Finite Group Databasebeta

← #14226130

Subgroups — #14226130

Order 1792.

1788 conjugacy classes of subgroups.

The subgroup lattice has 828 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C7×#533C211yesmaximal, characteristic, complemented
2C2×#90170C211yesmaximal, characteristic
3#11740812C212yesmaximal, complemented
4#11740807C214yesmaximal, complemented
5#11740805C214yesmaximal, complemented
6#11740795C212yesmaximal, complemented
7#11740787C212yesmaximal, complemented
8#11740783C212yesmaximal, complemented
9#11740663C212yesmaximal, complemented
10#11740662C212yesmaximal, complemented
11#11740463C214yesmaximal, complemented
12#11739665C212yesmaximal, complemented
13#11739662C212yesmaximal
14#11739494C211yesmaximal, characteristic, complemented
15C7×#533—21no—
16C7×#533—21no—
17C7×#533—21no—
18C7×#533—21no—
19C7×#533C2212yes—
20C7×#533C2212yes—
21C7×#533C2212yescomplemented
22C7×#533C2212yescomplemented
23C2×C7×C4⋊Q8C2211yescharacteristic, complemented
24C2×C7×C4⋊Q8C2211yescharacteristic, complemented
25C2×C7×#125C2212yescomplemented
26C2×C7×C22⋊Q8—21no—
27C2×C7×C22⋊Q8—21no—
28C2×C4×C7×Q8—21no—
29C2×C4×C7×Q8—21no—
30C2×C7×#117C2212yes—
31C22×C42×C7C2211yescharacteristic
32C2×#6493C2211yescharacteristic
33C2×#6492—21no—
34C2×C4×C22⋊D7—21no—
35C2×#6487C2211yescharacteristic
36#90170—21no—
37#90170—21no—
38#90170—21no—
39#90170—21no—
40#90170C2212yes—
41#90170C2212yes—
42#90170C2212yes—
43#90170C2212yes—
44C2×#6439—21no—
45C2×#6438C2211yescharacteristic
46C2×C4×D28C2211yescharacteristic
47C2×#6435—21no—
48C2×#6433C2211yescharacteristic
49C2×C4×Dic14C2211yescharacteristic
50#89979C2212yes—
51#89866C2214yescomplemented
52#89863C2214yescomplemented
53#89861C2214yescomplemented
54#89861C2214yescomplemented
55#89859C2214yescomplemented
56#89856C2214yescomplemented
57#89852C2214yescomplemented
58#89852C2214yescomplemented
59#89840C2218yescomplemented
60#89838C2218yescomplemented
61#89836C2218yescomplemented
62#89835C2218yescomplemented
63#89776C2214yes—
64#89775C2218yes—
65#89773C2214yes—
66#89768C2218yescomplemented
67#89767C2214yes—
68#89767C2214yes—
69#89743C2214yescomplemented
70#89742C2214yescomplemented
71#89740C2214yes—
72#89739C2214yes—
73#89698C2212yescomplemented
74#89698C2212yescomplemented
75#89697C2212yescomplemented
76#89697C2212yescomplemented
77#89696C2212yes—
78C4×#1136C2212yes—
79#60866—71nomaximal, Sylow
80C22×C7×Q8—21no—
81C22×C7×Q8—21no—
82C23×C4×C7D411yescharacteristic
83C23×C4×C7D411yescharacteristic
84C23×C4×C7C2311yescharacteristic
85C22×C22⋊D7—21no—
86C22×D28C2311yescharacteristic
87C22×C4×D7—21no—
88C22×Dic14C2311yescharacteristic
89C7×C4⋊Q8—21no—
90C7×C4⋊Q8—21no—
91C7×C4⋊Q8—21no—
92C7×C4⋊Q8—21no—
93C7×C4⋊Q8C2312yes—
94C7×C4⋊Q8C2312yes—
95C7×C4⋊Q8C2312yes—
96C7×C4⋊Q8C2312yes—
97C7×#125—22no—
98C7×#125—22no—
99C7×#125C2314yes—
100C7×#125C2314yes—
101C7×C22⋊Q8—22no—
102C7×C22⋊Q8—22no—
103C7×C22⋊Q8—22no—
104C7×C22⋊Q8—22no—
105C7×C22⋊Q8—22no—
106C7×C22⋊Q8—22no—
107C7×C22⋊Q8—22no—
108C7×C22⋊Q8—22no—
109C4×C7×Q8—22no—
110C4×C7×Q8—22no—
111C4×C7×Q8—22no—
112C4×C7×Q8—22no—
113C4×C7×Q8—22no—
114C4×C7×Q8—22no—
115C4×C7×Q8—22no—
116C4×C7×Q8—22no—
117C7×#117—22no—
118C7×#117—22no—
119C7×#117C2314yes—
120C7×#117C2314yes—
121C2×C7×C4⋊C4—22no—
122C2×C7×C4⋊C4—22no—
123C2×C7×C4⋊C4—21no—
124C2×C7×C4⋊C4—21no—
125C2×C7×C4⋊C4C2312yes—
126C2×C7×C4⋊C4C2312yes—
127C2×C7×C22⋊C4—22no—
128C2×C42×C7—22no—
129C2×C42×C7D411yescharacteristic
130C2×C42×C7D411yescharacteristic
131C2×C42×C7D411yescharacteristic
132C2×C42×C7D411yescharacteristic
133C2×C42×C7D411yescharacteristic
134C2×C42×C7D411yescharacteristic
135C2×C42×C7C2311yescharacteristic
136C2×C42×C7C2311yescharacteristic
137C2×C42×C7C2311yescharacteristic
138C2×C42×C7C2311yescharacteristic
139C2×C42×C7C2311yescharacteristic
140C2×C42×C7C2311yescharacteristic
141C2×C22⋊Dic7—21no—
142#6493—21no—
143#6493—21no—
144#6493C2312yes—
145#6493C2312yes—
146#6492—22no—
147#6492—22no—
148#6492—22no—
149#6492—22no—
150C4×C22⋊D7—22no—
151C4×C22⋊D7—22no—
152C4×C22⋊D7—22no—
153C4×C22⋊D7—22no—
154C2×(C2×D7)⋊C4—21no—
155C2×(C2×D7)⋊C4—21no—
156C2×(C2×D7)⋊C4—21no—
157C2×(C2×D7)⋊C4—21no—
158C2×C4⋊Dic7C2311yescharacteristic
159C2×C4⋊Dic7C2311yescharacteristic
160#6487—21no—
161#6487—21no—
162#6487C2312yes—
163#6487C2312yes—
164C2×Dic7⋊C4—21no—
165C2×Dic7⋊C4—21no—
166C2×Dic7⋊C4—21no—
167C2×Dic7⋊C4—21no—
168C2×C4×Dic7—21no—
169C2×#1136C2314yes—
170#6439—22no—
171#6439—22no—
172#6439—22no—
173#6439—22no—
174#6438—21no—
175#6438—21no—
176#6438C2312yes—
177#6438C2312yes—
178C4×D28—21no—
179C4×D28—21no—
180C4×D28C2312yes—
181C4×D28C2312yes—
182#6435—22no—
183#6435—22no—
184#6435—22no—
185#6435—22no—
186#6433—21no—
187#6433—21no—
188#6433C2312yes—
189#6433C2312yes—
190C4×Dic14—21no—
191C4×Dic14—21no—
192C4×Dic14C2312yes—
193C4×Dic14C2312yes—
194C22⋊(C7⋊C8)C2314yes—
195C22⋊(C7⋊C8)C2314yes—
196#6384C2318yes—
197#6384C2318yes—
198#6383C2318yes—
199#6383C2318yes—
200#6382C2318yes—
201#6382C2318yes—
202#6381C2318yes—
203#6381C2318yes—
204C4⋊(C7⋊C8)C2314yes—
205C4⋊(C7⋊C8)C2314yes—
206#6377C2314yes—
207C4×C7⋊C8C2314yes—
208C2×#533D711yescharacteristic, complemented
209C2×#529—71no—
210#3240—74no—
211#3239—72no—
212#3238—72no—
213#3233—74no—
214#3232—74no—
215#3166—72no—
216#3140—72no—
217#3095—72no—
218#3094—72no—
219#3078—72no—
220#3077—72no—
221#2920—71no—
222C24×C7C2×D411yescharacteristic
223C23×D7—21no—
224C2×C7×Q8—22no—
225C2×C7×Q8—22no—
226C2×C7×Q8—22no—
227C2×C7×Q8—22no—
228C2×C7×Q8—44no—
229C2×C7×Q8—44no—
230C22×C4×C7—24no—
231C22×C4×C7—22no—
232C22×C4×C7—22no—
233C22×C4×C7—42no—
234C22×C4×C7—42no—
235C22×C4×C7C2×D411yescharacteristic
236C22×C4×C7C2×D411yescharacteristic
237C22×C4×C7C2×D411yescharacteristic
238C22×C4×C7C2×D411yescharacteristic
239C22×C4×C7C2×D411yescharacteristic
240C22×C4×C7C2×D411yescharacteristic
241C22×C4×C7C2×D411yescharacteristic
242C22×C4×C7C2×D411yescharacteristic
243C22×C4×C7C2×D411yescharacteristic
244C22×C4×C7C2×D411yescharacteristic
245C22×C4×C7C2×D411yescharacteristic
246C22×C4×C7C2×D411yescharacteristic
247C22×C4×C7C2×D411yescharacteristic
248C22×C4×C7C2×D411yescharacteristic
249C22×C4×C7C2×D411yescharacteristic
250C22×C4×C7C2411yescharacteristic
251C22×C4×C7C2411yescharacteristic
252C22×C4×C7C2411yescharacteristic
253C2×C22⋊D7—22no—
254C2×C22⋊D7—22no—
255C2×C22⋊D7—44no—
256C22×Dic7—21no—
257C22×Dic7—21no—
258C22×Dic7—21no—
259C2×D28—24no—
260C2×D28—21no—
261C2×D28C2412yes—
262C2×C4×D7—22no—
263C2×C4×D7—22no—
264C2×C4×D7—44no—
265C2×Dic14—24no—
266C2×Dic14—21no—
267C2×Dic14C2412yes—
268C7×C4⋊C4—24no—
269C7×C4⋊C4—24no—
270C7×C4⋊C4—24no—
271C7×C4⋊C4—24no—
272C7×C4⋊C4—22no—
273C7×C4⋊C4—22no—
274C7×C4⋊C4—22no—
275C7×C4⋊C4—22no—
276C7×C4⋊C4—22no—
277C7×C4⋊C4—22no—
278C7×C4⋊C4C2414yes—
279C7×C4⋊C4C2414yes—
280C7×C22⋊C4—24no—
281C7×C22⋊C4—24no—
282C42×C7—24no—
283C42×C7—24no—
284C42×C7C2×D411yescharacteristic
285C42×C7C2×D411yescharacteristic
286C42×C7C2×D411yescharacteristic
287C42×C7C2×D411yescharacteristic
288C42×C7C2×D411yescharacteristic
289C42×C7C2×D411yescharacteristic
290C42×C7C2×D411yescharacteristic
291C42×C7C2×D411yescharacteristic
292C42×C7C2×D411yescharacteristic
293C42×C7C2×D411yescharacteristic
294C42×C7C2×D411yescharacteristic
295C42×C7C2×D411yescharacteristic
296C42×C7C2411yescharacteristic
297C42×C7C2411yescharacteristic
298C42×C7C2411yescharacteristic
299C42×C7C2411yescharacteristic
300C22⋊Dic7—22no—
301C22⋊Dic7—22no—
302(C2×D7)⋊C4—22no—
303(C2×D7)⋊C4—22no—
304(C2×D7)⋊C4—22no—
305(C2×D7)⋊C4—22no—
306(C2×D7)⋊C4—22no—
307(C2×D7)⋊C4—22no—
308(C2×D7)⋊C4—22no—
309(C2×D7)⋊C4—22no—
310C4⋊Dic7—21no—
311C4⋊Dic7—21no—
312C4⋊Dic7C2412yes—
313C4⋊Dic7C2412yes—
314Dic7⋊C4—22no—
315Dic7⋊C4—22no—
316Dic7⋊C4—22no—
317Dic7⋊C4—22no—
318Dic7⋊C4—22no—
319Dic7⋊C4—22no—
320Dic7⋊C4—22no—
321Dic7⋊C4—22no—
322C4×Dic7—22no—
323C4×Dic7—22no—
324#1136—28no—
325C2×C7⋊C8C2418yes—
326#533—21no—
327#533—21no—
328#533—21no—
329#533—21no—
330#533C2×D712yes—
331#533C2×D712yes—
332#533C2×D712yescomplemented
333#533C2×D712yescomplemented
334C2×C4⋊Q8C2×D711yescharacteristic, complemented
335C2×C4⋊Q8C2×D711yescharacteristic, complemented
336#529—72no—
337#529—72no—
338#529—72no—
339#529—72no—
340#529—141no—
341#529—141no—
342#529—141no—
343#529—141no—
344C2×#126—141no—
345C2×#125—71no—
346C2×#125C2×D712yescomplemented
347C2×#124—71no—
348C2×#123—141no—
349C2×C22⋊Q8—21no—
350C2×C22⋊Q8—21no—
351C2×C22⋊Q8—71no—
352C2×#121—71no—
353C2×C4×Q8—21no—
354C2×C4×Q8—21no—
355C2×C4×Q8—71no—
356C2×C4×D4—71no—
357C2×C4×D4—141no—
358C2×#117—141no—
359C2×#117C2×D712yes—
360C22×C42C2×D711yescharacteristic
361#501—74no—
362#501—74no—
363#499—78no—
364#489—74no—
365#489—74no—
366#488—78no—
367#485—78no—
368#484—74no—
369#483—74no—
370#482—78no—
371#481—74no—
372#480—74no—
373#479—78no—
374#478—78no—
375#477—74no—
376#476—74no—
377#475—74no—
378#474—74no—
379#432—72no—
380#432—72no—
381#431—72no—
382#431—72no—
383#428—74no—
384#428—74no—
385#423—72no—
386#419—74no—
387#418—74no—
388#407—72no—
389C4×M16—72no—
390C23×C7—22no—
391C23×C7—22no—
392C23×C7—41no—
393C23×C7C22×D411yescharacteristic
394C23×C7C22×D411yescharacteristic
395C23×C7C22×D411yescharacteristic
396C22×D7—22no—
397C22×D7—42no—
398C22×D7—42no—
399C22×D7—42no—
400C7×Q8—44no—
401C7×Q8—44no—
402C7×Q8—44no—
403C7×Q8—44no—
404C2×C4×C7—22no—
405C2×C4×C7—22no—
406C2×C4×C7—22no—
407C2×C4×C7—22no—
408C2×C4×C7—22no—
409C2×C4×C7—22no—
410C2×C4×C7—22no—
411C2×C4×C7—22no—
412C2×C4×C7—22no—
413C2×C4×C7—22no—
414C2×C4×C7—24no—
415C2×C4×C7—24no—
416C2×C4×C7—41no—
417C2×C4×C7—41no—
418C2×C4×C7—41no—
419C2×C4×C7—41no—
420C2×C4×C7—41no—
421C2×C4×C7—41no—
422C2×C4×C7—41no—
423C2×C4×C7—44no—
424C2×C4×C7—44no—
425C2×C4×C7C22×D411yescharacteristic
426C2×C4×C7C22×D411yescharacteristic
427C2×C4×C7C22×D411yescharacteristic
428C2×C4×C7C22×D411yescharacteristic
429C2×C4×C7C22×D411yescharacteristic
430C2×C4×C7C22×D411yescharacteristic
431C2×C4×C7C22×D411yescharacteristic
432C2×C4×C7C22×D411yescharacteristic
433C2×C4×C7C22×D411yescharacteristic
434C2×C4×C7C22×D411yescharacteristic
435C2×C4×C7C22×D411yescharacteristic
436C2×C4×C72−1+414yes—
437C2×C4×C7C2511yescharacteristic
438C22⋊D7—44no—
439C22⋊D7—44no—
440C2×Dic7—22no—
441C2×Dic7—22no—
442C2×Dic7—22no—
443C2×Dic7—42no—
444C2×Dic7—42no—
445C2×Dic7—42no—
446D28—24no—
447D28—42no—
448C4×D7—44no—
449C4×D7—44no—
450Dic14—24no—
451Dic14—42no—
452C7⋊C8—28no—
453C22×Q8—21no—
454C22×Q8—21no—
455C22×Q8—71no—
456C22×D4—71no—
457C22×D4—141no—
458C23×C4—141no—
459C23×C4C22⋊D711yescharacteristic
460C23×C4C22⋊D711yescharacteristic
461C23×C4C22×D711yescharacteristic
462C2×M16—74no—
463C4⋊Q8—21no—
464C4⋊Q8—21no—
465C4⋊Q8—21no—
466C4⋊Q8—21no—
467C4⋊Q8C22×D712yes—
468C4⋊Q8C22×D712yes—
469C4⋊Q8C22×D712yes—
470C4⋊Q8C22×D712yes—
471#126—142no—
472#126—142no—
473#126—142no—
474#126—142no—
475#125—22no—
476#125—22no—
477#125—72no—
478#125—72no—
479#125—141no—
480#125—141no—
481#125C22×D714yes—
482#125C22×D714yes—
483#124—72no—
484#124—72no—
485#124—141no—
486#124—141no—
487#123—142no—
488#123—142no—
489#123—142no—
490#123—142no—
491C22⋊Q8—22no—
492C22⋊Q8—22no—
493C22⋊Q8—22no—
494C22⋊Q8—22no—
495C22⋊Q8—22no—
496C22⋊Q8—22no—
497C22⋊Q8—22no—
498C22⋊Q8—22no—
499C22⋊Q8—72no—
500C22⋊Q8—72no—
501C22⋊Q8—141no—
502C22⋊Q8—141no—
503#121—72no—
504#121—72no—
505#121—141no—
506#121—141no—
507C4×Q8—22no—
508C4×Q8—22no—
509C4×Q8—22no—
510C4×Q8—22no—
511C4×Q8—22no—
512C4×Q8—22no—
513C4×Q8—22no—
514C4×Q8—22no—
515C4×Q8—72no—
516C4×Q8—72no—
517C4×Q8—141no—
518C4×Q8—141no—
519C4×D4—72no—
520C4×D4—72no—
521C4×D4—142no—
522C4×D4—142no—
523C4×D4—142no—
524C4×D4—142no—
525C4×D4—141no—
526C4×D4—141no—
527#117—22no—
528#117—22no—
529#117—142no—
530#117—142no—
531#117—142no—
532#117—142no—
533#117C22×D714yes—
534#117C22×D714yes—
535C2×C4⋊C4—22no—
536C2×C4⋊C4—22no—
537C2×C4⋊C4—21no—
538C2×C4⋊C4—21no—
539C2×C4⋊C4—71no—
540C2×C4⋊C4—71no—
541C2×C4⋊C4—141no—
542C2×C4⋊C4—141no—
543C2×C4⋊C4—141no—
544C2×C4⋊C4—141no—
545C2×C4⋊C4C22×D712yes—
546C2×C4⋊C4C22×D712yes—
547C2×C22⋊C4—22no—
548C2×C22⋊C4—141no—
549C2×C22⋊C4—141no—
550C2×C22⋊C4—141no—
551C2×C22⋊C4—141no—
552C2×C22⋊C4—141no—
553C2×C42—22no—
554C2×C42—141no—
555C2×C42C22⋊D711yescharacteristic
556C2×C42C22⋊D711yescharacteristic
557C2×C42C22⋊D711yescharacteristic
558C2×C42C22⋊D711yescharacteristic
559C2×C42C22⋊D711yescharacteristic
560C2×C42C22⋊D711yescharacteristic
561C2×C42C22×D711yescharacteristic
562C2×C42C22×D711yescharacteristic
563C2×C42C22×D711yescharacteristic
564C2×C42C22×D711yescharacteristic
565C2×C42C22×D711yescharacteristic
566C2×C42C22×D711yescharacteristic
567#107—78no—
568#107—78no—
569#106—78no—
570#106—78no—
571C4⋊C8—74no—
572C4⋊C8—74no—
573#103—78no—
574#103—78no—
575#102—78no—
576#102—78no—
577C22⋊C8—74no—
578C22⋊C8—74no—
579#97—74no—
580C4×C8—74no—
581C22×C7—21no—
582C22×C7—21no—
583C22×C7—21no—
584C22×C7—21no—
585C22×C7—21no—
586C22×C7—21no—
587C22×C7—21no—
588C22×C7—44no—
589C22×C7#53612yes—
590C22×C7#57512yes—
591C22×C7C23×D411yescharacteristic
592C2×D7—42no—
593C2×D7—42no—
594C2×D7—42no—
595C2×D7—84no—
596C4×C7—21no—
597C4×C7—21no—
598C4×C7—21no—
599C4×C7—21no—
600C4×C7—21no—
601C4×C7—21no—
602C4×C7—21no—
603C4×C7—21no—
604C4×C7—21no—
605C4×C7—44no—
606C4×C7—44no—
607C4×C7#53612yes—
608C4×C7#57512yes—
609C4×C7C2×2−1+412yes—
610Dic7—42no—
611Dic7—42no—
612Dic7—42no—
613C24—141no—
614C24C2×C22⋊D711yescharacteristic
615C2×Q8—22no—
616C2×Q8—22no—
617C2×Q8—22no—
618C2×Q8—22no—
619C2×Q8—44no—
620C2×Q8—44no—
621C2×Q8—72no—
622C2×Q8—141no—
623C2×Q8—144no—
624C2×D4—72no—
625C2×D4—142no—
626C2×D4—142no—
627C2×D4—144no—
628C2×D4—141no—
629C2×D4—284no—
630C22×C4—24no—
631C22×C4—22no—
632C22×C4—22no—
633C22×C4—42no—
634C22×C4—42no—
635C22×C4—141no—
636C22×C4—141no—
637C22×C4—141no—
638C22×C4—142no—
639C22×C4—142no—
640C22×C4—284no—
641C22×C4C2×C22⋊D711yescharacteristic
642C22×C4C2×C22⋊D711yescharacteristic
643C22×C4C2×C22⋊D711yescharacteristic
644C22×C4C2×C22⋊D711yescharacteristic
645C22×C4C2×C22⋊D711yescharacteristic
646C22×C4C2×C22⋊D711yescharacteristic
647C22×C4C2×C22⋊D711yescharacteristic
648C22×C4C2×C22⋊D711yescharacteristic
649C22×C4C2×C22⋊D711yescharacteristic
650C22×C4C2×C22⋊D711yescharacteristic
651C22×C4C2×C22⋊D711yescharacteristic
652C22×C4C2×C22⋊D711yescharacteristic
653C22×C4C2×C22⋊D711yescharacteristic
654C22×C4C2×C22⋊D711yescharacteristic
655C22×C4C2×C22⋊D711yescharacteristic
656C22×C4C23×D711yescharacteristic
657C22×C4C23×D711yescharacteristic
658C22×C4C23×D711yescharacteristic
659M16—148no—
660C2×C8—78no—
661C4⋊C4—24no—
662C4⋊C4—24no—
663C4⋊C4—24no—
664C4⋊C4—24no—
665C4⋊C4—22no—
666C4⋊C4—22no—
667C4⋊C4—22no—
668C4⋊C4—22no—
669C4⋊C4—22no—
670C4⋊C4—22no—
671C4⋊C4—72no—
672C4⋊C4—72no—
673C4⋊C4—142no—
674C4⋊C4—142no—
675C4⋊C4—142no—
676C4⋊C4—142no—
677C4⋊C4—142no—
678C4⋊C4—142no—
679C4⋊C4—142no—
680C4⋊C4—142no—
681C4⋊C4—141no—
682C4⋊C4—141no—
683C4⋊C4C23×D714yes—
684C4⋊C4C23×D714yes—
685C22⋊C4—24no—
686C22⋊C4—24no—
687C22⋊C4—142no—
688C22⋊C4—142no—
689C22⋊C4—142no—
690C22⋊C4—142no—
691C22⋊C4—142no—
692C22⋊C4—142no—
693C22⋊C4—142no—
694C22⋊C4—142no—
695C22⋊C4—142no—
696C22⋊C4—142no—
697C42—24no—
698C42—24no—
699C42—142no—
700C42—142no—
701C42C2×C22⋊D711yescharacteristic
702C42C2×C22⋊D711yescharacteristic
703C42C2×C22⋊D711yescharacteristic
704C42C2×C22⋊D711yescharacteristic
705C42C2×C22⋊D711yescharacteristic
706C42C2×C22⋊D711yescharacteristic
707C42C2×C22⋊D711yescharacteristic
708C42C2×C22⋊D711yescharacteristic
709C42C2×C22⋊D711yescharacteristic
710C42C2×C22⋊D711yescharacteristic
711C42C2×C22⋊D711yescharacteristic
712C42C2×C22⋊D711yescharacteristic
713C42C23×D711yescharacteristic
714C42C23×D711yescharacteristic
715C42C23×D711yescharacteristic
716C42C23×D711yescharacteristic
717C2×C7—22no—
718C2×C7—22no—
719C2×C7—41no—
720C2×C7C2×#53611yescharacteristic
721C2×C7C2×#57511yescharacteristic
722C2×C7C2×#57511yescharacteristic
723D7—82no—
724C23—22no—
725C23—22no—
726C23—41no—
727C23—142no—
728C23—282no—
729C23—282no—
730C23—282no—
731C23C22×C22⋊D711yescharacteristic
732C23C22×C22⋊D711yescharacteristic
733C23C22×C22⋊D711yescharacteristic
734Q8—44no—
735Q8—44no—
736Q8—44no—
737Q8—44no—
738Q8—144no—
739Q8—282no—
740D4—144no—
741D4—284no—
742D4—284no—
743D4—282no—
744C2×C4—22no—
745C2×C4—22no—
746C2×C4—22no—
747C2×C4—22no—
748C2×C4—22no—
749C2×C4—22no—
750C2×C4—22no—
751C2×C4—22no—
752C2×C4—22no—
753C2×C4—22no—
754C2×C4—24no—
755C2×C4—24no—
756C2×C4—41no—
757C2×C4—41no—
758C2×C4—41no—
759C2×C4—41no—
760C2×C4—41no—
761C2×C4—41no—
762C2×C4—41no—
763C2×C4—44no—
764C2×C4—44no—
765C2×C4—142no—
766C2×C4—142no—
767C2×C4—142no—
768C2×C4—284no—
769C2×C4—282no—
770C2×C4—282no—
771C2×C4—282no—
772C2×C4—284no—
773C2×C4#655114yes—
774C2×C4C22×C22⋊D711yescharacteristic
775C2×C4C22×C22⋊D711yescharacteristic
776C2×C4C22×C22⋊D711yescharacteristic
777C2×C4C22×C22⋊D711yescharacteristic
778C2×C4C22×C22⋊D711yescharacteristic
779C2×C4C22×C22⋊D711yescharacteristic
780C2×C4C22×C22⋊D711yescharacteristic
781C2×C4C22×C22⋊D711yescharacteristic
782C2×C4C22×C22⋊D711yescharacteristic
783C2×C4C22×C22⋊D711yescharacteristic
784C2×C4C22×C22⋊D711yescharacteristic
785C2×C4C24×D711yescharacteristic
786C8—148no—
787C7#6086611yescharacteristic, complemented, Sylow
788C22—21no—
789C22—21no—
790C22—21no—
791C22—21no—
792C22—21no—
793C22—21no—
794C22—21no—
795C22—44no—
796C22—282no—
797C22—282no—
798C22—282no—
799C22—564no—
800C22#9050712yes—
801C22#9051312yes—
802C22C23×C22⋊D711yescharacteristic
803C4—21no—
804C4—21no—
805C4—21no—
806C4—21no—
807C4—21no—
808C4—21no—
809C4—21no—
810C4—21no—
811C4—21no—
812C4—44no—
813C4—44no—
814C4—282no—
815C4—282no—
816C4—282no—
817C4#9050712yes—
818C4#9051312yes—
819C4C2×#655112yes—
820C2—22no—
821C2—22no—
822C2—41no—
823C2—562no—
824C2C2×#9050711yescharacteristic
825C2C2×#9051311yescharacteristic
826C2C2×#9051311yescharacteristic
subgroupG/H
centerC22C23×C22⋊D7
commutator, cosocleC2×C4×C7C25
FrattiniC2×C4C24×D7
FittingC2×C7×#533C2
socleC22×C7C23×D4
prime radicalC2×#6493C22
hypercenterC2×#533D7
hypocenterC7#60866
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. #11740812C2semidirect
4. #11740807C2semidirect
5. #11740805C2semidirect
6. #11740795C2semidirect
7. #11740787C2semidirect
8. #11740783C2semidirect
9. #11740663C2semidirect
10. #11740662C2semidirect
11. #11740463C2semidirect
12. #11739665C2semidirect
14. #11739494C2semidirect
21. C7×#533C22semidirect
22. C7×#533C22semidirect
23. C2×C7×C4⋊Q8C22semidirect
24. C2×C7×C4⋊Q8C22semidirect
25. C2×C7×#125C22semidirect
51. #89866C22semidirect
52. #89863C22semidirect
53. #89861C22semidirect
54. #89861C22semidirect
55. #89859C22semidirect
56. #89856C22semidirect
57. #89852C22semidirect
58. #89852C22semidirect
59. #89840C22semidirect
60. #89838C22semidirect
61. #89836C22semidirect
62. #89835C22semidirect
66. #89768C22semidirect
69. #89743C22semidirect
70. #89742C22semidirect
73. #89698C22semidirect
74. #89698C22semidirect
75. #89697C22semidirect
76. #89697C22semidirect
208. C2×#533D7semidirect
332. #533C2×D7semidirect
333. #533C2×D7semidirect
334. C2×C4⋊Q8C2×D7semidirect
335. C2×C4⋊Q8C2×D7semidirect
346. C2×#125C2×D7semidirect
787. C7#60866semidirect

Maximal subgroups

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

subgroupindex
C2×C7×#5332
C2×#901702
#117408122
#117408072
#117408052
#117407952
#117407872
#117407832
#117406632
#117406622
#117404632
#117396652
#117396622
#117394942
#608667