Finite Group Databasebeta

← C2×#22591778 #32165262

Subgroups — C2×#22591778 #32165262

Order 18176.

4782 conjugacy classes of subgroups.

The subgroup lattice has 744 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14556103C211yesmaximal, characteristic, complemented
2C22×#14556103C212yesmaximal, complemented
3C22×#14556103C211yesmaximal, characteristic, complemented
4C22×C4×D284C211yesmaximal, characteristic, complemented
5C22×C4⋊C4×D71C211yesmaximal, characteristic, complemented
6#22591778C2116yesmaximal, direct product factor
7C2×#17985921C212yesmaximal, complemented
8C2×#17985917C212yesmaximal, complemented
9C2×#17985901C211yesmaximal, characteristic, complemented
10C2×#17985877C212yesmaximal, complemented
11C2×#17985856C211yesmaximal, characteristic, complemented
12C2×#389×C71C211yesmaximal, characteristic, complemented
13C23×D284C2212yes—
14C23×D284C2211yescharacteristic
15C23×D284C2212yes—
16C23×D284C2211yescharacteristic
17C23×C4×D71C2211yescharacteristic
18C23×C4×D71C2212yes—
19C23×C4×D71C2211yescharacteristic
20C2×#14556103—28no—
21C2×#14556103—216no—
22C2×#14556103—28no—
23C2×#14556103C2218yescomplemented
24C2×#14556103C22116yescomplemented
25C2×#14556103C2218yescomplemented
26C2×C4×D284—28no—
27C2×C4×D284C2218yescomplemented
28C22×C4⋊Dic71C2211yescharacteristic
29C22×C4⋊Dic71C2211yescharacteristic
30C22×Dic71⋊C4C2212yes—
31C2×C4⋊C4×D71—28no—
32C2×C4⋊C4×D71C2218yescomplemented
33C22×(C2×D71)⋊C4C2211yescharacteristic
34C22×(C2×D71)⋊C4C2212yes—
35C22×(C2×D71)⋊C4C2211yescharacteristic
36C22×(C2×D71)⋊C4C2212yes—
37C22×(C2×D71)⋊C4C2212yes—
38C22×(C2×D71)⋊C4C2212yes—
39C22×(C2×D71)⋊C4C2212yes—
40#17985921C22116yescomplemented
41#17985917C22116yescomplemented
42#17985901C2218yescomplemented
43#17985877C22116yescomplemented
44#17985856C2218yescomplemented
45C2×C71⋊#95C2212yes—
46C22×C4⋊C4×C71C2212yes—
47C22×C4⋊C4×C71C2211yescharacteristic
48C22×C4⋊C4×C71C2211yescharacteristic
49C22×C42×C71C2211yescharacteristic
50#389×C71C2218yescomplemented
51C2×#95×C71C2212yes—
52C24×D71C2312yes—
53C24×D71C2311yescharacteristic
54C24×D71C2311yescharacteristic
55C22×D284—24no—
56C22×D284—24no—
57C22×D284—28no—
58C22×D284—28no—
59C22×D284—28no—
60C22×D284—28no—
61C22×D284—24no—
62C22×D284—28no—
63C22×D284—24no—
64C22×D284—24no—
65C22×D284—44no—
66C22×D284D418yescomplemented
67C22×D284C2318yes—
68C22×D284C2314yes—
69C22×D284C2318yes—
70C22×D284C2314yes—
71C23×Dic71C2311yescharacteristic
72C23×Dic71C2312yes—
73C23×Dic71C2311yescharacteristic
74C22×C4×D71—28no—
75C22×C4×D71—24no—
76C22×C4×D71—28no—
77C22×C4×D71—24no—
78C22×C4×D71—24no—
79C22×C4×D71—24no—
80C22×C4×D71—24no—
81C22×C4×D71—44no—
82C22×C4×D71D418yescomplemented
83C22×C4×D71C2314yes—
84C22×C4×D71C2318yes—
85C22×C4×D71C2314yes—
86#14556103—264no—
87#14556103—232no—
88#14556103—232no—
89C4×D284—232no—
90C2×C4⋊Dic71—24no—
91C2×C4⋊Dic71—24no—
92C2×C4⋊Dic71C2314yes—
93C2×C4⋊Dic71C2314yes—
94C2×Dic71⋊C4—28no—
95C2×Dic71⋊C4C2318yes—
96C4⋊C4×D71—232no—
97C2×(C2×D71)⋊C4—24no—
98C2×(C2×D71)⋊C4—28no—
99C2×(C2×D71)⋊C4—24no—
100C2×(C2×D71)⋊C4—28no—
101C2×(C2×D71)⋊C4—28no—
102C2×(C2×D71)⋊C4—28no—
103C2×(C2×D71)⋊C4—44no—
104C2×(C2×D71)⋊C4C2318yes—
105C2×(C2×D71)⋊C4C2314yes—
106C2×(C2×D71)⋊C4C2318yes—
107C2×(C2×D71)⋊C4C2318yes—
108C2×(C2×D71)⋊C4C2314yes—
109C2×(C2×D71)⋊C4C2318yes—
110C2×(C2×D71)⋊C4C2318yes—
111C71⋊#95C2318yes—
112C23×C4×C71C2312yes—
113C23×C4×C71C2311yescharacteristic
114C23×C4×C71C2312yes—
115C23×C4×C71C2311yescharacteristic
116C23×C4×C71C2311yescharacteristic
117C2×C4⋊C4×C71—28no—
118C2×C4⋊C4×C71—24no—
119C2×C4⋊C4×C71D418yescomplemented
120C2×C4⋊C4×C71C2314yes—
121C2×C4⋊C4×C71C2318yes—
122C2×C4⋊C4×C71C2314yes—
123C2×C42×C71—24no—
124C2×C42×C71C2314yes—
125#95×C71C2318yes—
126C23×D71—22no—
127C23×D71—22no—
128C23×D71—22no—
129C23×D71—22no—
130C23×D71—22no—
131C23×D71—22no—
132C23×D71—22no—
133C23×D71—22no—
134C23×D71—22no—
135C23×D71—22no—
136C23×D71—24no—
137C23×D71—24no—
138C23×D71—24no—
139C23×D71—24no—
140C23×D71—24no—
141C23×D71—24no—
142C23×D71—24no—
143C23×D71C2×D414yes—
144C23×D71C2×D414yes—
145C23×D71C2×D414yes—
146C23×D71#4114yes—
147C23×D71C2414yes—
148C23×D71C2412yes—
149C23×D71C2412yes—
150C2×D284—232no—
151C2×D284—28no—
152C2×D284—28no—
153C2×D284—216no—
154C2×D284—216no—
155C2×D284—216no—
156C2×D284—216no—
157C2×D284—28no—
158C2×D284—216no—
159C2×D284—28no—
160C2×D284—28no—
161C2×D284—48no—
162C2×D284—432no—
163C2×D284—432no—
164C2×D284—416no—
165C2×D284C2×D4116yescomplemented
166C22×Dic71—22no—
167C22×Dic71—22no—
168C22×Dic71—24no—
169C22×Dic71—22no—
170C22×Dic71—22no—
171C22×Dic71—24no—
172C22×Dic71—22no—
173C22×Dic71—24no—
174C22×Dic71C2×D414yes—
175C22×Dic71C2412yes—
176C22×Dic71C2414yes—
177C22×Dic71C2412yes—
178C2×C4×D71—232no—
179C2×C4×D71—28no—
180C2×C4×D71—28no—
181C2×C4×D71—216no—
182C2×C4×D71—216no—
183C2×C4×D71—28no—
184C2×C4×D71—28no—
185C2×C4×D71—28no—
186C2×C4×D71—48no—
187C2×C4×D71—432no—
188C2×C4×D71—416no—
189C2×C4×D71C2×D4116yescomplemented
190C4⋊Dic71—28no—
191C4⋊Dic71—28no—
192Dic71⋊C4—216no—
193(C2×D71)⋊C4—28no—
194(C2×D71)⋊C4—216no—
195(C2×D71)⋊C4—216no—
196(C2×D71)⋊C4—216no—
197(C2×D71)⋊C4—28no—
198(C2×D71)⋊C4—216no—
199(C2×D71)⋊C4—48no—
200C24×C71C2411yescharacteristic
201C22×C4×C71—24no—
202C22×C4×C71—22no—
203C22×C4×C71—22no—
204C22×C4×C71—24no—
205C22×C4×C71—24no—
206C22×C4×C71—24no—
207C22×C4×C71—22no—
208C22×C4×C71—24no—
209C22×C4×C71—22no—
210C22×C4×C71—22no—
211C22×C4×C71C2×D414yes—
212C22×C4×C71C2×D414yes—
213C22×C4×C71C2×D418yes—
214C22×C4×C71C2×D414yes—
215C22×C4×C71#4114yes—
216C22×C4×C71C2414yes—
217C22×C4×C71C2412yes—
218C22×C4×C71C2414yes—
219C22×C4×C71C2412yes—
220C22×C4×C71C2412yes—
221C4⋊C4×C71—216no—
222C4⋊C4×C71—28no—
223C4⋊C4×C71C2×D4116yescomplemented
224C42×C71—28no—
225C23×C71C22×D412yes—
226C23×C71C22×D412yes—
227C23×C71C22×D412yes—
228C23×C71C2×#4112yes—
229C23×C71C2×#4112yes—
230C23×C71H(5,𝔽2)12yes—
231C23×C712−1+412yes—
232C23×C71C2511yescharacteristic
233C22×D71—28no—
234C22×D71—28no—
235C22×D71—28no—
236C22×D71—28no—
237C22×D71—28no—
238C22×D71—28no—
239C22×D71—22no—
240C22×D71—22no—
241C22×D71—22no—
242C22×D71—22no—
243C22×D71—28no—
244C22×D71—28no—
245C22×D71—28no—
246C22×D71—22no—
247C22×D71—22no—
248C22×D71—22no—
249C22×D71—22no—
250C22×D71—22no—
251C22×D71—22no—
252C22×D71—24no—
253C22×D71—24no—
254C22×D71—24no—
255C22×D71—24no—
256C22×D71—24no—
257C22×D71—24no—
258C22×D71—24no—
259C22×D71—44no—
260C22×D71—44no—
261C22×D71—44no—
262C22×D71—44no—
263C22×D71—48no—
264C22×D71—48no—
265C22×D71—48no—
266C22×D71—48no—
267C22×D71—48no—
268C22×D71—48no—
269C22×D71—48no—
270C22×D71#121116yescomplemented
271C22×D71C22×D414yes—
272C22×D71C22×D414yes—
273C22×D71C22×D414yes—
274C22×D71C2×#4114yes—
275C2×C4×C71—28no—
276C2×C4×C71—216no—
277C2×C4×C71—22no—
278C2×C4×C71—24no—
279C2×C4×C71—22no—
280C2×C4×C71—24no—
281C2×C4×C71—22no—
282C2×C4×C71—24no—
283C2×C4×C71—24no—
284C2×C4×C71—24no—
285C2×C4×C71—22no—
286C2×C4×C71—22no—
287C2×C4×C71—48no—
288C2×C4×C71—44no—
289C2×C4×C71#121116yescomplemented
290C2×C4×C71C22×D414yes—
291C2×C4×C71C22×D414yes—
292C2×C4×C71C22×D418yes—
293C2×C4×C71C22×D414yes—
294C2×C4×C71C2×#4114yes—
295C2×Dic71—28no—
296C2×Dic71—22no—
297C2×Dic71—22no—
298C2×Dic71—24no—
299C2×Dic71—22no—
300C2×Dic71—22no—
301C2×Dic71—24no—
302C2×Dic71—22no—
303C2×Dic71—24no—
304C2×Dic71—44no—
305C2×Dic71—48no—
306C2×Dic71C22×D414yes—
307D284—232no—
308D284—432no—
309D284—432no—
310D284—416no—
311C4×D71—232no—
312C4×D71—432no—
313C4×D71—416no—
314C22×C71C2×#12114yes—
315C22×C71C2×#12114yes—
316C22×C71#53714yes—
317C22×C71D4214yes—
318C22×C71#54714yes—
319C22×C71#54814yes—
320C22×C71#55314yes—
321C22×C71C23×D411yescharacteristic
322C22×C71C23×D411yescharacteristic
323C22×C71C23×D411yescharacteristic
324C22×C71C22×#4111yescharacteristic
325C22×C71C22×#4111yescharacteristic
326C22×C71C2×H(5,𝔽2)11yescharacteristic
327C22×C71C2×2−1+411yescharacteristic
328C2×D71—24no—
329C2×D71—232no—
330C2×D71—24no—
331C2×D71—24no—
332C2×D71—24no—
333C2×D71—24no—
334C2×D71—24no—
335C2×D71—24no—
336C2×D71—24no—
337C2×D71—24no—
338C2×D71—42no—
339C2×D71—416no—
340C2×D71—42no—
341C2×D71—42no—
342C2×D71—42no—
343C2×D71—44no—
344C2×D71—44no—
345C2×D71—44no—
346C2×D71—44no—
347C2×D71—44no—
348C2×D71—44no—
349C2×D71—44no—
350C2×D71—816no—
351C2×D71C2×#12118yescomplemented
352C4×C71—24no—
353C4×C71—28no—
354C4×C71—44no—
355C4×C71—42no—
356C4×C71C2×#12118yescomplemented
357Dic71—24no—
358Dic71—42no—
359Dic71—44no—
360C2×#2416—711nomaximal, Sylow
361C2×C71#241618yescomplemented
362C2×C71C22×#12111yescharacteristic
363C2×C71C22×#12111yescharacteristic
364C2×C71C2×#53711yescharacteristic
365C2×C71C2×D4211yescharacteristic
366C2×C71C2×#54711yescharacteristic
367C2×C71C2×#54811yescharacteristic
368C2×C71C2×#55311yescharacteristic
369D71—28no—
370D71—44no—
371D71—84no—
372C22×#121—711no—
373C22×#121—712no—
374C22×#121—711no—
375C22×C4×D4—711no—
376C23×C4⋊C4—711no—
377#2416—7116no—
378C2×#396—712no—
379C2×#394—712no—
380C2×#390—711no—
381C2×#389D7111yescharacteristic, complemented
382C2×#386—712no—
383C2×#380—711no—
384C71C2×#241611yescharacteristic, complemented, Sylow
385C23×D4—712no—
386C23×D4—711no—
387C23×D4—712no—
388C23×D4—711no—
389C24×C4—712no—
390C24×C4—711no—
391C24×C4—711no—
392C2×#121—7116no—
393C2×#121—718no—
394C2×#121—718no—
395C2×#121—1428no—
396C2×#121—14216no—
397C2×#121—1428no—
398C2×C4×D4—718no—
399C2×C4×D4—1428no—
400C22×C4⋊C4—712no—
401C22×C4⋊C4—711no—
402C22×C4⋊C4—711no—
403C22×C4⋊C4—718no—
404C22×C4⋊C4—1428no—
405C22×C4⋊C4C2×D7112yes—
406C22×C4⋊C4C2×D7111yescharacteristic
407C22×C4⋊C4C2×D7111yescharacteristic
408C22×C22⋊C4—712no—
409C22×C22⋊C4—711no—
410C22×C22⋊C4—712no—
411C22×C22⋊C4—712no—
412C22×C22⋊C4—712no—
413C22×C22⋊C4—712no—
414C22×C22⋊C4—711no—
415C22×C42C2×D7111yescharacteristic
416#396—7116no—
417#394—7116no—
418#390—718no—
419#389C2×D7118yescomplemented
420#386—7116no—
421#380—718no—
422C2×#95—712no—
423C2×#95C2×D7112yes—
424C25—711no—
425C25—711no—
426C25—712no—
427C22×D4—2844no—
428C22×D4—718no—
429C22×D4—718no—
430C22×D4—714no—
431C22×D4—718no—
432C22×D4—714no—
433C22×D4—1428no—
434C22×D4—1428no—
435C22×D4—1428no—
436C22×D4—1428no—
437C22×D4—1424no—
438C22×D4—1424no—
439C22×D4—1424no—
440C22×D4—1428no—
441C22×D4—1424no—
442C22×D4—1424no—
443C23×C4—2844no—
444C23×C4—718no—
445C23×C4—711no—
446C23×C4—718no—
447C23×C4—714no—
448C23×C4—712no—
449C23×C4—711no—
450C23×C4—714no—
451C23×C4—1428no—
452C23×C4—1424no—
453C23×C4—1428no—
454C23×C4—1424no—
455C23×C4—1424no—
456C23×C4—1424no—
457C23×C4—1424no—
458C23×C4C22×D7111yescharacteristic
459C23×C4C22×D7112yes—
460C23×C4C22×D7111yescharacteristic
461C23×C4C22×D7112yes—
462C23×C4C22×D7111yescharacteristic
463#121—14232no—
464#121—14264no—
465#121—14232no—
466C4×D4—14232no—
467C2×C4⋊C4—28no—
468C2×C4⋊C4—24no—
469C2×C4⋊C4—714no—
470C2×C4⋊C4—718no—
471C2×C4⋊C4—714no—
472C2×C4⋊C4—1424no—
473C2×C4⋊C4—1428no—
474C2×C4⋊C4—1424no—
475C2×C4⋊C4—14232no—
476C2×C4⋊C4D28418yescomplemented
477C2×C4⋊C4C22×D7114yes—
478C2×C4⋊C4C22×D7118yes—
479C2×C4⋊C4C22×D7114yes—
480C2×C22⋊C4—2844no—
481C2×C22⋊C4—718no—
482C2×C22⋊C4—714no—
483C2×C22⋊C4—714no—
484C2×C22⋊C4—718no—
485C2×C22⋊C4—718no—
486C2×C22⋊C4—718no—
487C2×C22⋊C4—718no—
488C2×C22⋊C4—1424no—
489C2×C22⋊C4—1428no—
490C2×C22⋊C4—1424no—
491C2×C22⋊C4—1428no—
492C2×C22⋊C4—1428no—
493C2×C22⋊C4—1428no—
494C2×C42—24no—
495C2×C42C22×D7114yes—
496#95—718no—
497#95C22×D7118yes—
498C24—714no—
499C24—714no—
500C24—714no—
501C24—712no—
502C24—714no—
503C24—712no—
504C24—714no—
505C24—1424no—
506C24—1424no—
507C24—1424no—
508C24—1424no—
509C24—1424no—
510C24—1424no—
511C24—1424no—
512C24—1422no—
513C24—1422no—
514C24—1422no—
515C24—1422no—
516C24—1422no—
517C24—1422no—
518C24—1422no—
519C24—1422no—
520C24—1422no—
521C24—1422no—
522C24C23×D7111yescharacteristic
523C2×D4—28432no—
524C2×D4—2848no—
525C2×D4—28432no—
526C2×D4—28416no—
527C2×D4—7116no—
528C2×D4—14216no—
529C2×D4—14216no—
530C2×D4—14216no—
531C2×D4—14216no—
532C2×D4—1428no—
533C2×D4—1428no—
534C2×D4—14232no—
535C2×D4—1428no—
536C2×D4—14216no—
537C2×D4—1428no—
538C2×D4—1428no—
539C22×C4—22no—
540C22×C4—24no—
541C22×C4—22no—
542C22×C4—24no—
543C22×C4—22no—
544C22×C4—24no—
545C22×C4—24no—
546C22×C4—24no—
547C22×C4—22no—
548C22×C4—22no—
549C22×C4—28432no—
550C22×C4—2848no—
551C22×C4—28416no—
552C22×C4—714no—
553C22×C4—712no—
554C22×C4—7116no—
555C22×C4—712no—
556C22×C4—714no—
557C22×C4—14216no—
558C22×C4—1424no—
559C22×C4—1422no—
560C22×C4—1422no—
561C22×C4—1424no—
562C22×C4—1422no—
563C22×C4—1424no—
564C22×C4—1428no—
565C22×C4—14216no—
566C22×C4—1428no—
567C22×C4—1428no—
568C22×C4—1422no—
569C22×C4—1422no—
570C22×C4—1428no—
571C22×C4—1428no—
572C22×C4—14232no—
573C22×C4D4×D7114yes—
574C22×C4D4×D7114yes—
575C22×C4C2×D28418yes—
576C22×C4C2×D28414yes—
577C22×C4#1176586614yes—
578C22×C4C23×D7114yes—
579C22×C4C23×D7112yes—
580C22×C4C23×D7112yes—
581C22×C4C23×D7114yes—
582C22×C4C23×D7112yes—
583C4⋊C4—216no—
584C4⋊C4—28no—
585C4⋊C4—1428no—
586C4⋊C4—14216no—
587C4⋊C4—1428no—
588C4⋊C4C2×D284116yescomplemented
589C22⋊C4—2848no—
590C22⋊C4—1428no—
591C22⋊C4—14216no—
592C22⋊C4—1428no—
593C22⋊C4—14216no—
594C22⋊C4—14216no—
595C22⋊C4—14216no—
596C42—28no—
597C23—2844no—
598C23—2844no—
599C23—2844no—
600C23—2844no—
601C23—2848no—
602C23—2848no—
603C23—2848no—
604C23—2848no—
605C23—2848no—
606C23—2848no—
607C23—2848no—
608C23—714no—
609C23—714no—
610C23—714no—
611C23—7116no—
612C23—714no—
613C23—1424no—
614C23—1424no—
615C23—1424no—
616C23—1424no—
617C23—1424no—
618C23—1424no—
619C23—1424no—
620C23—1422no—
621C23—1422no—
622C23—1422no—
623C23—1422no—
624C23—1422no—
625C23—1422no—
626C23—1428no—
627C23—1428no—
628C23—1428no—
629C23—1422no—
630C23—1422no—
631C23—1422no—
632C23—1422no—
633C23—1428no—
634C23—1428no—
635C23—1428no—
636C23—1428no—
637C23—1428no—
638C23—1428no—
639C23C2×D4×D7112yes—
640C23C2×D4×D7112yes—
641C23C22×D28412yes—
642C23#41×D7112yes—
643C23C2×#1176586612yes—
644C23#1455617412yes—
645C23#1455617612yes—
646C23C24×D7111yescharacteristic
647D4—28432no—
648D4—28432no—
649D4—28416no—
650D4—14232no—
651C2×C4—22no—
652C2×C4—24no—
653C2×C4—22no—
654C2×C4—24no—
655C2×C4—216no—
656C2×C4—28no—
657C2×C4—22no—
658C2×C4—24no—
659C2×C4—24no—
660C2×C4—24no—
661C2×C4—22no—
662C2×C4—22no—
663C2×C4—44no—
664C2×C4—48no—
665C2×C4—28432no—
666C2×C4—2848no—
667C2×C4—2844no—
668C2×C4—28416no—
669C2×C4—714no—
670C2×C4—1424no—
671C2×C4—1422no—
672C2×C4—1422no—
673C2×C4—1424no—
674C2×C4—1422no—
675C2×C4—1424no—
676C2×C4—1422no—
677C2×C4—1422no—
678C2×C4—1428no—
679C2×C4—14232no—
680C2×C4#14556103116yescomplemented
681C2×C4C2×D4×D7114yes—
682C2×C4C2×D4×D7114yes—
683C2×C4C22×D28418yes—
684C2×C4C22×D28414yes—
685C2×C4C2×#1176586614yes—
686C22—28416no—
687C22—2842no—
688C22—2842no—
689C22—2842no—
690C22—2842no—
691C22—2844no—
692C22—2844no—
693C22—2844no—
694C22—2844no—
695C22—2844no—
696C22—2844no—
697C22—2844no—
698C22—56816no—
699C22—718no—
700C22—1424no—
701C22—1424no—
702C22—1424no—
703C22—14232no—
704C22—1424no—
705C22—1424no—
706C22—1424no—
707C22—1424no—
708C22—1424no—
709C22—1424no—
710C22#121×D7114yes—
711C22C2×#1455610314yes—
712C22#1798657914yes—
713C22D4×D28414yes—
714C22#1798665214yes—
715C22#1798666114yes—
716C22#1798670214yes—
717C22C22×D4×D7111yescharacteristic
718C22C22×D4×D7111yescharacteristic
719C22C23×D28411yescharacteristic
720C22C2×#41×D7111yescharacteristic
721C22C22×#1176586611yescharacteristic
722C22C2×#1455617411yescharacteristic
723C22C2×#1455617611yescharacteristic
724C4—28no—
725C4—24no—
726C4—44no—
727C4—42no—
728C4—2844no—
729C4—2842no—
730C4—1424no—
731C4C2×#1455610318yescomplemented
732C2—2844no—
733C2—5684no—
734C2—1428no—
735C2#2259177818yesdirect product factor
736C2C2×#121×D7111yescharacteristic
737C2C22×#1455610311yescharacteristic
738C2C2×#1798657911yescharacteristic
739C2C2×D4×D28411yescharacteristic
740C2C2×#1798665211yescharacteristic
741C2C2×#1798666111yescharacteristic
742C2C2×#1798670211yescharacteristic
subgroupG/H
centerC24C23×D71
commutator, cosocleC23×C71C25
FrattiniC23C24×D71
FittingC2×#389×C71C2
socleC24×C71C24
hypercenterC2×#389D71
hypocenterC71C2×#2416
LCSG ▷ C23×C71 ▷ C71
UCSC1 ◁ C24 ◁ C2×#389

Complements

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

NH ≅ G/Ntype
1. C22×#14556103C2semidirect
2. C22×#14556103C2semidirect
3. C22×#14556103C2semidirect
4. C22×C4×D284C2semidirect
5. C22×C4⋊C4×D71C2semidirect
6. #22591778C2direct (N × H)
7. C2×#17985921C2semidirect
8. C2×#17985917C2semidirect
9. C2×#17985901C2semidirect
10. C2×#17985877C2semidirect
11. C2×#17985856C2semidirect
12. C2×#389×C71C2semidirect
23. C2×#14556103C22semidirect
24. C2×#14556103C22semidirect
25. C2×#14556103C22semidirect
27. C2×C4×D284C22semidirect
32. C2×C4⋊C4×D71C22semidirect
40. #17985921C22semidirect
41. #17985917C22semidirect
42. #17985901C22semidirect
43. #17985877C22semidirect
44. #17985856C22semidirect
50. #389×C71C22semidirect
66. C22×D284D4semidirect
82. C22×C4×D71D4semidirect
119. C2×C4⋊C4×C71D4semidirect
165. C2×D284C2×D4semidirect
189. C2×C4×D71C2×D4semidirect
223. C4⋊C4×C71C2×D4semidirect
270. C22×D71#121semidirect
289. C2×C4×C71#121semidirect
351. C2×D71C2×#121semidirect
356. C4×C71C2×#121semidirect
361. C2×C71#2416semidirect
381. C2×#389D71semidirect
384. C71C2×#2416semidirect
419. #389C2×D71semidirect
476. C2×C4⋊C4D284semidirect
588. C4⋊C4C2×D284semidirect
680. C2×C4#14556103semidirect
731. C4C2×#14556103semidirect
735. C2#22591778direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#145561032
C22×C4×D2842
C22×C4⋊C4×D712
#225917782
C2×#179859212
C2×#179859172
C2×#179859012
C2×#179858772
C2×#179858562
C2×#389×C712
C2×#241671