Finite Group Databasebeta

← C2×#11737040 #14222039

Subgroups — C2×#11737040 #14222039

Order 1792.

2198 conjugacy classes of subgroups.

The subgroup lattice has 792 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#90253C211yesmaximal, characteristic, complemented
2C2×#90237C211yesmaximal, characteristic, complemented
3C2×C4×C7×D8C211yesmaximal, characteristic, complemented
4C2×#89930C211yesmaximal, characteristic, complemented
5C2×#89922C211yesmaximal, characteristic, complemented
6C2×#89786C211yesmaximal, characteristic, complemented
7C2×#89790C211yesmaximal, characteristic, complemented
8#11737040C2116yesmaximal, direct product factor
9C2×#89649C211yesmaximal, characteristic, complemented
10C2×#89654C211yesmaximal, characteristic, complemented
11C2×#89534C211yesmaximal, characteristic, complemented
12C2×#89549C211yesmaximal, characteristic, complemented
13C2×#89553C211yesmaximal, characteristic, complemented
14C2×#89535C211yesmaximal, characteristic, complemented
15C2×C4×#1132C211yesmaximal, characteristic, complemented
16C2×#89462C211yesmaximal, characteristic, complemented
17C22×#1159C2211yescharacteristic
18C22×C7×D8C2211yescharacteristic
19C2×C4×C7×D4C2211yescharacteristic
20C2×C4×C7×D4C2211yescharacteristic
21C2×#6503C2211yescharacteristic
22C2×#6501C2211yescharacteristic
23C2×D4×Dic7C2211yescharacteristic
24C22×#1142C2211yescharacteristic
25C22×#1141C2211yescharacteristic
26C2×#6493—21no—
27C2×#6492—21no—
28C2×C4×C22⋊D7—21no—
29C22×Dic7⋊C4—21no—
30C22×#1132C2211yescharacteristic
31#90253—24no—
32#90253C2218yescomplemented
33#90237—24no—
34#90237C2218yescomplemented
35C2×#6458C2211yescharacteristic
36C2×D7×C4⋊C4C2211yescharacteristic
37C2×#6453C2211yescharacteristic
38C2×#6450C2211yescharacteristic
39C2×#6447—21no—
40C2×#6446—21no—
41C2×(C22⋊D7)⋊C4—21no—
42C2×#6440—21no—
43C2×C4×D28C2211yescharacteristic
44C2×#6435C2211yescharacteristic
45C2×C4×Dic14C2211yescharacteristic
46C4×C7×D8C2218yescomplemented
47C2×C7×#107C2211yescharacteristic
48C2×C7×#102C2211yescharacteristic
49C2×C7×#102C2211yescharacteristic
50C2×C4×C7×C8C2211yescharacteristic
51C2×#6406C2211yescharacteristic
52C2×#6406C2211yescharacteristic
53#89930C2218yescomplemented
54#89922C2218yescomplemented
55C2×#6395C2211yescharacteristic
56C2×(C2×D7)⋊C8C2211yescharacteristic
57C2×(C2×D7)⋊C8C2211yescharacteristic
58C2×#6391C2211yescharacteristic
59C2×#6390C2211yescharacteristic
60C2×Dic7⋊C8C2211yescharacteristic
61C2×Dic7⋊C8C2211yescharacteristic
62#89790C2218yescomplemented
63#89786C2218yescomplemented
64C2×#6384C2211yescharacteristic
65C2×#6383C2211yescharacteristic
66C2×#6382C2211yescharacteristic
67C2×#6381C2211yescharacteristic
68C2×#6377C2211yescharacteristic
69#89654C2218yescomplemented
70#89649C2218yescomplemented
71#89553C2218yescomplemented
72#89549C2218yescomplemented
73#89535C2218yescomplemented
74#89534C2218yescomplemented
75C4×#1132C2218yescomplemented
76#89462C2218yescomplemented
77C2×#3119—71nomaximal, Sylow
78C22×C7×D4C2311yescharacteristic
79C22×C7×D4C2311yescharacteristic
80C23×C4×C7—21no—
81C23×C4×C7—21no—
82C22×C22⋊D7—21no—
83C22×C22⋊D7—21no—
84C22×C22⋊D7—21no—
85C22×C22⋊D7—21no—
86C23×Dic7—21no—
87C23×Dic7—21no—
88C2×#1159—24no—
89C2×#1159—22no—
90C2×#1159—24no—
91C2×#1159C2314yes—
92C22×D28—21no—
93C22×D28C2311yescharacteristic
94C22×C4×D7—21no—
95C22×C4×D7—21no—
96C22×C4×D7C2311yescharacteristic
97C22×Dic14C2311yescharacteristic
98C2×C7×D8—24no—
99C2×C7×D8C2314yes—
100C22×C7×C8C2311yescharacteristic
101C22×C7×C8C2311yescharacteristic
102C4×C7×D4—22no—
103C4×C7×D4—22no—
104C4×C7×D4C2314yes—
105C4×C7×D4C2314yes—
106C2×C7×C4⋊C4C2311yescharacteristic
107C2×C7×C4⋊C4C2311yescharacteristic
108C2×C7×C22⋊C4—21no—
109C2×C7×C22⋊C4—21no—
110C2×C42×C7C2311yescharacteristic
111C2×C22⋊Dic7—21no—
112C2×C22⋊Dic7—21no—
113#6503—22no—
114#6503C2314yes—
115#6501—22no—
116#6501C2314yes—
117D4×Dic7—22no—
118D4×Dic7C2314yes—
119C2×#1142—24no—
120C2×#1142C2314yes—
121C2×#1141—24no—
122C2×#1141C2314yes—
123#6493—28no—
124#6492—28no—
125C4×C22⋊D7—28no—
126C2×(C2×D7)⋊C4—21no—
127C2×(C2×D7)⋊C4—21no—
128C2×(C2×D7)⋊C4D411yescharacteristic
129C2×(C2×D7)⋊C4D411yescharacteristic
130C2×C4⋊Dic7—21no—
131C2×C4⋊Dic7C2311yescharacteristic
132C2×C4⋊Dic7C2311yescharacteristic
133C2×Dic7⋊C4—21no—
134C2×Dic7⋊C4—21no—
135C2×Dic7⋊C4—21no—
136C2×Dic7⋊C4—21no—
137C2×Dic7⋊C4—28no—
138C2×Dic7⋊C4D411yescharacteristic
139C2×Dic7⋊C4D411yescharacteristic
140C2×C4×Dic7—21no—
141C2×C4×Dic7—21no—
142C2×C4×Dic7C2311yescharacteristic
143C22×C7⋊C8C2311yescharacteristic
144C22×C7⋊C8C2311yescharacteristic
145C2×#1132—24no—
146C2×#1132C2314yes—
147#6458—22no—
148#6458C2314yes—
149D7×C4⋊C4—22no—
150D7×C4⋊C4C2314yes—
151#6453—22no—
152#6453C2314yes—
153#6450—22no—
154#6450C2314yes—
155#6447—28no—
156#6446—28no—
157(C22⋊D7)⋊C4—28no—
158#6440—28no—
159C4×D28—22no—
160C4×D28C2314yes—
161#6435D414yes—
162#6435C2314yes—
163C4×Dic14—22no—
164C4×Dic14C2314yes—
165C7×#107C2314yes—
166C7×#102C2314yes—
167C7×#102C2314yes—
168C4×C7×C8C2314yes—
169#6406C2314yes—
170#6406C2314yes—
171#6395C2314yes—
172(C2×D7)⋊C8C2314yes—
173(C2×D7)⋊C8C2314yes—
174#6391C2314yes—
175#6390C2314yes—
176Dic7⋊C8C2314yes—
177Dic7⋊C8C2314yes—
178#6384C2314yes—
179#6383C2314yes—
180#6382C2314yes—
181#6381C2314yes—
182#6377C2314yes—
183C2×#540—71no—
184C2×#520—71no—
185#3119—716no—
186C2×#481—71no—
187C2×#480—71no—
188C2×#479—71no—
189C2×#478—71no—
190C2×#460—71no—
191C2×#459—71no—
192C2×#449—71no—
193C2×#449—71no—
194C2×#442—71no—
195C2×#440—71no—
196C2×C4×SD16—71no—
197C2×C4×D8D711yescharacteristic, complemented
198C2×#433—71no—
199C24×C7—21no—
200C24×C7—21no—
201C23×D7—21no—
202C23×D7C2×D411yescharacteristic
203C2×C7×D4—21no—
204C2×C7×D4—21no—
205C2×C7×D4—22no—
206C2×C7×D4—22no—
207C2×C7×D4—22no—
208C2×C7×D4#4114yes—
209C2×C7×D4C2412yes—
210C2×C7×D4C2412yes—
211C22×C4×C7—21no—
212C22×C4×C7—21no—
213C22×C4×C7—24no—
214C22×C4×C7—24no—
215C22×C4×C7—82no—
216C22×C4×C7—82no—
217C22×C4×C7C2×D411yescharacteristic
218C22×C4×C7C2×D411yescharacteristic
219C22×C4×C7C2411yescharacteristic
220C2×C22⋊D7—28no—
221C2×C22⋊D7—24no—
222C2×C22⋊D7—24no—
223C2×C22⋊D7—24no—
224C2×C22⋊D7—24no—
225C2×C22⋊D7—82no—
226C2×C22⋊D7—82no—
227C2×C22⋊D7—82no—
228C22×Dic7—28no—
229C22×Dic7—21no—
230C22×Dic7—24no—
231C22×Dic7—21no—
232C22×Dic7—21no—
233C22×Dic7—24no—
234C22×Dic7—82no—
235C22×Dic7C2×D411yescharacteristic
236C22×Dic7C2×D411yescharacteristic
237C22×Dic7C2×D411yescharacteristic
238#1159—216no—
239#1159—28no—
240#1159—28no—
241C2×D28—22no—
242C2×D28—22no—
243C2×D28—21no—
244C2×D28—24no—
245C2×D28—82no—
246C2×D28C2412yes—
247C2×C4×D7—22no—
248C2×C4×D7—22no—
249C2×C4×D7—24no—
250C2×C4×D7—24no—
251C2×C4×D7—82no—
252C2×C4×D7—82no—
253C2×C4×D7C2×D412yes—
254C2×C4×D7C2412yes—
255C2×Dic14—21no—
256C2×Dic14—22no—
257C2×Dic14#4114yes—
258C2×Dic14C2412yes—
259C7×D8—28no—
260C2×C7×C8—22no—
261C2×C7×C8—22no—
262C2×C7×C8C2412yes—
263C2×C7×C8C2412yes—
264C7×C4⋊C4—21no—
265C7×C4⋊C4—21no—
266C7×C4⋊C4C2412yes—
267C7×C4⋊C4C2412yes—
268C7×C22⋊C4—24no—
269C7×C22⋊C4—24no—
270C42×C7C2×D412yes—
271C42×C7C2412yes—
272C22⋊Dic7—24no—
273C22⋊Dic7—24no—
274#1142—28no—
275#1141—28no—
276(C2×D7)⋊C4—24no—
277(C2×D7)⋊C4—24no—
278(C2×D7)⋊C4C2×D414yes—
279(C2×D7)⋊C4C2×D414yes—
280C4⋊Dic7—21no—
281C4⋊Dic7—21no—
282C4⋊Dic7—24no—
283C4⋊Dic7C2412yes—
284C4⋊Dic7C2412yes—
285Dic7⋊C4—24no—
286Dic7⋊C4—24no—
287Dic7⋊C4—24no—
288Dic7⋊C4—24no—
289Dic7⋊C4C2×D414yes—
290Dic7⋊C4C2×D414yes—
291C4×Dic7—24no—
292C4×Dic7—24no—
293C4×Dic7C2×D412yes—
294C4×Dic7C2412yes—
295C2×C7⋊C8—22no—
296C2×C7⋊C8—22no—
297C2×C7⋊C8C2412yes—
298C2×C7⋊C8C2412yes—
299#1132—28no—
300C22×#41—71no—
301C22×SD16—71no—
302C22×SD16—71no—
303C22×D8—71no—
304C22×D8C2×D711yescharacteristic
305#540—78no—
306#540—144no—
307C2×#127—71no—
308C2×#125—71no—
309C2×#123—141no—
310C2×#123—141no—
311C2×#121—71no—
312C2×#121—71no—
313C2×#121—141no—
314C2×#121—141no—
315#520—78no—
316#520—144no—
317C2×C4×Q8—71no—
318C2×C4×Q8—71no—
319C2×C4×D4—71no—
320C2×C4×D4—71no—
321C2×C4×D4—141no—
322C2×C4×D4—141no—
323C2×C4×D4C2×D711yescharacteristic
324C2×C4×D4C2×D711yescharacteristic
325C2×#117—71no—
326C2×#117—141no—
327C22×C4⋊C4—71no—
328C22×C4⋊C4—141no—
329#481—78no—
330#480—78no—
331#479—78no—
332#478—78no—
333#460—78no—
334#459—78no—
335#449—78no—
336#449—78no—
337#442—78no—
338#440—78no—
339C4×SD16—78no—
340C4×D8C2×D718yescomplemented
341#433—78no—
342C2×#107—71no—
343C2×#107C2×D711yescharacteristic
344C2×#106—71no—
345C2×#106—71no—
346C2×C4⋊C8—71no—
347C2×C4⋊C8—71no—
348C2×#103—71no—
349C2×#103—71no—
350C2×#102—71no—
351C2×#102—71no—
352C2×#102—71no—
353C2×#102—71no—
354C2×#102C2×D711yescharacteristic
355C2×#102C2×D711yescharacteristic
356C2×C22⋊C8—71no—
357C2×C22⋊C8—71no—
358C2×#97—71no—
359C2×C4×C8C2×D711yescharacteristic
360C23×C7—24no—
361C23×C7—22no—
362C23×C7—22no—
363C23×C7—42no—
364C23×C7—42no—
365C23×C7—42no—
366C23×C7—42no—
367C23×C7—42no—
368C23×C7C22×D411yescharacteristic
369C22×D7—22no—
370C22×D7—22no—
371C22×D7—22no—
372C22×D7—22no—
373C22×D7—42no—
374C22×D7—42no—
375C22×D7—42no—
376C22×D7C22×D412yes—
377C7×D4—24no—
378C7×D4—22no—
379C7×D4—22no—
380C7×D4—22no—
381C7×D4—42no—
382C7×D4C2×#4114yes—
383C2×C4×C7—22no—
384C2×C4×C7—22no—
385C2×C4×C7—22no—
386C2×C4×C7—22no—
387C2×C4×C7—42no—
388C2×C4×C7—42no—
389C2×C4×C7—84no—
390C2×C4×C7—84no—
391C2×C4×C7C22×D412yes—
392C2×C4×C7C22×D412yes—
393C2×C4×C7C22×D411yescharacteristic
394C2×C4×C7C2×#4112yes—
395C2×C4×C7C2×#4112yes—
396C2×C4×C7C2511yescharacteristic
397C22⋊D7—216no—
398C22⋊D7—84no—
399C22⋊D7—84no—
400C22⋊D7—84no—
401C2×Dic7—216no—
402C2×Dic7—24no—
403C2×Dic7—22no—
404C2×Dic7—22no—
405C2×Dic7—22no—
406C2×Dic7—22no—
407C2×Dic7—22no—
408C2×Dic7—22no—
409C2×Dic7—42no—
410C2×Dic7—42no—
411C2×Dic7—84no—
412C2×Dic7C22×D412yes—
413C2×Dic7C22×D412yes—
414C2×Dic7C22×D412yes—
415D28—22no—
416D28—22no—
417D28—42no—
418D28—84no—
419C4×D7—24no—
420C4×D7—22no—
421C4×D7—22no—
422C4×D7—84no—
423C4×D7—84no—
424Dic14—24no—
425Dic14—22no—
426Dic14C2×#4114yes—
427C7×C8—22no—
428C7×C8—22no—
429C7⋊C8—22no—
430C7⋊C8—22no—
431C2×#41—74no—
432C2×#41—142no—
433C2×#41—144no—
434C2×#41—144no—
435C22×Q8—71no—
436C22×D4—71no—
437C22×D4—141no—
438C22×D4—141no—
439C22×D4—141no—
440C22×D4—141no—
441C22×D4—141no—
442C22×D4C22×D711yescharacteristic
443C22×D4C22×D711yescharacteristic
444C23×C4—21no—
445C23×C4—21no—
446C23×C4—71no—
447C23×C4—141no—
448C23×C4—141no—
449C23×C4—141no—
450C23×C4—141no—
451C2×SD16—74no—
452C2×SD16—74no—
453C2×SD16—144no—
454C2×SD16—144no—
455C2×D8—24no—
456C2×D8—74no—
457C2×D8—144no—
458C2×D8C22×D714yes—
459C22×C8—71no—
460C22×C8—71no—
461C22×C8C22×D711yescharacteristic
462C22×C8C22×D711yescharacteristic
463#127—74no—
464#127—142no—
465#125—74no—
466#125—142no—
467#123—148no—
468#123—148no—
469#121—74no—
470#121—74no—
471#121—148no—
472#121—148no—
473#121—142no—
474#121—142no—
475C4×Q8—74no—
476C4×Q8—74no—
477C4×Q8—142no—
478C4×Q8—142no—
479C4×D4—22no—
480C4×D4—22no—
481C4×D4—74no—
482C4×D4—74no—
483C4×D4—142no—
484C4×D4—148no—
485C4×D4—148no—
486C4×D4—142no—
487C4×D4C22×D714yes—
488C4×D4C22×D714yes—
489#117—74no—
490#117—74no—
491#117—148no—
492C2×C4⋊C4—71no—
493C2×C4⋊C4—71no—
494C2×C4⋊C4—71no—
495C2×C4⋊C4—71no—
496C2×C4⋊C4—74no—
497C2×C4⋊C4—142no—
498C2×C4⋊C4—148no—
499C2×C4⋊C4—141no—
500C2×C4⋊C4—141no—
501C2×C4⋊C4—141no—
502C2×C4⋊C4—141no—
503C2×C4⋊C4—141no—
504C2×C4⋊C4C22×D711yescharacteristic
505C2×C4⋊C4C22×D711yescharacteristic
506C2×C22⋊C4—21no—
507C2×C22⋊C4—21no—
508C2×C22⋊C4—71no—
509C2×C22⋊C4—71no—
510C2×C22⋊C4—141no—
511C2×C22⋊C4—141no—
512C2×C22⋊C4—141no—
513C2×C22⋊C4—141no—
514C2×C42—71no—
515C2×C42—141no—
516C2×C42—141no—
517C2×C42C22×D711yescharacteristic
518#107—74no—
519#107C22×D714yes—
520#106—74no—
521#106—74no—
522C4⋊C8—74no—
523C4⋊C8—74no—
524#103—74no—
525#103—74no—
526#102—74no—
527#102—74no—
528#102—74no—
529#102—74no—
530#102C22×D714yes—
531#102C22×D714yes—
532C22⋊C8—74no—
533C22⋊C8—74no—
534#97—74no—
535C4×C8C22×D714yes—
536C22×C7—24no—
537C22×C7—48no—
538C22×C7—42no—
539C22×C7—42no—
540C22×C7—42no—
541C22×C7—42no—
542C22×C7—42no—
543C22×C7—84no—
544C22×C7#52512yes—
545C22×C7#57612yes—
546C22×C7#57712yes—
547C22×C7C23×D411yescharacteristic
548C2×D7—22no—
549C2×D7—22no—
550C2×D7—22no—
551C2×D7—44no—
552C2×D7—42no—
553C2×D7—42no—
554C2×D7—42no—
555C2×D7—84no—
556C4×C7—22no—
557C4×C7—22no—
558C4×C7—42no—
559C4×C7—42no—
560C4×C7#52512yes—
561C4×C7C22×#4111yescharacteristic
562C4×C7C22×#4111yescharacteristic
563Dic7—24no—
564Dic7—22no—
565Dic7—22no—
566Dic7—22no—
567Dic7—42no—
568Dic7—42no—
569C24—21no—
570C24—21no—
571C24—71no—
572C24—141no—
573#41—148no—
574#41—1416no—
575#41—148no—
576C2×Q8—74no—
577C2×Q8—72no—
578C2×Q8—142no—
579C2×Q8—141no—
580C2×D4—22no—
581C2×D4—21no—
582C2×D4—21no—
583C2×D4—22no—
584C2×D4—22no—
585C2×D4—72no—
586C2×D4—144no—
587C2×D4—144no—
588C2×D4—144no—
589C2×D4—144no—
590C2×D4—148no—
591C2×D4—144no—
592C2×D4—142no—
593C2×D4—141no—
594C2×D4—142no—
595C2×D4—562no—
596C2×D4—562no—
597C2×D4—562no—
598C2×D4—562no—
599C2×D4#115714yes—
600C2×D4C23×D712yes—
601C2×D4C23×D712yes—
602C22×C4—21no—
603C22×C4—21no—
604C22×C4—24no—
605C22×C4—24no—
606C22×C4—71no—
607C22×C4—71no—
608C22×C4—71no—
609C22×C4—72no—
610C22×C4—72no—
611C22×C4—82no—
612C22×C4—82no—
613C22×C4—144no—
614C22×C4—144no—
615C22×C4—144no—
616C22×C4—148no—
617C22×C4—141no—
618C22×C4—142no—
619C22×C4—142no—
620C22×C4—141no—
621C22×C4—141no—
622C22×C4—144no—
623C22×C4—562no—
624C22×C4—562no—
625C22×C4—562no—
626C22×C4D4×D711yescharacteristic
627C22×C4D4×D711yescharacteristic
628C22×C4C23×D711yescharacteristic
629SD16—148no—
630SD16—148no—
631D8—28no—
632D8—148no—
633C2×C8—22no—
634C2×C8—22no—
635C2×C8—72no—
636C2×C8—72no—
637C2×C8—142no—
638C2×C8—142no—
639C2×C8C23×D712yes—
640C2×C8C23×D712yes—
641C4⋊C4—21no—
642C4⋊C4—21no—
643C4⋊C4—74no—
644C4⋊C4—74no—
645C4⋊C4—72no—
646C4⋊C4—72no—
647C4⋊C4—144no—
648C4⋊C4—144no—
649C4⋊C4—144no—
650C4⋊C4—144no—
651C4⋊C4—144no—
652C4⋊C4—141no—
653C4⋊C4—141no—
654C4⋊C4C23×D712yes—
655C4⋊C4C23×D712yes—
656C22⋊C4—24no—
657C22⋊C4—24no—
658C22⋊C4—74no—
659C22⋊C4—74no—
660C22⋊C4—144no—
661C22⋊C4—144no—
662C22⋊C4—144no—
663C22⋊C4—144no—
664C42—72no—
665C42—72no—
666C42—144no—
667C42—144no—
668C42D4×D712yes—
669C42C23×D712yes—
670C2×C7—44no—
671C2×C7—82no—
672C2×C7#311914yescomplemented
673C2×C7C2×#52511yescharacteristic
674C2×C7C2×#57611yescharacteristic
675C2×C7C2×#57711yescharacteristic
676D7—42no—
677D7—82no—
678C23—24no—
679C23—22no—
680C23—22no—
681C23—42no—
682C23—42no—
683C23—42no—
684C23—42no—
685C23—42no—
686C23—72no—
687C23—142no—
688C23—142no—
689C23—142no—
690C23—142no—
691C23—282no—
692C23—282no—
693C23—282no—
694C23C2×D4×D711yescharacteristic
695Q8—74no—
696Q8—144no—
697Q8—142no—
698D4—24no—
699D4—22no—
700D4—22no—
701D4—22no—
702D4—42no—
703D4—1416no—
704D4—142no—
705D4—142no—
706D4—282no—
707D4—564no—
708D4—564no—
709D4—564no—
710D4—564no—
711D4C2×#115714yes—
712C2×C4—22no—
713C2×C4—22no—
714C2×C4—22no—
715C2×C4—22no—
716C2×C4—42no—
717C2×C4—42no—
718C2×C4—72no—
719C2×C4—72no—
720C2×C4—72no—
721C2×C4—84no—
722C2×C4—84no—
723C2×C4—1416no—
724C2×C4—142no—
725C2×C4—142no—
726C2×C4—142no—
727C2×C4—144no—
728C2×C4—142no—
729C2×C4—144no—
730C2×C4—142no—
731C2×C4—142no—
732C2×C4—142no—
733C2×C4—142no—
734C2×C4—282no—
735C2×C4—282no—
736C2×C4—564no—
737C2×C4—564no—
738C2×C4—564no—
739C2×C4C2×#115712yes—
740C2×C4C2×D4×D712yes—
741C2×C4C2×D4×D712yes—
742C2×C4C2×D4×D711yescharacteristic
743C2×C4D7×#4112yes—
744C2×C4C24×D711yescharacteristic
745C8—22no—
746C8—22no—
747C8—142no—
748C8—142no—
749C7C2×#311911yescharacteristic, complemented, Sylow
750C22—24no—
751C22—48no—
752C22—42no—
753C22—42no—
754C22—42no—
755C22—42no—
756C22—42no—
757C22—84no—
758C22—142no—
759C22—142no—
760C22—142no—
761C22—284no—
762C22—282no—
763C22—282no—
764C22—282no—
765C22—564no—
766C22#9023812yes—
767C22#9044812yes—
768C22#9046112yes—
769C22C22×D4×D711yescharacteristic
770C4—22no—
771C4—22no—
772C4—42no—
773C4—42no—
774C4—142no—
775C4—144no—
776C4—142no—
777C4—142no—
778C4—282no—
779C4—282no—
780C4#9023812yes—
781C4C22×#115711yescharacteristic
782C4C2×D7×#4111yescharacteristic
783C2—44no—
784C2—82no—
785C2—282no—
786C2—562no—
787C2#1173704014yesdirect product factor
788C2C2×#9023811yescharacteristic
789C2C2×#9044811yescharacteristic
790C2C2×#9046111yescharacteristic
subgroupG/H
centerC23C2×D4×D7
commutator, cosocleC2×C4×C7C25
FrattiniC2×C4C24×D7
FittingC2×C4×C7×D8C2
socleC23×C7C22×D4
hypercenterC2×C4×D8D7
hypocenterC7C2×#3119
LCSG ▷ C2×C4×C7 ▷ C2×C7 ▷ C7
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×C4×D8

Complements

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

NH ≅ G/Ntype
1. C2×#90253C2semidirect
2. C2×#90237C2semidirect
3. C2×C4×C7×D8C2semidirect
4. C2×#89930C2semidirect
5. C2×#89922C2semidirect
6. C2×#89786C2semidirect
7. C2×#89790C2semidirect
8. #11737040C2direct (N × H)
9. C2×#89649C2semidirect
10. C2×#89654C2semidirect
11. C2×#89534C2semidirect
12. C2×#89549C2semidirect
13. C2×#89553C2semidirect
14. C2×#89535C2semidirect
15. C2×C4×#1132C2semidirect
16. C2×#89462C2semidirect
32. #90253C22semidirect
34. #90237C22semidirect
46. C4×C7×D8C22semidirect
53. #89930C22semidirect
54. #89922C22semidirect
62. #89790C22semidirect
63. #89786C22semidirect
69. #89654C22semidirect
70. #89649C22semidirect
71. #89553C22semidirect
72. #89549C22semidirect
73. #89535C22semidirect
74. #89534C22semidirect
75. C4×#1132C22semidirect
76. #89462C22semidirect
197. C2×C4×D8D7semidirect
340. C4×D8C2×D7semidirect
672. C2×C7#3119semidirect
749. C7C2×#3119semidirect
787. C2#11737040direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#902532
C2×#902372
C2×C4×C7×D82
C2×#899302
C2×#899222
C2×#897862
C2×#897902
#117370402
C2×#896492
C2×#896542
C2×#895342
C2×#895492
C2×#895532
C2×#895352
C2×C4×#11322
C2×#894622
C2×#31197