Finite Group Databasebeta

← #13319785

Subgroups — #13319785

Order 1792.

1446 conjugacy classes of subgroups.

The subgroup lattice has 766 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#90482C211yesmaximal, characteristic
2C22×C7×C22⋊C8C211yesmaximal, characteristic, complemented
3C2×#89979C211yesmaximal, characteristic, complemented
4#11727677C212yesmaximal, complemented
5#11727675C212yesmaximal, complemented
6#11727674C214yesmaximal, complemented
7#11727673C214yesmaximal, complemented
8C24×C4×C7C2211yescharacteristic
9C22×#1157C411yescharacteristic
10C23×C7×C8—21no—
11C2×#6516C412yes—
12#90482—21no—
13#90482—21no—
14#90482—21no—
15#90482—21no—
16#90482—21no—
17#90482—21no—
18#90482—21no—
19#90482—21no—
20C2×#6493C411yescharacteristic
21C2×#6493C2211yescharacteristic
22C2×#6492C2212yes—
23C2×C4×C22⋊D7C412yes—
24C2×C4×C22⋊D7C2212yes—
25C2×#6489C411yescharacteristic
26C2×#6487C411yescharacteristic
27C2×#6487C2211yescharacteristic
28C22×#1136—21no—
29C2×C7×C22⋊C8—21no—
30C2×C7×C22⋊C8—21no—
31C2×C7×C22⋊C8—21no—
32C2×C7×C22⋊C8C2212yes—
33C2×C7×C22⋊C8C2212yes—
34C2×C7×C22⋊C8C2212yes—
35#89979—21no—
36#89979—21no—
37#89979C2212yes—
38#89979C2212yes—
39C2×C22⋊(C7⋊C8)—21no—
40C2×C22⋊(C7⋊C8)C2212yes—
41#89264C2218yescomplemented
42#89263C2218yescomplemented
43#17381—71nomaximal, Sylow
44C25×C7C2×C411yescharacteristic
45C23×C4×C7—44no—
46C23×C4×C7C2×C411yescharacteristic
47C23×C4×C7C2×C411yescharacteristic
48C23×C4×C7C2×C411yescharacteristic
49C23×C4×C7D411yescharacteristic
50C23×C4×C7D411yescharacteristic
51C23×C4×C7D411yescharacteristic
52C23×C4×C7D411yescharacteristic
53C23×C4×C7D411yescharacteristic
54C23×C4×C7D411yescharacteristic
55C23×C4×C7D411yescharacteristic
56C23×C4×C7D411yescharacteristic
57C23×C4×C7C2311yescharacteristic
58C23×C4×C7C2311yescharacteristic
59C23×C4×C7C2311yescharacteristic
60C22×C22⋊D7C2×C412yes—
61C22×C22⋊D7C2×C412yes—
62C22×C22⋊D7C2×C412yes—
63C2×#1157—21no—
64C2×#1157—21no—
65C2×#1157—21no—
66C2×#1157—21no—
67C2×#1157—44no—
68C22×D28C2×C411yescharacteristic
69C22×C4×D7C2×C412yes—
70C22×Dic14C2×C411yescharacteristic
71C22×C7×C8—22no—
72C22×C7×C8—22no—
73C22×C7×C8—22no—
74C22×C7×C8—44no—
75#6516—22no—
76#6516—22no—
77#6516—22no—
78#6516—22no—
79C2×C22⋊Dic7C2×C412yes—
80C2×C22⋊Dic7C2×C412yes—
81C2×C22⋊Dic7C2×C412yes—
82#6493—21no—
83#6493—21no—
84#6493—21no—
85#6493—21no—
86#6493—21no—
87#6493—21no—
88#6493—21no—
89#6493—21no—
90#6492—22no—
91#6492—22no—
92#6492—22no—
93#6492—22no—
94C4×C22⋊D7—22no—
95C4×C22⋊D7—22no—
96C4×C22⋊D7—22no—
97C4×C22⋊D7—22no—
98C4×C22⋊D7—22no—
99C4×C22⋊D7—22no—
100C4×C22⋊D7—22no—
101C4×C22⋊D7—22no—
102C2×(C2×D7)⋊C4C2×C412yes—
103C2×(C2×D7)⋊C4C2312yes—
104#6489—21no—
105#6489—21no—
106#6489—21no—
107#6489—21no—
108C2×C4⋊Dic7C2×C411yescharacteristic
109C2×C4⋊Dic7C2×C411yescharacteristic
110#6487—21no—
111#6487—21no—
112#6487—21no—
113#6487—21no—
114#6487—21no—
115#6487—21no—
116#6487—21no—
117#6487—21no—
118C2×Dic7⋊C4C2×C412yes—
119C2×Dic7⋊C4C2312yes—
120C2×C4×Dic7C2×C412yes—
121C2×#1136—22no—
122C2×#1136—22no—
123C2×#1136—44no—
124C22×C7⋊C8—22no—
125C7×C22⋊C8—22no—
126C7×C22⋊C8—22no—
127C7×C22⋊C8—22no—
128C7×C22⋊C8C2314yes—
129C22⋊(C7⋊C8)—22no—
130C22⋊(C7⋊C8)—22no—
131C22⋊(C7⋊C8)—22no—
132C22⋊(C7⋊C8)C2314yes—
133C2×#525—71no—
134C2×#407—71no—
135C22×C22⋊C8D711yescharacteristic, complemented
136#1472—72no—
137#1471—72no—
138#1468—74no—
139#1459—74no—
140C24×C7—24no—
141C24×C7—42no—
142C24×C7—42no—
143C24×C7C22⋊C411yescharacteristic
144C24×C7C22⋊C411yescharacteristic
145C24×C7C22⋊C411yescharacteristic
146C24×C7C22⋊C411yescharacteristic
147C24×C7C22×C411yescharacteristic
148C24×C7C22×C411yescharacteristic
149C24×C7C22×C411yescharacteristic
150C23×D7C22×C412yes—
151C22×C4×C7—24no—
152C22×C4×C7—24no—
153C22×C4×C7—24no—
154C22×C4×C7—42no—
155C22×C4×C7—42no—
156C22×C4×C7—42no—
157C22×C4×C7—42no—
158C22×C4×C7—42no—
159C22×C4×C7—42no—
160C22×C4×C7—42no—
161C22×C4×C7—42no—
162C22×C4×C7—42no—
163C22×C4×C7—42no—
164C22×C4×C7—42no—
165C22×C4×C7C22⋊C411yescharacteristic
166C22×C4×C7C22⋊C411yescharacteristic
167C22×C4×C7C22⋊C411yescharacteristic
168C22×C4×C7C22⋊C411yescharacteristic
169C22×C4×C7C22⋊C411yescharacteristic
170C22×C4×C7C22⋊C411yescharacteristic
171C22×C4×C7C22⋊C411yescharacteristic
172C22×C4×C7C22⋊C411yescharacteristic
173C22×C4×C7C22⋊C411yescharacteristic
174C22×C4×C7C22⋊C411yescharacteristic
175C22×C4×C7C22⋊C411yescharacteristic
176C22×C4×C7C22⋊C411yescharacteristic
177C22×C4×C7C22×C411yescharacteristic
178C22×C4×C7C22×C411yescharacteristic
179C22×C4×C7C22×C411yescharacteristic
180C22×C4×C7C2×D411yescharacteristic
181C22×C4×C7C2×D411yescharacteristic
182C22×C4×C7C2×D411yescharacteristic
183C22×C4×C7C2×D411yescharacteristic
184C22×C4×C7C2×D411yescharacteristic
185C22×C4×C7C2×D411yescharacteristic
186C22×C4×C7C2×D411yescharacteristic
187C22×C4×C7C2×D411yescharacteristic
188C22×C4×C7C2×D411yescharacteristic
189C22×C4×C7C2×D411yescharacteristic
190C22×C4×C7C2×D411yescharacteristic
191C22×C4×C7C2×D411yescharacteristic
192C22×C4×C7C2411yescharacteristic
193C2×C22⋊D7—22no—
194C2×C22⋊D7—22no—
195C2×C22⋊D7—22no—
196C2×C22⋊D7—22no—
197C2×C22⋊D7—22no—
198C2×C22⋊D7—22no—
199C2×C22⋊D7—28no—
200C2×C22⋊D7—44no—
201C2×C22⋊D7—44no—
202C22×Dic7C22×C412yes—
203C22×Dic7C22×C412yes—
204C22×Dic7C22×C412yes—
205#1157—44no—
206#1157—44no—
207#1157—44no—
208#1157—44no—
209C2×D28—21no—
210C2×D28—21no—
211C2×D28—42no—
212C2×C4×D7—22no—
213C2×C4×D7—22no—
214C2×C4×D7—44no—
215C2×Dic14—21no—
216C2×Dic14—21no—
217C2×Dic14—42no—
218C2×C7×C8—24no—
219C2×C7×C8—44no—
220C2×C7×C8—44no—
221C2×C7×C8—44no—
222C22⋊Dic7—22no—
223C22⋊Dic7—22no—
224C22⋊Dic7—22no—
225C22⋊Dic7—22no—
226C22⋊Dic7—22no—
227C22⋊Dic7—22no—
228(C2×D7)⋊C4—22no—
229(C2×D7)⋊C4—22no—
230(C2×D7)⋊C4—22no—
231(C2×D7)⋊C4—22no—
232C4⋊Dic7—21no—
233C4⋊Dic7—21no—
234C4⋊Dic7—21no—
235C4⋊Dic7—21no—
236Dic7⋊C4—22no—
237Dic7⋊C4—22no—
238Dic7⋊C4—22no—
239Dic7⋊C4—22no—
240C4×Dic7—22no—
241C4×Dic7—22no—
242#1136—44no—
243#1136—44no—
244C2×C7⋊C8—24no—
245C2×C7⋊C8—44no—
246C22×#41—71no—
247C24×C4C2×D711yescharacteristic
248C22×M16—141no—
249C23×C8—21no—
250#525—141no—
251#525—141no—
252#525—141no—
253#525—141no—
254#525—141no—
255#525—141no—
256#525—141no—
257#525—141no—
258C2×#123—72no—
259C2×C22⋊Q8—71no—
260C2×C22⋊Q8—71no—
261C2×#121—71no—
262C2×#121—71no—
263C2×#120—72no—
264C2×C4×D4—72no—
265C2×C4×D4—72no—
266C2×#117—71no—
267#407—72no—
268#407—72no—
269#407—141no—
270#407—141no—
271C2×C22⋊C8—21no—
272C2×C22⋊C8—21no—
273C2×C22⋊C8—21no—
274C2×C22⋊C8—72no—
275C2×C22⋊C8—141no—
276C2×C22⋊C8C2×D712yes—
277C2×C22⋊C8C2×D712yes—
278C2×C22⋊C8C2×D712yes—
279#324—78no—
280#323—78no—
281C23×C7—22no—
282C23×C7—22no—
283C23×C7—22no—
284C23×C7—22no—
285C23×C7—22no—
286C23×C7—22no—
287C23×C7—22no—
288C23×C7—22no—
289C23×C7—22no—
290C23×C7—22no—
291C23×C7—22no—
292C23×C7—22no—
293C23×C7—41no—
294C23×C7—41no—
295C23×C7—41no—
296C23×C7—41no—
297C23×C7—41no—
298C23×C7—41no—
299C23×C7—41no—
300C23×C7—41no—
301C23×C7—416no—
302C23×C7C2×C22⋊C411yescharacteristic
303C23×C7C2×C22⋊C411yescharacteristic
304C23×C7C2×C22⋊C411yescharacteristic
305C23×C7C2×C22⋊C411yescharacteristic
306C23×C7C2×C22⋊C411yescharacteristic
307C23×C7C2×C22⋊C411yescharacteristic
308C23×C7#13114yes—
309C23×C7C23×C411yescharacteristic
310C22×D7—22no—
311C22×D7—24no—
312C22×D7—42no—
313C22×D7—42no—
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—22no—
329C2×C4×C7—41no—
330C2×C4×C7—41no—
331C2×C4×C7—41no—
332C2×C4×C7—41no—
333C2×C4×C7—41no—
334C2×C4×C7—41no—
335C2×C4×C7—41no—
336C2×C4×C7—41no—
337C2×C4×C7—41no—
338C2×C4×C7—41no—
339C2×C4×C7—41no—
340C2×C4×C7—41no—
341C2×C4×C7#9914yes—
342C2×C4×C7C2×C22⋊C411yescharacteristic
343C2×C4×C7C2×C22⋊C411yescharacteristic
344C2×C4×C7C2×C22⋊C411yescharacteristic
345C2×C4×C7C2×C22⋊C411yescharacteristic
346C2×C4×C7C2×C22⋊C411yescharacteristic
347C2×C4×C7C2×C22⋊C411yescharacteristic
348C2×C4×C7C22×D411yescharacteristic
349C2×C4×C7C22×D411yescharacteristic
350C22⋊D7—44no—
351C22⋊D7—44no—
352C22⋊D7—44no—
353C22⋊D7—44no—
354C22⋊D7—44no—
355C22⋊D7—44no—
356C2×Dic7—22no—
357C2×Dic7—22no—
358C2×Dic7—22no—
359C2×Dic7—24no—
360C2×Dic7—42no—
361C2×Dic7—42no—
362D28—42no—
363D28—42no—
364C4×D7—44no—
365C4×D7—44no—
366Dic14—42no—
367Dic14—42no—
368C7×C8—44no—
369C7⋊C8—44no—
370C25C4×D711yescharacteristic
371C2×#41—141no—
372C2×#41—141no—
373C2×#41—141no—
374C2×#41—141no—
375C2×#41—284no—
376C22×Q8—71no—
377C22×D4—72no—
378C22×D4—72no—
379C22×D4—72no—
380C22×D4—71no—
381C23×C4—44no—
382C23×C4—72no—
383C23×C4C4×D711yescharacteristic
384C23×C4C4×D711yescharacteristic
385C23×C4C4×D711yescharacteristic
386C23×C4D2811yescharacteristic
387C23×C4D2811yescharacteristic
388C23×C4D2811yescharacteristic
389C23×C4D2811yescharacteristic
390C23×C4C22⋊D711yescharacteristic
391C23×C4C22⋊D711yescharacteristic
392C23×C4C22⋊D711yescharacteristic
393C23×C4C22⋊D711yescharacteristic
394C23×C4C22×D711yescharacteristic
395C23×C4C22×D711yescharacteristic
396C23×C4C22×D711yescharacteristic
397C2×M16—142no—
398C2×M16—142no—
399C2×M16—284no—
400C22×C8—22no—
401C22×C8—22no—
402C22×C8—22no—
403C22×C8—44no—
404C22×C8—142no—
405#123—142no—
406#123—142no—
407#123—142no—
408#123—142no—
409C22⋊Q8—141no—
410C22⋊Q8—141no—
411C22⋊Q8—141no—
412C22⋊Q8—141no—
413C22⋊Q8—141no—
414C22⋊Q8—141no—
415C22⋊Q8—141no—
416C22⋊Q8—141no—
417#121—141no—
418#121—141no—
419#121—141no—
420#121—141no—
421#121—141no—
422#121—141no—
423#121—141no—
424#121—141no—
425#120—142no—
426#120—142no—
427#120—142no—
428#120—142no—
429C4×D4—142no—
430C4×D4—142no—
431C4×D4—142no—
432C4×D4—142no—
433C4×D4—142no—
434C4×D4—142no—
435C4×D4—142no—
436C4×D4—142no—
437#117—141no—
438#117—141no—
439#117—141no—
440#117—141no—
441C2×C4⋊C4—71no—
442C2×C4⋊C4—71no—
443C2×C4⋊C4—72no—
444C2×C4⋊C4—72no—
445C2×C22⋊C4—72no—
446C2×C22⋊C4—72no—
447C2×C22⋊C4—72no—
448C2×C22⋊C4—72no—
449C2×C22⋊C4—72no—
450C2×C42—72no—
451C22⋊C8—22no—
452C22⋊C8—22no—
453C22⋊C8—22no—
454C22⋊C8—74no—
455C22⋊C8—142no—
456C22⋊C8—142no—
457C22⋊C8—142no—
458C22⋊C8C22×D714yes—
459C22×C7—28no—
460C22×C7—21no—
461C22×C7—21no—
462C22×C7—21no—
463C22×C7—21no—
464C22×C7—21no—
465C22×C7—21no—
466C22×C7—21no—
467C22×C7—21no—
468C22×C7—21no—
469C22×C7—21no—
470C22×C7—21no—
471C22×C7—21no—
472C22×C7—21no—
473C22×C7—21no—
474C22×C7—21no—
475C22×C7—21no—
476C22×C7—44no—
477C22×C7—44no—
478C22×C7—44no—
479C22×C7—44no—
480C22×C7—44no—
481C22×C7—44no—
482C22×C7#40812yes—
483C22×C7#40812yes—
484C22×C7C2×#9912yes—
485C22×C7#41312yes—
486C22×C7C22×C22⋊C411yescharacteristic
487C22×C7C2×#13112yes—
488C2×D7—42no—
489C2×D7—42no—
490C2×D7—42no—
491C2×D7—84no—
492C4×C7—21no—
493C4×C7—21no—
494C4×C7—21no—
495C4×C7—21no—
496C4×C7—21no—
497C4×C7—21no—
498C4×C7C2×#9912yes—
499C4×C7C2×#9912yes—
500Dic7—42no—
501Dic7—42no—
502Dic7—42no—
503C24—24no—
504C24—42no—
505C24—42no—
506C24—72no—
507C24(C2×D7)⋊C411yescharacteristic
508C24(C2×D7)⋊C411yescharacteristic
509C24(C2×D7)⋊C411yescharacteristic
510C24(C2×D7)⋊C411yescharacteristic
511C24C2×C4×D711yescharacteristic
512C24C2×C4×D711yescharacteristic
513C24C2×C4×D711yescharacteristic
514#41—284no—
515#41—284no—
516#41—284no—
517#41—284no—
518C2×Q8—141no—
519C2×Q8—141no—
520C2×Q8—282no—
521C2×D4—148no—
522C2×D4—142no—
523C2×D4—142no—
524C2×D4—142no—
525C2×D4—142no—
526C2×D4—142no—
527C2×D4—142no—
528C2×D4—141no—
529C2×D4—141no—
530C2×D4—282no—
531C2×D4—284no—
532C2×D4—284no—
533C22×C4—24no—
534C22×C4—24no—
535C22×C4—24no—
536C22×C4—42no—
537C22×C4—42no—
538C22×C4—42no—
539C22×C4—42no—
540C22×C4—42no—
541C22×C4—42no—
542C22×C4—42no—
543C22×C4—42no—
544C22×C4—42no—
545C22×C4—42no—
546C22×C4—42no—
547C22×C4—72no—
548C22×C4—72no—
549C22×C4—72no—
550C22×C4—142no—
551C22×C4—142no—
552C22×C4—284no—
553C22×C4(C2×D7)⋊C411yescharacteristic
554C22×C4(C2×D7)⋊C411yescharacteristic
555C22×C4(C2×D7)⋊C411yescharacteristic
556C22×C4(C2×D7)⋊C411yescharacteristic
557C22×C4(C2×D7)⋊C411yescharacteristic
558C22×C4(C2×D7)⋊C411yescharacteristic
559C22×C4(C2×D7)⋊C411yescharacteristic
560C22×C4(C2×D7)⋊C411yescharacteristic
561C22×C4(C2×D7)⋊C411yescharacteristic
562C22×C4(C2×D7)⋊C411yescharacteristic
563C22×C4(C2×D7)⋊C411yescharacteristic
564C22×C4(C2×D7)⋊C411yescharacteristic
565C22×C4C2×C4×D711yescharacteristic
566C22×C4C2×C4×D711yescharacteristic
567C22×C4C2×C4×D711yescharacteristic
568C22×C4C2×D2811yescharacteristic
569C22×C4C2×D2811yescharacteristic
570C22×C4C2×D2811yescharacteristic
571C22×C4C2×D2811yescharacteristic
572C22×C4C2×D2811yescharacteristic
573C22×C4C2×D2811yescharacteristic
574C22×C4C2×C22⋊D711yescharacteristic
575C22×C4C2×C22⋊D711yescharacteristic
576C22×C4C2×C22⋊D711yescharacteristic
577C22×C4C2×C22⋊D711yescharacteristic
578C22×C4C2×C22⋊D711yescharacteristic
579C22×C4C2×C22⋊D711yescharacteristic
580C22×C4C23×D711yescharacteristic
581M16—284no—
582M16—284no—
583C2×C8—24no—
584C2×C8—44no—
585C2×C8—44no—
586C2×C8—44no—
587C2×C8—144no—
588C2×C8—284no—
589C4⋊C4—142no—
590C4⋊C4—142no—
591C4⋊C4—141no—
592C4⋊C4—141no—
593C4⋊C4—141no—
594C4⋊C4—141no—
595C4⋊C4—142no—
596C4⋊C4—142no—
597C22⋊C4—142no—
598C22⋊C4—142no—
599C22⋊C4—142no—
600C22⋊C4—142no—
601C22⋊C4—142no—
602C22⋊C4—142no—
603C22⋊C4—142no—
604C22⋊C4—142no—
605C22⋊C4—142no—
606C22⋊C4—142no—
607C42—142no—
608C42—142no—
609C2×C7—22no—
610C2×C7—22no—
611C2×C7—22no—
612C2×C7—22no—
613C2×C7—22no—
614C2×C7—41no—
615C2×C7—41no—
616C2×C7C2×#40811yescharacteristic
617C2×C7C22×#9911yescharacteristic
618C2×C7C2×#41311yescharacteristic
619D7—82no—
620C23—22no—
621C23—22no—
622C23—22no—
623C23—22no—
624C23—22no—
625C23—22no—
626C23—22no—
627C23—22no—
628C23—22no—
629C23—22no—
630C23—22no—
631C23—22no—
632C23—41no—
633C23—41no—
634C23—41no—
635C23—41no—
636C23—41no—
637C23—41no—
638C23—41no—
639C23—41no—
640C23—416no—
641C23—142no—
642C23—144no—
643C23—282no—
644C23—282no—
645C23#646414yes—
646C23C2×(C2×D7)⋊C411yescharacteristic
647C23C2×(C2×D7)⋊C411yescharacteristic
648C23C2×(C2×D7)⋊C411yescharacteristic
649C23C2×(C2×D7)⋊C411yescharacteristic
650C23C2×(C2×D7)⋊C411yescharacteristic
651C23C2×(C2×D7)⋊C411yescharacteristic
652C23C22×C4×D711yescharacteristic
653Q8—282no—
654Q8—282no—
655D4—282no—
656D4—284no—
657D4—284no—
658D4—284no—
659D4—284no—
660D4—284no—
661D4—284no—
662D4—282no—
663C2×C4—22no—
664C2×C4—22no—
665C2×C4—22no—
666C2×C4—22no—
667C2×C4—22no—
668C2×C4—22no—
669C2×C4—22no—
670C2×C4—22no—
671C2×C4—22no—
672C2×C4—22no—
673C2×C4—22no—
674C2×C4—22no—
675C2×C4—22no—
676C2×C4—22no—
677C2×C4—22no—
678C2×C4—41no—
679C2×C4—41no—
680C2×C4—41no—
681C2×C4—41no—
682C2×C4—41no—
683C2×C4—41no—
684C2×C4—41no—
685C2×C4—41no—
686C2×C4—41no—
687C2×C4—41no—
688C2×C4—41no—
689C2×C4—41no—
690C2×C4—144no—
691C2×C4—142no—
692C2×C4—142no—
693C2×C4—142no—
694C2×C4—284no—
695C2×C4—284no—
696C2×C4—282no—
697C2×C4—282no—
698C2×C4#638014yes—
699C2×C4C2×(C2×D7)⋊C411yescharacteristic
700C2×C4C2×(C2×D7)⋊C411yescharacteristic
701C2×C4C2×(C2×D7)⋊C411yescharacteristic
702C2×C4C2×(C2×D7)⋊C411yescharacteristic
703C2×C4C2×(C2×D7)⋊C411yescharacteristic
704C2×C4C2×(C2×D7)⋊C411yescharacteristic
705C2×C4C22×D2811yescharacteristic
706C2×C4C22×C22⋊D711yescharacteristic
707C8—44no—
708C8—284no—
709C7#1738111yescharacteristic, complemented, Sylow
710C22—28no—
711C22—21no—
712C22—21no—
713C22—21no—
714C22—21no—
715C22—21no—
716C22—21no—
717C22—21no—
718C22—21no—
719C22—21no—
720C22—21no—
721C22—21no—
722C22—21no—
723C22—21no—
724C22—21no—
725C22—21no—
726C22—21no—
727C22—44no—
728C22—44no—
729C22—44no—
730C22—44no—
731C22—44no—
732C22—44no—
733C22—282no—
734C22—282no—
735C22—282no—
736C22—564no—
737C22C2×#638012yes—
738C22#8988212yes—
739C22#8988212yes—
740C22#8990412yes—
741C22C2×#646412yes—
742C22C22×(C2×D7)⋊C411yescharacteristic
743C4—21no—
744C4—21no—
745C4—21no—
746C4—21no—
747C4—21no—
748C4—21no—
749C4—282no—
750C4—282no—
751C4—282no—
752C4C2×#638012yes—
753C4C2×#638012yes—
754C2—22no—
755C2—22no—
756C2—22no—
757C2—22no—
758C2—22no—
759C2—41no—
760C2—41no—
761C2—562no—
762C2C22×#638011yescharacteristic
763C2C2×#8988211yescharacteristic
764C2C2×#8990411yescharacteristic
subgroupG/H
centerC2×C4C2×(C2×D7)⋊C4
commutatorC23×C7C23×C4
FrattiniC22×C4C23×D7
FittingC22×C7×C22⋊C8C2
socleC22×C7C22×C22⋊C4
prime radicalC2×#90482C2
cosocleC22×C4×C7C24
hypercenterC22×C22⋊C8D7
hypocenterC7#17381
LCSG ▷ C23×C7 ▷ C2×C7 ▷ C7
UCSC1 ◁ C2×C4 ◁ C24×C4 ◁ C22×C22⋊C8

Complements

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

NH ≅ G/Ntype
2. C22×C7×C22⋊C8C2semidirect
3. C2×#89979C2semidirect
4. #11727677C2semidirect
5. #11727675C2semidirect
6. #11727674C2semidirect
7. #11727673C2semidirect
41. #89264C22semidirect
42. #89263C22semidirect
135. C22×C22⋊C8D7semidirect
709. C7#17381semidirect

Maximal subgroups

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

subgroupindex
C2×#904822
C22×C7×C22⋊C82
C2×#899792
#117276772
#117276752
#117276742
#117276732
#173817