Finite Group Databasebeta

← C2×#11738943 #14222096

Subgroups — C2×#11738943 #14222096

Order 1792.

2210 conjugacy classes of subgroups.

The subgroup lattice has 772 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#90316C211yesmaximal, characteristic, complemented
2C2×#90212C211yesmaximal, characteristic
3C2×C7×#485C211yesmaximal, characteristic, complemented
4C2×#89818C211yesmaximal, characteristic
5C2×#89768C211yesmaximal, characteristic, complemented
6#11738943C2116yesmaximal, direct product factor
7C2×#89663C211yesmaximal, characteristic, complemented
8C2×#89661C211yesmaximal, characteristic, complemented
9C2×#89643C211yesmaximal, characteristic, complemented
10C2×#89624C211yesmaximal, characteristic, complemented
11C2×#89590C211yesmaximal, characteristic, complemented
12C2×#89590C211yesmaximal, characteristic, complemented
13C2×#89589C211yesmaximal, characteristic, complemented
14C2×#89560C211yesmaximal, characteristic, complemented
15C2×#89503C211yesmaximal, characteristic
16C2×#89492C211yesmaximal, characteristic, complemented
17C23×D28C2211yescharacteristic
18C2×C7×C22⋊Q8C2211yescharacteristic
19C2×C7×#117C2211yescharacteristic
20C2×Q8×Dic7C2211yescharacteristic, complemented
21C2×#6507C2211yescharacteristic, complemented
22C22×#1143C2211yescharacteristic
23C22×#1143C2211yescharacteristic
24C2×#6489C2211yescharacteristic
25C2×#6487C2211yescharacteristic
26C22×#1132C2211yescharacteristic
27C22×#1132C2211yescharacteristic
28#90316—24no—
29#90316C2218yescomplemented
30#90212—24no—
31#90212C2218yes—
32C2×#6456C2211yescharacteristic
33C2×#6456C2211yescharacteristic
34C2×#6456C2211yescharacteristic
35C2×#6456C2211yescharacteristic
36C2×#6453—21no—
37C2×#6453C2211yescharacteristic, complemented
38C2×#6452—21no—
39C2×#6450C2211yescharacteristic, complemented
40C2×D7×C22⋊C4—21no—
41C2×D7×C22⋊C4—21no—
42C2×#6442—21no—
43C2×#6442—21no—
44C2×C4×D28—21no—
45C2×C4×D28—21no—
46C7×#485C2218yescomplemented
47C2×C7×#107C2211yescharacteristic, complemented
48C2×C7×#106C2211yescharacteristic, complemented
49C2×C7×#103C2211yescharacteristic, complemented
50C2×C7×#103C2211yescharacteristic, complemented
51C2×C7×C22⋊C8C2211yescharacteristic
52C2×C22⋊(C7⋊C8)C2211yescharacteristic
53C2×#6395C2211yescharacteristic
54C2×#6395C2211yescharacteristic
55C2×#6389C2211yescharacteristic, complemented
56C2×Dic7⋊C8C2211yescharacteristic, complemented
57C2×Dic7⋊C8C2211yescharacteristic, complemented
58C2×C8×Dic7C2211yescharacteristic, complemented
59#89818C2218yes—
60#89768C2218yescomplemented
61C2×#6384C2211yescharacteristic, complemented
62C2×#6384C2211yescharacteristic, complemented
63C2×#6383C2211yescharacteristic
64C2×#6383C2211yescharacteristic
65C2×#6382C2211yescharacteristic, complemented
66C2×#6381C2211yescharacteristic, complemented
67#89663C2218yescomplemented
68#89661C2218yescomplemented
69#89643C2218yescomplemented
70#89624C2218yescomplemented
71#89590C2218yescomplemented
72#89590C2218yescomplemented
73#89589C2218yescomplemented
74#89560C2218yescomplemented
75#89503C2218yes—
76#89492C2218yescomplemented
77C2×#3123—71nomaximal, Sylow
78C24×D7—21no—
79C22×C7×Q8C2311yescharacteristic
80C23×C4×C7C2311yescharacteristic
81C22×D28—21no—
82C22×D28—22no—
83C22×D28—24no—
84C22×D28—24no—
85C22×D28C2314yes—
86C22×D28C2311yescharacteristic
87C22×D28C2311yescharacteristic
88C22×C4×D7—21no—
89C22×C4×D7—21no—
90C22×C4×D7—21no—
91C22×C4×D7—21no—
92C22×Dic14C2311yescharacteristic
93C22×C7×C8C2311yescharacteristic
94C22×C7×C8C2311yescharacteristic
95C7×C22⋊Q8—22no—
96C7×C22⋊Q8C2314yes—
97C7×#117—22no—
98C7×#117C2314yes—
99C2×C7×C4⋊C4—21no—
100C2×C7×C4⋊C4C2311yescharacteristic
101C2×C7×C4⋊C4C2311yescharacteristic
102C2×C7×C4⋊C4C2311yescharacteristic
103C2×C7×C22⋊C4—21no—
104C2×C7×C22⋊C4—21no—
105C2×C42×C7—21no—
106C2×C22⋊Dic7—21no—
107C2×C22⋊Dic7D411yescharacteristic
108C2×C22⋊Dic7D411yescharacteristic
109Q8×Dic7—22no—
110Q8×Dic7C2314yescomplemented
111#6507—22no—
112#6507C2314yescomplemented
113C2×#1143—24no—
114C2×#1143—24no—
115C2×#1143C2314yes—
116C2×#1143C2314yes—
117C2×(C2×D7)⋊C4—21no—
118C2×(C2×D7)⋊C4—21no—
119C2×(C2×D7)⋊C4—21no—
120C2×(C2×D7)⋊C4—21no—
121#6489D414yes—
122#6489C2314yes—
123C2×C4⋊Dic7—21no—
124C2×C4⋊Dic7—21no—
125C2×C4⋊Dic7D411yescharacteristic
126C2×C4⋊Dic7D411yescharacteristic
127C2×C4⋊Dic7C2311yescharacteristic
128#6487—22no—
129#6487C2314yes—
130C2×Dic7⋊C4—21no—
131C2×Dic7⋊C4—21no—
132C2×Dic7⋊C4—21no—
133C2×Dic7⋊C4—21no—
134C2×Dic7⋊C4—21no—
135C2×C4×Dic7—21no—
136C2×C4×Dic7—21no—
137C2×C4×Dic7C2311yescharacteristic
138C2×C4×Dic7C2311yescharacteristic
139C22×C7⋊C8C2311yescharacteristic
140C22×C7⋊C8C2311yescharacteristic
141C2×#1132—24no—
142C2×#1132—24no—
143C2×#1132C2314yes—
144C2×#1132C2314yes—
145#6456—22no—
146#6456—22no—
147#6456—22no—
148#6456—22no—
149#6456C2314yes—
150#6456C2314yes—
151#6456C2314yes—
152#6456C2314yes—
153#6453—28no—
154#6453—22no—
155#6453C2314yescomplemented
156#6452—28no—
157#6450—22no—
158#6450C2314yescomplemented
159D7×C22⋊C4—28no—
160D7×C22⋊C4—28no—
161#6442—28no—
162#6442—28no—
163C4×D28—28no—
164C4×D28—28no—
165C7×#107C2314yescomplemented
166C7×#106C2314yescomplemented
167C7×#103C2314yescomplemented
168C7×#103C2314yescomplemented
169C7×C22⋊C8C2314yes—
170C22⋊(C7⋊C8)C2314yes—
171#6395C2314yes—
172#6395C2314yes—
173#6389C2314yescomplemented
174Dic7⋊C8C2314yescomplemented
175Dic7⋊C8C2314yescomplemented
176C8×Dic7C2314yescomplemented
177#6384C2314yescomplemented
178#6384C2314yescomplemented
179#6383C2314yes—
180#6383C2314yes—
181#6382C2314yescomplemented
182#6381C2314yescomplemented
183C2×#541—71no—
184C2×#518—71no—
185#3123—716no—
186C2×#485—71no—
187C2×#485D711yescharacteristic, complemented
188C2×#478—71no—
189C2×#478—71no—
190C2×#461—71no—
191C2×#461—71no—
192C2×#450—71no—
193C2×#450—71no—
194C2×#440—71no—
195C2×#440—71no—
196C2×C4×SD16—71no—
197C2×C4×SD16—71no—
198C2×#433—71no—
199C24×C7C2×D411yescharacteristic
200C23×D7—21no—
201C23×D7—21no—
202C23×D7—28no—
203C23×D7—24no—
204C23×D7—82no—
205C23×D7—82no—
206C2×C7×Q8—21no—
207C2×C7×Q8—22no—
208C2×C7×Q8—22no—
209C2×C7×Q8C2412yes—
210C22×C4×C7—22no—
211C22×C4×C7—22no—
212C22×C4×C7—21no—
213C22×C4×C7—21no—
214C22×C4×C7—21no—
215C22×C4×C7—21no—
216C22×C4×C7C2×D411yescharacteristic
217C22×C4×C7C2×D412yes—
218C22×C4×C7C2412yes—
219C22×C4×C7C2411yescharacteristic
220C22×Dic7—21no—
221C22×Dic7—21no—
222C22×Dic7C2×D411yescharacteristic
223C22×Dic7C2×D411yescharacteristic
224C22×Dic7C2×D411yescharacteristic
225C22×Dic7C2×D411yescharacteristic
226C2×D28—28no—
227C2×D28—216no—
228C2×D28—24no—
229C2×D28—21no—
230C2×D28—21no—
231C2×D28—22no—
232C2×D28—22no—
233C2×D28—28no—
234C2×D28—28no—
235C2×D28#4114yes—
236C2×D28#4114yes—
237C2×D28C2412yes—
238C2×D28C2412yes—
239C2×C4×D7—24no—
240C2×C4×D7—24no—
241C2×C4×D7—24no—
242C2×C4×D7—24no—
243C2×C4×D7—82no—
244C2×C4×D7—82no—
245C2×C4×D7—82no—
246C2×C4×D7—82no—
247C2×Dic14—22no—
248C2×Dic14—22no—
249C2×Dic14—21no—
250C2×Dic14C2412yes—
251C2×C7×C8—22no—
252C2×C7×C8—22no—
253C2×C7×C8C2412yes—
254C2×C7×C8C2412yes—
255C7×C4⋊C4—21no—
256C7×C4⋊C4—24no—
257C7×C4⋊C4—21no—
258C7×C4⋊C4—21no—
259C7×C4⋊C4C2412yes—
260C7×C4⋊C4C2412yes—
261C7×C4⋊C4C2412yes—
262C7×C22⋊C4—24no—
263C7×C22⋊C4—24no—
264C42×C7—24no—
265C22⋊Dic7—24no—
266C22⋊Dic7C2×D414yes—
267C22⋊Dic7C2×D414yes—
268#1143—28no—
269#1143—28no—
270(C2×D7)⋊C4—24no—
271(C2×D7)⋊C4—24no—
272(C2×D7)⋊C4—24no—
273(C2×D7)⋊C4—24no—
274C4⋊Dic7—21no—
275C4⋊Dic7—24no—
276C4⋊Dic7—24no—
277C4⋊Dic7C2×D414yes—
278C4⋊Dic7C2×D414yes—
279C4⋊Dic7C2412yes—
280Dic7⋊C4—24no—
281Dic7⋊C4—24no—
282Dic7⋊C4—24no—
283Dic7⋊C4—24no—
284Dic7⋊C4—24no—
285C4×Dic7—24no—
286C4×Dic7—24no—
287C4×Dic7C2×D412yes—
288C4×Dic7C2×D412yes—
289C4×Dic7C2412yes—
290C4×Dic7C2412yes—
291C2×C7⋊C8—22no—
292C2×C7⋊C8—22no—
293C2×C7⋊C8C2412yes—
294C2×C7⋊C8C2412yes—
295#1132—28no—
296#1132—28no—
297C23×D4—71no—
298C22×SD16—71no—
299C22×SD16—71no—
300C22×SD16—71no—
301C22×SD16—71no—
302#541—78no—
303#541—144no—
304C2×C4⋊Q8—71no—
305C2×#126—141no—
306C2×#126—141no—
307C2×#125—71no—
308C2×#125—141no—
309C2×#125—141no—
310C2×C22⋊Q8—71no—
311C2×C22⋊Q8C2×D711yescharacteristic
312#518—78no—
313#518—144no—
314C2×C4×Q8—71no—
315C2×C4×Q8—71no—
316C2×C4×D4—71no—
317C2×C4×D4—71no—
318C2×C4×D4—71no—
319C2×C4×D4—71no—
320C2×C4×D4—141no—
321C2×C4×D4—141no—
322C2×#117—71no—
323C2×#117C2×D711yescharacteristic
324C22×C22⋊C4—141no—
325C22×C22⋊C4—141no—
326#485—78no—
327#485C2×D718yescomplemented
328#478—78no—
329#478—78no—
330#461—78no—
331#461—78no—
332#450—78no—
333#450—78no—
334#440—78no—
335#440—78no—
336C4×SD16—78no—
337C4×SD16—78no—
338#433—78no—
339C2×#107—71no—
340C2×#107C2×D711yescharacteristic, complemented
341C2×#106—71no—
342C2×#106C2×D711yescharacteristic, complemented
343C2×C4⋊C8—71no—
344C2×C4⋊C8—71no—
345C2×#103—71no—
346C2×#103—71no—
347C2×#103C2×D711yescharacteristic, complemented
348C2×#103C2×D711yescharacteristic, complemented
349C2×#102—71no—
350C2×#102—71no—
351C2×#102—71no—
352C2×#102—71no—
353C2×C22⋊C8—71no—
354C2×C22⋊C8C2×D711yescharacteristic
355C2×#97—71no—
356C2×C4×C8—71no—
357C23×C7—22no—
358C23×C7—22no—
359C23×C7—22no—
360C23×C7C22×D412yes—
361C23×C7C22×D411yescharacteristic
362C22×D7—24no—
363C22×D7—24no—
364C22×D7—22no—
365C22×D7—22no—
366C22×D7—216no—
367C22×D7—42no—
368C22×D7—42no—
369C22×D7—42no—
370C22×D7—42no—
371C22×D7—84no—
372C22×D7—84no—
373C22×D7—816no—
374C7×Q8—22no—
375C7×Q8—22no—
376C7×Q8—42no—
377C2×C4×C7—22no—
378C2×C4×C7—24no—
379C2×C4×C7—22no—
380C2×C4×C7—22no—
381C2×C4×C7—22no—
382C2×C4×C7—22no—
383C2×C4×C7—22no—
384C2×C4×C7—22no—
385C2×C4×C7—42no—
386C2×C4×C7—42no—
387C2×C4×C7—42no—
388C2×C4×C7—42no—
389C2×C4×C7C22×D412yes—
390C2×C4×C7C22×D411yescharacteristic
391C2×C4×C7C2×#4112yes—
392C2×C4×C7C2×#4112yes—
393C2×C4×C7C2511yescharacteristic
394C2×Dic7—22no—
395C2×Dic7—22no—
396C2×Dic7—22no—
397C2×Dic7—22no—
398C2×Dic7—22no—
399C2×Dic7—22no—
400C2×Dic7—42no—
401C2×Dic7—42no—
402C2×Dic7C22×D412yes—
403C2×Dic7C22×D412yes—
404C2×Dic7C22×D412yes—
405C2×Dic7C22×D412yes—
406D28—216no—
407D28—24no—
408D28—24no—
409D28—22no—
410D28—22no—
411D28C2×#4114yes—
412D28C2×#4114yes—
413C4×D7—84no—
414C4×D7—84no—
415C4×D7—84no—
416C4×D7—84no—
417Dic14—22no—
418Dic14—22no—
419Dic14—42no—
420C7×C8—22no—
421C7×C8—22no—
422C7⋊C8—22no—
423C7⋊C8—22no—
424C25—141no—
425C22×Q8—71no—
426C22×Q8C22×D711yescharacteristic
427C22×D4—71no—
428C22×D4—71no—
429C22×D4—74no—
430C22×D4—144no—
431C22×D4—144no—
432C22×D4—141no—
433C22×D4—142no—
434C23×C4—141no—
435C23×C4—141no—
436C23×C4—141no—
437C23×C4—141no—
438C23×C4C22×D711yescharacteristic
439C2×SD16—74no—
440C2×SD16—74no—
441C2×SD16—74no—
442C2×SD16—74no—
443C2×SD16—144no—
444C2×SD16—144no—
445C2×SD16—144no—
446C2×SD16—144no—
447C22×C8—71no—
448C22×C8—71no—
449C22×C8C22×D711yescharacteristic
450C22×C8C22×D711yescharacteristic
451C4⋊Q8—74no—
452C4⋊Q8—142no—
453#126—148no—
454#126—148no—
455#125—74no—
456#125—142no—
457#125—148no—
458#125—148no—
459C22⋊Q8—22no—
460C22⋊Q8—74no—
461C22⋊Q8—142no—
462C22⋊Q8C22×D714yes—
463C4×Q8—74no—
464C4×Q8—74no—
465C4×Q8—142no—
466C4×Q8—142no—
467C4×D4—74no—
468C4×D4—74no—
469C4×D4—74no—
470C4×D4—74no—
471C4×D4—148no—
472C4×D4—148no—
473C4×D4—142no—
474C4×D4—142no—
475C4×D4—142no—
476C4×D4—142no—
477#117—22no—
478#117—74no—
479#117—74no—
480#117C22×D714yes—
481C2×C4⋊C4—21no—
482C2×C4⋊C4—71no—
483C2×C4⋊C4—71no—
484C2×C4⋊C4—71no—
485C2×C4⋊C4—141no—
486C2×C4⋊C4—141no—
487C2×C4⋊C4—141no—
488C2×C4⋊C4—141no—
489C2×C4⋊C4—141no—
490C2×C4⋊C4—141no—
491C2×C4⋊C4—141no—
492C2×C4⋊C4C22×D711yescharacteristic
493C2×C4⋊C4C22×D711yescharacteristic
494C2×C4⋊C4C22×D711yescharacteristic
495C2×C22⋊C4—21no—
496C2×C22⋊C4—21no—
497C2×C22⋊C4—71no—
498C2×C22⋊C4—71no—
499C2×C22⋊C4—148no—
500C2×C22⋊C4—148no—
501C2×C22⋊C4—141no—
502C2×C22⋊C4—141no—
503C2×C22⋊C4—141no—
504C2×C22⋊C4—141no—
505C2×C22⋊C4—141no—
506C2×C42—21no—
507C2×C42—71no—
508C2×C42—71no—
509C2×C42—141no—
510C2×C42—141no—
511#107—74no—
512#107C22×D714yescomplemented
513#106—74no—
514#106C22×D714yescomplemented
515C4⋊C8—74no—
516C4⋊C8—74no—
517#103—74no—
518#103—74no—
519#103C22×D714yescomplemented
520#103C22×D714yescomplemented
521#102—74no—
522#102—74no—
523#102—74no—
524#102—74no—
525C22⋊C8—74no—
526C22⋊C8C22×D714yes—
527#97—74no—
528C4×C8—74no—
529C22×C7—22no—
530C22×C7—22no—
531C22×C7—22no—
532C22×C7—44no—
533C22×C7#52512yes—
534C22×C7#57712yes—
535C22×C7#57712yes—
536C22×C7C23×D411yescharacteristic
537C2×D7—24no—
538C2×D7—24no—
539C2×D7—48no—
540C2×D7—48no—
541C2×D7—42no—
542C2×D7—42no—
543C2×D7—42no—
544C2×D7—42no—
545C2×D7—816no—
546C4×C7—22no—
547C4×C7—42no—
548C4×C7—42no—
549C4×C7—42no—
550C4×C7—42no—
551C4×C7#52512yes—
552C4×C7C22×#4111yescharacteristic
553C4×C7C22×#4111yescharacteristic
554Dic7—22no—
555Dic7—22no—
556Dic7—22no—
557Dic7—22no—
558Dic7—42no—
559Dic7—42no—
560C24—148no—
561C24—141no—
562C24—141no—
563C24—144no—
564C24—562no—
565C24—562no—
566C24D4×D711yescharacteristic
567C2×Q8—21no—
568C2×Q8—22no—
569C2×Q8—22no—
570C2×Q8—72no—
571C2×Q8—141no—
572C2×Q8—142no—
573C2×Q8—142no—
574C2×Q8C23×D712yes—
575C2×D4—74no—
576C2×D4—74no—
577C2×D4—72no—
578C2×D4—72no—
579C2×D4—148no—
580C2×D4—148no—
581C2×D4—148no—
582C2×D4—1416no—
583C2×D4—144no—
584C2×D4—141no—
585C2×D4—141no—
586C2×D4—142no—
587C2×D4—142no—
588C22×C4—22no—
589C22×C4—22no—
590C22×C4—21no—
591C22×C4—21no—
592C22×C4—21no—
593C22×C4—21no—
594C22×C4—71no—
595C22×C4—71no—
596C22×C4—71no—
597C22×C4—71no—
598C22×C4—144no—
599C22×C4—144no—
600C22×C4—144no—
601C22×C4—144no—
602C22×C4—141no—
603C22×C4—141no—
604C22×C4—562no—
605C22×C4—562no—
606C22×C4—562no—
607C22×C4—562no—
608C22×C4D4×D712yes—
609C22×C4D4×D711yescharacteristic
610C22×C4C23×D712yes—
611C22×C4C23×D711yescharacteristic
612SD16—148no—
613SD16—148no—
614SD16—148no—
615SD16—148no—
616C2×C8—22no—
617C2×C8—22no—
618C2×C8—72no—
619C2×C8—72no—
620C2×C8—142no—
621C2×C8—142no—
622C2×C8C23×D712yes—
623C2×C8C23×D712yes—
624C4⋊C4—24no—
625C4⋊C4—21no—
626C4⋊C4—21no—
627C4⋊C4—21no—
628C4⋊C4—74no—
629C4⋊C4—74no—
630C4⋊C4—72no—
631C4⋊C4—144no—
632C4⋊C4—144no—
633C4⋊C4—144no—
634C4⋊C4—144no—
635C4⋊C4—144no—
636C4⋊C4—144no—
637C4⋊C4—144no—
638C4⋊C4—141no—
639C4⋊C4C23×D712yes—
640C4⋊C4C23×D712yes—
641C4⋊C4C23×D712yes—
642C22⋊C4—24no—
643C22⋊C4—24no—
644C22⋊C4—74no—
645C22⋊C4—74no—
646C22⋊C4—144no—
647C22⋊C4—144no—
648C22⋊C4—144no—
649C22⋊C4—144no—
650C22⋊C4—144no—
651C42—24no—
652C42—72no—
653C42—72no—
654C42—72no—
655C42—72no—
656C42—144no—
657C42—144no—
658C2×C7—42no—
659C2×C7#312314yescomplemented
660C2×C7C2×#52511yescharacteristic
661C2×C7C2×#57711yescharacteristic
662C2×C7C2×#57711yescharacteristic
663D7—44no—
664D7—44no—
665C23—22no—
666C23—22no—
667C23—22no—
668C23—1416no—
669C23—144no—
670C23—144no—
671C23—142no—
672C23—142no—
673C23—282no—
674C23—282no—
675C23—282no—
676C23—282no—
677C23—564no—
678C23—564no—
679C23—5616no—
680C23C2×D4×D712yes—
681C23C2×D4×D711yescharacteristic
682Q8—22no—
683Q8—22no—
684Q8—42no—
685Q8—142no—
686Q8—142no—
687Q8—282no—
688D4—74no—
689D4—74no—
690D4—1416no—
691D4—144no—
692D4—144no—
693D4—142no—
694D4—142no—
695C2×C4—22no—
696C2×C4—24no—
697C2×C4—22no—
698C2×C4—22no—
699C2×C4—22no—
700C2×C4—22no—
701C2×C4—22no—
702C2×C4—22no—
703C2×C4—42no—
704C2×C4—42no—
705C2×C4—42no—
706C2×C4—42no—
707C2×C4—72no—
708C2×C4—72no—
709C2×C4—72no—
710C2×C4—72no—
711C2×C4—142no—
712C2×C4—142no—
713C2×C4—142no—
714C2×C4—142no—
715C2×C4—142no—
716C2×C4—142no—
717C2×C4—282no—
718C2×C4—282no—
719C2×C4—564no—
720C2×C4—564no—
721C2×C4—564no—
722C2×C4—564no—
723C2×C4C2×D4×D712yes—
724C2×C4C2×D4×D711yescharacteristic
725C2×C4D7×#4112yes—
726C2×C4D7×#4112yes—
727C2×C4C24×D711yescharacteristic
728C8—22no—
729C8—22no—
730C8—142no—
731C8—142no—
732C7C2×#312311yescharacteristic, complemented, Sylow
733C22—22no—
734C22—22no—
735C22—22no—
736C22—44no—
737C22—144no—
738C22—144no—
739C22—282no—
740C22—282no—
741C22—288no—
742C22—288no—
743C22—282no—
744C22—282no—
745C22—5616no—
746C22#9034712yes—
747C22#9046112yes—
748C22#9046912yes—
749C22C22×D4×D711yescharacteristic
750C4—22no—
751C4—42no—
752C4—42no—
753C4—42no—
754C4—42no—
755C4—142no—
756C4—142no—
757C4—142no—
758C4—142no—
759C4—282no—
760C4—282no—
761C4#9034712yes—
762C4C2×D7×#4111yescharacteristic
763C4C2×D7×#4111yescharacteristic
764C2—42no—
765C2—284no—
766C2—284no—
767C2#1173894314yesdirect product factor
768C2C2×#9034711yescharacteristic
769C2C2×#9046111yescharacteristic
770C2C2×#9046911yescharacteristic
subgroupG/H
centerC23C2×D4×D7
commutator, cosocleC2×C4×C7C25
FrattiniC2×C4C24×D7
FittingC2×C7×#485C2
socleC23×C7C22×D4
prime radicalC23×D28C22
hypercenterC2×#485D7
hypocenterC7C2×#3123
LCSG ▷ C2×C4×C7 ▷ C2×C7 ▷ C7
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#485

Complements

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

NH ≅ G/Ntype
1. C2×#90316C2semidirect
3. C2×C7×#485C2semidirect
5. C2×#89768C2semidirect
6. #11738943C2direct (N × H)
7. C2×#89663C2semidirect
8. C2×#89661C2semidirect
9. C2×#89643C2semidirect
10. C2×#89624C2semidirect
11. C2×#89590C2semidirect
12. C2×#89590C2semidirect
13. C2×#89589C2semidirect
14. C2×#89560C2semidirect
16. C2×#89492C2semidirect
20. C2×Q8×Dic7C22semidirect
21. C2×#6507C22semidirect
29. #90316C22semidirect
37. C2×#6453C22semidirect
39. C2×#6450C22semidirect
46. C7×#485C22semidirect
47. C2×C7×#107C22semidirect
48. C2×C7×#106C22semidirect
49. C2×C7×#103C22semidirect
50. C2×C7×#103C22semidirect
55. C2×#6389C22semidirect
56. C2×Dic7⋊C8C22semidirect
57. C2×Dic7⋊C8C22semidirect
58. C2×C8×Dic7C22semidirect
60. #89768C22semidirect
61. C2×#6384C22semidirect
62. C2×#6384C22semidirect
65. C2×#6382C22semidirect
66. C2×#6381C22semidirect
67. #89663C22semidirect
68. #89661C22semidirect
69. #89643C22semidirect
70. #89624C22semidirect
71. #89590C22semidirect
72. #89590C22semidirect
73. #89589C22semidirect
74. #89560C22semidirect
76. #89492C22semidirect
110. Q8×Dic7C23semidirect
112. #6507C23semidirect
155. #6453C23semidirect
158. #6450C23semidirect
165. C7×#107C23semidirect
166. C7×#106C23semidirect
167. C7×#103C23semidirect
168. C7×#103C23semidirect
173. #6389C23semidirect
174. Dic7⋊C8C23semidirect
175. Dic7⋊C8C23semidirect
176. C8×Dic7C23semidirect
177. #6384C23semidirect
178. #6384C23semidirect
181. #6382C23semidirect
182. #6381C23semidirect
187. C2×#485D7semidirect
327. #485C2×D7semidirect
340. C2×#107C2×D7semidirect
342. C2×#106C2×D7semidirect
347. C2×#103C2×D7semidirect
348. C2×#103C2×D7semidirect
512. #107C22×D7semidirect
514. #106C22×D7semidirect
519. #103C22×D7semidirect
520. #103C22×D7semidirect
659. C2×C7#3123semidirect
732. C7C2×#3123semidirect
767. C2#11738943direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#903162
C2×#902122
C2×C7×#4852
C2×#898182
C2×#897682
#117389432
C2×#896632
C2×#896612
C2×#896432
C2×#896242
C2×#895902
C2×#895892
C2×#895602
C2×#895032
C2×#894922
C2×#31237