Finite Group Databasebeta

← #14223921

Subgroups — #14223921

Order 1792.

1976 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
1#11742748C211yesmaximal, characteristic
2C2×#90161C211yesmaximal, characteristic, complemented
3C2×C4×C7×M16C211yesmaximal, characteristic, complemented
4#11741221C214yesmaximal, complemented
5#11735985C212yesmaximal, complemented
6#11735984C214yesmaximal, complemented
7#11735983C211yesmaximal, characteristic, complemented
8#11735982C211yesmaximal, characteristic, complemented
9C4×#6472C214yesmaximal, complemented
10#11735978C212yesmaximal, complemented
11#11735973C211yesmaximal, characteristic, complemented
12#11735951C211yesmaximal, characteristic, complemented
13#11735949C214yesmaximal, complemented
14#11735920C212yesmaximal, complemented
15#11735913C212yesmaximal, complemented
16C22×C7×M16C2212yes—
17C22×C42×C7C2211yescharacteristic
18#90482—21no—
19#90482—21no—
20#90482C2212yes—
21C2×#6489—21no—
22C2×#6487—21no—
23C2×#6487C2212yes—
24C2×#6472C2214yes—
25#90170—21no—
26#90170—21no—
27#90170—21no—
28#90170—21no—
29#90170C2212yes—
30#90170C2212yes—
31#90168C2211yescharacteristic
32#90168C2211yescharacteristic
33#90168C2211yescharacteristic
34C4×#1157—21no—
35C4×#1157—21no—
36C4×#1157C2212yes—
37#90161—21no—
38#90161—21no—
39#90161—21no—
40#90161—21no—
41#90161C2211yescharacteristic
42#90161C2212yes—
43#90161C2212yes—
44#90161C2212yes—
45#90161C2212yes—
46#90161C2211yescharacteristic
47#90161C2211yescharacteristic
48C2×#6433—21no—
49C2×#6432C2211yescharacteristic
50C2×#6432C2211yescharacteristic
51C2×C4×Dic14—21no—
52C2×C4×Dic14C2212yes—
53C4×C7×M16C2211yescharacteristic
54C4×C7×M16C2211yescharacteristic
55C4×C7×M16C2212yes—
56C4×C7×M16C2212yes—
57C4×C7×M16C2212yes—
58C2×C7×#97C2212yes—
59C2×C4×C7×C8C2212yes—
60#89909C2218yes—
61#89906C2218yes—
62#89905C2214yes—
63#89893C2214yes—
64#89892C2214yes—
65#89888C2218yes—
66#89886C2218yes—
67#89488C2218yescomplemented
68#89487C2214yescomplemented
69#89486C2214yescomplemented
70#89482C2218yescomplemented
71#89475C2214yescomplemented
72#89474C2214yescomplemented
73#89471C2212yescomplemented
74C4×Dic28C2218yescomplemented
75#89466C2212yescomplemented
76#89465C2212yescomplemented
77C4×#1132C2218yescomplemented
78#89454C2212yescomplemented
79#89453C2212yescomplemented
80#89453C2212yescomplemented
81#89453C2212yescomplemented
82#89452C2212yescomplemented
83#60701—71nomaximal, Sylow
84C23×C4×C7D411yescharacteristic
85C23×C4×C7D411yescharacteristic
86C23×C4×C7C2311yescharacteristic
87C2×#1157—21no—
88C2×#1157—21no—
89C2×#1157C2312yes—
90C22×Dic14—21no—
91C22×Dic14C2312yes—
92C2×C7×M16—28no—
93C2×C7×M16C2312yes—
94C2×C7×M16C2314yes—
95C2×C7×M16C2312yes—
96C22×C7×C8C2314yes—
97C2×C42×C7D411yescharacteristic
98C2×C42×C7D411yescharacteristic
99C2×C42×C7D411yescharacteristic
100C2×C42×C7D411yescharacteristic
101C2×C42×C7D411yescharacteristic
102C2×C42×C7D411yescharacteristic
103C2×C42×C7C2311yescharacteristic
104C2×C42×C7C2311yescharacteristic
105C2×C42×C7C2311yescharacteristic
106C2×C42×C7C2311yescharacteristic
107C2×C42×C7C2311yescharacteristic
108C2×C42×C7C2311yescharacteristic
109#6516—22no—
110C2×C22⋊Dic7—22no—
111#6493—21no—
112#6493—21no—
113#6493—21no—
114#6493—21no—
115#6493C2312yes—
116#6493C2312yes—
117#6492—22no—
118#6492—22no—
119#6492—22no—
120C4×C22⋊D7—22no—
121C4×C22⋊D7—22no—
122C4×C22⋊D7—22no—
123C4×C22⋊D7—22no—
124C4×C22⋊D7—22no—
125C4×C22⋊D7—22no—
126#6489—22no—
127#6489—22no—
128#6489—22no—
129#6489—22no—
130#6489—21no—
131#6489—21no—
132#6489C2312yes—
133C2×C4⋊Dic7—21no—
134C2×C4⋊Dic7—21no—
135C2×C4⋊Dic7—21no—
136C2×C4⋊Dic7C2312yes—
137#6487—22no—
138#6487—22no—
139#6487—22no—
140#6487—22no—
141#6487—22no—
142#6487—22no—
143#6487—21no—
144#6487—21no—
145#6487—21no—
146#6487—21no—
147#6487C2314yes—
148#6487C2312yes—
149#6487C2314yes—
150#6487C2312yes—
151C2×Dic7⋊C4—22no—
152C2×Dic7⋊C4—22no—
153C2×C4×Dic7—22no—
154#6472—216no—
155C2×Dic28C2318yes—
156C2×#1132C2318yes—
157#6439—22no—
158#6439—22no—
159#6438—21no—
160#6438—21no—
161#6438C2312yes—
162#6437C2311yescharacteristic
163C4×D28—21no—
164C4×D28—21no—
165C4×D28—21no—
166C4×D28—21no—
167C4×D28C2312yes—
168C4×D28C2312yes—
169#6435—22no—
170#6435—22no—
171#6435—22no—
172C42×D7—22no—
173#6433—22no—
174#6433—22no—
175#6433—22no—
176#6433—22no—
177#6433—21no—
178#6433—21no—
179#6433C2312yes—
180#6432—21no—
181#6432—21no—
182#6432—21no—
183#6432—21no—
184#6432C2312yes—
185#6432C2312yes—
186#6432C2311yescharacteristic
187#6432C2312yes—
188#6432C2312yes—
189#6432C2311yescharacteristic
190#6432C2311yescharacteristic
191C4×Dic14—22no—
192C4×Dic14—22no—
193C4×Dic14—22no—
194C4×Dic14—22no—
195C4×Dic14—22no—
196C4×Dic14—22no—
197C4×Dic14—21no—
198C4×Dic14—21no—
199C4×Dic14—21no—
200C4×Dic14—21no—
201C4×Dic14C2314yes—
202C4×Dic14C2314yes—
203C4×Dic14C2312yes—
204C4×Dic14C2312yes—
205C7×#97C2312yes—
206C7×#97C2312yes—
207C7×#97C2314yes—
208C4×C7×C8C2312yes—
209C4×C7×C8C2312yes—
210C4×C7×C8C2314yes—
211#6395C2318yes—
212#6392C2318yes—
213#6391C2318yes—
214#6390C2318yes—
215#6390C2318yes—
216#6390C2318yes—
217#3444—71no—
218C2×#533—71no—
219#3185—72no—
220#3182—72no—
221#3181—74no—
222#3172—74no—
223#3170—72no—
224#3167—72no—
225#3165—71no—
226#3152—71no—
227#3141—71no—
228#3139—71no—
229#3056—74no—
230C4×#137—74no—
231C2×C4×M16D711yescharacteristic, complemented
232C24×C7C2×D411yescharacteristic
233C22×C4×C7—24no—
234C22×C4×C7—24no—
235C22×C4×C7—42no—
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×C7C2×D411yescharacteristic
251C22×C4×C7C2411yescharacteristic
252C22×C4×C7C2411yescharacteristic
253C22×C4×C7C2411yescharacteristic
254C2×C22⋊D7—22no—
255C2×C22⋊D7—22no—
256C2×C22⋊D7—22no—
257C22×Dic7—22no—
258C22×Dic7—22no—
259#1157—28no—
260#1157—44no—
261#1157—44no—
262C2×D28—21no—
263C2×D28—21no—
264C2×D28C2412yes—
265C2×C4×D7—22no—
266C2×C4×D7—22no—
267C2×C4×D7—22no—
268C2×Dic14—28no—
269C2×Dic14—22no—
270C2×Dic14—22no—
271C2×Dic14—22no—
272C2×Dic14—21no—
273C2×Dic14—21no—
274C2×Dic14—44no—
275C2×Dic14C2414yes—
276C2×Dic14C2412yes—
277C7×M16—24no—
278C7×M16—28no—
279C7×M16#4118yescomplemented
280C2×C7×C8—28no—
281C2×C7×C8C2414yes—
282C2×C7×C8C2414yes—
283C42×C7C2×D411yescharacteristic
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×C7C2411yescharacteristic
296C42×C7C2411yescharacteristic
297C42×C7C2411yescharacteristic
298C42×C7C2411yescharacteristic
299C22⋊Dic7—24no—
300C22⋊Dic7—24no—
301C22⋊Dic7—22no—
302C22⋊Dic7—22no—
303C22⋊Dic7—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—22no—
311C4⋊Dic7—22no—
312C4⋊Dic7—22no—
313C4⋊Dic7—21no—
314C4⋊Dic7—21no—
315C4⋊Dic7—21no—
316C4⋊Dic7—21no—
317C4⋊Dic7—22no—
318C4⋊Dic7—22no—
319C4⋊Dic7—22no—
320C4⋊Dic7—22no—
321C4⋊Dic7C2414yes—
322C4⋊Dic7C2412yes—
323C4⋊Dic7C2412yes—
324Dic7⋊C4—24no—
325Dic7⋊C4—24no—
326Dic7⋊C4—24no—
327Dic7⋊C4—24no—
328Dic7⋊C4—22no—
329Dic7⋊C4—22no—
330Dic7⋊C4—22no—
331Dic7⋊C4—22no—
332Dic7⋊C4—22no—
333Dic7⋊C4—22no—
334C4×Dic7—24no—
335C4×Dic7—24no—
336C4×Dic7—22no—
337C4×Dic7—22no—
338C4×Dic7—22no—
339Dic28—216no—
340#1132—216no—
341C2×#137—74no—
342C22×M16C2×D712yes—
343#533—71no—
344#533—72no—
345#533—71no—
346#533—72no—
347#533—72no—
348#533—72no—
349#533—71no—
350#533—141no—
351#533—141no—
352#533—141no—
353#533—141no—
354#532—71no—
355#532—71no—
356#532—71no—
357C2×C4⋊Q8—71no—
358C2×C4⋊Q8—71no—
359#529—72no—
360#529—72no—
361#529—141no—
362#529—141no—
363#529—141no—
364#529—141no—
365C2×#125—141no—
366#525—72no—
367#525—141no—
368#525—141no—
369C2×C22⋊Q8—72no—
370C2×C22⋊Q8—141no—
371C4×#41—72no—
372C4×#41—141no—
373C4×#41—141no—
374C2×C4×Q8—72no—
375C2×C4×Q8—141no—
376C2×#117—141no—
377C22×C42C2×D711yescharacteristic
378#501—74no—
379#500—72no—
380#498—72no—
381#497—74no—
382#494—72no—
383#492—72no—
384#491—74no—
385#489—74no—
386#487—72no—
387#487—72no—
388#487—72no—
389#486—72no—
390#470—78no—
391#468—78no—
392#467—78no—
393#465—78no—
394#441—78no—
395#440—78no—
396C4×Q16—78no—
397C4×SD16—78no—
398#428—74no—
399#419—74no—
400#417—74no—
401C4×M16C2×D711yescharacteristic
402C4×M16C2×D711yescharacteristic
403C4×M16C2×D712yes—
404C4×M16C2×D712yes—
405C4×M16C2×D712yes—
406C2×#97C2×D712yes—
407C2×C4×C8C2×D712yes—
408C23×C7—22no—
409C23×C7—22no—
410C23×C7—41no—
411C23×C7C22×D411yescharacteristic
412C23×C7C22×D411yescharacteristic
413C23×C7C22×D411yescharacteristic
414C22×D7—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—22no—
426C2×C4×C7—22no—
427C2×C4×C7—22no—
428C2×C4×C7—41no—
429C2×C4×C7—41no—
430C2×C4×C7—41no—
431C2×C4×C7#13714yescomplemented
432C2×C4×C7C22×D411yescharacteristic
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×C7C2×#4114yes—
444C2×C4×C7C2511yescharacteristic
445C22⋊D7—44no—
446C22⋊D7—44no—
447C22⋊D7—44no—
448C2×Dic7—24no—
449C2×Dic7—24no—
450C2×Dic7—22no—
451C2×Dic7—22no—
452C2×Dic7—22no—
453C2×Dic7—44no—
454C2×Dic7—44no—
455D28—24no—
456D28—42no—
457D28—42no—
458C4×D7—44no—
459C4×D7—44no—
460C4×D7—44no—
461Dic14—28no—
462Dic14—24no—
463Dic14—44no—
464Dic14—44no—
465Dic14—42no—
466Dic14—44no—
467Dic14—42no—
468C7×C8—24no—
469C7×C8C2×#4118yes—
470C2×#41—72no—
471C2×#41—141no—
472C2×#41—141no—
473C22×Q8—72no—
474C22×Q8—141no—
475C23×C4D2811yescharacteristic
476C23×C4D2811yescharacteristic
477C23×C4C22×D711yescharacteristic
478#137—1416no—
479C2×Q16—78no—
480C2×SD16—78no—
481C2×M16—28no—
482C2×M16C22×D712yes—
483C2×M16C22×D714yes—
484C2×M16C22×D712yes—
485C22×C8C22×D714yes—
486C4⋊Q8—72no—
487C4⋊Q8—72no—
488C4⋊Q8—71no—
489C4⋊Q8—71no—
490C4⋊Q8—72no—
491C4⋊Q8—72no—
492C4⋊Q8—71no—
493C4⋊Q8—141no—
494C4⋊Q8—141no—
495C4⋊Q8—141no—
496C4⋊Q8—141no—
497#127—71no—
498#126—142no—
499#126—142no—
500#125—72no—
501#125—142no—
502#125—142no—
503#125—142no—
504#125—142no—
505#125—141no—
506#125—141no—
507#124—72no—
508#124—141no—
509#124—141no—
510#123—142no—
511#123—142no—
512#123—142no—
513C22⋊Q8—74no—
514C22⋊Q8—74no—
515C22⋊Q8—72no—
516C22⋊Q8—72no—
517C22⋊Q8—142no—
518C22⋊Q8—142no—
519C22⋊Q8—142no—
520C22⋊Q8—142no—
521C22⋊Q8—142no—
522C22⋊Q8—142no—
523C22⋊Q8—141no—
524C22⋊Q8—141no—
525C22⋊Q8—141no—
526C22⋊Q8—141no—
527#121—72no—
528#121—72no—
529#121—141no—
530#121—141no—
531#121—141no—
532#121—141no—
533#120—142no—
534C4×Q8—74no—
535C4×Q8—74no—
536C4×Q8—72no—
537C4×Q8—72no—
538C4×Q8—142no—
539C4×Q8—142no—
540C4×Q8—142no—
541C4×Q8—142no—
542C4×Q8—142no—
543C4×Q8—142no—
544C4×Q8—141no—
545C4×Q8—141no—
546C4×Q8—141no—
547C4×Q8—141no—
548C4×D4—72no—
549C4×D4—72no—
550C4×D4—142no—
551C4×D4—142no—
552C4×D4—142no—
553C4×D4—142no—
554C4×D4—142no—
555C4×D4—142no—
556C4×D4—141no—
557C4×D4—141no—
558C4×D4—141no—
559C4×D4—141no—
560#117—72no—
561#117—142no—
562#117—142no—
563#117—142no—
564#117—142no—
565#117—141no—
566#117—141no—
567#117—142no—
568#117—142no—
569#117—142no—
570C2×C4⋊C4—72no—
571C2×C4⋊C4—141no—
572C2×C4⋊C4—141no—
573C2×C4⋊C4—142no—
574C2×C4⋊C4—142no—
575C2×C4⋊C4—141no—
576C2×C22⋊C4—142no—
577C2×C42—142no—
578C2×C42—142no—
579C2×C42D2811yescharacteristic
580C2×C42D2811yescharacteristic
581C2×C42D2811yescharacteristic
582C2×C42D2811yescharacteristic
583C2×C42D2811yescharacteristic
584C2×C42D2811yescharacteristic
585C2×C42C22×D711yescharacteristic
586C2×C42C22×D711yescharacteristic
587C2×C42C22×D711yescharacteristic
588C2×C42C22×D711yescharacteristic
589C2×C42C22×D711yescharacteristic
590C2×C42C22×D711yescharacteristic
591#107—78no—
592#106—78no—
593#103—78no—
594#103—78no—
595#103—78no—
596#102—78no—
597#97C22×D714yes—
598#97C22×D712yes—
599#97C22×D712yes—
600C4×C8C22×D714yes—
601C4×C8C22×D712yes—
602C4×C8C22×D712yes—
603C22×C7—21no—
604C22×C7—21no—
605C22×C7—21no—
606C22×C7—21no—
607C22×C7—21no—
608C22×C7—21no—
609C22×C7—21no—
610C22×C7—44no—
611C22×C7#53212yes—
612C22×C7C2×#13712yes—
613C22×C7C23×D411yescharacteristic
614C2×D7—42no—
615C2×D7—42no—
616C2×D7—42no—
617C4×C7—21no—
618C4×C7—21no—
619C4×C7—21no—
620C4×C7—21no—
621C4×C7—21no—
622C4×C7—21no—
623C4×C7—21no—
624C4×C7#53212yes—
625C4×C7C2×#13712yes—
626C4×C7C2×#13712yes—
627C4×C7#57512yes—
628C4×C7C22×#4112yes—
629Dic7—44no—
630Dic7—42no—
631Dic7—42no—
632Dic7—44no—
633Dic7—42no—
634C24C2×D2811yescharacteristic
635#41—148no—
636#41—284no—
637#41—284no—
638C2×Q8—72no—
639C2×Q8—74no—
640C2×Q8—141no—
641C2×Q8—141no—
642C2×Q8—142no—
643C2×Q8—142no—
644C2×Q8—142no—
645C2×Q8—148no—
646C2×Q8—284no—
647C2×D4—72no—
648C2×D4—142no—
649C2×D4—142no—
650C2×D4—142no—
651C2×D4—141no—
652C2×D4—141no—
653C22×C4—24no—
654C22×C4—24no—
655C22×C4—42no—
656C22×C4—142no—
657C22×C4—142no—
658C22×C4—142no—
659C22×C4—142no—
660C22×C4—142no—
661C22×C4C2×D2811yescharacteristic
662C22×C4C2×D2811yescharacteristic
663C22×C4C2×D2811yescharacteristic
664C22×C4C2×D2811yescharacteristic
665C22×C4C2×D2811yescharacteristic
666C22×C4C2×D2811yescharacteristic
667C22×C4C2×D2811yescharacteristic
668C22×C4C2×D2811yescharacteristic
669C22×C4C2×D2811yescharacteristic
670C22×C4C2×D2811yescharacteristic
671C22×C4C2×D2811yescharacteristic
672C22×C4C2×D2811yescharacteristic
673C22×C4C2×D2811yescharacteristic
674C22×C4C2×D2811yescharacteristic
675C22×C4C2×D2811yescharacteristic
676C22×C4C23×D711yescharacteristic
677C22×C4C23×D711yescharacteristic
678C22×C4C23×D711yescharacteristic
679Q16—1416no—
680SD16—1416no—
681M16—24no—
682M16—28no—
683M16#115718yescomplemented
684C2×C8—28no—
685C2×C8C23×D714yes—
686C2×C8C23×D714yes—
687C4⋊C4—74no—
688C4⋊C4—72no—
689C4⋊C4—72no—
690C4⋊C4—144no—
691C4⋊C4—144no—
692C4⋊C4—144no—
693C4⋊C4—144no—
694C4⋊C4—142no—
695C4⋊C4—142no—
696C4⋊C4—142no—
697C4⋊C4—142no—
698C4⋊C4—142no—
699C4⋊C4—142no—
700C4⋊C4—142no—
701C4⋊C4—142no—
702C4⋊C4—142no—
703C4⋊C4—142no—
704C4⋊C4—142no—
705C4⋊C4—142no—
706C4⋊C4—142no—
707C4⋊C4—141no—
708C4⋊C4—141no—
709C4⋊C4—141no—
710C4⋊C4—141no—
711C22⋊C4—144no—
712C22⋊C4—144no—
713C22⋊C4—142no—
714C22⋊C4—142no—
715C22⋊C4—142no—
716C22⋊C4—142no—
717C22⋊C4—142no—
718C22⋊C4—142no—
719C22⋊C4—142no—
720C22⋊C4—142no—
721C22⋊C4—142no—
722C42—142no—
723C42—142no—
724C42—144no—
725C42—142no—
726C42—144no—
727C42C2×D2811yescharacteristic
728C42C2×D2811yescharacteristic
729C42C2×D2811yescharacteristic
730C42C2×D2811yescharacteristic
731C42C2×D2811yescharacteristic
732C42C2×D2811yescharacteristic
733C42C2×D2811yescharacteristic
734C42C2×D2811yescharacteristic
735C42C2×D2811yescharacteristic
736C42C2×D2811yescharacteristic
737C42C2×D2811yescharacteristic
738C42C2×D2811yescharacteristic
739C42C23×D711yescharacteristic
740C42C23×D711yescharacteristic
741C42C23×D711yescharacteristic
742C42C23×D711yescharacteristic
743C2×C7—22no—
744C2×C7—22no—
745C2×C7—41no—
746C2×C7C2×#53211yescharacteristic
747C2×C7C22×#13711yescharacteristic
748C2×C7C2×#57511yescharacteristic
749D7—82no—
750C23—22no—
751C23—22no—
752C23—41no—
753C23—142no—
754C23C22×D2811yescharacteristic
755C23C22×D2811yescharacteristic
756C23C22×D2811yescharacteristic
757Q8—148no—
758Q8—144no—
759Q8—284no—
760Q8—284no—
761Q8—282no—
762Q8—284no—
763Q8—282no—
764D4—144no—
765D4—284no—
766D4—284no—
767D4—284no—
768D4—282no—
769D4—282no—
770C2×C4—22no—
771C2×C4—22no—
772C2×C4—22no—
773C2×C4—22no—
774C2×C4—22no—
775C2×C4—22no—
776C2×C4—22no—
777C2×C4—22no—
778C2×C4—22no—
779C2×C4—22no—
780C2×C4—22no—
781C2×C4—22no—
782C2×C4—22no—
783C2×C4—41no—
784C2×C4—41no—
785C2×C4—41no—
786C2×C4—142no—
787C2×C4—142no—
788C2×C4—142no—
789C2×C4—144no—
790C2×C4—144no—
791C2×C4—284no—
792C2×C4—284no—
793C2×C4—284no—
794C2×C4—284no—
795C2×C4—284no—
796C2×C4#647214yescomplemented
797C2×C4C22×D2811yescharacteristic
798C2×C4C22×D2811yescharacteristic
799C2×C4C22×D2811yescharacteristic
800C2×C4C22×D2811yescharacteristic
801C2×C4C22×D2811yescharacteristic
802C2×C4C22×D2811yescharacteristic
803C2×C4C22×D2811yescharacteristic
804C2×C4C22×D2811yescharacteristic
805C2×C4C22×D2811yescharacteristic
806C2×C4C22×D2811yescharacteristic
807C2×C4C22×D2811yescharacteristic
808C2×C4C2×#115714yes—
809C2×C4C24×D711yescharacteristic
810C8—24no—
811C8C2×#115718yes—
812C7#6070111yescharacteristic, complemented, Sylow
813C22—21no—
814C22—21no—
815C22—21no—
816C22—21no—
817C22—21no—
818C22—21no—
819C22—21no—
820C22—44no—
821C22—282no—
822C22—282no—
823C22—282no—
824C22#9016812yes—
825C22C2×#647212yes—
826C22C23×D2811yescharacteristic
827C4—21no—
828C4—21no—
829C4—21no—
830C4—21no—
831C4—21no—
832C4—21no—
833C4—21no—
834C4—282no—
835C4—284no—
836C4—282no—
837C4—284no—
838C4—282no—
839C4#9016812yes—
840C4C2×#647212yes—
841C4C2×#647212yes—
842C4#9043912yes—
843C4C22×#115712yes—
844C2—22no—
845C2—22no—
846C2—41no—
847C2—562no—
848C2C2×#9016811yescharacteristic
849C2C2×#9043911yescharacteristic
850C2C22×#647211yescharacteristic
subgroupG/H
centerC2×C4C22×D28
commutator, cosocleC2×C4×C7C25
FrattiniC2×C4C24×D7
FittingC2×C4×C7×M16C2
socleC22×C7C23×D4
prime radical#11742748C2
hypercenterC2×C4×M16D7
hypocenterC7#60701
LCSG ▷ C2×C4×C7 ▷ C2×C7 ▷ C7
UCSC1 ◁ C2×C4 ◁ C22×C42 ◁ C2×C4×M16

Complements

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

NH ≅ G/Ntype
2. C2×#90161C2semidirect
3. C2×C4×C7×M16C2semidirect
4. #11741221C2semidirect
5. #11735985C2semidirect
6. #11735984C2semidirect
7. #11735983C2semidirect
8. #11735982C2semidirect
9. C4×#6472C2semidirect
10. #11735978C2semidirect
11. #11735973C2semidirect
12. #11735951C2semidirect
13. #11735949C2semidirect
14. #11735920C2semidirect
15. #11735913C2semidirect
67. #89488C22semidirect
68. #89487C22semidirect
69. #89486C22semidirect
70. #89482C22semidirect
71. #89475C22semidirect
72. #89474C22semidirect
73. #89471C22semidirect
74. C4×Dic28C22semidirect
75. #89466C22semidirect
76. #89465C22semidirect
77. C4×#1132C22semidirect
78. #89454C22semidirect
79. #89453C22semidirect
80. #89453C22semidirect
81. #89453C22semidirect
82. #89452C22semidirect
231. C2×C4×M16D7semidirect
279. C7×M16#41semidirect
431. C2×C4×C7#137semidirect
683. M16#1157semidirect
796. C2×C4#6472semidirect
812. C7#60701semidirect

Maximal subgroups

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

subgroupindex
#117427482
C2×#901612
C2×C4×C7×M162
#117412212
#117359852
#117359842
#117359832
#117359822
C4×#64722
#117359782
#117359732
#117359512
#117359492
#117359202
#117359132
#607017