Finite Group Databasebeta

← C2×#11738880 #14232212

Subgroups — C2×#11738880 #14232212

Order 1792.

2158 conjugacy classes of subgroups.

The subgroup lattice has 756 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#90326C211yesmaximal, characteristic, complemented
2C2×#90198C211yesmaximal, characteristic
3C2×C7×#483C211yesmaximal, characteristic, complemented
4C2×#89820C211yesmaximal, characteristic, complemented
5C22×#6382C211yesmaximal, characteristic, complemented
6#11738880C2116yesmaximal, direct product factor
7C2×#89642C211yesmaximal, characteristic, complemented
8C2×#89635C211yesmaximal, characteristic, complemented
9C2×D7×#106C211yesmaximal, characteristic, complemented
10C2×#89627C211yesmaximal, characteristic, complemented
11C2×#89577C211yesmaximal, characteristic, complemented
12C2×#89579C211yesmaximal, characteristic, complemented
13C2×#89563C211yesmaximal, characteristic, complemented
14C2×#89560C211yesmaximal, characteristic, complemented
15C2×(C22⋊D7)⋊C8C211yesmaximal, characteristic, complemented
16C2×#89507C211yesmaximal, characteristic, complemented
17C22×#1157—21no—
18C2×C7×C22⋊Q8C2211yescharacteristic
19C22×C7×C4⋊C4C2211yescharacteristic
20C2×#6509C2211yescharacteristic
21C2×Q8×Dic7C2211yescharacteristic
22C22×#1143C2211yescharacteristic
23C2×#6493C2211yescharacteristic
24C2×#6492—21no—
25C2×C4×C22⋊D7C2211yescharacteristic
26C22×C4⋊Dic7C2211yescharacteristic
27C23×C7⋊C8C2211yescharacteristic
28C22×C8×D7C2211yescharacteristic
29#90326—24no—
30#90326C2218yescomplemented
31C2×#6460—21no—
32C2×#6459—21no—
33#90198—24no—
34#90198C2218yes—
35C2×#6458C2211yescharacteristic
36C2×#6457—21no—
37C2×#6456C2211yescharacteristic
38C2×D7×C4⋊C4C2211yescharacteristic
39C2×D7×C4⋊C4C2211yescharacteristic
40C2×#6452—21no—
41C2×#6451C2211yescharacteristic
42C2×#6451C2211yescharacteristic
43C2×(C22⋊D7)⋊C4—21no—
44C2×#6441—21no—
45C7×#483C2218yescomplemented
46C2×C7×#106C2211yescharacteristic
47C2×C7×#106C2211yescharacteristic
48C2×C7×#103C2211yescharacteristic
49C2×C7×#103C2211yescharacteristic
50C2×C7×C22⋊C8C2211yescharacteristic
51C2×#6409C2211yescharacteristic
52C2×#6395C2211yescharacteristic
53C2×#6395C2211yescharacteristic
54C2×(C2×D7)⋊C8C2211yescharacteristic
55C2×#6391C2211yescharacteristic
56C2×#6391C2211yescharacteristic
57C2×Dic7⋊C8C2211yescharacteristic
58C2×C8×Dic7C2211yescharacteristic
59#89820C2218yescomplemented
60C2×#6383C2211yescharacteristic
61C2×#6382C2211yescharacteristic
62C2×#6382C2211yescharacteristic
63C2×#6382C2211yescharacteristic
64C2×#6382C2211yescharacteristic
65C2×#6382C2211yescharacteristic
66C2×#6382C2218yescomplemented
67#89642C2218yescomplemented
68#89635C2218yescomplemented
69D7×#106C2218yescomplemented
70#89627C2218yescomplemented
71#89579C2218yescomplemented
72#89577C2218yescomplemented
73#89563C2218yescomplemented
74#89560C2218yescomplemented
75#89507C2218yescomplemented
76(C22⋊D7)⋊C8C2218yescomplemented
77C2×#3335—71nomaximal, Sylow
78C22×C7×Q8C2311yescharacteristic
79C23×C4×C7—21no—
80C23×C4×C7C2311yescharacteristic
81C22×C22⋊D7—21no—
82C22×C22⋊D7D411yescharacteristic
83C23×Dic7—21no—
84C2×#1157—28no—
85C2×#1157—48no—
86C22×D28—21no—
87C22×D28C2311yescharacteristic
88C22×C4×D7—21no—
89C22×C4×D7—21no—
90C22×C4×D7—21no—
91C22×C4×D7C2311yescharacteristic
92C22×Dic14—21no—
93C22×Dic14—21no—
94C22×C7×C8C2311yescharacteristic
95C22×C7×C8C2311yescharacteristic
96C7×C22⋊Q8—22no—
97C7×C22⋊Q8C2314yes—
98C2×C7×C4⋊C4—21no—
99C2×C7×C4⋊C4—21no—
100C2×C7×C4⋊C4—22no—
101C2×C7×C4⋊C4C2314yes—
102C2×C7×C4⋊C4C2311yescharacteristic
103C2×C7×C4⋊C4C2311yescharacteristic
104C2×C7×C4⋊C4C2311yescharacteristic
105C2×C7×C22⋊C4—21no—
106C2×C22⋊Dic7D411yescharacteristic
107#6509—22no—
108#6509C2314yes—
109Q8×Dic7—22no—
110Q8×Dic7C2314yes—
111C2×#1143—24no—
112C2×#1143C2314yes—
113#6493—22no—
114#6493C2314yes—
115#6492—28no—
116C4×C22⋊D7D414yes—
117C4×C22⋊D7C2314yes—
118C2×(C2×D7)⋊C4—21no—
119C2×(C2×D7)⋊C4—21no—
120C2×(C2×D7)⋊C4—21no—
121C2×(C2×D7)⋊C4—21no—
122C2×(C2×D7)⋊C4D411yescharacteristic
123C2×C4⋊Dic7—21no—
124C2×C4⋊Dic7—22no—
125C2×C4⋊Dic7—21no—
126C2×C4⋊Dic7C2311yescharacteristic
127C2×C4⋊Dic7C2311yescharacteristic
128C2×C4⋊Dic7C2311yescharacteristic
129C2×C4⋊Dic7C2314yes—
130C2×Dic7⋊C4—21no—
131C2×Dic7⋊C4—21no—
132C2×Dic7⋊C4—21no—
133C2×Dic7⋊C4—21no—
134C2×Dic7⋊C4—21no—
135C2×Dic7⋊C4D411yescharacteristic
136C2×C4×Dic7—21no—
137C2×C4×Dic7C2311yescharacteristic
138C22×C7⋊C8—24no—
139C22×C7⋊C8C2311yescharacteristic
140C22×C7⋊C8C2314yes—
141C22×C7⋊C8C2311yescharacteristic
142C2×C8×D7—24no—
143C2×C8×D7C2314yes—
144#6460—28no—
145#6459—28no—
146#6458—22no—
147#6458C2314yes—
148#6457—28no—
149#6456—22no—
150#6456C2314yes—
151D7×C4⋊C4—22no—
152D7×C4⋊C4—22no—
153D7×C4⋊C4C2314yes—
154D7×C4⋊C4C2314yes—
155#6452—28no—
156#6451—22no—
157#6451—22no—
158#6451C2314yes—
159#6451C2314yes—
160(C22⋊D7)⋊C4—28no—
161#6441—28no—
162C7×#106C2314yes—
163C7×#106C2314yes—
164C7×#103C2314yes—
165C7×#103C2314yes—
166C7×C22⋊C8C2314yes—
167#6409C2314yes—
168#6395C2314yes—
169#6395C2314yes—
170(C2×D7)⋊C8C2314yes—
171#6391C2314yes—
172#6391C2314yes—
173Dic7⋊C8C2314yes—
174C8×Dic7C2314yes—
175#6383C2314yes—
176#6382C2314yes—
177#6382C2314yes—
178#6382C2314yes—
179#6382C2314yes—
180#6382C2314yes—
181C2×#554—71no—
182C2×#547—71no—
183#3335—716no—
184C2×#498—71no—
185C2×#481—71no—
186C2×#481—71no—
187C2×#483—71no—
188C2×#483D711yescharacteristic, complemented
189C2×#475—71no—
190C2×#476—71no—
191C2×#465—71no—
192C2×#465—71no—
193C2×C4×SD16—71no—
194C2×C8×D4—71no—
195C22×#106—71no—
196C22×#106—71no—
197C24×C7C2×D411yescharacteristic
198C23×D7—21no—
199C23×D7C2×D411yescharacteristic
200C2×C7×Q8—21no—
201C2×C7×Q8—22no—
202C2×C7×Q8—22no—
203C2×C7×Q8C2412yes—
204C22×C4×C7—22no—
205C22×C4×C7—22no—
206C22×C4×C7—21no—
207C22×C4×C7—21no—
208C22×C4×C7—21no—
209C22×C4×C7—21no—
210C22×C4×C7—24no—
211C22×C4×C7—44no—
212C22×C4×C7C2×D411yescharacteristic
213C22×C4×C7C2×D412yes—
214C22×C4×C7C2412yes—
215C22×C4×C7C2411yescharacteristic
216C2×C22⋊D7—24no—
217C2×C22⋊D7—44no—
218C2×C22⋊D7SD1618yescomplemented
219C2×C22⋊D7C2×D414yes—
220C22×Dic7—21no—
221C22×Dic7—21no—
222C22×Dic7—21no—
223C22×Dic7—24no—
224C22×Dic7—82no—
225C22×Dic7C2×D411yescharacteristic
226C22×Dic7C2×D411yescharacteristic
227C22×Dic7C2×D411yescharacteristic
228#1157—432no—
229C2×D28—22no—
230C2×D28—22no—
231C2×D28—24no—
232C2×D28—21no—
233C2×D28—44no—
234C2×D28C2412yes—
235C2×C4×D7—22no—
236C2×C4×D7—22no—
237C2×C4×D7—24no—
238C2×C4×D7—24no—
239C2×C4×D7—24no—
240C2×C4×D7—44no—
241C2×C4×D7—44no—
242C2×C4×D7—82no—
243C2×C4×D7C2×D412yes—
244C2×C4×D7C2412yes—
245C2×Dic14—24no—
246C2×Dic14—24no—
247C2×Dic14—44no—
248C2×Dic14—82no—
249C2×C7×C8—22no—
250C2×C7×C8—22no—
251C2×C7×C8C2412yes—
252C2×C7×C8C2412yes—
253C7×C4⋊C4—21no—
254C7×C4⋊C4—21no—
255C7×C4⋊C4—24no—
256C7×C4⋊C4—21no—
257C7×C4⋊C4—24no—
258C7×C4⋊C4C2412yes—
259C7×C4⋊C4C2412yes—
260C7×C4⋊C4C2412yes—
261C7×C22⋊C4—24no—
262C22⋊Dic7C2×D414yes—
263#1143—28no—
264(C2×D7)⋊C4—24no—
265(C2×D7)⋊C4—24no—
266(C2×D7)⋊C4—24no—
267(C2×D7)⋊C4—24no—
268(C2×D7)⋊C4C2×D414yes—
269C4⋊Dic7—21no—
270C4⋊Dic7—21no—
271C4⋊Dic7—24no—
272C4⋊Dic7—21no—
273C4⋊Dic7—24no—
274C4⋊Dic7C2412yes—
275C4⋊Dic7C2412yes—
276C4⋊Dic7C2412yes—
277Dic7⋊C4—24no—
278Dic7⋊C4—24no—
279Dic7⋊C4—24no—
280Dic7⋊C4—24no—
281Dic7⋊C4—24no—
282Dic7⋊C4C2×D414yes—
283C4×Dic7—24no—
284C4×Dic7C2×D412yes—
285C4×Dic7C2412yes—
286C2×C7⋊C8—22no—
287C2×C7⋊C8—28no—
288C2×C7⋊C8#4114yescomplemented
289C2×C7⋊C8C2412yes—
290C2×C7⋊C8C2412yes—
291C8×D7—28no—
292C22×#41—141no—
293C22×SD16—71no—
294C23×C8—71no—
295C23×C8—71no—
296#554—78no—
297#554—144no—
298#547—78no—
299#547—144no—
300C2×C4⋊Q8—71no—
301C2×C4⋊Q8—71no—
302C2×#125—141no—
303C2×#123—141no—
304C2×#123—141no—
305C2×C22⋊Q8—71no—
306C2×C22⋊Q8—141no—
307C2×C22⋊Q8—141no—
308C2×C22⋊Q8—141no—
309C2×C22⋊Q8C2×D711yescharacteristic
310C2×#121—71no—
311C2×#121—71no—
312C2×C4×Q8—71no—
313C2×C4×D4—71no—
314C2×C4×D4—71no—
315C2×C4×D4—141no—
316C22×C4⋊C4—71no—
317C22×C4⋊C4—71no—
318C22×C4⋊C4—71no—
319C22×C4⋊C4C2×D711yescharacteristic
320#498—78no—
321#483—78no—
322#483C2×D718yescomplemented
323#481—78no—
324#481—78no—
325#476—78no—
326#475—78no—
327#465—78no—
328#465—78no—
329C4×SD16—78no—
330C8×D4—78no—
331C2×#106—71no—
332C2×#106—71no—
333C2×#106—71no—
334C2×#106—78no—
335C2×#106—71no—
336C2×#106—71no—
337C2×#106—71no—
338C2×#106—71no—
339C2×#106—78no—
340C2×#106C2×D711yescharacteristic
341C2×#106C2×D711yescharacteristic
342C2×C4⋊C8—71no—
343C2×#103—71no—
344C2×#103C2×D711yescharacteristic
345C2×#103C2×D711yescharacteristic
346C2×#102—71no—
347C2×#102—71no—
348C2×#102—71no—
349C2×C22⋊C8—71no—
350C2×C22⋊C8C2×D711yescharacteristic
351C2×C4×C8—71no—
352C23×C7—22no—
353C23×C7—22no—
354C23×C7C2×SD1614yes—
355C23×C7C22×D412yes—
356C23×C7C22×D411yescharacteristic
357C22×D7—22no—
358C22×D7—22no—
359C22×D7—22no—
360C22×D7—42no—
361C22×D7—42no—
362C22×D7—42no—
363C22×D7C2×SD1614yes—
364C22×D7C22×D412yes—
365C7×Q8—22no—
366C7×Q8—22no—
367C7×Q8—42no—
368C2×C4×C7—22no—
369C2×C4×C7—24no—
370C2×C4×C7—22no—
371C2×C4×C7—22no—
372C2×C4×C7—22no—
373C2×C4×C7—22no—
374C2×C4×C7—22no—
375C2×C4×C7—22no—
376C2×C4×C7—42no—
377C2×C4×C7—42no—
378C2×C4×C7—42no—
379C2×C4×C7—48no—
380C2×C4×C7—42no—
381C2×C4×C7C22×D412yes—
382C2×C4×C7C22×D411yescharacteristic
383C2×C4×C7C2×#4112yes—
384C2×C4×C72−1+412yes—
385C2×C4×C7C2511yescharacteristic
386C22⋊D7—48no—
387C22⋊D7C2×SD16116yescomplemented
388C2×Dic7—22no—
389C2×Dic7—22no—
390C2×Dic7—22no—
391C2×Dic7—22no—
392C2×Dic7—22no—
393C2×Dic7—42no—
394C2×Dic7—42no—
395C2×Dic7—42no—
396C2×Dic7—84no—
397C2×Dic7C2×SD1614yes—
398C2×Dic7C22×D412yes—
399C2×Dic7C22×D412yes—
400C2×Dic7C22×D412yes—
401D28—22no—
402D28—22no—
403D28—48no—
404D28—42no—
405C4×D7—24no—
406C4×D7—22no—
407C4×D7—22no—
408C4×D7—48no—
409C4×D7—48no—
410C4×D7—84no—
411Dic14—48no—
412Dic14—84no—
413C7×C8—22no—
414C7×C8—22no—
415C7⋊C8—22no—
416C7⋊C8C2×#4114yescomplemented
417C2×#41—148no—
418C2×#41—288no—
419C22×Q8—141no—
420C22×Q8—141no—
421C22×Q8C22×D711yescharacteristic
422C22×D4—71no—
423C22×D4—71no—
424C22×D4—141no—
425C22×D4—141no—
426C23×C4—21no—
427C23×C4—71no—
428C23×C4—141no—
429C23×C4—141no—
430C23×C4—141no—
431C23×C4—141no—
432C23×C4C22×D711yescharacteristic
433C2×SD16—74no—
434C2×SD16—144no—
435C22×C8—71no—
436C22×C8—71no—
437C22×C8—74no—
438C22×C8—74no—
439C22×C8—144no—
440C22×C8—144no—
441C22×C8C22×D711yescharacteristic
442C22×C8C22×D711yescharacteristic
443C4⋊Q8—74no—
444C4⋊Q8—74no—
445C4⋊Q8—142no—
446C4⋊Q8—142no—
447#125—148no—
448#123—148no—
449#123—148no—
450C22⋊Q8—22no—
451C22⋊Q8—74no—
452C22⋊Q8—148no—
453C22⋊Q8—148no—
454C22⋊Q8—148no—
455C22⋊Q8—142no—
456C22⋊Q8C22×D714yes—
457#121—74no—
458#121—74no—
459#121—142no—
460#121—142no—
461C4×Q8—74no—
462C4×Q8—142no—
463C4×D4—74no—
464C4×D4—74no—
465C4×D4—74no—
466C4×D4—142no—
467C4×D4—148no—
468C2×C4⋊C4—21no—
469C2×C4⋊C4—22no—
470C2×C4⋊C4—21no—
471C2×C4⋊C4—71no—
472C2×C4⋊C4—71no—
473C2×C4⋊C4—71no—
474C2×C4⋊C4—71no—
475C2×C4⋊C4—74no—
476C2×C4⋊C4—74no—
477C2×C4⋊C4—74no—
478C2×C4⋊C4—142no—
479C2×C4⋊C4—142no—
480C2×C4⋊C4—141no—
481C2×C4⋊C4—141no—
482C2×C4⋊C4—141no—
483C2×C4⋊C4—141no—
484C2×C4⋊C4—141no—
485C2×C4⋊C4—141no—
486C2×C4⋊C4—141no—
487C2×C4⋊C4—142no—
488C2×C4⋊C4C22×D711yescharacteristic
489C2×C4⋊C4C22×D711yescharacteristic
490C2×C4⋊C4C22×D711yescharacteristic
491C2×C4⋊C4C22×D714yes—
492C2×C22⋊C4—21no—
493C2×C22⋊C4—71no—
494C2×C22⋊C4—71no—
495C2×C22⋊C4—141no—
496C2×C22⋊C4—141no—
497C2×C22⋊C4—141no—
498C2×C22⋊C4—141no—
499C2×C42—71no—
500C2×C42—141no—
501#106—74no—
502#106—74no—
503#106—74no—
504#106—74no—
505#106—74no—
506#106—74no—
507#106—74no—
508#106C22×D714yes—
509#106C22×D714yes—
510C4⋊C8—74no—
511#103—74no—
512#103C22×D714yes—
513#103C22×D714yes—
514#102—74no—
515#102—74no—
516#102—74no—
517C22⋊C8—74no—
518C22⋊C8C22×D714yes—
519C4×C8—74no—
520C22×C7—28no—
521C22×C7—22no—
522C22×C7—22no—
523C22×C7#54712yes—
524C22×C7C22×SD1614yes—
525C22×C7C22×SD1612yes—
526C22×C7#57712yes—
527C22×C7C23×D411yescharacteristic
528C2×D7—28no—
529C2×D7—22no—
530C2×D7—22no—
531C2×D7—42no—
532C2×D7—42no—
533C2×D7—42no—
534C2×D7—84no—
535C2×D7C22×SD1614yes—
536C4×C7—22no—
537C4×C7—42no—
538C4×C7—42no—
539C4×C7—42no—
540C4×C7—42no—
541C4×C7#54712yes—
542C4×C7C22×#4111yescharacteristic
543C4×C7C2×2−1+411yescharacteristic
544Dic7—22no—
545Dic7—22no—
546Dic7—42no—
547Dic7—42no—
548Dic7—42no—
549Dic7C22×SD1614yes—
550C24—71no—
551C24—141no—
552C24D4×D711yescharacteristic
553#41—2832no—
554C2×Q8—21no—
555C2×Q8—22no—
556C2×Q8—22no—
557C2×Q8—144no—
558C2×Q8—144no—
559C2×Q8—284no—
560C2×Q8—562no—
561C2×Q8C23×D712yes—
562C2×D4—78no—
563C2×D4—74no—
564C2×D4—72no—
565C2×D4—144no—
566C2×D4—144no—
567C2×D4—141no—
568C2×D4—142no—
569C2×D4—142no—
570C2×D4—284no—
571C2×D4—284no—
572C22×C4—22no—
573C22×C4—22no—
574C22×C4—24no—
575C22×C4—21no—
576C22×C4—21no—
577C22×C4—21no—
578C22×C4—21no—
579C22×C4—44no—
580C22×C4—71no—
581C22×C4—71no—
582C22×C4—71no—
583C22×C4—72no—
584C22×C4—72no—
585C22×C4—144no—
586C22×C4—144no—
587C22×C4—144no—
588C22×C4—142no—
589C22×C4—142no—
590C22×C4—141no—
591C22×C4—141no—
592C22×C4—141no—
593C22×C4—144no—
594C22×C4—284no—
595C22×C4—284no—
596C22×C4—562no—
597C22×C4—562no—
598C22×C4D4×D712yes—
599C22×C4D4×D711yescharacteristic
600C22×C4C23×D712yes—
601C22×C4C23×D711yescharacteristic
602SD16—148no—
603C2×C8—22no—
604C2×C8—22no—
605C2×C8—74no—
606C2×C8—72no—
607C2×C8—72no—
608C2×C8—148no—
609C2×C8—148no—
610C2×C8—142no—
611C2×C8C23×D712yes—
612C2×C8C23×D712yes—
613C4⋊C4—21no—
614C4⋊C4—21no—
615C4⋊C4—24no—
616C4⋊C4—24no—
617C4⋊C4—21no—
618C4⋊C4—74no—
619C4⋊C4—72no—
620C4⋊C4—72no—
621C4⋊C4—72no—
622C4⋊C4—144no—
623C4⋊C4—144no—
624C4⋊C4—144no—
625C4⋊C4—144no—
626C4⋊C4—144no—
627C4⋊C4—144no—
628C4⋊C4—141no—
629C4⋊C4—141no—
630C4⋊C4—144no—
631C4⋊C4—141no—
632C4⋊C4C23×D712yes—
633C4⋊C4C23×D712yes—
634C4⋊C4C23×D712yes—
635C22⋊C4—24no—
636C22⋊C4—74no—
637C22⋊C4—74no—
638C22⋊C4—144no—
639C22⋊C4—144no—
640C22⋊C4—144no—
641C22⋊C4—144no—
642C42—72no—
643C42—72no—
644C42—144no—
645C2×C7—24no—
646C2×C7#333514yescomplemented
647C2×C7C2×#54711yescharacteristic
648C2×C7C23×SD1611yescharacteristic
649C2×C7C2×#57711yescharacteristic
650D7—24no—
651D7—82no—
652C23—22no—
653C23—22no—
654C23—74no—
655C23—72no—
656C23—142no—
657C23—142no—
658C23—142no—
659C23—282no—
660C23—282no—
661C23—282no—
662C23D7×SD1614yes—
663C23C2×D4×D712yes—
664C23C2×D4×D711yescharacteristic
665Q8—22no—
666Q8—22no—
667Q8—42no—
668Q8—288no—
669Q8—564no—
670D4—716no—
671D4—142no—
672D4—142no—
673D4—288no—
674D4—288no—
675D4—282no—
676C2×C4—22no—
677C2×C4—24no—
678C2×C4—22no—
679C2×C4—22no—
680C2×C4—22no—
681C2×C4—22no—
682C2×C4—22no—
683C2×C4—22no—
684C2×C4—42no—
685C2×C4—42no—
686C2×C4—48no—
687C2×C4—42no—
688C2×C4—42no—
689C2×C4—74no—
690C2×C4—72no—
691C2×C4—72no—
692C2×C4—72no—
693C2×C4—142no—
694C2×C4—142no—
695C2×C4—144no—
696C2×C4—142no—
697C2×C4—142no—
698C2×C4—142no—
699C2×C4—142no—
700C2×C4—142no—
701C2×C4—288no—
702C2×C4—288no—
703C2×C4—282no—
704C2×C4—282no—
705C2×C4—282no—
706C2×C4—564no—
707C2×C4—564no—
708C2×C4C2×D4×D712yes—
709C2×C4C2×D4×D711yescharacteristic
710C2×C4D7×#4112yes—
711C2×C4#655412yes—
712C2×C4C24×D711yescharacteristic
713C8—22no—
714C8—22no—
715C8—74no—
716C8—142no—
717C7C2×#333511yescharacteristic, complemented, Sylow
718C22—28no—
719C22—22no—
720C22—22no—
721C22—74no—
722C22—148no—
723C22—142no—
724C22—142no—
725C22—282no—
726C22—282no—
727C22—282no—
728C22—564no—
729C22#9034612yes—
730C22C2×D7×SD1614yes—
731C22C2×D7×SD1612yes—
732C22#9046912yes—
733C22C22×D4×D711yescharacteristic
734C4—22no—
735C4—42no—
736C4—42no—
737C4—42no—
738C4—42no—
739C4—74no—
740C4—142no—
741C4—142no—
742C4—282no—
743C4—282no—
744C4—282no—
745C4#9034612yes—
746C4C2×D7×#4111yescharacteristic
747C4C2×#655411yescharacteristic
748C2—24no—
749C2—144no—
750C2—562no—
751C2#1173888014yesdirect product factor
752C2C2×#9034611yescharacteristic
753C2C22×D7×SD1611yescharacteristic
754C2C2×#9046911yescharacteristic
subgroupG/H
centerC23C2×D4×D7
commutator, cosocleC2×C4×C7C25
FrattiniC2×C4C24×D7
FittingC2×C7×#483C2
socleC23×C7C22×D4
prime radicalC2×#90198C2
hypercenterC2×#483D7
hypocenterC7C2×#3335
LCSG ▷ C2×C4×C7 ▷ C2×C7 ▷ C7
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#483

Complements

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

NH ≅ G/Ntype
1. C2×#90326C2semidirect
3. C2×C7×#483C2semidirect
4. C2×#89820C2semidirect
5. C22×#6382C2semidirect
6. #11738880C2direct (N × H)
7. C2×#89642C2semidirect
8. C2×#89635C2semidirect
9. C2×D7×#106C2semidirect
10. C2×#89627C2semidirect
11. C2×#89577C2semidirect
12. C2×#89579C2semidirect
13. C2×#89563C2semidirect
14. C2×#89560C2semidirect
15. C2×(C22⋊D7)⋊C8C2semidirect
16. C2×#89507C2semidirect
30. #90326C22semidirect
45. C7×#483C22semidirect
59. #89820C22semidirect
66. C2×#6382C22semidirect
67. #89642C22semidirect
68. #89635C22semidirect
69. D7×#106C22semidirect
70. #89627C22semidirect
71. #89579C22semidirect
72. #89577C22semidirect
73. #89563C22semidirect
74. #89560C22semidirect
75. #89507C22semidirect
76. (C22⋊D7)⋊C8C22semidirect
188. C2×#483D7semidirect
218. C2×C22⋊D7SD16semidirect
288. C2×C7⋊C8#41semidirect
322. #483C2×D7semidirect
387. C22⋊D7C2×SD16semidirect
416. C7⋊C8C2×#41semidirect
646. C2×C7#3335semidirect
717. C7C2×#3335semidirect
751. C2#11738880direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#903262
C2×#901982
C2×C7×#4832
C2×#898202
C22×#63822
#117388802
C2×#896422
C2×#896352
C2×D7×#1062
C2×#896272
C2×#895772
C2×#895792
C2×#895632
C2×#895602
C2×(C22⋊D7)⋊C82
C2×#895072
C2×#33357