Finite Group Databasebeta

← C2×#11740964 #14232359

Subgroups — C2×#11740964 #14232359

Order 1792.

2158 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×C7×#547C211yesmaximal, characteristic, complemented
2C2×#90256C211yesmaximal, characteristic, complemented
3#11740964C2116yesmaximal, direct product factor
4C2×#89856C211yesmaximal, characteristic, complemented
5C2×#89852C211yesmaximal, characteristic, complemented
6C2×#89811C211yesmaximal, characteristic, complemented
7C2×#89810C211yesmaximal, characteristic, complemented
8C2×#89806C211yesmaximal, characteristic, complemented
9C2×#89807C211yesmaximal, characteristic, complemented
10C2×#89783C211yesmaximal, characteristic, complemented
11C2×#89781C211yesmaximal, characteristic, complemented
12C2×#89786C211yesmaximal, characteristic, complemented
13C2×#89740C211yesmaximal, characteristic, complemented
14C2×#89739C211yesmaximal, characteristic, complemented
15C2×#89736C211yesmaximal, characteristic, complemented
16C22×#6382C211yesmaximal, characteristic, complemented
17C22×C7×#41—21no—
18C7×#547—24no—
19C7×#547C2218yescomplemented
20C2×C7×C4⋊Q8C2211yescharacteristic
21C2×C7×#123—21no—
22C2×C7×#123—21no—
23C2×C7×C22⋊Q8—21no—
24C2×C7×#121C2211yescharacteristic
25C2×C7×#121C2211yescharacteristic
26C2×C4×C7×D4C2211yescharacteristic
27C2×C4×C7×D4C2211yescharacteristic
28C22×C7×C4⋊C4C2211yescharacteristic
29C22×C7×C4⋊C4C2211yescharacteristic
30C2×#6502—21no—
31C22×#1141C2211yescharacteristic
32C2×#6493C2211yescharacteristic
33C2×#6493C2211yescharacteristic
34C2×#6489C2211yescharacteristic
35C22×C4⋊Dic7C2211yescharacteristic
36C22×#1136C2211yescharacteristic
37C23×C7⋊C8C2211yescharacteristic
38#90256—24no—
39#90256C2218yescomplemented
40C2×#6461—21no—
41C2×#6446—21no—
42C2×(C22⋊D7)⋊C4—21no—
43C2×C4×D28C2211yescharacteristic
44C2×#6433C2211yescharacteristic
45C2×#6406C2211yescharacteristic
46C2×#6406C2211yescharacteristic
47C2×#6406C2211yescharacteristic
48C2×C22⋊(C7⋊C8)C2211yescharacteristic
49C2×C22⋊(C7⋊C8)C2211yescharacteristic
50#89856C2218yescomplemented
51#89852C2218yescomplemented
52#89811C2218yescomplemented
53#89810C2218yescomplemented
54#89807C2218yescomplemented
55#89806C2218yescomplemented
56#89786C2218yescomplemented
57#89783C2218yescomplemented
58#89781C2218yescomplemented
59#89740C2218yescomplemented
60#89739C2218yescomplemented
61C2×#6383C2211yescharacteristic
62C2×#6383C2211yescharacteristic
63C2×#6383C2211yescharacteristic
64#89736C2218yescomplemented
65C2×#6382C2211yescharacteristic
66C2×#6382C2211yescharacteristic
67C2×#6382C2211yescharacteristic
68C2×#6382C2211yescharacteristic
69C2×#6382C2211yescharacteristic
70C2×#6382C2211yescharacteristic
71C2×#6382C2218yescomplemented
72C2×#6381C2211yescharacteristic
73C2×#6381C2211yescharacteristic
74C2×#6381C2211yescharacteristic
75C2×C4⋊(C7⋊C8)C2211yescharacteristic
76C2×#6377C2211yescharacteristic
77C2×#3345—71nomaximal, Sylow
78C2×C7×#41—28no—
79C2×C7×#41—48no—
80C22×C7×Q8—21no—
81C22×C7×D4—21no—
82C22×C7×D4—21no—
83C22×C7×D4D411yescharacteristic
84C22×C7×D4C2311yescharacteristic
85C23×C4×C7—21no—
86C23×C4×C7—21no—
87C23×C4×C7—21no—
88C23×C4×C7C2311yescharacteristic
89C23×C4×C7C2311yescharacteristic
90C22×C22⋊D7—21no—
91C22×C22⋊D7—21no—
92C23×Dic7—21no—
93C22×D28C2311yescharacteristic
94C22×C4×D7—21no—
95C7×C4⋊Q8—22no—
96C7×C4⋊Q8C2314yes—
97C7×#123—28no—
98C7×#123—28no—
99C7×C22⋊Q8—28no—
100C7×#121—22no—
101C7×#121—22no—
102C7×#121C2314yes—
103C7×#121C2314yes—
104C4×C7×D4—22no—
105C4×C7×D4D414yes—
106C4×C7×D4C2314yes—
107C4×C7×D4C2314yes—
108C2×C7×C4⋊C4—21no—
109C2×C7×C4⋊C4—21no—
110C2×C7×C4⋊C4—22no—
111C2×C7×C4⋊C4—22no—
112C2×C7×C4⋊C4—21no—
113C2×C7×C4⋊C4D411yescharacteristic
114C2×C7×C4⋊C4C2311yescharacteristic
115C2×C7×C4⋊C4C2311yescharacteristic
116C2×C7×C4⋊C4C2311yescharacteristic
117C2×C7×C4⋊C4C2314yes—
118C2×C7×C4⋊C4C2314yes—
119C2×C7×C22⋊C4—21no—
120C2×C7×C22⋊C4—21no—
121C2×C7×C22⋊C4—21no—
122C2×C7×C22⋊C4D411yescharacteristic
123C2×C7×C22⋊C4D411yescharacteristic
124C2×C42×C7C2311yescharacteristic
125C2×C22⋊Dic7—21no—
126#6502—28no—
127C2×#1141—24no—
128C2×#1141C2314yes—
129#6493—22no—
130#6493—22no—
131#6493C2314yes—
132#6493C2314yes—
133C2×(C2×D7)⋊C4—21no—
134C2×(C2×D7)⋊C4—21no—
135C2×(C2×D7)⋊C4—21no—
136#6489—22no—
137#6489C2314yes—
138C2×C4⋊Dic7—21no—
139C2×C4⋊Dic7—22no—
140C2×C4⋊Dic7C2311yescharacteristic
141C2×C4⋊Dic7C2311yescharacteristic
142C2×C4⋊Dic7C2311yescharacteristic
143C2×C4⋊Dic7C2314yes—
144C2×Dic7⋊C4—21no—
145C2×Dic7⋊C4—21no—
146C2×C4×Dic7—21no—
147C2×#1136—24no—
148C2×#1136C2314yes—
149C22×C7⋊C8—24no—
150C22×C7⋊C8C2311yescharacteristic
151C22×C7⋊C8C2311yescharacteristic
152C22×C7⋊C8C2311yescharacteristic
153C22×C7⋊C8C2314yes—
154C22×C7⋊C8C2311yescharacteristic
155#6461—28no—
156#6446—28no—
157(C22⋊D7)⋊C4—28no—
158C4×D28—22no—
159C4×D28C2314yes—
160#6433—22no—
161#6433C2314yes—
162#6406C2314yes—
163#6406C2314yes—
164#6406C2314yes—
165C22⋊(C7⋊C8)C2314yes—
166C22⋊(C7⋊C8)C2314yes—
167#6383C2314yes—
168#6383C2314yes—
169#6383C2314yes—
170#6382C2314yes—
171#6382C2314yes—
172#6382C2314yes—
173#6382C2314yes—
174#6382C2314yes—
175#6382C2314yes—
176#6381C2314yes—
177#6381C2314yes—
178#6381C2314yes—
179C4⋊(C7⋊C8)C2314yes—
180#6377C2314yes—
181C2×#553—71no—
182C2×#547D711yescharacteristic, complemented
183#3345—716no—
184C2×#501—71no—
185C2×#481—71no—
186C2×#481—71no—
187C2×#482—71no—
188C2×#480—71no—
189C2×#478—71no—
190C2×#476—71no—
191C2×#469—71no—
192C2×#466—71no—
193C2×#442—71no—
194C2×#435—71no—
195C2×#428—71no—
196C22×#106—71no—
197C24×C7—21no—
198C24×C7C2×D411yescharacteristic
199C24×C7C2×D411yescharacteristic
200C23×D7—21no—
201C7×#41—432no—
202C2×C7×Q8—24no—
203C2×C7×Q8—44no—
204C2×C7×D4—24no—
205C2×C7×D4—24no—
206C2×C7×D4—24no—
207C2×C7×D4—21no—
208C2×C7×D4—22no—
209C2×C7×D4—22no—
210C2×C7×D4—44no—
211C2×C7×D4—44no—
212C2×C7×D4C2×D414yes—
213C2×C7×D4C2412yes—
214C22×C4×C7—22no—
215C22×C4×C7—22no—
216C22×C4×C7—22no—
217C22×C4×C7—22no—
218C22×C4×C7—21no—
219C22×C4×C7—21no—
220C22×C4×C7—21no—
221C22×C4×C7—24no—
222C22×C4×C7—24no—
223C22×C4×C7—24no—
224C22×C4×C7—44no—
225C22×C4×C7—44no—
226C22×C4×C7—44no—
227C22×C4×C7C2×D411yescharacteristic
228C22×C4×C7C2×D411yescharacteristic
229C22×C4×C7C2×D411yescharacteristic
230C22×C4×C7C2×D411yescharacteristic
231C22×C4×C7C2×D412yes—
232C22×C4×C7C2×D412yes—
233C22×C4×C7C2412yes—
234C22×C4×C7C2412yes—
235C22×C4×C7C2411yescharacteristic
236C2×C22⋊D7—24no—
237C2×C22⋊D7—24no—
238C2×C22⋊D7—44no—
239C2×C22⋊D7—82no—
240C22×Dic7—21no—
241C22×Dic7—21no—
242C22×Dic7—21no—
243C22×Dic7—24no—
244C22×Dic7—82no—
245C2×D28—22no—
246C2×D28—22no—
247C2×D28—21no—
248C2×D28C2412yes—
249C2×C4×D7—24no—
250C2×C4×D7—82no—
251C7×C4⋊C4—21no—
252C7×C4⋊C4—21no—
253C7×C4⋊C4—21no—
254C7×C4⋊C4—24no—
255C7×C4⋊C4—24no—
256C7×C4⋊C4—24no—
257C7×C4⋊C4C2×D414yes—
258C7×C4⋊C4C2412yes—
259C7×C4⋊C4C2412yes—
260C7×C4⋊C4C2412yes—
261C7×C22⋊C4—24no—
262C7×C22⋊C4—24no—
263C7×C22⋊C4—24no—
264C7×C22⋊C4C2×D414yes—
265C7×C22⋊C4C2×D414yes—
266C42×C7C2×D412yes—
267C42×C7C2412yes—
268C22⋊Dic7—24no—
269#1141—28no—
270(C2×D7)⋊C4—24no—
271(C2×D7)⋊C4—24no—
272(C2×D7)⋊C4—24no—
273C4⋊Dic7—21no—
274C4⋊Dic7—21no—
275C4⋊Dic7—21no—
276C4⋊Dic7—24no—
277C4⋊Dic7C2412yes—
278C4⋊Dic7C2412yes—
279C4⋊Dic7C2412yes—
280Dic7⋊C4—24no—
281Dic7⋊C4—24no—
282C4×Dic7—24no—
283#1136—28no—
284C2×C7⋊C8—22no—
285C2×C7⋊C8—22no—
286C2×C7⋊C8—22no—
287C2×C7⋊C8—28no—
288C2×C7⋊C8#4114yescomplemented
289C2×C7⋊C8C2412yes—
290C2×C7⋊C8C2412yes—
291C2×C7⋊C8C2412yes—
292C2×C7⋊C8C2412yes—
293C22×#41—21no—
294C22×D8—71no—
295C22×M16—71no—
296C23×C8—71no—
297#553—78no—
298#553—144no—
299#547—24no—
300#547C2×D718yescomplemented
301C2×C4⋊Q8C2×D711yescharacteristic
302C2×#126—141no—
303C2×#125—71no—
304C2×#123—21no—
305C2×#123—21no—
306C2×#123—141no—
307C2×C22⋊Q8—21no—
308C2×#121—71no—
309C2×#121—71no—
310C2×#121—141no—
311C2×#121C2×D711yescharacteristic
312C2×#121C2×D711yescharacteristic
313C2×C4×D4—71no—
314C2×C4×D4—141no—
315C2×C4×D4C2×D711yescharacteristic
316C2×C4×D4C2×D711yescharacteristic
317C2×#117—71no—
318C22×C4⋊C4—71no—
319C22×C4⋊C4C2×D711yescharacteristic
320C22×C4⋊C4C2×D711yescharacteristic
321#501—78no—
322#482—78no—
323#481—78no—
324#481—78no—
325#480—78no—
326#478—78no—
327#476—78no—
328#469—78no—
329#466—78no—
330#442—78no—
331#435—78no—
332#428—78no—
333C2×#107—71no—
334C2×#107—71no—
335C2×#107—71no—
336C2×#106—71no—
337C2×#106—71no—
338C2×#106—71no—
339C2×#106—71no—
340C2×#106—78no—
341C2×#106—71no—
342C2×#106—71no—
343C2×C4⋊C8—71no—
344C2×#102—71no—
345C2×#102—71no—
346C2×#102—71no—
347C2×#102—71no—
348C2×#102—71no—
349C2×#102—71no—
350C2×C22⋊C8—71no—
351C2×C22⋊C8—71no—
352C2×#97—71no—
353C23×C7—22no—
354C23×C7—22no—
355C23×C7—22no—
356C23×C7—22no—
357C23×C7—22no—
358C23×C7—22no—
359C23×C7—42no—
360C23×C7—42no—
361C23×C7—42no—
362C23×C7AGL(1,ℤ/8)14yes—
363C23×C7C22×D412yes—
364C23×C7C22×D412yes—
365C23×C7C22×D411yescharacteristic
366C22×D7—22no—
367C22×D7—42no—
368C22×D7—42no—
369C22×D7—42no—
370C7×Q8—48no—
371C7×D4—28no—
372C7×D4—22no—
373C7×D4—22no—
374C7×D4—48no—
375C7×D4—48no—
376C7×D4—42no—
377C2×C4×C7—22no—
378C2×C4×C7—22no—
379C2×C4×C7—22no—
380C2×C4×C7—22no—
381C2×C4×C7—24no—
382C2×C4×C7—24no—
383C2×C4×C7—22no—
384C2×C4×C7—22no—
385C2×C4×C7—22no—
386C2×C4×C7—22no—
387C2×C4×C7—22no—
388C2×C4×C7—22no—
389C2×C4×C7—22no—
390C2×C4×C7—48no—
391C2×C4×C7—48no—
392C2×C4×C7—42no—
393C2×C4×C7—42no—
394C2×C4×C7—42no—
395C2×C4×C7—48no—
396C2×C4×C7C22×D412yes—
397C2×C4×C7C22×D412yes—
398C2×C4×C7C22×D412yes—
399C2×C4×C7C22×D412yes—
400C2×C4×C7C22×D411yescharacteristic
401C2×C4×C7C2×#4112yes—
402C2×C4×C72−1+412yes—
403C2×C4×C7C2511yescharacteristic
404C22⋊D7—48no—
405C22⋊D7—84no—
406C2×Dic7—22no—
407C2×Dic7—22no—
408C2×Dic7—22no—
409C2×Dic7—42no—
410C2×Dic7—42no—
411C2×Dic7—42no—
412C2×Dic7—84no—
413D28—22no—
414D28—22no—
415D28—42no—
416C4×D7—84no—
417C7⋊C8—22no—
418C7⋊C8—22no—
419C7⋊C8—22no—
420C7⋊C8C2×#4114yescomplemented
421C2×#41—28no—
422C2×#41—48no—
423C22×Q8—21no—
424C22×D4—21no—
425C22×D4—21no—
426C22×D4—71no—
427C22×D4—141no—
428C22×D4—141no—
429C22×D4C22⋊D711yescharacteristic
430C22×D4C22×D711yescharacteristic
431C23×C4—21no—
432C23×C4—21no—
433C23×C4—21no—
434C23×C4—141no—
435C23×C4—141no—
436C23×C4C22×D711yescharacteristic
437C23×C4C22×D711yescharacteristic
438C2×D8—74no—
439C2×D8—144no—
440C2×M16—74no—
441C2×M16—144no—
442C22×C8—71no—
443C22×C8—71no—
444C22×C8—74no—
445C22×C8—71no—
446C22×C8—71no—
447C22×C8—144no—
448C4⋊Q8—22no—
449C4⋊Q8C22×D714yes—
450#126—148no—
451#125—74no—
452#125—142no—
453#123—28no—
454#123—28no—
455#123—148no—
456C22⋊Q8—28no—
457#121—22no—
458#121—22no—
459#121—74no—
460#121—74no—
461#121—148no—
462#121—142no—
463#121—142no—
464#121C22×D714yes—
465#121C22×D714yes—
466C4×D4—22no—
467C4×D4—74no—
468C4×D4—148no—
469C4×D4—142no—
470C4×D4C22⋊D714yes—
471C4×D4C22×D714yes—
472C4×D4C22×D714yes—
473#117—74no—
474#117—142no—
475C2×C4⋊C4—21no—
476C2×C4⋊C4—21no—
477C2×C4⋊C4—22no—
478C2×C4⋊C4—22no—
479C2×C4⋊C4—21no—
480C2×C4⋊C4—71no—
481C2×C4⋊C4—71no—
482C2×C4⋊C4—74no—
483C2×C4⋊C4—71no—
484C2×C4⋊C4—141no—
485C2×C4⋊C4—142no—
486C2×C4⋊C4—141no—
487C2×C4⋊C4—141no—
488C2×C4⋊C4C22⋊D711yescharacteristic
489C2×C4⋊C4C22×D711yescharacteristic
490C2×C4⋊C4C22×D711yescharacteristic
491C2×C4⋊C4C22×D711yescharacteristic
492C2×C4⋊C4C22×D714yes—
493C2×C4⋊C4C22×D714yes—
494C2×C22⋊C4—21no—
495C2×C22⋊C4—21no—
496C2×C22⋊C4—21no—
497C2×C22⋊C4—141no—
498C2×C22⋊C4—141no—
499C2×C22⋊C4—141no—
500C2×C22⋊C4—141no—
501C2×C22⋊C4C22⋊D711yescharacteristic
502C2×C22⋊C4C22⋊D711yescharacteristic
503C2×C42—141no—
504C2×C42C22×D711yescharacteristic
505#107—74no—
506#107—74no—
507#107—74no—
508#106—74no—
509#106—74no—
510#106—74no—
511#106—74no—
512#106—74no—
513#106—74no—
514C4⋊C8—74no—
515#102—74no—
516#102—74no—
517#102—74no—
518#102—74no—
519#102—74no—
520#102—74no—
521C22⋊C8—74no—
522C22⋊C8—74no—
523#97—74no—
524C22×C7—28no—
525C22×C7—22no—
526C22×C7—22no—
527C22×C7—22no—
528C22×C7—22no—
529C22×C7—22no—
530C22×C7—44no—
531C22×C7—42no—
532C22×C7—42no—
533C22×C7—42no—
534C22×C7—84no—
535C22×C7#54712yes—
536C22×C7C2×AGL(1,ℤ/8)14yes—
537C22×C7C2×AGL(1,ℤ/8)12yes—
538C22×C7#57712yes—
539C22×C7C23×D411yescharacteristic
540C2×D7—42no—
541C2×D7—42no—
542C2×D7—42no—
543C2×D7—84no—
544C4×C7—22no—
545C4×C7—22no—
546C4×C7—22no—
547C4×C7—22no—
548C4×C7—42no—
549C4×C7—42no—
550C4×C7—42no—
551C4×C7#54712yes—
552C4×C7C22×#4111yescharacteristic
553C4×C7C2×2−1+411yescharacteristic
554Dic7—42no—
555Dic7—42no—
556Dic7—42no—
557C24—21no—
558C24—141no—
559C24C2×C22⋊D711yescharacteristic
560C24C2×C22⋊D711yescharacteristic
561#41—432no—
562C2×Q8—24no—
563C2×Q8—44no—
564C2×D4—24no—
565C2×D4—24no—
566C2×D4—24no—
567C2×D4—22no—
568C2×D4—22no—
569C2×D4—21no—
570C2×D4—44no—
571C2×D4—44no—
572C2×D4—72no—
573C2×D4—144no—
574C2×D4—144no—
575C2×D4—142no—
576C2×D4—142no—
577C2×D4—141no—
578C2×D4—284no—
579C2×D4—562no—
580C2×D4C2×C22⋊D714yes—
581C2×D4C23×D712yes—
582C22×C4—22no—
583C22×C4—22no—
584C22×C4—22no—
585C22×C4—22no—
586C22×C4—24no—
587C22×C4—24no—
588C22×C4—21no—
589C22×C4—21no—
590C22×C4—21no—
591C22×C4—24no—
592C22×C4—44no—
593C22×C4—44no—
594C22×C4—44no—
595C22×C4—141no—
596C22×C4—141no—
597C22×C4—141no—
598C22×C4—144no—
599C22×C4—144no—
600C22×C4—562no—
601C22×C4—562no—
602C22×C4C2×C22⋊D712yes—
603C22×C4C2×C22⋊D712yes—
604C22×C4C2×C22⋊D711yescharacteristic
605C22×C4C2×C22⋊D711yescharacteristic
606C22×C4C2×C22⋊D711yescharacteristic
607C22×C4C2×C22⋊D711yescharacteristic
608C22×C4C23×D712yes—
609C22×C4C23×D712yes—
610C22×C4C23×D711yescharacteristic
611D8—148no—
612M16—148no—
613C2×C8—74no—
614C2×C8—72no—
615C2×C8—72no—
616C2×C8—72no—
617C2×C8—72no—
618C2×C8—148no—
619C2×C8—142no—
620C2×C8—142no—
621C2×C8—142no—
622C4⋊C4—21no—
623C4⋊C4—21no—
624C4⋊C4—21no—
625C4⋊C4—24no—
626C4⋊C4—24no—
627C4⋊C4—24no—
628C4⋊C4—72no—
629C4⋊C4—72no—
630C4⋊C4—72no—
631C4⋊C4—144no—
632C4⋊C4—144no—
633C4⋊C4—141no—
634C4⋊C4—141no—
635C4⋊C4—144no—
636C4⋊C4—141no—
637C4⋊C4C2×C22⋊D714yes—
638C4⋊C4C23×D712yes—
639C4⋊C4C23×D712yes—
640C4⋊C4C23×D712yes—
641C22⋊C4—24no—
642C22⋊C4—24no—
643C22⋊C4—24no—
644C22⋊C4—144no—
645C22⋊C4—144no—
646C22⋊C4—144no—
647C22⋊C4—144no—
648C22⋊C4C2×C22⋊D714yes—
649C22⋊C4C2×C22⋊D714yes—
650C42—144no—
651C42C2×C22⋊D712yes—
652C42C23×D712yes—
653C2×C7—24no—
654C2×C7—42no—
655C2×C7—82no—
656C2×C7#334514yescomplemented
657C2×C7C2×#54711yescharacteristic
658C2×C7C22×AGL(1,ℤ/8)11yescharacteristic
659C2×C7C2×#57711yescharacteristic
660D7—82no—
661C23—22no—
662C23—22no—
663C23—22no—
664C23—22no—
665C23—22no—
666C23—22no—
667C23—42no—
668C23—42no—
669C23—42no—
670C23—142no—
671C23—282no—
672C23—282no—
673C23—282no—
674C23#649514yes—
675C23C22×C22⋊D712yes—
676C23C22×C22⋊D712yes—
677C23C22×C22⋊D711yescharacteristic
678Q8—48no—
679D4—28no—
680D4—22no—
681D4—22no—
682D4—48no—
683D4—48no—
684D4—42no—
685D4—142no—
686D4—142no—
687D4—288no—
688D4—282no—
689D4—564no—
690C2×C4—22no—
691C2×C4—22no—
692C2×C4—22no—
693C2×C4—22no—
694C2×C4—24no—
695C2×C4—24no—
696C2×C4—22no—
697C2×C4—22no—
698C2×C4—22no—
699C2×C4—22no—
700C2×C4—22no—
701C2×C4—22no—
702C2×C4—22no—
703C2×C4—48no—
704C2×C4—48no—
705C2×C4—42no—
706C2×C4—42no—
707C2×C4—42no—
708C2×C4—48no—
709C2×C4—142no—
710C2×C4—142no—
711C2×C4—142no—
712C2×C4—282no—
713C2×C4—282no—
714C2×C4—282no—
715C2×C4—564no—
716C2×C4—564no—
717C2×C4D7×#4112yes—
718C2×C4#655412yes—
719C2×C4C22×C22⋊D712yes—
720C2×C4C22×C22⋊D712yes—
721C2×C4C22×C22⋊D712yes—
722C2×C4C22×C22⋊D712yes—
723C2×C4C22×C22⋊D711yescharacteristic
724C2×C4C24×D711yescharacteristic
725C8—74no—
726C8—142no—
727C8—142no—
728C8—142no—
729C7C2×#334511yescharacteristic, complemented, Sylow
730C22—28no—
731C22—22no—
732C22—22no—
733C22—22no—
734C22—22no—
735C22—22no—
736C22—44no—
737C22—42no—
738C22—42no—
739C22—42no—
740C22—84no—
741C22—282no—
742C22—282no—
743C22—282no—
744C22—564no—
745C22C2×#649514yes—
746C22C2×#649512yes—
747C22#9051512yes—
748C22#9052812yes—
749C22C23×C22⋊D711yescharacteristic
750C4—22no—
751C4—22no—
752C4—22no—
753C4—22no—
754C4—42no—
755C4—42no—
756C4—42no—
757C4—282no—
758C4—282no—
759C4—282no—
760C4#9051512yes—
761C4C2×D7×#4111yescharacteristic
762C4C2×#655411yescharacteristic
763C2—24no—
764C2—42no—
765C2—82no—
766C2—562no—
767C2#1174096414yesdirect product factor
768C2C22×#649511yescharacteristic
769C2C2×#9051511yescharacteristic
770C2C2×#9052811yescharacteristic
subgroupG/H
centerC23C22×C22⋊D7
commutator, cosocleC2×C4×C7C25
FrattiniC2×C4C24×D7
FittingC2×C7×#547C2
socleC23×C7C22×D4
hypercenterC2×#547D7
hypocenterC7C2×#3345
LCSG ▷ C2×C4×C7 ▷ C2×C7 ▷ C7
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×#547

Complements

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

NH ≅ G/Ntype
1. C2×C7×#547C2semidirect
2. C2×#90256C2semidirect
3. #11740964C2direct (N × H)
4. C2×#89856C2semidirect
5. C2×#89852C2semidirect
6. C2×#89811C2semidirect
7. C2×#89810C2semidirect
8. C2×#89806C2semidirect
9. C2×#89807C2semidirect
10. C2×#89783C2semidirect
11. C2×#89781C2semidirect
12. C2×#89786C2semidirect
13. C2×#89740C2semidirect
14. C2×#89739C2semidirect
15. C2×#89736C2semidirect
16. C22×#6382C2semidirect
19. C7×#547C22semidirect
39. #90256C22semidirect
50. #89856C22semidirect
51. #89852C22semidirect
52. #89811C22semidirect
53. #89810C22semidirect
54. #89807C22semidirect
55. #89806C22semidirect
56. #89786C22semidirect
57. #89783C22semidirect
58. #89781C22semidirect
59. #89740C22semidirect
60. #89739C22semidirect
64. #89736C22semidirect
71. C2×#6382C22semidirect
182. C2×#547D7semidirect
288. C2×C7⋊C8#41semidirect
300. #547C2×D7semidirect
420. C7⋊C8C2×#41semidirect
656. C2×C7#3345semidirect
729. C7C2×#3345semidirect
767. C2#11740964direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C7×#5472
C2×#902562
#117409642
C2×#898562
C2×#898522
C2×#898112
C2×#898102
C2×#898062
C2×#898072
C2×#897832
C2×#897812
C2×#897862
C2×#897402
C2×#897392
C2×#897362
C22×#63822
C2×#33457