Finite Group Databasebeta

← #14225889

Subgroups — #14225889

Order 1792.

1800 conjugacy classes of subgroups.

The subgroup lattice has 838 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C7×#533C211yesmaximal, characteristic, complemented
2#11742748C211yesmaximal, characteristic
3#11740816C212yesmaximal, complemented
4#11740805C214yesmaximal, complemented
5#11740804C212yesmaximal, complemented
6#11740794C214yesmaximal, complemented
7#11740784C212yesmaximal, complemented
8#11740779C212yesmaximal, complemented
9#11740669C211yesmaximal, characteristic, complemented
10#11740668C211yesmaximal, characteristic, complemented
11#11740661C211yesmaximal, characteristic, complemented
12#11740660C211yesmaximal, characteristic, complemented
13#11740463C214yesmaximal, complemented
14#11739660C214yesmaximal, complemented
15C2×#89697C211yesmaximal, characteristic, complemented
16C7×#533—21no—
17C7×#533—21no—
18C7×#533—21no—
19C7×#533—21no—
20C7×#533C2212yes—
21C7×#533C2212yes—
22C7×#533C2212yes—
23C7×#533C2212yes—
24C2×C7×C4⋊Q8C2211yescharacteristic
25C2×C7×C4⋊Q8C2211yescharacteristic
26C2×C7×#125C2212yes—
27C2×C7×C22⋊Q8—21no—
28C2×C7×C22⋊Q8—21no—
29C2×C4×C7×Q8—21no—
30C2×C4×C7×Q8—21no—
31C2×C7×#117C2212yes—
32C22×C42×C7C2211yescharacteristic
33#90482—21no—
34#90482—21no—
35#90482C2212yes—
36#90170—21no—
37#90170—21no—
38#90170—21no—
39#90170—21no—
40#90170C2212yes—
41#90170C2212yes—
42#90168C2211yescharacteristic
43#90168C2211yescharacteristic
44#90168C2211yescharacteristic
45C4×#1157—21no—
46C4×#1157—21no—
47C4×#1157C2212yes—
48#90161C2211yescharacteristic
49#90161C2211yescharacteristic
50#90161C2211yescharacteristic
51C2×C22⋊(C7⋊C8)C2212yes—
52#89866C2214yescomplemented
53#89865C2212yescomplemented
54#89865C2212yescomplemented
55#89863C2214yescomplemented
56#89860C2212yescomplemented
57#89860C2212yescomplemented
58#89859C2214yescomplemented
59#89856C2214yescomplemented
60#89851C2212yescomplemented
61#89851C2212yescomplemented
62#89850C2212yescomplemented
63#89850C2212yescomplemented
64#89840C2218yescomplemented
65#89838C2218yescomplemented
66#89836C2218yescomplemented
67#89835C2218yescomplemented
68#89775C2218yes—
69#89774C2218yes—
70#89770C2218yes—
71#89768C2218yes—
72#89743C2214yes—
73#89742C2214yes—
74#89740C2214yes—
75#89739C2214yes—
76#89697C2212yes—
77#89697C2212yes—
78#89697C2212yes—
79#89697C2211yescharacteristic
80#89697C2211yescharacteristic
81C2×C4⋊(C7⋊C8)C2212yes—
82C2×C4×C7⋊C8C2212yes—
83#60846—71nomaximal, Sylow
84C22×C7×Q8—21no—
85C22×C7×Q8—21no—
86C23×C4×C7D411yescharacteristic
87C23×C4×C7D411yescharacteristic
88C23×C4×C7C2311yescharacteristic
89C2×#1157—21no—
90C2×#1157—21no—
91C2×#1157C2312yes—
92C7×C4⋊Q8—21no—
93C7×C4⋊Q8—21no—
94C7×C4⋊Q8—21no—
95C7×C4⋊Q8—21no—
96C7×C4⋊Q8C2312yes—
97C7×C4⋊Q8C2312yes—
98C7×C4⋊Q8C2312yes—
99C7×C4⋊Q8C2312yes—
100C7×#125—22no—
101C7×#125—22no—
102C7×#125C2314yes—
103C7×#125C2314yes—
104C7×C22⋊Q8—22no—
105C7×C22⋊Q8—22no—
106C7×C22⋊Q8—22no—
107C7×C22⋊Q8—22no—
108C7×C22⋊Q8—22no—
109C7×C22⋊Q8—22no—
110C7×C22⋊Q8—22no—
111C7×C22⋊Q8—22no—
112C4×C7×Q8—22no—
113C4×C7×Q8—22no—
114C4×C7×Q8—22no—
115C4×C7×Q8—22no—
116C4×C7×Q8—22no—
117C4×C7×Q8—22no—
118C4×C7×Q8—22no—
119C4×C7×Q8—22no—
120C7×#117—22no—
121C7×#117—22no—
122C7×#117C2314yes—
123C7×#117C2314yes—
124C2×C7×C4⋊C4—22no—
125C2×C7×C4⋊C4—22no—
126C2×C7×C4⋊C4—21no—
127C2×C7×C4⋊C4—21no—
128C2×C7×C4⋊C4C2312yes—
129C2×C7×C4⋊C4C2312yes—
130C2×C7×C22⋊C4—22no—
131C2×C42×C7—22no—
132C2×C42×C7D411yescharacteristic
133C2×C42×C7D411yescharacteristic
134C2×C42×C7D411yescharacteristic
135C2×C42×C7D411yescharacteristic
136C2×C42×C7D411yescharacteristic
137C2×C42×C7D411yescharacteristic
138C2×C42×C7C2311yescharacteristic
139C2×C42×C7C2311yescharacteristic
140C2×C42×C7C2311yescharacteristic
141C2×C42×C7C2311yescharacteristic
142C2×C42×C7C2311yescharacteristic
143C2×C42×C7C2311yescharacteristic
144#6516—22no—
145#6493—21no—
146#6493—21no—
147#6493—21no—
148#6493—21no—
149#6493C2312yes—
150#6493C2312yes—
151#6492—22no—
152#6492—22no—
153#6492—22no—
154C4×C22⋊D7—22no—
155C4×C22⋊D7—22no—
156C4×C22⋊D7—22no—
157C4×C22⋊D7—22no—
158C4×C22⋊D7—22no—
159C4×C22⋊D7—22no—
160#6489—21no—
161#6489—21no—
162#6489C2312yes—
163#6487—21no—
164#6487—21no—
165#6487—21no—
166#6487—21no—
167#6487C2312yes—
168#6487C2312yes—
169C22×C7⋊C8C2314yes—
170#6439—22no—
171#6439—22no—
172#6438—21no—
173#6438—21no—
174#6438C2312yes—
175#6437C2311yescharacteristic
176C4×D28—21no—
177C4×D28—21no—
178C4×D28—21no—
179C4×D28—21no—
180C4×D28C2312yes—
181C4×D28C2312yes—
182#6435—22no—
183#6435—22no—
184#6435—22no—
185C42×D7—22no—
186#6433—21no—
187#6433—21no—
188#6433C2312yes—
189#6432C2311yescharacteristic
190#6432C2311yescharacteristic
191#6432C2311yescharacteristic
192C4×Dic14—21no—
193C4×Dic14—21no—
194C4×Dic14—21no—
195C4×Dic14—21no—
196C4×Dic14C2312yes—
197C4×Dic14C2312yes—
198C22⋊(C7⋊C8)C2312yes—
199C22⋊(C7⋊C8)C2312yes—
200C22⋊(C7⋊C8)C2314yes—
201#6384C2318yes—
202#6384C2318yes—
203#6383C2318yes—
204#6383C2318yes—
205#6382C2318yes—
206#6382C2318yes—
207#6381C2318yes—
208#6381C2318yes—
209C4⋊(C7⋊C8)C2312yes—
210C4⋊(C7⋊C8)C2312yes—
211C4⋊(C7⋊C8)C2314yes—
212C4×C7⋊C8C2312yes—
213C4×C7⋊C8C2312yes—
214C4×C7⋊C8C2314yes—
215#3444—71no—
216C2×#533D711yescharacteristic, complemented
217#3233—74no—
218#3232—74no—
219#3231—72no—
220#3230—71no—
221#3229—71no—
222#3228—72no—
223#3227—71no—
224#3226—71no—
225#3160—72no—
226#3131—72no—
227#3091—74no—
228#3076—74no—
229C2×#431—71no—
230C24×C7C2×D411yescharacteristic
231C2×C7×Q8—22no—
232C2×C7×Q8—22no—
233C2×C7×Q8—22no—
234C2×C7×Q8—22no—
235C2×C7×Q8—44no—
236C2×C7×Q8—44no—
237C22×C4×C7—24no—
238C22×C4×C7—24no—
239C22×C4×C7—22no—
240C22×C4×C7—22no—
241C22×C4×C7—42no—
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×C7C2×D411yescharacteristic
251C22×C4×C7C2×D411yescharacteristic
252C22×C4×C7C2×D411yescharacteristic
253C22×C4×C7C2×D411yescharacteristic
254C22×C4×C7C2×D411yescharacteristic
255C22×C4×C7C2×D411yescharacteristic
256C22×C4×C7C2×D411yescharacteristic
257C22×C4×C7C2411yescharacteristic
258C22×C4×C7C2411yescharacteristic
259C22×C4×C7C2411yescharacteristic
260C2×C22⋊D7—22no—
261C2×C22⋊D7—22no—
262C2×C22⋊D7—22no—
263#1157—28no—
264#1157—44no—
265#1157—44no—
266C2×D28—21no—
267C2×D28—21no—
268C2×D28C2412yes—
269C2×C4×D7—22no—
270C2×C4×D7—22no—
271C2×C4×D7—22no—
272C2×Dic14—21no—
273C2×Dic14—21no—
274C2×Dic14C2412yes—
275C7×C4⋊C4—24no—
276C7×C4⋊C4—24no—
277C7×C4⋊C4—24no—
278C7×C4⋊C4—24no—
279C7×C4⋊C4—22no—
280C7×C4⋊C4—22no—
281C7×C4⋊C4—22no—
282C7×C4⋊C4—22no—
283C7×C4⋊C4—22no—
284C7×C4⋊C4—22no—
285C7×C4⋊C4C2414yes—
286C7×C4⋊C4C2414yes—
287C7×C22⋊C4—24no—
288C7×C22⋊C4—24no—
289C42×C7—24no—
290C42×C7—24no—
291C42×C7C2×D411yescharacteristic
292C42×C7C2×D411yescharacteristic
293C42×C7C2×D411yescharacteristic
294C42×C7C2×D411yescharacteristic
295C42×C7C2×D411yescharacteristic
296C42×C7C2×D411yescharacteristic
297C42×C7C2×D411yescharacteristic
298C42×C7C2×D411yescharacteristic
299C42×C7C2×D411yescharacteristic
300C42×C7C2×D411yescharacteristic
301C42×C7C2×D411yescharacteristic
302C42×C7C2×D411yescharacteristic
303C42×C7C2411yescharacteristic
304C42×C7C2411yescharacteristic
305C42×C7C2411yescharacteristic
306C42×C7C2411yescharacteristic
307C22⋊Dic7—22no—
308C22⋊Dic7—22no—
309C22⋊Dic7—22no—
310(C2×D7)⋊C4—22no—
311(C2×D7)⋊C4—22no—
312(C2×D7)⋊C4—22no—
313(C2×D7)⋊C4—22no—
314(C2×D7)⋊C4—22no—
315(C2×D7)⋊C4—22no—
316C4⋊Dic7—21no—
317C4⋊Dic7—21no—
318C4⋊Dic7—21no—
319C4⋊Dic7—21no—
320C4⋊Dic7C2412yes—
321C4⋊Dic7C2412yes—
322Dic7⋊C4—22no—
323Dic7⋊C4—22no—
324Dic7⋊C4—22no—
325Dic7⋊C4—22no—
326Dic7⋊C4—22no—
327Dic7⋊C4—22no—
328C4×Dic7—22no—
329C4×Dic7—22no—
330C4×Dic7—22no—
331C2×C7⋊C8—28no—
332C2×C7⋊C8C2414yes—
333C2×C7⋊C8C2414yes—
334#533—21no—
335#533—21no—
336#533—21no—
337#533—21no—
338#533—71no—
339#533—71no—
340#533—71no—
341#533C2×D712yes—
342#533C2×D712yes—
343#533C2×D712yes—
344#533C2×D712yes—
345#532—71no—
346#532—71no—
347#532—71no—
348C2×C4⋊Q8C2×D711yescharacteristic
349C2×C4⋊Q8C2×D711yescharacteristic
350#529—72no—
351#529—72no—
352#529—141no—
353#529—141no—
354#529—141no—
355#529—141no—
356C2×#125C2×D712yes—
357#525—72no—
358#525—141no—
359#525—141no—
360C2×C22⋊Q8—21no—
361C2×C22⋊Q8—21no—
362C4×#41—72no—
363C4×#41—141no—
364C4×#41—141no—
365C2×C4×Q8—21no—
366C2×C4×Q8—21no—
367C2×#117C2×D712yes—
368C22×C42C2×D711yescharacteristic
369#500—72no—
370#500—72no—
371#499—78no—
372#498—72no—
373#498—72no—
374#488—78no—
375#487—72no—
376#487—72no—
377#486—72no—
378#486—72no—
379#485—78no—
380#484—74no—
381#483—74no—
382#482—78no—
383#481—74no—
384#480—74no—
385#479—78no—
386#478—78no—
387#477—74no—
388#476—74no—
389#475—74no—
390#474—74no—
391#431—71no—
392#431—71no—
393#431—72no—
394#431—72no—
395#431—72no—
396#427—78no—
397C2×C4⋊C8—72no—
398#416—78no—
399C2×C22⋊C8—72no—
400C2×C4×C8—72no—
401C23×C7—22no—
402C23×C7—22no—
403C23×C7—41no—
404C23×C7C22×D411yescharacteristic
405C23×C7C22×D411yescharacteristic
406C23×C7C22×D411yescharacteristic
407C22×D7—22no—
408C7×Q8—44no—
409C7×Q8—44no—
410C7×Q8—44no—
411C7×Q8—44no—
412C2×C4×C7—22no—
413C2×C4×C7—22no—
414C2×C4×C7—22no—
415C2×C4×C7—22no—
416C2×C4×C7—22no—
417C2×C4×C7—22no—
418C2×C4×C7—22no—
419C2×C4×C7—22no—
420C2×C4×C7—22no—
421C2×C4×C7—22no—
422C2×C4×C7—22no—
423C2×C4×C7—22no—
424C2×C4×C7—22no—
425C2×C4×C7—24no—
426C2×C4×C7—24no—
427C2×C4×C7—41no—
428C2×C4×C7—41no—
429C2×C4×C7—41no—
430C2×C4×C7—44no—
431C2×C4×C7—44no—
432C2×C4×C7#13514yes—
433C2×C4×C7C22×D411yescharacteristic
434C2×C4×C7C22×D411yescharacteristic
435C2×C4×C7C22×D411yescharacteristic
436C2×C4×C7C22×D411yescharacteristic
437C2×C4×C7C22×D411yescharacteristic
438C2×C4×C7C22×D411yescharacteristic
439C2×C4×C7C22×D411yescharacteristic
440C2×C4×C7C22×D411yescharacteristic
441C2×C4×C7C22×D411yescharacteristic
442C2×C4×C7C22×D411yescharacteristic
443C2×C4×C7C22×D411yescharacteristic
444C2×C4×C72−1+414yes—
445C2×C4×C7C2511yescharacteristic
446C22⋊D7—44no—
447C22⋊D7—44no—
448C22⋊D7—44no—
449C2×Dic7—22no—
450C2×Dic7—22no—
451C2×Dic7—22no—
452D28—24no—
453D28—42no—
454D28—42no—
455C4×D7—44no—
456C4×D7—44no—
457C4×D7—44no—
458Dic14—24no—
459Dic14—42no—
460Dic14—42no—
461C7⋊C8—24no—
462C7⋊C8—24no—
463C2×#41—72no—
464C2×#41—141no—
465C2×#41—141no—
466C22×Q8—21no—
467C22×Q8—21no—
468C23×C4C22⋊D711yescharacteristic
469C23×C4C22⋊D711yescharacteristic
470C23×C4C22×D711yescharacteristic
471C22×C8—74no—
472C4⋊Q8—21no—
473C4⋊Q8—21no—
474C4⋊Q8—21no—
475C4⋊Q8—21no—
476C4⋊Q8—71no—
477C4⋊Q8—71no—
478C4⋊Q8—71no—
479C4⋊Q8C22×D712yes—
480C4⋊Q8C22×D712yes—
481C4⋊Q8C22×D712yes—
482C4⋊Q8C22×D712yes—
483#127—71no—
484#126—142no—
485#126—142no—
486#125—22no—
487#125—22no—
488#125—72no—
489#125—141no—
490#125—141no—
491#125C22×D714yes—
492#125C22×D714yes—
493#124—72no—
494#124—141no—
495#124—141no—
496#123—142no—
497#123—142no—
498#123—142no—
499C22⋊Q8—22no—
500C22⋊Q8—22no—
501C22⋊Q8—22no—
502C22⋊Q8—22no—
503C22⋊Q8—22no—
504C22⋊Q8—22no—
505C22⋊Q8—22no—
506C22⋊Q8—22no—
507C22⋊Q8—72no—
508C22⋊Q8—72no—
509C22⋊Q8—141no—
510C22⋊Q8—141no—
511C22⋊Q8—141no—
512C22⋊Q8—141no—
513#121—72no—
514#121—72no—
515#121—141no—
516#121—141no—
517#121—141no—
518#121—141no—
519#120—142no—
520C4×Q8—22no—
521C4×Q8—22no—
522C4×Q8—22no—
523C4×Q8—22no—
524C4×Q8—22no—
525C4×Q8—22no—
526C4×Q8—22no—
527C4×Q8—22no—
528C4×Q8—72no—
529C4×Q8—72no—
530C4×Q8—141no—
531C4×Q8—141no—
532C4×Q8—141no—
533C4×Q8—141no—
534C4×D4—72no—
535C4×D4—72no—
536C4×D4—142no—
537C4×D4—142no—
538C4×D4—142no—
539C4×D4—142no—
540C4×D4—142no—
541C4×D4—142no—
542C4×D4—141no—
543C4×D4—141no—
544C4×D4—141no—
545C4×D4—141no—
546#117—22no—
547#117—22no—
548#117—72no—
549#117—141no—
550#117—141no—
551#117—142no—
552#117—142no—
553#117—142no—
554#117C22×D714yes—
555#117C22×D714yes—
556C2×C4⋊C4—22no—
557C2×C4⋊C4—22no—
558C2×C4⋊C4—21no—
559C2×C4⋊C4—21no—
560C2×C4⋊C4C22×D712yes—
561C2×C4⋊C4C22×D712yes—
562C2×C22⋊C4—22no—
563C2×C42—22no—
564C2×C42—142no—
565C2×C42C22⋊D711yescharacteristic
566C2×C42C22⋊D711yescharacteristic
567C2×C42C22⋊D711yescharacteristic
568C2×C42C22⋊D711yescharacteristic
569C2×C42C22⋊D711yescharacteristic
570C2×C42C22⋊D711yescharacteristic
571C2×C42C22×D711yescharacteristic
572C2×C42C22×D711yescharacteristic
573C2×C42C22×D711yescharacteristic
574C2×C42C22×D711yescharacteristic
575C2×C42C22×D711yescharacteristic
576C2×C42C22×D711yescharacteristic
577#107—78no—
578#107—78no—
579#106—78no—
580#106—78no—
581C4⋊C8—72no—
582C4⋊C8—72no—
583C4⋊C8—74no—
584#103—78no—
585#103—78no—
586#102—78no—
587#102—78no—
588C22⋊C8—72no—
589C22⋊C8—72no—
590C22⋊C8—74no—
591C4×C8—72no—
592C4×C8—72no—
593C4×C8—74no—
594C22×C7—21no—
595C22×C7—21no—
596C22×C7—21no—
597C22×C7—21no—
598C22×C7—21no—
599C22×C7—21no—
600C22×C7—21no—
601C22×C7—44no—
602C22×C7#53612yes—
603C22×C7C2×#13512yes—
604C22×C7C23×D411yescharacteristic
605C2×D7—42no—
606C2×D7—42no—
607C2×D7—42no—
608C4×C7—21no—
609C4×C7—21no—
610C4×C7—21no—
611C4×C7—21no—
612C4×C7—21no—
613C4×C7—21no—
614C4×C7—21no—
615C4×C7—44no—
616C4×C7—44no—
617C4×C7#53612yes—
618C4×C7C2×#13512yes—
619C4×C7C2×#13512yes—
620C4×C7#57512yes—
621C4×C7C2×2−1+412yes—
622Dic7—42no—
623Dic7—42no—
624Dic7—42no—
625C24C2×C22⋊D711yescharacteristic
626#41—148no—
627#41—284no—
628#41—284no—
629C2×Q8—22no—
630C2×Q8—22no—
631C2×Q8—22no—
632C2×Q8—22no—
633C2×Q8—44no—
634C2×Q8—44no—
635C2×Q8—72no—
636C2×Q8—141no—
637C2×Q8—141no—
638C2×D4—72no—
639C2×D4—142no—
640C2×D4—142no—
641C2×D4—142no—
642C2×D4—141no—
643C2×D4—141no—
644C22×C4—24no—
645C22×C4—24no—
646C22×C4—22no—
647C22×C4—22no—
648C22×C4—42no—
649C22×C4—142no—
650C22×C4—142no—
651C22×C4—142no—
652C22×C4C2×C22⋊D711yescharacteristic
653C22×C4C2×C22⋊D711yescharacteristic
654C22×C4C2×C22⋊D711yescharacteristic
655C22×C4C2×C22⋊D711yescharacteristic
656C22×C4C2×C22⋊D711yescharacteristic
657C22×C4C2×C22⋊D711yescharacteristic
658C22×C4C2×C22⋊D711yescharacteristic
659C22×C4C2×C22⋊D711yescharacteristic
660C22×C4C2×C22⋊D711yescharacteristic
661C22×C4C2×C22⋊D711yescharacteristic
662C22×C4C2×C22⋊D711yescharacteristic
663C22×C4C2×C22⋊D711yescharacteristic
664C22×C4C2×C22⋊D711yescharacteristic
665C22×C4C2×C22⋊D711yescharacteristic
666C22×C4C2×C22⋊D711yescharacteristic
667C22×C4C23×D711yescharacteristic
668C22×C4C23×D711yescharacteristic
669C22×C4C23×D711yescharacteristic
670C2×C8—74no—
671C2×C8—74no—
672C2×C8—148no—
673C4⋊C4—24no—
674C4⋊C4—24no—
675C4⋊C4—24no—
676C4⋊C4—24no—
677C4⋊C4—22no—
678C4⋊C4—22no—
679C4⋊C4—22no—
680C4⋊C4—22no—
681C4⋊C4—22no—
682C4⋊C4—22no—
683C4⋊C4—72no—
684C4⋊C4—72no—
685C4⋊C4—142no—
686C4⋊C4—142no—
687C4⋊C4—142no—
688C4⋊C4—142no—
689C4⋊C4—142no—
690C4⋊C4—142no—
691C4⋊C4—141no—
692C4⋊C4—141no—
693C4⋊C4—141no—
694C4⋊C4—141no—
695C4⋊C4C23×D714yes—
696C4⋊C4C23×D714yes—
697C22⋊C4—24no—
698C22⋊C4—24no—
699C22⋊C4—142no—
700C22⋊C4—142no—
701C22⋊C4—142no—
702C22⋊C4—142no—
703C22⋊C4—142no—
704C22⋊C4—142no—
705C22⋊C4—142no—
706C22⋊C4—142no—
707C22⋊C4—142no—
708C42—24no—
709C42—24no—
710C42—142no—
711C42—142no—
712C42—142no—
713C42C2×C22⋊D711yescharacteristic
714C42C2×C22⋊D711yescharacteristic
715C42C2×C22⋊D711yescharacteristic
716C42C2×C22⋊D711yescharacteristic
717C42C2×C22⋊D711yescharacteristic
718C42C2×C22⋊D711yescharacteristic
719C42C2×C22⋊D711yescharacteristic
720C42C2×C22⋊D711yescharacteristic
721C42C2×C22⋊D711yescharacteristic
722C42C2×C22⋊D711yescharacteristic
723C42C2×C22⋊D711yescharacteristic
724C42C2×C22⋊D711yescharacteristic
725C42C23×D711yescharacteristic
726C42C23×D711yescharacteristic
727C42C23×D711yescharacteristic
728C42C23×D711yescharacteristic
729C2×C7—22no—
730C2×C7—22no—
731C2×C7—41no—
732C2×C7C2×#53611yescharacteristic
733C2×C7C22×#13511yescharacteristic
734C2×C7C2×#57511yescharacteristic
735D7—82no—
736C23—22no—
737C23—22no—
738C23—41no—
739C23—142no—
740C23C22×C22⋊D711yescharacteristic
741C23C22×C22⋊D711yescharacteristic
742C23C22×C22⋊D711yescharacteristic
743Q8—44no—
744Q8—44no—
745Q8—44no—
746Q8—44no—
747Q8—144no—
748Q8—282no—
749Q8—282no—
750D4—144no—
751D4—284no—
752D4—284no—
753D4—284no—
754D4—282no—
755D4—282no—
756C2×C4—22no—
757C2×C4—22no—
758C2×C4—22no—
759C2×C4—22no—
760C2×C4—22no—
761C2×C4—22no—
762C2×C4—22no—
763C2×C4—22no—
764C2×C4—22no—
765C2×C4—22no—
766C2×C4—22no—
767C2×C4—22no—
768C2×C4—22no—
769C2×C4—24no—
770C2×C4—24no—
771C2×C4—41no—
772C2×C4—41no—
773C2×C4—41no—
774C2×C4—44no—
775C2×C4—44no—
776C2×C4—142no—
777C2×C4—142no—
778C2×C4—142no—
779C2×C4—284no—
780C2×C4—284no—
781C2×C4—284no—
782C2×C4#651314yes—
783C2×C4#655114yes—
784C2×C4C22×C22⋊D711yescharacteristic
785C2×C4C22×C22⋊D711yescharacteristic
786C2×C4C22×C22⋊D711yescharacteristic
787C2×C4C22×C22⋊D711yescharacteristic
788C2×C4C22×C22⋊D711yescharacteristic
789C2×C4C22×C22⋊D711yescharacteristic
790C2×C4C22×C22⋊D711yescharacteristic
791C2×C4C22×C22⋊D711yescharacteristic
792C2×C4C22×C22⋊D711yescharacteristic
793C2×C4C22×C22⋊D711yescharacteristic
794C2×C4C22×C22⋊D711yescharacteristic
795C2×C4C24×D711yescharacteristic
796C8—144no—
797C8—144no—
798C7#6084611yescharacteristic, complemented, Sylow
799C22—21no—
800C22—21no—
801C22—21no—
802C22—21no—
803C22—21no—
804C22—21no—
805C22—21no—
806C22—44no—
807C22—282no—
808C22—282no—
809C22—282no—
810C22#9050712yes—
811C22C2×#651312yes—
812C22C23×C22⋊D711yescharacteristic
813C4—21no—
814C4—21no—
815C4—21no—
816C4—21no—
817C4—21no—
818C4—21no—
819C4—21no—
820C4—44no—
821C4—44no—
822C4—282no—
823C4—282no—
824C4—282no—
825C4#9050712yes—
826C4C2×#651312yes—
827C4C2×#651312yes—
828C4#9051312yes—
829C4C2×#655112yes—
830C2—22no—
831C2—22no—
832C2—41no—
833C2—562no—
834C2C2×#9050711yescharacteristic
835C2C22×#651311yescharacteristic
836C2C2×#9051311yescharacteristic
subgroupG/H
centerC2×C4C22×C22⋊D7
commutator, cosocleC2×C4×C7C25
FrattiniC2×C4C24×D7
FittingC2×C7×#533C2
socleC22×C7C23×D4
prime radical#11742748C2
hypercenterC2×#533D7
hypocenterC7#60846
LCSG ▷ C2×C4×C7 ▷ C2×C7 ▷ C7
UCSC1 ◁ C2×C4 ◁ C22×C42 ◁ C2×#533

Complements

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

NH ≅ G/Ntype
1. C2×C7×#533C2semidirect
3. #11740816C2semidirect
4. #11740805C2semidirect
5. #11740804C2semidirect
6. #11740794C2semidirect
7. #11740784C2semidirect
8. #11740779C2semidirect
9. #11740669C2semidirect
10. #11740668C2semidirect
11. #11740661C2semidirect
12. #11740660C2semidirect
13. #11740463C2semidirect
14. #11739660C2semidirect
15. C2×#89697C2semidirect
52. #89866C22semidirect
53. #89865C22semidirect
54. #89865C22semidirect
55. #89863C22semidirect
56. #89860C22semidirect
57. #89860C22semidirect
58. #89859C22semidirect
59. #89856C22semidirect
60. #89851C22semidirect
61. #89851C22semidirect
62. #89850C22semidirect
63. #89850C22semidirect
64. #89840C22semidirect
65. #89838C22semidirect
66. #89836C22semidirect
67. #89835C22semidirect
216. C2×#533D7semidirect
798. C7#60846semidirect

Maximal subgroups

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

subgroupindex
C2×C7×#5332
#117427482
#117408162
#117408052
#117408042
#117407942
#117407842
#117407792
#117406692
#117406682
#117406612
#117406602
#117404632
#117396602
C2×#896972
#608467