Finite Group Databasebeta

← #14226106

Subgroups — #14226106

Order 1792.

2036 conjugacy classes of subgroups.

The subgroup lattice has 750 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C7×#533C211yesmaximal, characteristic, complemented
2C2×#90168C211yesmaximal, characteristic
3#11740806C214yesmaximal, complemented
4#11740804C214yesmaximal, complemented
5#11740795C214yesmaximal, complemented
6#11740786C212yesmaximal, complemented
7#11740781C212yesmaximal, complemented
8#11740661C212yesmaximal, complemented
9#11740660C212yesmaximal, complemented
10#11740464C214yesmaximal, complemented
11#11739662C214yesmaximal, complemented
12#11739494C211yesmaximal, characteristic, complemented
13C22×#1157—21no—
14C7×#533—21no—
15C7×#533—21no—
16C7×#533—21no—
17C7×#533—21no—
18C7×#533C2212yes—
19C7×#533C2212yes—
20C7×#533C2212yescomplemented
21C7×#533C2212yescomplemented
22C2×C7×C4⋊Q8C2211yescharacteristic, complemented
23C2×C7×C4⋊Q8C2211yescharacteristic, complemented
24C2×C7×#125C2212yescomplemented
25C2×C7×C22⋊Q8—21no—
26C2×C7×C22⋊Q8—21no—
27C2×C4×C7×Q8—21no—
28C2×C4×C7×Q8—21no—
29C2×C7×#117C2212yes—
30C22×C42×C7C2211yescharacteristic
31C2×#6493—21no—
32C2×#6493C2212yes—
33#90168—21no—
34#90168—21no—
35#90168—21no—
36#90168—21no—
37#90168C2212yes—
38#90168C2212yes—
39#90168C2212yes—
40#90168C2212yes—
41C2×#6438—21no—
42C2×#6437C2211yescharacteristic
43C2×C4×D28—21no—
44C2×C4×D28C2212yes—
45C2×#6432C2211yescharacteristic
46#89979C2212yes—
47#89860C2214yescomplemented
48#89860C2214yescomplemented
49#89859C2218yescomplemented
50#89856C2218yescomplemented
51#89851C2214yescomplemented
52#89850C2214yescomplemented
53#89839C2218yescomplemented
54#89838C22116yescomplemented
55#89837C2218yescomplemented
56#89775C22116yescomplemented
57#89773C2218yes—
58#89767C2218yes—
59#89740C2218yescomplemented
60#89739C2218yescomplemented
61#89698C2212yescomplemented
62#89698C2212yescomplemented
63#89697C2212yescomplemented
64#89697C2212yescomplemented
65#89696C2212yes—
66C4×#1136C2212yes—
67#60864—71nomaximal, Sylow
68C22×C7×Q8—21no—
69C22×C7×Q8—21no—
70C23×C4×C7D411yescharacteristic
71C23×C4×C7D411yescharacteristic
72C23×C4×C7C2311yescharacteristic
73C22×C22⋊D7—22no—
74C2×#1157—22no—
75C2×#1157—22no—
76C2×#1157—22no—
77C2×#1157—22no—
78C2×#1157—48no—
79C22×D28—21no—
80C22×D28—21no—
81C22×D28C2312yes—
82C22×C4×D7—22no—
83C22×Dic14—21no—
84C7×C4⋊Q8—21no—
85C7×C4⋊Q8—21no—
86C7×C4⋊Q8—21no—
87C7×C4⋊Q8—21no—
88C7×C4⋊Q8C2312yes—
89C7×C4⋊Q8C2312yes—
90C7×C4⋊Q8C2312yes—
91C7×C4⋊Q8C2312yes—
92C7×#125—22no—
93C7×#125—22no—
94C7×#125C2314yes—
95C7×#125C2314yes—
96C7×C22⋊Q8—22no—
97C7×C22⋊Q8—22no—
98C7×C22⋊Q8—22no—
99C7×C22⋊Q8—22no—
100C7×C22⋊Q8—22no—
101C7×C22⋊Q8—22no—
102C7×C22⋊Q8—22no—
103C7×C22⋊Q8—22no—
104C4×C7×Q8—22no—
105C4×C7×Q8—22no—
106C4×C7×Q8—22no—
107C4×C7×Q8—22no—
108C4×C7×Q8—22no—
109C4×C7×Q8—22no—
110C4×C7×Q8—22no—
111C4×C7×Q8—22no—
112C7×#117—22no—
113C7×#117—22no—
114C7×#117C2314yes—
115C7×#117C2314yes—
116C2×C7×C4⋊C4—22no—
117C2×C7×C4⋊C4—22no—
118C2×C7×C4⋊C4—21no—
119C2×C7×C4⋊C4—21no—
120C2×C7×C4⋊C4C2312yes—
121C2×C7×C4⋊C4C2312yes—
122C2×C7×C22⋊C4—22no—
123C2×C42×C7—22no—
124C2×C42×C7D411yescharacteristic
125C2×C42×C7D411yescharacteristic
126C2×C42×C7D411yescharacteristic
127C2×C42×C7D411yescharacteristic
128C2×C42×C7D411yescharacteristic
129C2×C42×C7D411yescharacteristic
130C2×C42×C7C2311yescharacteristic
131C2×C42×C7C2311yescharacteristic
132C2×C42×C7C2311yescharacteristic
133C2×C42×C7C2311yescharacteristic
134C2×C42×C7C2311yescharacteristic
135C2×C42×C7C2311yescharacteristic
136#6493—22no—
137#6493—22no—
138#6493—22no—
139#6493—22no—
140#6493—22no—
141#6493—22no—
142#6493C2314yes—
143#6493C2314yes—
144C2×(C2×D7)⋊C4—22no—
145C2×(C2×D7)⋊C4—22no—
146C2×C4⋊Dic7—21no—
147C2×C4⋊Dic7C2312yes—
148C2×#1136C2314yes—
149#6438—22no—
150#6438—22no—
151#6438—22no—
152#6438—22no—
153#6437—21no—
154#6437—21no—
155#6437C2312yes—
156#6437C2312yes—
157C4×D28—22no—
158C4×D28—22no—
159C4×D28—22no—
160C4×D28—22no—
161C4×D28—22no—
162C4×D28—22no—
163C4×D28C2314yes—
164C4×D28C2314yes—
165#6432—21no—
166#6432—21no—
167#6432C2312yes—
168#6432C2312yes—
169C22⋊(C7⋊C8)C2314yes—
170C22⋊(C7⋊C8)C2314yes—
171#6383C23116yes—
172#6383C23116yes—
173#6382C23116yes—
174#6381C23116yes—
175C4⋊(C7⋊C8)C2314yes—
176C4⋊(C7⋊C8)C2314yes—
177#6377C2314yes—
178C4×C7⋊C8C2314yes—
179C2×#533D711yescharacteristic, complemented
180C2×#532—71no—
181#3235—74no—
182#3234—74no—
183#3228—74no—
184#3227—72no—
185#3226—72no—
186#3165—72no—
187#3138—72no—
188#3094—74no—
189#3077—74no—
190#2920—71no—
191C24×C7C2×D411yescharacteristic
192C23×D7—22no—
193C2×C7×Q8—22no—
194C2×C7×Q8—22no—
195C2×C7×Q8—22no—
196C2×C7×Q8—22no—
197C2×C7×Q8—44no—
198C2×C7×Q8—44no—
199C22×C4×C7—24no—
200C22×C4×C7—24no—
201C22×C4×C7—22no—
202C22×C4×C7—22no—
203C22×C4×C7—42no—
204C22×C4×C7C2×D411yescharacteristic
205C22×C4×C7C2×D411yescharacteristic
206C22×C4×C7C2×D411yescharacteristic
207C22×C4×C7C2×D411yescharacteristic
208C22×C4×C7C2×D411yescharacteristic
209C22×C4×C7C2×D411yescharacteristic
210C22×C4×C7C2×D411yescharacteristic
211C22×C4×C7C2×D411yescharacteristic
212C22×C4×C7C2×D411yescharacteristic
213C22×C4×C7C2×D411yescharacteristic
214C22×C4×C7C2×D411yescharacteristic
215C22×C4×C7C2×D411yescharacteristic
216C22×C4×C7C2×D411yescharacteristic
217C22×C4×C7C2×D411yescharacteristic
218C22×C4×C7C2×D411yescharacteristic
219C22×C4×C7C2411yescharacteristic
220C22×C4×C7C2411yescharacteristic
221C22×C4×C7C2411yescharacteristic
222C2×C22⋊D7—24no—
223C2×C22⋊D7—24no—
224C2×C22⋊D7—48no—
225C22×Dic7—22no—
226#1157—48no—
227#1157—48no—
228#1157—48no—
229#1157—48no—
230C2×D28—28no—
231C2×D28—22no—
232C2×D28—22no—
233C2×D28—22no—
234C2×D28—22no—
235C2×D28—22no—
236C2×D28—44no—
237C2×D28—44no—
238C2×D28C2414yes—
239C2×C4×D7—24no—
240C2×C4×D7—24no—
241C2×C4×D7—48no—
242C2×Dic14—22no—
243C2×Dic14—22no—
244C2×Dic14—44no—
245C7×C4⋊C4—24no—
246C7×C4⋊C4—24no—
247C7×C4⋊C4—24no—
248C7×C4⋊C4—24no—
249C7×C4⋊C4—22no—
250C7×C4⋊C4—22no—
251C7×C4⋊C4—22no—
252C7×C4⋊C4—22no—
253C7×C4⋊C4—22no—
254C7×C4⋊C4—22no—
255C7×C4⋊C4C2414yes—
256C7×C4⋊C4C2414yes—
257C7×C22⋊C4—24no—
258C7×C22⋊C4—24no—
259C42×C7—24no—
260C42×C7—24no—
261C42×C7C2×D411yescharacteristic
262C42×C7C2×D411yescharacteristic
263C42×C7C2×D411yescharacteristic
264C42×C7C2×D411yescharacteristic
265C42×C7C2×D411yescharacteristic
266C42×C7C2×D411yescharacteristic
267C42×C7C2×D411yescharacteristic
268C42×C7C2×D411yescharacteristic
269C42×C7C2×D411yescharacteristic
270C42×C7C2×D411yescharacteristic
271C42×C7C2×D411yescharacteristic
272C42×C7C2×D411yescharacteristic
273C42×C7C2411yescharacteristic
274C42×C7C2411yescharacteristic
275C42×C7C2411yescharacteristic
276C42×C7C2411yescharacteristic
277(C2×D7)⋊C4—24no—
278(C2×D7)⋊C4—24no—
279(C2×D7)⋊C4—24no—
280(C2×D7)⋊C4—24no—
281C4⋊Dic7—22no—
282C4⋊Dic7—22no—
283C4⋊Dic7—22no—
284C4⋊Dic7C2414yes—
285#1136—28no—
286C2×C7⋊C8C2418yes—
287C22×#41—141no—
288#533—21no—
289#533—21no—
290#533—21no—
291#533—21no—
292#533C2×D712yes—
293#533C2×D712yes—
294#533C2×D712yescomplemented
295#533C2×D712yescomplemented
296#532—72no—
297#532—72no—
298#532—72no—
299#532—72no—
300#532—141no—
301#532—141no—
302#532—141no—
303#532—141no—
304C2×C4⋊Q8—71no—
305C2×C4⋊Q8C2×D711yescharacteristic, complemented
306C2×C4⋊Q8C2×D711yescharacteristic, complemented
307C2×#127—71no—
308C2×#125C2×D712yescomplemented
309C2×#124—141no—
310C2×C22⋊Q8—21no—
311C2×C22⋊Q8—21no—
312C2×#121—72no—
313C2×#121—141no—
314C2×C4×Q8—21no—
315C2×C4×Q8—21no—
316C2×C4×D4—72no—
317C2×C4×D4—141no—
318C2×#117C2×D712yes—
319C22×C42C2×D711yescharacteristic
320#501—78no—
321#500—74no—
322#498—74no—
323#490—78no—
324#486—74no—
325#486—74no—
326#482—716no—
327#481—78no—
328#480—78no—
329#478—716no—
330#476—78no—
331#474—78no—
332#432—72no—
333#432—72no—
334#431—72no—
335#431—72no—
336#428—78no—
337#423—72no—
338#418—78no—
339#407—72no—
340C4×M16—72no—
341C23×C7—22no—
342C23×C7—22no—
343C23×C7—41no—
344C23×C7C22×D411yescharacteristic
345C23×C7C22×D411yescharacteristic
346C23×C7C22×D411yescharacteristic
347C22×D7—24no—
348C22×D7—44no—
349C22×D7—44no—
350C22×D7—44no—
351C7×Q8—44no—
352C7×Q8—44no—
353C7×Q8—44no—
354C7×Q8—44no—
355C2×C4×C7—22no—
356C2×C4×C7—22no—
357C2×C4×C7—22no—
358C2×C4×C7—22no—
359C2×C4×C7—22no—
360C2×C4×C7—22no—
361C2×C4×C7—22no—
362C2×C4×C7—22no—
363C2×C4×C7—22no—
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—41no—
371C2×C4×C7—41no—
372C2×C4×C7—41no—
373C2×C4×C7—44no—
374C2×C4×C7—44no—
375C2×C4×C7AGL(1,ℤ/8)14yes—
376C2×C4×C7C22×D411yescharacteristic
377C2×C4×C7C22×D411yescharacteristic
378C2×C4×C7C22×D411yescharacteristic
379C2×C4×C7C22×D411yescharacteristic
380C2×C4×C7C22×D411yescharacteristic
381C2×C4×C7C22×D411yescharacteristic
382C2×C4×C7C22×D411yescharacteristic
383C2×C4×C7C22×D411yescharacteristic
384C2×C4×C7C22×D411yescharacteristic
385C2×C4×C7C22×D411yescharacteristic
386C2×C4×C7C22×D411yescharacteristic
387C2×C4×C72−1+414yes—
388C2×C4×C7C2511yescharacteristic
389C22⋊D7—48no—
390C22⋊D7—48no—
391C2×Dic7—24no—
392C2×Dic7—44no—
393D28—28no—
394D28—44no—
395D28—44no—
396D28—44no—
397D28—44no—
398D28—44no—
399C4×D7—48no—
400C4×D7—48no—
401Dic14—44no—
402Dic14—44no—
403C7⋊C8—28no—
404C2×#41—142no—
405C2×#41—142no—
406C2×#41—142no—
407C2×#41—142no—
408C2×#41—288no—
409C22×Q8—21no—
410C22×Q8—21no—
411C22×Q8—141no—
412C22×D4—72no—
413C22×D4—142no—
414C22×D4—141no—
415C22×D4—141no—
416C23×C4—142no—
417C23×C4C22⋊D711yescharacteristic
418C23×C4C22⋊D711yescharacteristic
419C23×C4C22×D711yescharacteristic
420C2×M16—74no—
421C4⋊Q8—21no—
422C4⋊Q8—21no—
423C4⋊Q8—21no—
424C4⋊Q8—21no—
425C4⋊Q8—72no—
426C4⋊Q8—72no—
427C4⋊Q8—141no—
428C4⋊Q8—141no—
429C4⋊Q8C22×D712yes—
430C4⋊Q8C22×D712yes—
431C4⋊Q8C22×D712yes—
432C4⋊Q8C22×D712yes—
433#127—72no—
434#127—72no—
435#127—141no—
436#127—141no—
437#125—22no—
438#125—22no—
439#125C22×D714yes—
440#125C22×D714yes—
441#124—142no—
442#124—142no—
443#124—142no—
444#124—142no—
445C22⋊Q8—22no—
446C22⋊Q8—22no—
447C22⋊Q8—22no—
448C22⋊Q8—22no—
449C22⋊Q8—22no—
450C22⋊Q8—22no—
451C22⋊Q8—22no—
452C22⋊Q8—22no—
453#121—74no—
454#121—74no—
455#121—142no—
456#121—142no—
457#121—142no—
458#121—142no—
459#121—142no—
460#121—142no—
461C4×Q8—22no—
462C4×Q8—22no—
463C4×Q8—22no—
464C4×Q8—22no—
465C4×Q8—22no—
466C4×Q8—22no—
467C4×Q8—22no—
468C4×Q8—22no—
469C4×D4—74no—
470C4×D4—74no—
471C4×D4—142no—
472C4×D4—142no—
473C4×D4—142no—
474C4×D4—142no—
475C4×D4—142no—
476C4×D4—142no—
477#117—22no—
478#117—22no—
479#117C22×D714yes—
480#117C22×D714yes—
481C2×C4⋊C4—22no—
482C2×C4⋊C4—22no—
483C2×C4⋊C4—21no—
484C2×C4⋊C4—21no—
485C2×C4⋊C4—72no—
486C2×C4⋊C4—141no—
487C2×C4⋊C4C22×D712yes—
488C2×C4⋊C4C22×D712yes—
489C2×C22⋊C4—22no—
490C2×C22⋊C4—142no—
491C2×C22⋊C4—142no—
492C2×C42—22no—
493C2×C42C22⋊D711yescharacteristic
494C2×C42C22⋊D711yescharacteristic
495C2×C42C22⋊D711yescharacteristic
496C2×C42C22⋊D711yescharacteristic
497C2×C42C22⋊D711yescharacteristic
498C2×C42C22⋊D711yescharacteristic
499C2×C42C22×D711yescharacteristic
500C2×C42C22×D711yescharacteristic
501C2×C42C22×D711yescharacteristic
502C2×C42C22×D711yescharacteristic
503C2×C42C22×D711yescharacteristic
504C2×C42C22×D711yescharacteristic
505#107—716no—
506#106—716no—
507C4⋊C8—74no—
508C4⋊C8—74no—
509#102—716no—
510#102—716no—
511C22⋊C8—74no—
512C22⋊C8—74no—
513#97—74no—
514C4×C8—74no—
515C22×C7—21no—
516C22×C7—21no—
517C22×C7—21no—
518C22×C7—21no—
519C22×C7—21no—
520C22×C7—21no—
521C22×C7—21no—
522C22×C7—44no—
523C22×C7#53612yes—
524C22×C7C2×AGL(1,ℤ/8)12yes—
525C22×C7C23×D411yescharacteristic
526C2×D7—44no—
527C2×D7—44no—
528C2×D7—44no—
529C2×D7—88no—
530C4×C7—21no—
531C4×C7—21no—
532C4×C7—21no—
533C4×C7—21no—
534C4×C7—21no—
535C4×C7—21no—
536C4×C7—21no—
537C4×C7—44no—
538C4×C7—44no—
539C4×C7#53612yes—
540C4×C7C2×AGL(1,ℤ/8)12yes—
541C4×C7C2×AGL(1,ℤ/8)12yes—
542C4×C7#57512yes—
543C4×C7C2×2−1+412yes—
544Dic7—44no—
545C24—142no—
546C24C2×C22⋊D711yescharacteristic
547#41—288no—
548#41—288no—
549#41—288no—
550#41—288no—
551C2×Q8—22no—
552C2×Q8—22no—
553C2×Q8—22no—
554C2×Q8—22no—
555C2×Q8—44no—
556C2×Q8—44no—
557C2×Q8—142no—
558C2×Q8—142no—
559C2×Q8—284no—
560C2×D4—74no—
561C2×D4—144no—
562C2×D4—144no—
563C2×D4—148no—
564C2×D4—142no—
565C2×D4—142no—
566C2×D4—142no—
567C2×D4—142no—
568C2×D4—142no—
569C2×D4—284no—
570C2×D4—284no—
571C2×D4—288no—
572C22×C4—24no—
573C22×C4—24no—
574C22×C4—22no—
575C22×C4—22no—
576C22×C4—42no—
577C22×C4—142no—
578C22×C4—144no—
579C22×C4—144no—
580C22×C4—288no—
581C22×C4C2×C22⋊D711yescharacteristic
582C22×C4C2×C22⋊D711yescharacteristic
583C22×C4C2×C22⋊D711yescharacteristic
584C22×C4C2×C22⋊D711yescharacteristic
585C22×C4C2×C22⋊D711yescharacteristic
586C22×C4C2×C22⋊D711yescharacteristic
587C22×C4C2×C22⋊D711yescharacteristic
588C22×C4C2×C22⋊D711yescharacteristic
589C22×C4C2×C22⋊D711yescharacteristic
590C22×C4C2×C22⋊D711yescharacteristic
591C22×C4C2×C22⋊D711yescharacteristic
592C22×C4C2×C22⋊D711yescharacteristic
593C22×C4C2×C22⋊D711yescharacteristic
594C22×C4C2×C22⋊D711yescharacteristic
595C22×C4C2×C22⋊D711yescharacteristic
596C22×C4C23×D711yescharacteristic
597C22×C4C23×D711yescharacteristic
598C22×C4C23×D711yescharacteristic
599M16—148no—
600C2×C8—78no—
601C4⋊C4—24no—
602C4⋊C4—24no—
603C4⋊C4—24no—
604C4⋊C4—24no—
605C4⋊C4—22no—
606C4⋊C4—22no—
607C4⋊C4—22no—
608C4⋊C4—22no—
609C4⋊C4—22no—
610C4⋊C4—22no—
611C4⋊C4—74no—
612C4⋊C4—142no—
613C4⋊C4—142no—
614C4⋊C4—142no—
615C4⋊C4C23×D714yes—
616C4⋊C4C23×D714yes—
617C22⋊C4—24no—
618C22⋊C4—24no—
619C22⋊C4—144no—
620C22⋊C4—144no—
621C22⋊C4—144no—
622C22⋊C4—144no—
623C42—24no—
624C42—24no—
625C42C2×C22⋊D711yescharacteristic
626C42C2×C22⋊D711yescharacteristic
627C42C2×C22⋊D711yescharacteristic
628C42C2×C22⋊D711yescharacteristic
629C42C2×C22⋊D711yescharacteristic
630C42C2×C22⋊D711yescharacteristic
631C42C2×C22⋊D711yescharacteristic
632C42C2×C22⋊D711yescharacteristic
633C42C2×C22⋊D711yescharacteristic
634C42C2×C22⋊D711yescharacteristic
635C42C2×C22⋊D711yescharacteristic
636C42C2×C22⋊D711yescharacteristic
637C42C23×D711yescharacteristic
638C42C23×D711yescharacteristic
639C42C23×D711yescharacteristic
640C42C23×D711yescharacteristic
641C2×C7—22no—
642C2×C7—22no—
643C2×C7—41no—
644C2×C7C2×#53611yescharacteristic
645C2×C7C22×AGL(1,ℤ/8)11yescharacteristic
646C2×C7C2×#57511yescharacteristic
647D7—84no—
648C23—22no—
649C23—22no—
650C23—41no—
651C23—144no—
652C23—284no—
653C23—284no—
654C23—284no—
655C23C22×C22⋊D711yescharacteristic
656C23C22×C22⋊D711yescharacteristic
657C23C22×C22⋊D711yescharacteristic
658Q8—44no—
659Q8—44no—
660Q8—44no—
661Q8—44no—
662Q8—284no—
663Q8—284no—
664D4—148no—
665D4—284no—
666D4—284no—
667D4—288no—
668D4—288no—
669D4—284no—
670D4—284no—
671D4—284no—
672C2×C4—22no—
673C2×C4—22no—
674C2×C4—22no—
675C2×C4—22no—
676C2×C4—22no—
677C2×C4—22no—
678C2×C4—22no—
679C2×C4—22no—
680C2×C4—22no—
681C2×C4—22no—
682C2×C4—22no—
683C2×C4—22no—
684C2×C4—22no—
685C2×C4—24no—
686C2×C4—24no—
687C2×C4—41no—
688C2×C4—41no—
689C2×C4—41no—
690C2×C4—44no—
691C2×C4—44no—
692C2×C4—144no—
693C2×C4—288no—
694C2×C4—284no—
695C2×C4—288no—
696C2×C4#651214yes—
697C2×C4#655114yes—
698C2×C4C22×C22⋊D711yescharacteristic
699C2×C4C22×C22⋊D711yescharacteristic
700C2×C4C22×C22⋊D711yescharacteristic
701C2×C4C22×C22⋊D711yescharacteristic
702C2×C4C22×C22⋊D711yescharacteristic
703C2×C4C22×C22⋊D711yescharacteristic
704C2×C4C22×C22⋊D711yescharacteristic
705C2×C4C22×C22⋊D711yescharacteristic
706C2×C4C22×C22⋊D711yescharacteristic
707C2×C4C22×C22⋊D711yescharacteristic
708C2×C4C22×C22⋊D711yescharacteristic
709C2×C4C24×D711yescharacteristic
710C8—148no—
711C7#6086411yescharacteristic, complemented, Sylow
712C22—21no—
713C22—21no—
714C22—21no—
715C22—21no—
716C22—21no—
717C22—21no—
718C22—21no—
719C22—44no—
720C22—284no—
721C22—284no—
722C22—284no—
723C22—568no—
724C22#9050712yes—
725C22C2×#651212yes—
726C22C23×C22⋊D711yescharacteristic
727C4—21no—
728C4—21no—
729C4—21no—
730C4—21no—
731C4—21no—
732C4—21no—
733C4—21no—
734C4—44no—
735C4—44no—
736C4—284no—
737C4#9050712yes—
738C4C2×#651212yes—
739C4C2×#651212yes—
740C4#9051312yes—
741C4C2×#655112yes—
742C2—22no—
743C2—22no—
744C2—41no—
745C2—564no—
746C2C2×#9050711yescharacteristic
747C2C22×#651211yescharacteristic
748C2C2×#9051311yescharacteristic
subgroupG/H
centerC22C23×C22⋊D7
commutator, cosocleC2×C4×C7C25
FrattiniC2×C4C24×D7
FittingC2×C7×#533C2
socleC22×C7C23×D4
prime radicalC2×#90168C2
hypercenterC2×#533D7
hypocenterC7#60864
LCSG ▷ C2×C4×C7 ▷ C2×C7 ▷ C7
UCSC1 ◁ C22 ◁ C22×C42 ◁ C2×#533

Complements

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

NH ≅ G/Ntype
1. C2×C7×#533C2semidirect
3. #11740806C2semidirect
4. #11740804C2semidirect
5. #11740795C2semidirect
6. #11740786C2semidirect
7. #11740781C2semidirect
8. #11740661C2semidirect
9. #11740660C2semidirect
10. #11740464C2semidirect
11. #11739662C2semidirect
12. #11739494C2semidirect
20. C7×#533C22semidirect
21. C7×#533C22semidirect
22. C2×C7×C4⋊Q8C22semidirect
23. C2×C7×C4⋊Q8C22semidirect
24. C2×C7×#125C22semidirect
47. #89860C22semidirect
48. #89860C22semidirect
49. #89859C22semidirect
50. #89856C22semidirect
51. #89851C22semidirect
52. #89850C22semidirect
53. #89839C22semidirect
54. #89838C22semidirect
55. #89837C22semidirect
56. #89775C22semidirect
59. #89740C22semidirect
60. #89739C22semidirect
61. #89698C22semidirect
62. #89698C22semidirect
63. #89697C22semidirect
64. #89697C22semidirect
179. C2×#533D7semidirect
294. #533C2×D7semidirect
295. #533C2×D7semidirect
305. C2×C4⋊Q8C2×D7semidirect
306. C2×C4⋊Q8C2×D7semidirect
308. C2×#125C2×D7semidirect
711. C7#60864semidirect

Maximal subgroups

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

subgroupindex
C2×C7×#5332
C2×#901682
#117408062
#117408042
#117407952
#117407862
#117407812
#117406612
#117406602
#117404642
#117396622
#117394942
#608647