Finite Group Databasebeta

← #14222185

Subgroups — #14222185

Order 1792.

2570 conjugacy classes of subgroups.

The subgroup lattice has 904 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11742748C211yesmaximal, characteristic, complemented
2C22×C4×D28C211yesmaximal, characteristic, complemented
3C7×#2920C211yesmaximal, characteristic, complemented
4#11736791C214yesmaximal, complemented
5#11736789C212yesmaximal, complemented
6#11736788C212yesmaximal, complemented
7#11736745C214yesmaximal, complemented
8#11736743C212yesmaximal, complemented
9#11736742C212yesmaximal, complemented
10#11736504C212yesmaximal, complemented
11#11736500C212yesmaximal, complemented
12#11736082C212yesmaximal, complemented
13#11736067C212yesmaximal, complemented
14C4×#6471C214yesmaximal, complemented
15C23×D28C2211yescharacteristic
16C23×C4×D7—21no—
17C22×C42×C7C2211yescharacteristic
18#90482—21no—
19#90482—21no—
20#90482C2212yes—
21C22×(C2×D7)⋊C4—21no—
22C22×C4⋊Dic7C2211yescharacteristic
23C2×#6471C2214yes—
24#90170—21no—
25#90170—21no—
26#90170—21no—
27#90170—21no—
28#90170C2212yescomplemented
29#90170C2212yescomplemented
30#90168C2211yescharacteristic, complemented
31#90168C2211yescharacteristic, complemented
32#90168C2211yescharacteristic, complemented
33C4×#1157—21no—
34C4×#1157—21no—
35C4×#1157C2212yescomplemented
36C2×C4×D28—21no—
37C2×C4×D28—21no—
38C2×C4×D28—21no—
39C2×C4×D28—21no—
40C2×C4×D28—21no—
41C2×C4×D28—21no—
42C2×C4×D28C2212yes—
43C2×C4×D28C2212yes—
44C2×C4×D28C2212yes—
45C2×C4×D28C2212yes—
46C2×C4×D28C2212yes—
47C2×C4×D28C2212yes—
48#90161C2211yescharacteristic, complemented
49#90161C2211yescharacteristic, complemented
50#90161C2211yescharacteristic, complemented
51C7×#432C2212yescomplemented
52C7×#432C2212yescomplemented
53C7×#431C2212yescomplemented
54C7×#431C2212yescomplemented
55C7×#423C2212yescomplemented
56C7×#407C2212yes—
57C4×C7×M16C2212yescomplemented
58#89905C2214yescomplemented
59#89903C2214yes—
60#89893C2214yescomplemented
61#89619C2218yescomplemented
62#89618C2214yescomplemented
63#89616C2218yescomplemented
64#89615C2214yescomplemented
65#89614C2214yescomplemented
66#89613C2214yescomplemented
67#89508C2214yescomplemented
68#89507C2214yescomplemented
69#89504C2214yes—
70#89504C2214yes—
71#89503C2214yes—
72#89503C2214yes—
73#89494C2214yescomplemented
74#89493C2214yescomplemented
75#89483C2218yescomplemented
76#89482C2218yescomplemented
77C4×D56C2218yescomplemented
78C4×#1132C2218yescomplemented
79#60558—71nomaximal, Sylow
80C24×D7—21no—
81C23×C4×C7D411yescharacteristic
82C23×C4×C7D411yescharacteristic
83C23×C4×C7C2311yescharacteristic
84C23×Dic7—21no—
85C2×#1157—21no—
86C2×#1157—21no—
87C2×#1157C2312yes—
88C22×D28—21no—
89C22×D28—21no—
90C22×D28—21no—
91C22×D28—28no—
92C22×D28C2312yes—
93C22×D28C2312yes—
94C22×D28C2312yes—
95C22×C4×D7—22no—
96C22×C4×D7—22no—
97C22×C4×D7—22no—
98C22×C4×D7—22no—
99C22×C4×D7—22no—
100C22×C4×D7—22no—
101C22×C4×D7—48no—
102C2×C7×M16C2314yes—
103C2×C42×C7D411yescharacteristic
104C2×C42×C7D411yescharacteristic
105C2×C42×C7D411yescharacteristic
106C2×C42×C7D411yescharacteristic
107C2×C42×C7D411yescharacteristic
108C2×C42×C7D411yescharacteristic
109C2×C42×C7C2311yescharacteristic
110C2×C42×C7C2311yescharacteristic
111C2×C42×C7C2311yescharacteristic
112C2×C42×C7C2311yescharacteristic
113C2×C42×C7C2311yescharacteristic
114C2×C42×C7C2311yescharacteristic
115#6516—22no—
116#6493—21no—
117#6493—21no—
118#6493—21no—
119#6493—21no—
120#6493C2312yes—
121#6493C2312yes—
122#6492—22no—
123#6492—22no—
124#6492—22no—
125C4×C22⋊D7—22no—
126C4×C22⋊D7—22no—
127C4×C22⋊D7—22no—
128C4×C22⋊D7—22no—
129C4×C22⋊D7—22no—
130C4×C22⋊D7—22no—
131C2×(C2×D7)⋊C4—22no—
132C2×(C2×D7)⋊C4—22no—
133C2×(C2×D7)⋊C4—22no—
134C2×(C2×D7)⋊C4—22no—
135C2×(C2×D7)⋊C4—22no—
136C2×(C2×D7)⋊C4—22no—
137#6489—21no—
138#6489—21no—
139#6489C2312yes—
140C2×C4⋊Dic7—21no—
141C2×C4⋊Dic7—21no—
142C2×C4⋊Dic7—21no—
143C2×C4⋊Dic7C2312yes—
144C2×C4⋊Dic7C2312yes—
145C2×C4⋊Dic7C2312yes—
146#6487—21no—
147#6487—21no—
148#6487—21no—
149#6487—21no—
150#6487C2312yes—
151#6487C2312yes—
152#6471—216no—
153C2×D56C2318yes—
154C2×#1132C2318yes—
155#6439—22no—
156#6439—22no—
157#6438—21no—
158#6438—21no—
159#6438C2312yescomplemented
160#6437C2311yescharacteristic, complemented
161C4×D28—22no—
162C4×D28—22no—
163C4×D28—22no—
164C4×D28—22no—
165C4×D28—22no—
166C4×D28—22no—
167C4×D28—22no—
168C4×D28—22no—
169C4×D28—22no—
170C4×D28—22no—
171C4×D28—22no—
172C4×D28—22no—
173C4×D28—21no—
174C4×D28—21no—
175C4×D28—21no—
176C4×D28—21no—
177C4×D28C2314yes—
178C4×D28C2314yes—
179C4×D28C2314yes—
180C4×D28C2314yes—
181C4×D28C2312yescomplemented
182C4×D28C2312yescomplemented
183#6435—22no—
184#6435—22no—
185#6435—22no—
186C42×D7—22no—
187#6433—21no—
188#6433—21no—
189#6433C2312yescomplemented
190#6432C2311yescharacteristic, complemented
191#6432C2311yescharacteristic, complemented
192#6432C2311yescharacteristic, complemented
193C4×Dic14—21no—
194C4×Dic14—21no—
195C4×Dic14—21no—
196C4×Dic14—21no—
197C4×Dic14C2312yescomplemented
198C4×Dic14C2312yescomplemented
199C7×C4⋊C8C2314yescomplemented
200C7×C4⋊C8C2314yescomplemented
201C7×C22⋊C8C2314yes—
202C7×C22⋊C8C2314yes—
203C7×#97C2314yescomplemented
204C4×C7×C8C2314yescomplemented
205#6395C2318yes—
206#6395C2318yes—
207#6395C2318yescomplemented
208#6392C2318yescomplemented
209#6391C2318yescomplemented
210#6390C2318yescomplemented
211#3444—71no—
212C22×C4×D4—71no—
213#3114—74no—
214#3110—72no—
215#3109—72no—
216#3105—74no—
217#3101—72no—
218#3100—72no—
219#3092—72no—
220#3077—72no—
221#3036—72no—
222#3003—72no—
223C4×AGL(1,ℤ/8)—74no—
224#2920D711yescharacteristic, complemented
225C24×C7C2×D411yescharacteristic
226C23×D7—28no—
227C23×D7—22no—
228C23×D7—22no—
229C23×D7—22no—
230C23×D7—44no—
231C23×D7—44no—
232C22×C4×C7—24no—
233C22×C4×C7—24no—
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—22no—
256C22×Dic7—22no—
257C22×Dic7—22no—
258C22×Dic7—22no—
259C22×Dic7—44no—
260#1157—28no—
261#1157—44no—
262#1157—44no—
263C2×D28—28no—
264C2×D28—28no—
265C2×D28—28no—
266C2×D28—22no—
267C2×D28—22no—
268C2×D28—22no—
269C2×D28—24no—
270C2×D28—28no—
271C2×D28—28no—
272C2×D28—21no—
273C2×D28—21no—
274C2×D28#4118yescomplemented
275C2×D28C2412yes—
276C2×D28C2414yes—
277C2×C4×D7—22no—
278C2×C4×D7—22no—
279C2×C4×D7—22no—
280C2×C4×D7—24no—
281C2×C4×D7—24no—
282C2×C4×D7—24no—
283C2×C4×D7—24no—
284C2×C4×D7—48no—
285C2×C4×D7—48no—
286C2×C4×D7—48no—
287C2×C4×D7—48no—
288C2×C4×D7—48no—
289C2×C4×D7—48no—
290C2×Dic14—21no—
291C2×Dic14—21no—
292C2×Dic14C2412yes—
293C7×M16—28no—
294C2×C7×C8C2418yes—
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×C7C2×D411yescharacteristic
304C42×C7C2×D411yescharacteristic
305C42×C7C2×D411yescharacteristic
306C42×C7C2×D411yescharacteristic
307C42×C7C2411yescharacteristic
308C42×C7C2411yescharacteristic
309C42×C7C2411yescharacteristic
310C42×C7C2411yescharacteristic
311C22⋊Dic7—22no—
312C22⋊Dic7—22no—
313C22⋊Dic7—22no—
314(C2×D7)⋊C4—22no—
315(C2×D7)⋊C4—22no—
316(C2×D7)⋊C4—22no—
317(C2×D7)⋊C4—22no—
318(C2×D7)⋊C4—22no—
319(C2×D7)⋊C4—22no—
320(C2×D7)⋊C4—24no—
321(C2×D7)⋊C4—24no—
322(C2×D7)⋊C4—24no—
323(C2×D7)⋊C4—24no—
324C4⋊Dic7—21no—
325C4⋊Dic7—21no—
326C4⋊Dic7—21no—
327C4⋊Dic7—21no—
328C4⋊Dic7—22no—
329C4⋊Dic7—22no—
330C4⋊Dic7—22no—
331C4⋊Dic7C2412yes—
332C4⋊Dic7C2412yes—
333C4⋊Dic7C2414yes—
334Dic7⋊C4—22no—
335Dic7⋊C4—22no—
336Dic7⋊C4—22no—
337Dic7⋊C4—22no—
338Dic7⋊C4—22no—
339Dic7⋊C4—22no—
340C4×Dic7—22no—
341C4×Dic7—22no—
342C4×Dic7—22no—
343D56—216no—
344#1132—216no—
345C23×D4—71no—
346C24×C4—141no—
347C2×AGL(1,ℤ/8)—74no—
348#533—71no—
349#533—71no—
350#533—71no—
351#532—71no—
352#532—71no—
353#532—71no—
354#529—72no—
355#529—72no—
356#529—141no—
357#529—141no—
358#529—141no—
359#529—141no—
360#525—72no—
361#525—141no—
362#525—141no—
363C4×#41—72no—
364C4×#41—141no—
365C4×#41—141no—
366C2×C4×D4—72no—
367C2×C4×D4—72no—
368C2×C4×D4—72no—
369C2×C4×D4—72no—
370C2×C4×D4—72no—
371C2×C4×D4—72no—
372C2×C4×D4—141no—
373C2×C4×D4—141no—
374C2×C4×D4—141no—
375C2×C4×D4—141no—
376C2×C4×D4—141no—
377C2×C4×D4—141no—
378C22×C4⋊C4—71no—
379C22×C22⋊C4—141no—
380C22×C42C2×D711yescharacteristic
381#484—74no—
382#483—74no—
383#481—74no—
384#480—74no—
385#478—78no—
386#476—74no—
387#474—74no—
388#463—78no—
389#461—74no—
390#459—74no—
391#450—74no—
392#450—74no—
393#447—74no—
394#447—74no—
395#442—78no—
396#440—78no—
397C4×SD16—78no—
398C4×D8—78no—
399#432C2×D712yescomplemented
400#432C2×D712yescomplemented
401#431C2×D712yescomplemented
402#431C2×D712yescomplemented
403#428—74no—
404#423C2×D712yescomplemented
405#418—74no—
406#417—74no—
407#407C2×D712yes—
408C4×M16C2×D712yescomplemented
409C23×C7—22no—
410C23×C7—22no—
411C23×C7—22no—
412C23×C7C22×D411yescharacteristic
413C23×C7C22×D411yescharacteristic
414C23×C7C22×D411yescharacteristic
415C22×D7—28no—
416C22×D7—28no—
417C22×D7—28no—
418C22×D7—24no—
419C22×D7—22no—
420C22×D7—44no—
421C22×D7—44no—
422C22×D7—432no—
423C22×D7—44no—
424C22×D7—44no—
425C22×D7—44no—
426C22×D7—44no—
427C2×C4×C7—22no—
428C2×C4×C7—22no—
429C2×C4×C7—22no—
430C2×C4×C7—22no—
431C2×C4×C7—22no—
432C2×C4×C7—22no—
433C2×C4×C7—22no—
434C2×C4×C7—22no—
435C2×C4×C7—22no—
436C2×C4×C7—22no—
437C2×C4×C7—22no—
438C2×C4×C7—22no—
439C2×C4×C7—41no—
440C2×C4×C7—41no—
441C2×C4×C7—41no—
442C2×C4×C7—41no—
443C2×C4×C7AGL(1,ℤ/8)14yescomplemented
444C2×C4×C7C22×D411yescharacteristic
445C2×C4×C7C22×D411yescharacteristic
446C2×C4×C7C22×D411yescharacteristic
447C2×C4×C7C22×D411yescharacteristic
448C2×C4×C7C22×D411yescharacteristic
449C2×C4×C7C22×D411yescharacteristic
450C2×C4×C7C22×D411yescharacteristic
451C2×C4×C7C22×D411yescharacteristic
452C2×C4×C7C22×D411yescharacteristic
453C2×C4×C7C22×D411yescharacteristic
454C2×C4×C7C22×D411yescharacteristic
455C2×C4×C7C2×#4114yes—
456C2×C4×C7C2511yescharacteristic
457C22⋊D7—44no—
458C22⋊D7—44no—
459C22⋊D7—44no—
460C2×Dic7—22no—
461C2×Dic7—22no—
462C2×Dic7—22no—
463C2×Dic7—24no—
464C2×Dic7—44no—
465C2×Dic7—44no—
466C2×Dic7—44no—
467D28—28no—
468D28—28no—
469D28—28no—
470D28—24no—
471D28—24no—
472D28—42no—
473D28—42no—
474D28C2×#4118yes—
475C4×D7—48no—
476C4×D7—48no—
477C4×D7—44no—
478C4×D7—44no—
479C4×D7—48no—
480C4×D7—48no—
481C4×D7—44no—
482Dic14—24no—
483Dic14—42no—
484Dic14—42no—
485C7×C8—28no—
486C25—141no—
487C2×#41—72no—
488C2×#41—141no—
489C2×#41—141no—
490C22×D4—72no—
491C22×D4—72no—
492C22×D4—72no—
493C22×D4—148no—
494C22×D4—141no—
495C22×D4—141no—
496C22×D4—141no—
497C23×C4—141no—
498C23×C4—142no—
499C23×C4—142no—
500C23×C4—142no—
501C23×C4—142no—
502C23×C4—142no—
503C23×C4—142no—
504C23×C4—288no—
505C23×C4D2811yescharacteristic
506C23×C4D2811yescharacteristic
507C23×C4C22×D711yescharacteristic
508AGL(1,ℤ/8)—1416no—
509C2×SD16—78no—
510C2×D8—78no—
511C2×M16C22×D714yes—
512C4⋊Q8—71no—
513C4⋊Q8—71no—
514C4⋊Q8—71no—
515#127—71no—
516#126—142no—
517#126—142no—
518#125—72no—
519#125—141no—
520#125—141no—
521#124—72no—
522#124—141no—
523#124—141no—
524#123—142no—
525#123—142no—
526#123—142no—
527C22⋊Q8—72no—
528C22⋊Q8—72no—
529C22⋊Q8—141no—
530C22⋊Q8—141no—
531C22⋊Q8—141no—
532C22⋊Q8—141no—
533#121—72no—
534#121—72no—
535#121—141no—
536#121—141no—
537#121—141no—
538#121—141no—
539#120—142no—
540C4×Q8—72no—
541C4×Q8—72no—
542C4×Q8—141no—
543C4×Q8—141no—
544C4×Q8—141no—
545C4×Q8—141no—
546C4×D4—74no—
547C4×D4—74no—
548C4×D4—74no—
549C4×D4—74no—
550C4×D4—72no—
551C4×D4—72no—
552C4×D4—142no—
553C4×D4—142no—
554C4×D4—142no—
555C4×D4—142no—
556C4×D4—142no—
557C4×D4—142no—
558C4×D4—142no—
559C4×D4—142no—
560C4×D4—142no—
561C4×D4—142no—
562C4×D4—142no—
563C4×D4—142no—
564C4×D4—142no—
565C4×D4—142no—
566C4×D4—142no—
567C4×D4—142no—
568C4×D4—142no—
569C4×D4—142no—
570C4×D4—141no—
571C4×D4—141no—
572C4×D4—141no—
573C4×D4—141no—
574#117—72no—
575#117—141no—
576#117—141no—
577#117—142no—
578#117—142no—
579#117—142no—
580C2×C4⋊C4—72no—
581C2×C4⋊C4—72no—
582C2×C4⋊C4—72no—
583C2×C4⋊C4—141no—
584C2×C4⋊C4—141no—
585C2×C4⋊C4—141no—
586C2×C22⋊C4—142no—
587C2×C22⋊C4—142no—
588C2×C22⋊C4—142no—
589C2×C22⋊C4—142no—
590C2×C22⋊C4—142no—
591C2×C22⋊C4—142no—
592C2×C42—142no—
593C2×C42D2811yescharacteristic
594C2×C42D2811yescharacteristic
595C2×C42D2811yescharacteristic
596C2×C42D2811yescharacteristic
597C2×C42D2811yescharacteristic
598C2×C42D2811yescharacteristic
599C2×C42C22×D711yescharacteristic
600C2×C42C22×D711yescharacteristic
601C2×C42C22×D711yescharacteristic
602C2×C42C22×D711yescharacteristic
603C2×C42C22×D711yescharacteristic
604C2×C42C22×D711yescharacteristic
605#107—78no—
606#106—78no—
607C4⋊C8C22×D714yescomplemented
608C4⋊C8C22×D714yescomplemented
609#103—78no—
610#102—78no—
611#102—78no—
612#102—78no—
613C22⋊C8C22×D714yes—
614C22⋊C8C22×D714yes—
615#97C22×D714yescomplemented
616C4×C8C22×D714yescomplemented
617C22×C7—28no—
618C22×C7—21no—
619C22×C7—21no—
620C22×C7—21no—
621C22×C7—21no—
622C22×C7—21no—
623C22×C7—21no—
624C22×C7#52512yes—
625C22×C7C2×AGL(1,ℤ/8)12yes—
626C22×C7#57512yes—
627C22×C7C23×D411yescharacteristic
628C2×D7—28no—
629C2×D7—416no—
630C2×D7—416no—
631C2×D7—416no—
632C2×D7—44no—
633C2×D7—44no—
634C2×D7—42no—
635C2×D7—42no—
636C2×D7—42no—
637C4×C7—21no—
638C4×C7—21no—
639C4×C7—21no—
640C4×C7—21no—
641C4×C7—21no—
642C4×C7—21no—
643C4×C7—21no—
644C4×C7—21no—
645C4×C7#52512yes—
646C4×C7C2×AGL(1,ℤ/8)12yes—
647C4×C7C2×AGL(1,ℤ/8)12yes—
648C4×C7C22×#4112yes—
649Dic7—42no—
650Dic7—42no—
651Dic7—44no—
652Dic7—42no—
653C24—148no—
654C24—142no—
655C24—142no—
656C24—142no—
657C24—284no—
658C24—284no—
659C24C2×D2811yescharacteristic
660#41—148no—
661#41—284no—
662#41—284no—
663C2×Q8—72no—
664C2×Q8—141no—
665C2×Q8—141no—
666C2×D4—78no—
667C2×D4—74no—
668C2×D4—72no—
669C2×D4—148no—
670C2×D4—148no—
671C2×D4—148no—
672C2×D4—148no—
673C2×D4—148no—
674C2×D4—142no—
675C2×D4—142no—
676C2×D4—142no—
677C2×D4—142no—
678C2×D4—142no—
679C2×D4—142no—
680C2×D4—141no—
681C2×D4—141no—
682C2×D4—144no—
683C22×C4—24no—
684C22×C4—24no—
685C22×C4—42no—
686C22×C4—142no—
687C22×C4—142no—
688C22×C4—142no—
689C22×C4—142no—
690C22×C4—142no—
691C22×C4—144no—
692C22×C4—144no—
693C22×C4—144no—
694C22×C4—142no—
695C22×C4—144no—
696C22×C4—288no—
697C22×C4—288no—
698C22×C4—288no—
699C22×C4—288no—
700C22×C4—288no—
701C22×C4—284no—
702C22×C4—288no—
703C22×C4C2×D2811yescharacteristic
704C22×C4C2×D2811yescharacteristic
705C22×C4C2×D2811yescharacteristic
706C22×C4C2×D2811yescharacteristic
707C22×C4C2×D2811yescharacteristic
708C22×C4C2×D2811yescharacteristic
709C22×C4C2×D2811yescharacteristic
710C22×C4C2×D2811yescharacteristic
711C22×C4C2×D2811yescharacteristic
712C22×C4C2×D2811yescharacteristic
713C22×C4C2×D2811yescharacteristic
714C22×C4C2×D2811yescharacteristic
715C22×C4C2×D2811yescharacteristic
716C22×C4C2×D2811yescharacteristic
717C22×C4C2×D2811yescharacteristic
718C22×C4C23×D711yescharacteristic
719C22×C4C23×D711yescharacteristic
720C22×C4C23×D711yescharacteristic
721SD16—1416no—
722D8—1416no—
723M16—28no—
724C2×C8C23×D718yes—
725C4⋊C4—72no—
726C4⋊C4—72no—
727C4⋊C4—74no—
728C4⋊C4—142no—
729C4⋊C4—142no—
730C4⋊C4—142no—
731C4⋊C4—142no—
732C4⋊C4—142no—
733C4⋊C4—142no—
734C4⋊C4—142no—
735C4⋊C4—142no—
736C4⋊C4—142no—
737C4⋊C4—141no—
738C4⋊C4—141no—
739C4⋊C4—141no—
740C4⋊C4—141no—
741C22⋊C4—142no—
742C22⋊C4—142no—
743C22⋊C4—142no—
744C22⋊C4—144no—
745C22⋊C4—144no—
746C22⋊C4—144no—
747C22⋊C4—144no—
748C22⋊C4—142no—
749C22⋊C4—142no—
750C22⋊C4—142no—
751C22⋊C4—142no—
752C22⋊C4—142no—
753C22⋊C4—142no—
754C42—142no—
755C42—142no—
756C42—142no—
757C42C2×D2811yescharacteristic
758C42C2×D2811yescharacteristic
759C42C2×D2811yescharacteristic
760C42C2×D2811yescharacteristic
761C42C2×D2811yescharacteristic
762C42C2×D2811yescharacteristic
763C42C2×D2811yescharacteristic
764C42C2×D2811yescharacteristic
765C42C2×D2811yescharacteristic
766C42C2×D2811yescharacteristic
767C42C2×D2811yescharacteristic
768C42C2×D2811yescharacteristic
769C42C23×D711yescharacteristic
770C42C23×D711yescharacteristic
771C42C23×D711yescharacteristic
772C42C23×D711yescharacteristic
773C2×C7—22no—
774C2×C7—22no—
775C2×C7—22no—
776C2×C7C2×#52511yescharacteristic
777C2×C7C22×AGL(1,ℤ/8)11yescharacteristic
778C2×C7C2×#57511yescharacteristic
779D7—48no—
780D7—82no—
781C23—22no—
782C23—22no—
783C23—22no—
784C23—148no—
785C23—148no—
786C23—148no—
787C23—144no—
788C23—142no—
789C23—284no—
790C23—284no—
791C23—2832no—
792C23—284no—
793C23—284no—
794C23—284no—
795C23—284no—
796C23C22×D2811yescharacteristic
797C23C22×D2811yescharacteristic
798C23C22×D2811yescharacteristic
799Q8—144no—
800Q8—282no—
801Q8—282no—
802D4—78no—
803D4—148no—
804D4—148no—
805D4—148no—
806D4—144no—
807D4—144no—
808D4—282no—
809D4—284no—
810D4—284no—
811D4—284no—
812D4—282no—
813C2×C4—22no—
814C2×C4—22no—
815C2×C4—22no—
816C2×C4—22no—
817C2×C4—22no—
818C2×C4—22no—
819C2×C4—22no—
820C2×C4—22no—
821C2×C4—22no—
822C2×C4—22no—
823C2×C4—22no—
824C2×C4—22no—
825C2×C4—41no—
826C2×C4—41no—
827C2×C4—41no—
828C2×C4—41no—
829C2×C4—142no—
830C2×C4—142no—
831C2×C4—142no—
832C2×C4—144no—
833C2×C4—288no—
834C2×C4—288no—
835C2×C4—284no—
836C2×C4—284no—
837C2×C4—284no—
838C2×C4—284no—
839C2×C4—288no—
840C2×C4—288no—
841C2×C4—284no—
842C2×C4—284no—
843C2×C4#647114yescomplemented
844C2×C4C22×D2811yescharacteristic
845C2×C4C22×D2811yescharacteristic
846C2×C4C22×D2811yescharacteristic
847C2×C4C22×D2811yescharacteristic
848C2×C4C22×D2811yescharacteristic
849C2×C4C22×D2811yescharacteristic
850C2×C4C22×D2811yescharacteristic
851C2×C4C22×D2811yescharacteristic
852C2×C4C22×D2811yescharacteristic
853C2×C4C22×D2811yescharacteristic
854C2×C4C22×D2811yescharacteristic
855C2×C4D7×#4114yes—
856C2×C4C24×D711yescharacteristic
857C8—28no—
858C7#6055811yescharacteristic, complemented, Sylow
859C22—28no—
860C22—21no—
861C22—21no—
862C22—21no—
863C22—21no—
864C22—21no—
865C22—21no—
866C22—148no—
867C22—2816no—
868C22—2816no—
869C22—2816no—
870C22—284no—
871C22—284no—
872C22—282no—
873C22—282no—
874C22—282no—
875C22#9021512yes—
876C22C2×#647112yes—
877C22#9043912yes—
878C22C23×D2811yescharacteristic
879C4—21no—
880C4—21no—
881C4—21no—
882C4—21no—
883C4—21no—
884C4—21no—
885C4—21no—
886C4—21no—
887C4—282no—
888C4—284no—
889C4—282no—
890C4—282no—
891C4#9021512yes—
892C4C2×#647112yes—
893C4C2×#647112yes—
894C4C2×D7×#4112yes—
895C2—22no—
896C2—22no—
897C2—22no—
898C2—288no—
899C2—562no—
900C2C2×#9021511yescharacteristic
901C2C22×#647111yescharacteristic
902C2C2×#9043911yescharacteristic
subgroupG/H
centerC2×C4C22×D28
commutator, cosocleC2×C4×C7C25
FrattiniC2×C4C24×D7
FittingC7×#2920C2
socleC22×C7C23×D4
hypercenter#2920D7
hypocenterC7#60558
LCSG ▷ C2×C4×C7 ▷ C2×C7 ▷ C7
UCSC1 ◁ C2×C4 ◁ C22×C42 ◁ #2920

Complements

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

NH ≅ G/Ntype
1. #11742748C2semidirect
2. C22×C4×D28C2semidirect
3. C7×#2920C2semidirect
4. #11736791C2semidirect
5. #11736789C2semidirect
6. #11736788C2semidirect
7. #11736745C2semidirect
8. #11736743C2semidirect
9. #11736742C2semidirect
10. #11736504C2semidirect
11. #11736500C2semidirect
12. #11736082C2semidirect
13. #11736067C2semidirect
14. C4×#6471C2semidirect
28. #90170C22semidirect
29. #90170C22semidirect
30. #90168C22semidirect
31. #90168C22semidirect
32. #90168C22semidirect
35. C4×#1157C22semidirect
48. #90161C22semidirect
49. #90161C22semidirect
50. #90161C22semidirect
51. C7×#432C22semidirect
52. C7×#432C22semidirect
53. C7×#431C22semidirect
54. C7×#431C22semidirect
55. C7×#423C22semidirect
57. C4×C7×M16C22semidirect
58. #89905C22semidirect
60. #89893C22semidirect
61. #89619C22semidirect
62. #89618C22semidirect
63. #89616C22semidirect
64. #89615C22semidirect
65. #89614C22semidirect
66. #89613C22semidirect
67. #89508C22semidirect
68. #89507C22semidirect
73. #89494C22semidirect
74. #89493C22semidirect
75. #89483C22semidirect
76. #89482C22semidirect
77. C4×D56C22semidirect
78. C4×#1132C22semidirect
159. #6438C23semidirect
160. #6437C23semidirect
181. C4×D28C23semidirect
182. C4×D28C23semidirect
189. #6433C23semidirect
190. #6432C23semidirect
191. #6432C23semidirect
192. #6432C23semidirect
197. C4×Dic14C23semidirect
198. C4×Dic14C23semidirect
199. C7×C4⋊C8C23semidirect
200. C7×C4⋊C8C23semidirect
203. C7×#97C23semidirect
204. C4×C7×C8C23semidirect
207. #6395C23semidirect
208. #6392C23semidirect
209. #6391C23semidirect
210. #6390C23semidirect
224. #2920D7semidirect
274. C2×D28#41semidirect
399. #432C2×D7semidirect
400. #432C2×D7semidirect
401. #431C2×D7semidirect
402. #431C2×D7semidirect
404. #423C2×D7semidirect
408. C4×M16C2×D7semidirect
443. C2×C4×C7AGL(1,ℤ/8)semidirect
607. C4⋊C8C22×D7semidirect
608. C4⋊C8C22×D7semidirect
615. #97C22×D7semidirect
616. C4×C8C22×D7semidirect
843. C2×C4#6471semidirect
858. C7#60558semidirect

Maximal subgroups

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

subgroupindex
#117427482
C22×C4×D282
C7×#29202
#117367912
#117367892
#117367882
#117367452
#117367432
#117367422
#117365042
#117365002
#117360822
#117360672
C4×#64712
#605587