Finite Group Databasebeta

← C2×#11737298 #14233484

Subgroups — C2×#11737298 #14233484

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×#90250C211yesmaximal, characteristic, complemented
2C2×D4×Dic14C211yesmaximal, characteristic, complemented
3C2×C7×#442C211yesmaximal, characteristic, complemented
4C2×#89925C211yesmaximal, characteristic, complemented
5C2×#89922C211yesmaximal, characteristic
6C2×#89788C211yesmaximal, characteristic, complemented
7C2×#89780C211yesmaximal, characteristic, complemented
8#11737298C2116yesmaximal, direct product factor
9C2×#89626C211yesmaximal, characteristic, complemented
10C2×#89642C211yesmaximal, characteristic, complemented
11C2×#89537C211yesmaximal, characteristic, complemented
12C2×#89532C211yesmaximal, characteristic, complemented
13C2×#89557C211yesmaximal, characteristic, complemented
14C2×#89530C211yesmaximal, characteristic, complemented
15C2×#89486C211yesmaximal, characteristic, complemented
16C2×#89473C211yesmaximal, characteristic, complemented
17C23×Dic14—21no—
18C22×C7×D8C2211yescharacteristic
19C2×C4×C7×D4C2211yescharacteristic
20C2×C4×C7×D4C2211yescharacteristic
21C2×#6503C2211yescharacteristic
22C2×#6499C2211yescharacteristic
23C2×D4×Dic7C2211yescharacteristic
24C2×D4×Dic7C2211yescharacteristic
25C22×#1142C2211yescharacteristic
26C22×#1141C2211yescharacteristic
27C2×#6492—21no—
28C2×C4×C22⋊D7—21no—
29C2×#6487—21no—
30#90250—24no—
31#90250C2218yescomplemented
32D4×Dic14—24no—
33D4×Dic14C2218yescomplemented
34C2×#6456C2211yescharacteristic
35C2×#6451C2211yescharacteristic
36C2×#6451C2211yescharacteristic
37C2×#6450C2211yescharacteristic
38C2×#6448—21no—
39C2×#6446—21no—
40C2×#6441—21no—
41C2×#6441—21no—
42C2×#6438C2211yescharacteristic
43C2×#6432C2211yescharacteristic
44C2×C4×Dic14C2211yescharacteristic
45C7×#442C2218yescomplemented
46C2×C7×#106C2211yescharacteristic
47C2×C7×#102C2211yescharacteristic
48C2×C7×#102C2211yescharacteristic
49C2×C7×#97C2211yescharacteristic
50C2×#6406C2211yescharacteristic
51C2×#6406C2211yescharacteristic
52#89925C2218yescomplemented
53#89922C2218yes—
54C2×#6395C2211yescharacteristic
55C2×#6395C2211yescharacteristic
56C2×#6390C2211yescharacteristic
57C2×#6390C2211yescharacteristic
58C2×#6389C2211yescharacteristic
59C2×Dic7⋊C8C2211yescharacteristic
60C2×Dic7⋊C8C2211yescharacteristic
61C2×C8×Dic7C2211yescharacteristic
62#89788C2218yescomplemented
63#89780C2218yescomplemented
64C2×#6384C2211yescharacteristic
65C2×#6383C2211yescharacteristic
66C2×#6382C2211yescharacteristic
67C2×#6382C2211yescharacteristic
68C2×C4⋊(C7⋊C8)C2211yescharacteristic
69#89642C2218yescomplemented
70#89626C2218yescomplemented
71#89557C2218yescomplemented
72#89537C2218yescomplemented
73#89532C2218yescomplemented
74#89530C2218yescomplemented
75#89486C2218yescomplemented
76#89473C2218yescomplemented
77C2×#3373—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—
86C22×D28C2311yescharacteristic
87C22×C4×D7—21no—
88C22×Dic14—21no—
89C22×Dic14—21no—
90C22×Dic14—21no—
91C22×Dic14—28no—
92C22×Dic14—48no—
93C22×Dic14D411yescharacteristic
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#6503—22no—
113#6503C2314yes—
114#6499—22no—
115#6499C2314yes—
116D4×Dic7—22no—
117D4×Dic7—22no—
118D4×Dic7C2314yes—
119D4×Dic7C2314yes—
120C2×#1142—24no—
121C2×#1142C2314yes—
122C2×#1141—24no—
123C2×#1141C2314yes—
124#6492—28no—
125C4×C22⋊D7—28no—
126C2×(C2×D7)⋊C4—21no—
127C2×(C2×D7)⋊C4—21no—
128C2×(C2×D7)⋊C4—21no—
129C2×C4⋊Dic7—21no—
130C2×C4⋊Dic7D411yescharacteristic
131C2×C4⋊Dic7C2311yescharacteristic
132C2×C4⋊Dic7C2311yescharacteristic
133#6487—28no—
134C2×Dic7⋊C4—21no—
135C2×Dic7⋊C4—21no—
136C2×Dic7⋊C4—21no—
137C2×Dic7⋊C4D411yescharacteristic
138C2×Dic7⋊C4D411yescharacteristic
139C2×C4×Dic7—21no—
140C2×C4×Dic7C2311yescharacteristic
141C2×C4×Dic7C2311yescharacteristic
142C22×C7⋊C8C2311yescharacteristic
143C22×C7⋊C8C2311yescharacteristic
144#6456—22no—
145#6456C2314yes—
146#6451—22no—
147#6451—22no—
148#6451C2314yes—
149#6451C2314yes—
150#6450—22no—
151#6450C2314yes—
152#6448—28no—
153#6446—28no—
154#6441—28no—
155#6441—28no—
156#6438—22no—
157#6438C2314yes—
158#6432—22no—
159#6432C2314yes—
160C4×Dic14D414yes—
161C4×Dic14C2314yes—
162C7×#106C2314yes—
163C7×#102C2314yes—
164C7×#102C2314yes—
165C7×#97C2314yes—
166#6406C2314yes—
167#6406C2314yes—
168#6395C2314yes—
169#6395C2314yes—
170#6390C2314yes—
171#6390C2314yes—
172#6389C2314yes—
173Dic7⋊C8C2314yes—
174Dic7⋊C8C2314yes—
175C8×Dic7C2314yes—
176#6384C2314yes—
177#6383C2314yes—
178#6382C2314yes—
179#6382C2314yes—
180C4⋊(C7⋊C8)C2314yes—
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×#476—71no—
190C2×#463—71no—
191C2×#463—71no—
192C2×#459—71no—
193C2×#446—71no—
194C2×#442—71no—
195C2×#442D711yescharacteristic, complemented
196C2×C4×SD16—71no—
197C24×C7—21no—
198C24×C7—21no—
199C23×D7—21no—
200C2×C7×D4—21no—
201C2×C7×D4—21no—
202C2×C7×D4—22no—
203C2×C7×D4—22no—
204C2×C7×D4—22no—
205C2×C7×D4#4114yes—
206C2×C7×D4C2412yes—
207C2×C7×D4C2412yes—
208C22×C4×C7—21no—
209C22×C4×C7—21no—
210C22×C4×C7—24no—
211C22×C4×C7—24no—
212C22×C4×C7—44no—
213C22×C4×C7—82no—
214C22×C4×C7C2×D411yescharacteristic
215C22×C4×C7C2×D411yescharacteristic
216C22×C4×C7C2411yescharacteristic
217C2×C22⋊D7—24no—
218C2×C22⋊D7—24no—
219C2×C22⋊D7—44no—
220C2×C22⋊D7—82no—
221C22×Dic7—21no—
222C22×Dic7—21no—
223C22×Dic7—21no—
224C22×Dic7—24no—
225C22×Dic7—24no—
226C22×Dic7—44no—
227C22×Dic7—44no—
228C22×Dic7C2×D411yescharacteristic
229C22×Dic7C2×D411yescharacteristic
230C22×Dic7C2×D411yescharacteristic
231C22×Dic7C2×D411yescharacteristic
232C2×D28—22no—
233C2×D28—22no—
234C2×D28—21no—
235C2×D28C2412yes—
236C2×C4×D7—24no—
237C2×C4×D7—82no—
238C2×Dic14—24no—
239C2×Dic14—22no—
240C2×Dic14—22no—
241C2×Dic14—24no—
242C2×Dic14—21no—
243C2×Dic14—24no—
244C2×Dic14—24no—
245C2×Dic14—432no—
246C2×Dic14—44no—
247C2×Dic14—44no—
248C2×Dic14—44no—
249C2×Dic14C2×D414yes—
250C2×Dic14C2412yes—
251C7×D8—28no—
252C2×C7×C8—22no—
253C2×C7×C8—22no—
254C2×C7×C8C2412yes—
255C2×C7×C8C2412yes—
256C7×C4⋊C4—21no—
257C7×C4⋊C4—21no—
258C7×C4⋊C4C2412yes—
259C7×C4⋊C4C2412yes—
260C7×C22⋊C4—24no—
261C7×C22⋊C4—24no—
262C42×C7C2×D412yes—
263C42×C7C2412yes—
264C22⋊Dic7—24no—
265C22⋊Dic7—24no—
266C22⋊Dic7—24no—
267C22⋊Dic7—24no—
268#1142—28no—
269#1141—28no—
270(C2×D7)⋊C4—24no—
271(C2×D7)⋊C4—24no—
272(C2×D7)⋊C4—24no—
273C4⋊Dic7—21no—
274C4⋊Dic7—21no—
275C4⋊Dic7—24no—
276C4⋊Dic7C2×D414yes—
277C4⋊Dic7C2412yes—
278C4⋊Dic7C2412yes—
279Dic7⋊C4—24no—
280Dic7⋊C4—24no—
281Dic7⋊C4—24no—
282Dic7⋊C4C2×D414yes—
283Dic7⋊C4C2×D414yes—
284C4×Dic7—24no—
285C4×Dic7C2×D412yes—
286C4×Dic7C2×D412yes—
287C4×Dic7C2412yes—
288C4×Dic7C2412yes—
289C2×C7⋊C8—22no—
290C2×C7⋊C8—22no—
291C2×C7⋊C8C2412yes—
292C2×C7⋊C8C2412yes—
293C23×Q8—141no—
294C22×SD16—71no—
295C22×D8—71no—
296C22×D8C2×D711yescharacteristic
297#559—78no—
298#559—144no—
299D4×Q8—78no—
300D4×Q8—144no—
301C2×C4⋊Q8—71no—
302C2×C4⋊Q8—71no—
303C2×C4⋊Q8—71no—
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—141no—
319C2×C4×D4C2×D711yescharacteristic
320C2×C4×D4C2×D711yescharacteristic
321#489—78no—
322#489—78no—
323#486—78no—
324#476—78no—
325#476—78no—
326#475—78no—
327#463—78no—
328#463—78no—
329#459—78no—
330#446—78no—
331#442—78no—
332#442C2×D718yescomplemented
333C4×SD16—78no—
334C2×#106—71no—
335C2×#106—71no—
336C2×#106C2×D711yescharacteristic
337C2×C4⋊C8—71no—
338C2×C4⋊C8—71no—
339C2×C4⋊C8—71no—
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×#97C2×D711yescharacteristic
352C2×C4×C8—71no—
353C23×C7—24no—
354C23×C7—22no—
355C23×C7—22no—
356C23×C7—42no—
357C23×C7—42no—
358C23×C7—42no—
359C23×C7—42no—
360C23×C7—42no—
361C23×C7C22×D411yescharacteristic
362C22×D7—22no—
363C22×D7—42no—
364C22×D7—42no—
365C22×D7—42no—
366C7×D4—24no—
367C7×D4—22no—
368C7×D4—22no—
369C7×D4—22no—
370C7×D4—42no—
371C7×D4C2×#4114yes—
372C2×C4×C7—22no—
373C2×C4×C7—22no—
374C2×C4×C7—22no—
375C2×C4×C7—22no—
376C2×C4×C7—48no—
377C2×C4×C7—42no—
378C2×C4×C7—42no—
379C2×C4×C7—84no—
380C2×C4×C7C22×D412yes—
381C2×C4×C7C22×D412yes—
382C2×C4×C7C22×D411yescharacteristic
383C2×C4×C7C2×#4112yes—
384C2×C4×C72−1+412yes—
385C2×C4×C7C2511yescharacteristic
386C22⋊D7—48no—
387C22⋊D7—84no—
388C2×Dic7—22no—
389C2×Dic7—22no—
390C2×Dic7—22no—
391C2×Dic7—22no—
392C2×Dic7—22no—
393C2×Dic7—22no—
394C2×Dic7—48no—
395C2×Dic7—42no—
396C2×Dic7—42no—
397C2×Dic7—42no—
398C2×Dic7—48no—
399C2×Dic7AGL(1,ℤ/8)14yes—
400C2×Dic7C22×D412yes—
401C2×Dic7C22×D412yes—
402C2×Dic7C22×D412yes—
403C2×Dic7C22×D412yes—
404D28—22no—
405D28—22no—
406D28—42no—
407C4×D7—84no—
408Dic14—28no—
409Dic14—22no—
410Dic14—22no—
411Dic14—48no—
412Dic14—48no—
413Dic14—42no—
414Dic14—48no—
415C7×C8—22no—
416C7×C8—22no—
417C7⋊C8—22no—
418C7⋊C8—22no—
419C22×Q8—71no—
420C22×Q8—71no—
421C22×Q8—141no—
422C22×Q8—141no—
423C22×Q8—148no—
424C22×Q8—141no—
425C22×Q8—288no—
426C22×D4—71no—
427C22×D4—141no—
428C22×D4—141no—
429C22×D4C22×D711yescharacteristic
430C22×D4C22×D711yescharacteristic
431C23×C4—21no—
432C23×C4—21no—
433C23×C4—141no—
434C23×C4—141no—
435C23×C4—141no—
436C2×SD16—74no—
437C2×SD16—144no—
438C2×D8—24no—
439C2×D8—74no—
440C2×D8—144no—
441C2×D8C22×D714yes—
442C22×C8—71no—
443C22×C8—71no—
444C22×C8C22×D711yescharacteristic
445C22×C8C22×D711yescharacteristic
446C4⋊Q8—74no—
447C4⋊Q8—74no—
448C4⋊Q8—74no—
449C4⋊Q8—142no—
450C4⋊Q8—142no—
451C4⋊Q8—142no—
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—22no—
470C4×D4—74no—
471C4×D4—74no—
472C4×D4—74no—
473C4×D4—142no—
474C4×D4—142no—
475C4×D4—142no—
476C4×D4—148no—
477C4×D4C22×D714yes—
478C4×D4C22×D714yes—
479C2×C4⋊C4—71no—
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⋊C4—141no—
488C2×C4⋊C4C22×D711yescharacteristic
489C2×C4⋊C4C22×D711yescharacteristic
490C2×C22⋊C4—21no—
491C2×C22⋊C4—21no—
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#106—74no—
505#106C22×D714yes—
506C4⋊C8—74no—
507C4⋊C8—74no—
508C4⋊C8—74no—
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#97C22×D714yes—
521C4×C8—74no—
522C22×C7—24no—
523C22×C7—48no—
524C22×C7—42no—
525C22×C7—42no—
526C22×C7—42no—
527C22×C7—42no—
528C22×C7—42no—
529C22×C7—84no—
530C22×C7#54812yes—
531C22×C7C2×AGL(1,ℤ/8)12yes—
532C22×C7#57712yes—
533C22×C7C23×D411yescharacteristic
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#54812yes—
543C4×C7C22×#4111yescharacteristic
544C4×C7C2×2−1+411yescharacteristic
545Dic7—22no—
546Dic7—22no—
547Dic7—22no—
548Dic7—42no—
549Dic7—42no—
550Dic7—42no—
551Dic7C2×AGL(1,ℤ/8)14yes—
552C24—21no—
553C24—21no—
554C24—141no—
555C2×Q8—74no—
556C2×Q8—72no—
557C2×Q8—144no—
558C2×Q8—144no—
559C2×Q8—144no—
560C2×Q8—141no—
561C2×Q8—144no—
562C2×Q8—142no—
563C2×Q8—142no—
564C2×Q8—284no—
565C2×Q8—284no—
566C2×Q8—284no—
567C2×Q8—2832no—
568C2×D4—22no—
569C2×D4—21no—
570C2×D4—21no—
571C2×D4—22no—
572C2×D4—22no—
573C2×D4—72no—
574C2×D4—144no—
575C2×D4—144no—
576C2×D4—142no—
577C2×D4—141no—
578C2×D4—142no—
579C2×D4—284no—
580C2×D4—562no—
581C2×D4#115714yes—
582C2×D4C23×D712yes—
583C2×D4C23×D712yes—
584C22×C4—21no—
585C22×C4—21no—
586C22×C4—24no—
587C22×C4—24no—
588C22×C4—44no—
589C22×C4—71no—
590C22×C4—71no—
591C22×C4—71no—
592C22×C4—71no—
593C22×C4—82no—
594C22×C4—144no—
595C22×C4—144no—
596C22×C4—144no—
597C22×C4—141no—
598C22×C4—141no—
599C22×C4—141no—
600C22×C4—284no—
601C22×C4—284no—
602C22×C4—562no—
603C22×C4D4×D711yescharacteristic
604C22×C4D4×D711yescharacteristic
605C22×C4C23×D711yescharacteristic
606SD16—148no—
607D8—28no—
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—21no—
618C4⋊C4—21no—
619C4⋊C4—74no—
620C4⋊C4—74no—
621C4⋊C4—74no—
622C4⋊C4—72no—
623C4⋊C4—72no—
624C4⋊C4—144no—
625C4⋊C4—144no—
626C4⋊C4—144no—
627C4⋊C4—141no—
628C4⋊C4—141no—
629C4⋊C4—144no—
630C4⋊C4C23×D712yes—
631C4⋊C4C23×D712yes—
632C22⋊C4—24no—
633C22⋊C4—24no—
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—44no—
649C2×C7—82no—
650C2×C7#337314yescomplemented
651C2×C7C2×#54811yescharacteristic
652C2×C7C22×AGL(1,ℤ/8)11yescharacteristic
653C2×C7C2×#57711yescharacteristic
654D7—82no—
655C23—24no—
656C23—22no—
657C23—22no—
658C23—42no—
659C23—42no—
660C23—42no—
661C23—42no—
662C23—42no—
663C23—142no—
664C23—282no—
665C23—282no—
666C23—282no—
667C23C2×D4×D711yescharacteristic
668Q8—148no—
669Q8—142no—
670Q8—142no—
671Q8—288no—
672Q8—288no—
673Q8—288no—
674Q8—282no—
675D4—24no—
676D4—22no—
677D4—22no—
678D4—22no—
679D4—42no—
680D4—142no—
681D4—142no—
682D4—288no—
683D4—282no—
684D4—564no—
685D4C2×#115714yes—
686C2×C4—22no—
687C2×C4—22no—
688C2×C4—22no—
689C2×C4—22no—
690C2×C4—48no—
691C2×C4—42no—
692C2×C4—42no—
693C2×C4—74no—
694C2×C4—72no—
695C2×C4—72no—
696C2×C4—72no—
697C2×C4—72no—
698C2×C4—84no—
699C2×C4—142no—
700C2×C4—142no—
701C2×C4—142no—
702C2×C4—142no—
703C2×C4—142no—
704C2×C4—142no—
705C2×C4—288no—
706C2×C4—288no—
707C2×C4—282no—
708C2×C4—282no—
709C2×C4—282no—
710C2×C4—564no—
711C2×C4C2×#115712yes—
712C2×C4C2×D4×D712yes—
713C2×C4C2×D4×D712yes—
714C2×C4C2×D4×D711yescharacteristic
715C2×C4#655412yes—
716C2×C4C24×D711yescharacteristic
717C8—22no—
718C8—22no—
719C8—142no—
720C8—142no—
721C7C2×#337311yescharacteristic, complemented, Sylow
722C22—24no—
723C22—42no—
724C22—42no—
725C22—48no—
726C22—42no—
727C22—42no—
728C22—42no—
729C22—84no—
730C22—282no—
731C22—282no—
732C22—282no—
733C22—564no—
734C22#9024312yes—
735C22D7×AGL(1,ℤ/8)12yes—
736C22#9046612yes—
737C22C22×D4×D711yescharacteristic
738C4—22no—
739C4—22no—
740C4—42no—
741C4—42no—
742C4—74no—
743C4—142no—
744C4—142no—
745C4—142no—
746C4—282no—
747C4—282no—
748C4—282no—
749C4#9024312yes—
750C4C22×#115711yescharacteristic
751C4C2×#655411yescharacteristic
752C2—44no—
753C2—82no—
754C2—562no—
755C2#1173729814yesdirect product factor
756C2C2×#9024311yescharacteristic
757C2C2×D7×AGL(1,ℤ/8)11yescharacteristic
758C2C2×#9046611yescharacteristic
subgroupG/H
centerC23C2×D4×D7
commutator, cosocleC2×C4×C7C25
FrattiniC2×C4C24×D7
FittingC2×C7×#442C2
socleC23×C7C22×D4
prime radicalC2×#89922C2
hypercenterC2×#442D7
hypocenterC7C2×#3373
LCSG ▷ C2×C4×C7 ▷ C2×C7 ▷ C7
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#442

Complements

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

NH ≅ G/Ntype
1. C2×#90250C2semidirect
2. C2×D4×Dic14C2semidirect
3. C2×C7×#442C2semidirect
4. C2×#89925C2semidirect
6. C2×#89788C2semidirect
7. C2×#89780C2semidirect
8. #11737298C2direct (N × H)
9. C2×#89626C2semidirect
10. C2×#89642C2semidirect
11. C2×#89537C2semidirect
12. C2×#89532C2semidirect
13. C2×#89557C2semidirect
14. C2×#89530C2semidirect
15. C2×#89486C2semidirect
16. C2×#89473C2semidirect
31. #90250C22semidirect
33. D4×Dic14C22semidirect
45. C7×#442C22semidirect
52. #89925C22semidirect
62. #89788C22semidirect
63. #89780C22semidirect
69. #89642C22semidirect
70. #89626C22semidirect
71. #89557C22semidirect
72. #89537C22semidirect
73. #89532C22semidirect
74. #89530C22semidirect
75. #89486C22semidirect
76. #89473C22semidirect
195. C2×#442D7semidirect
332. #442C2×D7semidirect
650. C2×C7#3373semidirect
721. C7C2×#3373semidirect
755. C2#11737298direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#902502
C2×D4×Dic142
C2×C7×#4422
C2×#899252
C2×#899222
C2×#897882
C2×#897802
#117372982
C2×#896262
C2×#896422
C2×#895372
C2×#895322
C2×#895572
C2×#895302
C2×#894862
C2×#894732
C2×#33737