C7⋊C8—21no—
40C4⋊C4×Dic7—21no—
41C22⋊C4×Dic7—22no—
42C4×C4⋊Dic7C2211yescharacteristic
43C42×Dic7C2211yescharacteristic
44#89696C2211yescharacteristic
45C4×#1136C2211yescharacteristic
46#89327C2212yes—
47#89327C2212yes—
48#89327C2212yes—
49#89327C2212yes—
50#89327C2211yescharacteristic
51#89327C2212yes—
52#89327C2211yescharacteristic
53#22505—71nomaximal, Sylow
54C2×C7×#41—21no—
55C2×C7×#41C2311yescharacteristic
56C22×C7×D4D411yescharacteristic
57C23×C4×C7C2312yes—
58C23×Dic7—22no—
59C7×C4⋊Q8C2×C411yescharacteristic, complemented
60C7×C4⋊Q8C2×C411yescharacteristic, complemented
61C7×#126—22no—
62C7×#126—22no—
63C7×#126—22no—
64C7×#125—22no—
65C7×#125—21no—
66C7×#125C2×C412yescomplemented
67C7×#124—21no—
68C7×#124—22no—
69C7×#123—22no—
70C7×#123—22no—
71C7×#123—22no—
72C7×#123—22no—
73C7×C22⋊Q8—21no—
74C7×C22⋊Q8—21no—
75C7×C22⋊Q8—21no—
76C7×C22⋊Q8—22no—
77C7×C22⋊Q8C2×C412yescomplemented
78C7×C22⋊Q8C2×C412yescomplemented
79C7×#121—22no—
80C7×#121—21no—
81C7×#121C2×C412yescomplemented
82C7×#121C2×C412yescomplemented
83C7×#120—22no—
84C4×C7×Q8—21no—
85C4×C7×Q8—21no—
86C4×C7×Q8—21no—
87C4×C7×Q8C2×C411yescharacteristic, complemented
88C4×C7×Q8C2×C411yescharacteristic, complemented
89C4×C7×D4—21no—
90C4×C7×D4—22no—
91C4×C7×D4—21no—
92C4×C7×D4—21no—
93C4×C7×D4—22no—
94C4×C7×D4—22no—
95C4×C7×D4C2×C411yescharacteristic
96C4×C7×D4C2×C412yes—
97C4×C7×D4C2×C411yescharacteristic
98C4×C7×D4C2×C411yescharacteristic, complemented
99C4×C7×D4C2×C411yescharacteristic, complemented
100C4×C7×D4D411yescharacteristic
101C4×C7×D4D412yes—
102C4×C7×D4D411yescharacteristic
103C7×#117—22no—
104C7×#117—22no—
105C7×#117—21no—
106C7×#117—22no—
107C7×#117—21no—
108C7×#117C2×C412yescomplemented
109C7×#117C2×C412yescomplemented
110C7×#117C2311yescharacteristic
111C7×#117C2312yes—
112C2×C7×C4⋊C4C2×C412yescomplemented
113C2×C7×C4⋊C4C2×C412yescomplemented
114C2×C7×C4⋊C4D411yescharacteristic
115C2×C7×C22⋊C4—22no—
116C2×C7×C22⋊C4D412yes—
117C2×C42×C7—22no—
118C2×C42×C7—21no—
119C2×C42×C7C2311yescharacteristic
120C2×C22⋊Dic7—22no—
121D4×Dic7—28no—
122C2×C4⋊Dic7—21no—
123C2×C4×Dic7—21no—
124C2×C4×Dic7—24no—
125C2×C4×Dic7—21no—
126C2×C4×Dic7—22no—
127C2×C4×Dic7—42no—
128C2×C4×Dic7C2311yescharacteristic
129C2×C4×Dic7C2312yes—
130C2×C4×Dic7C2311yescharacteristic
131C2×#1136—22no—
132C2×#1136—24no—
133C2×#1136—42no—
134C2×#1136C2311yescharacteristic
135C2×#1136C2312yes—
136C2×#1136C2311yescharacteristic
137C22×C7⋊C8—22no—
138#6411—22no—
139#6411—22no—
140#6411—42no—
141C7⋊#95—21no—
142C7⋊#95—22no—
143C22⋊(C7⋊C8)—22no—
144C22⋊(C7⋊C8)—22no—
145C4⋊(C7⋊C8)—21no—
146C4⋊(C7⋊C8)—21no—
147#6377—21no—
148C4×C7⋊C8—21no—
149#3475D711yescharacteristic
150D4×M16—71no—
151C42×D4—71no—
152#1994—71no—
153#1986—71no—
154#1896—72no—
155#1871—72no—
156#1826—72no—
157#1806—71no—
158C4×#104—71no—
159C2×#339—72no—
160C24×C7C2×D412yes—
161C7×#41—21no—
162C7×#41—21no—
163C7×#41—21no—
164C7×#41—21no—
165C7×#41—44no—
166C2×C7×Q8—21no—
167C2×C7×Q8—21no—
168C2×C7×Q8C22×C411yescharacteristic
169C2×C7×D4—24no—
170C2×C7×D4—22no—
171C2×C7×D4—21no—
172C2×C7×D4—22no—
173C2×C7×D4C22⋊C412yes—
174C2×C7×D4C22⋊C411yescharacteristic
175C2×C7×D4C22⋊C411yescharacteristic
176C2×C7×D4C22×C411yescharacteristic
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—21no—
184C22×C4×C7—21no—
185C22×C4×C7—21no—
186C22×C4×C7C22×C412yes—
187C22×C4×C7C22×C412yes—
188C22×C4×C7C2×D412yes—
189C22×C4×C7C2×D411yescharacteristic
190C22×C4×C7C2×D412yes—
191C22×C4×C7C2×D412yes—
192C22×C4×C7C2×D411yescharacteristic
193C22×C4×C7C2411yescharacteristic
194C22×Dic7—21no—
195C22×Dic7—28no—
196C22×Dic7—21no—
197C22×Dic7—22no—
198C22×Dic7—44no—
199C22×Dic7—44no—
200C7×C4⋊C4—22no—
201C7×C4⋊C4—22no—
202C7×C4⋊C4—21no—
203C7×C4⋊C4—22no—
204C7×C4⋊C4—22no—
205C7×C4⋊C4—21no—
206C7×C4⋊C4—21no—
207C7×C4⋊C4—22no—
208C7×C4⋊C4—22no—
209C7×C4⋊C4—21no—
210C7×C4⋊C4C22⋊C411yescharacteristic
211C7×C4⋊C4C22⋊C411yescharacteristic
212C7×C4⋊C4C22⋊C412yes—
213C7×C4⋊C4C22×C411yescharacteristic
214C7×C4⋊C4C22×C411yescharacteristic
215C7×C4⋊C4C22×C412yes—
216C7×C4⋊C4C22×C412yes—
217C7×C22⋊C4—22no—
218C7×C22⋊C4—22no—
219C7×C22⋊C4—22no—
220C7×C22⋊C4—22no—
221C7×C22⋊C4—21no—
222C7×C22⋊C4—22no—
223C7×C22⋊C4—22no—
224C7×C22⋊C4—21no—
225C7×C22⋊C4—21no—
226C7×C22⋊C4—22no—
227C7×C22⋊C4C22⋊C412yes—
228C7×C22⋊C4C22⋊C412yes—
229C7×C22⋊C4C22⋊C412yes—
230C7×C22⋊C4C22⋊C412yes—
231C42×C7—22no—
232C42×C7—21no—
233C42×C7—22no—
234C42×C7—21no—
235C42×C7—21no—
236C42×C7—22no—
237C42×C7C22×C411yescharacteristic
238C42×C7C22×C411yescharacteristic
239C42×C7C2×D411yescharacteristic
240C42×C7C2×D411yescharacteristic
241C22⋊Dic7—28no—
242C4⋊Dic7—24no—
243C4×Dic7—24no—
244C4×Dic7—21no—
245C4×Dic7—21no—
246C4×Dic7—22no—
247C4×Dic7—22no—
248C4×Dic7—21no—
249C4×Dic7—44no—
250C4×Dic7—42no—
251C4×Dic7#4112yescomplemented
252#1136—21no—
253#1136—21no—
254#1136—22no—
255#1136—22no—
256#1136—21no—
257#1136—44no—
258#1136#4112yescomplemented
259C2×C7⋊C8—21no—
260C2×C7⋊C8—21no—
261C2×C7⋊C8—22no—
262C2×C7⋊C8—44no—
263C22×M16—72no—
264#556Dic711yescharacteristic, complemented
265#555Dic711yescharacteristic, complemented
266#554Dic711yescharacteristic, complemented
267#553Dic712yescomplemented
268#552—21no—
269#552Dic712yescomplemented
270#551—22no—
271#547Dic711yescharacteristic, complemented
272#546—21no—
273#533C2×D711yescharacteristic
274#529—22no—
275#529—21no—
276#525C2×D712yes—
277C4×#41—21no—
278C4×#41C2×D711yescharacteristic
279C2×C4×D4—141no—
280C2×C4×D4C2×D711yescharacteristic
281C2×#117C2×D712yes—
282C22×C42—72no—
283#436—141no—
284#435—142no—
285C8×D4—141no—
286#423—71no—
287C2×#104—71no—
288C2×#104—71no—
289C2×#104—72no—
290#407—72no—
291C4×M16—71no—
292C4×C4⋊C4—71no—
293C4×C4⋊C4—141no—
294C4×C22⋊C4—72no—
295C4×C22⋊C4—142no—
296C43—71no—
297#339—72no—
298#339—71no—
299#339—72no—
300#339—72no—
301#339—72no—
302#339—72no—
303#339—71no—
304C23×C7—22no—
305C23×C7—22no—
306C23×C7—24no—
307C23×C7—21no—
308C23×C7—42no—
309C23×C7C2×C22⋊C412yes—
310C23×C7C2×C22⋊C412yes—
311C23×C7C22×D411yescharacteristic
312C7×Q8—21no—
313C7×Q8—21no—
314C7×Q8—42no—
315C7×Q8—81no—
316C7×D4—24no—
317C7×D4—21no—
318C7×D4—21no—
319C7×D4—22no—
320C7×D4—41no—
321C7×D4—41no—
322C7×D4—44no—
323C7×D4—82no—
324C7×D4#10414yescomplemented
325C2×C4×C7—22no—
326C2×C4×C7—22no—
327C2×C4×C7—22no—
328C2×C4×C7—22no—
329C2×C4×C7—22no—
330C2×C4×C7—22no—
331C2×C4×C7—22no—
332C2×C4×C7—22no—
333C2×C4×C7—22no—
334C2×C4×C7—22no—
335C2×C4×C7—22no—
336C2×C4×C7—21no—
337C2×C4×C7—21no—
338C2×C4×C7—21no—
339C2×C4×C7—22no—
340C2×C4×C7—22no—
341C2×C4×C7—41no—
342C2×C4×C7—44no—
343C2×C4×C7—41no—
344C2×C4×C7—41no—
345C2×C4×C7—42no—
346C2×C4×C7—81no—
347C2×C4×C7—82no—
348C2×C4×C7C2×C22⋊C412yes—
349C2×C4×C7C2×C22⋊C411yescharacteristic
350C2×C4×C7C2×C22⋊C411yescharacteristic
351C2×C4×C7C2×C22⋊C411yescharacteristic
352C2×C4×C7C2×C22⋊C412yes—
353C2×C4×C7C2×C22⋊C411yescharacteristic
354C2×C4×C7C23×C411yescharacteristic
355C2×C4×C7C22×D411yescharacteristic
356C2×C4×C7C2×#4111yescharacteristic
357C2×C4×C7C2×#4111yescharacteristic
358C2×C4×C7H(5,𝔽2)11yescharacteristic
359C2×C4×C72−1+411yescharacteristic
360C2×Dic7—22no—
361C2×Dic7—22no—
362C2×Dic7—22no—
363C2×Dic7—22no—
364C2×Dic7—24no—
365C2×Dic7—416no—
366C2×Dic7—41no—
367C2×Dic7—42no—
368C2×Dic7—42no—
369C2×Dic7—41no—
370C7⋊C8—22no—
371C7⋊C8—42no—
372C7⋊C8—41no—
373C2×#41—21no—
374C2×#41C22×D711yescharacteristic
375C22×D4C22⋊D711yescharacteristic
376C23×C4—142no—
377C23×C4C22×D712yes—
378C2×M16—71no—
379C2×M16—72no—
380C2×M16—71no—
381C2×M16—142no—
382C2×M16—144no—
383C2×M16—282no—
384C22×C8—142no—
385C4⋊Q8C2×Dic711yescharacteristic, complemented
386C4⋊Q8C2×Dic711yescharacteristic, complemented
387#126—22no—
388#126—22no—
389#126—22no—
390#125—22no—
391#125—21no—
392#125C2×Dic712yescomplemented
393#124—21no—
394#124—22no—
395#123—22no—
396#123—22no—
397#123—22no—
398#123—22no—
399C22⋊Q8—21no—
400C22⋊Q8—21no—
401C22⋊Q8—21no—
402C22⋊Q8—22no—
403C22⋊Q8C2×Dic712yescomplemented
404C22⋊Q8C2×Dic712yescomplemented
405#121—22no—
406#121—21no—
407#121C2×Dic712yescomplemented
408#121C2×Dic712yescomplemented
409#120—22no—
410C4×Q8—21no—
411C4×Q8—21no—
412C4×Q8—21no—
413C4×Q8C2×Dic711yescharacteristic, complemented
414C4×Q8C2×Dic711yescharacteristic, complemented
415C4×D4—21no—
416C4×D4—22no—
417C4×D4—21no—
418C4×D4—21no—
419C4×D4—22no—
420C4×D4—22no—
421C4×D4—148no—
422C4×D4C2×Dic711yescharacteristic
423C4×D4C2×Dic712yes—
424C4×D4C2×Dic711yescharacteristic
425C4×D4C2×Dic711yescharacteristic, complemented
426C4×D4C2×Dic711yescharacteristic, complemented
427C4×D4C22⋊D711yescharacteristic
428C4×D4C22⋊D712yes—
429C4×D4C22⋊D711yescharacteristic
430#117—22no—
431#117—22no—
432#117—21no—
433#117—22no—
434#117—21no—
435#117C2×Dic712yescomplemented
436#117C2×Dic712yescomplemented
437#117C22×D711yescharacteristic
438#117C22×D712yes—
439C2×C4⋊C4—141no—
440C2×C4⋊C4C2×Dic712yescomplemented
441C2×C4⋊C4C2×Dic712yescomplemented
442C2×C4⋊C4C22⋊D711yescharacteristic
443C2×C22⋊C4—22no—
444C2×C22⋊C4—142no—
445C2×C22⋊C4C22⋊D712yes—
446C2×C42—22no—
447C2×C42—21no—
448C2×C42—71no—
449C2×C42—71no—
450C2×C42—72no—
451C2×C42—144no—
452C2×C42—141no—
453C2×C42—141no—
454C2×C42—142no—
455C2×C42—282no—
456C2×C42C22×D711yescharacteristic
457C4⋊C8—141no—
458C4⋊C8—141no—
459#104—142no—
460#104—142no—
461#104—282no—
462C22⋊C8—142no—
463C22⋊C8—142no—
464#97—141no—
465C4×C8—141no—
466#95—142no—
467#95—141no—
468C22×C7—22no—
469C22×C7—21no—
470C22×C7—21no—
471C22×C7—22no—
472C22×C7—22no—
473C22×C7—22no—
474C22×C7—22no—
475C22×C7—44no—
476C22×C7—44no—
477C22×C7—41no—
478C22×C7—41no—
479C22×C7—41no—
480C22×C7C2×#10414yes—
481C22×C7C22×C22⋊C411yescharacteristic
482C22×C7#54611yescharacteristic
483C22×C7#54711yescharacteristic
484C4×C7—22no—
485C4×C7—22no—
486C4×C7—21no—
487C4×C7—21no—
488C4×C7—21no—
489C4×C7—41no—
490C4×C7—41no—
491C4×C7—42no—
492C4×C7—41no—
493C4×C7—42no—
494C4×C7C2×#10412yes—
495C4×C7C4×#4111yescharacteristic
496C4×C7#52011yescharacteristic
497C4×C7#54611yescharacteristic
498C4×C7#54711yescharacteristic
499Dic7—24no—
500Dic7—42no—
501Dic7—44no—
502C24C2×C22⋊D712yes—
503#41—21no—
504#41—21no—
505#41—21no—
506#41—21no—
507#41—44no—
508C2×Q8—21no—
509C2×Q8—21no—
510C2×Q8C22×Dic711yescharacteristic
511C2×D4—24no—
512C2×D4—22no—
513C2×D4—21no—
514C2×D4—22no—
515C2×D4C22⋊Dic712yes—
516C2×D4C22⋊Dic711yescharacteristic
517C2×D4C22⋊Dic711yescharacteristic
518C2×D4C22×Dic711yescharacteristic
519C22×C4—22no—
520C22×C4—22no—
521C22×C4—22no—
522C22×C4—22no—
523C22×C4—22no—
524C22×C4—22no—
525C22×C4—21no—
526C22×C4—21no—
527C22×C4—21no—
528C22×C4—141no—
529C22×C4—148no—
530C22×C4—141no—
531C22×C4—142no—
532C22×C4—284no—
533C22×C4—284no—
534C22×C4C22×Dic712yes—
535C22×C4C22×Dic712yes—
536C22×C4C2×C22⋊D712yes—
537C22×C4C2×C22⋊D711yescharacteristic
538C22×C4C2×C22⋊D712yes—
539C22×C4C2×C22⋊D712yes—
540C22×C4C2×C22⋊D711yescharacteristic
541C22×C4C23×D711yescharacteristic
542M16—72no—
543M16—141no—
544M16—141no—
545M16—142no—
546M16—142no—
547M16—141no—
548M16—284no—
549C2×C8—141no—
550C2×C8—141no—
551C2×C8—142no—
552C2×C8—284no—
553C4⋊C4—22no—
554C4⋊C4—22no—
555C4⋊C4—21no—
556C4⋊C4—22no—
557C4⋊C4—22no—
558C4⋊C4—21no—
559C4⋊C4—21no—
560C4⋊C4—22no—
561C4⋊C4—22no—
562C4⋊C4—21no—
563C4⋊C4—144no—
564C4⋊C4C22⋊Dic711yescharacteristic
565C4⋊C4C22⋊Dic711yescharacteristic
566C4⋊C4C22⋊Dic712yes—
567C4⋊C4C22×Dic711yescharacteristic
568C4⋊C4C22×Dic711yescharacteristic
569C4⋊C4C22×Dic712yes—
570C4⋊C4C22×Dic712yes—
571C22⋊C4—22no—
572C22⋊C4—22no—
573C22⋊C4—22no—
574C22⋊C4—22no—
575C22⋊C4—21no—
576C22⋊C4—22no—
577C22⋊C4—22no—
578C22⋊C4—21no—
579C22⋊C4—21no—
580C22⋊C4—22no—
581C22⋊C4—148no—
582C22⋊C4C22⋊Dic712yes—
583C22⋊C4C22⋊Dic712yes—
584C22⋊C4C22⋊Dic712yes—
585C22⋊C4C22⋊Dic712yes—
586C42—22no—
587C42—21no—
588C42—22no—
589C42—21no—
590C42—21no—
591C42—22no—
592C42—72no—
593C42—144no—
594C42—141no—
595C42—141no—
596C42—142no—
597C42—142no—
598C42—141no—
599C42—284no—
600C42—282no—
601C42C22×Dic711yescharacteristic
602C42C22×Dic711yescharacteristic
603C42C2×C22⋊D711yescharacteristic
604C42C2×C22⋊D711yescharacteristic
605C2×C7—21no—
606C2×C7—21no—
607C2×C7—24no—
608C2×C7—42no—
609C2×C7—81no—
610C2×C7#233911yescharacteristic
611C2×C7C22×#10411yescharacteristic
612C2×C7#290111yescharacteristic
613C23—22no—
614C23—24no—
615C23—22no—
616C23—21no—
617C23—42no—
618C23C2×C22⋊Dic712yes—
619C23C2×C22⋊Dic712yes—
620C23C22×C22⋊D711yescharacteristic
621Q8—21no—
622Q8—21no—
623Q8—42no—
624Q8—81no—
625D4—24no—
626D4—21no—
627D4—21no—
628D4—22no—
629D4—41no—
630D4—44no—
631D4—41no—
632D4—82no—
633D4#641114yescomplemented
634C2×C4—22no—
635C2×C4—22no—
636C2×C4—22no—
637C2×C4—22no—
638C2×C4—22no—
639C2×C4—22no—
640C2×C4—22no—
641C2×C4—22no—
642C2×C4—22no—
643C2×C4—22no—
644C2×C4—22no—
645C2×C4—21no—
646C2×C4—21no—
647C2×C4—21no—
648C2×C4—22no—
649C2×C4—22no—
650C2×C4—41no—
651C2×C4—44no—
652C2×C4—41no—
653C2×C4—42no—
654C2×C4—41no—
655C2×C4—81no—
656C2×C4—82no—
657C2×C4—142no—
658C2×C4—142no—
659C2×C4—142no—
660C2×C4—142no—
661C2×C4—144no—
662C2×C4—2816no—
663C2×C4—281no—
664C2×C4—282no—
665C2×C4—281no—
666C2×C4—282no—
667C2×C4C2×C22⋊Dic712yes—
668C2×C4C2×C22⋊Dic711yescharacteristic
669C2×C4C2×C22⋊Dic711yescharacteristic
670C2×C4C2×C22⋊Dic711yescharacteristic
671C2×C4C2×C22⋊Dic712yes—
672C2×C4C2×C22⋊Dic711yescharacteristic
673C2×C4D7×#4111yescharacteristic
674C2×C4D7×#4111yescharacteristic
675C2×C4#655311yescharacteristic
676C2×C4#655411yescharacteristic
677C2×C4C23×Dic711yescharacteristic
678C2×C4C22×C22⋊D711yescharacteristic
679C8—142no—
680C8—281no—
681C8—282no—
682C7#2250511yescharacteristic, complemented, Sylow
683C22—21no—
684C22—22no—
685C22—21no—
686C22—22no—
687C22—22no—
688C22—22no—
689C22—22no—
690C22—44no—
691C22—44no—
692C22—41no—
693C22—41no—
694C22—41no—
695C22C2×#641114yes—
696C22#9051511yescharacteristic
697C22#9052011yescharacteristic
698C22C22×C22⋊Dic711yescharacteristic
699C4—21no—
700C4—22no—
701C4—22no—
702C4—21no—
703C4—21no—
704C4—41no—
705C4—42no—
706C4—41no—
707C4—41no—
708C4—42no—
709C4—144no—
710C4—284no—
711C4—282no—
712C4C2×#641112yes—
713C4#9051511yescharacteristic
714C4#41×Dic711yescharacteristic
715C4#9051811yescharacteristic
716C4#9052011yescharacteristic
717C2—21no—
718C2—21no—
719C2—24no—
720C2—42no—
721C2—81no—
722C2C22×#641111yescharacteristic
723C2#1174153311yescharacteristic
724C2#1174156511yescharacteristic
subgroupG/H
centerC2×C4C22×C22⋊D7
commutatorC2×C4×C7C23×C4
FrattiniC22×C4C23×D7
Fitting, prime radicalC7×#3475C2
socleC22×C7C22×C22⋊C4
cosocleC22×C4×C7C24
hypercenter#3475D7
hypocenterC7#22505
LCSG ▷ C2×C4×C7 ▷ C2×C7 ▷ C7
UCSC1 ◁ C2×C4 ◁ C2×C4×D4 ◁ #3475

Complements

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

NH ≅ G/Ntype
2. C4×D4×Dic7C2semidirect
3. D4×#1136C2semidirect
4. #11729595C2semidirect
5. #11729593C2semidirect
6. #11729467C2semidirect
7. #11729465C2semidirect
8. #11729400C2semidirect
9. C4×#6411C2semidirect
10. #11729344C2semidirect
11. C2×#89327C2semidirect
12. C7×#556C4semidirect
13. C7×#555C4semidirect
14. C7×#554C4semidirect
15. C7×#553C4semidirect
17. C7×#552C4semidirect
19. C7×#547C4semidirect
59. C7×C4⋊Q8C2×C4semidirect
60. C7×C4⋊Q8C2×C4semidirect
66. C7×#125C2×C4semidirect
77. C7×C22⋊Q8C2×C4semidirect
78. C7×C22⋊Q8C2×C4semidirect
81. C7×#121C2×C4semidirect
82. C7×#121C2×C4semidirect
87. C4×C7×Q8C2×C4semidirect
88. C4×C7×Q8C2×C4semidirect
98. C4×C7×D4C2×C4semidirect
99. C4×C7×D4C2×C4semidirect
108. C7×#117C2×C4semidirect
109. C7×#117C2×C4semidirect
112. C2×C7×C4⋊C4C2×C4semidirect
113. C2×C7×C4⋊C4C2×C4semidirect
251. C4×Dic7#41semidirect
258. #1136#41semidirect
264. #556Dic7semidirect
265. #555Dic7semidirect
266. #554Dic7semidirect
267. #553Dic7semidirect
269. #552Dic7semidirect
271. #547Dic7semidirect
324. C7×D4#104semidirect
385. C4⋊Q8C2×Dic7semidirect
386. C4⋊Q8C2×Dic7semidirect
392. #125C2×Dic7semidirect
403. C22⋊Q8C2×Dic7semidirect
404. C22⋊Q8C2×Dic7semidirect
407. #121C2×Dic7semidirect
408. #121C2×Dic7semidirect
413. C4×Q8C2×Dic7semidirect
414. C4×Q8C2×Dic7semidirect
425. C4×D4C2×Dic7semidirect
426. C4×D4C2×Dic7semidirect
435. #117C2×Dic7semidirect
436. #117C2×Dic7semidirect
440. C2×C4⋊C4C2×Dic7semidirect
441. C2×C4⋊C4C2×Dic7semidirect
633. D4#6411semidirect
682. C7#22505semidirect

Maximal subgroups

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

subgroupindex
C7×#34752
C4×D4×Dic72
D4×#11362
#117295952
#117295932
#117294672
#117294652
#117294002
C4×#64112
#117293442
C2×#893272
#225057