Finite Group Databasebeta

← #14226145

Subgroups — #14226145

Order 1792.

1686 conjugacy classes of subgroups.

The subgroup lattice has 788 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C7×#544C211yesmaximal, characteristic, complemented
2#11742806C211yesmaximal, characteristic
3#11740926C214yesmaximal, complemented
4#11740924C214yesmaximal, complemented
5#11740923C214yesmaximal, complemented
6#11740922C214yesmaximal, complemented
7#11740657C212yesmaximal, complemented
8#11740652C211yesmaximal, characteristic, complemented
9#11740644C211yesmaximal, characteristic, complemented
10#11740462C212yesmaximal, complemented
11#11740460C211yesmaximal, characteristic, complemented
12#11740457C211yesmaximal, characteristic, complemented
13#11739661C212yesmaximal, complemented
14#11739654C211yesmaximal, characteristic, complemented
15#11739584C212yesmaximal, complemented
16C7×#544—22no—
17C7×#544—22no—
18C7×#544C2214yes—
19C7×#544C2214yes—
20C2×C7×C4⋊Q8—21no—
21C2×C7×C4⋊Q8C2211yescharacteristic
22C2×C7×C4⋊Q8C2211yescharacteristic
23C2×C7×#125—21no—
24C2×C7×#125C2211yescharacteristic
25C2×C7×#125C2211yescharacteristic
26C2×C7×C22⋊Q8—21no—
27C2×C7×C22⋊Q8—21no—
28C2×C7×#117C2211yescharacteristic
29C2×C7×#117C2211yescharacteristic
30C22×C7×C4⋊C4C2211yescharacteristic
31#90482C2212yes—
32#90226C2212yes—
33#90225C2212yes—
34#90225C2212yes—
35#90219—22no—
36#90219—22no—
37#90209C2212yes—
38#90206—21no—
39#90206—21no—
40#90185—21no—
41#90185—21no—
42#90168C2211yescharacteristic
43C4×#1157C2212yes—
44#90161C2211yescharacteristic
45#89979C2212yes—
46#89866C2214yescomplemented
47#89865C2212yescomplemented
48#89863C2214yescomplemented
49#89861C2214yescomplemented
50#89860C2212yescomplemented
51#89859C2214yescomplemented
52#89856C2214yescomplemented
53#89852C2214yescomplemented
54#89851C2212yescomplemented
55#89850C2212yescomplemented
56#89841C2212yescomplemented
57#89840C2214yescomplemented
58#89839C2212yescomplemented
59#89838C2214yescomplemented
60#89838C2214yescomplemented
61#89837C2212yescomplemented
62#89837C2212yescomplemented
63#89836C2214yescomplemented
64#89835C2214yescomplemented
65#89835C2214yescomplemented
66#89775C2214yes—
67#89775C2214yes—
68#89772C2214yes—
69#89772C2214yes—
70#89768C2214yes—
71#89768C2214yes—
72#89743C2214yes—
73#89742C2214yes—
74#89740C2214yes—
75#89739C2214yes—
76#89738C2212yes—
77#89738C2212yes—
78#89738C2212yes—
79#89738C2212yes—
80#89736C2212yes—
81#89736C2212yes—
82#89736C2212yes—
83#89736C2212yes—
84#89696C2212yes—
85C4×#1136C2211yescharacteristic
86C4×#1136C2211yescharacteristic
87#60867—71nomaximal, Sylow
88C22×C7×Q8—21no—
89C22×C7×Q8—21no—
90C23×C4×C7—21no—
91C23×C4×C7C2311yescharacteristic
92C2×#1157C2312yes—
93C7×C4⋊Q8—24no—
94C7×C4⋊Q8—24no—
95C7×C4⋊Q8—21no—
96C7×C4⋊Q8—21no—
97C7×C4⋊Q8—22no—
98C7×C4⋊Q8C2314yes—
99C7×C4⋊Q8C2312yes—
100C7×C4⋊Q8C2312yes—
101C7×#125—24no—
102C7×#125—24no—
103C7×#125—21no—
104C7×#125—21no—
105C7×#125—22no—
106C7×#125C2314yes—
107C7×#125C2312yes—
108C7×#125C2312yes—
109C7×C22⋊Q8—24no—
110C7×C22⋊Q8—24no—
111C7×C22⋊Q8—24no—
112C7×C22⋊Q8—24no—
113C7×#117—22no—
114C7×#117D412yes—
115C7×#117D412yes—
116C7×#117C2314yes—
117C7×#117C2312yes—
118C7×#117C2312yes—
119C2×C7×C4⋊C4—21no—
120C2×C7×C4⋊C4—22no—
121C2×C7×C4⋊C4—21no—
122C2×C7×C4⋊C4—21no—
123C2×C7×C4⋊C4—21no—
124C2×C7×C4⋊C4—21no—
125C2×C7×C4⋊C4—21no—
126C2×C7×C4⋊C4—21no—
127C2×C7×C4⋊C4D411yescharacteristic
128C2×C7×C4⋊C4D411yescharacteristic
129C2×C7×C4⋊C4C2311yescharacteristic
130C2×C7×C4⋊C4C2311yescharacteristic
131C2×C7×C4⋊C4C2311yescharacteristic
132C2×C7×C4⋊C4C2311yescharacteristic
133C2×C7×C4⋊C4C2314yes—
134C2×C7×C22⋊C4—21no—
135C2×C7×C22⋊C4D411yescharacteristic
136C2×C7×C22⋊C4D411yescharacteristic
137C2×C42×C7—21no—
138C2×C42×C7C2311yescharacteristic
139C2×C42×C7C2311yescharacteristic
140#6516—22no—
141#6493—21no—
142#6493—21no—
143#6493C2312yes—
144#6493C2312yes—
145#6492—22no—
146C4×C22⋊D7—22no—
147C4×C22⋊D7—22no—
148C4×C22⋊D7—22no—
149C4×C22⋊D7—22no—
150#6489C2312yes—
151#6487—21no—
152#6487—21no—
153#6487C2312yes—
154#6487C2312yes—
155C2×#1136C2312yes—
156C2×#1136C2312yes—
157#6461—22no—
158#6461—22no—
159#6459—22no—
160#6459—22no—
161#6457—22no—
162#6457—22no—
163#6452—22no—
164#6452—22no—
165#6448—22no—
166#6448—22no—
167#6447—22no—
168#6447—22no—
169#6446—22no—
170#6446—22no—
171#6442—22no—
172#6442—22no—
173#6438C2312yes—
174#6437C2311yescharacteristic
175C4×D28—21no—
176C4×D28—21no—
177C4×D28C2312yes—
178C4×D28C2312yes—
179#6435—22no—
180C42×D7—22no—
181#6433C2312yes—
182#6432C2311yescharacteristic
183#6432C2311yescharacteristic
184#6432C2311yescharacteristic
185C4×Dic14—21no—
186C4×Dic14—21no—
187C4×Dic14C2312yes—
188C4×Dic14C2312yes—
189C22⋊(C7⋊C8)C2314yes—
190C22⋊(C7⋊C8)C2314yes—
191#6384C2314yes—
192#6384C2314yes—
193#6384C2314yes—
194#6384C2314yes—
195#6383C2314yes—
196#6383C2314yes—
197#6383C2314yes—
198#6383C2314yes—
199#6382C2314yes—
200#6382C2314yes—
201#6382C2314yes—
202#6382C2314yes—
203#6381C2314yes—
204#6381C2314yes—
205#6381C2314yes—
206#6381C2314yes—
207C4⋊(C7⋊C8)C2314yes—
208C4⋊(C7⋊C8)C2314yes—
209#6377C2312yes—
210#6377C2312yes—
211C4×C7⋊C8C2312yes—
212C4×C7⋊C8C2312yes—
213C2×#544D711yescharacteristic, complemented
214#3455—71no—
215#3244—74no—
216#3243—74no—
217#3242—74no—
218#3241—74no—
219#3166—71no—
220#3165—71no—
221#3142—71no—
222#3141—71no—
223#3093—72no—
224#3092—72no—
225#3080—72no—
226#3079—72no—
227#2921—71no—
228C24×C7C2×D411yescharacteristic
229C2×C7×Q8—24no—
230C2×C7×Q8—22no—
231C2×C7×Q8—22no—
232C2×C7×Q8—82no—
233C2×C7×Q8—82no—
234C22×C4×C7—24no—
235C22×C4×C7—21no—
236C22×C4×C7—21no—
237C22×C4×C7—21no—
238C22×C4×C7—21no—
239C22×C4×C7—24no—
240C22×C4×C7—82no—
241C22×C4×C7C2×D412yes—
242C22×C4×C7C2×D411yescharacteristic
243C22×C4×C7C2×D411yescharacteristic
244C22×C4×C7C2×D411yescharacteristic
245C22×C4×C7C2×D411yescharacteristic
246C22×C4×C7C2×D411yescharacteristic
247C22×C4×C7C2412yes—
248C22×C4×C7C2411yescharacteristic
249C2×C22⋊D7—22no—
250C2×C22⋊D7—22no—
251C2×C22⋊D7—22no—
252#1157—28no—
253C2×D28—21no—
254C2×D28—21no—
255C2×D28C2412yes—
256C2×C4×D7—22no—
257C2×C4×D7—22no—
258C2×C4×D7—22no—
259C2×Dic14—21no—
260C2×Dic14—21no—
261C2×Dic14C2412yes—
262C7×C4⋊C4—24no—
263C7×C4⋊C4—21no—
264C7×C4⋊C4—21no—
265C7×C4⋊C4—24no—
266C7×C4⋊C4—22no—
267C7×C4⋊C4—22no—
268C7×C4⋊C4—24no—
269C7×C4⋊C4—22no—
270C7×C4⋊C4—22no—
271C7×C4⋊C4—24no—
272C7×C4⋊C4—22no—
273C7×C4⋊C4—22no—
274C7×C4⋊C4—21no—
275C7×C4⋊C4—21no—
276C7×C4⋊C4C2×D412yes—
277C7×C4⋊C4C2×D412yes—
278C7×C4⋊C4C2×D412yes—
279C7×C4⋊C4C2×D412yes—
280C7×C4⋊C4C2412yes—
281C7×C4⋊C4C2412yes—
282C7×C4⋊C4C2412yes—
283C7×C4⋊C4C2412yes—
284C7×C22⋊C4—24no—
285C7×C22⋊C4C2×D412yes—
286C7×C22⋊C4C2×D412yes—
287C7×C22⋊C4C2×D412yes—
288C7×C22⋊C4C2×D412yes—
289C42×C7—24no—
290C42×C7C2×D411yescharacteristic
291C42×C7C2×D411yescharacteristic
292C42×C7C2×D412yes—
293C42×C7C2412yes—
294C42×C7C2411yescharacteristic
295C42×C7C2411yescharacteristic
296C22⋊Dic7—22no—
297C22⋊Dic7—22no—
298C22⋊Dic7—22no—
299(C2×D7)⋊C4—22no—
300(C2×D7)⋊C4—22no—
301(C2×D7)⋊C4—22no—
302(C2×D7)⋊C4—22no—
303(C2×D7)⋊C4—22no—
304(C2×D7)⋊C4—22no—
305C4⋊Dic7—21no—
306C4⋊Dic7—21no—
307C4⋊Dic7—21no—
308C4⋊Dic7—21no—
309C4⋊Dic7C2412yes—
310C4⋊Dic7C2412yes—
311Dic7⋊C4—22no—
312Dic7⋊C4—22no—
313Dic7⋊C4—22no—
314Dic7⋊C4—22no—
315Dic7⋊C4—22no—
316Dic7⋊C4—22no—
317C4×Dic7—22no—
318C4×Dic7—22no—
319C4×Dic7—22no—
320#1136—24no—
321#1136—24no—
322C2×C7⋊C8C2414yes—
323C2×C7⋊C8C2414yes—
324#544—22no—
325#544—22no—
326#544C2×D714yes—
327#544C2×D714yes—
328#542—72no—
329#542—72no—
330#541—72no—
331#540—72no—
332#539—141no—
333#539—141no—
334#538—141no—
335#538—141no—
336#533—71no—
337#532—71no—
338C2×C4⋊Q8—21no—
339C2×C4⋊Q8C2×D711yescharacteristic
340C2×C4⋊Q8C2×D711yescharacteristic
341#529—142no—
342#529—142no—
343C2×#125—21no—
344C2×#125C2×D711yescharacteristic
345C2×#125C2×D711yescharacteristic
346#525—72no—
347C2×C22⋊Q8—21no—
348C2×C22⋊Q8—21no—
349C4×#41—72no—
350C2×#117C2×D711yescharacteristic
351C2×#117C2×D711yescharacteristic
352C22×C4⋊C4C2×D711yescharacteristic
353#501—74no—
354#501—72no—
355#501—72no—
356#500—72no—
357#499—74no—
358#498—72no—
359#491—72no—
360#490—72no—
361#489—74no—
362#488—74no—
363#487—72no—
364#486—72no—
365#485—74no—
366#485—74no—
367#484—74no—
368#483—74no—
369#482—74no—
370#482—74no—
371#481—74no—
372#480—74no—
373#479—74no—
374#479—74no—
375#478—74no—
376#478—74no—
377#477—74no—
378#476—74no—
379#475—74no—
380#474—74no—
381#433—74no—
382#433—74no—
383#428—72no—
384#428—72no—
385#428—72no—
386#428—72no—
387#423—72no—
388#417—72no—
389#417—72no—
390#417—72no—
391#417—72no—
392#407—72no—
393C4×M16—71no—
394C4×M16—71no—
395C23×C7—22no—
396C23×C7—41no—
397C23×C7—41no—
398C23×C7C22×D412yes—
399C23×C7C22×D411yescharacteristic
400C22×D7—22no—
401C7×Q8—82no—
402C7×Q8—84no—
403C7×Q8—82no—
404C2×C4×C7—22no—
405C2×C4×C7—24no—
406C2×C4×C7—24no—
407C2×C4×C7—22no—
408C2×C4×C7—22no—
409C2×C4×C7—22no—
410C2×C4×C7—22no—
411C2×C4×C7—41no—
412C2×C4×C7—41no—
413C2×C4×C7—41no—
414C2×C4×C7—41no—
415C2×C4×C7—42no—
416C2×C4×C7—42no—
417C2×C4×C7—42no—
418C2×C4×C7—42no—
419C2×C4×C7—84no—
420C2×C4×C7C22×D412yes—
421C2×C4×C7C22×D412yes—
422C2×C4×C7C22×D411yescharacteristic
423C2×C4×C7C22×D411yescharacteristic
424C2×C4×C7C22×D412yes—
425C2×C4×C7C22×D411yescharacteristic
426C2×C4×C7C22×D411yescharacteristic
427C2×C4×C7C22×D411yescharacteristic
428C2×C4×C72−1+414yes—
429C2×C4×C7C2511yescharacteristic
430C22⋊D7—44no—
431C22⋊D7—82no—
432C22⋊D7—82no—
433C2×Dic7—22no—
434C2×Dic7—22no—
435C2×Dic7—22no—
436D28—24no—
437D28—81no—
438D28—81no—
439C4×D7—44no—
440C4×D7—82no—
441C4×D7—82no—
442Dic14—24no—
443Dic14—81no—
444Dic14—81no—
445C7⋊C8—24no—
446C7⋊C8—24no—
447C2×#41—72no—
448C22×Q8—21no—
449C22×Q8—21no—
450C23×C4—21no—
451C23×C4C22×D711yescharacteristic
452C2×M16—72no—
453C2×M16—72no—
454C4⋊Q8—24no—
455C4⋊Q8—24no—
456C4⋊Q8—22no—
457C4⋊Q8—21no—
458C4⋊Q8—21no—
459C4⋊Q8—71no—
460C4⋊Q8—71no—
461C4⋊Q8—71no—
462C4⋊Q8C22×D714yes—
463C4⋊Q8C22×D712yes—
464C4⋊Q8C22×D712yes—
465#127—71no—
466#126—142no—
467#126—142no—
468#126—142no—
469#126—142no—
470#125—24no—
471#125—24no—
472#125—22no—
473#125—21no—
474#125—21no—
475#125—72no—
476#125—142no—
477#125—142no—
478#125C22×D714yes—
479#125C22×D712yes—
480#125C22×D712yes—
481#124—72no—
482#124—142no—
483#124—142no—
484#123—142no—
485#123—142no—
486#123—142no—
487#123—142no—
488#123—142no—
489C22⋊Q8—24no—
490C22⋊Q8—24no—
491C22⋊Q8—24no—
492C22⋊Q8—24no—
493C22⋊Q8—72no—
494C22⋊Q8—72no—
495C22⋊Q8—141no—
496C22⋊Q8—141no—
497C22⋊Q8—142no—
498C22⋊Q8—142no—
499#121—72no—
500#121—72no—
501#121—141no—
502#121—141no—
503#121—142no—
504#121—142no—
505#120—142no—
506C4×Q8—72no—
507C4×Q8—72no—
508C4×Q8—141no—
509C4×Q8—141no—
510C4×D4—72no—
511C4×D4—72no—
512C4×D4—142no—
513C4×D4—142no—
514C4×D4—142no—
515C4×D4—142no—
516C4×D4—141no—
517C4×D4—141no—
518#117—22no—
519#117—72no—
520#117—142no—
521#117C22⋊D712yes—
522#117C22⋊D712yes—
523#117C22×D714yes—
524#117C22×D712yes—
525#117C22×D712yes—
526C2×C4⋊C4—21no—
527C2×C4⋊C4—22no—
528C2×C4⋊C4—21no—
529C2×C4⋊C4—21no—
530C2×C4⋊C4—21no—
531C2×C4⋊C4—21no—
532C2×C4⋊C4—21no—
533C2×C4⋊C4—21no—
534C2×C4⋊C4C22⋊D711yescharacteristic
535C2×C4⋊C4C22⋊D711yescharacteristic
536C2×C4⋊C4C22×D711yescharacteristic
537C2×C4⋊C4C22×D711yescharacteristic
538C2×C4⋊C4C22×D714yes—
539C2×C4⋊C4C22×D711yescharacteristic
540C2×C4⋊C4C22×D711yescharacteristic
541C2×C22⋊C4—21no—
542C2×C22⋊C4C22⋊D711yescharacteristic
543C2×C22⋊C4C22⋊D711yescharacteristic
544C2×C42—21no—
545C2×C42—142no—
546C2×C42C22×D711yescharacteristic
547C2×C42C22×D711yescharacteristic
548#107—74no—
549#107—74no—
550#107—74no—
551#107—74no—
552#106—74no—
553#106—74no—
554#106—74no—
555#106—74no—
556C4⋊C8—74no—
557C4⋊C8—74no—
558#103—74no—
559#103—74no—
560#103—74no—
561#103—74no—
562#102—74no—
563#102—74no—
564#102—74no—
565#102—74no—
566C22⋊C8—74no—
567C22⋊C8—74no—
568#97—72no—
569#97—72no—
570C4×C8—72no—
571C4×C8—72no—
572C22×C7—21no—
573C22×C7—21no—
574C22×C7—22no—
575C22×C7—22no—
576C22×C7—22no—
577C22×C7—44no—
578C22×C7#53612yes—
579C22×C7C23×D411yescharacteristic
580C2×D7—42no—
581C2×D7—42no—
582C2×D7—42no—
583C4×C7—21no—
584C4×C7—22no—
585C4×C7—21no—
586C4×C7—21no—
587C4×C7—22no—
588C4×C7—21no—
589C4×C7—22no—
590C4×C7—42no—
591C4×C7—42no—
592C4×C7—42no—
593C4×C7—42no—
594C4×C7#53612yes—
595C4×C7C2×2−1+412yes—
596Dic7—42no—
597Dic7—42no—
598Dic7—42no—
599C24C2×C22⋊D711yescharacteristic
600#41—148no—
601C2×Q8—24no—
602C2×Q8—22no—
603C2×Q8—22no—
604C2×Q8—72no—
605C2×Q8—82no—
606C2×Q8—82no—
607C2×Q8—141no—
608C2×Q8—141no—
609C2×D4—72no—
610C2×D4—142no—
611C2×D4—142no—
612C2×D4—142no—
613C2×D4—141no—
614C2×D4—141no—
615C22×C4—24no—
616C22×C4—21no—
617C22×C4—21no—
618C22×C4—21no—
619C22×C4—21no—
620C22×C4—24no—
621C22×C4—82no—
622C22×C4—142no—
623C22×C4—142no—
624C22×C4—142no—
625C22×C4C2×C22⋊D711yescharacteristic
626C22×C4C2×C22⋊D712yes—
627C22×C4C2×C22⋊D711yescharacteristic
628C22×C4C2×C22⋊D711yescharacteristic
629C22×C4C2×C22⋊D711yescharacteristic
630C22×C4C2×C22⋊D711yescharacteristic
631C22×C4C23×D712yes—
632C22×C4C23×D711yescharacteristic
633M16—144no—
634M16—144no—
635C2×C8—74no—
636C2×C8—74no—
637C4⋊C4—24no—
638C4⋊C4—21no—
639C4⋊C4—21no—
640C4⋊C4—24no—
641C4⋊C4—22no—
642C4⋊C4—22no—
643C4⋊C4—24no—
644C4⋊C4—22no—
645C4⋊C4—22no—
646C4⋊C4—24no—
647C4⋊C4—22no—
648C4⋊C4—22no—
649C4⋊C4—21no—
650C4⋊C4—21no—
651C4⋊C4—72no—
652C4⋊C4—72no—
653C4⋊C4—142no—
654C4⋊C4—142no—
655C4⋊C4—142no—
656C4⋊C4—142no—
657C4⋊C4—142no—
658C4⋊C4—142no—
659C4⋊C4—141no—
660C4⋊C4—141no—
661C4⋊C4—141no—
662C4⋊C4—141no—
663C4⋊C4C2×C22⋊D712yes—
664C4⋊C4C2×C22⋊D712yes—
665C4⋊C4C2×C22⋊D712yes—
666C4⋊C4C2×C22⋊D712yes—
667C4⋊C4C23×D712yes—
668C4⋊C4C23×D712yes—
669C4⋊C4C23×D712yes—
670C4⋊C4C23×D712yes—
671C22⋊C4—24no—
672C22⋊C4—142no—
673C22⋊C4—142no—
674C22⋊C4—142no—
675C22⋊C4—142no—
676C22⋊C4—142no—
677C22⋊C4—142no—
678C22⋊C4—142no—
679C22⋊C4—142no—
680C22⋊C4—142no—
681C22⋊C4C2×C22⋊D712yes—
682C22⋊C4C2×C22⋊D712yes—
683C22⋊C4C2×C22⋊D712yes—
684C22⋊C4C2×C22⋊D712yes—
685C42—24no—
686C42—142no—
687C42—142no—
688C42—142no—
689C42C2×C22⋊D712yes—
690C42C2×C22⋊D711yescharacteristic
691C42C2×C22⋊D711yescharacteristic
692C42C23×D711yescharacteristic
693C42C23×D711yescharacteristic
694C42C23×D712yes—
695C2×C7—22no—
696C2×C7—42no—
697C2×C7C2×#53611yescharacteristic
698C2×C7#358511yescharacteristic
699C2×C7#358611yescharacteristic
700D7—82no—
701C23—22no—
702C23—41no—
703C23—41no—
704C23—142no—
705C23C22×C22⋊D712yes—
706C23C22×C22⋊D711yescharacteristic
707Q8—84no—
708Q8—82no—
709Q8—82no—
710Q8—144no—
711Q8—561no—
712Q8—561no—
713D4—144no—
714D4—284no—
715D4—561no—
716D4—561no—
717D4—562no—
718D4—562no—
719C2×C4—22no—
720C2×C4—24no—
721C2×C4—24no—
722C2×C4—22no—
723C2×C4—22no—
724C2×C4—22no—
725C2×C4—22no—
726C2×C4—41no—
727C2×C4—41no—
728C2×C4—41no—
729C2×C4—41no—
730C2×C4—42no—
731C2×C4—42no—
732C2×C4—42no—
733C2×C4—42no—
734C2×C4—84no—
735C2×C4—142no—
736C2×C4—142no—
737C2×C4—142no—
738C2×C4—284no—
739C2×C4—562no—
740C2×C4—562no—
741C2×C4#655114yes—
742C2×C4C22×C22⋊D712yes—
743C2×C4C22×C22⋊D712yes—
744C2×C4C22×C22⋊D712yes—
745C2×C4C22×C22⋊D711yescharacteristic
746C2×C4C22×C22⋊D711yescharacteristic
747C2×C4C22×C22⋊D711yescharacteristic
748C2×C4C22×C22⋊D711yescharacteristic
749C2×C4C22×C22⋊D711yescharacteristic
750C2×C4C24×D711yescharacteristic
751C8—144no—
752C8—144no—
753C7#6086711yescharacteristic, complemented, Sylow
754C22—21no—
755C22—21no—
756C22—22no—
757C22—22no—
758C22—22no—
759C22—44no—
760C22—282no—
761C22—282no—
762C22—282no—
763C22#9050712yes—
764C22C23×C22⋊D711yescharacteristic
765C4—22no—
766C4—22no—
767C4—21no—
768C4—21no—
769C4—22no—
770C4—21no—
771C4—21no—
772C4—42no—
773C4—42no—
774C4—42no—
775C4—42no—
776C4—282no—
777C4—282no—
778C4—282no—
779C4#9050712yes—
780C4C2×#655112yes—
781C2—22no—
782C2—42no—
783C2—562no—
784C2C2×#9050711yescharacteristic
785C2#1174434511yescharacteristic
786C2#1174435511yescharacteristic
subgroupG/H
centerC22C23×C22⋊D7
commutator, cosocleC2×C4×C7C25
FrattiniC2×C4C24×D7
FittingC2×C7×#544C2
socleC22×C7C23×D4
prime radical#11742806C2
hypercenterC2×#544D7
hypocenterC7#60867
LCSG ▷ C2×C4×C7 ▷ C2×C7 ▷ C7
UCSC1 ◁ C22 ◁ C2×#117 ◁ C2×#544

Complements

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

NH ≅ G/Ntype
1. C2×C7×#544C2semidirect
3. #11740926C2semidirect
4. #11740924C2semidirect
5. #11740923C2semidirect
6. #11740922C2semidirect
7. #11740657C2semidirect
8. #11740652C2semidirect
9. #11740644C2semidirect
10. #11740462C2semidirect
11. #11740460C2semidirect
12. #11740457C2semidirect
13. #11739661C2semidirect
14. #11739654C2semidirect
15. #11739584C2semidirect
46. #89866C22semidirect
47. #89865C22semidirect
48. #89863C22semidirect
49. #89861C22semidirect
50. #89860C22semidirect
51. #89859C22semidirect
52. #89856C22semidirect
53. #89852C22semidirect
54. #89851C22semidirect
55. #89850C22semidirect
56. #89841C22semidirect
57. #89840C22semidirect
58. #89839C22semidirect
59. #89838C22semidirect
60. #89838C22semidirect
61. #89837C22semidirect
62. #89837C22semidirect
63. #89836C22semidirect
64. #89835C22semidirect
65. #89835C22semidirect
213. C2×#544D7semidirect
753. C7#60867semidirect

Maximal subgroups

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

subgroupindex
C2×C7×#5442
#117428062
#117409262
#117409242
#117409232
#117409222
#117406572
#117406522
#117406442
#117404622
#117404602
#117404572
#117396612
#117396542
#117395842
#608677