Finite Group Databasebeta

← C2×#11737107 #14223507

Subgroups — C2×#11737107 #14223507

Order 1792.

2286 conjugacy classes of subgroups.

The subgroup lattice has 778 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#90269C211yesmaximal, characteristic, complemented
2C2×#90239C211yesmaximal, characteristic
3C2×C4×C7×SD16C211yesmaximal, characteristic, complemented
4C2×#89943C211yesmaximal, characteristic, complemented
5C2×#89947C211yesmaximal, characteristic, complemented
6C2×C4×#1143C211yesmaximal, characteristic, complemented
7C2×C4×#1142C211yesmaximal, characteristic, complemented
8#11737107C2116yesmaximal, direct product factor
9C2×#89636C211yesmaximal, characteristic, complemented
10C2×#89627C211yesmaximal, characteristic, complemented
11C2×#89579C211yesmaximal, characteristic, complemented
12C2×#89564C211yesmaximal, characteristic, complemented
13C2×#89550C211yesmaximal, characteristic, complemented
14C2×#89532C211yesmaximal, characteristic, complemented
15C2×C4×#1132C211yesmaximal, characteristic, complemented
16C2×C4×C8×D7C211yesmaximal, characteristic, complemented
17C22×#1157—21no—
18C22×C7×SD16C2211yescharacteristic
19C2×C4×C7×Q8C2211yescharacteristic
20C2×C4×C7×D4C2211yescharacteristic
21C2×#6509C2211yescharacteristic
22C2×#6507C2211yescharacteristic
23C22×#1143C2211yescharacteristic
24C2×#6503C2211yescharacteristic
25C2×#6501C2211yescharacteristic
26C22×#1142C2211yescharacteristic
27C2×C4×C22⋊D7—21no—
28C22×#1132C2211yescharacteristic
29C22×C8×D7C2211yescharacteristic
30C22×C8×D7C2211yescharacteristic
31#90269—24no—
32#90269C2218yescomplemented
33#90239—24no—
34#90239C2218yes—
35C2×#6460C2211yescharacteristic
36C2×#6459—21no—
37C2×#6458C2211yescharacteristic
38C2×#6452—21no—
39C2×#6451C2211yescharacteristic
40C2×#6451C2211yescharacteristic
41C2×#6448—21no—
42C2×#6447—21no—
43C2×C4×D28C2211yescharacteristic
44C2×#6435—21no—
45C2×C42×D7C2211yescharacteristic
46C2×C4×Dic14—21no—
47C2×C4×Dic14C2211yescharacteristic
48C4×C7×SD16C2218yescomplemented
49C2×C7×#106C2211yescharacteristic
50C2×C7×#103C2211yescharacteristic
51C2×C7×#102C2211yescharacteristic
52C2×C4×C7×C8C2211yescharacteristic
53C2×#6409C2211yescharacteristic
54C2×#6406C2211yescharacteristic
55#89947C2218yescomplemented
56#89943C2218yescomplemented
57C2×#6395C2211yescharacteristic
58C2×#6391C2211yescharacteristic
59C2×#6390C2211yescharacteristic
60C2×C8×Dic7C2211yescharacteristic
61C2×C8×Dic7C2211yescharacteristic
62C4×#1143C2218yescomplemented
63C4×#1142C2218yescomplemented
64C2×#6384C2211yescharacteristic
65C2×#6383C2211yescharacteristic
66C2×#6382C2211yescharacteristic
67C2×#6382C2211yescharacteristic
68C2×C4×C7⋊C8C2211yescharacteristic
69#89636C2218yescomplemented
70#89627C2218yescomplemented
71#89579C2218yescomplemented
72#89564C2218yescomplemented
73#89550C2218yescomplemented
74#89532C2218yescomplemented
75C4×#1132C2218yescomplemented
76C4×C8×D7C2218yescomplemented
77C2×#3167—71nomaximal, Sylow
78C22×C7×Q8C2311yescharacteristic
79C22×C7×D4C2311yescharacteristic
80C23×C4×C7—21no—
81C22×C22⋊D7—21no—
82C22×C22⋊D7—21no—
83C22×C22⋊D7—21no—
84C2×#1157—28no—
85C2×#1157—48no—
86C22×D28—21no—
87C22×D28C2311yescharacteristic
88C22×C4×D7—21no—
89C22×C4×D7D411yescharacteristic
90C22×C4×D7D411yescharacteristic
91C22×C4×D7C2311yescharacteristic
92C22×Dic14—21no—
93C22×Dic14—21no—
94C22×Dic14C2311yescharacteristic
95C2×C7×SD16—24no—
96C2×C7×SD16C2314yes—
97C22×C7×C8C2311yescharacteristic
98C22×C7×C8C2311yescharacteristic
99C4×C7×Q8—22no—
100C4×C7×Q8C2314yes—
101C4×C7×D4—22no—
102C4×C7×D4C2314yes—
103C2×C7×C4⋊C4—21no—
104C2×C7×C4⋊C4C2311yescharacteristic
105C2×C7×C4⋊C4C2311yescharacteristic
106C2×C7×C22⋊C4—21no—
107C2×C42×C7—21no—
108C2×C42×C7C2311yescharacteristic
109C2×C22⋊Dic7—21no—
110#6509—22no—
111#6509C2314yes—
112#6507—22no—
113#6507C2314yes—
114C2×#1143—24no—
115C2×#1143C2314yes—
116#6503—22no—
117#6503C2314yes—
118#6501—22no—
119#6501C2314yes—
120C2×#1142—24no—
121C2×#1142C2314yes—
122C4×C22⋊D7—28no—
123C2×(C2×D7)⋊C4—21no—
124C2×(C2×D7)⋊C4—21no—
125C2×(C2×D7)⋊C4—21no—
126C2×(C2×D7)⋊C4—21no—
127C2×C4⋊Dic7—21no—
128C2×C4⋊Dic7C2311yescharacteristic
129C2×C4⋊Dic7C2311yescharacteristic
130C2×Dic7⋊C4—21no—
131C2×Dic7⋊C4—21no—
132C2×Dic7⋊C4—21no—
133C2×Dic7⋊C4—21no—
134C2×Dic7⋊C4—21no—
135C2×Dic7⋊C4—21no—
136C2×C4×Dic7—21no—
137C2×C4×Dic7D411yescharacteristic
138C2×C4×Dic7D411yescharacteristic
139C2×C4×Dic7C2311yescharacteristic
140C22×C7⋊C8C2311yescharacteristic
141C22×C7⋊C8C2311yescharacteristic
142C2×#1132—24no—
143C2×#1132C2314yes—
144C2×C8×D7—24no—
145C2×C8×D7—24no—
146C2×C8×D7C2314yes—
147C2×C8×D7C2314yes—
148#6460—22no—
149#6460C2314yes—
150#6459—28no—
151#6458—22no—
152#6458C2314yes—
153#6452—28no—
154#6451—22no—
155#6451—22no—
156#6451C2314yes—
157#6451C2314yes—
158#6448—28no—
159#6447—28no—
160C4×D28—22no—
161C4×D28C2314yes—
162#6435—28no—
163C42×D7D414yes—
164C42×D7C2314yes—
165C4×Dic14—22no—
166C4×Dic14—28no—
167C4×Dic14C2314yes—
168C7×#106C2314yes—
169C7×#103C2314yes—
170C7×#102C2314yes—
171C4×C7×C8C2314yes—
172#6409C2314yes—
173#6406C2314yes—
174#6395C2314yes—
175#6391C2314yes—
176#6390C2314yes—
177C8×Dic7C2314yes—
178C8×Dic7C2314yes—
179#6384C2314yes—
180#6383C2314yes—
181#6382C2314yes—
182#6382C2314yes—
183C4×C7⋊C8C2314yes—
184C2×#533—71no—
185C2×#532—71no—
186#3167—716no—
187C2×#498—71no—
188C2×#492—71no—
189C2×#487—71no—
190C2×#486—71no—
191C2×#465—71no—
192C2×#465—71no—
193C2×#465—71no—
194C2×#465—71no—
195C2×C4×SD16—71no—
196C2×C4×SD16—71no—
197C2×C4×SD16—71no—
198C2×C4×SD16D711yescharacteristic, complemented
199C22×C4×C8—71no—
200C24×C7—21no—
201C23×D7—21no—
202C23×D7C2×D411yescharacteristic
203C2×C7×Q8—21no—
204C2×C7×Q8—22no—
205C2×C7×Q8—22no—
206C2×C7×Q8C2412yes—
207C2×C7×D4—21no—
208C2×C7×D4—22no—
209C2×C7×D4—22no—
210C2×C7×D4C2412yes—
211C22×C4×C7—21no—
212C22×C4×C7—21no—
213C22×C4×C7—21no—
214C22×C4×C7—24no—
215C22×C4×C7—44no—
216C22×C4×C7C2×D411yescharacteristic
217C22×C4×C7C2×D411yescharacteristic
218C22×C4×C7C2411yescharacteristic
219C2×C22⋊D7—24no—
220C2×C22⋊D7—24no—
221C2×C22⋊D7—24no—
222C2×C22⋊D7—44no—
223C2×C22⋊D7—44no—
224C2×C22⋊D7—44no—
225C22×Dic7—21no—
226C22×Dic7—21no—
227C22×Dic7—21no—
228C22×Dic7C2×D411yescharacteristic
229C22×Dic7C2×D411yescharacteristic
230C22×Dic7C2×D411yescharacteristic
231#1157—432no—
232C2×D28—22no—
233C2×D28—22no—
234C2×D28—24no—
235C2×D28—21no—
236C2×D28—44no—
237C2×D28C2412yes—
238C2×C4×D7—22no—
239C2×C4×D7—22no—
240C2×C4×D7—24no—
241C2×C4×D7—24no—
242C2×C4×D7—44no—
243C2×C4×D7SD1618yescomplemented
244C2×C4×D7C2×D412yes—
245C2×C4×D7C2×D414yes—
246C2×C4×D7C2×D414yes—
247C2×C4×D7C2412yes—
248C2×Dic14—22no—
249C2×Dic14—22no—
250C2×Dic14—21no—
251C2×Dic14—24no—
252C2×Dic14—24no—
253C2×Dic14—44no—
254C2×Dic14—44no—
255C2×Dic14C2412yes—
256C7×SD16—28no—
257C2×C7×C8—22no—
258C2×C7×C8#4114yescomplemented
259C2×C7×C8C2412yes—
260C2×C7×C8C2412yes—
261C7×C4⋊C4—21no—
262C7×C4⋊C4—21no—
263C7×C4⋊C4—24no—
264C7×C4⋊C4C2412yes—
265C7×C4⋊C4C2412yes—
266C7×C22⋊C4—24no—
267C42×C7—24no—
268C42×C7C2×D412yes—
269C42×C7C2412yes—
270C22⋊Dic7—24no—
271#1143—28no—
272#1142—28no—
273(C2×D7)⋊C4—24no—
274(C2×D7)⋊C4—24no—
275(C2×D7)⋊C4—24no—
276(C2×D7)⋊C4—24no—
277C4⋊Dic7—21no—
278C4⋊Dic7—21no—
279C4⋊Dic7—24no—
280C4⋊Dic7C2412yes—
281C4⋊Dic7C2412yes—
282Dic7⋊C4—24no—
283Dic7⋊C4—24no—
284Dic7⋊C4—24no—
285Dic7⋊C4—24no—
286Dic7⋊C4—24no—
287Dic7⋊C4—24no—
288C4×Dic7—24no—
289C4×Dic7C2×D414yes—
290C4×Dic7C2×D412yes—
291C4×Dic7C2×D414yes—
292C4×Dic7C2412yes—
293C2×C7⋊C8—22no—
294C2×C7⋊C8#4114yescomplemented
295C2×C7⋊C8C2412yes—
296C2×C7⋊C8C2412yes—
297#1132—28no—
298C8×D7—28no—
299C8×D7—28no—
300C22×#41—141no—
301C22×SD16—71no—
302C22×SD16—71no—
303C22×SD16—71no—
304C22×SD16C2×D711yescharacteristic
305C23×C8—71no—
306C23×C8—71no—
307#533—78no—
308#533—144no—
309#532—78no—
310#532—144no—
311C2×C4⋊Q8—71no—
312C2×C4⋊Q8—71no—
313C2×C4⋊Q8—71no—
314C2×#127—71no—
315C2×#125—141no—
316C2×#124—141no—
317C2×C22⋊Q8—71no—
318C2×C22⋊Q8—71no—
319C2×C22⋊Q8—141no—
320C2×#121—71no—
321C2×#121—71no—
322C2×#121—141no—
323C2×C4×Q8—71no—
324C2×C4×Q8—141no—
325C2×C4×Q8C2×D711yescharacteristic
326C2×C4×D4—71no—
327C2×C4×D4—141no—
328C2×C4×D4C2×D711yescharacteristic
329C2×#117—141no—
330C22×C42—71no—
331#498—78no—
332#492—78no—
333#487—78no—
334#486—78no—
335#465—78no—
336#465—78no—
337#465—78no—
338#465—78no—
339C4×SD16—78no—
340C4×SD16—78no—
341C4×SD16—78no—
342C4×SD16C2×D718yescomplemented
343C2×#106—71no—
344C2×#106—71no—
345C2×#106—71no—
346C2×#106C2×D711yescharacteristic
347C2×#103—71no—
348C2×#103—71no—
349C2×#103—71no—
350C2×#103C2×D711yescharacteristic
351C2×#102—71no—
352C2×#102—71no—
353C2×#102—71no—
354C2×#102C2×D711yescharacteristic
355C2×C4×C8—71no—
356C2×C4×C8—71no—
357C2×C4×C8—71no—
358C2×C4×C8—78no—
359C2×C4×C8C2×D711yescharacteristic
360C23×C7—22no—
361C23×C7—42no—
362C23×C7—42no—
363C23×C7—42no—
364C23×C7C22×D411yescharacteristic
365C22×D7—22no—
366C22×D7—22no—
367C22×D7—22no—
368C22×D7—42no—
369C22×D7—42no—
370C22×D7—42no—
371C22×D7C2×SD1614yes—
372C22×D7C22×D412yes—
373C7×Q8—22no—
374C7×Q8—22no—
375C7×Q8—42no—
376C7×D4—22no—
377C7×D4—22no—
378C7×D4—42no—
379C2×C4×C7—22no—
380C2×C4×C7—22no—
381C2×C4×C7—22no—
382C2×C4×C7—22no—
383C2×C4×C7—42no—
384C2×C4×C7—42no—
385C2×C4×C7—42no—
386C2×C4×C7—48no—
387C2×C4×C7C2×SD1614yes—
388C2×C4×C7C22×D412yes—
389C2×C4×C7C22×D411yescharacteristic
390C2×C4×C7C22×D412yes—
391C2×C4×C7C2×#4112yes—
392C2×C4×C7C2×#4112yes—
393C2×C4×C7C2511yescharacteristic
394C22⋊D7—48no—
395C22⋊D7—48no—
396C22⋊D7—48no—
397C2×Dic7—22no—
398C2×Dic7—22no—
399C2×Dic7—22no—
400C2×Dic7—22no—
401C2×Dic7—42no—
402C2×Dic7—42no—
403C2×Dic7—42no—
404C2×Dic7C2×SD1614yes—
405C2×Dic7#13514yes—
406C2×Dic7C22×D412yes—
407C2×Dic7C22×D412yes—
408C2×Dic7C22×D412yes—
409D28—22no—
410D28—22no—
411D28—48no—
412D28—42no—
413C4×D7—24no—
414C4×D7—22no—
415C4×D7—22no—
416C4×D7—28no—
417C4×D7—48no—
418C4×D7C2×SD16116yescomplemented
419Dic14—22no—
420Dic14—22no—
421Dic14—42no—
422Dic14—48no—
423Dic14—48no—
424C7×C8—22no—
425C7×C8C2×#4114yescomplemented
426C7⋊C8—22no—
427C7⋊C8C2×#4114yescomplemented
428C2×#41—148no—
429C2×#41—288no—
430C22×Q8—71no—
431C22×Q8—141no—
432C22×Q8—141no—
433C22×Q8C22×D711yescharacteristic
434C22×D4—71no—
435C22×D4—141no—
436C22×D4—141no—
437C22×D4—141no—
438C22×D4—141no—
439C22×D4C22×D711yescharacteristic
440C23×C4—21no—
441C23×C4—71no—
442C23×C4—71no—
443C23×C4—71no—
444C23×C4—141no—
445C2×SD16—24no—
446C2×SD16—74no—
447C2×SD16—74no—
448C2×SD16—74no—
449C2×SD16—144no—
450C2×SD16—144no—
451C2×SD16—144no—
452C2×SD16C22×D714yes—
453C22×C8—71no—
454C22×C8—71no—
455C22×C8—74no—
456C22×C8—74no—
457C22×C8—144no—
458C22×C8—144no—
459C22×C8C22×D711yescharacteristic
460C22×C8C22×D711yescharacteristic
461C4⋊Q8—74no—
462C4⋊Q8—74no—
463C4⋊Q8—74no—
464C4⋊Q8—142no—
465C4⋊Q8—142no—
466C4⋊Q8—142no—
467#127—74no—
468#127—142no—
469#125—148no—
470#124—148no—
471C22⋊Q8—74no—
472C22⋊Q8—74no—
473C22⋊Q8—142no—
474C22⋊Q8—148no—
475C22⋊Q8—142no—
476#121—74no—
477#121—74no—
478#121—148no—
479#121—142no—
480#121—142no—
481C4×Q8—22no—
482C4×Q8—74no—
483C4×Q8—148no—
484C4×Q8—142no—
485C4×Q8C22×D714yes—
486C4×D4—22no—
487C4×D4—74no—
488C4×D4—148no—
489C4×D4—142no—
490C4×D4C22×D714yes—
491#117—148no—
492C2×C4⋊C4—21no—
493C2×C4⋊C4—71no—
494C2×C4⋊C4—71no—
495C2×C4⋊C4—141no—
496C2×C4⋊C4—141no—
497C2×C4⋊C4—141no—
498C2×C4⋊C4—141no—
499C2×C4⋊C4—141no—
500C2×C4⋊C4—141no—
501C2×C4⋊C4—141no—
502C2×C4⋊C4C22×D711yescharacteristic
503C2×C4⋊C4C22×D711yescharacteristic
504C2×C22⋊C4—21no—
505C2×C22⋊C4—141no—
506C2×C22⋊C4—141no—
507C2×C22⋊C4—141no—
508C2×C22⋊C4—141no—
509C2×C22⋊C4—141no—
510C2×C42—21no—
511C2×C42—71no—
512C2×C42—71no—
513C2×C42—71no—
514C2×C42—74no—
515C2×C42—74no—
516C2×C42—141no—
517C2×C42C22×D711yescharacteristic
518#106—74no—
519#106—74no—
520#106—74no—
521#106C22×D714yes—
522#103—74no—
523#103—74no—
524#103—74no—
525#103C22×D714yes—
526#102—74no—
527#102—74no—
528#102—74no—
529#102C22×D714yes—
530C4×C8—74no—
531C4×C8—74no—
532C4×C8—74no—
533C4×C8C22×D714yes—
534C22×C7—42no—
535C22×C7—42no—
536C22×C7—42no—
537C22×C7—84no—
538C22×C7#53212yes—
539C22×C7C22×SD1612yes—
540C22×C7C2×#13512yes—
541C22×C7C23×D411yescharacteristic
542C2×D7—28no—
543C2×D7—22no—
544C2×D7—22no—
545C2×D7—42no—
546C2×D7—42no—
547C2×D7—42no—
548C2×D7—84no—
549C2×D7C22×SD1614yes—
550C4×C7—22no—
551C4×C7—42no—
552C4×C7—42no—
553C4×C7—42no—
554C4×C7#53212yes—
555C4×C7C22×SD1614yes—
556C4×C7C22×#4111yescharacteristic
557C4×C7C22×#4111yescharacteristic
558Dic7—22no—
559Dic7—42no—
560Dic7—42no—
561Dic7—42no—
562Dic7C22×SD1614yes—
563Dic7C2×#13514yes—
564C24—21no—
565C24—71no—
566C24—141no—
567#41—2832no—
568C2×Q8—21no—
569C2×Q8—22no—
570C2×Q8—22no—
571C2×Q8—72no—
572C2×Q8—144no—
573C2×Q8—144no—
574C2×Q8—141no—
575C2×Q8—142no—
576C2×Q8—142no—
577C2×Q8—284no—
578C2×Q8—284no—
579C2×Q8C23×D712yes—
580C2×D4—22no—
581C2×D4—21no—
582C2×D4—22no—
583C2×D4—72no—
584C2×D4—144no—
585C2×D4—144no—
586C2×D4—144no—
587C2×D4—144no—
588C2×D4—142no—
589C2×D4—141no—
590C2×D4—142no—
591C2×D4—284no—
592C2×D4—284no—
593C2×D4—284no—
594C2×D4—284no—
595C2×D4C23×D712yes—
596C22×C4—21no—
597C22×C4—21no—
598C22×C4—21no—
599C22×C4—24no—
600C22×C4—44no—
601C22×C4—71no—
602C22×C4—71no—
603C22×C4—78no—
604C22×C4—74no—
605C22×C4—71no—
606C22×C4—74no—
607C22×C4—72no—
608C22×C4—72no—
609C22×C4—144no—
610C22×C4—142no—
611C22×C4—142no—
612C22×C4—141no—
613C22×C4—141no—
614C22×C4—141no—
615C22×C4—144no—
616C22×C4—284no—
617C22×C4D4×D711yescharacteristic
618C22×C4D4×D711yescharacteristic
619C22×C4C23×D711yescharacteristic
620SD16—28no—
621SD16—148no—
622SD16—148no—
623SD16—148no—
624C2×C8—22no—
625C2×C8—74no—
626C2×C8—72no—
627C2×C8—72no—
628C2×C8—148no—
629C2×C8—142no—
630C2×C8—148no—
631C2×C8#115714yescomplemented
632C2×C8C23×D712yes—
633C2×C8C23×D712yes—
634C4⋊C4—24no—
635C4⋊C4—21no—
636C4⋊C4—21no—
637C4⋊C4—72no—
638C4⋊C4—72no—
639C4⋊C4—144no—
640C4⋊C4—144no—
641C4⋊C4—144no—
642C4⋊C4—144no—
643C4⋊C4—144no—
644C4⋊C4—144no—
645C4⋊C4—144no—
646C4⋊C4—141no—
647C4⋊C4—141no—
648C4⋊C4C23×D712yes—
649C4⋊C4C23×D712yes—
650C22⋊C4—24no—
651C22⋊C4—144no—
652C22⋊C4—144no—
653C22⋊C4—144no—
654C22⋊C4—144no—
655C22⋊C4—144no—
656C42—24no—
657C42—74no—
658C42—74no—
659C42—72no—
660C42—72no—
661C42—144no—
662C42D4×D712yes—
663C42C23×D712yes—
664C2×C7—82no—
665C2×C7#316714yescomplemented
666C2×C7C2×#53211yescharacteristic
667C2×C7C23×SD1611yescharacteristic
668C2×C7C22×#13511yescharacteristic
669D7—24no—
670D7—82no—
671C23—22no—
672C23—42no—
673C23—42no—
674C23—42no—
675C23—74no—
676C23—72no—
677C23—142no—
678C23—142no—
679C23—142no—
680C23—282no—
681C23—282no—
682C23—282no—
683C23C2×D4×D711yescharacteristic
684Q8—22no—
685Q8—22no—
686Q8—42no—
687Q8—142no—
688Q8—142no—
689Q8—288no—
690Q8—288no—
691Q8—282no—
692D4—22no—
693D4—22no—
694D4—42no—
695D4—142no—
696D4—142no—
697D4—288no—
698D4—288no—
699D4—288no—
700D4—288no—
701D4—282no—
702C2×C4—22no—
703C2×C4—22no—
704C2×C4—22no—
705C2×C4—22no—
706C2×C4—42no—
707C2×C4—42no—
708C2×C4—42no—
709C2×C4—48no—
710C2×C4—74no—
711C2×C4—74no—
712C2×C4—72no—
713C2×C4—72no—
714C2×C4—716no—
715C2×C4—72no—
716C2×C4—148no—
717C2×C4—142no—
718C2×C4—144no—
719C2×C4—142no—
720C2×C4—142no—
721C2×C4—142no—
722C2×C4—142no—
723C2×C4—142no—
724C2×C4—282no—
725C2×C4—282no—
726C2×C4—282no—
727C2×C4—288no—
728C2×C4D7×SD1614yes—
729C2×C4C2×#115712yes—
730C2×C4C2×D4×D712yes—
731C2×C4C2×D4×D712yes—
732C2×C4C2×D4×D711yescharacteristic
733C2×C4D7×#4112yes—
734C2×C4C24×D711yescharacteristic
735C8—22no—
736C8—74no—
737C8—142no—
738C8C2×#115714yescomplemented
739C7C2×#316711yescharacteristic, complemented, Sylow
740C22—42no—
741C22—42no—
742C22—42no—
743C22—74no—
744C22—84no—
745C22—148no—
746C22—142no—
747C22—142no—
748C22—282no—
749C22—282no—
750C22—282no—
751C22—564no—
752C22#9023912yes—
753C22C2×D7×SD1612yes—
754C22D7×#13512yes—
755C22C22×D4×D711yescharacteristic
756C4—22no—
757C4—42no—
758C4—42no—
759C4—42no—
760C4—74no—
761C4—74no—
762C4—142no—
763C4—282no—
764C4—282no—
765C4—282no—
766C4#9023912yes—
767C4C2×D7×SD1614yes—
768C4C22×#115711yescharacteristic
769C4C2×D7×#4111yescharacteristic
770C2—82no—
771C2—144no—
772C2—562no—
773C2#1173710714yesdirect product factor
774C2C2×#9023911yescharacteristic
775C2C22×D7×SD1611yescharacteristic
776C2C2×D7×#13511yescharacteristic
subgroupG/H
centerC22×C4D4×D7
commutator, cosocleC2×C4×C7C25
FrattiniC2×C4C24×D7
FittingC2×C4×C7×SD16C2
socleC23×C7C22×D4
prime radicalC2×#90239C2
hypercenterC2×C4×SD16D7
hypocenterC7C2×#3167
LCSG ▷ C2×C4×C7 ▷ C2×C7 ▷ C7
UCSC1 ◁ C22×C4 ◁ C2×C42 ◁ C2×C4×SD16

Complements

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

NH ≅ G/Ntype
1. C2×#90269C2semidirect
3. C2×C4×C7×SD16C2semidirect
4. C2×#89943C2semidirect
5. C2×#89947C2semidirect
6. C2×C4×#1143C2semidirect
7. C2×C4×#1142C2semidirect
8. #11737107C2direct (N × H)
9. C2×#89636C2semidirect
10. C2×#89627C2semidirect
11. C2×#89579C2semidirect
12. C2×#89564C2semidirect
13. C2×#89550C2semidirect
14. C2×#89532C2semidirect
15. C2×C4×#1132C2semidirect
16. C2×C4×C8×D7C2semidirect
32. #90269C22semidirect
48. C4×C7×SD16C22semidirect
55. #89947C22semidirect
56. #89943C22semidirect
62. C4×#1143C22semidirect
63. C4×#1142C22semidirect
69. #89636C22semidirect
70. #89627C22semidirect
71. #89579C22semidirect
72. #89564C22semidirect
73. #89550C22semidirect
74. #89532C22semidirect
75. C4×#1132C22semidirect
76. C4×C8×D7C22semidirect
198. C2×C4×SD16D7semidirect
243. C2×C4×D7SD16semidirect
258. C2×C7×C8#41semidirect
294. C2×C7⋊C8#41semidirect
342. C4×SD16C2×D7semidirect
418. C4×D7C2×SD16semidirect
425. C7×C8C2×#41semidirect
427. C7⋊C8C2×#41semidirect
631. C2×C8#1157semidirect
665. C2×C7#3167semidirect
738. C8C2×#1157semidirect
739. C7C2×#3167semidirect
773. C2#11737107direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#902692
C2×#902392
C2×C4×C7×SD162
C2×#899432
C2×#899472
C2×C4×#11432
C2×C4×#11422
#117371072
C2×#896362
C2×#896272
C2×#895792
C2×#895642
C2×#895502
C2×#895322
C2×C4×#11322
C2×C4×C8×D72
C2×#31677