Finite Group Databasebeta

← C2×#11737042 #14222107

Subgroups — C2×#11737042 #14222107

Order 1792.

2134 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×#90252C211yesmaximal, characteristic, complemented
2C2×#90237C211yesmaximal, characteristic, complemented
3C2×C4×C7×D8C211yesmaximal, characteristic, complemented
4C2×#89930C211yesmaximal, characteristic
5C2×#89925C211yesmaximal, characteristic, complemented
6C2×#89790C211yesmaximal, characteristic, complemented
7C2×#89790C211yesmaximal, characteristic, complemented
8#11737042C2116yesmaximal, direct product factor
9C2×#89647C211yesmaximal, characteristic, complemented
10C2×#89656C211yesmaximal, characteristic, complemented
11C2×#89539C211yesmaximal, characteristic, complemented
12C2×#89546C211yesmaximal, characteristic, complemented
13C2×#89555C211yesmaximal, characteristic, complemented
14C2×#89531C211yesmaximal, characteristic, complemented
15C2×C4×Dic28C211yesmaximal, characteristic, complemented
16C2×#89462C211yesmaximal, characteristic, complemented
17C22×#1159C2211yescharacteristic
18C22×C7×D8C2211yescharacteristic
19C2×C4×C7×D4C2211yescharacteristic
20C2×C4×C7×D4C2211yescharacteristic
21C2×#6501C2211yescharacteristic
22C2×#6499C2211yescharacteristic
23C2×D4×Dic7C2211yescharacteristic
24C22×#1142C2211yescharacteristic
25C22×#1142C2211yescharacteristic
26C2×#6492—21no—
27C2×C4×C22⋊D7—21no—
28C2×#6487—21no—
29C22×Dic7⋊C4—21no—
30C22×Dic28C2211yescharacteristic
31#90252—24no—
32#90252C2218yescomplemented
33#90237—24no—
34#90237C2218yescomplemented
35C2×#6460C2211yescharacteristic
36C2×D7×C4⋊C4C2211yescharacteristic
37C2×#6451C2211yescharacteristic
38C2×#6450C2211yescharacteristic
39C2×#6448—21no—
40C2×(C22⋊D7)⋊C4—21no—
41C2×#6442—21no—
42C2×#6440—21no—
43C2×#6435C2211yescharacteristic
44C2×C4×Dic14C2211yescharacteristic
45C2×C4×Dic14C2211yescharacteristic
46C4×C7×D8C2218yescomplemented
47C2×C7×#107C2211yescharacteristic
48C2×C7×#102C2211yescharacteristic
49C2×C7×#102C2211yescharacteristic
50C2×C4×C7×C8C2211yescharacteristic
51C2×#6406C2211yescharacteristic
52C2×#6406C2211yescharacteristic
53#89930C2218yes—
54#89925C2218yescomplemented
55C2×(C2×D7)⋊C8C2211yescharacteristic
56C2×(C2×D7)⋊C8C2211yescharacteristic
57C2×#6392C2211yescharacteristic
58C2×#6390C2211yescharacteristic
59C2×#6390C2211yescharacteristic
60C2×Dic7⋊C8C2211yescharacteristic
61C2×Dic7⋊C8C2211yescharacteristic
62#89790C2218yescomplemented
63#89790C2218yescomplemented
64C2×#6384C2211yescharacteristic
65C2×#6384C2211yescharacteristic
66C2×#6381C2211yescharacteristic
67C2×#6381C2211yescharacteristic
68C2×#6377C2211yescharacteristic
69#89656C2218yescomplemented
70#89647C2218yescomplemented
71#89555C2218yescomplemented
72#89546C2218yescomplemented
73#89539C2218yescomplemented
74#89531C2218yescomplemented
75C4×Dic28C2218yescomplemented
76#89462C2218yescomplemented
77C2×#3124—71nomaximal, Sylow
78C22×C7×D4C2311yescharacteristic
79C22×C7×D4C2311yescharacteristic
80C23×C4×C7—21no—
81C23×C4×C7—21no—
82C22×C22⋊D7—21no—
83C22×C22⋊D7—21no—
84C23×Dic7—21no—
85C23×Dic7—21no—
86C2×#1159—24no—
87C2×#1159—22no—
88C2×#1159—24no—
89C2×#1159C2314yes—
90C22×C4×D7—21no—
91C22×C4×D7C2311yescharacteristic
92C22×Dic14—21no—
93C22×Dic14C2311yescharacteristic
94C22×Dic14C2311yescharacteristic
95C2×C7×D8—24no—
96C2×C7×D8C2314yes—
97C22×C7×C8C2311yescharacteristic
98C22×C7×C8C2311yescharacteristic
99C4×C7×D4—22no—
100C4×C7×D4—22no—
101C4×C7×D4C2314yes—
102C4×C7×D4C2314yes—
103C2×C7×C4⋊C4C2311yescharacteristic
104C2×C7×C4⋊C4C2311yescharacteristic
105C2×C7×C22⋊C4—21no—
106C2×C7×C22⋊C4—21no—
107C2×C42×C7C2311yescharacteristic
108C2×C22⋊Dic7—21no—
109C2×C22⋊Dic7—21no—
110C2×C22⋊Dic7—21no—
111C2×C22⋊Dic7—21no—
112#6501—22no—
113#6501C2314yes—
114#6499—22no—
115#6499C2314yes—
116D4×Dic7—22no—
117D4×Dic7C2314yes—
118C2×#1142—24no—
119C2×#1142—24no—
120C2×#1142C2314yes—
121C2×#1142C2314yes—
122#6492—28no—
123C4×C22⋊D7—28no—
124C2×(C2×D7)⋊C4—21no—
125C2×(C2×D7)⋊C4D411yescharacteristic
126C2×(C2×D7)⋊C4D411yescharacteristic
127C2×C4⋊Dic7—21no—
128C2×C4⋊Dic7C2311yescharacteristic
129C2×C4⋊Dic7C2311yescharacteristic
130#6487—28no—
131C2×Dic7⋊C4—21no—
132C2×Dic7⋊C4—21no—
133C2×Dic7⋊C4—21no—
134C2×Dic7⋊C4—21no—
135C2×Dic7⋊C4—21no—
136C2×Dic7⋊C4—28no—
137C2×Dic7⋊C4D411yescharacteristic
138C2×Dic7⋊C4D411yescharacteristic
139C2×C4×Dic7—21no—
140C2×C4×Dic7—21no—
141C2×C4×Dic7—21no—
142C2×C4×Dic7C2311yescharacteristic
143C22×C7⋊C8C2311yescharacteristic
144C22×C7⋊C8C2311yescharacteristic
145C2×Dic28—24no—
146C2×Dic28C2314yes—
147#6460—22no—
148#6460C2314yes—
149D7×C4⋊C4—22no—
150D7×C4⋊C4C2314yes—
151#6451—22no—
152#6451C2314yes—
153#6450—22no—
154#6450C2314yes—
155#6448—28no—
156(C22⋊D7)⋊C4—28no—
157#6442—28no—
158#6440—28no—
159#6435D414yes—
160#6435C2314yes—
161C4×Dic14—22no—
162C4×Dic14—22no—
163C4×Dic14C2314yes—
164C4×Dic14C2314yes—
165C7×#107C2314yes—
166C7×#102C2314yes—
167C7×#102C2314yes—
168C4×C7×C8C2314yes—
169#6406C2314yes—
170#6406C2314yes—
171(C2×D7)⋊C8C2314yes—
172(C2×D7)⋊C8C2314yes—
173#6392C2314yes—
174#6390C2314yes—
175#6390C2314yes—
176Dic7⋊C8C2314yes—
177Dic7⋊C8C2314yes—
178#6384C2314yes—
179#6384C2314yes—
180#6381C2314yes—
181#6381C2314yes—
182#6377C2314yes—
183C2×#542—71no—
184C2×#520—71no—
185#3124—716no—
186C2×#484—71no—
187C2×#480—71no—
188C2×#477—71no—
189C2×#474—71no—
190C2×#464—71no—
191C2×#463—71no—
192C2×#452—71no—
193C2×#449—71no—
194C2×#440—71no—
195C2×#440—71no—
196C2×C4×Q16—71no—
197C2×C4×D8D711yescharacteristic, complemented
198C2×#433—71no—
199C24×C7—21no—
200C24×C7—21no—
201C23×D7C2×D411yescharacteristic
202C2×C7×D4—21no—
203C2×C7×D4—21no—
204C2×C7×D4—22no—
205C2×C7×D4—22no—
206C2×C7×D4—22no—
207C2×C7×D4#4114yes—
208C2×C7×D4C2412yes—
209C2×C7×D4C2412yes—
210C22×C4×C7—21no—
211C22×C4×C7—21no—
212C22×C4×C7—24no—
213C22×C4×C7—24no—
214C22×C4×C7—82no—
215C22×C4×C7—82no—
216C22×C4×C7C2×D411yescharacteristic
217C22×C4×C7C2×D411yescharacteristic
218C22×C4×C7C2411yescharacteristic
219C2×C22⋊D7—28no—
220C2×C22⋊D7—24no—
221C2×C22⋊D7—24no—
222C2×C22⋊D7—82no—
223C22×Dic7—28no—
224C22×Dic7—21no—
225C22×Dic7—24no—
226C22×Dic7—21no—
227C22×Dic7—21no—
228C22×Dic7—21no—
229C22×Dic7—24no—
230C22×Dic7—82no—
231C22×Dic7C2×D411yescharacteristic
232C22×Dic7C2×D411yescharacteristic
233C22×Dic7C2×D411yescharacteristic
234#1159—216no—
235#1159—28no—
236#1159—28no—
237C2×C4×D7—22no—
238C2×C4×D7—22no—
239C2×C4×D7—24no—
240C2×C4×D7—82no—
241C2×C4×D7C2×D412yes—
242C2×C4×D7C2412yes—
243C2×Dic14—21no—
244C2×Dic14—22no—
245C2×Dic14—22no—
246C2×Dic14—22no—
247C2×Dic14—21no—
248C2×Dic14—24no—
249C2×Dic14—82no—
250C2×Dic14#4114yes—
251C2×Dic14C2412yes—
252C2×Dic14C2412yes—
253C7×D8—28no—
254C2×C7×C8—22no—
255C2×C7×C8—22no—
256C2×C7×C8C2412yes—
257C2×C7×C8C2412yes—
258C7×C4⋊C4—21no—
259C7×C4⋊C4—21no—
260C7×C4⋊C4C2412yes—
261C7×C4⋊C4C2412yes—
262C7×C22⋊C4—24no—
263C7×C22⋊C4—24no—
264C42×C7C2×D412yes—
265C42×C7C2412yes—
266C22⋊Dic7—24no—
267C22⋊Dic7—24no—
268C22⋊Dic7—24no—
269C22⋊Dic7—24no—
270#1142—28no—
271#1142—28no—
272(C2×D7)⋊C4—24no—
273(C2×D7)⋊C4C2×D414yes—
274(C2×D7)⋊C4C2×D414yes—
275C4⋊Dic7—21no—
276C4⋊Dic7—21no—
277C4⋊Dic7—24no—
278C4⋊Dic7C2412yes—
279C4⋊Dic7C2412yes—
280Dic7⋊C4—24no—
281Dic7⋊C4—24no—
282Dic7⋊C4—24no—
283Dic7⋊C4—24no—
284Dic7⋊C4—24no—
285Dic7⋊C4C2×D414yes—
286Dic7⋊C4C2×D414yes—
287C4×Dic7—24no—
288C4×Dic7—24no—
289C4×Dic7—24no—
290C4×Dic7C2×D412yes—
291C4×Dic7C2412yes—
292C2×C7⋊C8—22no—
293C2×C7⋊C8—22no—
294C2×C7⋊C8C2412yes—
295C2×C7⋊C8C2412yes—
296Dic28—28no—
297C22×#41—71no—
298C22×Q16—71no—
299C22×SD16—71no—
300C22×SD16—71no—
301C22×D8C2×D711yescharacteristic
302#542—78no—
303#542—144no—
304C2×C4⋊Q8—71no—
305C2×#126—141no—
306C2×#124—71no—
307C2×#124—141no—
308C2×#123—141no—
309C2×C22⋊Q8—71no—
310C2×C22⋊Q8—141no—
311C2×#121—71no—
312#520—78no—
313#520—144no—
314C2×C4×Q8—71no—
315C2×C4×Q8—71no—
316C2×C4×Q8—71no—
317C2×C4×D4—71no—
318C2×C4×D4—141no—
319C2×C4×D4—141no—
320C2×C4×D4C2×D711yescharacteristic
321C2×C4×D4C2×D711yescharacteristic
322C2×#117—71no—
323C2×#117—141no—
324C22×C4⋊C4—71no—
325C22×C4⋊C4—141no—
326#484—78no—
327#480—78no—
328#477—78no—
329#474—78no—
330#464—78no—
331#463—78no—
332#452—78no—
333#449—78no—
334#440—78no—
335#440—78no—
336C4×Q16—78no—
337C4×D8C2×D718yescomplemented
338#433—78no—
339C2×#107—71no—
340C2×#107—71no—
341C2×#107—71no—
342C2×#107C2×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⋊C8—71no—
355C2×#97—71no—
356C2×C4×C8C2×D711yescharacteristic
357C23×C7—24no—
358C23×C7—22no—
359C23×C7—22no—
360C23×C7—42no—
361C23×C7—42no—
362C23×C7—42no—
363C23×C7—42no—
364C23×C7—42no—
365C23×C7C22×D411yescharacteristic
366C22×D7—22no—
367C22×D7—22no—
368C22×D7—22no—
369C22×D7C22×D412yes—
370C7×D4—24no—
371C7×D4—22no—
372C7×D4—22no—
373C7×D4—22no—
374C7×D4—42no—
375C7×D4C2×#4114yes—
376C2×C4×C7—22no—
377C2×C4×C7—22no—
378C2×C4×C7—22no—
379C2×C4×C7—22no—
380C2×C4×C7—42no—
381C2×C4×C7—42no—
382C2×C4×C7—84no—
383C2×C4×C7—84no—
384C2×C4×C7C22×D412yes—
385C2×C4×C7C22×D412yes—
386C2×C4×C7C22×D411yescharacteristic
387C2×C4×C7C2×#4112yes—
388C2×C4×C7C2×#4112yes—
389C2×C4×C7C2511yescharacteristic
390C22⋊D7—216no—
391C22⋊D7—84no—
392C2×Dic7—216no—
393C2×Dic7—24no—
394C2×Dic7—22no—
395C2×Dic7—22no—
396C2×Dic7—22no—
397C2×Dic7—22no—
398C2×Dic7—22no—
399C2×Dic7—22no—
400C2×Dic7—22no—
401C2×Dic7—42no—
402C2×Dic7—42no—
403C2×Dic7—42no—
404C2×Dic7—84no—
405C2×Dic7C22×D412yes—
406C2×Dic7C22×D412yes—
407C2×Dic7C22×D412yes—
408C4×D7—24no—
409C4×D7—22no—
410C4×D7—22no—
411C4×D7—84no—
412Dic14—24no—
413Dic14—22no—
414Dic14—22no—
415Dic14—22no—
416Dic14—42no—
417Dic14—84no—
418Dic14C2×#4114yes—
419C7×C8—22no—
420C7×C8—22no—
421C7⋊C8—22no—
422C7⋊C8—22no—
423C2×#41—74no—
424C2×#41—142no—
425C2×#41—144no—
426C2×#41—144no—
427C22×Q8—71no—
428C22×Q8—71no—
429C22×Q8—141no—
430C22×D4—141no—
431C22×D4—141no—
432C22×D4C22×D711yescharacteristic
433C22×D4C22×D711yescharacteristic
434C23×C4—21no—
435C23×C4—21no—
436C23×C4—71no—
437C23×C4—141no—
438C23×C4—141no—
439C23×C4—141no—
440C2×Q16—74no—
441C2×Q16—144no—
442C2×SD16—74no—
443C2×SD16—74no—
444C2×SD16—144no—
445C2×SD16—144no—
446C2×D8—24no—
447C2×D8C22×D714yes—
448C22×C8—71no—
449C22×C8—71no—
450C22×C8C22×D711yescharacteristic
451C22×C8C22×D711yescharacteristic
452C4⋊Q8—74no—
453C4⋊Q8—142no—
454#126—148no—
455#124—74no—
456#124—142no—
457#124—148no—
458#123—148no—
459C22⋊Q8—74no—
460C22⋊Q8—142no—
461C22⋊Q8—148no—
462#121—74no—
463#121—142no—
464C4×Q8—74no—
465C4×Q8—74no—
466C4×Q8—74no—
467C4×Q8—142no—
468C4×Q8—142no—
469C4×Q8—142no—
470C4×D4—22no—
471C4×D4—22no—
472C4×D4—74no—
473C4×D4—142no—
474C4×D4—148no—
475C4×D4—148no—
476C4×D4C22×D714yes—
477C4×D4C22×D714yes—
478#117—74no—
479#117—74no—
480#117—148no—
481C2×C4⋊C4—71no—
482C2×C4⋊C4—71no—
483C2×C4⋊C4—71no—
484C2×C4⋊C4—71no—
485C2×C4⋊C4—74no—
486C2×C4⋊C4—142no—
487C2×C4⋊C4—148no—
488C2×C4⋊C4—141no—
489C2×C4⋊C4—141no—
490C2×C4⋊C4—141no—
491C2×C4⋊C4—141no—
492C2×C4⋊C4—141no—
493C2×C4⋊C4—141no—
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×C22⋊C4—141no—
504C2×C22⋊C4—141no—
505C2×C42—71no—
506C2×C42—141no—
507C2×C42—141no—
508C2×C42—141no—
509C2×C42C22×D711yescharacteristic
510#107—74no—
511#107—74no—
512#107—74no—
513#107C22×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⋊C8—74no—
526#97—74no—
527C4×C8C22×D714yes—
528C22×C7—24no—
529C22×C7—48no—
530C22×C7—42no—
531C22×C7—42no—
532C22×C7—42no—
533C22×C7—42no—
534C22×C7—42no—
535C22×C7—84no—
536C22×C7#52512yes—
537C22×C7#57612yes—
538C22×C7#57812yes—
539C22×C7C23×D411yescharacteristic
540C2×D7—22no—
541C2×D7—22no—
542C2×D7—22no—
543C2×D7—44no—
544C4×C7—22no—
545C4×C7—22no—
546C4×C7—42no—
547C4×C7—42no—
548C4×C7#52512yes—
549C4×C7C22×#4111yescharacteristic
550C4×C7C22×#4111yescharacteristic
551Dic7—24no—
552Dic7—22no—
553Dic7—22no—
554Dic7—22no—
555Dic7—42no—
556Dic7—42no—
557Dic7—42no—
558C24—21no—
559C24—21no—
560C24—71no—
561#41—148no—
562#41—1416no—
563#41—148no—
564C2×Q8—74no—
565C2×Q8—72no—
566C2×Q8—72no—
567C2×Q8—144no—
568C2×Q8—142no—
569C2×Q8—141no—
570C2×Q8—141no—
571C2×Q8—142no—
572C2×Q8—142no—
573C2×Q8—562no—
574C2×D4—22no—
575C2×D4—21no—
576C2×D4—21no—
577C2×D4—22no—
578C2×D4—22no—
579C2×D4—144no—
580C2×D4—148no—
581C2×D4—144no—
582C2×D4—562no—
583C2×D4#115714yes—
584C2×D4C23×D712yes—
585C2×D4C23×D712yes—
586C22×C4—21no—
587C22×C4—21no—
588C22×C4—24no—
589C22×C4—24no—
590C22×C4—71no—
591C22×C4—71no—
592C22×C4—71no—
593C22×C4—72no—
594C22×C4—72no—
595C22×C4—82no—
596C22×C4—82no—
597C22×C4—144no—
598C22×C4—144no—
599C22×C4—144no—
600C22×C4—148no—
601C22×C4—141no—
602C22×C4—142no—
603C22×C4—142no—
604C22×C4—141no—
605C22×C4—141no—
606C22×C4—141no—
607C22×C4—562no—
608C22×C4—562no—
609C22×C4D4×D711yescharacteristic
610C22×C4D4×D711yescharacteristic
611C22×C4C23×D711yescharacteristic
612Q16—148no—
613SD16—148no—
614SD16—148no—
615D8—28no—
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—74no—
627C4⋊C4—74no—
628C4⋊C4—72no—
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⋊C4—141no—
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—
647C22⋊C4—144no—
648C22⋊C4—144no—
649C42—72no—
650C42—72no—
651C42—144no—
652C42—144no—
653C42—144no—
654C42D4×D712yes—
655C42C23×D712yes—
656C2×C7—44no—
657C2×C7—82no—
658C2×C7#312414yescomplemented
659C2×C7C2×#52511yescharacteristic
660C2×C7C2×#57611yescharacteristic
661C2×C7C2×#57811yescharacteristic
662D7—42no—
663C23—24no—
664C23—22no—
665C23—22no—
666C23—42no—
667C23—42no—
668C23—42no—
669C23—42no—
670C23—42no—
671C23—72no—
672C23—142no—
673C23—142no—
674C23—142no—
675C23C2×D4×D711yescharacteristic
676Q8—74no—
677Q8—144no—
678Q8—142no—
679Q8—142no—
680Q8—142no—
681Q8—282no—
682Q8—564no—
683D4—24no—
684D4—22no—
685D4—22no—
686D4—22no—
687D4—42no—
688D4—1416no—
689D4—564no—
690D4C2×#115714yes—
691C2×C4—22no—
692C2×C4—22no—
693C2×C4—22no—
694C2×C4—22no—
695C2×C4—42no—
696C2×C4—42no—
697C2×C4—72no—
698C2×C4—72no—
699C2×C4—72no—
700C2×C4—84no—
701C2×C4—84no—
702C2×C4—1416no—
703C2×C4—142no—
704C2×C4—142no—
705C2×C4—142no—
706C2×C4—144no—
707C2×C4—142no—
708C2×C4—144no—
709C2×C4—142no—
710C2×C4—142no—
711C2×C4—142no—
712C2×C4—142no—
713C2×C4—142no—
714C2×C4—282no—
715C2×C4—282no—
716C2×C4—282no—
717C2×C4—564no—
718C2×C4—564no—
719C2×C4C2×#115712yes—
720C2×C4C2×D4×D712yes—
721C2×C4C2×D4×D712yes—
722C2×C4C2×D4×D711yescharacteristic
723C2×C4D7×#4112yes—
724C2×C4C24×D711yescharacteristic
725C8—22no—
726C8—22no—
727C8—142no—
728C8—142no—
729C7C2×#312411yescharacteristic, complemented, Sylow
730C22—24no—
731C22—48no—
732C22—42no—
733C22—42no—
734C22—42no—
735C22—42no—
736C22—42no—
737C22—84no—
738C22—142no—
739C22—142no—
740C22—142no—
741C22—284no—
742C22#9023812yes—
743C22#9044812yes—
744C22#9046212yes—
745C22C22×D4×D711yescharacteristic
746C4—22no—
747C4—22no—
748C4—42no—
749C4—42no—
750C4—142no—
751C4—144no—
752C4—142no—
753C4—142no—
754C4—282no—
755C4—282no—
756C4—282no—
757C4#9023812yes—
758C4C22×#115711yescharacteristic
759C4C2×D7×#4111yescharacteristic
760C2—44no—
761C2—82no—
762C2—282no—
763C2#1173704214yesdirect product factor
764C2C2×#9023811yescharacteristic
765C2C2×#9044811yescharacteristic
766C2C2×#9046211yescharacteristic
subgroupG/H
centerC23C2×D4×D7
commutator, cosocleC2×C4×C7C25
FrattiniC2×C4C24×D7
FittingC2×C4×C7×D8C2
socleC23×C7C22×D4
prime radicalC2×#89930C2
hypercenterC2×C4×D8D7
hypocenterC7C2×#3124
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×#90252C2semidirect
2. C2×#90237C2semidirect
3. C2×C4×C7×D8C2semidirect
5. C2×#89925C2semidirect
6. C2×#89790C2semidirect
7. C2×#89790C2semidirect
8. #11737042C2direct (N × H)
9. C2×#89647C2semidirect
10. C2×#89656C2semidirect
11. C2×#89539C2semidirect
12. C2×#89546C2semidirect
13. C2×#89555C2semidirect
14. C2×#89531C2semidirect
15. C2×C4×Dic28C2semidirect
16. C2×#89462C2semidirect
32. #90252C22semidirect
34. #90237C22semidirect
46. C4×C7×D8C22semidirect
54. #89925C22semidirect
62. #89790C22semidirect
63. #89790C22semidirect
69. #89656C22semidirect
70. #89647C22semidirect
71. #89555C22semidirect
72. #89546C22semidirect
73. #89539C22semidirect
74. #89531C22semidirect
75. C4×Dic28C22semidirect
76. #89462C22semidirect
197. C2×C4×D8D7semidirect
337. C4×D8C2×D7semidirect
658. C2×C7#3124semidirect
729. C7C2×#3124semidirect
763. C2#11737042direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#902522
C2×#902372
C2×C4×C7×D82
C2×#899302
C2×#899252
C2×#897902
#117370422
C2×#896472
C2×#896562
C2×#895392
C2×#895462
C2×#895552
C2×#895312
C2×C4×Dic282
C2×#894622
C2×#31247