Finite Group Databasebeta

← C2×#11738274 #14232322

Subgroups — C2×#11738274 #14232322

Order 1792.

2094 conjugacy classes of subgroups.

The subgroup lattice has 748 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#90330C211yesmaximal, characteristic, complemented
2C2×#90302C211yesmaximal, characteristic
3C2×C7×#468C211yesmaximal, characteristic, complemented
4C2×#89943C211yesmaximal, characteristic, complemented
5C2×#89936C211yesmaximal, characteristic, complemented
6C2×#89899C211yesmaximal, characteristic, complemented
7C2×#89893C211yesmaximal, characteristic, complemented
8C2×#89816C211yesmaximal, characteristic, complemented
9C2×#89807C211yesmaximal, characteristic, complemented
10#11738274C2116yesmaximal, direct product factor
11C2×D7×#107C211yesmaximal, characteristic, complemented
12C2×#89648C211yesmaximal, characteristic, complemented
13C2×#89577C211yesmaximal, characteristic, complemented
14C2×#89566C211yesmaximal, characteristic, complemented
15C2×#89546C211yesmaximal, characteristic, complemented
16C2×#89535C211yesmaximal, characteristic, complemented
17C22×#1159—21no—
18C22×C7×SD16C2211yescharacteristic
19C22×C7×M16C2211yescharacteristic
20C2×C7×C22⋊Q8C2211yescharacteristic
21C2×C7×#121C2211yescharacteristic
22C2×#6509C2211yescharacteristic
23C2×Q8×Dic7C2211yescharacteristic
24C2×#6501C2211yescharacteristic
25C2×#6498—21no—
26C2×D4×Dic7C2211yescharacteristic
27C2×C4×C22⋊D7C2211yescharacteristic
28C2×#6489C2211yescharacteristic
29C22×C4⋊Dic7C2211yescharacteristic
30C22×C8×D7C2211yescharacteristic
31#90330—24no—
32#90330C2218yescomplemented
33#90302—24no—
34#90302C2218yes—
35C2×#6455—21no—
36C2×D7×C4⋊C4C2211yescharacteristic
37C2×D7×C4⋊C4C2211yescharacteristic
38C2×#6453C2211yescharacteristic
39C2×#6452—21no—
40C2×#6451C2211yescharacteristic
41C2×#6446—21no—
42C2×#6446—21no—
43C2×#6442—21no—
44C2×#6441—21no—
45C7×#468C2218yescomplemented
46C2×C7×#107C2211yescharacteristic
47C2×C7×#103C2211yescharacteristic
48C2×C7×#102C2211yescharacteristic
49C2×#6409C2211yescharacteristic
50C2×#6409C2211yescharacteristic
51C2×#6406C2211yescharacteristic
52C2×#6406C2211yescharacteristic
53C2×C22⋊(C7⋊C8)C2211yescharacteristic
54#89943C2218yescomplemented
55#89936C2218yescomplemented
56#89899C2218yescomplemented
57#89893C2218yescomplemented
58C2×(C2×D7)⋊C8C2211yescharacteristic
59C2×#6392C2211yescharacteristic
60C2×#6392C2211yescharacteristic
61C2×#6391C2211yescharacteristic
62C2×#6391C2211yescharacteristic
63C2×#6389C2211yescharacteristic
64C2×Dic7⋊C8C2211yescharacteristic
65#89816C2218yescomplemented
66#89807C2218yescomplemented
67C2×#6382C2211yescharacteristic
68C2×#6381C2211yescharacteristic
69C2×#6381C2211yescharacteristic
70C2×#6381C2211yescharacteristic
71D7×#107C2218yescomplemented
72#89648C2218yescomplemented
73#89577C2218yescomplemented
74#89566C2218yescomplemented
75#89546C2218yescomplemented
76#89535C2218yescomplemented
77C2×#3343—71nomaximal, Sylow
78C22×C7×Q8C2311yescharacteristic
79C22×C7×D4—21no—
80C22×C7×D4C2311yescharacteristic
81C23×C4×C7C2311yescharacteristic
82C22×C22⋊D7—21no—
83C22×C22⋊D7D411yescharacteristic
84C23×Dic7—21no—
85C23×Dic7—21no—
86C2×#1159—28no—
87C2×#1159—48no—
88C22×C4×D7—21no—
89C22×C4×D7—21no—
90C22×C4×D7C2311yescharacteristic
91C22×Dic14—21no—
92C2×C7×SD16—24no—
93C2×C7×SD16C2314yes—
94C2×C7×M16—24no—
95C2×C7×M16C2314yes—
96C22×C7×C8C2311yescharacteristic
97C22×C7×C8C2311yescharacteristic
98C7×C22⋊Q8—22no—
99C7×C22⋊Q8C2314yes—
100C7×#121—22no—
101C7×#121C2314yes—
102C2×C7×C4⋊C4—21no—
103C2×C7×C4⋊C4C2311yescharacteristic
104C2×C7×C4⋊C4C2311yescharacteristic
105C2×C7×C22⋊C4—21no—
106C2×C7×C22⋊C4—21no—
107C2×C22⋊Dic7—21no—
108C2×C22⋊Dic7—21no—
109C2×C22⋊Dic7—21no—
110C2×C22⋊Dic7D411yescharacteristic
111#6509—22no—
112#6509C2314yes—
113Q8×Dic7—22no—
114Q8×Dic7C2314yes—
115#6501—22no—
116#6501C2314yes—
117#6498—28no—
118D4×Dic7—22no—
119D4×Dic7C2314yes—
120C4×C22⋊D7D414yes—
121C4×C22⋊D7C2314yes—
122C2×(C2×D7)⋊C4—21no—
123C2×(C2×D7)⋊C4D411yescharacteristic
124#6489—22no—
125#6489C2314yes—
126C2×C4⋊Dic7—21no—
127C2×C4⋊Dic7—22no—
128C2×C4⋊Dic7—21no—
129C2×C4⋊Dic7—21no—
130C2×C4⋊Dic7C2311yescharacteristic
131C2×C4⋊Dic7C2311yescharacteristic
132C2×C4⋊Dic7C2311yescharacteristic
133C2×C4⋊Dic7C2311yescharacteristic
134C2×C4⋊Dic7C2314yes—
135C2×Dic7⋊C4—21no—
136C2×Dic7⋊C4—21no—
137C2×Dic7⋊C4—21no—
138C2×Dic7⋊C4—21no—
139C2×Dic7⋊C4—21no—
140C2×Dic7⋊C4D411yescharacteristic
141C2×C4×Dic7—21no—
142C2×C4×Dic7—21no—
143C2×C4×Dic7C2311yescharacteristic
144C22×C7⋊C8C2311yescharacteristic
145C22×C7⋊C8C2311yescharacteristic
146C2×C8×D7—24no—
147C2×C8×D7C2314yes—
148#6455—28no—
149D7×C4⋊C4—22no—
150D7×C4⋊C4—22no—
151D7×C4⋊C4C2314yes—
152D7×C4⋊C4C2314yes—
153#6453—22no—
154#6453C2314yes—
155#6452—28no—
156#6451—22no—
157#6451C2314yes—
158#6446—28no—
159#6446—28no—
160#6442—28no—
161#6441—28no—
162C7×#107C2314yes—
163C7×#103C2314yes—
164C7×#102C2314yes—
165#6409C2314yes—
166#6409C2314yes—
167#6406C2314yes—
168#6406C2314yes—
169C22⋊(C7⋊C8)C2314yes—
170(C2×D7)⋊C8C2314yes—
171#6392C2314yes—
172#6392C2314yes—
173#6391C2314yes—
174#6391C2314yes—
175#6389C2314yes—
176Dic7⋊C8C2314yes—
177#6382C2314yes—
178#6381C2314yes—
179#6381C2314yes—
180#6381C2314yes—
181C2×#552—71no—
182C2×#547—71no—
183#3343—716no—
184C2×#501—71no—
185C2×#484—71no—
186C2×#482—71no—
187C2×#483—71no—
188C2×#480—71no—
189C2×#477—71no—
190C2×#478—71no—
191C2×#468D711yescharacteristic, complemented
192C2×#465—71no—
193C2×#440—71no—
194C2×#435—71no—
195C2×#428—71no—
196C22×#107—71no—
197C24×C7—21no—
198C24×C7C2×D411yescharacteristic
199C23×D7C2×D411yescharacteristic
200C2×C7×Q8—21no—
201C2×C7×Q8—22no—
202C2×C7×Q8—22no—
203C2×C7×Q8C2412yes—
204C2×C7×D4—24no—
205C2×C7×D4—21no—
206C2×C7×D4—22no—
207C2×C7×D4—22no—
208C2×C7×D4—44no—
209C2×C7×D4C2412yes—
210C22×C4×C7—22no—
211C22×C4×C7—22no—
212C22×C4×C7—21no—
213C22×C4×C7—21no—
214C22×C4×C7—21no—
215C22×C4×C7C2×D411yescharacteristic
216C22×C4×C7C2×D412yes—
217C22×C4×C7C2412yes—
218C22×C4×C7C2411yescharacteristic
219C2×C22⋊D7—24no—
220C2×C22⋊D7—24no—
221C2×C22⋊D7—44no—
222C2×C22⋊D7C2×D414yes—
223C22×Dic7—21no—
224C22×Dic7—21no—
225C22×Dic7—21no—
226C22×Dic7—21no—
227C22×Dic7—24no—
228C22×Dic7—24no—
229C22×Dic7—44no—
230C22×Dic7—44no—
231C22×Dic7C2×D411yescharacteristic
232C22×Dic7C2×D411yescharacteristic
233C22×Dic7C2×D411yescharacteristic
234#1159—432no—
235C2×C4×D7—22no—
236C2×C4×D7—22no—
237C2×C4×D7—24no—
238C2×C4×D7—24no—
239C2×C4×D7—44no—
240C2×C4×D7—44no—
241C2×C4×D7C2×D412yes—
242C2×C4×D7C2412yes—
243C2×Dic14—24no—
244C2×Dic14—44no—
245C7×SD16—28no—
246C7×M16—28no—
247C2×C7×C8—22no—
248C2×C7×C8#4114yescomplemented
249C2×C7×C8C2412yes—
250C2×C7×C8C2412yes—
251C7×C4⋊C4—21no—
252C7×C4⋊C4—24no—
253C7×C4⋊C4—21no—
254C7×C4⋊C4C2412yes—
255C7×C4⋊C4C2412yes—
256C7×C22⋊C4—24no—
257C7×C22⋊C4—24no—
258C22⋊Dic7—24no—
259C22⋊Dic7—24no—
260C22⋊Dic7—24no—
261C22⋊Dic7C2×D414yes—
262(C2×D7)⋊C4—24no—
263(C2×D7)⋊C4C2×D414yes—
264C4⋊Dic7—24no—
265C4⋊Dic7—21no—
266C4⋊Dic7—21no—
267C4⋊Dic7—21no—
268C4⋊Dic7—21no—
269C4⋊Dic7—24no—
270C4⋊Dic7—24no—
271C4⋊Dic7C2412yes—
272C4⋊Dic7C2412yes—
273C4⋊Dic7C2412yes—
274C4⋊Dic7C2412yes—
275Dic7⋊C4—24no—
276Dic7⋊C4—24no—
277Dic7⋊C4—24no—
278Dic7⋊C4—24no—
279Dic7⋊C4—24no—
280Dic7⋊C4C2×D414yes—
281C4×Dic7—24no—
282C4×Dic7—24no—
283C4×Dic7C2×D412yes—
284C4×Dic7C2412yes—
285C2×C7⋊C8—22no—
286C2×C7⋊C8—22no—
287C2×C7⋊C8C2412yes—
288C2×C7⋊C8C2412yes—
289C8×D7—28no—
290C22×#41—141no—
291C22×SD16C2×D711yescharacteristic
292C22×M16C2×D711yescharacteristic
293C23×C8—71no—
294#552—78no—
295#552—144no—
296#547—78no—
297#547—144no—
298C2×C4⋊Q8—71no—
299C2×#126—141no—
300C2×#125—71no—
301C2×#125—141no—
302C2×#123—141no—
303C2×#123—141no—
304C2×#123—141no—
305C2×C22⋊Q8—71no—
306C2×C22⋊Q8—141no—
307C2×C22⋊Q8C2×D711yescharacteristic
308C2×#121—71no—
309C2×#121C2×D711yescharacteristic
310C2×C4×Q8—71no—
311C2×C4×D4—71no—
312C2×C4×D4—71no—
313C2×#117—71no—
314C2×#117—141no—
315C22×C4⋊C4—71no—
316C22×C4⋊C4—71no—
317C22×C4⋊C4—71no—
318#501—78no—
319#484—78no—
320#483—78no—
321#482—78no—
322#480—78no—
323#478—78no—
324#477—78no—
325#468C2×D718yescomplemented
326#465—78no—
327#440—78no—
328#435—78no—
329#428—78no—
330C2×#107—71no—
331C2×#107—71no—
332C2×#107—71no—
333C2×#107—71no—
334C2×#107—71no—
335C2×#107—78no—
336C2×#107C2×D711yescharacteristic
337C2×#106—71no—
338C2×#106—71no—
339C2×#106—71no—
340C2×C4⋊C8—71no—
341C2×#103—71no—
342C2×#103—71no—
343C2×#103C2×D711yescharacteristic
344C2×#102—71no—
345C2×#102—71no—
346C2×#102C2×D711yescharacteristic
347C2×C22⋊C8—71no—
348C2×C22⋊C8—71no—
349C2×#97—71no—
350C23×C7—22no—
351C23×C7—22no—
352C23×C7—22no—
353C23×C7—22no—
354C23×C7—42no—
355C23×C7—42no—
356C23×C7—42no—
357C23×C7C22×D412yes—
358C23×C7C22×D411yescharacteristic
359C22×D7—22no—
360C22×D7—22no—
361C22×D7AGL(1,ℤ/8)14yes—
362C22×D7C22×D412yes—
363C7×Q8—22no—
364C7×Q8—22no—
365C7×Q8—42no—
366C7×D4—22no—
367C7×D4—22no—
368C7×D4—48no—
369C7×D4—42no—
370C2×C4×C7—22no—
371C2×C4×C7—24no—
372C2×C4×C7—22no—
373C2×C4×C7—22no—
374C2×C4×C7—22no—
375C2×C4×C7—22no—
376C2×C4×C7—22no—
377C2×C4×C7—42no—
378C2×C4×C7—42no—
379C2×C4×C7—42no—
380C2×C4×C7C22×D412yes—
381C2×C4×C7C22×D411yescharacteristic
382C2×C4×C7C2×#4112yes—
383C2×C4×C72−1+412yes—
384C2×C4×C7C2511yescharacteristic
385C22⋊D7—28no—
386C22⋊D7—48no—
387C2×Dic7—22no—
388C2×Dic7—22no—
389C2×Dic7—22no—
390C2×Dic7—22no—
391C2×Dic7—22no—
392C2×Dic7—22no—
393C2×Dic7—22no—
394C2×Dic7—48no—
395C2×Dic7—48no—
396C2×Dic7—42no—
397C2×Dic7—42no—
398C2×Dic7—42no—
399C2×Dic7—42no—
400C2×Dic7C22×D412yes—
401C2×Dic7C22×D412yes—
402C2×Dic7C22×D412yes—
403C4×D7—24no—
404C4×D7—22no—
405C4×D7—22no—
406C4×D7—48no—
407C4×D7—48no—
408Dic14—48no—
409C7×C8—22no—
410C7×C8C2×#4114yescomplemented
411C7⋊C8—22no—
412C7⋊C8—22no—
413C2×#41—148no—
414C2×#41—288no—
415C22×Q8—141no—
416C22×Q8C22×D711yescharacteristic
417C22×D4—21no—
418C22×D4—71no—
419C22×D4—141no—
420C22×D4C22×D711yescharacteristic
421C23×C4—71no—
422C23×C4—141no—
423C23×C4—141no—
424C23×C4—141no—
425C23×C4—141no—
426C23×C4C22×D711yescharacteristic
427C2×SD16—24no—
428C2×SD16C22×D714yes—
429C2×M16—24no—
430C2×M16C22×D714yes—
431C22×C8—71no—
432C22×C8—71no—
433C22×C8—74no—
434C22×C8—144no—
435C22×C8C22×D711yescharacteristic
436C22×C8C22×D711yescharacteristic
437C4⋊Q8—74no—
438C4⋊Q8—142no—
439#126—148no—
440#125—74no—
441#125—142no—
442#125—148no—
443#123—148no—
444#123—148no—
445#123—148no—
446C22⋊Q8—22no—
447C22⋊Q8—74no—
448C22⋊Q8—148no—
449C22⋊Q8—142no—
450C22⋊Q8C22×D714yes—
451#121—22no—
452#121—74no—
453#121—142no—
454#121C22×D714yes—
455C4×Q8—74no—
456C4×Q8—142no—
457C4×D4—74no—
458C4×D4—74no—
459C4×D4—74no—
460C4×D4—142no—
461#117—74no—
462#117—148no—
463#117—142no—
464C2×C4⋊C4—21no—
465C2×C4⋊C4—71no—
466C2×C4⋊C4—71no—
467C2×C4⋊C4—71no—
468C2×C4⋊C4—71no—
469C2×C4⋊C4—74no—
470C2×C4⋊C4—71no—
471C2×C4⋊C4—74no—
472C2×C4⋊C4—74no—
473C2×C4⋊C4—142no—
474C2×C4⋊C4—142no—
475C2×C4⋊C4—141no—
476C2×C4⋊C4—141no—
477C2×C4⋊C4—141no—
478C2×C4⋊C4—141no—
479C2×C4⋊C4—141no—
480C2×C4⋊C4—141no—
481C2×C4⋊C4—141no—
482C2×C4⋊C4—141no—
483C2×C4⋊C4—142no—
484C2×C4⋊C4C22×D711yescharacteristic
485C2×C4⋊C4C22×D711yescharacteristic
486C2×C22⋊C4—21no—
487C2×C22⋊C4—21no—
488C2×C22⋊C4—71no—
489C2×C22⋊C4—71no—
490C2×C22⋊C4—141no—
491C2×C22⋊C4—141no—
492C2×C22⋊C4—141no—
493C2×C22⋊C4—141no—
494C2×C42—71no—
495C2×C42—141no—
496C2×C42—141no—
497#107—74no—
498#107—74no—
499#107—74no—
500#107—74no—
501#107—74no—
502#107C22×D714yes—
503#106—74no—
504#106—74no—
505#106—74no—
506C4⋊C8—74no—
507#103—74no—
508#103—74no—
509#103C22×D714yes—
510#102—74no—
511#102—74no—
512#102C22×D714yes—
513C22⋊C8—74no—
514C22⋊C8—74no—
515#97—74no—
516C22×C7—22no—
517C22×C7—22no—
518C22×C7—22no—
519C22×C7—44no—
520C22×C7—42no—
521C22×C7—42no—
522C22×C7—42no—
523C22×C7—84no—
524C22×C7#54712yes—
525C22×C7C2×AGL(1,ℤ/8)12yes—
526C22×C7#57812yes—
527C22×C7C23×D411yescharacteristic
528C2×D7—28no—
529C2×D7—22no—
530C2×D7—22no—
531C2×D7C2×AGL(1,ℤ/8)14yes—
532C4×C7—22no—
533C4×C7—42no—
534C4×C7—42no—
535C4×C7—42no—
536C4×C7#54712yes—
537C4×C7C22×#4111yescharacteristic
538C4×C7C2×2−1+411yescharacteristic
539Dic7—22no—
540Dic7—22no—
541Dic7—22no—
542Dic7—42no—
543Dic7—42no—
544Dic7—42no—
545Dic7—42no—
546C24—21no—
547C24—71no—
548C24D4×D711yescharacteristic
549#41—2832no—
550C2×Q8—21no—
551C2×Q8—22no—
552C2×Q8—22no—
553C2×Q8—144no—
554C2×Q8—284no—
555C2×Q8C23×D712yes—
556C2×D4—24no—
557C2×D4—21no—
558C2×D4—22no—
559C2×D4—22no—
560C2×D4—44no—
561C2×D4—74no—
562C2×D4—144no—
563C2×D4—144no—
564C2×D4—284no—
565C2×D4C23×D712yes—
566C22×C4—22no—
567C22×C4—22no—
568C22×C4—21no—
569C22×C4—21no—
570C22×C4—21no—
571C22×C4—71no—
572C22×C4—71no—
573C22×C4—71no—
574C22×C4—72no—
575C22×C4—72no—
576C22×C4—144no—
577C22×C4—144no—
578C22×C4—144no—
579C22×C4—142no—
580C22×C4—142no—
581C22×C4—144no—
582C22×C4—141no—
583C22×C4—141no—
584C22×C4—141no—
585C22×C4—141no—
586C22×C4—284no—
587C22×C4—284no—
588C22×C4—284no—
589C22×C4—284no—
590C22×C4D4×D712yes—
591C22×C4D4×D711yescharacteristic
592C22×C4C23×D712yes—
593C22×C4C23×D711yescharacteristic
594SD16—28no—
595M16—28no—
596C2×C8—22no—
597C2×C8—72no—
598C2×C8—72no—
599C2×C8—142no—
600C2×C8—142no—
601C2×C8—148no—
602C2×C8#115914yescomplemented
603C2×C8C23×D712yes—
604C2×C8C23×D712yes—
605C4⋊C4—24no—
606C4⋊C4—21no—
607C4⋊C4—21no—
608C4⋊C4—74no—
609C4⋊C4—72no—
610C4⋊C4—72no—
611C4⋊C4—72no—
612C4⋊C4—72no—
613C4⋊C4—144no—
614C4⋊C4—144no—
615C4⋊C4—144no—
616C4⋊C4—144no—
617C4⋊C4—144no—
618C4⋊C4—144no—
619C4⋊C4—144no—
620C4⋊C4—141no—
621C4⋊C4—141no—
622C4⋊C4—141no—
623C4⋊C4—144no—
624C4⋊C4—141no—
625C4⋊C4C23×D712yes—
626C4⋊C4C23×D712yes—
627C22⋊C4—24no—
628C22⋊C4—24no—
629C22⋊C4—74no—
630C22⋊C4—74no—
631C22⋊C4—144no—
632C22⋊C4—144no—
633C22⋊C4—144no—
634C22⋊C4—144no—
635C42—72no—
636C42—72no—
637C42—144no—
638C42—144no—
639C2×C7—42no—
640C2×C7—82no—
641C2×C7#334314yescomplemented
642C2×C7C2×#54711yescharacteristic
643C2×C7C22×AGL(1,ℤ/8)11yescharacteristic
644C2×C7C2×#57811yescharacteristic
645D7—24no—
646C23—22no—
647C23—22no—
648C23—22no—
649C23—22no—
650C23—42no—
651C23—42no—
652C23—42no—
653C23—74no—
654C23—72no—
655C23—142no—
656C23—142no—
657C23C2×D4×D712yes—
658C23C2×D4×D711yescharacteristic
659Q8—22no—
660Q8—22no—
661Q8—42no—
662Q8—288no—
663D4—22no—
664D4—22no—
665D4—48no—
666D4—42no—
667D4—148no—
668D4—288no—
669C2×C4—22no—
670C2×C4—24no—
671C2×C4—22no—
672C2×C4—22no—
673C2×C4—22no—
674C2×C4—22no—
675C2×C4—22no—
676C2×C4—42no—
677C2×C4—42no—
678C2×C4—42no—
679C2×C4—72no—
680C2×C4—72no—
681C2×C4—72no—
682C2×C4—142no—
683C2×C4—142no—
684C2×C4—142no—
685C2×C4—144no—
686C2×C4—142no—
687C2×C4—142no—
688C2×C4—142no—
689C2×C4—142no—
690C2×C4—142no—
691C2×C4—142no—
692C2×C4—288no—
693C2×C4—288no—
694C2×C4—288no—
695C2×C4—288no—
696C2×C4—282no—
697C2×C4—282no—
698C2×C4—282no—
699C2×C4—282no—
700C2×C4C2×D4×D712yes—
701C2×C4C2×D4×D711yescharacteristic
702C2×C4C2×#115912yes—
703C2×C4#655412yes—
704C2×C4C24×D711yescharacteristic
705C8—22no—
706C8—142no—
707C8—142no—
708C8C2×#115914yescomplemented
709C7C2×#334311yescharacteristic, complemented, Sylow
710C22—22no—
711C22—22no—
712C22—22no—
713C22—44no—
714C22—42no—
715C22—42no—
716C22—42no—
717C22—74no—
718C22—84no—
719C22—142no—
720C22—142no—
721C22—148no—
722C22#9030212yes—
723C22D7×AGL(1,ℤ/8)12yes—
724C22#9047012yes—
725C22C22×D4×D711yescharacteristic
726C4—22no—
727C4—42no—
728C4—42no—
729C4—42no—
730C4—142no—
731C4—142no—
732C4—142no—
733C4—282no—
734C4—282no—
735C4—282no—
736C4—282no—
737C4#9030212yes—
738C4C22×#115911yescharacteristic
739C4C2×#655411yescharacteristic
740C2—42no—
741C2—82no—
742C2—144no—
743C2#1173827414yesdirect product factor
744C2C2×#9030211yescharacteristic
745C2C2×D7×AGL(1,ℤ/8)11yescharacteristic
746C2C2×#9047011yescharacteristic
subgroupG/H
centerC23C2×D4×D7
commutator, cosocleC2×C4×C7C25
FrattiniC2×C4C24×D7
FittingC2×C7×#468C2
socleC23×C7C22×D4
prime radicalC2×#90302C2
hypercenterC2×#468D7
hypocenterC7C2×#3343
LCSG ▷ C2×C4×C7 ▷ C2×C7 ▷ C7
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#468

Complements

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

NH ≅ G/Ntype
1. C2×#90330C2semidirect
3. C2×C7×#468C2semidirect
4. C2×#89943C2semidirect
5. C2×#89936C2semidirect
6. C2×#89899C2semidirect
7. C2×#89893C2semidirect
8. C2×#89816C2semidirect
9. C2×#89807C2semidirect
10. #11738274C2direct (N × H)
11. C2×D7×#107C2semidirect
12. C2×#89648C2semidirect
13. C2×#89577C2semidirect
14. C2×#89566C2semidirect
15. C2×#89546C2semidirect
16. C2×#89535C2semidirect
32. #90330C22semidirect
45. C7×#468C22semidirect
54. #89943C22semidirect
55. #89936C22semidirect
56. #89899C22semidirect
57. #89893C22semidirect
65. #89816C22semidirect
66. #89807C22semidirect
71. D7×#107C22semidirect
72. #89648C22semidirect
73. #89577C22semidirect
74. #89566C22semidirect
75. #89546C22semidirect
76. #89535C22semidirect
191. C2×#468D7semidirect
248. C2×C7×C8#41semidirect
325. #468C2×D7semidirect
410. C7×C8C2×#41semidirect
602. C2×C8#1159semidirect
641. C2×C7#3343semidirect
708. C8C2×#1159semidirect
709. C7C2×#3343semidirect
743. C2#11738274direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#903302
C2×#903022
C2×C7×#4682
C2×#899432
C2×#899362
C2×#898992
C2×#898932
C2×#898162
C2×#898072
#117382742
C2×D7×#1072
C2×#896482
C2×#895772
C2×#895662
C2×#895462
C2×#895352
C2×#33437