Finite Group Databasebeta

← C2×#11738497 #14233486

Subgroups — C2×#11738497 #14233486

Order 1792.

2134 conjugacy classes of subgroups.

The subgroup lattice has 760 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#90418C211yesmaximal, characteristic, complemented
2C2×#90250C211yesmaximal, characteristic, complemented
3C2×C7×#476C211yesmaximal, characteristic, complemented
4C2×#89861C211yesmaximal, characteristic, complemented
5C2×#89786C211yesmaximal, characteristic, complemented
6#11738497C2116yesmaximal, direct product factor
7C2×#89626C211yesmaximal, characteristic, complemented
8C2×#89642C211yesmaximal, characteristic, complemented
9C2×#89641C211yesmaximal, characteristic, complemented
10C2×#89624C211yesmaximal, characteristic, complemented
11C2×#89616C211yesmaximal, characteristic, complemented
12C2×#89600C211yesmaximal, characteristic, complemented
13C2×#89559C211yesmaximal, characteristic, complemented
14C2×#89558C211yesmaximal, characteristic
15C2×#89537C211yesmaximal, characteristic, complemented
16C2×#89532C211yesmaximal, characteristic, complemented
17C22×Q8×D7—21no—
18C2×C7×C4⋊Q8C2211yescharacteristic
19C2×C4×C7×D4C2211yescharacteristic
20C2×#6509—21no—
21C2×#6503C2211yescharacteristic
22C2×#6499C2211yescharacteristic
23C22×#1141C2211yescharacteristic
24C2×#6492—21no—
25C2×C4×C22⋊D7—21no—
26C22×D56C2211yescharacteristic
27C22×#1132C2211yescharacteristic
28#90418—24no—
29#90418C2218yescomplemented
30#90250—24no—
31#90250C2218yescomplemented
32C2×#6459—21no—
33C2×#6459—21no—
34C2×#6456C2211yescharacteristic
35C2×#6456C2211yescharacteristic
36C2×#6456C2211yescharacteristic
37C2×#6451C2211yescharacteristic
38C2×#6451C2211yescharacteristic
39C2×#6450C2211yescharacteristic
40C2×#6448—21no—
41C2×#6446—21no—
42C2×#6438C2211yescharacteristic
43C2×C4×D28C2211yescharacteristic
44C2×C4×Dic14C2211yescharacteristic
45C7×#476C2218yescomplemented
46C2×C7×#106C2211yescharacteristic
47C2×C7×#106C2211yescharacteristic
48C2×C7×C4⋊C8C2211yescharacteristic
49C2×C7×#102C2211yescharacteristic
50C2×C7×#102C2211yescharacteristic
51C2×#6406C2211yescharacteristic
52C2×#6395C2211yescharacteristic
53C2×#6390C2211yescharacteristic
54C2×#6389C2211yescharacteristic
55C2×Dic7⋊C8C2211yescharacteristic
56C2×Dic7⋊C8C2211yescharacteristic
57C2×C8×Dic7C2211yescharacteristic
58#89861C2218yescomplemented
59#89786C2218yescomplemented
60C2×#6384C2211yescharacteristic
61C2×#6384C2211yescharacteristic
62C2×#6383C2211yescharacteristic
63C2×#6383C2211yescharacteristic
64C2×#6383C2211yescharacteristic
65C2×#6382C2211yescharacteristic
66C2×#6377C2211yescharacteristic
67#89642C2218yescomplemented
68#89641C2218yescomplemented
69#89626C2218yescomplemented
70#89624C2218yescomplemented
71#89616C2218yescomplemented
72#89600C2218yescomplemented
73#89559C2218yescomplemented
74#89558C2218yes—
75#89537C2218yescomplemented
76#89532C2218yescomplemented
77C2×#3373—71nomaximal, Sylow
78C22×C7×Q8—21no—
79C22×C7×D4C2311yescharacteristic
80C23×C4×C7—21no—
81C22×C22⋊D7—21no—
82C22×C22⋊D7—21no—
83C2×Q8×D7—28no—
84C2×Q8×D7—48no—
85C22×D28C2311yescharacteristic
86C22×D28C2311yescharacteristic
87C22×C4×D7—21no—
88C22×C4×D7—21no—
89C22×C4×D7—21no—
90C22×C4×D7—21no—
91C22×Dic14—21no—
92C22×Dic14—21no—
93C22×Dic14D411yescharacteristic
94C22×Dic14C2311yescharacteristic
95C22×C7×C8C2311yescharacteristic
96C22×C7×C8C2311yescharacteristic
97C7×C4⋊Q8—22no—
98C7×C4⋊Q8C2314yes—
99C4×C7×D4—22no—
100C4×C7×D4C2314yes—
101C2×C7×C4⋊C4—21no—
102C2×C7×C4⋊C4C2311yescharacteristic
103C2×C7×C4⋊C4C2311yescharacteristic
104C2×C7×C4⋊C4C2311yescharacteristic
105C2×C7×C22⋊C4—21no—
106C2×C42×C7C2311yescharacteristic
107C2×C22⋊Dic7—21no—
108C2×C22⋊Dic7—21no—
109#6509—28no—
110#6503—22no—
111#6503C2314yes—
112#6499—22no—
113#6499C2314yes—
114C2×#1141—24no—
115C2×#1141C2314yes—
116#6492—28no—
117C4×C22⋊D7—28no—
118C2×(C2×D7)⋊C4—21no—
119C2×(C2×D7)⋊C4—21no—
120C2×(C2×D7)⋊C4—21no—
121C2×(C2×D7)⋊C4—21no—
122C2×(C2×D7)⋊C4—21no—
123C2×(C2×D7)⋊C4—21no—
124C2×C4⋊Dic7D411yescharacteristic
125C2×C4⋊Dic7C2311yescharacteristic
126C2×Dic7⋊C4—21no—
127C2×Dic7⋊C4—21no—
128C2×Dic7⋊C4—21no—
129C2×Dic7⋊C4D411yescharacteristic
130C2×Dic7⋊C4D411yescharacteristic
131C2×C4×Dic7—21no—
132C2×C4×Dic7C2311yescharacteristic
133C2×C4×Dic7C2311yescharacteristic
134C22×C7⋊C8C2311yescharacteristic
135C22×C7⋊C8C2311yescharacteristic
136C2×D56—24no—
137C2×D56C2314yes—
138C2×#1132—24no—
139C2×#1132C2314yes—
140#6459—28no—
141#6459—28no—
142#6456—22no—
143#6456—22no—
144#6456—22no—
145#6456C2314yes—
146#6456C2314yes—
147#6456C2314yes—
148#6451—22no—
149#6451—22no—
150#6451C2314yes—
151#6451C2314yes—
152#6450—22no—
153#6450C2314yes—
154#6448—28no—
155#6446—28no—
156#6438—22no—
157#6438C2314yes—
158C4×D28—22no—
159C4×D28C2314yes—
160C4×Dic14D414yes—
161C4×Dic14C2314yes—
162C7×#106C2314yes—
163C7×#106C2314yes—
164C7×C4⋊C8C2314yes—
165C7×#102C2314yes—
166C7×#102C2314yes—
167#6406C2314yes—
168#6395C2314yes—
169#6390C2314yes—
170#6389C2314yes—
171Dic7⋊C8C2314yes—
172Dic7⋊C8C2314yes—
173C8×Dic7C2314yes—
174#6384C2314yes—
175#6384C2314yes—
176#6383C2314yes—
177#6383C2314yes—
178#6383C2314yes—
179#6382C2314yes—
180#6377C2314yes—
181C2×#559—71no—
182C2×D4×Q8—71no—
183#3373—716no—
184C2×#489—71no—
185C2×#489—71no—
186C2×#486—71no—
187C2×#475—71no—
188C2×#476—71no—
189C2×#476D711yescharacteristic, complemented
190C2×#463—71no—
191C2×#463—71no—
192C2×#459—71no—
193C2×#446—71no—
194C2×#442—71no—
195C2×#442—71no—
196C2×C4×SD16—71no—
197C24×C7—21no—
198C23×D7—21no—
199C23×D7—21no—
200C2×C7×Q8—24no—
201C2×C7×Q8—44no—
202C2×C7×D4—21no—
203C2×C7×D4—22no—
204C2×C7×D4—22no—
205C2×C7×D4C2412yes—
206C22×C4×C7—21no—
207C22×C4×C7—21no—
208C22×C4×C7—21no—
209C22×C4×C7—24no—
210C22×C4×C7—82no—
211C22×C4×C7C2×D411yescharacteristic
212C22×C4×C7C2×D411yescharacteristic
213C22×C4×C7C2411yescharacteristic
214C2×C22⋊D7—24no—
215C2×C22⋊D7—24no—
216C2×C22⋊D7—44no—
217C2×C22⋊D7—82no—
218C22×Dic7—21no—
219C22×Dic7—21no—
220C22×Dic7C2×D411yescharacteristic
221C22×Dic7C2×D411yescharacteristic
222C22×Dic7C2×D411yescharacteristic
223C22×Dic7C2×D411yescharacteristic
224Q8×D7—432no—
225C2×D28—21no—
226C2×D28—22no—
227C2×D28—22no—
228C2×D28—22no—
229C2×D28—21no—
230C2×D28#4114yes—
231C2×D28C2412yes—
232C2×D28C2412yes—
233C2×C4×D7—24no—
234C2×C4×D7—24no—
235C2×C4×D7—24no—
236C2×C4×D7—24no—
237C2×C4×D7—44no—
238C2×C4×D7—44no—
239C2×C4×D7—44no—
240C2×C4×D7—82no—
241C2×Dic14—24no—
242C2×Dic14—22no—
243C2×Dic14—22no—
244C2×Dic14—21no—
245C2×Dic14—24no—
246C2×Dic14—24no—
247C2×Dic14—44no—
248C2×Dic14—44no—
249C2×Dic14C2×D414yes—
250C2×Dic14C2412yes—
251C2×C7×C8—22no—
252C2×C7×C8—22no—
253C2×C7×C8C2412yes—
254C2×C7×C8C2412yes—
255C7×C4⋊C4—21no—
256C7×C4⋊C4—21no—
257C7×C4⋊C4—21no—
258C7×C4⋊C4—24no—
259C7×C4⋊C4C2412yes—
260C7×C4⋊C4C2412yes—
261C7×C4⋊C4C2412yes—
262C7×C22⋊C4—24no—
263C42×C7C2×D412yes—
264C42×C7C2412yes—
265C22⋊Dic7—24no—
266C22⋊Dic7—24no—
267#1141—28no—
268(C2×D7)⋊C4—24no—
269(C2×D7)⋊C4—24no—
270(C2×D7)⋊C4—24no—
271(C2×D7)⋊C4—24no—
272(C2×D7)⋊C4—24no—
273(C2×D7)⋊C4—24no—
274C4⋊Dic7—21no—
275C4⋊Dic7C2×D414yes—
276C4⋊Dic7C2412yes—
277Dic7⋊C4—24no—
278Dic7⋊C4—24no—
279Dic7⋊C4—24no—
280Dic7⋊C4C2×D414yes—
281Dic7⋊C4C2×D414yes—
282C4×Dic7—24no—
283C4×Dic7C2×D412yes—
284C4×Dic7C2×D412yes—
285C4×Dic7C2412yes—
286C4×Dic7C2412yes—
287C2×C7⋊C8—22no—
288C2×C7⋊C8—22no—
289C2×C7⋊C8C2412yes—
290C2×C7⋊C8C2412yes—
291D56—28no—
292#1132—28no—
293C23×Q8—141no—
294C22×SD16—71no—
295C22×D8—71no—
296C22×D8—71no—
297#559—78no—
298#559—144no—
299D4×Q8—78no—
300D4×Q8—144no—
301C2×C4⋊Q8—71no—
302C2×C4⋊Q8—71no—
303C2×C4⋊Q8C2×D711yescharacteristic
304C2×#127—71no—
305C2×#124—71no—
306C2×#124—71no—
307C2×#124—141no—
308C2×#123—141no—
309C2×#123—141no—
310C2×C22⋊Q8—141no—
311C2×C22⋊Q8—141no—
312C2×C22⋊Q8—141no—
313C2×C4×Q8—71no—
314C2×C4×Q8—71no—
315C2×C4×D4—71no—
316C2×C4×D4—71no—
317C2×C4×D4—71no—
318C2×C4×D4—71no—
319C2×C4×D4—141no—
320C2×C4×D4C2×D711yescharacteristic
321#489—78no—
322#489—78no—
323#486—78no—
324#476—78no—
325#476C2×D718yescomplemented
326#475—78no—
327#463—78no—
328#463—78no—
329#459—78no—
330#446—78no—
331#442—78no—
332#442—78no—
333C4×SD16—78no—
334C2×#106—71no—
335C2×#106C2×D711yescharacteristic
336C2×#106C2×D711yescharacteristic
337C2×C4⋊C8—71no—
338C2×C4⋊C8—71no—
339C2×C4⋊C8C2×D711yescharacteristic
340C2×#103—71no—
341C2×#103—71no—
342C2×#103—71no—
343C2×#102—71no—
344C2×#102—71no—
345C2×#102—71no—
346C2×#102—71no—
347C2×#102—71no—
348C2×#102C2×D711yescharacteristic
349C2×#102C2×D711yescharacteristic
350C2×#97—71no—
351C2×#97—71no—
352C2×C4×C8—71no—
353C23×C7—22no—
354C23×C7—42no—
355C23×C7—42no—
356C23×C7—42no—
357C23×C7C22×D411yescharacteristic
358C22×D7—24no—
359C22×D7—22no—
360C22×D7—22no—
361C22×D7—42no—
362C22×D7—42no—
363C22×D7—42no—
364C22×D7—42no—
365C22×D7—42no—
366C7×Q8—48no—
367C7×D4—22no—
368C7×D4—22no—
369C7×D4—42no—
370C2×C4×C7—22no—
371C2×C4×C7—22no—
372C2×C4×C7—22no—
373C2×C4×C7—22no—
374C2×C4×C7—22no—
375C2×C4×C7—42no—
376C2×C4×C7—42no—
377C2×C4×C7—42no—
378C2×C4×C7—84no—
379C2×C4×C7C22×D412yes—
380C2×C4×C7C22×D412yes—
381C2×C4×C7C22×D411yescharacteristic
382C2×C4×C7C2×#4112yes—
383C2×C4×C72−1+412yes—
384C2×C4×C7C2511yescharacteristic
385C22⋊D7—48no—
386C22⋊D7—84no—
387C2×Dic7—22no—
388C2×Dic7—22no—
389C2×Dic7—22no—
390C2×Dic7—22no—
391C2×Dic7—22no—
392C2×Dic7—42no—
393C2×Dic7—42no—
394C2×Dic7AGL(1,ℤ/8)14yes—
395C2×Dic7C22×D412yes—
396C2×Dic7C22×D412yes—
397C2×Dic7C22×D412yes—
398C2×Dic7C22×D412yes—
399D28—24no—
400D28—22no—
401D28—22no—
402D28—22no—
403D28—42no—
404D28C2×#4114yes—
405C4×D7—48no—
406C4×D7—48no—
407C4×D7—48no—
408C4×D7—84no—
409Dic14—28no—
410Dic14—22no—
411Dic14—22no—
412Dic14—48no—
413Dic14—42no—
414Dic14—48no—
415C7×C8—22no—
416C7×C8—22no—
417C7⋊C8—22no—
418C7⋊C8—22no—
419C22×Q8—21no—
420C22×Q8—71no—
421C22×Q8—71no—
422C22×Q8—141no—
423C22×Q8—141no—
424C22×Q8—148no—
425C22×Q8—288no—
426C22×D4—71no—
427C22×D4—71no—
428C22×D4—141no—
429C22×D4—141no—
430C22×D4C22×D711yescharacteristic
431C23×C4—21no—
432C23×C4—141no—
433C23×C4—141no—
434C23×C4—141no—
435C23×C4—141no—
436C2×SD16—74no—
437C2×SD16—144no—
438C2×D8—74no—
439C2×D8—74no—
440C2×D8—144no—
441C2×D8—144no—
442C22×C8—71no—
443C22×C8—71no—
444C22×C8C22×D711yescharacteristic
445C22×C8C22×D711yescharacteristic
446C4⋊Q8—22no—
447C4⋊Q8—74no—
448C4⋊Q8—74no—
449C4⋊Q8—142no—
450C4⋊Q8—142no—
451C4⋊Q8C22×D714yes—
452#127—74no—
453#127—142no—
454#124—74no—
455#124—74no—
456#124—142no—
457#124—148no—
458#124—142no—
459#123—148no—
460#123—148no—
461C22⋊Q8—148no—
462C22⋊Q8—148no—
463C22⋊Q8—148no—
464C4×Q8—74no—
465C4×Q8—74no—
466C4×Q8—74no—
467C4×Q8—142no—
468C4×D4—22no—
469C4×D4—74no—
470C4×D4—74no—
471C4×D4—74no—
472C4×D4—74no—
473C4×D4—142no—
474C4×D4—142no—
475C4×D4—142no—
476C4×D4—148no—
477C4×D4—142no—
478C4×D4C22×D714yes—
479C2×C4⋊C4—21no—
480C2×C4⋊C4—71no—
481C2×C4⋊C4—71no—
482C2×C4⋊C4—71no—
483C2×C4⋊C4—71no—
484C2×C4⋊C4—141no—
485C2×C4⋊C4—141no—
486C2×C4⋊C4—141no—
487C2×C4⋊C4C22×D711yescharacteristic
488C2×C4⋊C4C22×D711yescharacteristic
489C2×C4⋊C4C22×D711yescharacteristic
490C2×C22⋊C4—21no—
491C2×C22⋊C4—141no—
492C2×C22⋊C4—141no—
493C2×C22⋊C4—141no—
494C2×C22⋊C4—141no—
495C2×C22⋊C4—141no—
496C2×C22⋊C4—141no—
497C2×C22⋊C4—141no—
498C2×C22⋊C4—141no—
499C2×C42—71no—
500C2×C42—71no—
501C2×C42—141no—
502C2×C42C22×D711yescharacteristic
503#106—74no—
504#106C22×D714yes—
505#106C22×D714yes—
506C4⋊C8—74no—
507C4⋊C8—74no—
508C4⋊C8C22×D714yes—
509#103—74no—
510#103—74no—
511#103—74no—
512#102—74no—
513#102—74no—
514#102—74no—
515#102—74no—
516#102—74no—
517#102C22×D714yes—
518#102C22×D714yes—
519#97—74no—
520#97—74no—
521C4×C8—74no—
522C22×C7—42no—
523C22×C7—42no—
524C22×C7—42no—
525C22×C7—84no—
526C22×C7#54812yes—
527C22×C7C2×AGL(1,ℤ/8)12yes—
528C22×C7#57712yes—
529C22×C7C23×D411yescharacteristic
530C2×D7—24no—
531C2×D7—48no—
532C2×D7—42no—
533C2×D7—42no—
534C2×D7—42no—
535C2×D7—42no—
536C2×D7—42no—
537C2×D7—84no—
538C4×C7—22no—
539C4×C7—22no—
540C4×C7—42no—
541C4×C7—42no—
542C4×C7—42no—
543C4×C7#54812yes—
544C4×C7C22×#4111yescharacteristic
545C4×C7C2×2−1+411yescharacteristic
546Dic7—22no—
547Dic7—22no—
548Dic7—22no—
549Dic7—42no—
550Dic7—42no—
551Dic7C2×AGL(1,ℤ/8)14yes—
552C24—21no—
553C24—141no—
554C24—141no—
555C2×Q8—24no—
556C2×Q8—44no—
557C2×Q8—74no—
558C2×Q8—72no—
559C2×Q8—144no—
560C2×Q8—144no—
561C2×Q8—144no—
562C2×Q8—141no—
563C2×Q8—142no—
564C2×Q8—142no—
565C2×Q8—284no—
566C2×Q8—284no—
567C2×Q8—2832no—
568C2×D4—21no—
569C2×D4—22no—
570C2×D4—22no—
571C2×D4—74no—
572C2×D4—72no—
573C2×D4—72no—
574C2×D4—144no—
575C2×D4—144no—
576C2×D4—141no—
577C2×D4—141no—
578C2×D4—142no—
579C2×D4—142no—
580C2×D4—142no—
581C2×D4—284no—
582C2×D4—562no—
583C2×D4C23×D712yes—
584C22×C4—21no—
585C22×C4—21no—
586C22×C4—21no—
587C22×C4—24no—
588C22×C4—71no—
589C22×C4—71no—
590C22×C4—71no—
591C22×C4—71no—
592C22×C4—82no—
593C22×C4—144no—
594C22×C4—144no—
595C22×C4—144no—
596C22×C4—141no—
597C22×C4—141no—
598C22×C4—144no—
599C22×C4—284no—
600C22×C4—284no—
601C22×C4—284no—
602C22×C4—562no—
603C22×C4D4×D711yescharacteristic
604C22×C4D4×D711yescharacteristic
605C22×C4C23×D711yescharacteristic
606SD16—148no—
607D8—148no—
608D8—148no—
609C2×C8—22no—
610C2×C8—22no—
611C2×C8—72no—
612C2×C8—72no—
613C2×C8—142no—
614C2×C8—142no—
615C2×C8C23×D712yes—
616C2×C8C23×D712yes—
617C4⋊C4—24no—
618C4⋊C4—21no—
619C4⋊C4—21no—
620C4⋊C4—21no—
621C4⋊C4—74no—
622C4⋊C4—74no—
623C4⋊C4—74no—
624C4⋊C4—72no—
625C4⋊C4—144no—
626C4⋊C4—144no—
627C4⋊C4—144no—
628C4⋊C4—141no—
629C4⋊C4C23×D712yes—
630C4⋊C4C23×D712yes—
631C4⋊C4C23×D712yes—
632C22⋊C4—24no—
633C22⋊C4—144no—
634C22⋊C4—144no—
635C22⋊C4—144no—
636C22⋊C4—144no—
637C22⋊C4—144no—
638C22⋊C4—144no—
639C22⋊C4—144no—
640C22⋊C4—144no—
641C42—72no—
642C42—72no—
643C42—72no—
644C42—72no—
645C42—144no—
646C42D4×D712yes—
647C42C23×D712yes—
648C2×C7—82no—
649C2×C7#337314yescomplemented
650C2×C7C2×#54811yescharacteristic
651C2×C7C22×AGL(1,ℤ/8)11yescharacteristic
652C2×C7C2×#57711yescharacteristic
653D7—44no—
654D7—82no—
655C23—22no—
656C23—42no—
657C23—42no—
658C23—42no—
659C23—144no—
660C23—142no—
661C23—142no—
662C23—282no—
663C23—282no—
664C23—282no—
665C23—282no—
666C23—282no—
667C23C2×D4×D711yescharacteristic
668Q8—48no—
669Q8—148no—
670Q8—142no—
671Q8—142no—
672Q8—288no—
673Q8—288no—
674Q8—282no—
675D4—22no—
676D4—22no—
677D4—42no—
678D4—74no—
679D4—144no—
680D4—142no—
681D4—142no—
682D4—142no—
683D4—288no—
684D4—282no—
685D4—564no—
686C2×C4—22no—
687C2×C4—22no—
688C2×C4—22no—
689C2×C4—22no—
690C2×C4—22no—
691C2×C4—42no—
692C2×C4—42no—
693C2×C4—42no—
694C2×C4—74no—
695C2×C4—72no—
696C2×C4—72no—
697C2×C4—72no—
698C2×C4—72no—
699C2×C4—84no—
700C2×C4—142no—
701C2×C4—142no—
702C2×C4—142no—
703C2×C4—142no—
704C2×C4—142no—
705C2×C4—288no—
706C2×C4—288no—
707C2×C4—288no—
708C2×C4—282no—
709C2×C4—282no—
710C2×C4—564no—
711C2×C4C2×D4×D712yes—
712C2×C4C2×D4×D712yes—
713C2×C4C2×D4×D711yescharacteristic
714C2×C4#655112yes—
715C2×C4D7×#4112yes—
716C2×C4C24×D711yescharacteristic
717C8—22no—
718C8—22no—
719C8—142no—
720C8—142no—
721C7C2×#337311yescharacteristic, complemented, Sylow
722C22—42no—
723C22—42no—
724C22—42no—
725C22—84no—
726C22—144no—
727C22—282no—
728C22—288no—
729C22—282no—
730C22—282no—
731C22—282no—
732C22—282no—
733C22—564no—
734C22#9032412yes—
735C22#9045312yes—
736C22D7×AGL(1,ℤ/8)12yes—
737C22C22×D4×D711yescharacteristic
738C4—22no—
739C4—22no—
740C4—42no—
741C4—42no—
742C4—42no—
743C4—74no—
744C4—142no—
745C4—142no—
746C4—142no—
747C4—282no—
748C4—282no—
749C4#9032412yes—
750C4C2×#655111yescharacteristic
751C4C2×D7×#4111yescharacteristic
752C2—82no—
753C2—284no—
754C2—562no—
755C2#1173849714yesdirect product factor
756C2C2×#9032411yescharacteristic
757C2C2×#9045311yescharacteristic
758C2C2×D7×AGL(1,ℤ/8)11yescharacteristic
subgroupG/H
centerC23C2×D4×D7
commutator, cosocleC2×C4×C7C25
FrattiniC2×C4C24×D7
FittingC2×C7×#476C2
socleC23×C7C22×D4
prime radicalC2×#89558C2
hypercenterC2×#476D7
hypocenterC7C2×#3373
LCSG ▷ C2×C4×C7 ▷ C2×C7 ▷ C7
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#476

Complements

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

NH ≅ G/Ntype
1. C2×#90418C2semidirect
2. C2×#90250C2semidirect
3. C2×C7×#476C2semidirect
4. C2×#89861C2semidirect
5. C2×#89786C2semidirect
6. #11738497C2direct (N × H)
7. C2×#89626C2semidirect
8. C2×#89642C2semidirect
9. C2×#89641C2semidirect
10. C2×#89624C2semidirect
11. C2×#89616C2semidirect
12. C2×#89600C2semidirect
13. C2×#89559C2semidirect
15. C2×#89537C2semidirect
16. C2×#89532C2semidirect
29. #90418C22semidirect
31. #90250C22semidirect
45. C7×#476C22semidirect
58. #89861C22semidirect
59. #89786C22semidirect
67. #89642C22semidirect
68. #89641C22semidirect
69. #89626C22semidirect
70. #89624C22semidirect
71. #89616C22semidirect
72. #89600C22semidirect
73. #89559C22semidirect
75. #89537C22semidirect
76. #89532C22semidirect
189. C2×#476D7semidirect
325. #476C2×D7semidirect
649. C2×C7#3373semidirect
721. C7C2×#3373semidirect
755. C2#11738497direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#904182
C2×#902502
C2×C7×#4762
C2×#898612
C2×#897862
#117384972
C2×#896262
C2×#896422
C2×#896412
C2×#896242
C2×#896162
C2×#896002
C2×#895592
C2×#895582
C2×#895372
C2×#895322
C2×#33737