Finite Group Databasebeta

← C2×#11737251 #14232332

Subgroups — C2×#11737251 #14232332

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×#90272C211yesmaximal, characteristic, complemented
2C2×#90242C211yesmaximal, characteristic
3C2×C7×#440C211yesmaximal, characteristic, complemented
4C2×#89946C211yesmaximal, characteristic, complemented
5C2×#89943C211yesmaximal, characteristic, complemented
6C2×#89793C211yesmaximal, characteristic, complemented
7C2×#89781C211yesmaximal, characteristic, complemented
8#11737251C2116yesmaximal, direct product factor
9C2×#89653C211yesmaximal, characteristic, complemented
10C2×D7×#107C211yesmaximal, characteristic, complemented
11C2×#89581C211yesmaximal, characteristic, complemented
12C2×#89577C211yesmaximal, characteristic, complemented
13C2×#89546C211yesmaximal, characteristic, complemented
14C2×#89551C211yesmaximal, characteristic, complemented
15C2×#89478C211yesmaximal, characteristic, complemented
16C2×#89474C211yesmaximal, characteristic, complemented
17C22×#1157—21no—
18C22×C7×SD16C2211yescharacteristic
19C2×C4×C7×Q8C2211yescharacteristic
20C2×C4×C7×D4C2211yescharacteristic
21C2×#6509C2211yescharacteristic
22C2×#6509C2211yescharacteristic
23C2×#6501C2211yescharacteristic
24C2×#6501C2211yescharacteristic
25C2×#6487—21no—
26C22×#1131C2211yescharacteristic
27C22×C8×D7C2211yescharacteristic
28#90272—24no—
29#90272C2218yescomplemented
30#90242—24no—
31#90242C2218yes—
32C2×#6457—21no—
33C2×#6455C2211yescharacteristic
34C2×D7×C4⋊C4C2211yescharacteristic
35C2×D7×C4⋊C4C2211yescharacteristic
36C2×D7×C4⋊C4C2211yescharacteristic
37C2×#6452—21no—
38C2×#6446—21no—
39C2×#6446—21no—
40C2×#6439—21no—
41C2×C4×D28C2211yescharacteristic
42C2×#6435—21no—
43C2×#6433C2211yescharacteristic
44C2×#6432C2211yescharacteristic
45C7×#440C2218yescomplemented
46C2×C7×#107C2211yescharacteristic
47C2×C7×#103C2211yescharacteristic
48C2×C7×#102C2211yescharacteristic
49C2×C7×#97C2211yescharacteristic
50C2×#6409C2211yescharacteristic
51C2×#6409C2211yescharacteristic
52C2×#6406C2211yescharacteristic
53C2×#6406C2211yescharacteristic
54#89946C2218yescomplemented
55#89943C2218yescomplemented
56C2×(C2×D7)⋊C8C2211yescharacteristic
57C2×(C2×D7)⋊C8C2211yescharacteristic
58C2×#6392C2211yescharacteristic
59C2×#6392C2211yescharacteristic
60C2×#6391C2211yescharacteristic
61C2×#6391C2211yescharacteristic
62#89793C2218yescomplemented
63#89781C2218yescomplemented
64C2×#6382C2211yescharacteristic
65C2×#6381C2211yescharacteristic
66C2×#6381C2211yescharacteristic
67C2×#6381C2211yescharacteristic
68C2×C4⋊(C7⋊C8)C2211yescharacteristic
69#89653C2218yescomplemented
70D7×#107C2218yescomplemented
71#89581C2218yescomplemented
72#89577C2218yescomplemented
73#89551C2218yescomplemented
74#89546C2218yescomplemented
75#89478C2218yescomplemented
76#89474C2218yescomplemented
77C2×#3343—71nomaximal, Sylow
78C22×C7×Q8C2311yescharacteristic
79C22×C7×D4C2311yescharacteristic
80C23×C4×C7—21no—
81C22×C22⋊D7—21no—
82C22×C22⋊D7—21no—
83C2×#1157—28no—
84C2×#1157—48no—
85C22×D28D411yescharacteristic
86C22×C4×D7—21no—
87C22×C4×D7—21no—
88C22×C4×D7—21no—
89C22×C4×D7C2311yescharacteristic
90C22×C4×D7C2311yescharacteristic
91C22×Dic14—21no—
92C2×C7×SD16—24no—
93C2×C7×SD16C2314yes—
94C22×C7×C8C2311yescharacteristic
95C22×C7×C8C2311yescharacteristic
96C4×C7×Q8—22no—
97C4×C7×Q8C2314yes—
98C4×C7×D4—22no—
99C4×C7×D4C2314yes—
100C2×C7×C4⋊C4—21no—
101C2×C7×C4⋊C4C2311yescharacteristic
102C2×C7×C4⋊C4C2311yescharacteristic
103C2×C7×C22⋊C4—21no—
104C2×C42×C7—21no—
105C2×C42×C7C2311yescharacteristic
106C2×C22⋊Dic7—21no—
107C2×C22⋊Dic7—21no—
108#6509—22no—
109#6509—22no—
110#6509C2314yes—
111#6509C2314yes—
112#6501—22no—
113#6501—22no—
114#6501C2314yes—
115#6501C2314yes—
116C2×(C2×D7)⋊C4—21no—
117C2×(C2×D7)⋊C4—21no—
118C2×(C2×D7)⋊C4—21no—
119C2×(C2×D7)⋊C4D411yescharacteristic
120C2×(C2×D7)⋊C4D411yescharacteristic
121C2×C4⋊Dic7—21no—
122C2×C4⋊Dic7D411yescharacteristic
123C2×C4⋊Dic7C2311yescharacteristic
124C2×C4⋊Dic7C2311yescharacteristic
125C2×C4⋊Dic7C2311yescharacteristic
126C2×C4⋊Dic7C2311yescharacteristic
127#6487—28no—
128C2×Dic7⋊C4—21no—
129C2×Dic7⋊C4—21no—
130C2×Dic7⋊C4—21no—
131C2×Dic7⋊C4—21no—
132C2×Dic7⋊C4—21no—
133C2×Dic7⋊C4—21no—
134C2×Dic7⋊C4—21no—
135C2×C4×Dic7—21no—
136C22×C7⋊C8C2311yescharacteristic
137C22×C7⋊C8C2311yescharacteristic
138C2×#1131—24no—
139C2×#1131C2314yes—
140C2×C8×D7—24no—
141C2×C8×D7C2314yes—
142#6457—28no—
143#6455—22no—
144#6455C2314yes—
145D7×C4⋊C4—22no—
146D7×C4⋊C4—22no—
147D7×C4⋊C4—22no—
148D7×C4⋊C4C2314yes—
149D7×C4⋊C4C2314yes—
150D7×C4⋊C4C2314yes—
151#6452—28no—
152#6446—28no—
153#6446—28no—
154#6439—28no—
155C4×D28D414yes—
156C4×D28C2314yes—
157#6435—28no—
158#6433—22no—
159#6433C2314yes—
160#6432—22no—
161#6432C2314yes—
162C7×#107C2314yes—
163C7×#103C2314yes—
164C7×#102C2314yes—
165C7×#97C2314yes—
166#6409C2314yes—
167#6409C2314yes—
168#6406C2314yes—
169#6406C2314yes—
170(C2×D7)⋊C8C2314yes—
171(C2×D7)⋊C8C2314yes—
172#6392C2314yes—
173#6392C2314yes—
174#6391C2314yes—
175#6391C2314yes—
176#6382C2314yes—
177#6381C2314yes—
178#6381C2314yes—
179#6381C2314yes—
180C4⋊(C7⋊C8)C2314yes—
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×#468—71no—
192C2×#465—71no—
193C2×#440D711yescharacteristic, complemented
194C2×#435—71no—
195C2×#428—71no—
196C22×#107—71no—
197C24×C7—21no—
198C23×D7C2×D411yescharacteristic
199C23×D7C2×D411yescharacteristic
200C2×C7×Q8—21no—
201C2×C7×Q8—22no—
202C2×C7×Q8—22no—
203C2×C7×Q8C2412yes—
204C2×C7×D4—21no—
205C2×C7×D4—22no—
206C2×C7×D4—22no—
207C2×C7×D4C2412yes—
208C22×C4×C7—21no—
209C22×C4×C7—21no—
210C22×C4×C7—21no—
211C22×C4×C7—24no—
212C22×C4×C7—44no—
213C22×C4×C7C2×D411yescharacteristic
214C22×C4×C7C2×D411yescharacteristic
215C22×C4×C7C2411yescharacteristic
216C2×C22⋊D7—24no—
217C2×C22⋊D7—24no—
218C2×C22⋊D7—44no—
219C2×C22⋊D7—44no—
220C22×Dic7—21no—
221C22×Dic7—21no—
222C22×Dic7—21no—
223C22×Dic7—21no—
224C22×Dic7C2×D411yescharacteristic
225C22×Dic7C2×D411yescharacteristic
226#1157—432no—
227C2×D28—24no—
228C2×D28C2×D414yes—
229C2×C4×D7—22no—
230C2×C4×D7—22no—
231C2×C4×D7—22no—
232C2×C4×D7—22no—
233C2×C4×D7—24no—
234C2×C4×D7—24no—
235C2×C4×D7—24no—
236C2×C4×D7—44no—
237C2×C4×D7—44no—
238C2×C4×D7—44no—
239C2×C4×D7C2×D412yes—
240C2×C4×D7C2×D412yes—
241C2×C4×D7C2412yes—
242C2×C4×D7C2412yes—
243C2×Dic14—24no—
244C2×Dic14—44no—
245C7×SD16—28no—
246C2×C7×C8—22no—
247C2×C7×C8#4114yescomplemented
248C2×C7×C8C2412yes—
249C2×C7×C8C2412yes—
250C7×C4⋊C4—24no—
251C7×C4⋊C4—21no—
252C7×C4⋊C4—21no—
253C7×C4⋊C4C2412yes—
254C7×C4⋊C4C2412yes—
255C7×C22⋊C4—24no—
256C42×C7—24no—
257C42×C7C2×D412yes—
258C42×C7C2412yes—
259C22⋊Dic7—24no—
260C22⋊Dic7—24no—
261(C2×D7)⋊C4—24no—
262(C2×D7)⋊C4—24no—
263(C2×D7)⋊C4—24no—
264(C2×D7)⋊C4C2×D414yes—
265(C2×D7)⋊C4C2×D414yes—
266C4⋊Dic7—21no—
267C4⋊Dic7—21no—
268C4⋊Dic7—24no—
269C4⋊Dic7—21no—
270C4⋊Dic7—21no—
271C4⋊Dic7C2×D414yes—
272C4⋊Dic7C2412yes—
273C4⋊Dic7C2412yes—
274C4⋊Dic7C2412yes—
275C4⋊Dic7C2412yes—
276Dic7⋊C4—24no—
277Dic7⋊C4—24no—
278Dic7⋊C4—24no—
279Dic7⋊C4—24no—
280Dic7⋊C4—24no—
281Dic7⋊C4—24no—
282Dic7⋊C4—24no—
283C4×Dic7—24no—
284C2×C7⋊C8—22no—
285C2×C7⋊C8—22no—
286C2×C7⋊C8C2412yes—
287C2×C7⋊C8C2412yes—
288#1131—28no—
289C8×D7—28no—
290C22×#41—141no—
291C22×SD16C2×D711yescharacteristic
292C22×M16—71no—
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—71no—
307C2×C22⋊Q8—141no—
308C2×#121—71no—
309C2×#121—71no—
310C2×C4×Q8C2×D711yescharacteristic
311C2×C4×D4—71no—
312C2×C4×D4C2×D711yescharacteristic
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#468—78no—
326#465—78no—
327#440C2×D718yescomplemented
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×#97C2×D711yescharacteristic
350C23×C7—22no—
351C23×C7—42no—
352C23×C7—42no—
353C23×C7—42no—
354C23×C7C22×D411yescharacteristic
355C22×D7—22no—
356C22×D7—22no—
357C22×D7—22no—
358C22×D7—22no—
359C22×D7—22no—
360C22×D7AGL(1,ℤ/8)14yes—
361C22×D7C22×D412yes—
362C22×D7C22×D412yes—
363C7×Q8—22no—
364C7×Q8—22no—
365C7×Q8—42no—
366C7×D4—22no—
367C7×D4—22no—
368C7×D4—42no—
369C2×C4×C7—22no—
370C2×C4×C7—22no—
371C2×C4×C7—22no—
372C2×C4×C7—22no—
373C2×C4×C7—22no—
374C2×C4×C7—48no—
375C2×C4×C7—42no—
376C2×C4×C7—42no—
377C2×C4×C7—42no—
378C2×C4×C7C22×D412yes—
379C2×C4×C7C22×D412yes—
380C2×C4×C7C22×D411yescharacteristic
381C2×C4×C7C2×#4112yes—
382C2×C4×C72−1+412yes—
383C2×C4×C7C2511yescharacteristic
384C22⋊D7—48no—
385C22⋊D7—48no—
386C2×Dic7—22no—
387C2×Dic7—22no—
388C2×Dic7—22no—
389C2×Dic7—22no—
390C2×Dic7—22no—
391C2×Dic7—22no—
392C2×Dic7—42no—
393C2×Dic7—42no—
394C2×Dic7—42no—
395C2×Dic7—42no—
396C2×Dic7C22×D412yes—
397C2×Dic7C22×D412yes—
398D28—28no—
399C4×D7—24no—
400C4×D7—24no—
401C4×D7—22no—
402C4×D7—22no—
403C4×D7—22no—
404C4×D7—22no—
405C4×D7—48no—
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—71no—
418C22×D4—141no—
419C22×D4—141no—
420C22×D4C22×D711yescharacteristic
421C23×C4—21no—
422C23×C4—71no—
423C23×C4—71no—
424C23×C4—141no—
425C23×C4—141no—
426C23×C4—141no—
427C2×SD16—24no—
428C2×SD16C22×D714yes—
429C2×M16—74no—
430C2×M16—144no—
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—148no—
442#125—142no—
443#123—148no—
444#123—148no—
445#123—148no—
446C22⋊Q8—74no—
447C22⋊Q8—74no—
448C22⋊Q8—148no—
449C22⋊Q8—142no—
450C22⋊Q8—142no—
451#121—74no—
452#121—74no—
453#121—142no—
454#121—142no—
455C4×Q8—22no—
456C4×Q8C22×D714yes—
457C4×D4—22no—
458C4×D4—74no—
459C4×D4—74no—
460C4×D4C22×D714yes—
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—71no—
470C2×C4⋊C4—74no—
471C2×C4⋊C4—74no—
472C2×C4⋊C4—74no—
473C2×C4⋊C4—142no—
474C2×C4⋊C4—142no—
475C2×C4⋊C4—142no—
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—141no—
484C2×C4⋊C4C22×D711yescharacteristic
485C2×C4⋊C4C22×D711yescharacteristic
486C2×C22⋊C4—21no—
487C2×C22⋊C4—71no—
488C2×C22⋊C4—71no—
489C2×C22⋊C4—141no—
490C2×C22⋊C4—141no—
491C2×C22⋊C4—141no—
492C2×C22⋊C4—141no—
493C2×C22⋊C4—141no—
494C2×C42—21no—
495C2×C42—141no—
496C2×C42C22×D711yescharacteristic
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#97C22×D714yes—
516C22×C7—42no—
517C22×C7—42no—
518C22×C7—42no—
519C22×C7—84no—
520C22×C7#54712yes—
521C22×C7C2×AGL(1,ℤ/8)12yes—
522C22×C7#57812yes—
523C22×C7C23×D411yescharacteristic
524C2×D7—28no—
525C2×D7—22no—
526C2×D7—22no—
527C2×D7—22no—
528C2×D7—22no—
529C2×D7—22no—
530C2×D7—44no—
531C2×D7C2×AGL(1,ℤ/8)14yes—
532C4×C7—22no—
533C4×C7—22no—
534C4×C7—42no—
535C4×C7—42no—
536C4×C7—42no—
537C4×C7#54712yes—
538C4×C7C22×#4111yescharacteristic
539C4×C7C2×2−1+411yescharacteristic
540Dic7—22no—
541Dic7—22no—
542Dic7—42no—
543Dic7—42no—
544Dic7—42no—
545Dic7—42no—
546C24—21no—
547C24—71no—
548C24—71no—
549#41—2832no—
550C2×Q8—21no—
551C2×Q8—22no—
552C2×Q8—22no—
553C2×Q8—144no—
554C2×Q8—284no—
555C2×Q8C23×D712yes—
556C2×D4—22no—
557C2×D4—21no—
558C2×D4—22no—
559C2×D4—74no—
560C2×D4—144no—
561C2×D4—144no—
562C2×D4—144no—
563C2×D4—284no—
564C2×D4—284no—
565C2×D4C23×D712yes—
566C22×C4—21no—
567C22×C4—21no—
568C22×C4—21no—
569C22×C4—24no—
570C22×C4—44no—
571C22×C4—71no—
572C22×C4—71no—
573C22×C4—72no—
574C22×C4—72no—
575C22×C4—72no—
576C22×C4—72no—
577C22×C4—144no—
578C22×C4—144no—
579C22×C4—144no—
580C22×C4—142no—
581C22×C4—142no—
582C22×C4—142no—
583C22×C4—142no—
584C22×C4—141no—
585C22×C4—141no—
586C22×C4—141no—
587C22×C4—141no—
588C22×C4—284no—
589C22×C4—284no—
590C22×C4—284no—
591C22×C4D4×D711yescharacteristic
592C22×C4D4×D711yescharacteristic
593C22×C4C23×D711yescharacteristic
594SD16—28no—
595M16—148no—
596C2×C8—22no—
597C2×C8—72no—
598C2×C8—72no—
599C2×C8—142no—
600C2×C8—142no—
601C2×C8—148no—
602C2×C8#115714yescomplemented
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—141no—
624C4⋊C4—144no—
625C4⋊C4C23×D712yes—
626C4⋊C4C23×D712yes—
627C22⋊C4—24no—
628C22⋊C4—74no—
629C22⋊C4—74no—
630C22⋊C4—144no—
631C22⋊C4—144no—
632C22⋊C4—144no—
633C22⋊C4—144no—
634C22⋊C4—144no—
635C42—24no—
636C42—144no—
637C42D4×D712yes—
638C42C23×D712yes—
639C2×C7—82no—
640C2×C7#334314yescomplemented
641C2×C7C2×#54711yescharacteristic
642C2×C7C22×AGL(1,ℤ/8)11yescharacteristic
643C2×C7C2×#57811yescharacteristic
644D7—24no—
645D7—42no—
646C23—22no—
647C23—42no—
648C23—42no—
649C23—42no—
650C23—74no—
651C23—72no—
652C23—72no—
653C23—142no—
654C23—142no—
655C23—142no—
656C23—142no—
657C23—142no—
658C23C2×D4×D711yescharacteristic
659Q8—22no—
660Q8—22no—
661Q8—42no—
662Q8—288no—
663D4—22no—
664D4—22no—
665D4—42no—
666D4—148no—
667D4—288no—
668D4—288no—
669C2×C4—22no—
670C2×C4—22no—
671C2×C4—22no—
672C2×C4—22no—
673C2×C4—22no—
674C2×C4—48no—
675C2×C4—42no—
676C2×C4—42no—
677C2×C4—42no—
678C2×C4—72no—
679C2×C4—72no—
680C2×C4—142no—
681C2×C4—142no—
682C2×C4—144no—
683C2×C4—144no—
684C2×C4—142no—
685C2×C4—142no—
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—282no—
696C2×C4—282no—
697C2×C4—282no—
698C2×C4—282no—
699C2×C4C2×#115712yes—
700C2×C4C2×D4×D712yes—
701C2×C4C2×D4×D712yes—
702C2×C4C2×D4×D711yescharacteristic
703C2×C4#655412yes—
704C2×C4C24×D711yescharacteristic
705C8—22no—
706C8—142no—
707C8—142no—
708C8C2×#115714yescomplemented
709C7C2×#334311yescharacteristic, complemented, Sylow
710C22—42no—
711C22—42no—
712C22—42no—
713C22—74no—
714C22—84no—
715C22—142no—
716C22—142no—
717C22—148no—
718C22—142no—
719C22—142no—
720C22—142no—
721C22—284no—
722C22#9024212yes—
723C22D7×AGL(1,ℤ/8)12yes—
724C22#9047012yes—
725C22C22×D4×D711yescharacteristic
726C4—22no—
727C4—22no—
728C4—42no—
729C4—42no—
730C4—42no—
731C4—142no—
732C4—142no—
733C4—282no—
734C4—282no—
735C4—282no—
736C4—282no—
737C4#9024212yes—
738C4C22×#115711yescharacteristic
739C4C2×#655411yescharacteristic
740C2—82no—
741C2—144no—
742C2—282no—
743C2#1173725114yesdirect product factor
744C2C2×#9024211yescharacteristic
745C2C2×D7×AGL(1,ℤ/8)11yescharacteristic
746C2C2×#9047011yescharacteristic
subgroupG/H
centerC23C2×D4×D7
commutator, cosocleC2×C4×C7C25
FrattiniC2×C4C24×D7
FittingC2×C7×#440C2
socleC23×C7C22×D4
prime radicalC2×#90242C2
hypercenterC2×#440D7
hypocenterC7C2×#3343
LCSG ▷ C2×C4×C7 ▷ C2×C7 ▷ C7
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#440

Complements

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

NH ≅ G/Ntype
1. C2×#90272C2semidirect
3. C2×C7×#440C2semidirect
4. C2×#89946C2semidirect
5. C2×#89943C2semidirect
6. C2×#89793C2semidirect
7. C2×#89781C2semidirect
8. #11737251C2direct (N × H)
9. C2×#89653C2semidirect
10. C2×D7×#107C2semidirect
11. C2×#89581C2semidirect
12. C2×#89577C2semidirect
13. C2×#89546C2semidirect
14. C2×#89551C2semidirect
15. C2×#89478C2semidirect
16. C2×#89474C2semidirect
29. #90272C22semidirect
45. C7×#440C22semidirect
54. #89946C22semidirect
55. #89943C22semidirect
62. #89793C22semidirect
63. #89781C22semidirect
69. #89653C22semidirect
70. D7×#107C22semidirect
71. #89581C22semidirect
72. #89577C22semidirect
73. #89551C22semidirect
74. #89546C22semidirect
75. #89478C22semidirect
76. #89474C22semidirect
193. C2×#440D7semidirect
247. C2×C7×C8#41semidirect
327. #440C2×D7semidirect
410. C7×C8C2×#41semidirect
602. C2×C8#1157semidirect
640. C2×C7#3343semidirect
708. C8C2×#1157semidirect
709. C7C2×#3343semidirect
743. C2#11737251direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#902722
C2×#902422
C2×C7×#4402
C2×#899462
C2×#899432
C2×#897932
C2×#897812
#117372512
C2×#896532
C2×D7×#1072
C2×#895812
C2×#895772
C2×#895462
C2×#895512
C2×#894782
C2×#894742
C2×#33437