Finite Group Databasebeta

← C2×#22598297 #32865278

Subgroups — C2×#22598297 #32865278

Order 18176.

2362 conjugacy classes of subgroups.

The subgroup lattice has 826 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#17986565C211yesmaximal, characteristic
2C2×#17986480C211yesmaximal, characteristic, complemented
3#22598297C2116yesmaximal, direct product factor
4C2×#17986319C211yesmaximal, characteristic, complemented
5C2×#17986325C211yesmaximal, characteristic, complemented
6C2×#17986324C211yesmaximal, characteristic, complemented
7C2×#17986322C211yesmaximal, characteristic, complemented
8C2×#17986320C211yesmaximal, characteristic, complemented
9C2×#17986312C211yesmaximal, characteristic, complemented
10C2×#17986311C211yesmaximal, characteristic, complemented
11C2×#17986038C211yesmaximal, characteristic, complemented
12C2×#17986034C211yesmaximal, characteristic, complemented
13C2×#17986002C211yesmaximal, characteristic, complemented
14C2×#102×D71C211yesmaximal, characteristic, complemented
15C2×#17985964C211yesmaximal, characteristic, complemented
16C2×#481×C71C211yesmaximal, characteristic, complemented
17C22×#11765865C2211yescharacteristic
18C22×D4×D71C2211yescharacteristic
19C22×#11765848C2211yescharacteristic
20C22×C8×D71C2211yescharacteristic
21#17986565—24no—
22#17986565C2218yes—
23C2×#14556124—21no—
24C2×#14556114—21no—
25C2×#14556103C2211yescharacteristic
26C2×#14556102C2211yescharacteristic
27C2×#14556099C2211yescharacteristic
28C2×#14556098—21no—
29C2×#14556096—21no—
30#17986480—24no—
31#17986480C2218yescomplemented
32C2×#14556093—21no—
33C2×#14556090—21no—
34C2×C4×C22⋊D71—21no—
35C2×C4×C22⋊D71—21no—
36C2×#14556087C2211yescharacteristic, complemented
37C2×#14556086C2211yescharacteristic
38C2×#14556086C2211yescharacteristic
39C2×#14556086C2211yescharacteristic, complemented
40C2×C4⋊C4×D71C2211yescharacteristic
41C2×C4⋊C4×D71C2211yescharacteristic, complemented
42#17986325C2218yescomplemented
43#17986324C2218yescomplemented
44#17986322C2218yescomplemented
45#17986320C2218yescomplemented
46#17986319C2218yescomplemented
47#17986312C2218yescomplemented
48#17986311C2218yescomplemented
49#17986038C2218yescomplemented
50#17986034C2218yescomplemented
51C2×#14556062C2211yescharacteristic, complemented
52C2×#14556061C2211yescharacteristic, complemented
53C2×#14556061C2211yescharacteristic, complemented
54C2×#14556061C2211yescharacteristic, complemented
55C2×#14556060C2211yescharacteristic, complemented
56C2×#14556059C2211yescharacteristic, complemented
57#17986002C2218yescomplemented
58C2×#14556050C2211yescharacteristic
59C2×#14556050C2211yescharacteristic
60C2×#14556049C2211yescharacteristic
61C2×#14556049C2211yescharacteristic
62C2×#14556048C2211yescharacteristic
63C2×#14556048C2211yescharacteristic
64#102×D71C2218yescomplemented
65#17985964C2218yescomplemented
66C2×C22⋊(C71⋊C8)C2211yescharacteristic, complemented
67C2×(C2×D71)⋊C8C2211yescharacteristic, complemented
68C2×(C2×D71)⋊C8C2211yescharacteristic, complemented
69C2×#121×C71C2211yescharacteristic
70C22×C4⋊C4×C71C2211yescharacteristic, complemented
71#481×C71C2218yescomplemented
72C2×#106×C71C2211yescharacteristic, complemented
73C2×#106×C71C2211yescharacteristic, complemented
74C2×#102×C71C2211yescharacteristic
75C2×#102×C71C2211yescharacteristic
76C2×C22⋊C8×C71C2211yescharacteristic, complemented
77C24×D71—21no—
78C2×#11765865—24no—
79C2×#11765865—24no—
80C2×#11765865D414yes—
81C2×#11765865C2314yes—
82C22×Dic142D411yescharacteristic
83C22×D284—21no—
84C22×D284D411yescharacteristic
85C22×D284C2311yescharacteristic
86C22×C22⋊D71—21no—
87C22×C22⋊D71—21no—
88C22×C22⋊D71—21no—
89C22×C22⋊D71D411yescharacteristic
90C22×C22⋊D71D411yescharacteristic
91C2×D4×D71—22no—
92C2×D4×D71—24no—
93C2×D4×D71—24no—
94C2×D4×D71C2314yes—
95C22×C4×D71—21no—
96C22×C4×D71—21no—
97C22×C4×D71C2311yescharacteristic
98C22×C4×D71C2311yescharacteristic
99C2×#11765848—24no—
100C2×#11765848C2314yes—
101C22×C71⋊C8C2311yescharacteristic
102C22×C71⋊C8C2311yescharacteristic
103C2×C8×D71—24no—
104C2×C8×D71C2314yes—
105#14556124—28no—
106#14556114—28no—
107#14556103—22no—
108#14556103C2314yes—
109#14556102—22no—
110#14556102C2314yes—
111#14556099—22no—
112#14556099C2314yes—
113#14556098—28no—
114#14556096—28no—
115#14556093—28no—
116#14556090—28no—
117C4×C22⋊D71—28no—
118C4×C22⋊D71—28no—
119#14556087—22no—
120#14556087C2314yescomplemented
121#14556086—22no—
122#14556086—22no—
123#14556086—22no—
124#14556086C2314yes—
125#14556086C2314yes—
126#14556086C2314yescomplemented
127C2×C4⋊Dic71C2311yescharacteristic
128C2×C4⋊Dic71C2311yescharacteristic
129C2×C4⋊Dic71C2311yescharacteristic
130C2×Dic71⋊C4—21no—
131C2×Dic71⋊C4—21no—
132C4⋊C4×D71—22no—
133C4⋊C4×D71—22no—
134C4⋊C4×D71C2314yes—
135C4⋊C4×D71C2314yescomplemented
136C2×C22⋊Dic71—21no—
137C2×C22⋊Dic71—21no—
138C2×(C2×D71)⋊C4—21no—
139C2×(C2×D71)⋊C4—21no—
140C2×(C2×D71)⋊C4—21no—
141C2×(C2×D71)⋊C4—21no—
142C2×(C2×D71)⋊C4—21no—
143C2×C4×Dic71—21no—
144C2×C4×Dic71—21no—
145C2×C4×Dic71—21no—
146C2×C4×Dic71—21no—
147#14556062C2314yescomplemented
148#14556061C2314yescomplemented
149#14556061C2314yescomplemented
150#14556061C2314yescomplemented
151#14556060C2314yescomplemented
152#14556059C2314yescomplemented
153#14556050C2314yes—
154#14556050C2314yes—
155#14556049C2314yes—
156#14556049C2314yes—
157#14556048C2314yes—
158#14556048C2314yes—
159C22⋊(C71⋊C8)C2314yescomplemented
160(C2×D71)⋊C8C2314yescomplemented
161(C2×D71)⋊C8C2314yescomplemented
162C22×D4×C71—21no—
163C22×D4×C71C2311yescharacteristic
164C23×C4×C71—21no—
165C23×C4×C71C2311yescharacteristic
166C22×C8×C71C2311yescharacteristic
167C22×C8×C71C2311yescharacteristic
168#121×C71—22no—
169#121×C71C2314yes—
170C2×C4⋊C4×C71—21no—
171C2×C4⋊C4×C71—22no—
172C2×C4⋊C4×C71C2311yescharacteristic
173C2×C4⋊C4×C71C2311yescharacteristic
174C2×C4⋊C4×C71C2311yescharacteristic
175C2×C4⋊C4×C71C2314yescomplemented
176C2×C22⋊C4×C71—21no—
177#106×C71C2314yescomplemented
178#106×C71C2314yescomplemented
179#102×C71C2314yes—
180#102×C71C2314yes—
181C22⋊C8×C71C2314yescomplemented
182C23×D71—21no—
183C23×D71—24no—
184C23×D71—44no—
185C23×D71—82no—
186C23×D71—82no—
187C23×D71C2×D411yescharacteristic
188C23×D71C2×D411yescharacteristic
189#11765865—216no—
190#11765865—28no—
191#11765865—28no—
192C2×Dic142—24no—
193C2×Dic142C2×D414yes—
194C2×D284—24no—
195C2×D284—22no—
196C2×D284—22no—
197C2×D284—21no—
198C2×D284—24no—
199C2×D284—82no—
200C2×D284C2×D414yes—
201C2×D284C2412yes—
202C2×C22⋊D71—24no—
203C2×C22⋊D71—24no—
204C2×C22⋊D71—24no—
205C2×C22⋊D71—24no—
206C2×C22⋊D71—24no—
207C2×C22⋊D71—44no—
208C2×C22⋊D71—82no—
209C2×C22⋊D71—82no—
210C2×C22⋊D71C2×D414yes—
211C2×C22⋊D71C2×D414yes—
212D4×D71—28no—
213D4×D71—28no—
214D4×D71—48no—
215C22×Dic71—21no—
216C22×Dic71—21no—
217C22×Dic71—21no—
218C22×Dic71C2×D411yescharacteristic
219C22×Dic71C2×D411yescharacteristic
220C2×C4×D71—22no—
221C2×C4×D71—22no—
222C2×C4×D71—24no—
223C2×C4×D71—24no—
224C2×C4×D71—82no—
225C2×C4×D71—82no—
226C2×C4×D71C2×D412yes—
227C2×C4×D71C2×D412yes—
228C2×C4×D71#4114yes—
229C2×C4×D71#4114yes—
230C2×C4×D71C2412yes—
231C2×C4×D71C2412yes—
232#11765848—28no—
233C2×C71⋊C8—22no—
234C2×C71⋊C8—22no—
235C2×C71⋊C8C2412yes—
236C2×C71⋊C8C2412yes—
237C8×D71—28no—
238C4⋊Dic71—21no—
239C4⋊Dic71—21no—
240C4⋊Dic71—21no—
241C4⋊Dic71C2412yes—
242C4⋊Dic71C2412yes—
243C4⋊Dic71C2412yes—
244Dic71⋊C4—24no—
245Dic71⋊C4—24no—
246C22⋊Dic71—24no—
247C22⋊Dic71—24no—
248(C2×D71)⋊C4—24no—
249(C2×D71)⋊C4—24no—
250(C2×D71)⋊C4—24no—
251(C2×D71)⋊C4—24no—
252(C2×D71)⋊C4—24no—
253C4×Dic71—24no—
254C4×Dic71—24no—
255C4×Dic71—24no—
256C4×Dic71—24no—
257C24×C71—21no—
258C24×C71C2×D411yescharacteristic
259C2×D4×C71—24no—
260C2×D4×C71—21no—
261C2×D4×C71—22no—
262C2×D4×C71—22no—
263C2×D4×C71—82no—
264C2×D4×C71C2412yes—
265C22×C4×C71—22no—
266C22×C4×C71—22no—
267C22×C4×C71—21no—
268C22×C4×C71—21no—
269C22×C4×C71—21no—
270C22×C4×C71—24no—
271C22×C4×C71—82no—
272C22×C4×C71C2×D411yescharacteristic
273C22×C4×C71C2×D412yes—
274C22×C4×C71C2412yes—
275C22×C4×C71C2411yescharacteristic
276C2×C8×C71—22no—
277C2×C8×C71—22no—
278C2×C8×C71C2412yes—
279C2×C8×C71C2412yes—
280C4⋊C4×C71—21no—
281C4⋊C4×C71—21no—
282C4⋊C4×C71—24no—
283C4⋊C4×C71—21no—
284C4⋊C4×C71C2412yes—
285C4⋊C4×C71C2412yes—
286C4⋊C4×C71C2412yes—
287C22⋊C4×C71—24no—
288C23×C71—22no—
289C23×C71—22no—
290C23×C71—22no—
291C23×C71—22no—
292C23×C71—42no—
293C23×C71—42no—
294C23×C71—42no—
295C23×C71C22×D412yes—
296C23×C71C22×D411yescharacteristic
297C22×D71—22no—
298C22×D71—22no—
299C22×D71—22no—
300C22×D71—22no—
301C22×D71—22no—
302C22×D71—22no—
303C22×D71—42no—
304C22×D71—42no—
305C22×D71—42no—
306C22×D71—48no—
307C22×D71—84no—
308C22×D71—84no—
309C22×D71—816no—
310C22×D71#12314yes—
311C22×D71C22×D412yes—
312C22×D71C22×D412yes—
313D4×C71—22no—
314D4×C71—22no—
315D4×C71—42no—
316D4×C71—84no—
317C2×C4×C71—22no—
318C2×C4×C71—24no—
319C2×C4×C71—22no—
320C2×C4×C71—22no—
321C2×C4×C71—22no—
322C2×C4×C71—22no—
323C2×C4×C71—22no—
324C2×C4×C71—42no—
325C2×C4×C71—42no—
326C2×C4×C71—42no—
327C2×C4×C71—84no—
328C2×C4×C71C22×D412yes—
329C2×C4×C71C22×D411yescharacteristic
330C2×C4×C71C2×#4112yes—
331C2×C4×C71C2×#4112yes—
332C2×C4×C71C2511yescharacteristic
333C22⋊D71—28no—
334C22⋊D71—28no—
335C22⋊D71—48no—
336C22⋊D71—84no—
337C22⋊D71—84no—
338C2×Dic71—22no—
339C2×Dic71—22no—
340C2×Dic71—22no—
341C2×Dic71—22no—
342C2×Dic71—42no—
343C2×Dic71—42no—
344C2×Dic71—42no—
345C2×Dic71#12314yes—
346C2×Dic71C22×D412yes—
347C2×Dic71C22×D412yes—
348D284—28no—
349D284—22no—
350D284—22no—
351D284—42no—
352D284—84no—
353C4×D71—24no—
354C4×D71—22no—
355C4×D71—22no—
356C4×D71—84no—
357C4×D71—84no—
358C4×D71#12318yes—
359C4×D71C2×#4114yes—
360C4×D71C2×#4114yes—
361Dic142—28no—
362C8×C71—22no—
363C8×C71—22no—
364C71⋊C8—22no—
365C71⋊C8—22no—
366C22×C71—22no—
367C22×C71—22no—
368C22×C71—22no—
369C22×C71—44no—
370C22×C71—42no—
371C22×C71—42no—
372C22×C71—42no—
373C22×C71—84no—
374C22×C71C2×#12312yes—
375C22×C71#57612yes—
376C22×C71#57712yes—
377C22×C71C23×D411yescharacteristic
378C2×D71—28no—
379C2×D71—22no—
380C2×D71—22no—
381C2×D71—22no—
382C2×D71—22no—
383C2×D71—22no—
384C2×D71—44no—
385C2×D71—42no—
386C2×D71—42no—
387C2×D71—42no—
388C2×D71—816no—
389C2×D71—84no—
390C2×D71C2×#12314yes—
391C4×C71—22no—
392C4×C71—42no—
393C4×C71—42no—
394C4×C71—42no—
395C4×C71C2×#12312yes—
396C4×C71C22×#4111yescharacteristic
397C4×C71C22×#4111yescharacteristic
398Dic71—22no—
399Dic71—42no—
400Dic71—42no—
401Dic71—42no—
402Dic71C2×#12314yes—
403C2×#3096—711nomaximal, Sylow
404C2×C71—42no—
405C2×C71—82no—
406C2×C71#309614yescomplemented
407C2×C71C22×#12311yescharacteristic
408C2×C71C2×#57611yescharacteristic
409C2×C71C2×#57711yescharacteristic
410D71—24no—
411D71—42no—
412D71—82no—
413C2×#535—711no—
414C2×#520—711no—
415#3096—7116no—
416C2×#481—711no—
417C2×#481D7111yescharacteristic, complemented
418C2×#482—711no—
419C2×#482—711no—
420C2×#482—711no—
421C2×#482—711no—
422C2×#480—711no—
423C2×#480—711no—
424C2×#428—711no—
425C2×#427—711no—
426C2×#418—711no—
427C22×#102—711no—
428C2×#408—711no—
429C71C2×#309611yescharacteristic, complemented, Sylow
430C22×#41—711no—
431C23×D4—711no—
432C22×M16—711no—
433C23×C8—711no—
434#535—718no—
435#535—1424no—
436C2×#127—1421no—
437C2×#124—1421no—
438C2×#121—711no—
439C2×#121—711no—
440C2×#121—711no—
441C2×#121C2×D7111yescharacteristic
442C2×#120—1421no—
443C2×#120—1421no—
444#520—718no—
445#520—1424no—
446C2×C4×Q8—1421no—
447C2×C4×D4—1421no—
448C2×C4×D4—1421no—
449C2×C4×D4—1421no—
450C2×#117—711no—
451C2×#117—711no—
452C2×#117—711no—
453C2×#117—711no—
454C22×C4⋊C4—711no—
455C22×C4⋊C4—711no—
456C22×C4⋊C4C2×D7111yescharacteristic, complemented
457#482—718no—
458#482—718no—
459#482—718no—
460#482—718no—
461#481—718no—
462#481C2×D7118yescomplemented
463#480—718no—
464#480—718no—
465#428—718no—
466#427—718no—
467C2×#107—711no—
468C2×#107—711no—
469C2×#107—711no—
470C2×#107—711no—
471C2×#106—711no—
472C2×#106—711no—
473C2×#106C2×D7111yescharacteristic, complemented
474C2×#106C2×D7111yescharacteristic, complemented
475#418—718no—
476C2×#102—711no—
477C2×#102—711no—
478C2×#102—711no—
479C2×#102—711no—
480C2×#102—711no—
481C2×#102—711no—
482C2×#102—718no—
483C2×#102C2×D7111yescharacteristic
484C2×#102C2×D7111yescharacteristic
485#408—718no—
486C2×C22⋊C8—711no—
487C2×C22⋊C8—711no—
488C2×C22⋊C8—711no—
489C2×C22⋊C8C2×D7111yescharacteristic, complemented
490C25—1421no—
491C2×#41—714no—
492C2×#41—714no—
493C2×#41—1424no—
494C2×#41—1424no—
495C22×Q8—711no—
496C22×D4—21no—
497C22×D4—711no—
498C22×D4—711no—
499C22×D4—714no—
500C22×D4—711no—
501C22×D4—711no—
502C22×D4—1421no—
503C22×D4—1422no—
504C22×D4—1424no—
505C22×D4—1424no—
506C22×D4—1421no—
507C22×D4—1421no—
508C22×D4—1421no—
509C22×D4C22×D7111yescharacteristic
510C23×C4—21no—
511C23×C4—711no—
512C23×C4—711no—
513C23×C4—1421no—
514C23×C4—1421no—
515C23×C4C22×D7111yescharacteristic
516C2×M16—714no—
517C2×M16—1424no—
518C22×C8—711no—
519C22×C8—711no—
520C22×C8—714no—
521C22×C8—1424no—
522C22×C8C22×D7111yescharacteristic
523C22×C8C22×D7111yescharacteristic
524#127—1428no—
525#124—1428no—
526#121—22no—
527#121—714no—
528#121—714no—
529#121—714no—
530#121—1422no—
531#121—1422no—
532#121—1422no—
533#121C22×D7114yes—
534#120—1428no—
535#120—1428no—
536C4×Q8—1428no—
537C4×D4—1428no—
538C4×D4—1428no—
539C4×D4—1428no—
540#117—714no—
541#117—714no—
542#117—714no—
543#117—714no—
544#117—1422no—
545#117—1422no—
546#117—1422no—
547#117—1422no—
548C2×C4⋊C4—21no—
549C2×C4⋊C4—22no—
550C2×C4⋊C4—711no—
551C2×C4⋊C4—711no—
552C2×C4⋊C4—711no—
553C2×C4⋊C4—714no—
554C2×C4⋊C4—714no—
555C2×C4⋊C4—1422no—
556C2×C4⋊C4—1422no—
557C2×C4⋊C4—1421no—
558C2×C4⋊C4—1421no—
559C2×C4⋊C4C22×D7111yescharacteristic
560C2×C4⋊C4C22×D7111yescharacteristic
561C2×C4⋊C4C22×D7111yescharacteristic
562C2×C4⋊C4C22×D7114yescomplemented
563C2×C22⋊C4—21no—
564C2×C22⋊C4—1421no—
565C2×C22⋊C4—1421no—
566C2×C22⋊C4—1421no—
567C2×C22⋊C4—1421no—
568C2×C22⋊C4—1421no—
569C2×C22⋊C4—1421no—
570C2×C22⋊C4—1421no—
571C2×C42—1421no—
572C2×C42—1421no—
573C2×C42—1421no—
574C2×C42—1421no—
575#107—714no—
576#107—714no—
577#107—714no—
578#107—714no—
579#106—714no—
580#106—714no—
581#106C22×D7114yescomplemented
582#106C22×D7114yescomplemented
583#102—714no—
584#102—714no—
585#102—714no—
586#102—714no—
587#102—714no—
588#102—714no—
589#102C22×D7114yes—
590#102C22×D7114yes—
591C22⋊C8—714no—
592C22⋊C8—714no—
593C22⋊C8—714no—
594C22⋊C8C22×D7114yescomplemented
595C24—21no—
596C24—2844no—
597C24—5682no—
598C24—5682no—
599C24—711no—
600C24—711no—
601C24—1424no—
602C24—1421no—
603C24D4×D7111yescharacteristic
604#41—1428no—
605#41—1428no—
606#41—14216no—
607C2×Q8—714no—
608C2×Q8—1424no—
609C2×D4—24no—
610C2×D4—21no—
611C2×D4—22no—
612C2×D4—22no—
613C2×D4—82no—
614C2×D4—2848no—
615C2×D4—2844no—
616C2×D4—5682no—
617C2×D4—5682no—
618C2×D4—5682no—
619C2×D4—714no—
620C2×D4—714no—
621C2×D4—714no—
622C2×D4—712no—
623C2×D4—1424no—
624C2×D4—1424no—
625C2×D4—1428no—
626C2×D4—1428no—
627C2×D4—1424no—
628C2×D4—1424no—
629C2×D4—1424no—
630C2×D4—1424no—
631C2×D4—1424no—
632C2×D4—1421no—
633C2×D4—1422no—
634C2×D4—1422no—
635C2×D4C23×D7112yes—
636C22×C4—22no—
637C22×C4—22no—
638C22×C4—21no—
639C22×C4—21no—
640C22×C4—21no—
641C22×C4—24no—
642C22×C4—82no—
643C22×C4—5682no—
644C22×C4—5682no—
645C22×C4—711no—
646C22×C4—712no—
647C22×C4—714no—
648C22×C4—714no—
649C22×C4—712no—
650C22×C4—711no—
651C22×C4—712no—
652C22×C4—712no—
653C22×C4—1424no—
654C22×C4—1424no—
655C22×C4—1421no—
656C22×C4—1421no—
657C22×C4—1421no—
658C22×C4—1422no—
659C22×C4—1422no—
660C22×C4D4×D7112yes—
661C22×C4D4×D7111yescharacteristic
662C22×C4C23×D7112yes—
663C22×C4C23×D7111yescharacteristic
664M16—1428no—
665C2×C8—22no—
666C2×C8—22no—
667C2×C8—712no—
668C2×C8—712no—
669C2×C8—1428no—
670C2×C8—1422no—
671C2×C8—1422no—
672C2×C8C23×D7112yes—
673C2×C8C23×D7112yes—
674C4⋊C4—21no—
675C4⋊C4—21no—
676C4⋊C4—24no—
677C4⋊C4—21no—
678C4⋊C4—712no—
679C4⋊C4—712no—
680C4⋊C4—712no—
681C4⋊C4—1424no—
682C4⋊C4—1424no—
683C4⋊C4—1421no—
684C4⋊C4—1421no—
685C4⋊C4—1421no—
686C4⋊C4C23×D7112yes—
687C4⋊C4C23×D7112yes—
688C4⋊C4C23×D7112yes—
689C22⋊C4—24no—
690C22⋊C4—1424no—
691C22⋊C4—1424no—
692C22⋊C4—1424no—
693C22⋊C4—1424no—
694C22⋊C4—1424no—
695C22⋊C4—1424no—
696C22⋊C4—1424no—
697C42—1424no—
698C42—1424no—
699C42—1424no—
700C42—1424no—
701C23—22no—
702C23—22no—
703C23—22no—
704C23—22no—
705C23—42no—
706C23—42no—
707C23—42no—
708C23—2848no—
709C23—2842no—
710C23—2842no—
711C23—2842no—
712C23—5684no—
713C23—5684no—
714C23—56816no—
715C23—712no—
716C23—714no—
717C23—712no—
718C23—1422no—
719C23—1422no—
720C23—1422no—
721C23—1422no—
722C23—1422no—
723C23—1422no—
724C23C2×D4×D7112yes—
725C23C2×D4×D7111yescharacteristic
726Q8—1428no—
727D4—22no—
728D4—22no—
729D4—42no—
730D4—84no—
731D4—2848no—
732D4—2842no—
733D4—5684no—
734D4—5684no—
735D4—5684no—
736D4—1428no—
737D4—1428no—
738D4—1428no—
739D4—1422no—
740D4—1422no—
741C2×C4—22no—
742C2×C4—22no—
743C2×C4—22no—
744C2×C4—24no—
745C2×C4—22no—
746C2×C4—22no—
747C2×C4—22no—
748C2×C4—42no—
749C2×C4—42no—
750C2×C4—42no—
751C2×C4—84no—
752C2×C4—2842no—
753C2×C4—2842no—
754C2×C4—2842no—
755C2×C4—5684no—
756C2×C4—5684no—
757C2×C4—712no—
758C2×C4—714no—
759C2×C4—714no—
760C2×C4—714no—
761C2×C4—718no—
762C2×C4—712no—
763C2×C4—1422no—
764C2×C4—1422no—
765C2×C4—1422no—
766C2×C4—1422no—
767C2×C4—1422no—
768C2×C4—1422no—
769C2×C4—1424no—
770C2×C4C2×D4×D7112yes—
771C2×C4C2×D4×D7111yescharacteristic
772C2×C4#41×D7112yes—
773C2×C4#41×D7112yes—
774C2×C4C24×D7111yescharacteristic
775C8—22no—
776C8—22no—
777C8—1422no—
778C8—1422no—
779C22—22no—
780C22—22no—
781C22—22no—
782C22—44no—
783C22—42no—
784C22—42no—
785C22—42no—
786C22—84no—
787C22—2844no—
788C22—2842no—
789C22—2842no—
790C22—2842no—
791C22—56816no—
792C22—5684no—
793C22—714no—
794C22—1422no—
795C22—1422no—
796C22—1422no—
797C22—1422no—
798C22—1422no—
799C22—1428no—
800C22#123×D7112yes—
801C22#1798680312yes—
802C22#1798680512yes—
803C22C22×D4×D7111yescharacteristic
804C4—22no—
805C4—42no—
806C4—42no—
807C4—42no—
808C4—2842no—
809C4—2842no—
810C4—2842no—
811C4—714no—
812C4—1422no—
813C4#123×D7112yes—
814C4C2×#41×D7111yescharacteristic
815C4C2×#41×D7111yescharacteristic
816C2—42no—
817C2—82no—
818C2—2842no—
819C2—5682no—
820C2—1424no—
821C2#2259829714yesdirect product factor
822C2C2×#123×D7111yescharacteristic
823C2C2×#1798680311yescharacteristic
824C2C2×#1798680511yescharacteristic
subgroupG/H
centerC23C2×D4×D71
commutator, cosocleC2×C4×C71C25
FrattiniC2×C4C24×D71
FittingC2×#481×C71C2
socleC23×C71C22×D4
prime radicalC2×#17986565C2
hypercenterC2×#481D71
hypocenterC71C2×#3096
LCSG ▷ C2×C4×C71 ▷ C2×C71 ▷ C71
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#481

Complements

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

NH ≅ G/Ntype
2. C2×#17986480C2semidirect
3. #22598297C2direct (N × H)
4. C2×#17986319C2semidirect
5. C2×#17986325C2semidirect
6. C2×#17986324C2semidirect
7. C2×#17986322C2semidirect
8. C2×#17986320C2semidirect
9. C2×#17986312C2semidirect
10. C2×#17986311C2semidirect
11. C2×#17986038C2semidirect
12. C2×#17986034C2semidirect
13. C2×#17986002C2semidirect
14. C2×#102×D71C2semidirect
15. C2×#17985964C2semidirect
16. C2×#481×C71C2semidirect
31. #17986480C22semidirect
36. C2×#14556087C22semidirect
39. C2×#14556086C22semidirect
41. C2×C4⋊C4×D71C22semidirect
42. #17986325C22semidirect
43. #17986324C22semidirect
44. #17986322C22semidirect
45. #17986320C22semidirect
46. #17986319C22semidirect
47. #17986312C22semidirect
48. #17986311C22semidirect
49. #17986038C22semidirect
50. #17986034C22semidirect
51. C2×#14556062C22semidirect
52. C2×#14556061C22semidirect
53. C2×#14556061C22semidirect
54. C2×#14556061C22semidirect
55. C2×#14556060C22semidirect
56. C2×#14556059C22semidirect
57. #17986002C22semidirect
64. #102×D71C22semidirect
65. #17985964C22semidirect
66. C2×C22⋊(C71⋊C8)C22semidirect
67. C2×(C2×D71)⋊C8C22semidirect
68. C2×(C2×D71)⋊C8C22semidirect
70. C22×C4⋊C4×C71C22semidirect
71. #481×C71C22semidirect
72. C2×#106×C71C22semidirect
73. C2×#106×C71C22semidirect
76. C2×C22⋊C8×C71C22semidirect
120. #14556087C23semidirect
126. #14556086C23semidirect
135. C4⋊C4×D71C23semidirect
147. #14556062C23semidirect
148. #14556061C23semidirect
149. #14556061C23semidirect
150. #14556061C23semidirect
151. #14556060C23semidirect
152. #14556059C23semidirect
159. C22⋊(C71⋊C8)C23semidirect
160. (C2×D71)⋊C8C23semidirect
161. (C2×D71)⋊C8C23semidirect
175. C2×C4⋊C4×C71C23semidirect
177. #106×C71C23semidirect
178. #106×C71C23semidirect
181. C22⋊C8×C71C23semidirect
406. C2×C71#3096semidirect
417. C2×#481D71semidirect
429. C71C2×#3096semidirect
456. C22×C4⋊C4C2×D71semidirect
462. #481C2×D71semidirect
473. C2×#106C2×D71semidirect
474. C2×#106C2×D71semidirect
489. C2×C22⋊C8C2×D71semidirect
562. C2×C4⋊C4C22×D71semidirect
581. #106C22×D71semidirect
582. #106C22×D71semidirect
594. C22⋊C8C22×D71semidirect
821. C2#22598297direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#179865652
C2×#179864802
#225982972
C2×#179863192
C2×#179863252
C2×#179863242
C2×#179863222
C2×#179863202
C2×#179863122
C2×#179863112
C2×#179860382
C2×#179860342
C2×#179860022
C2×#102×D712
C2×#179859642
C2×#481×C712
C2×#309671