Finite Group Databasebeta

← C2×#11738800 #14222138

Subgroups — C2×#11738800 #14222138

Order 1792.

2122 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×#90310C211yesmaximal, characteristic
2C2×#90207C211yesmaximal, characteristic, complemented
3C2×C7×#482C211yesmaximal, characteristic, complemented
4C2×#89812C211yesmaximal, characteristic, complemented
5C2×#89775C211yesmaximal, characteristic, complemented
6#11738800C2116yesmaximal, direct product factor
7C2×#89649C211yesmaximal, characteristic, complemented
8C2×#89661C211yesmaximal, characteristic, complemented
9C2×#89629C211yesmaximal, characteristic, complemented
10C2×#89624C211yesmaximal, characteristic, complemented
11C2×#89534C211yesmaximal, characteristic, complemented
12C2×#89534C211yesmaximal, characteristic, complemented
13C2×#89529C211yesmaximal, characteristic, complemented
14C2×#89530C211yesmaximal, characteristic, complemented
15C2×#89510C211yesmaximal, characteristic, complemented
16C2×#89492C211yesmaximal, characteristic, complemented
17C23×Dic14C2211yescharacteristic
18C2×C7×#121C2211yescharacteristic
19C2×C7×#117C2211yescharacteristic
20C2×#6503C2211yescharacteristic
21C2×#6502—21no—
22C2×#6501—21no—
23C2×D4×Dic7C2211yescharacteristic
24C22×#1142C2211yescharacteristic
25C22×#1142C2211yescharacteristic
26C2×#6493C2211yescharacteristic
27C2×#6489C2211yescharacteristic
28C22×#1132C2211yescharacteristic
29C22×#1132C2211yescharacteristic
30#90310—24no—
31#90310C2218yes—
32#90207—24no—
33#90207C2218yescomplemented
34C2×#6456C2211yescharacteristic
35C2×#6453C2211yescharacteristic
36C2×#6450C2211yescharacteristic
37C2×#6450C2211yescharacteristic
38C2×#6450C2211yescharacteristic
39C2×#6450C2211yescharacteristic
40C2×#6449—21no—
41C2×#6446—21no—
42C2×#6440—21no—
43C2×#6440—21no—
44C2×C4×Dic14—21no—
45C2×C4×Dic14—21no—
46C7×#482C2218yescomplemented
47C2×C7×#107C2211yescharacteristic
48C2×C7×#106C2211yescharacteristic
49C2×C7×#102C2211yescharacteristic
50C2×C7×#102C2211yescharacteristic
51C2×C7×C22⋊C8C2211yescharacteristic
52C2×C22⋊(C7⋊C8)C2211yescharacteristic
53C2×#6390C2211yescharacteristic
54C2×#6390C2211yescharacteristic
55C2×#6389C2211yescharacteristic
56C2×Dic7⋊C8C2211yescharacteristic
57C2×Dic7⋊C8C2211yescharacteristic
58C2×C8×Dic7C2211yescharacteristic
59#89812C2218yescomplemented
60#89775C2218yescomplemented
61C2×#6384C2211yescharacteristic
62C2×#6384C2211yescharacteristic
63C2×#6383C2211yescharacteristic
64C2×#6383C2211yescharacteristic
65C2×#6382C2211yescharacteristic
66C2×#6381C2211yescharacteristic
67#89661C2218yescomplemented
68#89649C2218yescomplemented
69#89629C2218yescomplemented
70#89624C2218yescomplemented
71#89534C2218yescomplemented
72#89534C2218yescomplemented
73#89530C2218yescomplemented
74#89529C2218yescomplemented
75#89510C2218yescomplemented
76#89492C2218yescomplemented
77C2×#3126—71nomaximal, Sylow
78C22×C7×D4—21no—
79C22×C7×D4C2311yescharacteristic
80C23×C4×C7C2311yescharacteristic
81C22×C22⋊D7—21no—
82C22×C22⋊D7—21no—
83C22×C22⋊D7—21no—
84C23×Dic7—21no—
85C23×Dic7—21no—
86C22×D28C2311yescharacteristic
87C22×C4×D7—21no—
88C22×Dic14—21no—
89C22×Dic14—22no—
90C22×Dic14—24no—
91C22×Dic14—24no—
92C22×Dic14C2314yes—
93C22×Dic14C2311yescharacteristic
94C22×Dic14C2311yescharacteristic
95C22×C7×C8C2311yescharacteristic
96C22×C7×C8C2311yescharacteristic
97C7×#121—22no—
98C7×#121C2314yes—
99C7×#117—22no—
100C7×#117C2314yes—
101C2×C7×C4⋊C4C2311yescharacteristic
102C2×C7×C4⋊C4C2311yescharacteristic
103C2×C7×C4⋊C4C2311yescharacteristic
104C2×C7×C22⋊C4—21no—
105C2×C7×C22⋊C4—21no—
106C2×C42×C7—21no—
107C2×C22⋊Dic7—21no—
108C2×C22⋊Dic7D411yescharacteristic
109C2×C22⋊Dic7D411yescharacteristic
110#6503—22no—
111#6503C2314yes—
112#6502—28no—
113#6501—28no—
114D4×Dic7—22no—
115D4×Dic7C2314yes—
116C2×#1142—24no—
117C2×#1142—24no—
118C2×#1142C2314yes—
119C2×#1142C2314yes—
120#6493—22no—
121#6493C2314yes—
122C2×(C2×D7)⋊C4—21no—
123C2×(C2×D7)⋊C4—21no—
124#6489D414yes—
125#6489C2314yes—
126C2×C4⋊Dic7—21no—
127C2×C4⋊Dic7D411yescharacteristic
128C2×C4⋊Dic7D411yescharacteristic
129C2×C4⋊Dic7C2311yescharacteristic
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×Dic7—21no—
138C2×C4×Dic7—21no—
139C2×C4×Dic7C2311yescharacteristic
140C2×C4×Dic7C2311yescharacteristic
141C22×C7⋊C8C2311yescharacteristic
142C22×C7⋊C8C2311yescharacteristic
143C2×#1132—24no—
144C2×#1132—24no—
145C2×#1132C2314yes—
146C2×#1132C2314yes—
147#6456—22no—
148#6456C2314yes—
149#6453—22no—
150#6453C2314yes—
151#6450—22no—
152#6450—22no—
153#6450—22no—
154#6450—22no—
155#6450C2314yes—
156#6450C2314yes—
157#6450C2314yes—
158#6450C2314yes—
159#6449—28no—
160#6446—28no—
161#6440—28no—
162#6440—28no—
163C4×Dic14—28no—
164C4×Dic14—28no—
165C7×#107C2314yes—
166C7×#106C2314yes—
167C7×#102C2314yes—
168C7×#102C2314yes—
169C7×C22⋊C8C2314yes—
170C22⋊(C7⋊C8)C2314yes—
171#6390C2314yes—
172#6390C2314yes—
173#6389C2314yes—
174Dic7⋊C8C2314yes—
175Dic7⋊C8C2314yes—
176C8×Dic7C2314yes—
177#6384C2314yes—
178#6384C2314yes—
179#6383C2314yes—
180#6383C2314yes—
181#6382C2314yes—
182#6381C2314yes—
183C2×#540—71no—
184C2×#519—71no—
185#3126—716no—
186C2×#482—71no—
187C2×#482D711yescharacteristic, complemented
188C2×#479—71no—
189C2×#479—71no—
190C2×#460—71no—
191C2×#460—71no—
192C2×#448—71no—
193C2×#448—71no—
194C2×#440—71no—
195C2×#440—71no—
196C2×C4×SD16—71no—
197C2×C4×SD16—71no—
198C2×#433—71no—
199C24×C7—21no—
200C24×C7C2×D411yescharacteristic
201C23×D7—21no—
202C2×C7×D4—24no—
203C2×C7×D4—21no—
204C2×C7×D4—22no—
205C2×C7×D4—22no—
206C2×C7×D4—82no—
207C2×C7×D4C2412yes—
208C22×C4×C7—22no—
209C22×C4×C7—22no—
210C22×C4×C7—21no—
211C22×C4×C7—21no—
212C22×C4×C7—21no—
213C22×C4×C7C2×D411yescharacteristic
214C22×C4×C7C2×D412yes—
215C22×C4×C7C2412yes—
216C22×C4×C7C2411yescharacteristic
217C2×C22⋊D7—24no—
218C2×C22⋊D7—24no—
219C2×C22⋊D7—24no—
220C2×C22⋊D7—82no—
221C2×C22⋊D7—82no—
222C2×C22⋊D7—82no—
223C22×Dic7—28no—
224C22×Dic7—24no—
225C22×Dic7—21no—
226C22×Dic7—21no—
227C22×Dic7—21no—
228C22×Dic7—24no—
229C22×Dic7—82no—
230C22×Dic7C2×D411yescharacteristic
231C22×Dic7C2×D411yescharacteristic
232C22×Dic7C2×D411yescharacteristic
233C22×Dic7C2×D411yescharacteristic
234C2×D28—22no—
235C2×D28—22no—
236C2×D28—21no—
237C2×D28C2412yes—
238C2×C4×D7—24no—
239C2×C4×D7—82no—
240C2×Dic14—28no—
241C2×Dic14—216no—
242C2×Dic14—24no—
243C2×Dic14—21no—
244C2×Dic14—21no—
245C2×Dic14—22no—
246C2×Dic14—22no—
247C2×Dic14—28no—
248C2×Dic14—28no—
249C2×Dic14#4114yes—
250C2×Dic14#4114yes—
251C2×Dic14C2412yes—
252C2×Dic14C2412yes—
253C2×C7×C8—22no—
254C2×C7×C8—22no—
255C2×C7×C8C2412yes—
256C2×C7×C8C2412yes—
257C7×C4⋊C4—21no—
258C7×C4⋊C4—21no—
259C7×C4⋊C4—21no—
260C7×C4⋊C4C2412yes—
261C7×C4⋊C4C2412yes—
262C7×C4⋊C4C2412yes—
263C7×C22⋊C4—24no—
264C7×C22⋊C4—24no—
265C42×C7—24no—
266C22⋊Dic7—24no—
267C22⋊Dic7C2×D414yes—
268C22⋊Dic7C2×D414yes—
269#1142—28no—
270#1142—28no—
271(C2×D7)⋊C4—24no—
272(C2×D7)⋊C4—24no—
273C4⋊Dic7—21no—
274C4⋊Dic7—24no—
275C4⋊Dic7C2×D414yes—
276C4⋊Dic7C2×D414yes—
277C4⋊Dic7C2412yes—
278Dic7⋊C4—24no—
279Dic7⋊C4—24no—
280Dic7⋊C4—24no—
281Dic7⋊C4—24no—
282Dic7⋊C4—24no—
283C4×Dic7—24no—
284C4×Dic7—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×Q8—71no—
298C22×SD16—71no—
299C22×SD16—71no—
300C22×SD16—71no—
301C22×SD16—71no—
302#540—78no—
303#540—144no—
304C2×#127—71no—
305C2×#125—71no—
306C2×#123—141no—
307C2×#123—141no—
308C2×#121—71no—
309C2×#121—141no—
310C2×#121—141no—
311C2×#121C2×D711yescharacteristic
312#519—78no—
313#519—144no—
314C2×C4×Q8—71no—
315C2×C4×Q8—71no—
316C2×C4×Q8—71no—
317C2×C4×Q8—71no—
318C2×C4×Q8—141no—
319C2×C4×Q8—141no—
320C2×C4×D4—71no—
321C2×C4×D4—71no—
322C2×#117—71no—
323C2×#117—141no—
324C2×#117—141no—
325C2×#117C2×D711yescharacteristic
326#482—78no—
327#482C2×D718yescomplemented
328#479—78no—
329#479—78no—
330#460—78no—
331#460—78no—
332#448—78no—
333#448—78no—
334#440—78no—
335#440—78no—
336C4×SD16—78no—
337C4×SD16—78no—
338#433—78no—
339C2×#107—71no—
340C2×#107C2×D711yescharacteristic
341C2×#106—71no—
342C2×#106C2×D711yescharacteristic
343C2×C4⋊C8—71no—
344C2×C4⋊C8—71no—
345C2×#103—71no—
346C2×#103—71no—
347C2×#103—71no—
348C2×#103—71no—
349C2×#102—71no—
350C2×#102—71no—
351C2×#102C2×D711yescharacteristic
352C2×#102C2×D711yescharacteristic
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×C7—22no—
361C23×C7—42no—
362C23×C7—42no—
363C23×C7—42no—
364C23×C7C22×D412yes—
365C23×C7C22×D411yescharacteristic
366C22×D7—22no—
367C22×D7—42no—
368C22×D7—42no—
369C22×D7—42no—
370C7×D4—22no—
371C7×D4—22no—
372C7×D4—42no—
373C7×D4—84no—
374C2×C4×C7—22no—
375C2×C4×C7—24no—
376C2×C4×C7—22no—
377C2×C4×C7—22no—
378C2×C4×C7—22no—
379C2×C4×C7—22no—
380C2×C4×C7—22no—
381C2×C4×C7—42no—
382C2×C4×C7—42no—
383C2×C4×C7—42no—
384C2×C4×C7C22×D412yes—
385C2×C4×C7C22×D411yescharacteristic
386C2×C4×C7C2×#4112yes—
387C2×C4×C7C2×#4112yes—
388C2×C4×C7C2511yescharacteristic
389C22⋊D7—84no—
390C22⋊D7—84no—
391C22⋊D7—84no—
392C2×Dic7—216no—
393C2×Dic7—24no—
394C2×Dic7—24no—
395C2×Dic7—22no—
396C2×Dic7—22no—
397C2×Dic7—22no—
398C2×Dic7—22no—
399C2×Dic7—22no—
400C2×Dic7—22no—
401C2×Dic7—22no—
402C2×Dic7—42no—
403C2×Dic7—84no—
404C2×Dic7C22×D412yes—
405C2×Dic7C22×D412yes—
406C2×Dic7C22×D412yes—
407C2×Dic7C22×D412yes—
408D28—22no—
409D28—22no—
410D28—42no—
411C4×D7—84no—
412Dic14—216no—
413Dic14—24no—
414Dic14—24no—
415Dic14—22no—
416Dic14—22no—
417Dic14C2×#4114yes—
418Dic14C2×#4114yes—
419C7×C8—22no—
420C7×C8—22no—
421C7⋊C8—22no—
422C7⋊C8—22no—
423C22×Q8—71no—
424C22×Q8—71no—
425C22×Q8—74no—
426C22×Q8—144no—
427C22×Q8—144no—
428C22×Q8—141no—
429C22×Q8—142no—
430C22×D4—21no—
431C22×D4—71no—
432C22×D4—141no—
433C22×D4—141no—
434C22×D4—141no—
435C22×D4C22×D711yescharacteristic
436C23×C4—141no—
437C23×C4—141no—
438C23×C4—141no—
439C23×C4C22×D711yescharacteristic
440C2×SD16—74no—
441C2×SD16—74no—
442C2×SD16—74no—
443C2×SD16—74no—
444C2×SD16—144no—
445C2×SD16—144no—
446C2×SD16—144no—
447C2×SD16—144no—
448C22×C8—71no—
449C22×C8—71no—
450C22×C8C22×D711yescharacteristic
451C22×C8C22×D711yescharacteristic
452#127—74no—
453#127—142no—
454#125—74no—
455#125—142no—
456#123—148no—
457#123—148no—
458#121—22no—
459#121—74no—
460#121—148no—
461#121—148no—
462#121—142no—
463#121C22×D714yes—
464C4×Q8—74no—
465C4×Q8—74no—
466C4×Q8—74no—
467C4×Q8—74no—
468C4×Q8—148no—
469C4×Q8—148no—
470C4×Q8—142no—
471C4×Q8—142no—
472C4×Q8—142no—
473C4×Q8—142no—
474C4×D4—74no—
475C4×D4—74no—
476C4×D4—142no—
477C4×D4—142no—
478#117—22no—
479#117—74no—
480#117—74no—
481#117—148no—
482#117—148no—
483#117C22×D714yes—
484C2×C4⋊C4—71no—
485C2×C4⋊C4—71no—
486C2×C4⋊C4—71no—
487C2×C4⋊C4—141no—
488C2×C4⋊C4—141no—
489C2×C4⋊C4—141no—
490C2×C4⋊C4—141no—
491C2×C4⋊C4—141no—
492C2×C4⋊C4—141no—
493C2×C4⋊C4C22×D711yescharacteristic
494C2×C4⋊C4C22×D711yescharacteristic
495C2×C4⋊C4C22×D711yescharacteristic
496C2×C22⋊C4—21no—
497C2×C22⋊C4—21no—
498C2×C22⋊C4—71no—
499C2×C22⋊C4—71no—
500C2×C22⋊C4—141no—
501C2×C22⋊C4—141no—
502C2×C22⋊C4—141no—
503C2×C42—21no—
504C2×C42—71no—
505C2×C42—71no—
506C2×C42—141no—
507C2×C42—141no—
508C2×C42—141no—
509C2×C42—141no—
510#107—74no—
511#107C22×D714yes—
512#106—74no—
513#106C22×D714yes—
514C4⋊C8—74no—
515C4⋊C8—74no—
516#103—74no—
517#103—74no—
518#103—74no—
519#103—74no—
520#102—74no—
521#102—74no—
522#102C22×D714yes—
523#102C22×D714yes—
524C22⋊C8—74no—
525C22⋊C8C22×D714yes—
526#97—74no—
527C4×C8—74no—
528C22×C7—22no—
529C22×C7—22no—
530C22×C7—22no—
531C22×C7—44no—
532C22×C7—42no—
533C22×C7—42no—
534C22×C7—42no—
535C22×C7—84no—
536C22×C7#52512yes—
537C22×C7#57712yes—
538C22×C7#57712yes—
539C22×C7C23×D411yescharacteristic
540C2×D7—42no—
541C2×D7—42no—
542C2×D7—42no—
543C2×D7—84no—
544C4×C7—22no—
545C4×C7—42no—
546C4×C7—42no—
547C4×C7—42no—
548C4×C7#52512yes—
549C4×C7C22×#4111yescharacteristic
550C4×C7C22×#4111yescharacteristic
551Dic7—24no—
552Dic7—24no—
553Dic7—22no—
554Dic7—22no—
555Dic7—22no—
556Dic7—22no—
557Dic7—42no—
558C24—21no—
559C24—141no—
560C24D4×D711yescharacteristic
561C2×Q8—74no—
562C2×Q8—74no—
563C2×Q8—72no—
564C2×Q8—72no—
565C2×Q8—148no—
566C2×Q8—148no—
567C2×Q8—148no—
568C2×Q8—1416no—
569C2×Q8—144no—
570C2×Q8—141no—
571C2×Q8—141no—
572C2×Q8—142no—
573C2×Q8—142no—
574C2×D4—24no—
575C2×D4—21no—
576C2×D4—22no—
577C2×D4—22no—
578C2×D4—72no—
579C2×D4—82no—
580C2×D4—144no—
581C2×D4—144no—
582C2×D4—144no—
583C2×D4—141no—
584C2×D4—142no—
585C2×D4—142no—
586C2×D4—562no—
587C2×D4—562no—
588C2×D4—562no—
589C2×D4C23×D712yes—
590C22×C4—22no—
591C22×C4—22no—
592C22×C4—21no—
593C22×C4—21no—
594C22×C4—21no—
595C22×C4—71no—
596C22×C4—71no—
597C22×C4—71no—
598C22×C4—71no—
599C22×C4—144no—
600C22×C4—144no—
601C22×C4—148no—
602C22×C4—144no—
603C22×C4—141no—
604C22×C4—141no—
605C22×C4—141no—
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—21no—
625C4⋊C4—21no—
626C4⋊C4—21no—
627C4⋊C4—74no—
628C4⋊C4—74no—
629C4⋊C4—72no—
630C4⋊C4—144no—
631C4⋊C4—144no—
632C4⋊C4—144no—
633C4⋊C4—144no—
634C4⋊C4—144no—
635C4⋊C4—144no—
636C4⋊C4—141no—
637C4⋊C4C23×D712yes—
638C4⋊C4C23×D712yes—
639C4⋊C4C23×D712yes—
640C22⋊C4—24no—
641C22⋊C4—24no—
642C22⋊C4—74no—
643C22⋊C4—74no—
644C22⋊C4—144no—
645C22⋊C4—144no—
646C22⋊C4—144no—
647C42—24no—
648C42—72no—
649C42—72no—
650C42—72no—
651C42—72no—
652C42—144no—
653C42—144no—
654C42—144no—
655C42—144no—
656C2×C7—42no—
657C2×C7—82no—
658C2×C7#312614yescomplemented
659C2×C7C2×#52511yescharacteristic
660C2×C7C2×#57711yescharacteristic
661C2×C7C2×#57711yescharacteristic
662D7—82no—
663C23—22no—
664C23—22no—
665C23—22no—
666C23—22no—
667C23—42no—
668C23—42no—
669C23—42no—
670C23—142no—
671C23—282no—
672C23—282no—
673C23—282no—
674C23C2×D4×D712yes—
675C23C2×D4×D711yescharacteristic
676Q8—74no—
677Q8—74no—
678Q8—1416no—
679Q8—144no—
680Q8—144no—
681Q8—142no—
682Q8—142no—
683D4—22no—
684D4—22no—
685D4—42no—
686D4—84no—
687D4—142no—
688D4—142no—
689D4—282no—
690D4—564no—
691D4—564no—
692D4—564no—
693C2×C4—22no—
694C2×C4—24no—
695C2×C4—22no—
696C2×C4—22no—
697C2×C4—22no—
698C2×C4—22no—
699C2×C4—22no—
700C2×C4—42no—
701C2×C4—42no—
702C2×C4—42no—
703C2×C4—72no—
704C2×C4—72no—
705C2×C4—72no—
706C2×C4—72no—
707C2×C4—1416no—
708C2×C4—142no—
709C2×C4—142no—
710C2×C4—142no—
711C2×C4—142no—
712C2×C4—144no—
713C2×C4—144no—
714C2×C4—142no—
715C2×C4—142no—
716C2×C4—142no—
717C2×C4—282no—
718C2×C4—564no—
719C2×C4—564no—
720C2×C4C2×D4×D712yes—
721C2×C4C2×D4×D711yescharacteristic
722C2×C4D7×#4112yes—
723C2×C4D7×#4112yes—
724C2×C4C24×D711yescharacteristic
725C8—22no—
726C8—22no—
727C8—142no—
728C8—142no—
729C7C2×#312611yescharacteristic, complemented, Sylow
730C22—22no—
731C22—22no—
732C22—22no—
733C22—44no—
734C22—42no—
735C22—42no—
736C22—42no—
737C22—84no—
738C22—282no—
739C22—282no—
740C22—282no—
741C22—564no—
742C22#9034712yes—
743C22#9046112yes—
744C22#9046612yes—
745C22C22×D4×D711yescharacteristic
746C4—22no—
747C4—42no—
748C4—42no—
749C4—42no—
750C4—142no—
751C4—142no—
752C4—144no—
753C4—144no—
754C4—142no—
755C4—142no—
756C4—282no—
757C4#9034712yes—
758C4C2×D7×#4111yescharacteristic
759C4C2×D7×#4111yescharacteristic
760C2—42no—
761C2—82no—
762C2—562no—
763C2#1173880014yesdirect product factor
764C2C2×#9034711yescharacteristic
765C2C2×#9046111yescharacteristic
766C2C2×#9046611yescharacteristic
subgroupG/H
centerC23C2×D4×D7
commutator, cosocleC2×C4×C7C25
FrattiniC2×C4C24×D7
FittingC2×C7×#482C2
socleC23×C7C22×D4
prime radicalC2×#90310C2
hypercenterC2×#482D7
hypocenterC7C2×#3126
LCSG ▷ C2×C4×C7 ▷ C2×C7 ▷ C7
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#482

Complements

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

NH ≅ G/Ntype
2. C2×#90207C2semidirect
3. C2×C7×#482C2semidirect
4. C2×#89812C2semidirect
5. C2×#89775C2semidirect
6. #11738800C2direct (N × H)
7. C2×#89649C2semidirect
8. C2×#89661C2semidirect
9. C2×#89629C2semidirect
10. C2×#89624C2semidirect
11. C2×#89534C2semidirect
12. C2×#89534C2semidirect
13. C2×#89529C2semidirect
14. C2×#89530C2semidirect
15. C2×#89510C2semidirect
16. C2×#89492C2semidirect
33. #90207C22semidirect
46. C7×#482C22semidirect
59. #89812C22semidirect
60. #89775C22semidirect
67. #89661C22semidirect
68. #89649C22semidirect
69. #89629C22semidirect
70. #89624C22semidirect
71. #89534C22semidirect
72. #89534C22semidirect
73. #89530C22semidirect
74. #89529C22semidirect
75. #89510C22semidirect
76. #89492C22semidirect
187. C2×#482D7semidirect
327. #482C2×D7semidirect
658. C2×C7#3126semidirect
729. C7C2×#3126semidirect
763. C2#11738800direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#903102
C2×#902072
C2×C7×#4822
C2×#898122
C2×#897752
#117388002
C2×#896492
C2×#896612
C2×#896292
C2×#896242
C2×#895342
C2×#895292
C2×#895302
C2×#895102
C2×#894922
C2×#31267