Finite Group Databasebeta

← C2×#22600422 #32873979

Subgroups — C2×#22600422 #32873979

Order 18176.

2298 conjugacy classes of subgroups.

The subgroup lattice has 824 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#17986704C211yesmaximal, characteristic, complemented
2C2×#17986637C211yesmaximal, characteristic
3#22600422C2116yesmaximal, direct product factor
4C2×#17986360C211yesmaximal, characteristic, complemented
5C2×#17986333C211yesmaximal, characteristic, complemented
6C2×#17986312C211yesmaximal, characteristic, complemented
7C2×#17986277C211yesmaximal, characteristic, complemented
8C2×#17986245C211yesmaximal, characteristic, complemented
9C2×#17986239C211yesmaximal, characteristic, complemented
10C2×#17986224C211yesmaximal, characteristic, complemented
11C2×#17986161C211yesmaximal, characteristic, complemented
12C2×#17986151C211yesmaximal, characteristic, complemented
13C2×#17986096C211yesmaximal, characteristic, complemented
14C2×#17986068C211yesmaximal, characteristic, complemented
15C2×#102×D71C211yesmaximal, characteristic, complemented
16C2×#417×C71C211yesmaximal, characteristic, complemented
17C22×D4×D71C2211yescharacteristic
18C22×#11765855C2211yescharacteristic, complemented
19C22×#11765854C2211yescharacteristic
20C22×#11765853C2211yescharacteristic
21C22×C8×D71C2211yescharacteristic
22#17986704—24no—
23#17986704C2218yescomplemented
24#17986637—24no—
25#17986637C2218yes—
26C2×#14556127C2211yescharacteristic, complemented
27C2×#14556118—21no—
28C2×#14556117C2211yescharacteristic
29C2×#14556111—21no—
30C2×#14556108C2211yescharacteristic
31C2×#14556107—21no—
32C2×#14556107C2211yescharacteristic, complemented
33C2×#14556106—21no—
34C2×#14556104C2211yescharacteristic
35C2×#14556102C2211yescharacteristic
36C2×#14556100—21no—
37C2×#14556096—21no—
38C2×#14556093C2211yescharacteristic, complemented
39C2×D4×Dic71C2211yescharacteristic
40C2×C4×C22⋊D71—21no—
41C2×C4×C22⋊D71C2211yescharacteristic
42C2×C4⋊C4×D71C2211yescharacteristic
43C22×(C2×D71)⋊C4—21no—
44#17986360C2218yescomplemented
45#17986333C2218yescomplemented
46#17986312C2218yescomplemented
47#17986277C2218yescomplemented
48#17986245C2218yescomplemented
49#17986239C2218yescomplemented
50#17986224C2218yescomplemented
51#17986161C2218yescomplemented
52#17986151C2218yescomplemented
53#17986096C2218yescomplemented
54#17986068C2218yescomplemented
55C2×#14556062C2211yescharacteristic, complemented
56C2×#14556061C2211yescharacteristic, complemented
57C2×#14556061C2211yescharacteristic, complemented
58C2×Dic71⋊C8C2211yescharacteristic, complemented
59C2×#14556053C2211yescharacteristic, complemented
60C2×#14556052C2211yescharacteristic, complemented
61C2×#14556050C2211yescharacteristic
62C2×#14556049C2211yescharacteristic
63C2×#14556048C2211yescharacteristic
64C2×#14556048C2211yescharacteristic
65#102×D71C2218yescomplemented
66C2×C22⋊(C71⋊C8)C2211yescharacteristic, complemented
67C2×(C2×D71)⋊C8C2211yescharacteristic
68C2×#14556038C2211yescharacteristic, complemented
69C22×#41×C71C2211yescharacteristic
70C22×M16×C71C2211yescharacteristic, complemented
71C22×C4⋊C4×C71C2211yescharacteristic, complemented
72#417×C71C2218yescomplemented
73C2×#103×C71C2211yescharacteristic, complemented
74C2×#103×C71C2211yescharacteristic, complemented
75C2×#102×C71C2211yescharacteristic
76C2×#102×C71C2211yescharacteristic
77C24×D71—21no—
78C22×Dic142—21no—
79C22×Dic142C2311yescharacteristic
80C22×D284C2311yescharacteristic
81C22×C22⋊D71—21no—
82C22×C22⋊D71—21no—
83C22×C22⋊D71D411yescharacteristic
84C2×D4×D71—22no—
85C2×D4×D71—24no—
86C2×D4×D71—42no—
87C2×D4×D71C2314yes—
88C23×Dic71—21no—
89C22×C4×D71—21no—
90C22×C4×D71C2311yescharacteristic
91C2×#11765855—42no—
92C2×#11765855C2314yescomplemented
93C2×#11765854—42no—
94C2×#11765854C2314yes—
95C2×#11765853—24no—
96C2×#11765853C2314yes—
97C22×C71⋊C8C2311yescharacteristic
98C22×C71⋊C8C2311yescharacteristic
99C2×C8×D71—42no—
100C2×C8×D71C2314yes—
101#14556127—22no—
102#14556127C2314yescomplemented
103#14556118—28no—
104#14556117—22no—
105#14556117C2314yes—
106#14556111—28no—
107#14556108—22no—
108#14556108C2314yes—
109#14556107—28no—
110#14556107—22no—
111#14556107C2314yescomplemented
112#14556106—28no—
113#14556104—22no—
114#14556104C2314yes—
115#14556102—22no—
116#14556102C2314yes—
117#14556100—28no—
118#14556096—28no—
119#14556093—22no—
120#14556093C2314yescomplemented
121D4×Dic71—22no—
122D4×Dic71C2314yes—
123C4×C22⋊D71—28no—
124C4×C22⋊D71D414yes—
125C4×C22⋊D71C2314yes—
126C2×C4⋊Dic71—21no—
127C2×C4⋊Dic71C2311yescharacteristic
128C2×C4⋊Dic71C2311yescharacteristic
129C2×Dic71⋊C4—21no—
130C2×Dic71⋊C4—21no—
131C2×Dic71⋊C4—21no—
132C2×Dic71⋊C4—21no—
133C2×Dic71⋊C4—21no—
134C2×Dic71⋊C4D411yescharacteristic
135C4⋊C4×D71—22no—
136C4⋊C4×D71C2314yes—
137C2×C22⋊Dic71—21no—
138C2×C22⋊Dic71—21no—
139C2×C22⋊Dic71D411yescharacteristic
140C2×(C2×D71)⋊C4—21no—
141C2×(C2×D71)⋊C4—21no—
142C2×(C2×D71)⋊C4—21no—
143C2×(C2×D71)⋊C4—21no—
144C2×(C2×D71)⋊C4—28no—
145C2×(C2×D71)⋊C4—21no—
146C2×(C2×D71)⋊C4D411yescharacteristic
147C2×C4×Dic71—21no—
148C2×C4×Dic71C2311yescharacteristic
149#14556062C2314yescomplemented
150#14556061C2314yescomplemented
151#14556061C2314yescomplemented
152Dic71⋊C8C2314yescomplemented
153#14556053C2314yescomplemented
154#14556052C2314yescomplemented
155#14556050C2314yes—
156#14556049C2314yes—
157#14556048C2314yes—
158#14556048C2314yes—
159C22⋊(C71⋊C8)C2314yescomplemented
160(C2×D71)⋊C8C2314yes—
161#14556038C2314yescomplemented
162C2×#41×C71—22no—
163C2×#41×C71—24no—
164C2×#41×C71—42no—
165C2×#41×C71C2314yes—
166C22×Q8×C71C2311yescharacteristic
167C22×D4×C71—21no—
168C22×D4×C71C2311yescharacteristic
169C23×C4×C71—21no—
170C23×C4×C71—21no—
171C23×C4×C71C2311yescharacteristic
172C2×M16×C71—42no—
173C2×M16×C71C2314yescomplemented
174C22×C8×C71C2311yescharacteristic
175C22×C8×C71C2311yescharacteristic
176C2×C4⋊C4×C71—22no—
177C2×C4⋊C4×C71—21no—
178C2×C4⋊C4×C71C2311yescharacteristic
179C2×C4⋊C4×C71C2311yescharacteristic
180C2×C4⋊C4×C71C2314yescomplemented
181#103×C71C2314yescomplemented
182#103×C71C2314yescomplemented
183#102×C71C2314yes—
184#102×C71C2314yes—
185C23×D71—21no—
186C23×D71—24no—
187C23×D71—44no—
188C23×D71—44no—
189C23×D71—82no—
190C23×D71C2×D411yescharacteristic
191C2×Dic142—22no—
192C2×Dic142—22no—
193C2×Dic142—21no—
194C2×Dic142—24no—
195C2×Dic142—82no—
196C2×Dic142C2412yes—
197C2×D284—22no—
198C2×D284—22no—
199C2×D284—21no—
200C2×D284C2412yes—
201C2×C22⋊D71—24no—
202C2×C22⋊D71—24no—
203C2×C22⋊D71—24no—
204C2×C22⋊D71—44no—
205C2×C22⋊D71—82no—
206C2×C22⋊D71C2×D414yes—
207D4×D71—28no—
208D4×D71—44no—
209D4×D71—48no—
210C22×Dic71—21no—
211C22×Dic71—21no—
212C22×Dic71—21no—
213C22×Dic71—24no—
214C22×Dic71—82no—
215C22×Dic71C2×D411yescharacteristic
216C22×Dic71C2×D411yescharacteristic
217C22×Dic71C2×D411yescharacteristic
218C2×C4×D71—22no—
219C2×C4×D71—22no—
220C2×C4×D71—24no—
221C2×C4×D71—82no—
222C2×C4×D71C2×D412yes—
223C2×C4×D71C2412yes—
224#11765855—44no—
225#11765854—44no—
226#11765853—28no—
227C2×C71⋊C8—22no—
228C2×C71⋊C8—22no—
229C2×C71⋊C8C2412yes—
230C2×C71⋊C8C2412yes—
231C8×D71—44no—
232C4⋊Dic71—21no—
233C4⋊Dic71—21no—
234C4⋊Dic71—24no—
235C4⋊Dic71C2412yes—
236C4⋊Dic71C2412yes—
237Dic71⋊C4—24no—
238Dic71⋊C4—24no—
239Dic71⋊C4—24no—
240Dic71⋊C4—24no—
241Dic71⋊C4—24no—
242Dic71⋊C4C2×D414yes—
243C22⋊Dic71—24no—
244C22⋊Dic71—24no—
245C22⋊Dic71C2×D414yes—
246(C2×D71)⋊C4—24no—
247(C2×D71)⋊C4—24no—
248(C2×D71)⋊C4—24no—
249(C2×D71)⋊C4—24no—
250(C2×D71)⋊C4—24no—
251(C2×D71)⋊C4C2×D414yes—
252C4×Dic71—24no—
253C4×Dic71C2×D412yes—
254C4×Dic71C2412yes—
255C24×C71—21no—
256C24×C71C2×D411yescharacteristic
257#41×C71—28no—
258#41×C71—44no—
259#41×C71—48no—
260C2×Q8×C71—21no—
261C2×Q8×C71—22no—
262C2×Q8×C71—22no—
263C2×Q8×C71C2412yes—
264C2×D4×C71—24no—
265C2×D4×C71—21no—
266C2×D4×C71—22no—
267C2×D4×C71—44no—
268C2×D4×C71#4114yes—
269C2×D4×C71C2412yes—
270C22×C4×C71—22no—
271C22×C4×C71—22no—
272C22×C4×C71—21no—
273C22×C4×C71—21no—
274C22×C4×C71—21no—
275C22×C4×C71—24no—
276C22×C4×C71—24no—
277C22×C4×C71—44no—
278C22×C4×C71—82no—
279C22×C4×C71C2×D411yescharacteristic
280C22×C4×C71C2×D412yes—
281C22×C4×C71C2412yes—
282C22×C4×C71C2411yescharacteristic
283M16×C71—44no—
284C2×C8×C71—22no—
285C2×C8×C71—22no—
286C2×C8×C71C2412yes—
287C2×C8×C71C2412yes—
288C4⋊C4×C71—21no—
289C4⋊C4×C71—21no—
290C4⋊C4×C71—24no—
291C4⋊C4×C71C2412yes—
292C4⋊C4×C71C2412yes—
293C23×C71—22no—
294C23×C71—24no—
295C23×C71—22no—
296C23×C71—22no—
297C23×C71—22no—
298C23×C71—42no—
299C23×C71—42no—
300C23×C71C22×D412yes—
301C23×C71C22×D411yescharacteristic
302C22×D71—22no—
303C22×D71—22no—
304C22×D71—22no—
305C22×D71—48no—
306C22×D71—42no—
307C22×D71—42no—
308C22×D71—42no—
309C22×D71—48no—
310C22×D71—84no—
311C22×D71—816no—
312C22×D71#13714yes—
313C22×D71C22×D412yes—
314Q8×C71—22no—
315Q8×C71—22no—
316Q8×C71—42no—
317D4×C71—24no—
318D4×C71—22no—
319D4×C71—48no—
320D4×C71C2×#4114yes—
321C2×C4×C71—22no—
322C2×C4×C71—24no—
323C2×C4×C71—22no—
324C2×C4×C71—22no—
325C2×C4×C71—22no—
326C2×C4×C71—22no—
327C2×C4×C71—22no—
328C2×C4×C71—48no—
329C2×C4×C71—42no—
330C2×C4×C71—42no—
331C2×C4×C71—42no—
332C2×C4×C71—84no—
333C2×C4×C71C22×D412yes—
334C2×C4×C71C22×D411yescharacteristic
335C2×C4×C71C2×#4112yes—
336C2×C4×C71H(5,𝔽2)12yes—
337C2×C4×C71C2511yescharacteristic
338C22⋊D71—28no—
339C22⋊D71—48no—
340C22⋊D71—84no—
341C2×Dic71—22no—
342C2×Dic71—22no—
343C2×Dic71—22no—
344C2×Dic71—22no—
345C2×Dic71—22no—
346C2×Dic71—22no—
347C2×Dic71—42no—
348C2×Dic71—42no—
349C2×Dic71—42no—
350C2×Dic71—84no—
351C2×Dic71C22×D412yes—
352C2×Dic71C22×D412yes—
353C2×Dic71C22×D412yes—
354D284—22no—
355D284—22no—
356D284—42no—
357C4×D71—24no—
358C4×D71—22no—
359C4×D71—22no—
360C4×D71—84no—
361Dic142—22no—
362Dic142—22no—
363Dic142—42no—
364Dic142—84no—
365C8×C71—22no—
366C8×C71—22no—
367C71⋊C8—22no—
368C71⋊C8—22no—
369C22×C71—24no—
370C22×C71—22no—
371C22×C71—22no—
372C22×C71—22no—
373C22×C71—48no—
374C22×C71—44no—
375C22×C71—42no—
376C22×C71—42no—
377C22×C71#54612yes—
378C22×C71C2×#13712yes—
379C22×C71#57612yes—
380C22×C71C23×D411yescharacteristic
381C2×D71—22no—
382C2×D71—28no—
383C2×D71—22no—
384C2×D71—42no—
385C2×D71—42no—
386C2×D71—42no—
387C2×D71—816no—
388C2×D71—84no—
389C2×D71C2×#13714yes—
390C4×C71—22no—
391C4×C71—42no—
392C4×C71—42no—
393C4×C71—42no—
394C4×C71#54612yes—
395C4×C71C22×#4111yescharacteristic
396C4×C71C2×H(5,𝔽2)11yescharacteristic
397Dic71—22no—
398Dic71—22no—
399Dic71—22no—
400Dic71—42no—
401Dic71—42no—
402Dic71—42no—
403C2×#3314—711nomaximal, Sylow
404C2×C71—44no—
405C2×C71—42no—
406C2×C71#331414yescomplemented
407C2×C71C2×#54611yescharacteristic
408C2×C71C22×#13711yescharacteristic
409C2×C71C2×#57611yescharacteristic
410D71—24no—
411D71—82no—
412C2×#554—711no—
413C2×#546—711no—
414#3314—7116no—
415C2×#489—711no—
416C2×#484—711no—
417C2×#480—711no—
418C2×#474—711no—
419C2×#468—711no—
420C2×#467—711no—
421C2×#464—711no—
422C2×#452—711no—
423C2×#450—711no—
424C2×#440—711no—
425C2×#435—711no—
426C2×#417D7111yescharacteristic, complemented
427C22×#102—711no—
428C71C2×#331411yescharacteristic, complemented, Sylow
429C22×#41C2×D7111yescharacteristic
430C23×D4—711no—
431C22×Q16—711no—
432C22×SD16—711no—
433C22×SD16—711no—
434C22×M16C2×D7111yescharacteristic, complemented
435C23×C8—711no—
436#554—718no—
437#554—1424no—
438#546—718no—
439#546—1424no—
440C2×C4⋊Q8—711no—
441C2×#125—1421no—
442C2×#124—711no—
443C2×#123—1421no—
444C2×C22⋊Q8—711no—
445C2×C22⋊Q8—711no—
446C2×C22⋊Q8—711no—
447C2×C22⋊Q8—1421no—
448C2×C22⋊Q8—1421no—
449C2×#121—711no—
450C2×#121—1421no—
451C2×#120—1421no—
452C2×C4×Q8—711no—
453C2×C4×D4—711no—
454C2×C4×D4—711no—
455C2×C4×D4—1421no—
456C22×C4⋊C4—711no—
457C22×C4⋊C4C2×D7111yescharacteristic, complemented
458C22×C22⋊C4—1421no—
459#489—718no—
460#484—718no—
461#480—718no—
462#474—718no—
463#468—718no—
464#467—718no—
465#464—718no—
466#452—718no—
467#450—718no—
468#440—718no—
469#435—718no—
470C2×#107—711no—
471C2×#107—711no—
472C2×#107—711no—
473C2×C4⋊C8—711no—
474#417C2×D7118yescomplemented
475C2×#103—711no—
476C2×#103—711no—
477C2×#103C2×D7111yescharacteristic, complemented
478C2×#103C2×D7111yescharacteristic, complemented
479C2×#102—711no—
480C2×#102—711no—
481C2×#102—711no—
482C2×#102—711no—
483C2×#102—718no—
484C2×#102C2×D7111yescharacteristic
485C2×#102C2×D7111yescharacteristic
486C2×C22⋊C8—711no—
487C2×C22⋊C8—711no—
488C2×#97—711no—
489C25—1421no—
490C2×#41—22no—
491C2×#41—24no—
492C2×#41—42no—
493C2×#41C22×D7114yes—
494C22×Q8—711no—
495C22×Q8—1421no—
496C22×Q8C22×D7111yescharacteristic
497C22×D4—21no—
498C22×D4—2842no—
499C22×D4—714no—
500C22×D4—711no—
501C22×D4—711no—
502C22×D4—1422no—
503C22×D4—1421no—
504C22×D4—1424no—
505C22×D4—1421no—
506C22×D4C22×D7111yescharacteristic
507C23×C4—21no—
508C23×C4—21no—
509C23×C4—711no—
510C23×C4—1421no—
511C23×C4—1421no—
512C23×C4C22×D7111yescharacteristic
513C2×Q16—2842no—
514C2×Q16—714no—
515C2×SD16—2842no—
516C2×SD16—714no—
517C2×SD16—714no—
518C2×SD16—1424no—
519C2×M16—42no—
520C2×M16C22×D7114yescomplemented
521C22×C8—2842no—
522C22×C8—714no—
523C22×C8—711no—
524C22×C8—711no—
525C22×C8C22×D7111yescharacteristic
526C22×C8C22×D7111yescharacteristic
527C4⋊Q8—714no—
528C4⋊Q8—1422no—
529#125—1428no—
530#124—714no—
531#124—1422no—
532#123—1428no—
533C22⋊Q8—714no—
534C22⋊Q8—714no—
535C22⋊Q8—714no—
536C22⋊Q8—1428no—
537C22⋊Q8—1428no—
538C22⋊Q8—1422no—
539C22⋊Q8—1422no—
540C22⋊Q8—1422no—
541#121—714no—
542#121—1428no—
543#121—1422no—
544#120—1428no—
545C4×Q8—714no—
546C4×Q8—1422no—
547C4×D4—714no—
548C4×D4—714no—
549C4×D4—714no—
550C4×D4—1422no—
551C4×D4—1428no—
552C2×C4⋊C4—21no—
553C2×C4⋊C4—22no—
554C2×C4⋊C4—711no—
555C2×C4⋊C4—711no—
556C2×C4⋊C4—711no—
557C2×C4⋊C4—714no—
558C2×C4⋊C4—1422no—
559C2×C4⋊C4—1421no—
560C2×C4⋊C4—1421no—
561C2×C4⋊C4—1421no—
562C2×C4⋊C4—1421no—
563C2×C4⋊C4—1421no—
564C2×C4⋊C4—1421no—
565C2×C4⋊C4C22×D7111yescharacteristic
566C2×C4⋊C4C22×D7111yescharacteristic
567C2×C4⋊C4C22×D7114yescomplemented
568C2×C22⋊C4—711no—
569C2×C22⋊C4—711no—
570C2×C22⋊C4—1428no—
571C2×C22⋊C4—1421no—
572C2×C22⋊C4—1421no—
573C2×C22⋊C4—1421no—
574C2×C22⋊C4—1421no—
575C2×C22⋊C4—1421no—
576C2×C22⋊C4—1421no—
577C2×C22⋊C4—1421no—
578C2×C42—711no—
579C2×C42—1421no—
580#107—714no—
581#107—714no—
582#107—714no—
583C4⋊C8—714no—
584#103—714no—
585#103—714no—
586#103C22×D7114yescomplemented
587#103C22×D7114yescomplemented
588#102—714no—
589#102—714no—
590#102—714no—
591#102—714no—
592#102C22×D7114yes—
593#102C22×D7114yes—
594C22⋊C8—714no—
595C22⋊C8—714no—
596#97—714no—
597C24—21no—
598C24—2844no—
599C24—2844no—
600C24—5682no—
601C24—711no—
602C24—1424no—
603C24—1421no—
604C24D4×D7111yescharacteristic
605#41—28no—
606#41—44no—
607#41—48no—
608C2×Q8—21no—
609C2×Q8—22no—
610C2×Q8—22no—
611C2×Q8—5682no—
612C2×Q8—712no—
613C2×Q8—1424no—
614C2×Q8—1422no—
615C2×Q8—1422no—
616C2×Q8—1421no—
617C2×Q8C23×D7112yes—
618C2×D4—24no—
619C2×D4—21no—
620C2×D4—22no—
621C2×D4—44no—
622C2×D4—2848no—
623C2×D4—2844no—
624C2×D4—2844no—
625C2×D4—5682no—
626C2×D4—714no—
627C2×D4—712no—
628C2×D4—1424no—
629C2×D4—1428no—
630C2×D4—1424no—
631C2×D4—1424no—
632C2×D4—1421no—
633C2×D4—1422no—
634C2×D4—1422no—
635C2×D4#1176586514yes—
636C2×D4C23×D7112yes—
637C22×C4—22no—
638C22×C4—22no—
639C22×C4—21no—
640C22×C4—21no—
641C22×C4—21no—
642C22×C4—24no—
643C22×C4—24no—
644C22×C4—44no—
645C22×C4—82no—
646C22×C4—5682no—
647C22×C4—5682no—
648C22×C4—711no—
649C22×C4—711no—
650C22×C4—711no—
651C22×C4—712no—
652C22×C4—712no—
653C22×C4—1424no—
654C22×C4—1421no—
655C22×C4—1421no—
656C22×C4—1421no—
657C22×C4—1424no—
658C22×C4—1422no—
659C22×C4—1422no—
660C22×C4D4×D7112yes—
661C22×C4D4×D7111yescharacteristic
662C22×C4C23×D7112yes—
663C22×C4C23×D7111yescharacteristic
664Q16—2844no—
665SD16—2844no—
666SD16—1428no—
667M16—44no—
668C2×C8—22no—
669C2×C8—22no—
670C2×C8—2844no—
671C2×C8—712no—
672C2×C8—712no—
673C2×C8—1422no—
674C2×C8—1422no—
675C2×C8C23×D7112yes—
676C2×C8C23×D7112yes—
677C4⋊C4—21no—
678C4⋊C4—21no—
679C4⋊C4—24no—
680C4⋊C4—714no—
681C4⋊C4—712no—
682C4⋊C4—712no—
683C4⋊C4—1424no—
684C4⋊C4—1424no—
685C4⋊C4—1424no—
686C4⋊C4—1424no—
687C4⋊C4—1424no—
688C4⋊C4—1424no—
689C4⋊C4—1421no—
690C4⋊C4—1421no—
691C4⋊C4C23×D7112yes—
692C4⋊C4C23×D7112yes—
693C22⋊C4—714no—
694C22⋊C4—714no—
695C22⋊C4—1424no—
696C22⋊C4—1424no—
697C22⋊C4—1424no—
698C22⋊C4—1424no—
699C22⋊C4—1424no—
700C22⋊C4—1424no—
701C22⋊C4—1424no—
702C42—712no—
703C42—712no—
704C42—1424no—
705C23—22no—
706C23—22no—
707C23—24no—
708C23—22no—
709C23—22no—
710C23—42no—
711C23—42no—
712C23—2848no—
713C23—2848no—
714C23—2842no—
715C23—2842no—
716C23—2842no—
717C23—5684no—
718C23—56816no—
719C23—712no—
720C23—714no—
721C23—1422no—
722C23—1422no—
723C23—1422no—
724C23C2×D4×D7112yes—
725C23C2×D4×D7111yescharacteristic
726Q8—22no—
727Q8—22no—
728Q8—42no—
729Q8—2842no—
730Q8—5684no—
731Q8—1422no—
732Q8—1422no—
733D4—22no—
734D4—24no—
735D4—48no—
736D4—2848no—
737D4—2842no—
738D4—5684no—
739D4—1428no—
740D4—1422no—
741D4—1422no—
742D4C2×#1176586514yes—
743C2×C4—22no—
744C2×C4—22no—
745C2×C4—22no—
746C2×C4—24no—
747C2×C4—22no—
748C2×C4—22no—
749C2×C4—22no—
750C2×C4—48no—
751C2×C4—42no—
752C2×C4—42no—
753C2×C4—42no—
754C2×C4—84no—
755C2×C4—2842no—
756C2×C4—2842no—
757C2×C4—2842no—
758C2×C4—5684no—
759C2×C4—5684no—
760C2×C4—712no—
761C2×C4—712no—
762C2×C4—712no—
763C2×C4—1422no—
764C2×C4—1422no—
765C2×C4—1422no—
766C2×C4—1422no—
767C2×C4—1422no—
768C2×C4—1422no—
769C2×C4—1422no—
770C2×C4—1422no—
771C2×C4—1424no—
772C2×C4C2×D4×D7112yes—
773C2×C4C2×D4×D7111yescharacteristic
774C2×C4C2×#1176586512yes—
775C2×C4#1455617312yes—
776C2×C4C24×D7111yescharacteristic
777C8—22no—
778C8—22no—
779C8—1422no—
780C8—1422no—
781C22—22no—
782C22—24no—
783C22—22no—
784C22—22no—
785C22—42no—
786C22—42no—
787C22—44no—
788C22—48no—
789C22—2842no—
790C22—2842no—
791C22—2842no—
792C22—56816no—
793C22—5684no—
794C22—714no—
795C22—1422no—
796C22—1422no—
797C22—1428no—
798C22#1798663912yes—
799C22#137×D7112yes—
800C22#1798680312yes—
801C22C22×D4×D7111yescharacteristic
802C4—22no—
803C4—42no—
804C4—42no—
805C4—42no—
806C4—2842no—
807C4—2842no—
808C4—2842no—
809C4—1422no—
810C4—1422no—
811C4—1422no—
812C4#1798663912yes—
813C4C22×#1176586511yescharacteristic
814C4C2×#1455617311yescharacteristic
815C2—42no—
816C2—44no—
817C2—5682no—
818C2—1424no—
819C2#2260042214yesdirect product factor
820C2C2×#1798663911yescharacteristic
821C2C2×#137×D7111yescharacteristic
822C2C2×#1798680311yescharacteristic
subgroupG/H
centerC23C2×D4×D71
commutator, cosocleC2×C4×C71C25
FrattiniC2×C4C24×D71
FittingC2×#417×C71C2
socleC23×C71C22×D4
prime radicalC2×#17986637C2
hypercenterC2×#417D71
hypocenterC71C2×#3314
LCSG ▷ C2×C4×C71 ▷ C2×C71 ▷ C71
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#417

Complements

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

NH ≅ G/Ntype
1. C2×#17986704C2semidirect
3. #22600422C2direct (N × H)
4. C2×#17986360C2semidirect
5. C2×#17986333C2semidirect
6. C2×#17986312C2semidirect
7. C2×#17986277C2semidirect
8. C2×#17986245C2semidirect
9. C2×#17986239C2semidirect
10. C2×#17986224C2semidirect
11. C2×#17986161C2semidirect
12. C2×#17986151C2semidirect
13. C2×#17986096C2semidirect
14. C2×#17986068C2semidirect
15. C2×#102×D71C2semidirect
16. C2×#417×C71C2semidirect
18. C22×#11765855C22semidirect
23. #17986704C22semidirect
26. C2×#14556127C22semidirect
32. C2×#14556107C22semidirect
38. C2×#14556093C22semidirect
44. #17986360C22semidirect
45. #17986333C22semidirect
46. #17986312C22semidirect
47. #17986277C22semidirect
48. #17986245C22semidirect
49. #17986239C22semidirect
50. #17986224C22semidirect
51. #17986161C22semidirect
52. #17986151C22semidirect
53. #17986096C22semidirect
54. #17986068C22semidirect
55. C2×#14556062C22semidirect
56. C2×#14556061C22semidirect
57. C2×#14556061C22semidirect
58. C2×Dic71⋊C8C22semidirect
59. C2×#14556053C22semidirect
60. C2×#14556052C22semidirect
65. #102×D71C22semidirect
66. C2×C22⋊(C71⋊C8)C22semidirect
68. C2×#14556038C22semidirect
70. C22×M16×C71C22semidirect
71. C22×C4⋊C4×C71C22semidirect
72. #417×C71C22semidirect
73. C2×#103×C71C22semidirect
74. C2×#103×C71C22semidirect
92. C2×#11765855C23semidirect
102. #14556127C23semidirect
111. #14556107C23semidirect
120. #14556093C23semidirect
149. #14556062C23semidirect
150. #14556061C23semidirect
151. #14556061C23semidirect
152. Dic71⋊C8C23semidirect
153. #14556053C23semidirect
154. #14556052C23semidirect
159. C22⋊(C71⋊C8)C23semidirect
161. #14556038C23semidirect
173. C2×M16×C71C23semidirect
180. C2×C4⋊C4×C71C23semidirect
181. #103×C71C23semidirect
182. #103×C71C23semidirect
406. C2×C71#3314semidirect
426. C2×#417D71semidirect
428. C71C2×#3314semidirect
434. C22×M16C2×D71semidirect
457. C22×C4⋊C4C2×D71semidirect
474. #417C2×D71semidirect
477. C2×#103C2×D71semidirect
478. C2×#103C2×D71semidirect
520. C2×M16C22×D71semidirect
567. C2×C4⋊C4C22×D71semidirect
586. #103C22×D71semidirect
587. #103C22×D71semidirect
819. C2#22600422direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#179867042
C2×#179866372
#226004222
C2×#179863602
C2×#179863332
C2×#179863122
C2×#179862772
C2×#179862452
C2×#179862392
C2×#179862242
C2×#179861612
C2×#179861512
C2×#179860962
C2×#179860682
C2×#102×D712
C2×#417×C712
C2×#331471