Finite Group Databasebeta

← C2×#11738372 #14230676

Subgroups — C2×#11738372 #14230676

Order 1792.

2082 conjugacy classes of subgroups.

The subgroup lattice has 772 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#90332C211yesmaximal, characteristic
2C2×#90323C211yesmaximal, characteristic
3C2×C7×#470C211yesmaximal, characteristic, complemented
4C2×#89958C211yesmaximal, characteristic, complemented
5C2×#89954C211yesmaximal, characteristic, complemented
6C2×#89892C211yesmaximal, characteristic, complemented
7C2×#89900C211yesmaximal, characteristic
8C2×#89822C211yesmaximal, characteristic, complemented
9C2×#89817C211yesmaximal, characteristic, complemented
10#11738372C2116yesmaximal, direct product factor
11C2×#89626C211yesmaximal, characteristic, complemented
12C2×#89639C211yesmaximal, characteristic, complemented
13C2×#89588C211yesmaximal, characteristic, complemented
14C2×#89574C211yesmaximal, characteristic, complemented
15C2×#89564C211yesmaximal, characteristic, complemented
16C2×#89562C211yesmaximal, characteristic, complemented
17C22×Q8×D7C2211yescharacteristic
18C23×Dic14C2211yescharacteristic
19C22×C7×Q16C2211yescharacteristic
20C22×C7×M16C2211yescharacteristic
21C2×C7×C22⋊Q8C2211yescharacteristic
22C2×C7×C22⋊Q8C2211yescharacteristic
23C2×#6509C2211yescharacteristic
24C2×Q8×Dic7C2211yescharacteristic
25C2×#6507C2211yescharacteristic
26C22×#1144C2211yescharacteristic
27C22×#1144C2211yescharacteristic
28C2×C4×C22⋊D7C2211yescharacteristic
29C2×#6489C2211yescharacteristic
30C22×#1131C2211yescharacteristic
31#90332—24no—
32#90332C2218yes—
33#90323—24no—
34#90323C2218yes—
35C2×#6461—21no—
36C2×#6460C2211yescharacteristic
37C2×#6459—21no—
38C2×#6455C2211yescharacteristic
39C2×#6451—21no—
40C2×#6451C2211yescharacteristic
41C2×#6450—21no—
42C2×#6450C2211yescharacteristic
43C2×#6448—21no—
44C2×(C22⋊D7)⋊C4—21no—
45C2×#6442—21no—
46C2×#6441—21no—
47C7×#470C2218yescomplemented
48C2×C7×#106C2211yescharacteristic
49C2×C7×#103C2211yescharacteristic
50C2×C7×#103C2211yescharacteristic
51C2×#6409C2211yescharacteristic
52C2×#6409C2211yescharacteristic
53C2×C22⋊(C7⋊C8)C2211yescharacteristic
54#89958C2218yescomplemented
55#89954C2218yescomplemented
56#89900C2218yes—
57#89892C2218yescomplemented
58C2×(C2×D7)⋊C8C2211yescharacteristic
59C2×#6390C2211yescharacteristic
60C2×#6390C2211yescharacteristic
61C2×#6390C2211yescharacteristic
62C2×#6390C2211yescharacteristic
63C2×Dic7⋊C8C2211yescharacteristic
64C2×C8×Dic7C2211yescharacteristic
65#89822C2218yescomplemented
66#89817C2218yescomplemented
67C2×#6384C2211yescharacteristic
68C2×#6384C2211yescharacteristic
69C2×#6382C2211yescharacteristic
70C2×#6381C2211yescharacteristic
71#89639C2218yescomplemented
72#89626C2218yescomplemented
73#89588C2218yescomplemented
74#89574C2218yescomplemented
75#89564C2218yescomplemented
76#89562C2218yescomplemented
77C2×#3328—71nomaximal, Sylow
78C22×C7×Q8C2311yescharacteristic
79C22×C7×Q8C2311yescharacteristic
80C23×C4×C7C2311yescharacteristic
81C22×C22⋊D7D411yescharacteristic
82C23×Dic7—21no—
83C2×Q8×D7—22no—
84C2×Q8×D7—24no—
85C2×Q8×D7—42no—
86C2×Q8×D7C2314yes—
87C22×C4×D7—21no—
88C22×C4×D7C2311yescharacteristic
89C22×Dic14—24no—
90C22×Dic14—21no—
91C22×Dic14—22no—
92C22×Dic14—21no—
93C22×Dic14—21no—
94C22×Dic14—42no—
95C22×Dic14C2311yescharacteristic
96C22×Dic14C2314yes—
97C22×Dic14C2311yescharacteristic
98C2×C7×Q16—42no—
99C2×C7×Q16C2314yes—
100C2×C7×M16—42no—
101C2×C7×M16C2314yes—
102C22×C7×C8C2311yescharacteristic
103C22×C7×C8C2311yescharacteristic
104C7×C22⋊Q8—22no—
105C7×C22⋊Q8—22no—
106C7×C22⋊Q8C2314yes—
107C7×C22⋊Q8C2314yes—
108C2×C7×C4⋊C4—21no—
109C2×C7×C4⋊C4—21no—
110C2×C7×C4⋊C4C2311yescharacteristic
111C2×C7×C4⋊C4C2311yescharacteristic
112C2×C7×C22⋊C4—21no—
113C2×C7×C22⋊C4—21no—
114C2×C22⋊Dic7—21no—
115C2×C22⋊Dic7D411yescharacteristic
116#6509—22no—
117#6509C2314yes—
118Q8×Dic7—22no—
119Q8×Dic7C2314yes—
120#6507—22no—
121#6507C2314yes—
122C2×#1144—24no—
123C2×#1144—42no—
124C2×#1144C2314yes—
125C2×#1144C2314yes—
126C4×C22⋊D7D414yes—
127C4×C22⋊D7C2314yes—
128C2×(C2×D7)⋊C4—21no—
129C2×(C2×D7)⋊C4—21no—
130C2×(C2×D7)⋊C4—21no—
131C2×(C2×D7)⋊C4D411yescharacteristic
132#6489—22no—
133#6489C2314yes—
134C2×C4⋊Dic7—21no—
135C2×C4⋊Dic7—21no—
136C2×C4⋊Dic7C2311yescharacteristic
137C2×C4⋊Dic7C2311yescharacteristic
138C2×Dic7⋊C4—21no—
139C2×Dic7⋊C4—21no—
140C2×Dic7⋊C4—21no—
141C2×Dic7⋊C4—21no—
142C2×Dic7⋊C4—21no—
143C2×Dic7⋊C4D411yescharacteristic
144C2×C4×Dic7—21no—
145C2×C4×Dic7—21no—
146C2×C4×Dic7—21no—
147C2×C4×Dic7—21no—
148C2×C4×Dic7C2311yescharacteristic
149C22×C7⋊C8C2311yescharacteristic
150C22×C7⋊C8C2311yescharacteristic
151C2×#1131—42no—
152C2×#1131C2314yes—
153#6461—28no—
154#6460—22no—
155#6460C2314yes—
156#6459—28no—
157#6455—22no—
158#6455C2314yes—
159#6451—28no—
160#6451—22no—
161#6451C2314yes—
162#6450—28no—
163#6450—22no—
164#6450C2314yes—
165#6448—28no—
166(C22⋊D7)⋊C4—28no—
167#6442—28no—
168#6441—28no—
169C7×#106C2314yes—
170C7×#103C2314yes—
171C7×#103C2314yes—
172#6409C2314yes—
173#6409C2314yes—
174C22⋊(C7⋊C8)C2314yes—
175(C2×D7)⋊C8C2314yes—
176#6390C2314yes—
177#6390C2314yes—
178#6390C2314yes—
179#6390C2314yes—
180Dic7⋊C8C2314yes—
181C8×Dic7C2314yes—
182#6384C2314yes—
183#6384C2314yes—
184#6382C2314yes—
185#6381C2314yes—
186C2×#556—71no—
187C2×D4×Q8—71no—
188#3328—716no—
189C2×#487—71no—
190C2×#485—71no—
191C2×#485—71no—
192C2×#475—71no—
193C2×#470—71no—
194C2×#470D711yescharacteristic, complemented
195C2×#462—71no—
196C2×#451—71no—
197C2×#451—71no—
198C2×C4×Q16—71no—
199C2×#436—71no—
200C2×#419—71no—
201C2×#419—71no—
202C24×C7C2×D411yescharacteristic
203C23×D7C2×D411yescharacteristic
204C2×C7×Q8—21no—
205C2×C7×Q8—21no—
206C2×C7×Q8—22no—
207C2×C7×Q8—22no—
208C2×C7×Q8—22no—
209C2×C7×Q8—22no—
210C2×C7×Q8C2412yes—
211C2×C7×Q8C2412yes—
212C22×C4×C7—22no—
213C22×C4×C7—22no—
214C22×C4×C7—21no—
215C22×C4×C7—21no—
216C22×C4×C7—21no—
217C22×C4×C7—21no—
218C22×C4×C7C2×D411yescharacteristic
219C22×C4×C7C2×D412yes—
220C22×C4×C7C2412yes—
221C22×C4×C7C2411yescharacteristic
222C2×C22⋊D7—24no—
223C2×C22⋊D7C2×D414yes—
224C22×Dic7—21no—
225C22×Dic7—24no—
226C22×Dic7—21no—
227C22×Dic7—21no—
228C22×Dic7—21no—
229C22×Dic7—44no—
230C22×Dic7C2×D411yescharacteristic
231C22×Dic7C2×D411yescharacteristic
232C22×Dic7C2×D411yescharacteristic
233Q8×D7—28no—
234Q8×D7—44no—
235Q8×D7—48no—
236C2×C4×D7—22no—
237C2×C4×D7—22no—
238C2×C4×D7—24no—
239C2×C4×D7—44no—
240C2×C4×D7C2×D412yes—
241C2×C4×D7C2412yes—
242C2×Dic14—21no—
243C2×Dic14—22no—
244C2×Dic14—22no—
245C2×Dic14—22no—
246C2×Dic14—28no—
247C2×Dic14—24no—
248C2×Dic14—21no—
249C2×Dic14—24no—
250C2×Dic14—24no—
251C2×Dic14—44no—
252C2×Dic14—48no—
253C2×Dic14—44no—
254C2×Dic14—44no—
255C2×Dic14—44no—
256C2×Dic14#4114yes—
257C2×Dic14C2412yes—
258C2×Dic14C2412yes—
259C7×Q16—44no—
260C7×M16—44no—
261C2×C7×C8—22no—
262C2×C7×C8—22no—
263C2×C7×C8C2412yes—
264C2×C7×C8C2412yes—
265C7×C4⋊C4—21no—
266C7×C4⋊C4—24no—
267C7×C4⋊C4—21no—
268C7×C4⋊C4—24no—
269C7×C4⋊C4C2412yes—
270C7×C4⋊C4C2412yes—
271C7×C22⋊C4—24no—
272C7×C22⋊C4—24no—
273C22⋊Dic7—24no—
274C22⋊Dic7C2×D414yes—
275#1144—28no—
276#1144—44no—
277(C2×D7)⋊C4—24no—
278(C2×D7)⋊C4—24no—
279(C2×D7)⋊C4—24no—
280(C2×D7)⋊C4C2×D414yes—
281C4⋊Dic7—21no—
282C4⋊Dic7—21no—
283C4⋊Dic7—24no—
284C4⋊Dic7—24no—
285C4⋊Dic7C2412yes—
286C4⋊Dic7C2412yes—
287Dic7⋊C4—24no—
288Dic7⋊C4—24no—
289Dic7⋊C4—24no—
290Dic7⋊C4—24no—
291Dic7⋊C4—24no—
292Dic7⋊C4C2×D414yes—
293C4×Dic7—24no—
294C4×Dic7—24no—
295C4×Dic7—24no—
296C4×Dic7—24no—
297C4×Dic7C2×D412yes—
298C4×Dic7C2412yes—
299C2×C7⋊C8—22no—
300C2×C7⋊C8—22no—
301C2×C7⋊C8C2412yes—
302C2×C7⋊C8C2412yes—
303#1131—44no—
304C23×Q8—71no—
305C23×Q8—71no—
306C22×Q16—71no—
307C22×Q16—71no—
308C22×Q16C2×D711yescharacteristic
309C22×M16—71no—
310C22×M16C2×D711yescharacteristic
311#556—78no—
312#556—144no—
313D4×Q8—78no—
314D4×Q8—144no—
315C2×C4⋊Q8—71no—
316C2×C4⋊Q8—71no—
317C2×C4⋊Q8—141no—
318C2×#126—141no—
319C2×#126—141no—
320C2×#124—141no—
321C2×C22⋊Q8—71no—
322C2×C22⋊Q8—71no—
323C2×C22⋊Q8—141no—
324C2×C22⋊Q8—141no—
325C2×C22⋊Q8C2×D711yescharacteristic
326C2×C22⋊Q8C2×D711yescharacteristic
327C2×C4×Q8—71no—
328C2×C4×Q8—71no—
329C2×C4×Q8—141no—
330C2×C4×D4—71no—
331C2×C4×D4—141no—
332C2×#117—71no—
333C2×#117—71no—
334#487—78no—
335#485—78no—
336#485—78no—
337#475—78no—
338#470—78no—
339#470C2×D718yescomplemented
340#462—78no—
341#451—78no—
342#451—78no—
343C4×Q16—78no—
344#436—78no—
345C2×#107—71no—
346C2×#106—71no—
347C2×#106C2×D711yescharacteristic
348C2×C4⋊C8—71no—
349#419—78no—
350#419—78no—
351C2×#103—71no—
352C2×#103—71no—
353C2×#103—71no—
354C2×#103—71no—
355C2×#103—71no—
356C2×#103—71no—
357C2×#103—71no—
358C2×#103—71no—
359C2×#103C2×D711yescharacteristic
360C2×#103C2×D711yescharacteristic
361C2×C22⋊C8—71no—
362C2×C22⋊C8—71no—
363C2×C4×C8—71no—
364C23×C7—22no—
365C23×C7—22no—
366C23×C7—22no—
367C23×C7C22×D412yes—
368C23×C7C22×D411yescharacteristic
369C22×D7—22no—
370C22×D7—22no—
371C22×D7—22no—
372C22×D7C22×D412yes—
373C7×Q8—22no—
374C7×Q8—22no—
375C7×Q8—22no—
376C7×Q8—22no—
377C7×Q8—42no—
378C7×Q8—42no—
379C2×C4×C7—22no—
380C2×C4×C7—24no—
381C2×C4×C7—22no—
382C2×C4×C7—22no—
383C2×C4×C7—22no—
384C2×C4×C7—22no—
385C2×C4×C7—22no—
386C2×C4×C7—22no—
387C2×C4×C7—42no—
388C2×C4×C7—42no—
389C2×C4×C7—42no—
390C2×C4×C7—42no—
391C2×C4×C7C22×D412yes—
392C2×C4×C7C22×D411yescharacteristic
393C2×C4×C7C2×#4112yes—
394C2×C4×C7H(5,𝔽2)12yes—
395C2×C4×C7C2511yescharacteristic
396C22⋊D7—28no—
397C2×Dic7—24no—
398C2×Dic7—22no—
399C2×Dic7—22no—
400C2×Dic7—22no—
401C2×Dic7—22no—
402C2×Dic7—22no—
403C2×Dic7—22no—
404C2×Dic7—48no—
405C2×Dic7—42no—
406C2×Dic7—42no—
407C2×Dic7—42no—
408C2×Dic7#13714yes—
409C2×Dic7C22×D412yes—
410C2×Dic7C22×D412yes—
411C2×Dic7C22×D412yes—
412C4×D7—24no—
413C4×D7—22no—
414C4×D7—22no—
415C4×D7—48no—
416Dic14—24no—
417Dic14—22no—
418Dic14—22no—
419Dic14—22no—
420Dic14—48no—
421Dic14—48no—
422Dic14—42no—
423Dic14—48no—
424Dic14C2×#4114yes—
425C7×C8—22no—
426C7×C8—22no—
427C7⋊C8—22no—
428C7⋊C8—22no—
429C22×Q8—74no—
430C22×Q8—71no—
431C22×Q8—71no—
432C22×Q8—74no—
433C22×Q8—141no—
434C22×Q8—141no—
435C22×Q8—144no—
436C22×Q8—142no—
437C22×Q8—141no—
438C22×Q8—142no—
439C22×Q8—144no—
440C22×Q8—282no—
441C22×Q8—282no—
442C22×Q8C22×D711yescharacteristic
443C22×Q8C22×D711yescharacteristic
444C22×D4—71no—
445C23×C4—71no—
446C23×C4—141no—
447C23×C4—141no—
448C23×C4C22×D711yescharacteristic
449C2×Q16—42no—
450C2×Q16—74no—
451C2×Q16—74no—
452C2×Q16—144no—
453C2×Q16—282no—
454C2×Q16C22×D714yes—
455C2×M16—42no—
456C2×M16—74no—
457C2×M16—282no—
458C2×M16C22×D714yes—
459C22×C8—71no—
460C22×C8—71no—
461C22×C8C22×D711yescharacteristic
462C22×C8C22×D711yescharacteristic
463C4⋊Q8—74no—
464C4⋊Q8—74no—
465C4⋊Q8—142no—
466C4⋊Q8—142no—
467C4⋊Q8—148no—
468#126—148no—
469#126—148no—
470#124—148no—
471C22⋊Q8—22no—
472C22⋊Q8—22no—
473C22⋊Q8—74no—
474C22⋊Q8—74no—
475C22⋊Q8—148no—
476C22⋊Q8—148no—
477C22⋊Q8—142no—
478C22⋊Q8—142no—
479C22⋊Q8C22×D714yes—
480C22⋊Q8C22×D714yes—
481C4×Q8—74no—
482C4×Q8—74no—
483C4×Q8—142no—
484C4×Q8—142no—
485C4×Q8—148no—
486C4×D4—74no—
487C4×D4—74no—
488C4×D4—148no—
489#117—74no—
490#117—74no—
491#117—142no—
492#117—142no—
493C2×C4⋊C4—21no—
494C2×C4⋊C4—21no—
495C2×C4⋊C4—71no—
496C2×C4⋊C4—71no—
497C2×C4⋊C4—71no—
498C2×C4⋊C4—141no—
499C2×C4⋊C4—141no—
500C2×C4⋊C4—141no—
501C2×C4⋊C4—141no—
502C2×C4⋊C4—141no—
503C2×C4⋊C4—141no—
504C2×C4⋊C4—141no—
505C2×C4⋊C4C22×D711yescharacteristic
506C2×C4⋊C4C22×D711yescharacteristic
507C2×C22⋊C4—21no—
508C2×C22⋊C4—21no—
509C2×C22⋊C4—71no—
510C2×C22⋊C4—71no—
511C2×C22⋊C4—141no—
512C2×C22⋊C4—141no—
513C2×C22⋊C4—141no—
514C2×C22⋊C4—141no—
515C2×C42—71no—
516C2×C42—141no—
517C2×C42—141no—
518C2×C42—141no—
519C2×C42—141no—
520#107—74no—
521#106—74no—
522#106C22×D714yes—
523C4⋊C8—74no—
524#103—74no—
525#103—74no—
526#103—74no—
527#103—74no—
528#103—74no—
529#103—74no—
530#103—74no—
531#103—74no—
532#103C22×D714yes—
533#103C22×D714yes—
534C22⋊C8—74no—
535C22⋊C8—74no—
536C4×C8—74no—
537C22×C7—22no—
538C22×C7—22no—
539C22×C7—22no—
540C22×C7—44no—
541C22×C7#54612yes—
542C22×C7C2×#13712yes—
543C22×C7#57812yes—
544C22×C7C23×D411yescharacteristic
545C2×D7—22no—
546C2×D7—22no—
547C2×D7—22no—
548C2×D7—44no—
549C4×C7—22no—
550C4×C7—42no—
551C4×C7—42no—
552C4×C7—42no—
553C4×C7—42no—
554C4×C7#54612yes—
555C4×C7C22×#4111yescharacteristic
556C4×C7C2×H(5,𝔽2)11yescharacteristic
557Dic7—24no—
558Dic7—22no—
559Dic7—22no—
560Dic7—42no—
561Dic7—42no—
562Dic7—42no—
563Dic7C2×#13714yes—
564C24—71no—
565C24D4×D711yescharacteristic
566C2×Q8—21no—
567C2×Q8—21no—
568C2×Q8—22no—
569C2×Q8—22no—
570C2×Q8—22no—
571C2×Q8—22no—
572C2×Q8—74no—
573C2×Q8—72no—
574C2×Q8—72no—
575C2×Q8—144no—
576C2×Q8—144no—
577C2×Q8—148no—
578C2×Q8—141no—
579C2×Q8—144no—
580C2×Q8—141no—
581C2×Q8—142no—
582C2×Q8—148no—
583C2×Q8—142no—
584C2×Q8—142no—
585C2×Q8—284no—
586C2×Q8—284no—
587C2×Q8—288no—
588C2×Q8—284no—
589C2×Q8—284no—
590C2×Q8—284no—
591C2×Q8—288no—
592C2×Q8C23×D712yes—
593C2×Q8C23×D712yes—
594C2×D4—74no—
595C2×D4—144no—
596C22×C4—22no—
597C22×C4—22no—
598C22×C4—21no—
599C22×C4—21no—
600C22×C4—21no—
601C22×C4—21no—
602C22×C4—71no—
603C22×C4—71no—
604C22×C4—71no—
605C22×C4—72no—
606C22×C4—72no—
607C22×C4—144no—
608C22×C4—141no—
609C22×C4—142no—
610C22×C4—142no—
611C22×C4—144no—
612C22×C4—141no—
613C22×C4—141no—
614C22×C4—141no—
615C22×C4—284no—
616C22×C4—284no—
617C22×C4D4×D712yes—
618C22×C4D4×D711yescharacteristic
619C22×C4C23×D712yes—
620C22×C4C23×D711yescharacteristic
621Q16—44no—
622Q16—148no—
623Q16—284no—
624M16—44no—
625M16—284no—
626C2×C8—22no—
627C2×C8—22no—
628C2×C8—72no—
629C2×C8—72no—
630C2×C8—142no—
631C2×C8—142no—
632C2×C8C23×D712yes—
633C2×C8C23×D712yes—
634C4⋊C4—24no—
635C4⋊C4—24no—
636C4⋊C4—21no—
637C4⋊C4—21no—
638C4⋊C4—74no—
639C4⋊C4—72no—
640C4⋊C4—72no—
641C4⋊C4—144no—
642C4⋊C4—144no—
643C4⋊C4—144no—
644C4⋊C4—144no—
645C4⋊C4—144no—
646C4⋊C4—144no—
647C4⋊C4—144no—
648C4⋊C4—141no—
649C4⋊C4—141no—
650C4⋊C4C23×D712yes—
651C4⋊C4C23×D712yes—
652C22⋊C4—24no—
653C22⋊C4—24no—
654C22⋊C4—74no—
655C22⋊C4—74no—
656C22⋊C4—144no—
657C22⋊C4—144no—
658C22⋊C4—144no—
659C22⋊C4—144no—
660C42—72no—
661C42—72no—
662C42—144no—
663C42—144no—
664C42—144no—
665C42—144no—
666C2×C7—42no—
667C2×C7#332814yescomplemented
668C2×C7C2×#54611yescharacteristic
669C2×C7C22×#13711yescharacteristic
670C2×C7C2×#57811yescharacteristic
671D7—42no—
672C23—22no—
673C23—22no—
674C23—22no—
675C23—72no—
676C23—142no—
677C23—142no—
678C23—142no—
679C23C2×D4×D712yes—
680C23C2×D4×D711yescharacteristic
681Q8—22no—
682Q8—22no—
683Q8—22no—
684Q8—22no—
685Q8—42no—
686Q8—42no—
687Q8—74no—
688Q8—144no—
689Q8—142no—
690Q8—142no—
691Q8—142no—
692Q8—288no—
693Q8—288no—
694Q8—288no—
695Q8—282no—
696D4—148no—
697C2×C4—22no—
698C2×C4—24no—
699C2×C4—22no—
700C2×C4—22no—
701C2×C4—22no—
702C2×C4—22no—
703C2×C4—22no—
704C2×C4—22no—
705C2×C4—42no—
706C2×C4—42no—
707C2×C4—42no—
708C2×C4—42no—
709C2×C4—74no—
710C2×C4—72no—
711C2×C4—72no—
712C2×C4—72no—
713C2×C4—142no—
714C2×C4—142no—
715C2×C4—144no—
716C2×C4—142no—
717C2×C4—144no—
718C2×C4—142no—
719C2×C4—142no—
720C2×C4—142no—
721C2×C4—142no—
722C2×C4—142no—
723C2×C4—288no—
724C2×C4—288no—
725C2×C4—282no—
726C2×C4—282no—
727C2×C4—282no—
728C2×C4C2×D4×D712yes—
729C2×C4C2×D4×D711yescharacteristic
730C2×C4#654812yes—
731C2×C4D7×#4112yes—
732C2×C4C24×D711yescharacteristic
733C8—22no—
734C8—22no—
735C8—142no—
736C8—142no—
737C7C2×#332811yescharacteristic, complemented, Sylow
738C22—22no—
739C22—22no—
740C22—22no—
741C22—44no—
742C22—142no—
743C22—142no—
744C22—142no—
745C22—284no—
746C22#9030112yes—
747C22D7×#13712yes—
748C22#9047012yes—
749C22C22×D4×D711yescharacteristic
750C4—22no—
751C4—42no—
752C4—42no—
753C4—42no—
754C4—42no—
755C4—74no—
756C4—142no—
757C4—142no—
758C4—144no—
759C4—282no—
760C4—282no—
761C4—282no—
762C4#9030112yes—
763C4C2×#654811yescharacteristic
764C4C2×D7×#4111yescharacteristic
765C2—42no—
766C2—282no—
767C2#1173837214yesdirect product factor
768C2C2×#9030111yescharacteristic
769C2C2×D7×#13711yescharacteristic
770C2C2×#9047011yescharacteristic
subgroupG/H
centerC23C2×D4×D7
commutator, cosocleC2×C4×C7C25
FrattiniC2×C4C24×D7
FittingC2×C7×#470C2
socleC23×C7C22×D4
prime radicalC22×C22⋊D7D4
hypercenterC2×#470D7
hypocenterC7C2×#3328
LCSG ▷ C2×C4×C7 ▷ C2×C7 ▷ C7
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#470

Complements

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

NH ≅ G/Ntype
3. C2×C7×#470C2semidirect
4. C2×#89958C2semidirect
5. C2×#89954C2semidirect
6. C2×#89892C2semidirect
8. C2×#89822C2semidirect
9. C2×#89817C2semidirect
10. #11738372C2direct (N × H)
11. C2×#89626C2semidirect
12. C2×#89639C2semidirect
13. C2×#89588C2semidirect
14. C2×#89574C2semidirect
15. C2×#89564C2semidirect
16. C2×#89562C2semidirect
47. C7×#470C22semidirect
54. #89958C22semidirect
55. #89954C22semidirect
57. #89892C22semidirect
65. #89822C22semidirect
66. #89817C22semidirect
71. #89639C22semidirect
72. #89626C22semidirect
73. #89588C22semidirect
74. #89574C22semidirect
75. #89564C22semidirect
76. #89562C22semidirect
194. C2×#470D7semidirect
339. #470C2×D7semidirect
667. C2×C7#3328semidirect
737. C7C2×#3328semidirect
767. C2#11738372direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#903322
C2×#903232
C2×C7×#4702
C2×#899582
C2×#899542
C2×#898922
C2×#899002
C2×#898222
C2×#898172
#117383722
C2×#896262
C2×#896392
C2×#895882
C2×#895742
C2×#895642
C2×#895622
C2×#33287