Finite Group Databasebeta

← #14226842

Subgroups — #14226842

Order 1792.

1822 conjugacy classes of subgroups.

The subgroup lattice has 852 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C7×#542C211yesmaximal, characteristic, complemented
2#11742806C211yesmaximal, characteristic, complemented
3#11740914C214yesmaximal, complemented
4#11740913C214yesmaximal, complemented
5#11740911C214yesmaximal, complemented
6#11740910C214yesmaximal, complemented
7#11740657C212yesmaximal, complemented
8#11740390C212yesmaximal, complemented
9#11740177C212yesmaximal, complemented
10#11740066C212yesmaximal, complemented
11#11739886C211yesmaximal, characteristic, complemented
12#11739876C211yesmaximal, characteristic, complemented
13#11739752C211yesmaximal, characteristic, complemented
14#11739741C211yesmaximal, characteristic, complemented
15#11739649C211yesmaximal, characteristic, complemented
16C7×#542—22no—
17C7×#542—22no—
18C7×#542C2214yes—
19C7×#542C2214yes—
20C2×C7×C4⋊Q8C2211yescharacteristic
21C2×C7×#126—21no—
22C2×C7×#124—21no—
23C2×C7×#124C2211yescharacteristic
24C2×C7×#123—21no—
25C2×C7×C22⋊Q8—21no—
26C2×C7×C22⋊Q8C2211yescharacteristic
27C2×C7×#121C2211yescharacteristic
28C2×C4×C7×Q8C2211yescharacteristic
29C2×C4×C7×D4C2211yescharacteristic
30C2×C7×#117C2211yescharacteristic
31C2×#6505C2212yes—
32C2×#6495C2212yes—
33#90482C2212yes—
34C22×#1136C2212yes—
35#90226C2212yescomplemented
36#90225C2212yescomplemented
37#90225C2212yescomplemented
38#90219—22no—
39#90219—22no—
40#90209C2212yescomplemented
41#90206—21no—
42#90206—21no—
43#90185—21no—
44#90185—21no—
45#90168C2211yescharacteristic
46C4×#1157C2212yes—
47#90161C2211yescharacteristic
48#89997C2212yes—
49#89987C2212yes—
50#89866C2214yescomplemented
51#89863C2214yescomplemented
52#89859C2214yescomplemented
53#89856C2214yescomplemented
54#89829C2214yescomplemented
55#89829C2214yescomplemented
56#89826C2214yescomplemented
57#89826C2214yescomplemented
58#89824C2214yescomplemented
59#89823C2214yescomplemented
60#89821C2214yescomplemented
61#89820C2214yescomplemented
62#89814C2214yes—
63#89813C2214yes—
64#89811C2214yes—
65#89810C2214yes—
66#89803C2212yescomplemented
67#89800C2214yescomplemented
68#89799C2212yescomplemented
69#89794C2214yescomplemented
70#89793C2212yescomplemented
71#89792C2212yescomplemented
72#89791C2212yescomplemented
73#89788C2214yescomplemented
74#89787C2212yescomplemented
75#89781C2214yescomplemented
76#89780C2212yescomplemented
77#89779C2212yescomplemented
78#89771C2214yescomplemented
79#89771C2214yescomplemented
80#89738C2212yes—
81#89738C2212yes—
82#89736C2212yes—
83#89736C2212yes—
84#89696C2211yescharacteristic
85#89696C2211yescharacteristic
86#89696C2212yes—
87#60919—71nomaximal, Sylow
88C22×C7×Q8—21no—
89C22×C7×Q8C2311yescharacteristic
90C22×C7×D4—21no—
91C22×C7×D4C2311yescharacteristic
92C23×C4×C7—21no—
93C23×C4×C7C2311yescharacteristic
94C2×#1157C2312yes—
95C7×C4⋊Q8—22no—
96C7×C4⋊Q8C2314yes—
97C7×#126—24no—
98C7×#126—24no—
99C7×#124—24no—
100C7×#124—24no—
101C7×#124—22no—
102C7×#124C2314yes—
103C7×#123—24no—
104C7×#123—24no—
105C7×C22⋊Q8—22no—
106C7×C22⋊Q8—24no—
107C7×C22⋊Q8—24no—
108C7×C22⋊Q8C2314yes—
109C7×#121—22no—
110C7×#121C2314yes—
111C4×C7×Q8—21no—
112C4×C7×Q8—21no—
113C4×C7×Q8C2312yes—
114C4×C7×Q8C2312yes—
115C4×C7×D4—21no—
116C4×C7×D4—21no—
117C4×C7×D4C2312yes—
118C4×C7×D4C2312yes—
119C7×#117D412yes—
120C7×#117D412yes—
121C7×#117C2312yes—
122C7×#117C2312yes—
123C2×C7×C4⋊C4—21no—
124C2×C7×C4⋊C4—21no—
125C2×C7×C4⋊C4—21no—
126C2×C7×C4⋊C4D411yescharacteristic
127C2×C7×C4⋊C4D411yescharacteristic
128C2×C7×C4⋊C4C2311yescharacteristic
129C2×C7×C4⋊C4C2311yescharacteristic
130C2×C7×C22⋊C4—21no—
131C2×C7×C22⋊C4—21no—
132C2×C7×C22⋊C4—21no—
133C2×C7×C22⋊C4—21no—
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—
141C2×#1144C2314yes—
142#6505—44no—
143C2×#1143C2314yes—
144C2×#1142C2314yes—
145#6495—44no—
146C2×#1141C2314yes—
147#6493—21no—
148#6493—21no—
149#6493C2312yes—
150#6493C2312yes—
151#6492—22no—
152C4×C22⋊D7—22no—
153C4×C22⋊D7—22no—
154C4×C22⋊D7—22no—
155C4×C22⋊D7—22no—
156#6489C2312yes—
157#6487—21no—
158#6487—21no—
159#6487C2312yes—
160#6487C2312yes—
161C2×#1136—44no—
162C2×#1136C2312yes—
163C2×#1136C2312yes—
164C2×#1136C2314yes—
165C22×C7⋊C8C2314yes—
166#6461—22no—
167#6461—22no—
168#6459—22no—
169#6459—22no—
170#6457—22no—
171#6457—22no—
172#6452—22no—
173#6452—22no—
174#6448—22no—
175#6448—22no—
176#6447—22no—
177#6447—22no—
178#6446—22no—
179#6446—22no—
180#6442—22no—
181#6442—22no—
182#6438C2312yes—
183#6437C2311yescharacteristic
184C4×D28—21no—
185C4×D28—21no—
186C4×D28C2312yes—
187C4×D28C2312yes—
188#6435—22no—
189C42×D7—22no—
190#6433C2312yes—
191#6432C2311yescharacteristic
192#6432C2311yescharacteristic
193#6432C2311yescharacteristic
194C4×Dic14—21no—
195C4×Dic14—21no—
196C4×Dic14C2312yes—
197C4×Dic14C2312yes—
198#6409C2314yes—
199#6409C2314yes—
200#6406C2314yes—
201#6406C2314yes—
202#6384C2314yes—
203#6384C2314yes—
204#6383C2314yes—
205#6383C2314yes—
206#6382C2314yes—
207#6382C2314yes—
208#6381C2314yes—
209#6381C2314yes—
210C4⋊(C7⋊C8)C2314yes—
211C4⋊(C7⋊C8)C2314yes—
212C4⋊(C7⋊C8)C2312yes—
213C4⋊(C7⋊C8)C2312yes—
214C4⋊(C7⋊C8)C2312yes—
215C4⋊(C7⋊C8)C2312yes—
216#3455—71no—
217C2×#542D711yescharacteristic, complemented
218#3263—74no—
219#3262—74no—
220#3258—74no—
221#3257—74no—
222#3079—72no—
223#3078—71no—
224#3077—71no—
225#3056—72no—
226#3055—72no—
227#3040—72no—
228#3037—71no—
229#3036—71no—
230#2905—71no—
231C24×C7—21no—
232C24×C7C2×D411yescharacteristic
233C2×C7×Q8—21no—
234C2×C7×Q8—24no—
235C2×C7×Q8—22no—
236C2×C7×Q8—22no—
237C2×C7×Q8—82no—
238C2×C7×Q8C2412yes—
239C2×C7×D4—24no—
240C2×C7×D4—21no—
241C2×C7×D4—22no—
242C2×C7×D4—22no—
243C2×C7×D4—82no—
244C2×C7×D4C2412yes—
245C22×C4×C7—22no—
246C22×C4×C7—22no—
247C22×C4×C7—21no—
248C22×C4×C7—21no—
249C22×C4×C7—21no—
250C22×C4×C7—22no—
251C22×C4×C7—22no—
252C22×C4×C7—82no—
253C22×C4×C7C2×D412yes—
254C22×C4×C7C2×D411yescharacteristic
255C22×C4×C7C2×D411yescharacteristic
256C22×C4×C7C2×D411yescharacteristic
257C22×C4×C7C2×D411yescharacteristic
258C22×C4×C7C2×D411yescharacteristic
259C22×C4×C7C2412yes—
260C22×C4×C7C2411yescharacteristic
261C2×C22⋊D7—22no—
262C2×C22⋊D7—22no—
263C2×C22⋊D7—22no—
264#1157—24no—
265#1157—24no—
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—22no—
276C7×C4⋊C4—22no—
277C7×C4⋊C4—24no—
278C7×C4⋊C4—24no—
279C7×C4⋊C4—21no—
280C7×C4⋊C4—21no—
281C7×C4⋊C4C2×D412yes—
282C7×C4⋊C4C2×D412yes—
283C7×C4⋊C4C2×D412yes—
284C7×C4⋊C4C2×D412yes—
285C7×C4⋊C4C2412yes—
286C7×C4⋊C4C2412yes—
287C7×C22⋊C4—24no—
288C7×C22⋊C4—22no—
289C7×C22⋊C4—22no—
290C7×C22⋊C4—24no—
291C7×C22⋊C4—24no—
292C7×C22⋊C4—24no—
293C7×C22⋊C4C2×D412yes—
294C7×C22⋊C4C2×D412yes—
295C7×C22⋊C4C2×D412yes—
296C7×C22⋊C4C2×D412yes—
297C42×C7—22no—
298C42×C7—22no—
299C42×C7C2×D411yescharacteristic
300C42×C7C2×D411yescharacteristic
301C42×C7C2×D412yes—
302C42×C7C2412yes—
303C42×C7C2411yescharacteristic
304C42×C7C2411yescharacteristic
305C22⋊Dic7—22no—
306C22⋊Dic7—22no—
307C22⋊Dic7—22no—
308#1144—44no—
309#1143—44no—
310#1142—44no—
311#1141—44no—
312(C2×D7)⋊C4—22no—
313(C2×D7)⋊C4—22no—
314(C2×D7)⋊C4—22no—
315(C2×D7)⋊C4—22no—
316(C2×D7)⋊C4—22no—
317(C2×D7)⋊C4—22no—
318C4⋊Dic7—21no—
319C4⋊Dic7—21no—
320C4⋊Dic7—21no—
321C4⋊Dic7—21no—
322C4⋊Dic7C2412yes—
323C4⋊Dic7C2412yes—
324Dic7⋊C4—22no—
325Dic7⋊C4—22no—
326Dic7⋊C4—22no—
327Dic7⋊C4—22no—
328Dic7⋊C4—22no—
329Dic7⋊C4—22no—
330C4×Dic7—22no—
331C4×Dic7—22no—
332C4×Dic7—22no—
333#1136—24no—
334#1136—24no—
335#1136—44no—
336C2×C7⋊C8—44no—
337C2×C7⋊C8C2414yes—
338C2×C7⋊C8C2414yes—
339C2×#137—72no—
340C2×AGL(1,ℤ/8)—72no—
341C22×M16—72no—
342#542—22no—
343#542—22no—
344#542—72no—
345#542—72no—
346#542C2×D714yes—
347#542C2×D714yes—
348#541—72no—
349#540—72no—
350#539—141no—
351#539—141no—
352#538—141no—
353#538—141no—
354#533—71no—
355#532—71no—
356C2×C4⋊Q8C2×D711yescharacteristic
357#529—142no—
358#529—142no—
359C2×#126—21no—
360C2×#124—21no—
361C2×#124C2×D711yescharacteristic
362#525—72no—
363C2×#123—21no—
364C2×C22⋊Q8—21no—
365C2×C22⋊Q8C2×D711yescharacteristic
366C2×#121C2×D711yescharacteristic
367C4×#41—72no—
368C2×C4×Q8C2×D711yescharacteristic
369C2×C4×D4C2×D711yescharacteristic
370C2×#117C2×D711yescharacteristic
371#479—74no—
372#478—74no—
373#477—74no—
374#477—72no—
375#476—74no—
376#476—72no—
377#475—74no—
378#475—72no—
379#474—74no—
380#474—72no—
381#470—74no—
382#469—74no—
383#468—74no—
384#468—74no—
385#467—74no—
386#466—74no—
387#465—74no—
388#465—74no—
389#464—74no—
390#464—74no—
391#464—74no—
392#463—74no—
393#463—74no—
394#463—74no—
395#462—72no—
396#461—72no—
397#460—72no—
398#459—72no—
399#428—72no—
400#428—72no—
401#424—74no—
402#424—74no—
403#423—71no—
404#423—71no—
405#423—72no—
406#419—72no—
407#418—72no—
408#417—72no—
409#417—72no—
410C23×C7—22no—
411C23×C7—22no—
412C23×C7—41no—
413C23×C7—41no—
414C23×C7—42no—
415C23×C7—42no—
416C23×C7—42no—
417C23×C7C22×D412yes—
418C23×C7C22×D411yescharacteristic
419C22×D7—22no—
420C7×Q8—22no—
421C7×Q8—22no—
422C7×Q8—42no—
423C7×Q8—84no—
424C7×D4—22no—
425C7×D4—22no—
426C7×D4—42no—
427C7×D4—84no—
428C2×C4×C7—22no—
429C2×C4×C7—24no—
430C2×C4×C7—22no—
431C2×C4×C7—22no—
432C2×C4×C7—22no—
433C2×C4×C7—22no—
434C2×C4×C7—22no—
435C2×C4×C7—41no—
436C2×C4×C7—41no—
437C2×C4×C7—41no—
438C2×C4×C7—41no—
439C2×C4×C7—42no—
440C2×C4×C7—42no—
441C2×C4×C7—42no—
442C2×C4×C7—82no—
443C2×C4×C7—82no—
444C2×C4×C7C22×D412yes—
445C2×C4×C7C22×D412yes—
446C2×C4×C7C22×D411yescharacteristic
447C2×C4×C7C22×D411yescharacteristic
448C2×C4×C7C22×D412yes—
449C2×C4×C7C22×D411yescharacteristic
450C2×C4×C7C22×D411yescharacteristic
451C2×C4×C7C22×D411yescharacteristic
452C2×C4×C7H(5,𝔽2)12yes—
453C2×C4×C72−1+412yes—
454C2×C4×C7C2511yescharacteristic
455C22⋊D7—44no—
456C22⋊D7—82no—
457C22⋊D7—82no—
458C2×Dic7—22no—
459C2×Dic7—22no—
460C2×Dic7—22no—
461D28—22no—
462D28—22no—
463D28—81no—
464D28—81no—
465C4×D7—44no—
466C4×D7—82no—
467C4×D7—82no—
468Dic14—22no—
469Dic14—22no—
470Dic14—81no—
471Dic14—81no—
472C7⋊C8—24no—
473C7⋊C8—24no—
474C2×#41—72no—
475C22×Q8—21no—
476C22×Q8C22×D711yescharacteristic
477C22×D4—21no—
478C22×D4C22×D711yescharacteristic
479C23×C4—21no—
480C23×C4C22×D711yescharacteristic
481#137—284no—
482AGL(1,ℤ/8)—284no—
483C2×Q16—74no—
484C2×SD16—74no—
485C2×SD16—74no—
486C2×D8—74no—
487C2×M16—72no—
488C2×M16—72no—
489C2×M16—74no—
490C2×M16—284no—
491C22×C8—74no—
492C4⋊Q8—22no—
493C4⋊Q8—71no—
494C4⋊Q8—71no—
495C4⋊Q8—71no—
496C4⋊Q8C22×D714yes—
497#127—71no—
498#126—24no—
499#126—24no—
500#126—142no—
501#126—142no—
502#126—142no—
503#126—142no—
504#125—72no—
505#125—142no—
506#125—142no—
507#124—24no—
508#124—24no—
509#124—22no—
510#124—72no—
511#124—142no—
512#124—142no—
513#124C22×D714yes—
514#123—24no—
515#123—24no—
516#123—142no—
517#123—142no—
518#123—142no—
519#123—142no—
520#123—142no—
521C22⋊Q8—22no—
522C22⋊Q8—24no—
523C22⋊Q8—24no—
524C22⋊Q8—72no—
525C22⋊Q8—72no—
526C22⋊Q8—141no—
527C22⋊Q8—141no—
528C22⋊Q8—142no—
529C22⋊Q8—142no—
530C22⋊Q8C22×D714yes—
531#121—22no—
532#121—72no—
533#121—72no—
534#121—141no—
535#121—141no—
536#121—142no—
537#121—142no—
538#121C22×D714yes—
539#120—142no—
540C4×Q8—21no—
541C4×Q8—21no—
542C4×Q8—72no—
543C4×Q8—72no—
544C4×Q8—141no—
545C4×Q8—141no—
546C4×Q8C22×D712yes—
547C4×Q8C22×D712yes—
548C4×D4—21no—
549C4×D4—21no—
550C4×D4—72no—
551C4×D4—72no—
552C4×D4—142no—
553C4×D4—142no—
554C4×D4—142no—
555C4×D4—142no—
556C4×D4—141no—
557C4×D4—141no—
558C4×D4C22×D712yes—
559C4×D4C22×D712yes—
560#117—72no—
561#117—142no—
562#117C22⋊D712yes—
563#117C22⋊D712yes—
564#117C22×D712yes—
565#117C22×D712yes—
566C2×C4⋊C4—21no—
567C2×C4⋊C4—21no—
568C2×C4⋊C4—21no—
569C2×C4⋊C4C22⋊D711yescharacteristic
570C2×C4⋊C4C22⋊D711yescharacteristic
571C2×C4⋊C4C22×D711yescharacteristic
572C2×C4⋊C4C22×D711yescharacteristic
573C2×C22⋊C4—21no—
574C2×C22⋊C4—21no—
575C2×C22⋊C4—21no—
576C2×C22⋊C4—21no—
577C2×C22⋊C4—21no—
578C2×C22⋊C4C22⋊D711yescharacteristic
579C2×C22⋊C4C22⋊D711yescharacteristic
580C2×C42—21no—
581C2×C42—142no—
582C2×C42C22×D711yescharacteristic
583C2×C42C22×D711yescharacteristic
584#107—74no—
585#107—74no—
586#106—74no—
587#106—74no—
588C4⋊C8—72no—
589C4⋊C8—72no—
590C4⋊C8—72no—
591C4⋊C8—74no—
592C4⋊C8—74no—
593C4⋊C8—72no—
594#103—74no—
595#103—74no—
596#103—74no—
597#103—74no—
598#102—74no—
599#102—74no—
600#102—74no—
601#102—74no—
602C22×C7—21no—
603C22×C7—21no—
604C22×C7—22no—
605C22×C7—22no—
606C22×C7—22no—
607C22×C7—42no—
608C22×C7—42no—
609C22×C7—42no—
610C22×C7—82no—
611C22×C7—84no—
612C22×C7#53712yes—
613C22×C7C23×D411yescharacteristic
614C2×D7—42no—
615C2×D7—42no—
616C2×D7—42no—
617C4×C7—21no—
618C4×C7—22no—
619C4×C7—21no—
620C4×C7—21no—
621C4×C7—22no—
622C4×C7—21no—
623C4×C7—22no—
624C4×C7—42no—
625C4×C7—42no—
626C4×C7—42no—
627C4×C7#53712yes—
628C4×C7C2×H(5,𝔽2)11yescharacteristic
629C4×C7C2×2−1+411yescharacteristic
630Dic7—42no—
631Dic7—42no—
632Dic7—42no—
633C24—21no—
634C24C2×C22⋊D711yescharacteristic
635#41—144no—
636#41—144no—
637C2×Q8—21no—
638C2×Q8—24no—
639C2×Q8—22no—
640C2×Q8—22no—
641C2×Q8—72no—
642C2×Q8—82no—
643C2×Q8—141no—
644C2×Q8—141no—
645C2×Q8C23×D712yes—
646C2×D4—24no—
647C2×D4—22no—
648C2×D4—22no—
649C2×D4—21no—
650C2×D4—72no—
651C2×D4—82no—
652C2×D4—142no—
653C2×D4—142no—
654C2×D4—142no—
655C2×D4—141no—
656C2×D4—141no—
657C2×D4C23×D712yes—
658C22×C4—22no—
659C22×C4—22no—
660C22×C4—21no—
661C22×C4—21no—
662C22×C4—21no—
663C22×C4—22no—
664C22×C4—22no—
665C22×C4—82no—
666C22×C4—142no—
667C22×C4—142no—
668C22×C4—142no—
669C22×C4C2×C22⋊D711yescharacteristic
670C22×C4C2×C22⋊D712yes—
671C22×C4C2×C22⋊D711yescharacteristic
672C22×C4C2×C22⋊D711yescharacteristic
673C22×C4C2×C22⋊D711yescharacteristic
674C22×C4C2×C22⋊D711yescharacteristic
675C22×C4C23×D712yes—
676C22×C4C23×D711yescharacteristic
677Q16—284no—
678SD16—284no—
679SD16—284no—
680D8—284no—
681M16—144no—
682M16—144no—
683M16—284no—
684C2×C8—74no—
685C2×C8—74no—
686C2×C8—284no—
687C4⋊C4—22no—
688C4⋊C4—22no—
689C4⋊C4—24no—
690C4⋊C4—24no—
691C4⋊C4—21no—
692C4⋊C4—21no—
693C4⋊C4—72no—
694C4⋊C4—72no—
695C4⋊C4—142no—
696C4⋊C4—142no—
697C4⋊C4—142no—
698C4⋊C4—142no—
699C4⋊C4—142no—
700C4⋊C4—142no—
701C4⋊C4—141no—
702C4⋊C4—141no—
703C4⋊C4—141no—
704C4⋊C4—141no—
705C4⋊C4C2×C22⋊D712yes—
706C4⋊C4C2×C22⋊D712yes—
707C4⋊C4C2×C22⋊D712yes—
708C4⋊C4C2×C22⋊D712yes—
709C4⋊C4C23×D712yes—
710C4⋊C4C23×D712yes—
711C22⋊C4—24no—
712C22⋊C4—22no—
713C22⋊C4—22no—
714C22⋊C4—24no—
715C22⋊C4—24no—
716C22⋊C4—24no—
717C22⋊C4—142no—
718C22⋊C4—142no—
719C22⋊C4—142no—
720C22⋊C4—142no—
721C22⋊C4—142no—
722C22⋊C4—142no—
723C22⋊C4—142no—
724C22⋊C4—142no—
725C22⋊C4—142no—
726C22⋊C4C2×C22⋊D712yes—
727C22⋊C4C2×C22⋊D712yes—
728C22⋊C4C2×C22⋊D712yes—
729C22⋊C4C2×C22⋊D712yes—
730C42—22no—
731C42—22no—
732C42—142no—
733C42—142no—
734C42—142no—
735C42C2×C22⋊D712yes—
736C42C2×C22⋊D711yescharacteristic
737C42C2×C22⋊D711yescharacteristic
738C42C23×D712yes—
739C42C23×D711yescharacteristic
740C42C23×D711yescharacteristic
741C2×C7—22no—
742C2×C7—42no—
743C2×C7—82no—
744C2×C7C2×#53711yescharacteristic
745C2×C7#358511yescharacteristic
746C2×C7#358611yescharacteristic
747D7—82no—
748C23—22no—
749C23—22no—
750C23—41no—
751C23—41no—
752C23—42no—
753C23—42no—
754C23—42no—
755C23—142no—
756C23C22×C22⋊D712yes—
757C23C22×C22⋊D711yescharacteristic
758Q8—22no—
759Q8—22no—
760Q8—42no—
761Q8—84no—
762Q8—142no—
763Q8—142no—
764Q8—561no—
765Q8—561no—
766D4—22no—
767D4—22no—
768D4—42no—
769D4—84no—
770D4—142no—
771D4—142no—
772D4—284no—
773D4—561no—
774D4—561no—
775D4—562no—
776D4—562no—
777C2×C4—22no—
778C2×C4—24no—
779C2×C4—22no—
780C2×C4—22no—
781C2×C4—22no—
782C2×C4—22no—
783C2×C4—22no—
784C2×C4—41no—
785C2×C4—41no—
786C2×C4—41no—
787C2×C4—41no—
788C2×C4—42no—
789C2×C4—42no—
790C2×C4—42no—
791C2×C4—82no—
792C2×C4—82no—
793C2×C4—142no—
794C2×C4—142no—
795C2×C4—142no—
796C2×C4—284no—
797C2×C4—562no—
798C2×C4—562no—
799C2×C4#655312yes—
800C2×C4#655412yes—
801C2×C4C22×C22⋊D711yescharacteristic
802C2×C4C22×C22⋊D711yescharacteristic
803C2×C4C22×C22⋊D712yes—
804C2×C4C22×C22⋊D712yes—
805C2×C4C22×C22⋊D711yescharacteristic
806C2×C4C22×C22⋊D711yescharacteristic
807C2×C4C22×C22⋊D712yes—
808C2×C4C22×C22⋊D711yescharacteristic
809C2×C4C24×D711yescharacteristic
810C8—144no—
811C8—144no—
812C7#6091911yescharacteristic, complemented, Sylow
813C22—21no—
814C22—21no—
815C22—22no—
816C22—22no—
817C22—22no—
818C22—42no—
819C22—42no—
820C22—42no—
821C22—82no—
822C22—84no—
823C22—282no—
824C22—282no—
825C22—282no—
826C22#9052412yes—
827C22C23×C22⋊D711yescharacteristic
828C4—22no—
829C4—21no—
830C4—21no—
831C4—22no—
832C4—22no—
833C4—21no—
834C4—21no—
835C4—42no—
836C4—42no—
837C4—42no—
838C4—282no—
839C4—282no—
840C4—282no—
841C4#9052412yes—
842C4C2×#655311yescharacteristic
843C4C2×#655411yescharacteristic
844C2—22no—
845C2—42no—
846C2—82no—
847C2—562no—
848C2C2×#9052411yescharacteristic
849C2#1174434511yescharacteristic
850C2#1174435511yescharacteristic
subgroupG/H
centerC22C23×C22⋊D7
commutator, cosocleC2×C4×C7C25
FrattiniC2×C4C24×D7
FittingC2×C7×#542C2
socleC22×C7C23×D4
hypercenterC2×#542D7
hypocenterC7#60919
LCSG ▷ C2×C4×C7 ▷ C2×C7 ▷ C7
UCSC1 ◁ C22 ◁ C2×#117 ◁ C2×#542

Complements

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

NH ≅ G/Ntype
1. C2×C7×#542C2semidirect
2. #11742806C2semidirect
3. #11740914C2semidirect
4. #11740913C2semidirect
5. #11740911C2semidirect
6. #11740910C2semidirect
7. #11740657C2semidirect
8. #11740390C2semidirect
9. #11740177C2semidirect
10. #11740066C2semidirect
11. #11739886C2semidirect
12. #11739876C2semidirect
13. #11739752C2semidirect
14. #11739741C2semidirect
15. #11739649C2semidirect
35. #90226C22semidirect
36. #90225C22semidirect
37. #90225C22semidirect
40. #90209C22semidirect
50. #89866C22semidirect
51. #89863C22semidirect
52. #89859C22semidirect
53. #89856C22semidirect
54. #89829C22semidirect
55. #89829C22semidirect
56. #89826C22semidirect
57. #89826C22semidirect
58. #89824C22semidirect
59. #89823C22semidirect
60. #89821C22semidirect
61. #89820C22semidirect
66. #89803C22semidirect
67. #89800C22semidirect
68. #89799C22semidirect
69. #89794C22semidirect
70. #89793C22semidirect
71. #89792C22semidirect
72. #89791C22semidirect
73. #89788C22semidirect
74. #89787C22semidirect
75. #89781C22semidirect
76. #89780C22semidirect
77. #89779C22semidirect
78. #89771C22semidirect
79. #89771C22semidirect
217. C2×#542D7semidirect
812. C7#60919semidirect

Maximal subgroups

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

subgroupindex
C2×C7×#5422
#117428062
#117409142
#117409132
#117409112
#117409102
#117406572
#117403902
#117401772
#117400662
#117398862
#117398762
#117397522
#117397412
#117396492
#609197