Finite Group Databasebeta

← C2×#11738611 #14221305

Subgroups — C2×#11738611 #14221305

Order 1792.

2530 conjugacy classes of subgroups.

The subgroup lattice has 768 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#90379C211yesmaximal, characteristic, complemented
2C2×C4×D4×D7C211yesmaximal, characteristic
3C2×C7×#478C211yesmaximal, characteristic, complemented
4C2×#89838C211yesmaximal, characteristic, complemented
5C2×#89781C211yesmaximal, characteristic, complemented
6#11738611C2116yesmaximal, direct product factor
7C2×#89662C211yesmaximal, characteristic, complemented
8C2×#89653C211yesmaximal, characteristic, complemented
9C2×#89642C211yesmaximal, characteristic, complemented
10C2×#89633C211yesmaximal, characteristic, complemented
11C2×#89619C211yesmaximal, characteristic, complemented
12C2×#89609C211yesmaximal, characteristic, complemented
13C2×#89542C211yesmaximal, characteristic
14C2×#89542C211yesmaximal, characteristic
15C2×#89533C211yesmaximal, characteristic, complemented
16C2×#89531C211yesmaximal, characteristic, complemented
17C22×D4×D7C2211yescharacteristic
18C23×C4×D7—21no—
19C2×C7×#125C2211yescharacteristic, complemented
20C2×C4×C7×D4C2211yescharacteristic
21C2×D4×Dic7C2211yescharacteristic
22C2×C4×C22⋊D7—21no—
23C22×#1131C2211yescharacteristic
24C22×#1131C2211yescharacteristic
25#90379—24no—
26#90379C2218yescomplemented
27C4×D4×D7—24no—
28C4×D4×D7C2218yes—
29C2×#6459—21no—
30C2×#6459—21no—
31C2×#6456C2211yescharacteristic
32C2×#6455C2211yescharacteristic
33C2×#6455C2211yescharacteristic
34C2×D7×C4⋊C4C2211yescharacteristic
35C2×#6451C2211yescharacteristic, complemented
36C2×#6451C2211yescharacteristic, complemented
37C2×#6450—21no—
38C2×#6450—21no—
39C2×(C22⋊D7)⋊C4—21no—
40C2×D7×C22⋊C4—21no—
41C2×C4×D28C2211yescharacteristic
42C2×C42×D7C2211yescharacteristic
43C2×#6433C2211yescharacteristic, complemented
44C7×#478C2218yescomplemented
45C2×C7×#107C2211yescharacteristic, complemented
46C2×C7×#106C2211yescharacteristic, complemented
47C2×C7×C4⋊C8C2211yescharacteristic, complemented
48C2×C7×#102C2211yescharacteristic
49C2×C7×#102C2211yescharacteristic
50C2×#6406C2211yescharacteristic
51C2×#6406C2211yescharacteristic
52C2×#6395C2211yescharacteristic
53C2×#6395C2211yescharacteristic
54C2×#6392C2211yescharacteristic, complemented
55C2×#6391C2211yescharacteristic, complemented
56C2×Dic7⋊C8C2211yescharacteristic, complemented
57C2×Dic7⋊C8C2211yescharacteristic, complemented
58#89838C2218yescomplemented
59#89781C2218yescomplemented
60C2×#6383C2211yescharacteristic
61C2×#6383C2211yescharacteristic
62C2×#6382C2211yescharacteristic, complemented
63C2×#6382C2211yescharacteristic, complemented
64C2×#6381C2211yescharacteristic, complemented
65C2×#6381C2211yescharacteristic, complemented
66C2×C4⋊(C7⋊C8)C2211yescharacteristic, complemented
67#89662C2218yescomplemented
68#89653C2218yescomplemented
69#89642C2218yescomplemented
70#89633C2218yescomplemented
71#89619C2218yescomplemented
72#89609C2218yescomplemented
73#89542C2218yes—
74#89542C2218yes—
75#89533C2218yescomplemented
76#89531C2218yescomplemented
77C2×#3077—71nomaximal, Sylow
78C24×D7—21no—
79C22×C7×D4C2311yescharacteristic
80C23×C4×C7—21no—
81C22×C22⋊D7—21no—
82C23×Dic7—21no—
83C2×D4×D7—22no—
84C2×D4×D7—24no—
85C2×D4×D7Q818yescomplemented
86C2×D4×D7C2314yes—
87C22×D28C2311yescharacteristic
88C22×C4×D7—21no—
89C22×C4×D7—21no—
90C22×C4×D7—21no—
91C22×C4×D7—28no—
92C22×C4×D7—48no—
93C22×C4×D7D411yescharacteristic
94C22×C4×D7D411yescharacteristic
95C22×C4×D7C2311yescharacteristic
96C22×Dic14—21no—
97C22×Dic14—21no—
98C22×C7×C8C2311yescharacteristic
99C22×C7×C8C2311yescharacteristic
100C7×#125—22no—
101C7×#125C2314yescomplemented
102C4×C7×D4—22no—
103C4×C7×D4C2314yes—
104C2×C7×C4⋊C4—21no—
105C2×C7×C4⋊C4—21no—
106C2×C7×C4⋊C4C2311yescharacteristic
107C2×C7×C4⋊C4C2311yescharacteristic
108C2×C7×C4⋊C4C2311yescharacteristic
109C2×C7×C22⋊C4—21no—
110C2×C42×C7C2311yescharacteristic
111C2×C22⋊Dic7—21no—
112D4×Dic7—22no—
113D4×Dic7C2314yes—
114C4×C22⋊D7—28no—
115C2×(C2×D7)⋊C4—21no—
116C2×(C2×D7)⋊C4—21no—
117C2×(C2×D7)⋊C4—21no—
118C2×(C2×D7)⋊C4—21no—
119C2×C4⋊Dic7C2311yescharacteristic
120C2×C4⋊Dic7C2311yescharacteristic
121C2×C4⋊Dic7C2311yescharacteristic
122C2×Dic7⋊C4—21no—
123C2×Dic7⋊C4—21no—
124C2×Dic7⋊C4—21no—
125C2×Dic7⋊C4—21no—
126C2×Dic7⋊C4—21no—
127C2×C4×Dic7—21no—
128C2×C4×Dic7—21no—
129C2×C4×Dic7D411yescharacteristic
130C2×C4×Dic7D411yescharacteristic
131C2×C4×Dic7C2311yescharacteristic
132C22×C7⋊C8C2311yescharacteristic
133C22×C7⋊C8C2311yescharacteristic
134C2×#1131—24no—
135C2×#1131—24no—
136C2×#1131C2314yes—
137C2×#1131C2314yes—
138#6459—28no—
139#6459—28no—
140#6456—22no—
141#6456C2314yes—
142#6455—22no—
143#6455—22no—
144#6455C2314yes—
145#6455C2314yes—
146D7×C4⋊C4—22no—
147D7×C4⋊C4C2314yes—
148#6451—22no—
149#6451—22no—
150#6451C2314yescomplemented
151#6451C2314yescomplemented
152#6450—28no—
153#6450—28no—
154(C22⋊D7)⋊C4—28no—
155D7×C22⋊C4—28no—
156C4×D28—22no—
157C4×D28C2314yes—
158C42×D7D414yes—
159C42×D7C2314yes—
160#6433—22no—
161#6433C2314yescomplemented
162C7×#107C2314yescomplemented
163C7×#106C2314yescomplemented
164C7×C4⋊C8C2314yescomplemented
165C7×#102C2314yes—
166C7×#102C2314yes—
167#6406C2314yes—
168#6406C2314yes—
169#6395C2314yes—
170#6395C2314yes—
171#6392C2314yescomplemented
172#6391C2314yescomplemented
173Dic7⋊C8C2314yescomplemented
174Dic7⋊C8C2314yescomplemented
175#6383C2314yes—
176#6383C2314yes—
177#6382C2314yescomplemented
178#6382C2314yescomplemented
179#6381C2314yescomplemented
180#6381C2314yescomplemented
181C4⋊(C7⋊C8)C2314yescomplemented
182C2×#533—71no—
183C22×C4×D4—71no—
184#3077—716no—
185C2×#478—71no—
186C2×#478—71no—
187C2×#478—71no—
188C2×#478D711yescharacteristic, complemented
189C2×#476—71no—
190C2×#476—71no—
191C2×#474—71no—
192C2×#474—71no—
193C2×#428—71no—
194C2×#428—71no—
195C2×#423—71no—
196C2×#418—71no—
197C2×#418—71no—
198C24×C7—21no—
199C23×D7—21no—
200C23×D7—28no—
201C23×D7—24no—
202C23×D7—44no—
203C23×D7—44no—
204C23×D7C2×D411yescharacteristic
205C2×C7×D4—21no—
206C2×C7×D4—22no—
207C2×C7×D4C2×Q814yes—
208C2×C7×D4C2412yes—
209C22×C4×C7—21no—
210C22×C4×C7—21no—
211C22×C4×C7—21no—
212C22×C4×C7—24no—
213C22×C4×C7—44no—
214C22×C4×C7C2×D411yescharacteristic
215C22×C4×C7C2×D411yescharacteristic
216C22×C4×C7C2411yescharacteristic
217C2×C22⋊D7—28no—
218C2×C22⋊D7—24no—
219C22×Dic7—21no—
220C22×Dic7—21no—
221C22×Dic7—21no—
222C22×Dic7—24no—
223C22×Dic7—44no—
224C22×Dic7C2×D411yescharacteristic
225C22×Dic7C2×D411yescharacteristic
226C22×Dic7C2×D411yescharacteristic
227D4×D7—216no—
228D4×D7—28no—
229D4×D7C2×Q8116yescomplemented
230C2×D28—21no—
231C2×D28—22no—
232C2×D28C2×Q814yes—
233C2×D28C2412yes—
234C2×C4×D7—24no—
235C2×C4×D7—24no—
236C2×C4×D7—24no—
237C2×C4×D7—24no—
238C2×C4×D7—432no—
239C2×C4×D7—42no—
240C2×C4×D7—44no—
241C2×C4×D7—44no—
242C2×C4×D7—44no—
243C2×C4×D7C2×D414yes—
244C2×C4×D7C2×D414yes—
245C2×C4×D7C2×D412yes—
246C2×C4×D7C2×Q814yes—
247C2×C4×D7#4114yes—
248C2×C4×D7C2412yes—
249C2×Dic14—24no—
250C2×Dic14—24no—
251C2×Dic14—44no—
252C2×Dic14—44no—
253C2×C7×C8—22no—
254C2×C7×C8—22no—
255C2×C7×C8C2412yes—
256C2×C7×C8C2412yes—
257C7×C4⋊C4—24no—
258C7×C4⋊C4—24no—
259C7×C4⋊C4—21no—
260C7×C4⋊C4—21no—
261C7×C4⋊C4—21no—
262C7×C4⋊C4C2412yes—
263C7×C4⋊C4C2412yes—
264C7×C4⋊C4C2412yes—
265C7×C22⋊C4—24no—
266C42×C7C2×D412yes—
267C42×C7C2412yes—
268C22⋊Dic7—24no—
269(C2×D7)⋊C4—24no—
270(C2×D7)⋊C4—24no—
271(C2×D7)⋊C4—24no—
272(C2×D7)⋊C4—24no—
273C4⋊Dic7—21no—
274C4⋊Dic7—21no—
275C4⋊Dic7—21no—
276C4⋊Dic7C2412yes—
277C4⋊Dic7C2412yes—
278C4⋊Dic7C2412yes—
279Dic7⋊C4—24no—
280Dic7⋊C4—24no—
281Dic7⋊C4—24no—
282Dic7⋊C4—24no—
283Dic7⋊C4—24no—
284C4×Dic7—24no—
285C4×Dic7—24no—
286C4×Dic7C2×D412yes—
287C4×Dic7C2×D414yes—
288C4×Dic7C2×D414yes—
289C4×Dic7C2412yes—
290C2×C7⋊C8—22no—
291C2×C7⋊C8—22no—
292C2×C7⋊C8C2412yes—
293C2×C7⋊C8C2412yes—
294#1131—28no—
295#1131—28no—
296C23×D4—71no—
297C24×C4—141no—
298C22×M16—71no—
299C22×M16—71no—
300#533—78no—
301#533—144no—
302C2×C4⋊Q8—71no—
303C2×C4⋊Q8—71no—
304C2×#125—71no—
305C2×#125C2×D711yescharacteristic, complemented
306C2×C22⋊Q8—141no—
307C2×C22⋊Q8—141no—
308C2×C4×Q8—141no—
309C2×C4×Q8—141no—
310C2×C4×D4—71no—
311C2×C4×D4—78no—
312C2×C4×D4—71no—
313C2×C4×D4—71no—
314C2×C4×D4—141no—
315C2×C4×D4—144no—
316C2×C4×D4—141no—
317C2×C4×D4C2×D711yescharacteristic
318C2×#117—71no—
319C2×#117—71no—
320C22×C4⋊C4—71no—
321C22×C22⋊C4—141no—
322C22×C42—71no—
323#478—78no—
324#478—78no—
325#478—78no—
326#478C2×D718yescomplemented
327#476—78no—
328#476—78no—
329#474—78no—
330#474—78no—
331#428—78no—
332#428—78no—
333C2×#107—71no—
334C2×#107—71no—
335C2×#107—71no—
336C2×#107C2×D711yescharacteristic, complemented
337C2×#106—71no—
338C2×#106—71no—
339C2×#106—71no—
340C2×#106C2×D711yescharacteristic, complemented
341#423—78no—
342C2×C4⋊C8—71no—
343C2×C4⋊C8—71no—
344C2×C4⋊C8—71no—
345C2×C4⋊C8C2×D711yescharacteristic, complemented
346#418—78no—
347#418—78no—
348C2×#102—71no—
349C2×#102—71no—
350C2×#102—71no—
351C2×#102—71no—
352C2×#102—71no—
353C2×#102—71no—
354C2×#102C2×D711yescharacteristic
355C2×#102C2×D711yescharacteristic
356C23×C7—24no—
357C23×C7—22no—
358C23×C7—42no—
359C23×C7—42no—
360C23×C7C22×D411yescharacteristic
361C22×D7—22no—
362C22×D7—22no—
363C22×D7—24no—
364C22×D7—22no—
365C22×D7—216no—
366C22×D7—48no—
367C22×D7—432no—
368C22×D7—48no—
369C22×D7—42no—
370C22×D7—42no—
371C22×D7C22⋊Q814yes—
372C22×D7C22×D412yes—
373C7×D4—24no—
374C7×D4—22no—
375C7×D4C22×Q814yes—
376C2×C4×C7—22no—
377C2×C4×C7—22no—
378C2×C4×C7—22no—
379C2×C4×C7—22no—
380C2×C4×C7—22no—
381C2×C4×C7—48no—
382C2×C4×C7—42no—
383C2×C4×C7—42no—
384C2×C4×C7—42no—
385C2×C4×C7C22×D412yes—
386C2×C4×C7C22×D412yes—
387C2×C4×C7C22×D411yescharacteristic
388C2×C4×C7C22×Q812yes—
389C2×C4×C7C2×#4112yes—
390C2×C4×C7C2511yescharacteristic
391C22⋊D7—216no—
392C2×Dic7—22no—
393C2×Dic7—22no—
394C2×Dic7—22no—
395C2×Dic7—22no—
396C2×Dic7—42no—
397C2×Dic7—42no—
398C2×Dic7—42no—
399C2×Dic7—48no—
400C2×Dic7C22⋊Q814yes—
401C2×Dic7AGL(1,ℤ/8)14yes—
402C2×Dic7C22×D412yes—
403C2×Dic7C22×D412yes—
404C2×Dic7C22×D412yes—
405D28—24no—
406D28—22no—
407D28C22×Q814yes—
408C4×D7—28no—
409C4×D7—44no—
410C4×D7—48no—
411C4×D7—48no—
412C4×D7—48no—
413C4×D7C22⋊Q818yes—
414C4×D7C22×Q814yes—
415C4×D7C2×#4114yes—
416Dic14—48no—
417Dic14—48no—
418C7×C8—22no—
419C7×C8—22no—
420C7⋊C8—22no—
421C7⋊C8—22no—
422C25—141no—
423C22×Q8—141no—
424C22×Q8—141no—
425C22×D4—78no—
426C22×D4—74no—
427C22×D4—71no—
428C22×D4—142no—
429C22×D4—144no—
430C22×D4—141no—
431C22×D4C22×D711yescharacteristic
432C23×C4—21no—
433C23×C4—71no—
434C23×C4—71no—
435C23×C4—71no—
436C23×C4—141no—
437C23×C4—148no—
438C23×C4—141no—
439C23×C4—141no—
440C23×C4—141no—
441C23×C4—288no—
442C2×M16—74no—
443C2×M16—74no—
444C2×M16—144no—
445C2×M16—144no—
446C22×C8—71no—
447C22×C8—71no—
448C22×C8C22×D711yescharacteristic
449C22×C8C22×D711yescharacteristic
450C4⋊Q8—74no—
451C4⋊Q8—74no—
452C4⋊Q8—142no—
453C4⋊Q8—142no—
454#125—22no—
455#125—74no—
456#125—142no—
457#125C22×D714yescomplemented
458C22⋊Q8—148no—
459C22⋊Q8—148no—
460C4×Q8—148no—
461C4×Q8—148no—
462C4×D4—22no—
463C4×D4—74no—
464C4×D4—74no—
465C4×D4—74no—
466C4×D4—148no—
467C4×D4—142no—
468C4×D4—148no—
469C4×D4—142no—
470C4×D4—142no—
471C4×D4C22×D714yes—
472#117—74no—
473#117—74no—
474#117—142no—
475#117—142no—
476C2×C4⋊C4—21no—
477C2×C4⋊C4—21no—
478C2×C4⋊C4—71no—
479C2×C4⋊C4—71no—
480C2×C4⋊C4—71no—
481C2×C4⋊C4—74no—
482C2×C4⋊C4—142no—
483C2×C4⋊C4—141no—
484C2×C4⋊C4—141no—
485C2×C4⋊C4—141no—
486C2×C4⋊C4—141no—
487C2×C4⋊C4—141no—
488C2×C4⋊C4C22×D711yescharacteristic
489C2×C4⋊C4C22×D711yescharacteristic
490C2×C4⋊C4C22×D711yescharacteristic
491C2×C22⋊C4—21no—
492C2×C22⋊C4—148no—
493C2×C22⋊C4—141no—
494C2×C22⋊C4—141no—
495C2×C22⋊C4—141no—
496C2×C22⋊C4—141no—
497C2×C22⋊C4—141no—
498C2×C42—71no—
499C2×C42—71no—
500C2×C42—71no—
501C2×C42—74no—
502C2×C42—74no—
503C2×C42—141no—
504C2×C42—141no—
505C2×C42C22×D711yescharacteristic
506#107—74no—
507#107—74no—
508#107—74no—
509#107C22×D714yescomplemented
510#106—74no—
511#106—74no—
512#106—74no—
513#106C22×D714yescomplemented
514C4⋊C8—74no—
515C4⋊C8—74no—
516C4⋊C8—74no—
517C4⋊C8C22×D714yescomplemented
518#102—74no—
519#102—74no—
520#102—74no—
521#102—74no—
522#102—74no—
523#102—74no—
524#102C22×D714yes—
525#102C22×D714yes—
526C22×C7—24no—
527C22×C7—48no—
528C22×C7—42no—
529C22×C7—42no—
530C22×C7C2×C22⋊Q812yes—
531C22×C7C2×AGL(1,ℤ/8)12yes—
532C22×C7#57512yes—
533C22×C7C23×D411yescharacteristic
534C2×D7—28no—
535C2×D7—22no—
536C2×D7—22no—
537C2×D7—24no—
538C2×D7—432no—
539C2×D7—48no—
540C2×D7—42no—
541C2×D7—42no—
542C2×D7C2×C22⋊Q814yes—
543C4×C7—22no—
544C4×C7—22no—
545C4×C7—42no—
546C4×C7—42no—
547C4×C7—42no—
548C4×C7C2×C22⋊Q812yes—
549C4×C7C23×Q811yescharacteristic
550C4×C7C22×#4111yescharacteristic
551Dic7—22no—
552Dic7—42no—
553Dic7—42no—
554Dic7—42no—
555Dic7C2×C22⋊Q814yes—
556Dic7C2×AGL(1,ℤ/8)14yes—
557C24—21no—
558C24—71no—
559C24—144no—
560C24—148no—
561C24—141no—
562C24—284no—
563C24—284no—
564C2×Q8—144no—
565C2×Q8—144no—
566C2×Q8—284no—
567C2×Q8—284no—
568C2×D4—21no—
569C2×D4—22no—
570C2×D4—716no—
571C2×D4—74no—
572C2×D4—72no—
573C2×D4—1416no—
574C2×D4—148no—
575C2×D4—144no—
576C2×D4—148no—
577C2×D4—141no—
578C2×D4—142no—
579C2×D4Q8×D714yes—
580C2×D4C23×D712yes—
581C22×C4—21no—
582C22×C4—21no—
583C22×C4—21no—
584C22×C4—24no—
585C22×C4—44no—
586C22×C4—71no—
587C22×C4—71no—
588C22×C4—72no—
589C22×C4—74no—
590C22×C4—74no—
591C22×C4—72no—
592C22×C4—71no—
593C22×C4—74no—
594C22×C4—74no—
595C22×C4—144no—
596C22×C4—144no—
597C22×C4—144no—
598C22×C4—144no—
599C22×C4—141no—
600C22×C4—141no—
601C22×C4—141no—
602C22×C4—144no—
603C22×C4—282no—
604C22×C4—284no—
605C22×C4—284no—
606C22×C4—2832no—
607C22×C4—284no—
608C22×C4—284no—
609C22×C4D4×D711yescharacteristic
610C22×C4D4×D711yescharacteristic
611C22×C4C23×D711yescharacteristic
612M16—148no—
613M16—148no—
614C2×C8—22no—
615C2×C8—22no—
616C2×C8—72no—
617C2×C8—72no—
618C2×C8—142no—
619C2×C8—142no—
620C2×C8C23×D712yes—
621C2×C8C23×D712yes—
622C4⋊C4—24no—
623C4⋊C4—24no—
624C4⋊C4—21no—
625C4⋊C4—21no—
626C4⋊C4—21no—
627C4⋊C4—72no—
628C4⋊C4—72no—
629C4⋊C4—72no—
630C4⋊C4—144no—
631C4⋊C4—144no—
632C4⋊C4—144no—
633C4⋊C4—144no—
634C4⋊C4—144no—
635C4⋊C4—141no—
636C4⋊C4—141no—
637C4⋊C4—141no—
638C4⋊C4C23×D712yes—
639C4⋊C4C23×D712yes—
640C4⋊C4C23×D712yes—
641C22⋊C4—24no—
642C22⋊C4—144no—
643C22⋊C4—144no—
644C22⋊C4—144no—
645C22⋊C4—144no—
646C22⋊C4—144no—
647C42—74no—
648C42—74no—
649C42—72no—
650C42—72no—
651C42—144no—
652C42—144no—
653C42D4×D712yes—
654C42C23×D712yes—
655C2×C7—44no—
656C2×C7#307714yescomplemented
657C2×C7C22×C22⋊Q811yescharacteristic
658C2×C7C22×AGL(1,ℤ/8)11yescharacteristic
659C2×C7C2×#57511yescharacteristic
660D7—24no—
661D7—44no—
662C23—24no—
663C23—22no—
664C23—42no—
665C23—42no—
666C23—74no—
667C23—72no—
668C23—1416no—
669C23—142no—
670C23—142no—
671C23—144no—
672C23—142no—
673C23—288no—
674C23—2832no—
675C23—288no—
676C23—282no—
677C23—282no—
678C23C2×D4×D711yescharacteristic
679Q8—288no—
680Q8—288no—
681D4—24no—
682D4—22no—
683D4—74no—
684D4—1416no—
685D4—144no—
686D4—142no—
687D4C2×Q8×D714yes—
688C2×C4—22no—
689C2×C4—22no—
690C2×C4—22no—
691C2×C4—22no—
692C2×C4—22no—
693C2×C4—48no—
694C2×C4—42no—
695C2×C4—42no—
696C2×C4—42no—
697C2×C4—74no—
698C2×C4—74no—
699C2×C4—72no—
700C2×C4—72no—
701C2×C4—78no—
702C2×C4—74no—
703C2×C4—74no—
704C2×C4—72no—
705C2×C4—148no—
706C2×C4—142no—
707C2×C4—142no—
708C2×C4—142no—
709C2×C4—142no—
710C2×C4—284no—
711C2×C4—288no—
712C2×C4—288no—
713C2×C4—288no—
714C2×C4—288no—
715C2×C4—282no—
716C2×C4—282no—
717C2×C4—282no—
718C2×C4C2×D4×D712yes—
719C2×C4C2×D4×D712yes—
720C2×C4C2×D4×D711yescharacteristic
721C2×C4C2×Q8×D712yes—
722C2×C4D7×#4112yes—
723C2×C4C24×D711yescharacteristic
724C8—22no—
725C8—22no—
726C8—142no—
727C8—142no—
728C7C2×#307711yescharacteristic, complemented, Sylow
729C22—24no—
730C22—42no—
731C22—48no—
732C22—42no—
733C22—74no—
734C22—142no—
735C22—148no—
736C22—142no—
737C22—144no—
738C22—2832no—
739C22—282no—
740C22—288no—
741C22—282no—
742C22D7×C22⋊Q812yes—
743C22#9045912yes—
744C22D7×AGL(1,ℤ/8)12yes—
745C22C22×D4×D711yescharacteristic
746C4—22no—
747C4—22no—
748C4—42no—
749C4—42no—
750C4—42no—
751C4—74no—
752C4—74no—
753C4—142no—
754C4—282no—
755C4—282no—
756C4—282no—
757C4D7×C22⋊Q812yes—
758C4C22×Q8×D711yescharacteristic
759C4C2×D7×#4111yescharacteristic
760C2—44no—
761C2—144no—
762C2—284no—
763C2#1173861114yesdirect product factor
764C2C2×D7×C22⋊Q811yescharacteristic
765C2C2×#9045911yescharacteristic
766C2C2×D7×AGL(1,ℤ/8)11yescharacteristic
subgroupG/H
centerC23C2×D4×D7
commutator, cosocleC2×C4×C7C25
FrattiniC2×C4C24×D7
FittingC2×C7×#478C2
socleC23×C7C22×D4
prime radicalC22×D4×D7C22
hypercenterC2×#478D7
hypocenterC7C2×#3077
LCSG ▷ C2×C4×C7 ▷ C2×C7 ▷ C7
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#478

Complements

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

NH ≅ G/Ntype
1. C2×#90379C2semidirect
3. C2×C7×#478C2semidirect
4. C2×#89838C2semidirect
5. C2×#89781C2semidirect
6. #11738611C2direct (N × H)
7. C2×#89662C2semidirect
8. C2×#89653C2semidirect
9. C2×#89642C2semidirect
10. C2×#89633C2semidirect
11. C2×#89619C2semidirect
12. C2×#89609C2semidirect
15. C2×#89533C2semidirect
16. C2×#89531C2semidirect
19. C2×C7×#125C22semidirect
26. #90379C22semidirect
35. C2×#6451C22semidirect
36. C2×#6451C22semidirect
43. C2×#6433C22semidirect
44. C7×#478C22semidirect
45. C2×C7×#107C22semidirect
46. C2×C7×#106C22semidirect
47. C2×C7×C4⋊C8C22semidirect
54. C2×#6392C22semidirect
55. C2×#6391C22semidirect
56. C2×Dic7⋊C8C22semidirect
57. C2×Dic7⋊C8C22semidirect
58. #89838C22semidirect
59. #89781C22semidirect
62. C2×#6382C22semidirect
63. C2×#6382C22semidirect
64. C2×#6381C22semidirect
65. C2×#6381C22semidirect
66. C2×C4⋊(C7⋊C8)C22semidirect
67. #89662C22semidirect
68. #89653C22semidirect
69. #89642C22semidirect
70. #89633C22semidirect
71. #89619C22semidirect
72. #89609C22semidirect
75. #89533C22semidirect
76. #89531C22semidirect
85. C2×D4×D7Q8semidirect
101. C7×#125C23semidirect
150. #6451C23semidirect
151. #6451C23semidirect
161. #6433C23semidirect
162. C7×#107C23semidirect
163. C7×#106C23semidirect
164. C7×C4⋊C8C23semidirect
171. #6392C23semidirect
172. #6391C23semidirect
173. Dic7⋊C8C23semidirect
174. Dic7⋊C8C23semidirect
177. #6382C23semidirect
178. #6382C23semidirect
179. #6381C23semidirect
180. #6381C23semidirect
181. C4⋊(C7⋊C8)C23semidirect
188. C2×#478D7semidirect
229. D4×D7C2×Q8semidirect
305. C2×#125C2×D7semidirect
326. #478C2×D7semidirect
336. C2×#107C2×D7semidirect
340. C2×#106C2×D7semidirect
345. C2×C4⋊C8C2×D7semidirect
457. #125C22×D7semidirect
509. #107C22×D7semidirect
513. #106C22×D7semidirect
517. C4⋊C8C22×D7semidirect
656. C2×C7#3077semidirect
728. C7C2×#3077semidirect
763. C2#11738611direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#903792
C2×C4×D4×D72
C2×C7×#4782
C2×#898382
C2×#897812
#117386112
C2×#896622
C2×#896532
C2×#896422
C2×#896332
C2×#896192
C2×#896092
C2×#895422
C2×#895332
C2×#895312
C2×#30777