Finite Group Databasebeta

← #32865966

Subgroups — #32865966

Order 18176.

2074 conjugacy classes of subgroups.

The subgroup lattice has 872 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#17986620C211yesmaximal, characteristic, complemented
2#22598617C214yesmaximal, complemented
3#22598602C214yesmaximal, complemented
4#22598569C214yesmaximal, complemented
5#22598524C214yesmaximal, complemented
6#22598288C211yesmaximal, characteristic, complemented
7#22598280C211yesmaximal, characteristic, complemented
8#22598155C212yesmaximal, complemented
9#22597834C212yesmaximal, complemented
10#22597600C211yesmaximal, characteristic, complemented
11#22597592C211yesmaximal, characteristic
12C4×#14556158C212yesmaximal, complemented
13C4×#14556153C212yesmaximal, complemented
14#22596978C211yesmaximal, characteristic, complemented
15C71×#3428C211yesmaximal, characteristic, complemented
16C2×#14556158C2212yes—
17C2×#14556153C2212yes—
18#17986620—22no—
19#17986620—22no—
20#17986620C2214yes—
21#17986620C2214yescomplemented
22C2×#14556128C2211yescharacteristic, complemented
23C2×#14556123—21no—
24C2×#14556116C2211yescharacteristic, complemented
25C2×#14556114—21no—
26C2×#14556110—21no—
27C2×#14556107C2211yescharacteristic
28C2×#14556106—21no—
29C2×#14556102C2211yescharacteristic
30C2×C4×Dic142C2211yescharacteristic, complemented
31C2×C4×D284C2211yescharacteristic, complemented
32#17986340C2214yescomplemented
33#17986334C2212yescomplemented
34#17986329C2212yescomplemented
35#17986323C2214yes—
36#17986317C2212yescomplemented
37#17986312C2212yescomplemented
38#17986294C2214yescomplemented
39#17986289C2214yescomplemented
40#17986284C2214yescomplemented
41#17986279C2214yescomplemented
42#17986221C2214yescomplemented
43#17986221C2214yescomplemented
44#17986214C2214yescomplemented
45#17986214C2214yescomplemented
46#17986161C2214yescomplemented
47#17986155C2212yescomplemented
48#17986150C2212yescomplemented
49#17986144C2214yes—
50#17986138C2212yes—
51#17986133C2212yes—
52#17986109C2214yescomplemented
53#17986104C2214yescomplemented
54#17986099C2214yescomplemented
55#17986097C2214yescomplemented
56C4×#11765855C2214yescomplemented
57C4×#11765852C2214yescomplemented
58C4×#11765853C2214yescomplemented
59C4×#11765850C2214yescomplemented
60#17986060C2214yescomplemented
61#17986060C2214yescomplemented
62#17986042C2212yescomplemented
63#17986042C2212yescomplemented
64#17986023C2212yescomplemented
65#17986007C2212yescomplemented
66#17986003C2212yescomplemented
67#17986000C2212yes—
68#17986000C2212yes—
69#17985963C2211yescharacteristic
70#17985963C2211yescharacteristic
71C4×#11765849C2212yescomplemented
72C22×#41×C71C2211yescharacteristic
73#520×C71—21no—
74#520×C71—21no—
75#520×C71C2212yescomplemented
76#520×C71C2212yescomplemented
77#519×C71C2212yescomplemented
78#518×C71—21no—
79#518×C71—21no—
80#518×C71C2212yescomplemented
81C4×#41×C71—22no—
82C4×#41×C71C2212yes—
83C4×#41×C71C2212yes—
84C2×#117×C71—22no—
85C2×#117×C71C2211yescharacteristic
86C2×#117×C71C2211yescharacteristic
87C22×Dic142—21no—
88C22×Dic142C2311yescharacteristic
89C22×D284C2311yescharacteristic
90C22×C22⋊D71—21no—
91C22×C4×D71—21no—
92#14556158—28no—
93#14556153—28no—
94C2×#11765855C2314yes—
95C2×#11765853C2314yes—
96C2×#11765852C2314yes—
97C2×#11765850C2314yes—
98C2×#11765849C2312yes—
99C2×#11765849C2312yes—
100#14556128—22no—
101#14556128C2314yes—
102#14556123—24no—
103#14556123—24no—
104#14556116—22no—
105#14556116C2314yes—
106#14556114—24no—
107#14556114—24no—
108#14556110—24no—
109#14556110—24no—
110#14556107—21no—
111#14556107—21no—
112#14556107C2312yes—
113#14556107C2312yes—
114#14556106—24no—
115#14556106—24no—
116#14556102—21no—
117#14556102—21no—
118#14556102C2312yes—
119#14556102C2312yes—
120C4×Dic142—22no—
121C4×Dic142C2314yes—
122C4×D284—22no—
123C4×D284C2314yes—
124C2×C4⋊Dic71—21no—
125C2×C4⋊Dic71C2311yescharacteristic
126C2×C4⋊Dic71C2311yescharacteristic
127C2×Dic71⋊C4—21no—
128C2×Dic71⋊C4—21no—
129C2×C22⋊Dic71—21no—
130C2×(C2×D71)⋊C4—21no—
131C2×(C2×D71)⋊C4—21no—
132C2×(C2×D71)⋊C4—21no—
133C2×(C2×D71)⋊C4—21no—
134C2×C4×Dic71—21no—
135#14556061C2314yes—
136#14556061C2314yes—
137#14556059C2314yes—
138#14556059C2314yes—
139C4⋊(C71⋊C8)C2314yes—
140C4⋊(C71⋊C8)C2314yes—
141#14556052C2314yes—
142#14556052C2314yes—
143#14556051C2314yes—
144#14556051C2314yes—
145#14556049C2314yes—
146#14556049C2314yes—
147#14556048C2314yes—
148#14556048C2314yes—
149C22⋊(C71⋊C8)C2312yes—
150C22⋊(C71⋊C8)C2312yes—
151C22⋊(C71⋊C8)C2312yes—
152C22⋊(C71⋊C8)C2312yes—
153#14556039C2314yes—
154C4×C71⋊C8C2314yes—
155C2×#41×C71—28no—
156C2×#41×C71—21no—
157C2×#41×C71—21no—
158C2×#41×C71C2312yes—
159C2×#41×C71C2312yes—
160C22×Q8×C71C2311yescharacteristic
161C22×D4×C71—21no—
162C22×D4×C71C2311yescharacteristic
163C23×C4×C71—21no—
164C23×C4×C71C2311yescharacteristic
165C4×Q8×C71—22no—
166C4×Q8×C71—22no—
167C4×Q8×C71C2312yes—
168C4×Q8×C71C2312yes—
169C4×Q8×C71C2312yes—
170C4×Q8×C71C2312yes—
171C4×D4×C71—22no—
172C4×D4×C71—22no—
173C4×D4×C71—22no—
174C4×D4×C71—22no—
175C4×D4×C71—22no—
176C4×D4×C71—22no—
177C4×D4×C71—22no—
178C4×D4×C71—22no—
179C4×D4×C71—22no—
180C4×D4×C71—22no—
181C4×D4×C71C2312yes—
182C4×D4×C71C2312yes—
183C4×D4×C71C2312yes—
184C4×D4×C71C2312yes—
185#117×C71—21no—
186#117×C71—21no—
187#117×C71—22no—
188#117×C71—22no—
189#117×C71—22no—
190#117×C71—22no—
191#117×C71—22no—
192#117×C71—22no—
193#117×C71D412yes—
194#117×C71D412yes—
195#117×C71C2312yes—
196#117×C71C2312yes—
197#117×C71C2312yes—
198#117×C71C2312yes—
199C2×C4⋊C4×C71—22no—
200C2×C4⋊C4×C71—22no—
201C2×C4⋊C4×C71D411yescharacteristic
202C2×C4⋊C4×C71D411yescharacteristic
203C2×C4⋊C4×C71C2311yescharacteristic
204C2×C4⋊C4×C71C2311yescharacteristic
205C2×C22⋊C4×C71—21no—
206C2×C22⋊C4×C71—22no—
207C2×C22⋊C4×C71—22no—
208C2×C22⋊C4×C71D411yescharacteristic
209C2×C22⋊C4×C71D411yescharacteristic
210C2×C42×C71—21no—
211C2×C42×C71—22no—
212C2×C42×C71—22no—
213C2×C42×C71C2311yescharacteristic
214C2×C42×C71C2311yescharacteristic
215C23×D71—21no—
216C2×Dic142—24no—
217C2×Dic142—21no—
218C2×Dic142—24no—
219C2×Dic142—82no—
220C2×Dic142C2412yes—
221C2×D284—24no—
222C2×D284—21no—
223C2×D284C2412yes—
224C2×C22⋊D71—22no—
225C2×C22⋊D71—22no—
226C2×C22⋊D71—82no—
227C22×Dic71—21no—
228C22×Dic71—21no—
229C22×Dic71—21no—
230C2×C4×D71—24no—
231C2×C4×D71—82no—
232#11765855—28no—
233#11765853—28no—
234#11765852—28no—
235#11765850—28no—
236#11765849—24no—
237#11765849—24no—
238C2×C71⋊C8C2414yes—
239C2×C71⋊C8C2414yes—
240C4⋊Dic71—24no—
241C4⋊Dic71—21no—
242C4⋊Dic71—21no—
243C4⋊Dic71C2412yes—
244C4⋊Dic71C2412yes—
245Dic71⋊C4—24no—
246Dic71⋊C4—22no—
247Dic71⋊C4—22no—
248C22⋊Dic71—22no—
249C22⋊Dic71—22no—
250(C2×D71)⋊C4—24no—
251(C2×D71)⋊C4—22no—
252(C2×D71)⋊C4—22no—
253(C2×D71)⋊C4—24no—
254(C2×D71)⋊C4—24no—
255C4×Dic71—24no—
256C24×C71—21no—
257C24×C71C2×D411yescharacteristic
258#41×C71—28no—
259#41×C71—28no—
260#41×C71—24no—
261#41×C71—24no—
262#41×C71—24no—
263#41×C71#4118yes—
264C2×Q8×C71—24no—
265C2×Q8×C71—21no—
266C2×Q8×C71C2412yes—
267C2×D4×C71—28no—
268C2×D4×C71—22no—
269C2×D4×C71—22no—
270C2×D4×C71—24no—
271C2×D4×C71—21no—
272C2×D4×C71C2412yes—
273C22×C4×C71—28no—
274C22×C4×C71—21no—
275C22×C4×C71—22no—
276C22×C4×C71—22no—
277C22×C4×C71—24no—
278C22×C4×C71—21no—
279C22×C4×C71—21no—
280C22×C4×C71—22no—
281C22×C4×C71—22no—
282C22×C4×C71—22no—
283C22×C4×C71—22no—
284C22×C4×C71C2×D411yescharacteristic
285C22×C4×C71C2×D411yescharacteristic
286C22×C4×C71C2×D411yescharacteristic
287C22×C4×C71C2×D411yescharacteristic
288C22×C4×C71C2×D411yescharacteristic
289C22×C4×C71C2×D411yescharacteristic
290C22×C4×C71C2×D411yescharacteristic
291C22×C4×C71C2411yescharacteristic
292C22×C4×C71C2411yescharacteristic
293C22×C4×C71C2411yescharacteristic
294C4⋊C4×C71—21no—
295C4⋊C4×C71—21no—
296C4⋊C4×C71—22no—
297C4⋊C4×C71—22no—
298C4⋊C4×C71—22no—
299C4⋊C4×C71—22no—
300C4⋊C4×C71C2×D412yes—
301C4⋊C4×C71C2×D412yes—
302C4⋊C4×C71C2×D412yes—
303C4⋊C4×C71C2×D412yes—
304C4⋊C4×C71C2412yes—
305C4⋊C4×C71C2412yes—
306C22⋊C4×C71—22no—
307C22⋊C4×C71—22no—
308C22⋊C4×C71—22no—
309C22⋊C4×C71—22no—
310C22⋊C4×C71—22no—
311C22⋊C4×C71—22no—
312C22⋊C4×C71C2×D412yes—
313C22⋊C4×C71C2×D412yes—
314C22⋊C4×C71C2×D412yes—
315C22⋊C4×C71C2×D412yes—
316C42×C71—22no—
317C42×C71—22no—
318C42×C71—22no—
319C42×C71—22no—
320C42×C71—22no—
321C42×C71—22no—
322C42×C71C2×D412yes—
323C42×C71C2×D412yes—
324C42×C71C2412yes—
325C42×C71C2412yes—
326C23×C71—24no—
327C23×C71—22no—
328C23×C71—22no—
329C23×C71—41no—
330C23×C71—41no—
331C23×C71—81no—
332C23×C71—81no—
333C23×C71C22×D411yescharacteristic
334C23×C71C22×D411yescharacteristic
335C23×C71C22×D411yescharacteristic
336C22×D71—22no—
337C22×D71—42no—
338C22×D71—42no—
339C22×D71—42no—
340Q8×C71—24no—
341Q8×C71—22no—
342Q8×C71C2×#4114yes—
343D4×C71—28no—
344D4×C71—24no—
345D4×C71—28no—
346D4×C71—22no—
347D4×C71C2×#4114yes—
348C2×C4×C71—24no—
349C2×C4×C71—28no—
350C2×C4×C71—22no—
351C2×C4×C71—22no—
352C2×C4×C71—22no—
353C2×C4×C71—28no—
354C2×C4×C71—22no—
355C2×C4×C71—22no—
356C2×C4×C71—22no—
357C2×C4×C71—22no—
358C2×C4×C71—22no—
359C2×C4×C71—41no—
360C2×C4×C71—41no—
361C2×C4×C71—41no—
362C2×C4×C71—41no—
363C2×C4×C71—82no—
364C2×C4×C71—82no—
365C2×C4×C71—82no—
366C2×C4×C71—82no—
367C2×C4×C71—81no—
368C2×C4×C71—81no—
369C2×C4×C71C22×D411yescharacteristic
370C2×C4×C71C22×D412yes—
371C2×C4×C71C22×D412yes—
372C2×C4×C71C22×D412yes—
373C2×C4×C71C22×D412yes—
374C2×C4×C71C22×D411yescharacteristic
375C2×C4×C71C22×D411yescharacteristic
376C2×C4×C71C2×#4114yes—
377C2×C4×C71C2511yescharacteristic
378C22⋊D71—82no—
379C22⋊D71—82no—
380C2×Dic71—22no—
381C2×Dic71—22no—
382C2×Dic71—22no—
383C2×Dic71—42no—
384C2×Dic71—42no—
385C2×Dic71—42no—
386D284—24no—
387D284—42no—
388C4×D71—84no—
389Dic142—24no—
390Dic142—42no—
391Dic142—84no—
392C71⋊C8—24no—
393C71⋊C8—24no—
394C22×C71—21no—
395C22×C71—21no—
396C22×C71—21no—
397C22×C71—21no—
398C22×C71—21no—
399C22×C71—21no—
400C22×C71—21no—
401C22×C71—21no—
402C22×C71—24no—
403C22×C71—42no—
404C22×C71—42no—
405C22×C71—82no—
406C22×C71—84no—
407C22×C71#52512yes—
408C22×C71C23×D411yescharacteristic
409C2×D71—42no—
410C2×D71—42no—
411C2×D71—42no—
412C2×D71—84no—
413C4×C71—22no—
414C4×C71—22no—
415C4×C71—22no—
416C4×C71—22no—
417C4×C71—21no—
418C4×C71—24no—
419C4×C71—21no—
420C4×C71—42no—
421C4×C71—42no—
422C4×C71#52512yes—
423C4×C71C22×#4112yes—
424Dic71—42no—
425Dic71—42no—
426Dic71—42no—
427#60567—711nomaximal, Sylow
428C2×C71—22no—
429C2×C71—41no—
430C2×C71—41no—
431C2×C71—44no—
432C2×C71C2×#52511yescharacteristic
433C2×C71#358511yescharacteristic
434C2×C71#358611yescharacteristic
435D71—82no—
436C2×#542—711no—
437#3428D7111yescharacteristic, complemented
438#3125—714no—
439#3124—714no—
440#3121—714no—
441#3118—714no—
442#3095—711no—
443#3094—711no—
444#3079—712no—
445#3040—712no—
446#3007—711no—
447#3006—711no—
448C4×#137—712no—
449C4×AGL(1,ℤ/8)—712no—
450#2921—711no—
451C71#6056711yescharacteristic, complemented, Sylow
452C22×#41C2×D7111yescharacteristic
453C2×#137—712no—
454C2×AGL(1,ℤ/8)—712no—
455#542—714no—
456#542—714no—
457#542—1422no—
458#542—1422no—
459C2×C4⋊Q8—711no—
460C2×#126—1421no—
461C2×#124—711no—
462C2×#124—1421no—
463C2×#123—1421no—
464C2×C22⋊Q8—711no—
465C2×C22⋊Q8—1421no—
466C2×#121—711no—
467#520—21no—
468#520—21no—
469#520C2×D7112yescomplemented
470#520C2×D7112yescomplemented
471#519C2×D7112yescomplemented
472#518—21no—
473#518—21no—
474#518C2×D7112yescomplemented
475C4×#41—22no—
476C4×#41C2×D7112yes—
477C4×#41C2×D7112yes—
478C2×C4×Q8—711no—
479C2×C4×D4—711no—
480C2×#117—22no—
481C2×#117C2×D7111yescharacteristic
482C2×#117C2×D7111yescharacteristic
483#485—714no—
484#484—712no—
485#483—712no—
486#482—714no—
487#481—712no—
488#480—712no—
489#477—714no—
490#476—714no—
491#475—714no—
492#474—714no—
493#464—714no—
494#464—714no—
495#463—714no—
496#463—714no—
497#452—714no—
498#451—712no—
499#450—712no—
500#449—714no—
501#448—712no—
502#447—712no—
503#442—714no—
504#441—714no—
505#440—714no—
506#440—714no—
507C4×Q16—714no—
508C4×SD16—714no—
509C4×SD16—714no—
510C4×D8—714no—
511#433—714no—
512#433—714no—
513#428—712no—
514#428—712no—
515#423—712no—
516#419—712no—
517#418—712no—
518#417—712no—
519#417—712no—
520#407—711no—
521#407—711no—
522C4×M16—712no—
523C2×#41—28no—
524C2×#41—21no—
525C2×#41—21no—
526C2×#41C22×D7112yes—
527C2×#41C22×D7112yes—
528C22×Q8—711no—
529C22×Q8—1421no—
530C22×Q8C22×D7111yescharacteristic
531C22×D4—21no—
532C22×D4—711no—
533C22×D4—1421no—
534C22×D4C22×D7111yescharacteristic
535C23×C4—21no—
536C23×C4—1421no—
537C23×C4C22×D7111yescharacteristic
538#137—1428no—
539AGL(1,ℤ/8)—1428no—
540C2×Q16—714no—
541C2×SD16—714no—
542C2×SD16—714no—
543C2×D8—714no—
544C2×M16—712no—
545C2×M16—712no—
546C4⋊Q8—714no—
547C4⋊Q8—1422no—
548#126—1424no—
549#126—1424no—
550#124—714no—
551#124—1424no—
552#124—1424no—
553#124—1422no—
554#123—1424no—
555#123—1424no—
556C22⋊Q8—712no—
557C22⋊Q8—712no—
558C22⋊Q8—1421no—
559C22⋊Q8—1421no—
560C22⋊Q8—1424no—
561C22⋊Q8—1424no—
562#121—712no—
563#121—712no—
564#121—1421no—
565#121—1421no—
566C4×Q8—22no—
567C4×Q8—22no—
568C4×Q8—714no—
569C4×Q8—1422no—
570C4×Q8C22×D7112yes—
571C4×Q8C22×D7112yes—
572C4×Q8C22×D7112yes—
573C4×Q8C22×D7112yes—
574C4×D4—22no—
575C4×D4—22no—
576C4×D4—22no—
577C4×D4—22no—
578C4×D4—22no—
579C4×D4—22no—
580C4×D4—22no—
581C4×D4—22no—
582C4×D4—22no—
583C4×D4—22no—
584C4×D4—714no—
585C4×D4—1422no—
586C4×D4C22×D7112yes—
587C4×D4C22×D7112yes—
588C4×D4C22×D7112yes—
589C4×D4C22×D7112yes—
590#117—21no—
591#117—21no—
592#117—22no—
593#117—22no—
594#117—22no—
595#117—22no—
596#117—22no—
597#117—22no—
598#117C22⋊D7112yes—
599#117C22⋊D7112yes—
600#117C22×D7112yes—
601#117C22×D7112yes—
602#117C22×D7112yes—
603#117C22×D7112yes—
604C2×C4⋊C4—22no—
605C2×C4⋊C4—22no—
606C2×C4⋊C4—711no—
607C2×C4⋊C4—711no—
608C2×C4⋊C4—1421no—
609C2×C4⋊C4—1421no—
610C2×C4⋊C4—1421no—
611C2×C4⋊C4C22⋊D7111yescharacteristic
612C2×C4⋊C4C22⋊D7111yescharacteristic
613C2×C4⋊C4C22×D7111yescharacteristic
614C2×C4⋊C4C22×D7111yescharacteristic
615C2×C22⋊C4—21no—
616C2×C22⋊C4—22no—
617C2×C22⋊C4—22no—
618C2×C22⋊C4—1421no—
619C2×C22⋊C4—1421no—
620C2×C22⋊C4—1421no—
621C2×C22⋊C4—1421no—
622C2×C22⋊C4—1421no—
623C2×C22⋊C4C22⋊D7111yescharacteristic
624C2×C22⋊C4C22⋊D7111yescharacteristic
625C2×C42—21no—
626C2×C42—22no—
627C2×C42—22no—
628C2×C42—1421no—
629C2×C42C22×D7111yescharacteristic
630C2×C42C22×D7111yescharacteristic
631#107—714no—
632#107—714no—
633#106—714no—
634#106—714no—
635C4⋊C8—714no—
636C4⋊C8—714no—
637#103—714no—
638#103—714no—
639#103—714no—
640#103—714no—
641#102—714no—
642#102—714no—
643#102—714no—
644#102—714no—
645C22⋊C8—712no—
646C22⋊C8—712no—
647C22⋊C8—712no—
648C22⋊C8—712no—
649#97—714no—
650C4×C8—714no—
651C24—21no—
652C24—1421no—
653C24C2×C22⋊D7111yescharacteristic
654#41—28no—
655#41—28no—
656#41—24no—
657#41—24no—
658#41—24no—
659#41#1176586518yes—
660C2×Q8—24no—
661C2×Q8—21no—
662C2×Q8—5682no—
663C2×Q8—712no—
664C2×Q8—1424no—
665C2×Q8—1421no—
666C2×Q8—1424no—
667C2×Q8C23×D7112yes—
668C2×D4—28no—
669C2×D4—22no—
670C2×D4—22no—
671C2×D4—24no—
672C2×D4—21no—
673C2×D4—5682no—
674C2×D4—712no—
675C2×D4—1422no—
676C2×D4—1422no—
677C2×D4—1421no—
678C2×D4—1424no—
679C2×D4C23×D7112yes—
680C22×C4—28no—
681C22×C4—21no—
682C22×C4—22no—
683C22×C4—22no—
684C22×C4—24no—
685C22×C4—21no—
686C22×C4—21no—
687C22×C4—22no—
688C22×C4—22no—
689C22×C4—22no—
690C22×C4—22no—
691C22×C4—5682no—
692C22×C4—1421no—
693C22×C4—1421no—
694C22×C4—1421no—
695C22×C4—1424no—
696C22×C4C2×C22⋊D7111yescharacteristic
697C22×C4C2×C22⋊D7111yescharacteristic
698C22×C4C2×C22⋊D7111yescharacteristic
699C22×C4C2×C22⋊D7111yescharacteristic
700C22×C4C2×C22⋊D7111yescharacteristic
701C22×C4C2×C22⋊D7111yescharacteristic
702C22×C4C2×C22⋊D7111yescharacteristic
703C22×C4C23×D7111yescharacteristic
704C22×C4C23×D7111yescharacteristic
705C22×C4C23×D7111yescharacteristic
706Q16—1428no—
707SD16—1428no—
708SD16—1428no—
709D8—1428no—
710M16—1424no—
711M16—1424no—
712C2×C8—714no—
713C2×C8—714no—
714C4⋊C4—21no—
715C4⋊C4—21no—
716C4⋊C4—22no—
717C4⋊C4—22no—
718C4⋊C4—22no—
719C4⋊C4—22no—
720C4⋊C4—712no—
721C4⋊C4—712no—
722C4⋊C4—1424no—
723C4⋊C4—1422no—
724C4⋊C4—1422no—
725C4⋊C4—1421no—
726C4⋊C4—1421no—
727C4⋊C4—1424no—
728C4⋊C4C2×C22⋊D7112yes—
729C4⋊C4C2×C22⋊D7112yes—
730C4⋊C4C2×C22⋊D7112yes—
731C4⋊C4C2×C22⋊D7112yes—
732C4⋊C4C23×D7112yes—
733C4⋊C4C23×D7112yes—
734C22⋊C4—22no—
735C22⋊C4—22no—
736C22⋊C4—22no—
737C22⋊C4—22no—
738C22⋊C4—22no—
739C22⋊C4—22no—
740C22⋊C4—1422no—
741C22⋊C4—1422no—
742C22⋊C4—1424no—
743C22⋊C4—1422no—
744C22⋊C4—1422no—
745C22⋊C4—1424no—
746C22⋊C4—1424no—
747C22⋊C4C2×C22⋊D7112yes—
748C22⋊C4C2×C22⋊D7112yes—
749C22⋊C4C2×C22⋊D7112yes—
750C22⋊C4C2×C22⋊D7112yes—
751C42—22no—
752C42—22no—
753C42—22no—
754C42—22no—
755C42—22no—
756C42—22no—
757C42—1424no—
758C42C2×C22⋊D7112yes—
759C42C2×C22⋊D7112yes—
760C42C23×D7112yes—
761C42C23×D7112yes—
762C23—24no—
763C23—22no—
764C23—22no—
765C23—41no—
766C23—41no—
767C23—81no—
768C23—81no—
769C23—2842no—
770C23—2842no—
771C23—2842no—
772C23—1422no—
773C23C22×C22⋊D7111yescharacteristic
774C23C22×C22⋊D7111yescharacteristic
775C23C22×C22⋊D7111yescharacteristic
776Q8—24no—
777Q8—22no—
778Q8—2842no—
779Q8—5684no—
780Q8—1424no—
781Q8C2×#1176586514yes—
782D4—28no—
783D4—24no—
784D4—28no—
785D4—22no—
786D4—2842no—
787D4—5682no—
788D4—5682no—
789D4—1424no—
790D4C2×#1176586514yes—
791C2×C4—24no—
792C2×C4—28no—
793C2×C4—22no—
794C2×C4—22no—
795C2×C4—22no—
796C2×C4—22no—
797C2×C4—22no—
798C2×C4—28no—
799C2×C4—22no—
800C2×C4—22no—
801C2×C4—22no—
802C2×C4—41no—
803C2×C4—41no—
804C2×C4—41no—
805C2×C4—41no—
806C2×C4—82no—
807C2×C4—82no—
808C2×C4—82no—
809C2×C4—82no—
810C2×C4—81no—
811C2×C4—81no—
812C2×C4—2842no—
813C2×C4—2842no—
814C2×C4—2842no—
815C2×C4—5684no—
816C2×C4—1422no—
817C2×C4—1422no—
818C2×C4—1422no—
819C2×C4C22×C22⋊D7111yescharacteristic
820C2×C4C22×C22⋊D7112yes—
821C2×C4C22×C22⋊D7112yes—
822C2×C4C22×C22⋊D7112yes—
823C2×C4C22×C22⋊D7112yes—
824C2×C4C22×C22⋊D7111yescharacteristic
825C2×C4C22×C22⋊D7111yescharacteristic
826C2×C4C2×#1176586514yes—
827C2×C4C24×D7111yescharacteristic
828C8—1424no—
829C8—1424no—
830C22—21no—
831C22—21no—
832C22—21no—
833C22—21no—
834C22—24no—
835C22—21no—
836C22—21no—
837C22—21no—
838C22—21no—
839C22—42no—
840C22—42no—
841C22—82no—
842C22—84no—
843C22—2842no—
844C22—2842no—
845C22—2842no—
846C22—5684no—
847C22#1798651012yes—
848C22C23×C22⋊D7111yescharacteristic
849C4—21no—
850C4—24no—
851C4—21no—
852C4—22no—
853C4—22no—
854C4—22no—
855C4—22no—
856C4—42no—
857C4—42no—
858C4—2842no—
859C4—2842no—
860C4—2842no—
861C4#1798651012yes—
862C4C22×#1176586512yes—
863C2—22no—
864C2—41no—
865C2—41no—
866C2—44no—
867C2—5682no—
868C2C2×#1798651011yescharacteristic
869C2#2260311911yescharacteristic
870C2#2260312611yescharacteristic
subgroupG/H
centerC22C23×C22⋊D71
commutator, cosocleC2×C4×C71C25
FrattiniC2×C4C24×D71
FittingC71×#3428C2
socleC22×C71C23×D4
prime radical#22597592C2
hypercenter#3428D71
hypocenterC71#60567
LCSG ▷ C2×C4×C71 ▷ C2×C71 ▷ C71
UCSC1 ◁ C22 ◁ C2×#117 ◁ #3428

Complements

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

NH ≅ G/Ntype
1. C2×#17986620C2semidirect
2. #22598617C2semidirect
3. #22598602C2semidirect
4. #22598569C2semidirect
5. #22598524C2semidirect
6. #22598288C2semidirect
7. #22598280C2semidirect
8. #22598155C2semidirect
9. #22597834C2semidirect
10. #22597600C2semidirect
12. C4×#14556158C2semidirect
13. C4×#14556153C2semidirect
14. #22596978C2semidirect
15. C71×#3428C2semidirect
21. #17986620C22semidirect
22. C2×#14556128C22semidirect
24. C2×#14556116C22semidirect
30. C2×C4×Dic142C22semidirect
31. C2×C4×D284C22semidirect
32. #17986340C22semidirect
33. #17986334C22semidirect
34. #17986329C22semidirect
36. #17986317C22semidirect
37. #17986312C22semidirect
38. #17986294C22semidirect
39. #17986289C22semidirect
40. #17986284C22semidirect
41. #17986279C22semidirect
42. #17986221C22semidirect
43. #17986221C22semidirect
44. #17986214C22semidirect
45. #17986214C22semidirect
46. #17986161C22semidirect
47. #17986155C22semidirect
48. #17986150C22semidirect
52. #17986109C22semidirect
53. #17986104C22semidirect
54. #17986099C22semidirect
55. #17986097C22semidirect
56. C4×#11765855C22semidirect
57. C4×#11765852C22semidirect
58. C4×#11765853C22semidirect
59. C4×#11765850C22semidirect
60. #17986060C22semidirect
61. #17986060C22semidirect
62. #17986042C22semidirect
63. #17986042C22semidirect
64. #17986023C22semidirect
65. #17986007C22semidirect
66. #17986003C22semidirect
71. C4×#11765849C22semidirect
75. #520×C71C22semidirect
76. #520×C71C22semidirect
77. #519×C71C22semidirect
80. #518×C71C22semidirect
437. #3428D71semidirect
451. C71#60567semidirect
469. #520C2×D71semidirect
470. #520C2×D71semidirect
471. #519C2×D71semidirect
474. #518C2×D71semidirect

Maximal subgroups

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

subgroupindex
C2×#179866202
#225986172
#225986022
#225985692
#225985242
#225982882
#225982802
#225981552
#225978342
#225976002
#225975922
C4×#145561582
C4×#145561532
#225969782
C71×#34282
#6056771