Finite Group Databasebeta

← #13362913

Subgroups — #13362913

Order 1792.

1390 conjugacy classes of subgroups.

The subgroup lattice has 872 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C7×#537C211yesmaximal, characteristic
2#11741532C211yesmaximal, characteristic, complemented
3C2×#90006C211yesmaximal, characteristic, complemented
4#11729889C211yesmaximal, characteristic, complemented
5#11729889C211yesmaximal, characteristic, complemented
6#11729451C211yesmaximal, characteristic, complemented
7#11729450C211yesmaximal, characteristic, complemented
8#11729447C211yesmaximal, characteristic, complemented
9#11729446C211yesmaximal, characteristic, complemented
10#11729436C211yesmaximal, characteristic, complemented
11#11729435C211yesmaximal, characteristic, complemented
12#11729432C211yesmaximal, characteristic, complemented
13#11729431C211yesmaximal, characteristic, complemented
14#11729308C211yesmaximal, characteristic, complemented
15#11729307C211yesmaximal, characteristic, complemented
16C22×C7×#41C2211yescharacteristic
17C22×C7×#41C2211yescharacteristic
18C7×#537—24no—
19C7×#537C418yescomplemented
20C2×C7×C22⋊Q8—21no—
21C2×C7×C22⋊Q8C2211yescharacteristic
22C2×C7×C22⋊Q8C2211yescharacteristic
23C2×C7×#121—21no—
24C2×C7×#121—21no—
25C2×C7×#121—21no—
26C2×C7×#121C2211yescharacteristic
27C2×C7×#121C2211yescharacteristic
28C22×C7×C4⋊C4C2211yescharacteristic
29C2×#6489C2211yescharacteristic
30C22×C4⋊Dic7C2211yescharacteristic
31C22×#1136C2211yescharacteristic
32C23×C7⋊C8C2211yescharacteristic
33#90006—24no—
34#90002—21no—
35C2×#6409C2211yescharacteristic
36C2×#6409C2211yescharacteristic
37C2×#6409C2211yescharacteristic
38C2×#6409C2211yescharacteristic
39#89993—21no—
40#89992—21no—
41#89992—21no—
42C2×#6406C2211yescharacteristic
43C2×#6406C2211yescharacteristic
44C2×#6406C2211yescharacteristic
45C2×#6406C2211yescharacteristic
46#89984C2211yescharacteristic
47#89984C2211yescharacteristic
48#89984C2211yescharacteristic
49#89984C2211yescharacteristic
50C2×C22⋊(C7⋊C8)C2211yescharacteristic
51C2×C22⋊(C7⋊C8)C2211yescharacteristic
52C2×C22⋊(C7⋊C8)C2211yescharacteristic
53C2×C22⋊(C7⋊C8)C2211yescharacteristic
54#89324C2211yescharacteristic
55#89324C2211yescharacteristic
56#89324C2211yescharacteristic
57#89324C2211yescharacteristic
58#89324C2211yescharacteristic
59#89324C2211yescharacteristic
60#89324C2211yescharacteristic
61#89324C2211yescharacteristic
62#21772—71nomaximal, Sylow
63C2×C7×#41—22no—
64C2×C7×#41—41no—
65C2×C7×#41—41no—
66C2×C7×#41—41no—
67C2×C7×#41—41no—
68C2×C7×#41—41no—
69C2×C7×#41—41no—
70C2×C7×#41—41no—
71C2×C7×#41—41no—
72C2×C7×#41C2×C414yes—
73C2×C7×#41C2×C414yescomplemented
74C2×C7×#41D414yes—
75C22×C7×Q8D411yescharacteristic
76C22×C7×Q8C2311yescharacteristic
77C22×C7×D4—21no—
78C22×C7×D4—21no—
79C22×C7×D4—21no—
80C22×C7×D4D411yescharacteristic
81C22×C7×D4D411yescharacteristic
82C22×C7×D4D411yescharacteristic
83C22×C7×D4C2311yescharacteristic
84C23×C4×C7—21no—
85C23×C4×C7—21no—
86C23×C4×C7C2311yescharacteristic
87C23×C4×C7C2311yescharacteristic
88C23×C4×C7C2311yescharacteristic
89C23×Dic7—21no—
90C7×C22⋊Q8—28no—
91C7×C22⋊Q8—22no—
92C7×C22⋊Q8—22no—
93C7×C22⋊Q8C2×C414yes—
94C7×C22⋊Q8C2×C414yescomplemented
95C7×#121—28no—
96C7×#121—28no—
97C7×#121—28no—
98C7×#121—22no—
99C7×#121—22no—
100C7×#121C2×C414yes—
101C7×#121C2×C414yescomplemented
102C2×C7×C4⋊C4—21no—
103C2×C7×C4⋊C4—22no—
104C2×C7×C4⋊C4—21no—
105C2×C7×C4⋊C4—21no—
106C2×C7×C4⋊C4C2×C414yescomplemented
107C2×C7×C4⋊C4C2311yescharacteristic
108C2×C7×C4⋊C4C2311yescharacteristic
109C2×C7×C22⋊C4—21no—
110C2×C7×C22⋊C4—21no—
111C2×C7×C22⋊C4—21no—
112C2×C7×C22⋊C4—21no—
113C2×C22⋊Dic7—21no—
114C2×C22⋊Dic7—21no—
115C2×C22⋊Dic7—21no—
116C2×C22⋊Dic7—21no—
117C2×C22⋊Dic7—21no—
118#6489—41no—
119#6489—41no—
120C2×C4⋊Dic7—21no—
121C2×C4⋊Dic7—41no—
122C2×C4⋊Dic7—41no—
123C2×C4⋊Dic7C2311yescharacteristic
124C2×C4⋊Dic7C2311yescharacteristic
125C2×C4⋊Dic7C2311yescharacteristic
126C2×C4⋊Dic7C2311yescharacteristic
127C2×C4×Dic7—21no—
128C2×#1136—22no—
129C2×#1136—41no—
130C2×#1136—41no—
131C22×C7⋊C8—22no—
132C22×C7⋊C8—41no—
133C22×C7⋊C8—41no—
134C22×C7⋊C8C2311yescharacteristic
135C22×C7⋊C8C2311yescharacteristic
136C22×C7⋊C8C2311yescharacteristic
137C22×C7⋊C8C2311yescharacteristic
138#6409—41no—
139#6409—41no—
140#6409—41no—
141#6409—41no—
142#6406—41no—
143#6406—41no—
144#6406—41no—
145#6406—41no—
146C7⋊#95—21no—
147C7⋊#95—21no—
148C7⋊#95—21no—
149C7⋊#95—21no—
150C22⋊(C7⋊C8)—22no—
151C22⋊(C7⋊C8)—22no—
152C22⋊(C7⋊C8)—22no—
153C22⋊(C7⋊C8)—22no—
154C2×#537D711yescharacteristic
155C2×#408—71no—
156#2311—71no—
157#1895—71no—
158#1894—71no—
159#1893—71no—
160#1892—71no—
161#1875—71no—
162#1874—71no—
163#1873—71no—
164#1872—71no—
165#1824—71no—
166#1823—71no—
167#1788—71no—
168#1788—71no—
169C24×C7—21no—
170C24×C7C2×D411yescharacteristic
171C24×C7C2×D411yescharacteristic
172C24×C7C2×D411yescharacteristic
173C7×#41—44no—
174C7×#41—44no—
175C7×#41—44no—
176C7×#41—44no—
177C7×#41—44no—
178C7×#41—44no—
179C7×#41—44no—
180C7×#41—44no—
181C2×C7×Q8—21no—
182C2×C7×Q8—21no—
183C2×C7×Q8—21no—
184C2×C7×Q8—21no—
185C2×C7×Q8—21no—
186C2×C7×Q8—41no—
187C2×C7×Q8—41no—
188C2×C7×Q8C22⋊C414yes—
189C2×C7×Q8C22×C412yes—
190C2×C7×D4—24no—
191C2×C7×D4—24no—
192C2×C7×D4—24no—
193C2×C7×D4—21no—
194C2×C7×D4—21no—
195C2×C7×D4—21no—
196C2×C7×D4—21no—
197C2×C7×D4—21no—
198C2×C7×D4—41no—
199C2×C7×D4—41no—
200C2×C7×D4—41no—
201C2×C7×D4—41no—
202C2×C7×D4—41no—
203C2×C7×D4—41no—
204C2×C7×D4—42no—
205C2×C7×D4—42no—
206C2×C7×D4—81no—
207C2×C7×D4—81no—
208C2×C7×D4—81no—
209C2×C7×D4—81no—
210C2×C7×D4C22⋊C414yes—
211C2×C7×D4C22⋊C414yes—
212C2×C7×D4C22⋊C414yes—
213C2×C7×D4C22×C412yes—
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—24no—
230C22×C4×C7—24no—
231C22×C4×C7—42no—
232C22×C4×C7—42no—
233C22×C4×C7—81no—
234C22×C4×C7—81no—
235C22×C4×C7C22×C412yes—
236C22×C4×C7C22×C412yes—
237C22×C4×C7C22×C412yes—
238C22×C4×C7C2×D411yescharacteristic
239C22×C4×C7C2×D411yescharacteristic
240C22×C4×C7C2×D411yescharacteristic
241C22×C4×C7C2×D412yes—
242C22×C4×C7C2×D412yes—
243C22×C4×C7C2×D412yes—
244C22×C4×C7C2411yescharacteristic
245C22×Dic7—21no—
246C22×Dic7—21no—
247C22×Dic7—21no—
248C22×Dic7—21no—
249C22×Dic7—42no—
250C22×Dic7—81no—
251C22×Dic7—81no—
252C7×C4⋊C4—24no—
253C7×C4⋊C4—24no—
254C7×C4⋊C4—24no—
255C7×C4⋊C4—21no—
256C7×C4⋊C4—21no—
257C7×C4⋊C4C22×C412yes—
258C7×C4⋊C4C22×C412yes—
259C7×C22⋊C4—24no—
260C7×C22⋊C4—24no—
261C7×C22⋊C4—24no—
262C7×C22⋊C4—24no—
263C22⋊Dic7—42no—
264C22⋊Dic7—81no—
265C22⋊Dic7—81no—
266C22⋊Dic7—81no—
267C22⋊Dic7—81no—
268C4⋊Dic7—21no—
269C4⋊Dic7—21no—
270C4⋊Dic7—21no—
271C4⋊Dic7—21no—
272C4⋊Dic7—21no—
273C4⋊Dic7—21no—
274C4⋊Dic7—21no—
275C4⋊Dic7—21no—
276C4⋊Dic7—42no—
277C4×Dic7—42no—
278#1136—44no—
279C2×C7⋊C8—21no—
280C2×C7⋊C8—21no—
281C2×C7⋊C8—21no—
282C2×C7⋊C8—21no—
283C2×C7⋊C8—21no—
284C2×C7⋊C8—21no—
285C2×C7⋊C8—21no—
286C2×C7⋊C8—21no—
287C2×C7⋊C8—21no—
288C2×C7⋊C8—21no—
289C2×C7⋊C8—21no—
290C2×C7⋊C8—21no—
291C2×C7⋊C8—44no—
292C22×#41C2×D711yescharacteristic
293C22×#41C2×D711yescharacteristic
294C22×M16—71no—
295C23×C8—71no—
296#537—24no—
297#537Dic718yescomplemented
298C2×C22⋊Q8—21no—
299C2×C22⋊Q8C2×D711yescharacteristic
300C2×C22⋊Q8C2×D711yescharacteristic
301C2×#121—21no—
302C2×#121—21no—
303C2×#121—21no—
304C2×#121C2×D711yescharacteristic
305C2×#121C2×D711yescharacteristic
306C2×#117—71no—
307C22×C4⋊C4—71no—
308C22×C4⋊C4C2×D711yescharacteristic
309C2×#103—71no—
310C2×#103—71no—
311C2×#103—71no—
312C2×#103—71no—
313C2×#102—71no—
314C2×#102—71no—
315C2×#102—71no—
316C2×#102—71no—
317#408—144no—
318C2×C22⋊C8—71no—
319C2×C22⋊C8—71no—
320C2×C22⋊C8—71no—
321C2×C22⋊C8—71no—
322#391—141no—
323#390—141no—
324#386—141no—
325#386—141no—
326#380—71no—
327#380—71no—
328#380—71no—
329#380—71no—
330#340—71no—
331#340—71no—
332#340—71no—
333#340—71no—
334#340—71no—
335#340—71no—
336#340—71no—
337#340—71no—
338C23×C7—21no—
339C23×C7—21no—
340C23×C7—21no—
341C23×C7—21no—
342C23×C7—21no—
343C23×C7—21no—
344C23×C7—21no—
345C23×C7—21no—
346C23×C7—21no—
347C23×C7—21no—
348C23×C7—21no—
349C23×C7—21no—
350C23×C7—21no—
351C23×C7—21no—
352C23×C7—21no—
353C23×C7—21no—
354C23×C7—21no—
355C23×C7—21no—
356C23×C7—22no—
357C23×C7—41no—
358C23×C7—41no—
359C23×C7—41no—
360C23×C7—41no—
361C23×C7—41no—
362C23×C7—41no—
363C23×C7C2×C22⋊C412yes—
364C23×C7C2×C22⋊C412yes—
365C23×C7C2×C22⋊C412yes—
366C23×C7C22×D411yescharacteristic
367C7×Q8—22no—
368C7×Q8—22no—
369C7×Q8—44no—
370C7×Q8—41no—
371C7×Q8—41no—
372C7×D4—22no—
373C7×D4—22no—
374C7×D4—44no—
375C7×D4—44no—
376C7×D4—44no—
377C7×D4—48no—
378C7×D4—41no—
379C7×D4—41no—
380C7×D4—84no—
381C7×D4—84no—
382C2×C4×C7—21no—
383C2×C4×C7—21no—
384C2×C4×C7—21no—
385C2×C4×C7—21no—
386C2×C4×C7—21no—
387C2×C4×C7—21no—
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—48no—
404C2×C4×C7—41no—
405C2×C4×C7—41no—
406C2×C4×C7—41no—
407C2×C4×C7—41no—
408C2×C4×C7—41no—
409C2×C4×C7—41no—
410C2×C4×C7—84no—
411C2×C4×C7C2×C22⋊C412yes—
412C2×C4×C7C2×C22⋊C412yes—
413C2×C4×C7C2×C22⋊C412yes—
414C2×C4×C7C23×C411yescharacteristic
415C2×C4×C7C22×D411yescharacteristic
416C2×C4×C7H(5,𝔽2)11yescharacteristic
417C2×C4×C7H(5,𝔽2)11yescharacteristic
418C2×C4×C7H(5,𝔽2)11yescharacteristic
419C2×C4×C7H(5,𝔽2)11yescharacteristic
420C2×Dic7—41no—
421C2×Dic7—41no—
422C2×Dic7—41no—
423C2×Dic7—41no—
424C2×Dic7—41no—
425C2×Dic7—41no—
426C2×Dic7—41no—
427C2×Dic7—41no—
428C2×Dic7—41no—
429C2×Dic7—41no—
430C2×Dic7—41no—
431C2×Dic7—41no—
432C2×Dic7—84no—
433C7⋊C8—41no—
434C7⋊C8—41no—
435C7⋊C8—41no—
436C7⋊C8—41no—
437C2×#41—22no—
438C2×#41—41no—
439C2×#41—41no—
440C2×#41—41no—
441C2×#41—41no—
442C2×#41—41no—
443C2×#41—41no—
444C2×#41—41no—
445C2×#41—41no—
446C2×#41C2×Dic714yes—
447C2×#41C2×Dic714yescomplemented
448C2×#41C22⋊D714yes—
449C22×Q8C22⋊D711yescharacteristic
450C22×Q8C22×D711yescharacteristic
451C22×D4—21no—
452C22×D4—21no—
453C22×D4—21no—
454C22×D4C22⋊D711yescharacteristic
455C22×D4C22⋊D711yescharacteristic
456C22×D4C22⋊D711yescharacteristic
457C22×D4C22×D711yescharacteristic
458C23×C4—21no—
459C23×C4—21no—
460C23×C4—141no—
461C23×C4C22×D711yescharacteristic
462C23×C4C22×D711yescharacteristic
463C23×C4C22×D711yescharacteristic
464C2×M16—142no—
465C2×M16—281no—
466C2×M16—281no—
467C22×C8—71no—
468C22×C8—71no—
469C22×C8—71no—
470C22×C8—71no—
471C22×C8—142no—
472C22×C8—281no—
473C22×C8—281no—
474C22⋊Q8—28no—
475C22⋊Q8—22no—
476C22⋊Q8—22no—
477C22⋊Q8C2×Dic714yes—
478C22⋊Q8C2×Dic714yescomplemented
479#121—28no—
480#121—28no—
481#121—28no—
482#121—22no—
483#121—22no—
484#121C2×Dic714yes—
485#121C2×Dic714yescomplemented
486#117—281no—
487#117—281no—
488C2×C4⋊C4—21no—
489C2×C4⋊C4—22no—
490C2×C4⋊C4—21no—
491C2×C4⋊C4—21no—
492C2×C4⋊C4—71no—
493C2×C4⋊C4—71no—
494C2×C4⋊C4—71no—
495C2×C4⋊C4—71no—
496C2×C4⋊C4—141no—
497C2×C4⋊C4—281no—
498C2×C4⋊C4—281no—
499C2×C4⋊C4C2×Dic714yescomplemented
500C2×C4⋊C4C22×D711yescharacteristic
501C2×C4⋊C4C22×D711yescharacteristic
502C2×C22⋊C4—21no—
503C2×C22⋊C4—21no—
504C2×C22⋊C4—21no—
505C2×C22⋊C4—21no—
506C2×C22⋊C4—141no—
507C2×C22⋊C4—141no—
508C2×C22⋊C4—141no—
509C2×C22⋊C4—141no—
510C2×C22⋊C4—141no—
511C2×C42—141no—
512#103—281no—
513#103—281no—
514#103—281no—
515#103—281no—
516#102—281no—
517#102—281no—
518#102—281no—
519#102—281no—
520C22⋊C8—142no—
521C22⋊C8—142no—
522C22⋊C8—142no—
523C22⋊C8—142no—
524#95—141no—
525#95—141no—
526#95—141no—
527#95—141no—
528C22×C7—22no—
529C22×C7—22no—
530C22×C7—22no—
531C22×C7—22no—
532C22×C7—22no—
533C22×C7—22no—
534C22×C7—22no—
535C22×C7—22no—
536C22×C7—22no—
537C22×C7—41no—
538C22×C7—41no—
539C22×C7—41no—
540C22×C7—41no—
541C22×C7—41no—
542C22×C7—41no—
543C22×C7—41no—
544C22×C7—41no—
545C22×C7—41no—
546C22×C7—41no—
547C22×C7—41no—
548C22×C7—41no—
549C22×C7—42no—
550C22×C7—42no—
551C22×C7—42no—
552C22×C7—81no—
553C22×C7—81no—
554C22×C7—81no—
555C22×C7—81no—
556C22×C7C22×C22⋊C411yescharacteristic
557C22×C7#53411yescharacteristic
558C22×C7#53411yescharacteristic
559C22×C7#57611yescharacteristic
560C22×C7#57711yescharacteristic
561C22×C7#57711yescharacteristic
562C22×C7#57811yescharacteristic
563C4×C7—22no—
564C4×C7—22no—
565C4×C7—22no—
566C4×C7—42no—
567C4×C7—42no—
568C4×C7—42no—
569C4×C7#51811yescharacteristic
570C4×C7#51811yescharacteristic
571C4×C7#53411yescharacteristic
572C4×C7#53411yescharacteristic
573Dic7—81no—
574Dic7—81no—
575Dic7—81no—
576Dic7—81no—
577C24—21no—
578C24C2×C22⋊D711yescharacteristic
579C24C2×C22⋊D711yescharacteristic
580C24C2×C22⋊D711yescharacteristic
581#41—44no—
582#41—44no—
583#41—44no—
584#41—44no—
585#41—44no—
586#41—44no—
587#41—44no—
588#41—44no—
589C2×Q8—21no—
590C2×Q8—21no—
591C2×Q8—21no—
592C2×Q8—21no—
593C2×Q8—21no—
594C2×Q8—41no—
595C2×Q8—41no—
596C2×Q8C22⋊Dic714yes—
597C2×Q8C22×Dic712yes—
598C2×D4—24no—
599C2×D4—24no—
600C2×D4—24no—
601C2×D4—21no—
602C2×D4—21no—
603C2×D4—21no—
604C2×D4—21no—
605C2×D4—21no—
606C2×D4—41no—
607C2×D4—41no—
608C2×D4—41no—
609C2×D4—41no—
610C2×D4—41no—
611C2×D4—41no—
612C2×D4—42no—
613C2×D4—42no—
614C2×D4—81no—
615C2×D4—81no—
616C2×D4—81no—
617C2×D4—81no—
618C2×D4C22⋊Dic714yes—
619C2×D4C22⋊Dic714yes—
620C2×D4C22⋊Dic714yes—
621C2×D4C22×Dic712yes—
622C22×C4—21no—
623C22×C4—21no—
624C22×C4—21no—
625C22×C4—21no—
626C22×C4—21no—
627C22×C4—21no—
628C22×C4—21no—
629C22×C4—21no—
630C22×C4—21no—
631C22×C4—21no—
632C22×C4—21no—
633C22×C4—21no—
634C22×C4—21no—
635C22×C4—21no—
636C22×C4—21no—
637C22×C4—24no—
638C22×C4—24no—
639C22×C4—42no—
640C22×C4—42no—
641C22×C4—81no—
642C22×C4—81no—
643C22×C4—141no—
644C22×C4—141no—
645C22×C4—141no—
646C22×C4—141no—
647C22×C4—282no—
648C22×C4—561no—
649C22×C4—561no—
650C22×C4C22×Dic712yes—
651C22×C4C22×Dic712yes—
652C22×C4C22×Dic712yes—
653C22×C4C2×C22⋊D711yescharacteristic
654C22×C4C2×C22⋊D711yescharacteristic
655C22×C4C2×C22⋊D711yescharacteristic
656C22×C4C2×C22⋊D712yes—
657C22×C4C2×C22⋊D712yes—
658C22×C4C2×C22⋊D712yes—
659C22×C4C23×D711yescharacteristic
660M16—284no—
661C2×C8—141no—
662C2×C8—141no—
663C2×C8—141no—
664C2×C8—141no—
665C2×C8—141no—
666C2×C8—141no—
667C2×C8—141no—
668C2×C8—141no—
669C2×C8—141no—
670C2×C8—141no—
671C2×C8—141no—
672C2×C8—141no—
673C2×C8—284no—
674C4⋊C4—24no—
675C4⋊C4—24no—
676C4⋊C4—24no—
677C4⋊C4—21no—
678C4⋊C4—21no—
679C4⋊C4—141no—
680C4⋊C4—141no—
681C4⋊C4—141no—
682C4⋊C4—141no—
683C4⋊C4—141no—
684C4⋊C4—141no—
685C4⋊C4—141no—
686C4⋊C4—141no—
687C4⋊C4—282no—
688C4⋊C4C22×Dic712yes—
689C4⋊C4C22×Dic712yes—
690C22⋊C4—24no—
691C22⋊C4—24no—
692C22⋊C4—24no—
693C22⋊C4—24no—
694C22⋊C4—282no—
695C22⋊C4—561no—
696C22⋊C4—561no—
697C22⋊C4—561no—
698C22⋊C4—561no—
699C42—282no—
700C2×C7—42no—
701C2×C7—42no—
702C2×C7—42no—
703C2×C7—82no—
704C2×C7#230811yescharacteristic
705C2×C7#289711yescharacteristic
706C2×C7#289811yescharacteristic
707C2×C7#319811yescharacteristic
708C2×C7#320111yescharacteristic
709C2×C7#320311yescharacteristic
710C2×C7#320411yescharacteristic
711C23—21no—
712C23—21no—
713C23—21no—
714C23—21no—
715C23—21no—
716C23—21no—
717C23—21no—
718C23—21no—
719C23—21no—
720C23—21no—
721C23—21no—
722C23—21no—
723C23—21no—
724C23—21no—
725C23—21no—
726C23—21no—
727C23—21no—
728C23—21no—
729C23—22no—
730C23—41no—
731C23—41no—
732C23—41no—
733C23—41no—
734C23—41no—
735C23—41no—
736C23C2×C22⋊Dic712yes—
737C23C2×C22⋊Dic712yes—
738C23C2×C22⋊Dic712yes—
739C23C22×C22⋊D711yescharacteristic
740Q8—22no—
741Q8—22no—
742Q8—44no—
743Q8—41no—
744Q8—41no—
745D4—22no—
746D4—22no—
747D4—44no—
748D4—44no—
749D4—44no—
750D4—48no—
751D4—41no—
752D4—41no—
753D4—84no—
754D4—84no—
755C2×C4—21no—
756C2×C4—21no—
757C2×C4—21no—
758C2×C4—21no—
759C2×C4—21no—
760C2×C4—21no—
761C2×C4—22no—
762C2×C4—22no—
763C2×C4—22no—
764C2×C4—22no—
765C2×C4—22no—
766C2×C4—22no—
767C2×C4—22no—
768C2×C4—22no—
769C2×C4—22no—
770C2×C4—22no—
771C2×C4—22no—
772C2×C4—22no—
773C2×C4—22no—
774C2×C4—22no—
775C2×C4—22no—
776C2×C4—48no—
777C2×C4—41no—
778C2×C4—41no—
779C2×C4—41no—
780C2×C4—41no—
781C2×C4—41no—
782C2×C4—41no—
783C2×C4—84no—
784C2×C4—281no—
785C2×C4—281no—
786C2×C4—281no—
787C2×C4—281no—
788C2×C4—281no—
789C2×C4—281no—
790C2×C4—281no—
791C2×C4—281no—
792C2×C4—281no—
793C2×C4—281no—
794C2×C4—281no—
795C2×C4—281no—
796C2×C4—564no—
797C2×C4C2×C22⋊Dic712yes—
798C2×C4C2×C22⋊Dic712yes—
799C2×C4C2×C22⋊Dic712yes—
800C2×C4#654811yescharacteristic
801C2×C4#654811yescharacteristic
802C2×C4#654811yescharacteristic
803C2×C4#654811yescharacteristic
804C2×C4C23×Dic711yescharacteristic
805C2×C4C22×C22⋊D711yescharacteristic
806C8—281no—
807C8—281no—
808C8—281no—
809C8—281no—
810C7#2177211yescharacteristic, complemented, Sylow
811C22—22no—
812C22—22no—
813C22—22no—
814C22—22no—
815C22—22no—
816C22—22no—
817C22—22no—
818C22—22no—
819C22—22no—
820C22—41no—
821C22—41no—
822C22—41no—
823C22—41no—
824C22—41no—
825C22—41no—
826C22—41no—
827C22—41no—
828C22—41no—
829C22—41no—
830C22—41no—
831C22—41no—
832C22—42no—
833C22—42no—
834C22—42no—
835C22—81no—
836C22—81no—
837C22—81no—
838C22—81no—
839C22#9049511yescharacteristic
840C22#9049511yescharacteristic
841C22#9052611yescharacteristic
842C22#9052711yescharacteristic
843C22#9052811yescharacteristic
844C22#9052911yescharacteristic
845C22C22×C22⋊Dic711yescharacteristic
846C4—22no—
847C4—22no—
848C4—22no—
849C4—42no—
850C4—42no—
851C4—42no—
852C4—561no—
853C4—561no—
854C4—561no—
855C4—561no—
856C4#9048911yescharacteristic
857C4#9048911yescharacteristic
858C4#9049511yescharacteristic
859C4#9049511yescharacteristic
860C2—42no—
861C2—42no—
862C2—42no—
863C2—82no—
864C2#1174087011yescharacteristic
865C2#1174087111yescharacteristic
866C2#1174087311yescharacteristic
867C2#1174087411yescharacteristic
868C2#1174148811yescharacteristic
869C2#1174154411yescharacteristic
870C2#1174155611yescharacteristic
subgroupG/H
centerC23C22×C22⋊D7
commutatorC2×C4×C7C23×C4
FrattiniC22×C4C23×D7
Fitting, prime radicalC2×C7×#537C2
socleC23×C7C22×D4
cosocleC22×C4×C7C24
hypercenterC2×#537D7
hypocenterC7#21772
LCSG ▷ C2×C4×C7 ▷ C2×C7 ▷ C7
UCSC1 ◁ C23 ◁ C22×#41 ◁ C2×#537

Complements

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

NH ≅ G/Ntype
2. #11741532C2semidirect
3. C2×#90006C2semidirect
4. #11729889C2semidirect
5. #11729889C2semidirect
6. #11729451C2semidirect
7. #11729450C2semidirect
8. #11729447C2semidirect
9. #11729446C2semidirect
10. #11729436C2semidirect
11. #11729435C2semidirect
12. #11729432C2semidirect
13. #11729431C2semidirect
14. #11729308C2semidirect
15. #11729307C2semidirect
19. C7×#537C4semidirect
73. C2×C7×#41C2×C4semidirect
94. C7×C22⋊Q8C2×C4semidirect
101. C7×#121C2×C4semidirect
106. C2×C7×C4⋊C4C2×C4semidirect
297. #537Dic7semidirect
447. C2×#41C2×Dic7semidirect
478. C22⋊Q8C2×Dic7semidirect
485. #121C2×Dic7semidirect
499. C2×C4⋊C4C2×Dic7semidirect
810. C7#21772semidirect

Maximal subgroups

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

subgroupindex
C2×C7×#5372
#117415322
C2×#900062
#117298892
#117294512
#117294502
#117294472
#117294462
#117294362
#117294352
#117294322
#117294312
#117293082
#117293072
#217727