Finite Group Databasebeta

← C2×#11736679 #14232496

Subgroups — C2×#11736679 #14232496

Order 1792.

2082 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×#90224C211yesmaximal, characteristic, complemented
2C2×#90198C211yesmaximal, characteristic
3C2×C7×#428C211yesmaximal, characteristic, complemented
4C2×#89906C211yesmaximal, characteristic, complemented
5C2×#89900C211yesmaximal, characteristic, complemented
6C2×#89775C211yesmaximal, characteristic, complemented
7C2×#89742C211yesmaximal, characteristic, complemented
8#11736679C2116yesmaximal, direct product factor
9C2×#89662C211yesmaximal, characteristic, complemented
10C2×#89656C211yesmaximal, characteristic, complemented
11C2×#89658C211yesmaximal, characteristic, complemented
12C2×#89646C211yesmaximal, characteristic, complemented
13C2×#89626C211yesmaximal, characteristic, complemented
14C2×#89638C211yesmaximal, characteristic, complemented
15C2×#89633C211yesmaximal, characteristic, complemented
16C2×#89624C211yesmaximal, characteristic, complemented
17C22×#1157—21no—
18C22×C7×M16C2211yescharacteristic
19C2×C7×#117C2211yescharacteristic
20C22×C7×C4⋊C4C2211yescharacteristic
21C2×#6493C2211yescharacteristic
22C2×#6492—21no—
23C2×C4×C22⋊D7C2211yescharacteristic
24C2×#6487C2211yescharacteristic
25C22×#1132C2211yescharacteristic
26C22×#1131C2211yescharacteristic
27#90224—24no—
28#90224C2218yescomplemented
29C2×#6460C2211yescharacteristic
30C2×#6459—21no—
31#90198—24no—
32#90198C2218yes—
33C2×#6458C2211yescharacteristic
34C2×#6457—21no—
35C2×#6456C2211yescharacteristic
36C2×#6455C2211yescharacteristic
37C2×D7×C4⋊C4C2211yescharacteristic
38C2×#6451C2211yescharacteristic
39C2×#6451C2211yescharacteristic
40C2×#6450C2211yescharacteristic
41C2×#6448—21no—
42C2×#6442—21no—
43C2×#6439—21no—
44C2×C4×Dic14—21no—
45C7×#428C2218yescomplemented
46C2×C7×#107C2211yescharacteristic
47C2×C7×#107C2211yescharacteristic
48C2×C7×#106C2211yescharacteristic
49C2×C7×#106C2211yescharacteristic
50C2×C22⋊(C7⋊C8)C2211yescharacteristic
51#89906C2218yescomplemented
52#89900C2218yescomplemented
53C2×#6395C2211yescharacteristic
54C2×(C2×D7)⋊C8C2211yescharacteristic
55C2×#6392C2211yescharacteristic
56C2×#6390C2211yescharacteristic
57C2×Dic7⋊C8C2211yescharacteristic
58C2×C8×Dic7C2211yescharacteristic
59#89775C2218yescomplemented
60#89742C2218yescomplemented
61C2×#6384C2211yescharacteristic
62C2×#6384C2211yescharacteristic
63C2×#6383C2211yescharacteristic
64C2×#6383C2211yescharacteristic
65C2×#6382C2211yescharacteristic
66C2×#6381C2211yescharacteristic
67C2×#6381C2211yescharacteristic
68C2×#6381C2211yescharacteristic
69#89662C2218yescomplemented
70#89658C2218yescomplemented
71#89656C2218yescomplemented
72#89646C2218yescomplemented
73#89638C2218yescomplemented
74#89633C2218yescomplemented
75#89626C2218yescomplemented
76#89624C2218yescomplemented
77C2×#3353—71nomaximal, Sylow
78C23×C4×C7—21no—
79C23×C4×C7C2311yescharacteristic
80C22×C22⋊D7—21no—
81C22×C22⋊D7D411yescharacteristic
82C2×#1157—28no—
83C2×#1157—48no—
84C22×D28—21no—
85C22×D28C2311yescharacteristic
86C22×C4×D7—21no—
87C22×C4×D7—21no—
88C22×C4×D7C2311yescharacteristic
89C22×Dic14—21no—
90C22×Dic14—21no—
91C22×Dic14C2311yescharacteristic
92C2×C7×M16—24no—
93C2×C7×M16C2314yes—
94C22×C7×C8C2311yescharacteristic
95C22×C7×C8C2311yescharacteristic
96C7×#117—22no—
97C7×#117C2314yes—
98C2×C7×C4⋊C4—21no—
99C2×C7×C4⋊C4—22no—
100C2×C7×C4⋊C4C2311yescharacteristic
101C2×C7×C4⋊C4C2311yescharacteristic
102C2×C7×C4⋊C4C2311yescharacteristic
103C2×C7×C4⋊C4C2311yescharacteristic
104C2×C7×C4⋊C4C2314yes—
105C2×C7×C22⋊C4—21no—
106C2×C42×C7—21no—
107C2×C22⋊Dic7—21no—
108C2×C22⋊Dic7D411yescharacteristic
109#6493—22no—
110#6493C2314yes—
111#6492—28no—
112C4×C22⋊D7D414yes—
113C4×C22⋊D7C2314yes—
114C2×(C2×D7)⋊C4—21no—
115C2×(C2×D7)⋊C4—21no—
116C2×(C2×D7)⋊C4—21no—
117C2×(C2×D7)⋊C4—21no—
118C2×(C2×D7)⋊C4—21no—
119C2×(C2×D7)⋊C4D411yescharacteristic
120C2×C4⋊Dic7—21no—
121C2×C4⋊Dic7C2311yescharacteristic
122C2×C4⋊Dic7C2311yescharacteristic
123#6487—22no—
124#6487C2314yes—
125C2×Dic7⋊C4—21no—
126C2×Dic7⋊C4—21no—
127C2×Dic7⋊C4—21no—
128C2×Dic7⋊C4—21no—
129C2×Dic7⋊C4—21no—
130C2×Dic7⋊C4D411yescharacteristic
131C2×C4×Dic7—21no—
132C2×C4×Dic7—21no—
133C2×C4×Dic7C2311yescharacteristic
134C22×C7⋊C8C2311yescharacteristic
135C22×C7⋊C8C2311yescharacteristic
136C2×#1132—24no—
137C2×#1132C2314yes—
138C2×#1131—24no—
139C2×#1131C2314yes—
140#6460—22no—
141#6460C2314yes—
142#6459—28no—
143#6458—22no—
144#6458C2314yes—
145#6457—28no—
146#6456—22no—
147#6456C2314yes—
148#6455—22no—
149#6455C2314yes—
150D7×C4⋊C4—22no—
151D7×C4⋊C4C2314yes—
152#6451—22no—
153#6451—22no—
154#6451C2314yes—
155#6451C2314yes—
156#6450—22no—
157#6450C2314yes—
158#6448—28no—
159#6442—28no—
160#6439—28no—
161C4×Dic14—28no—
162C7×#107C2314yes—
163C7×#107C2314yes—
164C7×#106C2314yes—
165C7×#106C2314yes—
166C22⋊(C7⋊C8)C2314yes—
167#6395C2314yes—
168(C2×D7)⋊C8C2314yes—
169#6392C2314yes—
170#6390C2314yes—
171Dic7⋊C8C2314yes—
172C8×Dic7C2314yes—
173#6384C2314yes—
174#6384C2314yes—
175#6383C2314yes—
176#6383C2314yes—
177#6382C2314yes—
178#6381C2314yes—
179#6381C2314yes—
180#6381C2314yes—
181C2×#556—71no—
182C2×#547—71no—
183#3353—716no—
184C2×#500—71no—
185C2×#484—71no—
186C2×#484—71no—
187C2×#482—71no—
188C2×#482—71no—
189C2×#475—71no—
190C2×#474—71no—
191C2×#468—71no—
192C2×#468—71no—
193C2×C4×SD16—71no—
194C2×#436—71no—
195C2×#428—71no—
196C2×#428D711yescharacteristic, complemented
197C24×C7C2×D411yescharacteristic
198C23×D7—21no—
199C23×D7C2×D411yescharacteristic
200C22×C4×C7—22no—
201C22×C4×C7—22no—
202C22×C4×C7—21no—
203C22×C4×C7—21no—
204C22×C4×C7—21no—
205C22×C4×C7—21no—
206C22×C4×C7—24no—
207C22×C4×C7—44no—
208C22×C4×C7C2×D411yescharacteristic
209C22×C4×C7C2×D412yes—
210C22×C4×C7C2412yes—
211C22×C4×C7C2411yescharacteristic
212C2×C22⋊D7—24no—
213C2×C22⋊D7—24no—
214C2×C22⋊D7—44no—
215C2×C22⋊D7C2×D414yes—
216C22×Dic7—21no—
217C22×Dic7—21no—
218C22×Dic7—21no—
219C22×Dic7C2×D411yescharacteristic
220C22×Dic7C2×D411yescharacteristic
221C22×Dic7C2×D411yescharacteristic
222#1157—432no—
223C2×D28—22no—
224C2×D28—22no—
225C2×D28—24no—
226C2×D28—21no—
227C2×D28—44no—
228C2×D28C2412yes—
229C2×C4×D7—22no—
230C2×C4×D7—22no—
231C2×C4×D7—24no—
232C2×C4×D7—24no—
233C2×C4×D7—44no—
234C2×C4×D7—44no—
235C2×C4×D7C2×D412yes—
236C2×C4×D7C2412yes—
237C2×Dic14—22no—
238C2×Dic14—22no—
239C2×Dic14—21no—
240C2×Dic14—24no—
241C2×Dic14—24no—
242C2×Dic14—44no—
243C2×Dic14—44no—
244C2×Dic14C2412yes—
245C7×M16—28no—
246C2×C7×C8—22no—
247C2×C7×C8#4114yescomplemented
248C2×C7×C8C2412yes—
249C2×C7×C8C2412yes—
250C7×C4⋊C4—21no—
251C7×C4⋊C4—21no—
252C7×C4⋊C4—21no—
253C7×C4⋊C4—21no—
254C7×C4⋊C4—24no—
255C7×C4⋊C4C2412yes—
256C7×C4⋊C4C2412yes—
257C7×C4⋊C4C2412yes—
258C7×C4⋊C4C2412yes—
259C7×C22⋊C4—24no—
260C42×C7—24no—
261C22⋊Dic7—24no—
262C22⋊Dic7C2×D414yes—
263(C2×D7)⋊C4—24no—
264(C2×D7)⋊C4—24no—
265(C2×D7)⋊C4—24no—
266(C2×D7)⋊C4—24no—
267(C2×D7)⋊C4—24no—
268(C2×D7)⋊C4C2×D414yes—
269C4⋊Dic7—21no—
270C4⋊Dic7—21no—
271C4⋊Dic7—24no—
272C4⋊Dic7C2412yes—
273C4⋊Dic7C2412yes—
274Dic7⋊C4—24no—
275Dic7⋊C4—24no—
276Dic7⋊C4—24no—
277Dic7⋊C4—24no—
278Dic7⋊C4—24no—
279Dic7⋊C4C2×D414yes—
280C4×Dic7—24no—
281C4×Dic7—24no—
282C4×Dic7C2×D412yes—
283C4×Dic7C2412yes—
284C2×C7⋊C8—22no—
285C2×C7⋊C8—22no—
286C2×C7⋊C8C2412yes—
287C2×C7⋊C8C2412yes—
288#1132—28no—
289#1131—28no—
290C22×#41—141no—
291C22×SD16—71no—
292C22×M16—71no—
293C22×M16C2×D711yescharacteristic
294#556—78no—
295#556—144no—
296#547—78no—
297#547—144no—
298C2×C4⋊Q8—71no—
299C2×C4⋊Q8—71no—
300C2×#126—141no—
301C2×#126—141no—
302C2×#124—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×Q8—71no—
311C2×C4×Q8—141no—
312C2×C4×D4—71no—
313C2×C4×D4—71no—
314C2×#117—71no—
315C2×#117C2×D711yescharacteristic
316C22×C4⋊C4—71no—
317C22×C4⋊C4C2×D711yescharacteristic
318#500—78no—
319#484—78no—
320#484—78no—
321#482—78no—
322#482—78no—
323#475—78no—
324#474—78no—
325#468—78no—
326#468—78no—
327C4×SD16—78no—
328#436—78no—
329#428—78no—
330#428C2×D718yescomplemented
331C2×#107—71no—
332C2×#107—71no—
333C2×#107—71no—
334C2×#107—71no—
335C2×#107C2×D711yescharacteristic
336C2×#107C2×D711yescharacteristic
337C2×#106—71no—
338C2×#106C2×D711yescharacteristic
339C2×#106C2×D711yescharacteristic
340C2×C4⋊C8—71no—
341C2×#103—71no—
342C2×#103—71no—
343C2×#103—71no—
344C2×#102—71no—
345C2×#102—71no—
346C2×#102—71no—
347C2×C22⋊C8—71no—
348C2×C22⋊C8—71no—
349C2×C4×C8—71no—
350C23×C7—22no—
351C23×C7—22no—
352C23×C7—22no—
353C23×C7C22×D412yes—
354C23×C7C22×D411yescharacteristic
355C22×D7—22no—
356C22×D7—22no—
357C22×D7—22no—
358C22×D7—22no—
359C22×D7—42no—
360C22×D7—42no—
361C22×D7—42no—
362C22×D7C22×D412yes—
363C2×C4×C7—22no—
364C2×C4×C7—24no—
365C2×C4×C7—22no—
366C2×C4×C7—22no—
367C2×C4×C7—22no—
368C2×C4×C7—22no—
369C2×C4×C7—22no—
370C2×C4×C7—22no—
371C2×C4×C7—48no—
372C2×C4×C7—42no—
373C2×C4×C7—42no—
374C2×C4×C7—42no—
375C2×C4×C7—42no—
376C2×C4×C7C22×D412yes—
377C2×C4×C7C22×D411yescharacteristic
378C2×C4×C7C2×#4112yes—
379C2×C4×C72−1+412yes—
380C2×C4×C7C2511yescharacteristic
381C22⋊D7—28no—
382C22⋊D7—48no—
383C2×Dic7—22no—
384C2×Dic7—22no—
385C2×Dic7—22no—
386C2×Dic7—22no—
387C2×Dic7—22no—
388C2×Dic7—42no—
389C2×Dic7—42no—
390C2×Dic7—42no—
391C2×Dic7AGL(1,ℤ/8)14yes—
392C2×Dic7C22×D412yes—
393C2×Dic7C22×D412yes—
394C2×Dic7C22×D412yes—
395D28—22no—
396D28—22no—
397D28—48no—
398D28—42no—
399C4×D7—24no—
400C4×D7—22no—
401C4×D7—22no—
402C4×D7—48no—
403C4×D7—48no—
404Dic14—22no—
405Dic14—22no—
406Dic14—42no—
407Dic14—48no—
408Dic14—48no—
409C7×C8—22no—
410C7×C8C2×#4114yescomplemented
411C7⋊C8—22no—
412C7⋊C8—22no—
413C2×#41—148no—
414C2×#41—288no—
415C22×Q8—71no—
416C22×Q8—141no—
417C22×Q8—141no—
418C22×D4—71no—
419C22×D4—71no—
420C22×D4—141no—
421C22×D4—141no—
422C23×C4—21no—
423C23×C4—71no—
424C23×C4—141no—
425C23×C4—141no—
426C23×C4C22×D711yescharacteristic
427C2×SD16—74no—
428C2×SD16—144no—
429C2×M16—24no—
430C2×M16—74no—
431C2×M16—144no—
432C2×M16C22×D714yes—
433C22×C8—71no—
434C22×C8—71no—
435C22×C8C22×D711yescharacteristic
436C22×C8C22×D711yescharacteristic
437C4⋊Q8—74no—
438C4⋊Q8—74no—
439C4⋊Q8—142no—
440C4⋊Q8—142no—
441#126—148no—
442#126—148no—
443#124—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—74no—
456C4×Q8—148no—
457C4×Q8—142no—
458C4×D4—74no—
459C4×D4—74no—
460C4×D4—74no—
461C4×D4—142no—
462#117—22no—
463#117—74no—
464#117—142no—
465#117C22×D714yes—
466C2×C4⋊C4—21no—
467C2×C4⋊C4—22no—
468C2×C4⋊C4—71no—
469C2×C4⋊C4—71no—
470C2×C4⋊C4—71no—
471C2×C4⋊C4—74no—
472C2×C4⋊C4—142no—
473C2×C4⋊C4—141no—
474C2×C4⋊C4—141no—
475C2×C4⋊C4—141no—
476C2×C4⋊C4—141no—
477C2×C4⋊C4—141no—
478C2×C4⋊C4—141no—
479C2×C4⋊C4C22×D711yescharacteristic
480C2×C4⋊C4C22×D711yescharacteristic
481C2×C4⋊C4C22×D714yes—
482C2×C4⋊C4C22×D711yescharacteristic
483C2×C4⋊C4C22×D711yescharacteristic
484C2×C22⋊C4—21no—
485C2×C22⋊C4—71no—
486C2×C22⋊C4—71no—
487C2×C22⋊C4—141no—
488C2×C22⋊C4—141no—
489C2×C22⋊C4—141no—
490C2×C22⋊C4—141no—
491C2×C22⋊C4—141no—
492C2×C22⋊C4—141no—
493C2×C42—21no—
494C2×C42—71no—
495C2×C42—141no—
496C2×C42—141no—
497#107—74no—
498#107—74no—
499#107—74no—
500#107—74no—
501#107C22×D714yes—
502#107C22×D714yes—
503#106—74no—
504#106C22×D714yes—
505#106C22×D714yes—
506C4⋊C8—74no—
507#103—74no—
508#103—74no—
509#103—74no—
510#102—74no—
511#102—74no—
512#102—74no—
513C22⋊C8—74no—
514C22⋊C8—74no—
515C4×C8—74no—
516C22×C7—22no—
517C22×C7—22no—
518C22×C7—22no—
519C22×C7—44no—
520C22×C7#54712yes—
521C22×C7C2×AGL(1,ℤ/8)12yes—
522C22×C7#57812yes—
523C22×C7C23×D411yescharacteristic
524C2×D7—22no—
525C2×D7—22no—
526C2×D7—22no—
527C2×D7—44no—
528C2×D7—42no—
529C2×D7—42no—
530C2×D7—42no—
531C2×D7—84no—
532C4×C7—22no—
533C4×C7—42no—
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—
545Dic7C2×AGL(1,ℤ/8)14yes—
546C24—71no—
547C24—141no—
548C24D4×D711yescharacteristic
549#41—2832no—
550C2×Q8—72no—
551C2×Q8—144no—
552C2×Q8—144no—
553C2×Q8—141no—
554C2×Q8—142no—
555C2×Q8—142no—
556C2×Q8—284no—
557C2×Q8—284no—
558C2×D4—74no—
559C2×D4—72no—
560C2×D4—144no—
561C2×D4—144no—
562C2×D4—144no—
563C2×D4—142no—
564C2×D4—141no—
565C2×D4—142no—
566C2×D4—284no—
567C2×D4—284no—
568C22×C4—22no—
569C22×C4—22no—
570C22×C4—24no—
571C22×C4—21no—
572C22×C4—21no—
573C22×C4—21no—
574C22×C4—21no—
575C22×C4—44no—
576C22×C4—71no—
577C22×C4—71no—
578C22×C4—71no—
579C22×C4—72no—
580C22×C4—72no—
581C22×C4—144no—
582C22×C4—144no—
583C22×C4—142no—
584C22×C4—142no—
585C22×C4—141no—
586C22×C4—141no—
587C22×C4—141no—
588C22×C4—284no—
589C22×C4—284no—
590C22×C4D4×D712yes—
591C22×C4D4×D711yescharacteristic
592C22×C4C23×D712yes—
593C22×C4C23×D711yescharacteristic
594SD16—148no—
595M16—28no—
596M16—148no—
597C2×C8—22no—
598C2×C8—72no—
599C2×C8—72no—
600C2×C8—142no—
601C2×C8—142no—
602C2×C8#115714yescomplemented
603C2×C8C23×D712yes—
604C2×C8C23×D712yes—
605C4⋊C4—21no—
606C4⋊C4—21no—
607C4⋊C4—24no—
608C4⋊C4—21no—
609C4⋊C4—21no—
610C4⋊C4—74no—
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—141no—
620C4⋊C4—141no—
621C4⋊C4C23×D712yes—
622C4⋊C4C23×D712yes—
623C4⋊C4C23×D712yes—
624C4⋊C4C23×D712yes—
625C22⋊C4—24no—
626C22⋊C4—74no—
627C22⋊C4—74no—
628C22⋊C4—144no—
629C22⋊C4—144no—
630C22⋊C4—144no—
631C22⋊C4—144no—
632C22⋊C4—144no—
633C22⋊C4—144no—
634C42—24no—
635C42—72no—
636C42—72no—
637C42—144no—
638C42—144no—
639C2×C7—42no—
640C2×C7#335314yescomplemented
641C2×C7C2×#54711yescharacteristic
642C2×C7C22×AGL(1,ℤ/8)11yescharacteristic
643C2×C7C2×#57811yescharacteristic
644D7—42no—
645D7—82no—
646C23—22no—
647C23—22no—
648C23—22no—
649C23—72no—
650C23—142no—
651C23—142no—
652C23—142no—
653C23—142no—
654C23—282no—
655C23—282no—
656C23—282no—
657C23C2×D4×D712yes—
658C23C2×D4×D711yescharacteristic
659Q8—142no—
660Q8—142no—
661Q8—288no—
662Q8—288no—
663Q8—282no—
664D4—148no—
665D4—142no—
666D4—142no—
667D4—288no—
668D4—288no—
669D4—282no—
670C2×C4—22no—
671C2×C4—24no—
672C2×C4—22no—
673C2×C4—22no—
674C2×C4—22no—
675C2×C4—22no—
676C2×C4—22no—
677C2×C4—22no—
678C2×C4—48no—
679C2×C4—42no—
680C2×C4—42no—
681C2×C4—42no—
682C2×C4—42no—
683C2×C4—74no—
684C2×C4—72no—
685C2×C4—72no—
686C2×C4—72no—
687C2×C4—142no—
688C2×C4—142no—
689C2×C4—144no—
690C2×C4—142no—
691C2×C4—142no—
692C2×C4—142no—
693C2×C4—142no—
694C2×C4—142no—
695C2×C4—288no—
696C2×C4—288no—
697C2×C4—282no—
698C2×C4—282no—
699C2×C4—282no—
700C2×C4C2×#115712yes—
701C2×C4C2×D4×D712yes—
702C2×C4C2×D4×D711yescharacteristic
703C2×C4#655112yes—
704C2×C4C24×D711yescharacteristic
705C8—22no—
706C8—142no—
707C8—142no—
708C8C2×#115714yescomplemented
709C7C2×#335311yescharacteristic, complemented, Sylow
710C22—22no—
711C22—22no—
712C22—22no—
713C22—44no—
714C22—142no—
715C22—142no—
716C22—142no—
717C22—284no—
718C22—282no—
719C22—282no—
720C22—282no—
721C22—564no—
722C22#9019812yes—
723C22D7×AGL(1,ℤ/8)12yes—
724C22#9047012yes—
725C22C22×D4×D711yescharacteristic
726C4—22no—
727C4—42no—
728C4—42no—
729C4—42no—
730C4—42no—
731C4—74no—
732C4—142no—
733C4—142no—
734C4—282no—
735C4—282no—
736C4—282no—
737C4#9019812yes—
738C4C22×#115711yescharacteristic
739C4C2×#655111yescharacteristic
740C2—42no—
741C2—282no—
742C2—562no—
743C2#1173667914yesdirect product factor
744C2C2×#9019811yescharacteristic
745C2C2×D7×AGL(1,ℤ/8)11yescharacteristic
746C2C2×#9047011yescharacteristic
subgroupG/H
centerC23C2×D4×D7
commutator, cosocleC2×C4×C7C25
FrattiniC2×C4C24×D7
FittingC2×C7×#428C2
socleC23×C7C22×D4
prime radicalC2×#90198C2
hypercenterC2×#428D7
hypocenterC7C2×#3353
LCSG ▷ C2×C4×C7 ▷ C2×C7 ▷ C7
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#428

Complements

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

NH ≅ G/Ntype
1. C2×#90224C2semidirect
3. C2×C7×#428C2semidirect
4. C2×#89906C2semidirect
5. C2×#89900C2semidirect
6. C2×#89775C2semidirect
7. C2×#89742C2semidirect
8. #11736679C2direct (N × H)
9. C2×#89662C2semidirect
10. C2×#89656C2semidirect
11. C2×#89658C2semidirect
12. C2×#89646C2semidirect
13. C2×#89626C2semidirect
14. C2×#89638C2semidirect
15. C2×#89633C2semidirect
16. C2×#89624C2semidirect
28. #90224C22semidirect
45. C7×#428C22semidirect
51. #89906C22semidirect
52. #89900C22semidirect
59. #89775C22semidirect
60. #89742C22semidirect
69. #89662C22semidirect
70. #89658C22semidirect
71. #89656C22semidirect
72. #89646C22semidirect
73. #89638C22semidirect
74. #89633C22semidirect
75. #89626C22semidirect
76. #89624C22semidirect
196. C2×#428D7semidirect
247. C2×C7×C8#41semidirect
330. #428C2×D7semidirect
410. C7×C8C2×#41semidirect
602. C2×C8#1157semidirect
640. C2×C7#3353semidirect
708. C8C2×#1157semidirect
709. C7C2×#3353semidirect
743. C2#11736679direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#902242
C2×#901982
C2×C7×#4282
C2×#899062
C2×#899002
C2×#897752
C2×#897422
#117366792
C2×#896622
C2×#896562
C2×#896582
C2×#896462
C2×#896262
C2×#896382
C2×#896332
C2×#896242
C2×#33537