Finite Group Databasebeta

← C2×#22600423 #32873980

Subgroups — C2×#22600423 #32873980

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×#17986706C211yesmaximal, characteristic, complemented
2C2×#17986645C211yesmaximal, characteristic
3#22600423C2116yesmaximal, direct product factor
4C2×#17986359C211yesmaximal, characteristic, complemented
5C2×#17986335C211yesmaximal, characteristic, complemented
6C2×#17986313C211yesmaximal, characteristic, complemented
7C2×#17986280C211yesmaximal, characteristic, complemented
8C2×#17986245C211yesmaximal, characteristic, complemented
9C2×#17986240C211yesmaximal, characteristic, complemented
10C2×#17986222C211yesmaximal, characteristic, complemented
11C2×#17986163C211yesmaximal, characteristic, complemented
12C2×#17986152C211yesmaximal, characteristic, complemented
13C2×#17986101C211yesmaximal, characteristic, complemented
14C2×#17986001C211yesmaximal, characteristic, complemented
15C22×#14556050C211yesmaximal, characteristic, complemented
16C2×#435×C71C211yesmaximal, characteristic, complemented
17C22×#11765865C2211yescharacteristic
18C23×D284C2211yescharacteristic
19C22×Dic284C2211yescharacteristic, complemented
20C22×#11765854C2211yescharacteristic
21C22×#11765854C2211yescharacteristic
22#17986706—24no—
23#17986706C2218yescomplemented
24#17986645—24no—
25#17986645C2218yes—
26C2×#14556128C2211yescharacteristic, complemented
27C2×#14556119—21no—
28C2×#14556116C2211yescharacteristic
29C2×#14556113—21no—
30C2×#14556107C2211yescharacteristic
31C2×#14556107C2211yescharacteristic
32C2×#14556107C2211yescharacteristic, complemented
33C2×#14556105—21no—
34C2×#14556105—21no—
35C2×#14556102C2211yescharacteristic
36C2×#14556101—21no—
37C2×#14556096—21no—
38C2×C4×Dic142C2211yescharacteristic, complemented
39C2×C4×D284C2211yescharacteristic
40C2×D4×Dic71—21no—
41C22×C4⋊Dic71C2211yescharacteristic
42C22×C4⋊Dic71C2211yescharacteristic, complemented
43C2×C22⋊C4×D71—21no—
44#17986359C2218yescomplemented
45#17986335C2218yescomplemented
46#17986313C2218yescomplemented
47#17986280C2218yescomplemented
48#17986245C2218yescomplemented
49#17986240C2218yescomplemented
50#17986222C2218yescomplemented
51#17986163C2218yescomplemented
52#17986152C2218yescomplemented
53#17986101C2218yescomplemented
54C2×#14556062C2211yescharacteristic, complemented
55C2×#14556062C2211yescharacteristic, complemented
56C2×#14556062C2211yescharacteristic, complemented
57#17986001C2218yescomplemented
58C2×#14556053C2211yescharacteristic, complemented
59C2×#14556053C2211yescharacteristic, complemented
60C2×#14556053C2211yescharacteristic, complemented
61C2×#14556053C2211yescharacteristic, complemented
62C2×#14556050C2211yescharacteristic
63C2×#14556050C2211yescharacteristic
64C2×#14556050C2211yescharacteristic
65C2×#14556050C2211yescharacteristic
66C2×#14556050C2211yescharacteristic
67C2×#14556050C2211yescharacteristic
68C2×#14556050C2218yescomplemented
69C22×M16×C71C2211yescharacteristic, complemented
70C23×C8×C71C2211yescharacteristic
71C2×C4×D4×C71C2211yescharacteristic
72#435×C71C2218yescomplemented
73C2×C4⋊C8×C71C2211yescharacteristic, complemented
74C2×C22⋊C8×C71C2211yescharacteristic
75C2×C22⋊C8×C71C2211yescharacteristic, complemented
76C2×#97×C71C2211yescharacteristic, complemented
77C24×D71—21no—
78C2×#11765865—24no—
79C2×#11765865—22no—
80C2×#11765865—42no—
81C2×#11765865C2314yes—
82C22×Dic142—21no—
83C22×Dic142C2311yescharacteristic
84C22×Dic142C2311yescharacteristic
85C22×D284—24no—
86C22×D284—22no—
87C22×D284—21no—
88C22×D284—42no—
89C22×D284C2311yescharacteristic
90C22×D284C2314yes—
91C22×D284C2311yescharacteristic
92C22×C22⋊D71—21no—
93C22×C22⋊D71—21no—
94C23×Dic71—21no—
95C23×Dic71—21no—
96C22×C4×D71—21no—
97C22×C4×D71—21no—
98C2×Dic284—42no—
99C2×Dic284C2314yescomplemented
100C2×#11765854—24no—
101C2×#11765854—42no—
102C2×#11765854C2314yes—
103C2×#11765854C2314yes—
104#14556128—22no—
105#14556128C2314yescomplemented
106#14556119—28no—
107#14556116—22no—
108#14556116C2314yes—
109#14556113—28no—
110#14556107—22no—
111#14556107—22no—
112#14556107—22no—
113#14556107C2314yes—
114#14556107C2314yes—
115#14556107C2314yescomplemented
116#14556105—28no—
117#14556105—28no—
118#14556102—22no—
119#14556102C2314yes—
120#14556101—28no—
121#14556096—28no—
122C4×Dic142—22no—
123C4×Dic142C2314yescomplemented
124C4×D284—22no—
125C4×D284C2314yes—
126D4×Dic71—28no—
127C2×C4⋊Dic71—22no—
128C2×C4⋊Dic71—21no—
129C2×C4⋊Dic71—22no—
130C2×C4⋊Dic71—21no—
131C2×C4⋊Dic71—21no—
132C2×C4⋊Dic71C2314yes—
133C2×C4⋊Dic71C2311yescharacteristic
134C2×C4⋊Dic71C2311yescharacteristic
135C2×C4⋊Dic71C2311yescharacteristic
136C2×C4⋊Dic71C2311yescharacteristic
137C2×C4⋊Dic71C2314yescomplemented
138C2×Dic71⋊C4—21no—
139C2×Dic71⋊C4—21no—
140C2×Dic71⋊C4—21no—
141C2×Dic71⋊C4—21no—
142C2×C22⋊Dic71—21no—
143C2×C22⋊Dic71—21no—
144C2×C22⋊Dic71—21no—
145C2×(C2×D71)⋊C4—21no—
146C2×(C2×D71)⋊C4—21no—
147C2×(C2×D71)⋊C4—21no—
148C2×(C2×D71)⋊C4—21no—
149C22⋊C4×D71—28no—
150C2×C4×Dic71—21no—
151#14556062C2314yescomplemented
152#14556062C2314yescomplemented
153#14556062C2314yescomplemented
154#14556053C2314yescomplemented
155#14556053C2314yescomplemented
156#14556053C2314yescomplemented
157#14556053C2314yescomplemented
158#14556050C2314yes—
159#14556050C2314yes—
160#14556050C2314yes—
161#14556050C2314yes—
162#14556050C2314yes—
163#14556050C2314yes—
164C22×D4×C71D411yescharacteristic
165C23×C4×C71C2311yescharacteristic
166C23×C4×C71C2311yescharacteristic
167C2×M16×C71—42no—
168C2×M16×C71C2314yescomplemented
169C22×C8×C71—42no—
170C22×C8×C71C2311yescharacteristic
171C22×C8×C71C2311yescharacteristic
172C22×C8×C71C2311yescharacteristic
173C22×C8×C71C2311yescharacteristic
174C22×C8×C71C2314yes—
175C4×D4×C71D414yes—
176C4×D4×C71C2314yes—
177C2×C4⋊C4×C71D411yescharacteristic
178C2×C22⋊C4×C71D411yescharacteristic
179C2×C22⋊C4×C71D411yescharacteristic
180C2×C42×C71C2311yescharacteristic
181C4⋊C8×C71C2314yescomplemented
182C22⋊C8×C71C2314yes—
183C22⋊C8×C71C2314yescomplemented
184#97×C71C2314yescomplemented
185C23×D71—21no—
186C23×D71—21no—
187C23×D71—24no—
188C23×D71—44no—
189C23×D71—44no—
190C23×D71—82no—
191#11765865—28no—
192#11765865—44no—
193#11765865—48no—
194C2×Dic142—22no—
195C2×Dic142—22no—
196C2×Dic142—22no—
197C2×Dic142—22no—
198C2×Dic142—21no—
199C2×Dic142—21no—
200C2×Dic142—24no—
201C2×Dic142—82no—
202C2×Dic142C2412yes—
203C2×Dic142C2412yes—
204C2×D284—21no—
205C2×D284—22no—
206C2×D284—22no—
207C2×D284—22no—
208C2×D284—28no—
209C2×D284—24no—
210C2×D284—21no—
211C2×D284—44no—
212C2×D284—48no—
213C2×D284—44no—
214C2×D284#4114yes—
215C2×D284C2412yes—
216C2×D284C2412yes—
217C2×C22⋊D71—24no—
218C2×C22⋊D71—24no—
219C2×C22⋊D71—44no—
220C2×C22⋊D71—82no—
221C22×Dic71—21no—
222C22×Dic71—21no—
223C22×Dic71—21no—
224C22×Dic71—21no—
225C22×Dic71—21no—
226C22×Dic71—21no—
227C22×Dic71—24no—
228C22×Dic71—24no—
229C22×Dic71—82no—
230C22×Dic71—82no—
231C2×C4×D71—24no—
232C2×C4×D71—24no—
233C2×C4×D71—44no—
234C2×C4×D71—82no—
235Dic284—44no—
236#11765854—28no—
237#11765854—44no—
238C4⋊Dic71—21no—
239C4⋊Dic71—24no—
240C4⋊Dic71—21no—
241C4⋊Dic71—21no—
242C4⋊Dic71—24no—
243C4⋊Dic71—24no—
244C4⋊Dic71—21no—
245C4⋊Dic71C2412yes—
246C4⋊Dic71C2412yes—
247C4⋊Dic71C2412yes—
248C4⋊Dic71C2412yes—
249Dic71⋊C4—24no—
250Dic71⋊C4—24no—
251Dic71⋊C4—24no—
252Dic71⋊C4—24no—
253C22⋊Dic71—24no—
254C22⋊Dic71—24no—
255C22⋊Dic71—24no—
256(C2×D71)⋊C4—24no—
257(C2×D71)⋊C4—24no—
258(C2×D71)⋊C4—24no—
259(C2×D71)⋊C4—24no—
260C4×Dic71—24no—
261C24×C71C2×D411yescharacteristic
262C24×C71C2×D411yescharacteristic
263C2×D4×C71—24no—
264C2×D4×C71C2×D414yes—
265C22×C4×C71—22no—
266C22×C4×C71—22no—
267C22×C4×C71—22no—
268C22×C4×C71—22no—
269C22×C4×C71C2×D411yescharacteristic
270C22×C4×C71C2×D411yescharacteristic
271C22×C4×C71C2×D411yescharacteristic
272C22×C4×C71C2×D412yes—
273C22×C4×C71C2×D412yes—
274C22×C4×C71C2×D411yescharacteristic
275C22×C4×C71C2412yes—
276C22×C4×C71C2412yes—
277C22×C4×C71C2411yescharacteristic
278M16×C71—44no—
279C2×C8×C71—22no—
280C2×C8×C71—22no—
281C2×C8×C71—22no—
282C2×C8×C71—22no—
283C2×C8×C71—44no—
284C2×C8×C71C2412yes—
285C2×C8×C71C2412yes—
286C2×C8×C71C2412yes—
287C2×C8×C71C2412yes—
288C4⋊C4×C71C2×D414yes—
289C22⋊C4×C71C2×D414yes—
290C22⋊C4×C71C2×D414yes—
291C42×C71C2×D412yes—
292C42×C71C2412yes—
293C23×C71—22no—
294C23×C71—22no—
295C23×C71—22no—
296C23×C71—22no—
297C23×C71—22no—
298C23×C71#13714yes—
299C23×C71C22×D412yes—
300C23×C71C22×D412yes—
301C23×C71C22×D411yescharacteristic
302C22×D71—24no—
303C22×D71—22no—
304C22×D71—22no—
305C22×D71—48no—
306C22×D71—42no—
307C22×D71—42no—
308C22×D71—42no—
309C22×D71—48no—
310C22×D71—42no—
311C22×D71—42no—
312C22×D71—84no—
313C22×D71—816no—
314D4×C71—28no—
315C2×C4×C71—22no—
316C2×C4×C71—22no—
317C2×C4×C71—22no—
318C2×C4×C71—22no—
319C2×C4×C71—24no—
320C2×C4×C71—24no—
321C2×C4×C71—22no—
322C2×C4×C71—22no—
323C2×C4×C71—22no—
324C2×C4×C71—22no—
325C2×C4×C71C22×D412yes—
326C2×C4×C71C22×D412yes—
327C2×C4×C71C22×D412yes—
328C2×C4×C71C22×D412yes—
329C2×C4×C71C22×D411yescharacteristic
330C2×C4×C71C2×#4112yes—
331C2×C4×C71H(5,𝔽2)12yes—
332C2×C4×C71C2511yescharacteristic
333C22⋊D71—48no—
334C22⋊D71—84no—
335C2×Dic71—22no—
336C2×Dic71—22no—
337C2×Dic71—22no—
338C2×Dic71—22no—
339C2×Dic71—22no—
340C2×Dic71—22no—
341C2×Dic71—42no—
342C2×Dic71—42no—
343C2×Dic71—42no—
344C2×Dic71—42no—
345C2×Dic71—42no—
346C2×Dic71—42no—
347C2×Dic71—84no—
348C2×Dic71—84no—
349D284—24no—
350D284—22no—
351D284—22no—
352D284—22no—
353D284—48no—
354D284—42no—
355D284C2×#4114yes—
356C4×D71—48no—
357C4×D71—84no—
358Dic142—22no—
359Dic142—22no—
360Dic142—22no—
361Dic142—22no—
362Dic142—42no—
363Dic142—42no—
364Dic142—84no—
365C8×C71—22no—
366C8×C71—22no—
367C8×C71—22no—
368C8×C71—22no—
369C22×C71—22no—
370C22×C71—28no—
371C22×C71—22no—
372C22×C71—22no—
373C22×C71—22no—
374C22×C71—22no—
375C22×C71—44no—
376C22×C71#54612yes—
377C22×C71C2×#13714yes—
378C22×C71C2×#13712yes—
379C22×C71#57612yes—
380C22×C71C23×D411yescharacteristic
381C2×D71—24no—
382C2×D71—48no—
383C2×D71—42no—
384C2×D71—42no—
385C2×D71—42no—
386C2×D71—42no—
387C2×D71—42no—
388C2×D71—816no—
389C2×D71—84no—
390C4×C71—22no—
391C4×C71—22no—
392C4×C71—22no—
393C4×C71—22no—
394C4×C71#54612yes—
395C4×C71C22×#4111yescharacteristic
396C4×C71C2×H(5,𝔽2)11yescharacteristic
397Dic71—42no—
398Dic71—42no—
399Dic71—42no—
400Dic71—42no—
401Dic71—42no—
402Dic71—42no—
403C2×#3314—711nomaximal, Sylow
404C2×C71—24no—
405C2×C71—42no—
406C2×C71#331414yescomplemented
407C2×C71C2×#54611yescharacteristic
408C2×C71C22×#13711yescharacteristic
409C2×C71C2×#57611yescharacteristic
410D71—44no—
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×#435D7111yescharacteristic, complemented
426C2×#417—711no—
427C22×#102—711no—
428C71C2×#331411yescharacteristic, complemented, Sylow
429C22×#41—711no—
430C23×D4—711no—
431C22×Q16—711no—
432C22×SD16—711no—
433C22×SD16—711no—
434C22×M16C2×D7111yescharacteristic, complemented
435C23×C8C2×D7111yescharacteristic
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—1421no—
455C2×C4×D4C2×D7111yescharacteristic
456C22×C4⋊C4—711no—
457C22×C4⋊C4—711no—
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#435C2×D7118yescomplemented
470C2×#107—711no—
471C2×#107—711no—
472C2×#107—711no—
473C2×C4⋊C8C2×D7111yescharacteristic, complemented
474#417—718no—
475C2×#103—711no—
476C2×#103—711no—
477C2×#103—711no—
478C2×#103—711no—
479C2×#102—711no—
480C2×#102—711no—
481C2×#102—711no—
482C2×#102—711no—
483C2×#102—711no—
484C2×#102—718no—
485C2×#102—711no—
486C2×C22⋊C8C2×D7111yescharacteristic
487C2×C22⋊C8C2×D7111yescharacteristic, complemented
488C2×#97C2×D7111yescharacteristic, complemented
489C25—1421no—
490C2×#41—2842no—
491C2×#41—714no—
492C2×#41—1424no—
493C2×#41—1422no—
494C22×Q8—711no—
495C22×Q8—711no—
496C22×Q8—1421no—
497C22×D4—2842no—
498C22×D4—714no—
499C22×D4—711no—
500C22×D4—711no—
501C22×D4—1424no—
502C22×D4—1421no—
503C22×D4—1421no—
504C22×D4—1421no—
505C22×D4—1422no—
506C22×D4D28411yescharacteristic
507C23×C4—1421no—
508C23×C4—1421no—
509C23×C4—1421no—
510C23×C4—1421no—
511C23×C4C22×D7111yescharacteristic
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—42no—
522C22×C8C22×D7111yescharacteristic
523C22×C8C22×D7111yescharacteristic
524C22×C8C22×D7111yescharacteristic
525C22×C8C22×D7111yescharacteristic
526C22×C8C22×D7114yes—
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—1422no—
537C22⋊Q8—1422no—
538C22⋊Q8—1422no—
539C22⋊Q8—1428no—
540C22⋊Q8—1428no—
541#121—714no—
542#121—1422no—
543#121—1428no—
544#120—1428no—
545C4×Q8—714no—
546C4×Q8—1422no—
547C4×D4—714no—
548C4×D4—1428no—
549C4×D4—1422no—
550C4×D4D28414yes—
551C4×D4C22×D7114yes—
552C2×C4⋊C4—711no—
553C2×C4⋊C4—711no—
554C2×C4⋊C4—711no—
555C2×C4⋊C4—714no—
556C2×C4⋊C4—714no—
557C2×C4⋊C4—711no—
558C2×C4⋊C4—1421no—
559C2×C4⋊C4—1421no—
560C2×C4⋊C4—1422no—
561C2×C4⋊C4—1422no—
562C2×C4⋊C4—1421no—
563C2×C4⋊C4—1421no—
564C2×C4⋊C4—1421no—
565C2×C4⋊C4—1421no—
566C2×C4⋊C4—1421no—
567C2×C4⋊C4D28411yescharacteristic
568C2×C22⋊C4—1421no—
569C2×C22⋊C4—1421no—
570C2×C22⋊C4—1421no—
571C2×C22⋊C4—1421no—
572C2×C22⋊C4—1421no—
573C2×C22⋊C4—1421no—
574C2×C22⋊C4—1421no—
575C2×C22⋊C4—1428no—
576C2×C22⋊C4D28411yescharacteristic
577C2×C22⋊C4D28411yescharacteristic
578C2×C42—1421no—
579C2×C42C22×D7111yescharacteristic
580#107—714no—
581#107—714no—
582#107—714no—
583C4⋊C8C22×D7114yescomplemented
584#103—714no—
585#103—714no—
586#103—714no—
587#103—714no—
588#102—714no—
589#102—714no—
590#102—714no—
591#102—714no—
592#102—714no—
593#102—714no—
594C22⋊C8C22×D7114yes—
595C22⋊C8C22×D7114yescomplemented
596#97C22×D7114yescomplemented
597C24—2844no—
598C24—2844no—
599C24—5682no—
600C24—1421no—
601C24—1424no—
602C24—1421no—
603C24C2×D28411yescharacteristic
604C24C2×D28411yescharacteristic
605#41—2848no—
606#41—2844no—
607#41—1428no—
608C2×Q8—5682no—
609C2×Q8—712no—
610C2×Q8—712no—
611C2×Q8—1422no—
612C2×Q8—1422no—
613C2×Q8—1422no—
614C2×Q8—1422no—
615C2×Q8—1421no—
616C2×Q8—1421no—
617C2×Q8—1424no—
618C2×D4—24no—
619C2×D4—2844no—
620C2×D4—2848no—
621C2×D4—2844no—
622C2×D4—2844no—
623C2×D4—5682no—
624C2×D4—714no—
625C2×D4—712no—
626C2×D4—712no—
627C2×D4—1428no—
628C2×D4—1424no—
629C2×D4—1424no—
630C2×D4—1424no—
631C2×D4—1421no—
632C2×D4—1421no—
633C2×D4—1422no—
634C2×D4—1422no—
635C2×D4—1422no—
636C2×D4C2×D28414yes—
637C22×C4—22no—
638C22×C4—22no—
639C22×C4—22no—
640C22×C4—22no—
641C22×C4—2844no—
642C22×C4—5682no—
643C22×C4—5682no—
644C22×C4—5682no—
645C22×C4—1421no—
646C22×C4—1421no—
647C22×C4—1421no—
648C22×C4—1421no—
649C22×C4—1421no—
650C22×C4—1421no—
651C22×C4—1424no—
652C22×C4—1424no—
653C22×C4—1424no—
654C22×C4—1424no—
655C22×C4C2×D28412yes—
656C22×C4C2×D28412yes—
657C22×C4C2×D28411yescharacteristic
658C22×C4C2×D28411yescharacteristic
659C22×C4C2×D28411yescharacteristic
660C22×C4C2×D28411yescharacteristic
661C22×C4C23×D7112yes—
662C22×C4C23×D7112yes—
663C22×C4C23×D7111yescharacteristic
664Q16—2844no—
665SD16—2844no—
666SD16—1428no—
667M16—44no—
668C2×C8—22no—
669C2×C8—22no—
670C2×C8—22no—
671C2×C8—22no—
672C2×C8—44no—
673C2×C8C23×D7112yes—
674C2×C8C23×D7112yes—
675C2×C8C23×D7112yes—
676C2×C8C23×D7112yes—
677C4⋊C4—712no—
678C4⋊C4—712no—
679C4⋊C4—712no—
680C4⋊C4—712no—
681C4⋊C4—1424no—
682C4⋊C4—1424no—
683C4⋊C4—1424no—
684C4⋊C4—1424no—
685C4⋊C4—1421no—
686C4⋊C4—1424no—
687C4⋊C4—1424no—
688C4⋊C4—1421no—
689C4⋊C4—1421no—
690C4⋊C4—1421no—
691C4⋊C4—1424no—
692C4⋊C4C2×D28414yes—
693C22⋊C4—1424no—
694C22⋊C4—1424no—
695C22⋊C4—1424no—
696C22⋊C4—1424no—
697C22⋊C4—1424no—
698C22⋊C4—1424no—
699C22⋊C4—1424no—
700C22⋊C4C2×D28414yes—
701C22⋊C4C2×D28414yes—
702C42—1424no—
703C42C2×D28412yes—
704C42C23×D7112yes—
705C23—22no—
706C23—22no—
707C23—22no—
708C23—22no—
709C23—22no—
710C23—2848no—
711C23—2842no—
712C23—2842no—
713C23—2842no—
714C23—2848no—
715C23—2842no—
716C23—2842no—
717C23—5684no—
718C23—56816no—
719C23—1422no—
720C23—1422no—
721C23—1424no—
722C23#1455616114yes—
723C23C22×D28412yes—
724C23C22×D28412yes—
725C23C22×D28411yescharacteristic
726Q8—2842no—
727Q8—2842no—
728Q8—5684no—
729Q8—1422no—
730Q8—1422no—
731Q8—1422no—
732Q8—1422no—
733D4—28no—
734D4—2848no—
735D4—2848no—
736D4—2842no—
737D4—5684no—
738D4—714no—
739D4—1422no—
740D4—1422no—
741D4—1422no—
742D4—1424no—
743C2×C4—22no—
744C2×C4—22no—
745C2×C4—22no—
746C2×C4—22no—
747C2×C4—22no—
748C2×C4—22no—
749C2×C4—22no—
750C2×C4—22no—
751C2×C4—24no—
752C2×C4—24no—
753C2×C4—2848no—
754C2×C4—2842no—
755C2×C4—2842no—
756C2×C4—2842no—
757C2×C4—2842no—
758C2×C4—2842no—
759C2×C4—2842no—
760C2×C4—5684no—
761C2×C4—5684no—
762C2×C4—5684no—
763C2×C4—1422no—
764C2×C4—1422no—
765C2×C4—1422no—
766C2×C4—1422no—
767C2×C4—1422no—
768C2×C4—1422no—
769C2×C4C22×D28412yes—
770C2×C4C22×D28412yes—
771C2×C4C22×D28412yes—
772C2×C4C22×D28412yes—
773C2×C4C22×D28411yescharacteristic
774C2×C4#41×D7112yes—
775C2×C4#1455617312yes—
776C2×C4C24×D7111yescharacteristic
777C8—22no—
778C8—22no—
779C8—22no—
780C8—22no—
781C22—22no—
782C22—22no—
783C22—28no—
784C22—22no—
785C22—22no—
786C22—22no—
787C22—44no—
788C22—2842no—
789C22—2842no—
790C22—2848no—
791C22—2842no—
792C22—2842no—
793C22—2842no—
794C22—56816no—
795C22—5684no—
796C22—1424no—
797C22#1798664412yes—
798C22C2×#1455616114yes—
799C22C2×#1455616112yes—
800C22#1798680412yes—
801C22C23×D28411yescharacteristic
802C4—22no—
803C4—22no—
804C4—22no—
805C4—22no—
806C4—2842no—
807C4—2842no—
808C4—2842no—
809C4—2842no—
810C4—2842no—
811C4—2842no—
812C4#1798664412yes—
813C4C2×#41×D7111yescharacteristic
814C4C2×#1455617311yescharacteristic
815C2—24no—
816C2—42no—
817C2—2844no—
818C2—5682no—
819C2#2260042314yesdirect product factor
820C2C2×#1798664411yescharacteristic
821C2C22×#1455616111yescharacteristic
822C2C2×#1798680411yescharacteristic
subgroupG/H
centerC23C22×D284
commutator, cosocleC2×C4×C71C25
FrattiniC2×C4C24×D71
FittingC2×#435×C71C2
socleC23×C71C22×D4
prime radicalC2×#17986645C2
hypercenterC2×#435D71
hypocenterC71C2×#3314
LCSG ▷ C2×C4×C71 ▷ C2×C71 ▷ C71
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×#435

Complements

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

NH ≅ G/Ntype
1. C2×#17986706C2semidirect
3. #22600423C2direct (N × H)
4. C2×#17986359C2semidirect
5. C2×#17986335C2semidirect
6. C2×#17986313C2semidirect
7. C2×#17986280C2semidirect
8. C2×#17986245C2semidirect
9. C2×#17986240C2semidirect
10. C2×#17986222C2semidirect
11. C2×#17986163C2semidirect
12. C2×#17986152C2semidirect
13. C2×#17986101C2semidirect
14. C2×#17986001C2semidirect
15. C22×#14556050C2semidirect
16. C2×#435×C71C2semidirect
19. C22×Dic284C22semidirect
23. #17986706C22semidirect
26. C2×#14556128C22semidirect
32. C2×#14556107C22semidirect
38. C2×C4×Dic142C22semidirect
42. C22×C4⋊Dic71C22semidirect
44. #17986359C22semidirect
45. #17986335C22semidirect
46. #17986313C22semidirect
47. #17986280C22semidirect
48. #17986245C22semidirect
49. #17986240C22semidirect
50. #17986222C22semidirect
51. #17986163C22semidirect
52. #17986152C22semidirect
53. #17986101C22semidirect
54. C2×#14556062C22semidirect
55. C2×#14556062C22semidirect
56. C2×#14556062C22semidirect
57. #17986001C22semidirect
58. C2×#14556053C22semidirect
59. C2×#14556053C22semidirect
60. C2×#14556053C22semidirect
61. C2×#14556053C22semidirect
68. C2×#14556050C22semidirect
69. C22×M16×C71C22semidirect
72. #435×C71C22semidirect
73. C2×C4⋊C8×C71C22semidirect
75. C2×C22⋊C8×C71C22semidirect
76. C2×#97×C71C22semidirect
99. C2×Dic284C23semidirect
105. #14556128C23semidirect
115. #14556107C23semidirect
123. C4×Dic142C23semidirect
137. C2×C4⋊Dic71C23semidirect
151. #14556062C23semidirect
152. #14556062C23semidirect
153. #14556062C23semidirect
154. #14556053C23semidirect
155. #14556053C23semidirect
156. #14556053C23semidirect
157. #14556053C23semidirect
168. C2×M16×C71C23semidirect
181. C4⋊C8×C71C23semidirect
183. C22⋊C8×C71C23semidirect
184. #97×C71C23semidirect
406. C2×C71#3314semidirect
425. C2×#435D71semidirect
428. C71C2×#3314semidirect
434. C22×M16C2×D71semidirect
469. #435C2×D71semidirect
473. C2×C4⋊C8C2×D71semidirect
487. C2×C22⋊C8C2×D71semidirect
488. C2×#97C2×D71semidirect
520. C2×M16C22×D71semidirect
583. C4⋊C8C22×D71semidirect
595. C22⋊C8C22×D71semidirect
596. #97C22×D71semidirect
819. C2#22600423direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#179867062
C2×#179866452
#226004232
C2×#179863592
C2×#179863352
C2×#179863132
C2×#179862802
C2×#179862452
C2×#179862402
C2×#179862222
C2×#179861632
C2×#179861522
C2×#179861012
C2×#179860012
C22×#145560502
C2×#435×C712
C2×#331471