Finite Group Databasebeta

← C2×#11736914 #14232329

Subgroups — C2×#11736914 #14232329

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×#90232C211yesmaximal, characteristic, complemented
2C2×#90246C211yesmaximal, characteristic
3C2×C7×#435C211yesmaximal, characteristic, complemented
4C2×#89906C211yesmaximal, characteristic, complemented
5C2×#89893C211yesmaximal, characteristic, complemented
6C2×#89886C211yesmaximal, characteristic, complemented
7C22×#6392C211yesmaximal, characteristic, complemented
8#11736914C2116yesmaximal, direct product factor
9C2×#89622C211yesmaximal, characteristic, complemented
10C2×#89619C211yesmaximal, characteristic, complemented
11C2×#89494C211yesmaximal, characteristic, complemented
12C2×#89509C211yesmaximal, characteristic, complemented
13C2×#89493C211yesmaximal, characteristic, complemented
14C2×#89508C211yesmaximal, characteristic, complemented
15C2×#89482C211yesmaximal, characteristic, complemented
16C2×#89474C211yesmaximal, characteristic, complemented
17C22×#1159—21no—
18C22×C7×M16C2211yescharacteristic
19C23×C7×C8C2211yescharacteristic
20C2×C4×C7×D4C2211yescharacteristic
21C2×#6498—21no—
22C2×#6493C2211yescharacteristic
23C2×#6493C2211yescharacteristic
24C2×#6489C2211yescharacteristic
25C22×C4⋊Dic7C2211yescharacteristic
26C22×C4⋊Dic7C2211yescharacteristic
27C22×C4⋊Dic7C2211yescharacteristic
28C2×#6487C2211yescharacteristic
29C2×#6487C2211yescharacteristic
30C22×#1132C2211yescharacteristic
31#90246—24no—
32#90246C2218yes—
33#90232—24no—
34#90232C2218yescomplemented
35C2×#6460—21no—
36C2×#6452—21no—
37C2×#6449—21no—
38C2×#6449—21no—
39C2×#6442—21no—
40C2×#6440—21no—
41C2×C4×D28C2211yescharacteristic
42C2×#6433C2211yescharacteristic
43C2×#6432C2211yescharacteristic
44C2×C4×Dic14C2211yescharacteristic
45C7×#435C2218yescomplemented
46C2×C7×C4⋊C8C2211yescharacteristic
47C2×C7×C22⋊C8C2211yescharacteristic
48C2×C7×C22⋊C8C2211yescharacteristic
49C2×C7×#97C2211yescharacteristic
50#89906C2218yescomplemented
51#89893C2218yescomplemented
52#89886C2218yescomplemented
53C2×#6395C2211yescharacteristic
54C2×#6395C2211yescharacteristic
55C2×#6395C2211yescharacteristic
56C2×#6392C2211yescharacteristic
57C2×#6392C2211yescharacteristic
58C2×#6392C2211yescharacteristic
59C2×#6392C2211yescharacteristic
60C2×#6392C2211yescharacteristic
61C2×#6392C2211yescharacteristic
62C2×#6392C2218yescomplemented
63C2×#6391C2211yescharacteristic
64C2×#6391C2211yescharacteristic
65C2×#6391C2211yescharacteristic
66C2×#6390C2211yescharacteristic
67C2×#6390C2211yescharacteristic
68C2×#6390C2211yescharacteristic
69#89622C2218yescomplemented
70#89619C2218yescomplemented
71#89509C2218yescomplemented
72#89508C2218yescomplemented
73#89494C2218yescomplemented
74#89493C2218yescomplemented
75#89482C2218yescomplemented
76#89474C2218yescomplemented
77C2×#3343—71nomaximal, Sylow
78C22×C7×D4D411yescharacteristic
79C23×C4×C7C2311yescharacteristic
80C23×C4×C7C2311yescharacteristic
81C22×C22⋊D7—21no—
82C22×C22⋊D7—21no—
83C23×Dic7—21no—
84C23×Dic7—21no—
85C23×Dic7—21no—
86C2×#1159—28no—
87C2×#1159—48no—
88C22×D28C2311yescharacteristic
89C22×C4×D7—21no—
90C22×Dic14—21no—
91C22×Dic14C2311yescharacteristic
92C2×C7×M16—24no—
93C2×C7×M16C2314yes—
94C22×C7×C8—24no—
95C22×C7×C8C2311yescharacteristic
96C22×C7×C8C2311yescharacteristic
97C22×C7×C8C2311yescharacteristic
98C22×C7×C8C2314yes—
99C22×C7×C8C2311yescharacteristic
100C4×C7×D4D414yes—
101C4×C7×D4C2314yes—
102C2×C7×C4⋊C4D411yescharacteristic
103C2×C7×C22⋊C4D411yescharacteristic
104C2×C7×C22⋊C4D411yescharacteristic
105C2×C42×C7C2311yescharacteristic
106C2×C22⋊Dic7—21no—
107C2×C22⋊Dic7—21no—
108C2×C22⋊Dic7—21no—
109#6498—28no—
110#6493—22no—
111#6493—22no—
112#6493C2314yes—
113#6493C2314yes—
114C2×(C2×D7)⋊C4—21no—
115C2×(C2×D7)⋊C4—21no—
116C2×(C2×D7)⋊C4—21no—
117#6489—22no—
118#6489C2314yes—
119C2×C4⋊Dic7—21no—
120C2×C4⋊Dic7—21no—
121C2×C4⋊Dic7—21no—
122C2×C4⋊Dic7—21no—
123C2×C4⋊Dic7—22no—
124C2×C4⋊Dic7—22no—
125C2×C4⋊Dic7—22no—
126C2×C4⋊Dic7C2311yescharacteristic
127C2×C4⋊Dic7C2311yescharacteristic
128C2×C4⋊Dic7C2311yescharacteristic
129C2×C4⋊Dic7C2311yescharacteristic
130C2×C4⋊Dic7C2311yescharacteristic
131C2×C4⋊Dic7C2311yescharacteristic
132C2×C4⋊Dic7C2314yes—
133C2×C4⋊Dic7C2314yes—
134C2×C4⋊Dic7C2314yes—
135#6487—22no—
136#6487—22no—
137#6487C2314yes—
138#6487C2314yes—
139C2×Dic7⋊C4—21no—
140C2×Dic7⋊C4—21no—
141C2×Dic7⋊C4—21no—
142C2×Dic7⋊C4—21no—
143C2×Dic7⋊C4—21no—
144C2×C4×Dic7—21no—
145C2×C4×Dic7—21no—
146C2×#1132—24no—
147C2×#1132C2314yes—
148#6460—28no—
149#6452—28no—
150#6449—28no—
151#6449—28no—
152#6442—28no—
153#6440—28no—
154C4×D28—22no—
155C4×D28C2314yes—
156#6433—22no—
157#6433C2314yes—
158#6432—22no—
159#6432C2314yes—
160C4×Dic14—22no—
161C4×Dic14C2314yes—
162C7×C4⋊C8C2314yes—
163C7×C22⋊C8C2314yes—
164C7×C22⋊C8C2314yes—
165C7×#97C2314yes—
166#6395C2314yes—
167#6395C2314yes—
168#6395C2314yes—
169#6392C2314yes—
170#6392C2314yes—
171#6392C2314yes—
172#6392C2314yes—
173#6392C2314yes—
174#6392C2314yes—
175#6391C2314yes—
176#6391C2314yes—
177#6391C2314yes—
178#6390C2314yes—
179#6390C2314yes—
180#6390C2314yes—
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×#440—71no—
194C2×#435D711yescharacteristic, complemented
195C2×#428—71no—
196C22×#107—71no—
197C24×C7C2×D411yescharacteristic
198C24×C7C2×D411yescharacteristic
199C23×D7—21no—
200C2×C7×D4—24no—
201C2×C7×D4C2×D414yes—
202C22×C4×C7—22no—
203C22×C4×C7—22no—
204C22×C4×C7—22no—
205C22×C4×C7—22no—
206C22×C4×C7C2×D411yescharacteristic
207C22×C4×C7C2×D411yescharacteristic
208C22×C4×C7C2×D411yescharacteristic
209C22×C4×C7C2×D411yescharacteristic
210C22×C4×C7C2×D412yes—
211C22×C4×C7C2×D412yes—
212C22×C4×C7C2412yes—
213C22×C4×C7C2412yes—
214C22×C4×C7C2411yescharacteristic
215C2×C22⋊D7—24no—
216C2×C22⋊D7—24no—
217C2×C22⋊D7—44no—
218C2×C22⋊D7—44no—
219C22×Dic7—24no—
220C22×Dic7—24no—
221C22×Dic7—24no—
222C22×Dic7—21no—
223C22×Dic7—21no—
224C22×Dic7—21no—
225C22×Dic7—21no—
226C22×Dic7—21no—
227C22×Dic7—21no—
228C22×Dic7—21no—
229C22×Dic7—44no—
230C22×Dic7—44no—
231C22×Dic7—44no—
232#1159—432no—
233C2×D28—22no—
234C2×D28—22no—
235C2×D28—21no—
236C2×D28C2412yes—
237C2×C4×D7—24no—
238C2×C4×D7—44no—
239C2×Dic14—22no—
240C2×Dic14—22no—
241C2×Dic14—21no—
242C2×Dic14—24no—
243C2×Dic14—44no—
244C2×Dic14C2412yes—
245C7×M16—28no—
246C2×C7×C8—22no—
247C2×C7×C8—22no—
248C2×C7×C8—22no—
249C2×C7×C8—28no—
250C2×C7×C8#4114yescomplemented
251C2×C7×C8C2412yes—
252C2×C7×C8C2412yes—
253C2×C7×C8C2412yes—
254C2×C7×C8C2412yes—
255C7×C4⋊C4C2×D414yes—
256C7×C22⋊C4C2×D414yes—
257C7×C22⋊C4C2×D414yes—
258C42×C7C2×D412yes—
259C42×C7C2412yes—
260C22⋊Dic7—24no—
261C22⋊Dic7—24no—
262C22⋊Dic7—24no—
263(C2×D7)⋊C4—24no—
264(C2×D7)⋊C4—24no—
265(C2×D7)⋊C4—24no—
266C4⋊Dic7—21no—
267C4⋊Dic7—21no—
268C4⋊Dic7—21no—
269C4⋊Dic7—24no—
270C4⋊Dic7—21no—
271C4⋊Dic7—21no—
272C4⋊Dic7—21no—
273C4⋊Dic7—24no—
274C4⋊Dic7—24no—
275C4⋊Dic7—24no—
276C4⋊Dic7C2412yes—
277C4⋊Dic7C2412yes—
278C4⋊Dic7C2412yes—
279C4⋊Dic7C2412yes—
280C4⋊Dic7C2412yes—
281C4⋊Dic7C2412yes—
282Dic7⋊C4—24no—
283Dic7⋊C4—24no—
284Dic7⋊C4—24no—
285Dic7⋊C4—24no—
286Dic7⋊C4—24no—
287C4×Dic7—24no—
288C4×Dic7—24no—
289#1132—28no—
290C22×#41—141no—
291C22×SD16—71no—
292C22×M16C2×D711yescharacteristic
293C23×C8C2×D711yescharacteristic
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×Q8—71no—
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#440—78no—
328#435C2×D718yescomplemented
329#428—78no—
330C2×#107—71no—
331C2×#107—71no—
332C2×#107—71no—
333C2×#107—71no—
334C2×#107—78no—
335C2×#107—71no—
336C2×#107—71no—
337C2×#106—71no—
338C2×#106—71no—
339C2×#106—71no—
340C2×C4⋊C8C2×D711yescharacteristic
341C2×#103—71no—
342C2×#103—71no—
343C2×#103—71no—
344C2×#102—71no—
345C2×#102—71no—
346C2×#102—71no—
347C2×C22⋊C8C2×D711yescharacteristic
348C2×C22⋊C8C2×D711yescharacteristic
349C2×#97C2×D711yescharacteristic
350C23×C7—22no—
351C23×C7—22no—
352C23×C7—22no—
353C23×C7—22no—
354C23×C7—22no—
355C23×C7AGL(1,ℤ/8)14yes—
356C23×C7C22×D412yes—
357C23×C7C22×D412yes—
358C23×C7C22×D411yescharacteristic
359C22×D7—22no—
360C22×D7—42no—
361C22×D7—42no—
362C22×D7—42no—
363C7×D4—28no—
364C2×C4×C7—22no—
365C2×C4×C7—22no—
366C2×C4×C7—22no—
367C2×C4×C7—22no—
368C2×C4×C7—24no—
369C2×C4×C7—24no—
370C2×C4×C7—22no—
371C2×C4×C7—22no—
372C2×C4×C7—22no—
373C2×C4×C7—22no—
374C2×C4×C7C22×D412yes—
375C2×C4×C7C22×D412yes—
376C2×C4×C7C22×D412yes—
377C2×C4×C7C22×D412yes—
378C2×C4×C7C22×D411yescharacteristic
379C2×C4×C7C2×#4112yes—
380C2×C4×C72−1+412yes—
381C2×C4×C7C2511yescharacteristic
382C22⋊D7—48no—
383C22⋊D7—48no—
384C2×Dic7—22no—
385C2×Dic7—22no—
386C2×Dic7—22no—
387C2×Dic7—22no—
388C2×Dic7—22no—
389C2×Dic7—22no—
390C2×Dic7—22no—
391C2×Dic7—48no—
392C2×Dic7—42no—
393C2×Dic7—42no—
394C2×Dic7—42no—
395C2×Dic7—42no—
396C2×Dic7—48no—
397C2×Dic7—48no—
398C2×Dic7—42no—
399C2×Dic7—42no—
400C2×Dic7—42no—
401D28—22no—
402D28—22no—
403D28—42no—
404C4×D7—48no—
405Dic14—22no—
406Dic14—22no—
407Dic14—48no—
408Dic14—42no—
409C7×C8—22no—
410C7×C8—22no—
411C7×C8—22no—
412C7×C8C2×#4114yescomplemented
413C2×#41—148no—
414C2×#41—288no—
415C22×Q8—71no—
416C22×Q8—141no—
417C22×D4—71no—
418C22×D4—141no—
419C22×D4—141no—
420C22×D4D2811yescharacteristic
421C23×C4—141no—
422C23×C4—141no—
423C23×C4—141no—
424C23×C4—141no—
425C23×C4C22×D711yescharacteristic
426C23×C4C22×D711yescharacteristic
427C2×SD16—74no—
428C2×SD16—144no—
429C2×M16—24no—
430C2×M16C22×D714yes—
431C22×C8—24no—
432C22×C8C22×D711yescharacteristic
433C22×C8C22×D714yes—
434C22×C8C22×D711yescharacteristic
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—142no—
449C22⋊Q8—142no—
450C22⋊Q8—148no—
451#121—74no—
452#121—74no—
453#121—142no—
454#121—142no—
455C4×Q8—74no—
456C4×Q8—142no—
457C4×D4—74no—
458C4×D4—142no—
459C4×D4D2814yes—
460C4×D4C22×D714yes—
461#117—74no—
462#117—142no—
463#117—148no—
464C2×C4⋊C4—71no—
465C2×C4⋊C4—71no—
466C2×C4⋊C4—71no—
467C2×C4⋊C4—71no—
468C2×C4⋊C4—71no—
469C2×C4⋊C4—74no—
470C2×C4⋊C4—74no—
471C2×C4⋊C4—74no—
472C2×C4⋊C4—71no—
473C2×C4⋊C4—141no—
474C2×C4⋊C4—141no—
475C2×C4⋊C4—141no—
476C2×C4⋊C4—142no—
477C2×C4⋊C4—142no—
478C2×C4⋊C4—142no—
479C2×C4⋊C4—141no—
480C2×C4⋊C4—141no—
481C2×C4⋊C4—141no—
482C2×C4⋊C4—141no—
483C2×C4⋊C4—141no—
484C2×C4⋊C4—141no—
485C2×C4⋊C4D2811yescharacteristic
486C2×C22⋊C4—141no—
487C2×C22⋊C4—141no—
488C2×C22⋊C4—141no—
489C2×C22⋊C4—141no—
490C2×C22⋊C4—141no—
491C2×C22⋊C4—141no—
492C2×C22⋊C4D2811yescharacteristic
493C2×C22⋊C4D2811yescharacteristic
494C2×C42—141no—
495C2×C42—141no—
496C2×C42C22×D711yescharacteristic
497#107—74no—
498#107—74no—
499#107—74no—
500#107—74no—
501#107—74no—
502#107—74no—
503#106—74no—
504#106—74no—
505#106—74no—
506C4⋊C8C22×D714yes—
507#103—74no—
508#103—74no—
509#103—74no—
510#102—74no—
511#102—74no—
512#102—74no—
513C22⋊C8C22×D714yes—
514C22⋊C8C22×D714yes—
515#97C22×D714yes—
516C22×C7—28no—
517C22×C7—22no—
518C22×C7—22no—
519C22×C7—22no—
520C22×C7—22no—
521C22×C7—22no—
522C22×C7—44no—
523C22×C7#54712yes—
524C22×C7C2×AGL(1,ℤ/8)14yes—
525C22×C7C2×AGL(1,ℤ/8)12yes—
526C22×C7#57812yes—
527C22×C7C23×D411yescharacteristic
528C2×D7—42no—
529C2×D7—42no—
530C2×D7—42no—
531C2×D7—84no—
532C4×C7—22no—
533C4×C7—22no—
534C4×C7—22no—
535C4×C7—22no—
536C4×C7#54712yes—
537C4×C7C22×#4111yescharacteristic
538C4×C7C2×2−1+411yescharacteristic
539Dic7—42no—
540Dic7—42no—
541Dic7—42no—
542Dic7—42no—
543Dic7—42no—
544Dic7—42no—
545Dic7—42no—
546C24—141no—
547C24C2×D2811yescharacteristic
548C24C2×D2811yescharacteristic
549#41—2832no—
550C2×Q8—72no—
551C2×Q8—141no—
552C2×Q8—144no—
553C2×Q8—142no—
554C2×Q8—142no—
555C2×Q8—284no—
556C2×D4—24no—
557C2×D4—72no—
558C2×D4—144no—
559C2×D4—144no—
560C2×D4—141no—
561C2×D4—142no—
562C2×D4—142no—
563C2×D4—284no—
564C2×D4—284no—
565C2×D4C2×D2814yes—
566C22×C4—22no—
567C22×C4—22no—
568C22×C4—22no—
569C22×C4—22no—
570C22×C4—144no—
571C22×C4—144no—
572C22×C4—144no—
573C22×C4—141no—
574C22×C4—141no—
575C22×C4—141no—
576C22×C4—141no—
577C22×C4—141no—
578C22×C4—141no—
579C22×C4—141no—
580C22×C4—144no—
581C22×C4—284no—
582C22×C4—284no—
583C22×C4—284no—
584C22×C4—284no—
585C22×C4C2×D2812yes—
586C22×C4C2×D2812yes—
587C22×C4C2×D2811yescharacteristic
588C22×C4C2×D2811yescharacteristic
589C22×C4C2×D2811yescharacteristic
590C22×C4C2×D2811yescharacteristic
591C22×C4C23×D712yes—
592C22×C4C23×D712yes—
593C22×C4C23×D711yescharacteristic
594SD16—148no—
595M16—28no—
596C2×C8—22no—
597C2×C8—22no—
598C2×C8—22no—
599C2×C8—28no—
600C2×C8#115914yescomplemented
601C2×C8C23×D712yes—
602C2×C8C23×D712yes—
603C2×C8C23×D712yes—
604C2×C8C23×D712yes—
605C4⋊C4—72no—
606C4⋊C4—72no—
607C4⋊C4—72no—
608C4⋊C4—72no—
609C4⋊C4—72no—
610C4⋊C4—72no—
611C4⋊C4—144no—
612C4⋊C4—144no—
613C4⋊C4—144no—
614C4⋊C4—144no—
615C4⋊C4—144no—
616C4⋊C4—141no—
617C4⋊C4—141no—
618C4⋊C4—141no—
619C4⋊C4—141no—
620C4⋊C4—144no—
621C4⋊C4—144no—
622C4⋊C4—141no—
623C4⋊C4—144no—
624C4⋊C4—141no—
625C4⋊C4—144no—
626C4⋊C4C2×D2814yes—
627C22⋊C4—144no—
628C22⋊C4—144no—
629C22⋊C4—144no—
630C22⋊C4—144no—
631C22⋊C4—144no—
632C22⋊C4—144no—
633C22⋊C4C2×D2814yes—
634C22⋊C4C2×D2814yes—
635C42—144no—
636C42—144no—
637C42C2×D2812yes—
638C42C23×D712yes—
639C2×C7—24no—
640C2×C7—42no—
641C2×C7#334314yescomplemented
642C2×C7C2×#54711yescharacteristic
643C2×C7C22×AGL(1,ℤ/8)11yescharacteristic
644C2×C7C2×#57811yescharacteristic
645D7—82no—
646C23—22no—
647C23—22no—
648C23—22no—
649C23—22no—
650C23—22no—
651C23—142no—
652C23—282no—
653C23—282no—
654C23—282no—
655C23#647114yes—
656C23C22×D2812yes—
657C23C22×D2812yes—
658C23C22×D2811yescharacteristic
659Q8—142no—
660Q8—142no—
661Q8—288no—
662Q8—282no—
663D4—28no—
664D4—142no—
665D4—142no—
666D4—288no—
667D4—288no—
668D4—282no—
669C2×C4—22no—
670C2×C4—22no—
671C2×C4—22no—
672C2×C4—22no—
673C2×C4—24no—
674C2×C4—24no—
675C2×C4—22no—
676C2×C4—22no—
677C2×C4—22no—
678C2×C4—22no—
679C2×C4—142no—
680C2×C4—142no—
681C2×C4—142no—
682C2×C4—142no—
683C2×C4—142no—
684C2×C4—142no—
685C2×C4—142no—
686C2×C4—288no—
687C2×C4—288no—
688C2×C4—288no—
689C2×C4—282no—
690C2×C4—282no—
691C2×C4—282no—
692C2×C4—282no—
693C2×C4—282no—
694C2×C4—288no—
695C2×C4—282no—
696C2×C4—282no—
697C2×C4C22×D2812yes—
698C2×C4C22×D2812yes—
699C2×C4C22×D2812yes—
700C2×C4C22×D2812yes—
701C2×C4C22×D2811yescharacteristic
702C2×C4C2×#115912yes—
703C2×C4#655412yes—
704C2×C4C24×D711yescharacteristic
705C8—22no—
706C8—22no—
707C8—22no—
708C8C2×#115914yescomplemented
709C7C2×#334311yescharacteristic, complemented, Sylow
710C22—28no—
711C22—22no—
712C22—22no—
713C22—22no—
714C22—22no—
715C22—22no—
716C22—44no—
717C22—282no—
718C22—282no—
719C22—282no—
720C22—564no—
721C22#9024612yes—
722C22C2×#647114yes—
723C22C2×#647112yes—
724C22#9044412yes—
725C22C23×D2811yescharacteristic
726C4—22no—
727C4—22no—
728C4—22no—
729C4—22no—
730C4—282no—
731C4—282no—
732C4—282no—
733C4—282no—
734C4—282no—
735C4—282no—
736C4—282no—
737C4#9024612yes—
738C4C22×#115911yescharacteristic
739C4C2×#655411yescharacteristic
740C2—24no—
741C2—42no—
742C2—562no—
743C2#1173691414yesdirect product factor
744C2C2×#9024611yescharacteristic
745C2C22×#647111yescharacteristic
746C2C2×#9044411yescharacteristic
subgroupG/H
centerC23C22×D28
commutator, cosocleC2×C4×C7C25
FrattiniC2×C4C24×D7
FittingC2×C7×#435C2
socleC23×C7C22×D4
prime radicalC2×#90246C2
hypercenterC2×#435D7
hypocenterC7C2×#3343
LCSG ▷ C2×C4×C7 ▷ C2×C7 ▷ C7
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×#435

Complements

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

NH ≅ G/Ntype
1. C2×#90232C2semidirect
3. C2×C7×#435C2semidirect
4. C2×#89906C2semidirect
5. C2×#89893C2semidirect
6. C2×#89886C2semidirect
7. C22×#6392C2semidirect
8. #11736914C2direct (N × H)
9. C2×#89622C2semidirect
10. C2×#89619C2semidirect
11. C2×#89494C2semidirect
12. C2×#89509C2semidirect
13. C2×#89493C2semidirect
14. C2×#89508C2semidirect
15. C2×#89482C2semidirect
16. C2×#89474C2semidirect
34. #90232C22semidirect
45. C7×#435C22semidirect
50. #89906C22semidirect
51. #89893C22semidirect
52. #89886C22semidirect
62. C2×#6392C22semidirect
69. #89622C22semidirect
70. #89619C22semidirect
71. #89509C22semidirect
72. #89508C22semidirect
73. #89494C22semidirect
74. #89493C22semidirect
75. #89482C22semidirect
76. #89474C22semidirect
194. C2×#435D7semidirect
250. C2×C7×C8#41semidirect
328. #435C2×D7semidirect
412. C7×C8C2×#41semidirect
600. C2×C8#1159semidirect
641. C2×C7#3343semidirect
708. C8C2×#1159semidirect
709. C7C2×#3343semidirect
743. C2#11736914direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#902322
C2×#902462
C2×C7×#4352
C2×#899062
C2×#898932
C2×#898862
C22×#63922
#117369142
C2×#896222
C2×#896192
C2×#894942
C2×#895092
C2×#894932
C2×#895082
C2×#894822
C2×#894742
C2×#33437