Finite Group Databasebeta

← #25113349

Subgroups — #25113349

Order 11008.

1172 conjugacy classes of subgroups.

The subgroup lattice has 1118 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583592C211yesmaximal, characteristic
2#19137473C211yesmaximal, characteristic, complemented
3#19137467C211yesmaximal, characteristic, complemented
4#19135432C211yesmaximal, characteristic, complemented
5#19135429C211yesmaximal, characteristic, complemented
6#19135429C211yesmaximal, characteristic, complemented
7#19135429C211yesmaximal, characteristic, complemented
8#19135429C211yesmaximal, characteristic, complemented
9#19134581C211yesmaximal, characteristic, complemented
10#19134581C211yesmaximal, characteristic, complemented
11#19134580C211yesmaximal, characteristic, complemented
12#99×Dic43C211yesmaximal, characteristic, complemented
13#99×Dic43C211yesmaximal, characteristic, complemented
14C4×#13063239C211yesmaximal, characteristic, complemented
15C43×#1964C211yesmaximal, characteristic, complemented
16#14583592—21no—
17#14583592—21no—
18#14583592—21no—
19#14583592—21no—
20#14583592—21no—
21#14583592—21no—
22#14583592—21no—
23#14583592—21no—
24C2×#13063320C411yescharacteristic, complemented
25C2×#13063318C411yescharacteristic, complemented
26C2×#13063315C411yescharacteristic, complemented
27C2×#13063307C411yescharacteristic, complemented
28C2×#13063306C411yescharacteristic, complemented
29C2×#13063297C411yescharacteristic, complemented
30C2×#13063297C2211yescharacteristic
31C2×#13063297C2211yescharacteristic
32C2×D4×Dic43C2211yescharacteristic
33C2×D4×Dic43C2211yescharacteristic
34C2×C4×C22⋊D43C2211yescharacteristic
35C2×(C22⋊D43)⋊C4C411yescharacteristic, complemented
36C2×#13063281C411yescharacteristic, complemented
37C22×Dic43⋊C4C2211yescharacteristic
38C2×#13063240C2211yescharacteristic
39C2×#13063240C2211yescharacteristic
40C2×#13063240C2211yescharacteristic
41C2×#13063240C2211yescharacteristic
42C2×#13063239C2211yescharacteristic
43C2×#13063239C2211yescharacteristic
44C2×#13063239C2211yescharacteristic
45C2×#13063239C2211yescharacteristic
46#14582796—21no—
47#14582794—21no—
48#14582786—21no—
49#14582783—21no—
50#14582781—21no—
51#14582780—21no—
52#14582759C2211yescharacteristic
53#14582757C2211yescharacteristic
54#14582757C2211yescharacteristic
55#14582757C2211yescharacteristic
56#14582757C2211yescharacteristic
57C4×Dic43⋊C4—21no—
58#14582750—21no—
59C22⋊C4×Dic43C2211yescharacteristic
60C22⋊C4×Dic43C2211yescharacteristic
61C22⋊C4×Dic43C2211yescharacteristic
62C22⋊C4×Dic43C2211yescharacteristic
63C4×C22⋊Dic43C2211yescharacteristic
64#14582665C2211yescharacteristic
65#14582665C2211yescharacteristic
66#14582665C2211yescharacteristic
67#14582665C2211yescharacteristic
68C2×#121×C43C2211yescharacteristic
69C2×#99×C43C2211yescharacteristic
70C2×#99×C43C2211yescharacteristic
71C2×#99×C43C2211yescharacteristic
72C2×#99×C43C2211yescharacteristic
73C43×#380C2211yescharacteristic
74C4×C22⋊C4×C43C2211yescharacteristic
75C22×C22⋊D43C2×C411yescharacteristic
76C22×C22⋊D43C2×C411yescharacteristic
77C22×C22⋊D43C2311yescharacteristic
78C23×Dic43C2×C411yescharacteristic
79C23×Dic43C2×C411yescharacteristic
80C23×Dic43C2311yescharacteristic
81C23×Dic43C2311yescharacteristic
82C22×C4×D43C2×C411yescharacteristic
83#13063320—21no—
84#13063320—21no—
85#13063320—21no—
86#13063320—21no—
87#13063318—21no—
88#13063318—21no—
89#13063318—21no—
90#13063318—21no—
91#13063315—21no—
92#13063315—21no—
93#13063315—21no—
94#13063315—21no—
95#13063307—21no—
96#13063307—21no—
97#13063307—21no—
98#13063307—21no—
99#13063306—21no—
100#13063306—21no—
101#13063306—21no—
102#13063306—21no—
103#13063297—21no—
104#13063297—21no—
105#13063297—21no—
106#13063297—21no—
107#13063297—21no—
108#13063297—21no—
109#13063297—21no—
110#13063297—21no—
111#13063297—21no—
112#13063297—21no—
113#13063297—21no—
114#13063297—21no—
115D4×Dic43—21no—
116D4×Dic43—21no—
117D4×Dic43—21no—
118D4×Dic43—21no—
119D4×Dic43—21no—
120D4×Dic43—21no—
121D4×Dic43—21no—
122D4×Dic43—21no—
123C4×C22⋊D43—21no—
124C4×C22⋊D43—21no—
125C4×C22⋊D43—21no—
126C4×C22⋊D43—21no—
127(C22⋊D43)⋊C4—21no—
128(C22⋊D43)⋊C4—21no—
129(C22⋊D43)⋊C4—21no—
130(C22⋊D43)⋊C4—21no—
131#13063281—21no—
132#13063281—21no—
133#13063281—21no—
134#13063281—21no—
135C2×C4⋊Dic43—21no—
136C2×C4⋊Dic43C2×C411yescharacteristic
137C2×C4⋊Dic43C2×C411yescharacteristic
138C2×Dic43⋊C4—21no—
139C2×Dic43⋊C4—21no—
140C2×Dic43⋊C4—21no—
141C2×Dic43⋊C4—21no—
142C2×Dic43⋊C4C2×C411yescharacteristic
143C2×Dic43⋊C4C2×C411yescharacteristic
144C2×Dic43⋊C4C2×C411yescharacteristic
145C2×Dic43⋊C4C2×C411yescharacteristic
146C2×Dic43⋊C4C2×C411yescharacteristic
147C2×Dic43⋊C4C2×C411yescharacteristic
148C2×Dic43⋊C4C2×C411yescharacteristic
149C2×Dic43⋊C4D411yescharacteristic
150C2×Dic43⋊C4D411yescharacteristic
151C2×Dic43⋊C4D411yescharacteristic
152C2×Dic43⋊C4D411yescharacteristic
153C2×Dic43⋊C4D411yescharacteristic
154C2×Dic43⋊C4D411yescharacteristic
155C2×Dic43⋊C4D411yescharacteristic
156C2×Dic43⋊C4D411yescharacteristic
157C2×C22⋊Dic43C2×C411yescharacteristic
158C2×C22⋊Dic43C2×C411yescharacteristic
159C2×C22⋊Dic43C2×C411yescharacteristic
160C2×C22⋊Dic43C2×C411yescharacteristic
161C2×C22⋊Dic43C2311yescharacteristic
162C2×C22⋊Dic43C2311yescharacteristic
163C2×C22⋊Dic43C2311yescharacteristic
164C2×C22⋊Dic43C2311yescharacteristic
165C2×C22⋊Dic43C2311yescharacteristic
166C2×(C2×D43)⋊C4C2×C411yescharacteristic
167C2×(C2×D43)⋊C4C2×C411yescharacteristic
168C2×(C2×D43)⋊C4C2×C411yescharacteristic
169C2×C4×Dic43—21no—
170C2×C4×Dic43—21no—
171C2×C4×Dic43—21no—
172C2×C4×Dic43—21no—
173C2×C4×Dic43—21no—
174C2×C4×Dic43C2×C411yescharacteristic
175C2×C4×Dic43C2×C411yescharacteristic
176C2×C4×Dic43C2×C411yescharacteristic
177#13063240—22no—
178#13063240—22no—
179#13063240—41no—
180#13063240—41no—
181#13063239—22no—
182#13063239—22no—
183#13063239—41no—
184#13063239—41no—
185C43⋊#95—21no—
186C43⋊#95—21no—
187C43⋊#95—21no—
188C43⋊#95—21no—
189C43⋊#95—21no—
190C43⋊#95—21no—
191C43⋊#95—21no—
192C43⋊#95—21no—
193C43⋊#95—21no—
194C43⋊#95—21no—
195C22×D4×C43C2×C411yescharacteristic
196C22×D4×C43C2311yescharacteristic
197C22×D4×C43C2311yescharacteristic
198C23×C4×C43C2311yescharacteristic
199#121×C43—21no—
200#121×C43—21no—
201#121×C43—21no—
202#121×C43—21no—
203C2×C4⋊C4×C43—21no—
204C2×C4⋊C4×C43C2×C411yescharacteristic
205C2×C22⋊C4×C43C2×C411yescharacteristic
206C2×C22⋊C4×C43C2×C411yescharacteristic
207C2×C22⋊C4×C43C2311yescharacteristic
208C2×C22⋊C4×C43C2311yescharacteristic
209C2×C22⋊C4×C43C2311yescharacteristic
210C2×C22⋊C4×C43C2311yescharacteristic
211C2×C42×C43—21no—
212#99×C43—22no—
213#99×C43—22no—
214#99×C43—41no—
215#99×C43—41no—
216#95×C43—21no—
217#95×C43—21no—
218C24×C43C22×C411yescharacteristic
219C24×C43C22×C411yescharacteristic
220C24×C43C2411yescharacteristic
221C23×D43C22×C411yescharacteristic
222C2×D4×C43—21no—
223C2×D4×C43—21no—
224C2×D4×C43—21no—
225C2×D4×C43—21no—
226C2×D4×C43—21no—
227C2×D4×C43—21no—
228C2×D4×C43—21no—
229C2×D4×C43—21no—
230C2×D4×C43—21no—
231C2×D4×C43—21no—
232C2×D4×C43—21no—
233C2×D4×C43—21no—
234C2×D4×C43—21no—
235C2×D4×C43—21no—
236C2×D4×C43—81no—
237C22×C4×C43—21no—
238C22×C4×C43—21no—
239C22×C4×C43—21no—
240C22×C4×C43—21no—
241C22×C4×C43—81no—
242C22×C4×C43C22×C411yescharacteristic
243C22×C4×C43C22×C411yescharacteristic
244C22×C4×C43C22×C411yescharacteristic
245C22×C4×C43C22×C411yescharacteristic
246C22×C4×C43C2×D411yescharacteristic
247C22×C4×C43C2×D411yescharacteristic
248C22×C4×C43C2×D411yescharacteristic
249C22×C4×C43C2×D411yescharacteristic
250C2×C22⋊D43—21no—
251C2×C22⋊D43—21no—
252C2×C22⋊D43—21no—
253C2×C22⋊D43—21no—
254C2×C22⋊D43—21no—
255C2×C22⋊D43—21no—
256C2×C22⋊D43—21no—
257C2×C22⋊D43—21no—
258C2×C22⋊D43—21no—
259C2×C22⋊D43—21no—
260C2×C22⋊D43—42no—
261C2×C22⋊D43—81no—
262C22×Dic43—21no—
263C22×Dic43—21no—
264C22×Dic43—21no—
265C22×Dic43—21no—
266C22×Dic43—21no—
267C22×Dic43—21no—
268C22×Dic43—21no—
269C22×Dic43—21no—
270C22×Dic43—42no—
271C22×Dic43—42no—
272C22×Dic43—81no—
273C22×Dic43—81no—
274C22×Dic43C22×C411yescharacteristic
275C22×Dic43C22×C411yescharacteristic
276C22×Dic43C22×C411yescharacteristic
277C22×Dic43C22×C411yescharacteristic
278C22×Dic43C22×C411yescharacteristic
279C22×Dic43C22×C411yescharacteristic
280C22×Dic43C22×C411yescharacteristic
281C22×Dic43C2×D411yescharacteristic
282C22×Dic43C2×D411yescharacteristic
283C22×Dic43C2×D411yescharacteristic
284C22×Dic43C2×D411yescharacteristic
285C22×Dic43C2×D411yescharacteristic
286C22×Dic43C2×D411yescharacteristic
287C22×Dic43C2×D411yescharacteristic
288C22×Dic43C2×D411yescharacteristic
289C2×C4×D43—21no—
290C2×C4×D43—21no—
291C2×C4×D43—81no—
292C4⋊C4×C43—21no—
293C4⋊C4×C43—21no—
294C4⋊C4×C43—81no—
295C22⋊C4×C43—21no—
296C22⋊C4×C43—21no—
297C22⋊C4×C43—21no—
298C22⋊C4×C43—21no—
299C22⋊C4×C43—21no—
300C22⋊C4×C43—21no—
301C22⋊C4×C43—21no—
302C22⋊C4×C43—21no—
303C22⋊C4×C43—21no—
304C22⋊C4×C43—21no—
305C22⋊C4×C43—21no—
306C22⋊C4×C43#4112yes—
307C42×C43—81no—
308C22⋊Dic43—21no—
309C22⋊Dic43—21no—
310C22⋊Dic43—21no—
311C22⋊Dic43—21no—
312C22⋊Dic43—21no—
313C22⋊Dic43—21no—
314C22⋊Dic43—21no—
315C22⋊Dic43—21no—
316C22⋊Dic43—21no—
317C22⋊Dic43—21no—
318C22⋊Dic43—21no—
319C22⋊Dic43—21no—
320C22⋊Dic43—21no—
321C22⋊Dic43—21no—
322C22⋊Dic43—21no—
323C22⋊Dic43—21no—
324C22⋊Dic43—21no—
325C22⋊Dic43#4112yes—
326(C2×D43)⋊C4—21no—
327(C2×D43)⋊C4—21no—
328(C2×D43)⋊C4—21no—
329(C2×D43)⋊C4—21no—
330(C2×D43)⋊C4—21no—
331(C2×D43)⋊C4—21no—
332C4⋊Dic43—21no—
333C4⋊Dic43—21no—
334C4⋊Dic43—21no—
335C4⋊Dic43—21no—
336C4⋊Dic43—81no—
337Dic43⋊C4—21no—
338Dic43⋊C4—21no—
339Dic43⋊C4—21no—
340Dic43⋊C4—21no—
341Dic43⋊C4—21no—
342Dic43⋊C4—21no—
343Dic43⋊C4—42no—
344Dic43⋊C4—42no—
345Dic43⋊C4—81no—
346Dic43⋊C4—81no—
347Dic43⋊C4C22⋊C411yescharacteristic
348Dic43⋊C4C22⋊C411yescharacteristic
349Dic43⋊C4C22⋊C411yescharacteristic
350Dic43⋊C4C22⋊C411yescharacteristic
351Dic43⋊C4C22⋊C411yescharacteristic
352Dic43⋊C4C22⋊C411yescharacteristic
353Dic43⋊C4C22⋊C411yescharacteristic
354Dic43⋊C4C22⋊C411yescharacteristic
355Dic43⋊C4C22⋊C411yescharacteristic
356Dic43⋊C4C22⋊C411yescharacteristic
357Dic43⋊C4C22⋊C411yescharacteristic
358Dic43⋊C4C22⋊C411yescharacteristic
359Dic43⋊C4C22⋊C411yescharacteristic
360Dic43⋊C4C22⋊C411yescharacteristic
361Dic43⋊C4C22⋊C411yescharacteristic
362Dic43⋊C4C22⋊C411yescharacteristic
363C4×Dic43—21no—
364C4×Dic43—21no—
365C4×Dic43—21no—
366C4×Dic43—21no—
367C4×Dic43—21no—
368C4×Dic43—21no—
369C4×Dic43—42no—
370C4×Dic43—42no—
371C4×Dic43—81no—
372C4×Dic43—81no—
373C4×Dic43—81no—
374C23×C43—21no—
375C23×C43—21no—
376C23×C43—21no—
377C23×C43—21no—
378C23×C43—21no—
379C23×C43—21no—
380C23×C43—41no—
381C23×C43—41no—
382C23×C43—41no—
383C23×C43—41no—
384C23×C43—41no—
385C23×C43—41no—
386C23×C43C23×C411yescharacteristic
387C23×C43C22×D411yescharacteristic
388C23×C43C22×D411yescharacteristic
389C23×C43C2×#4111yescharacteristic
390C23×C43C2×#4111yescharacteristic
391C23×C43H(5,𝔽2)11yescharacteristic
392C23×C432−1+411yescharacteristic
393C22×D43—21no—
394C22×D43—21no—
395C22×D43—21no—
396C22×D43—41no—
397C22×D43—41no—
398D4×C43—41no—
399D4×C43—41no—
400D4×C43—41no—
401D4×C43—41no—
402D4×C43—41no—
403D4×C43—41no—
404D4×C43—41no—
405D4×C43—41no—
406D4×C43—81no—
407D4×C43—81no—
408C2×C4×C43—21no—
409C2×C4×C43—21no—
410C2×C4×C43—21no—
411C2×C4×C43—21no—
412C2×C4×C43—21no—
413C2×C4×C43—21no—
414C2×C4×C43—22no—
415C2×C4×C43—41no—
416C2×C4×C43—41no—
417C2×C4×C43—41no—
418C2×C4×C43—41no—
419C2×C4×C43—41no—
420C2×C4×C43—41no—
421C2×C4×C43—41no—
422C2×C4×C43—41no—
423C2×C4×C43—41no—
424C2×C4×C43—41no—
425C2×C4×C43—41no—
426C2×C4×C43—41no—
427C2×C4×C43—41no—
428C2×C4×C43—41no—
429C2×C4×C43—41no—
430C2×C4×C43—41no—
431C2×C4×C43—41no—
432C2×C4×C43C2×C22⋊C411yescharacteristic
433C2×C4×C43C2×C22⋊C411yescharacteristic
434C2×C4×C43C2×C22⋊C411yescharacteristic
435C2×C4×C43C2×C22⋊C411yescharacteristic
436C22⋊D43—42no—
437C22⋊D43—41no—
438C22⋊D43—41no—
439C22⋊D43—41no—
440C22⋊D43—41no—
441C22⋊D43—42no—
442C22⋊D43—81no—
443C22⋊D43—81no—
444C2×Dic43—22no—
445C2×Dic43—22no—
446C2×Dic43—22no—
447C2×Dic43—21no—
448C2×Dic43—21no—
449C2×Dic43—21no—
450C2×Dic43—21no—
451C2×Dic43—21no—
452C2×Dic43—22no—
453C2×Dic43—41no—
454C2×Dic43—41no—
455C2×Dic43—41no—
456C2×Dic43—41no—
457C2×Dic43—41no—
458C2×Dic43—41no—
459C2×Dic43—41no—
460C2×Dic43—41no—
461C2×Dic43—41no—
462C2×Dic43—42no—
463C2×Dic43—41no—
464C2×Dic43—41no—
465C2×Dic43—42no—
466C2×Dic43—41no—
467C2×Dic43—41no—
468C2×Dic43—41no—
469C2×Dic43—41no—
470C2×Dic43—41no—
471C2×Dic43—41no—
472C2×Dic43—41no—
473C2×Dic43—41no—
474C2×Dic43—41no—
475C2×Dic43—41no—
476C2×Dic43—41no—
477C2×Dic43—81no—
478C2×Dic43—81no—
479C2×Dic43C2×C22⋊C411yescharacteristic
480C2×Dic43C2×C22⋊C411yescharacteristic
481C2×Dic43C2×C22⋊C411yescharacteristic
482C2×Dic43C2×C22⋊C411yescharacteristic
483C2×Dic43C2×C22⋊C411yescharacteristic
484C2×Dic43C2×C22⋊C411yescharacteristic
485C2×Dic43C2×C22⋊C411yescharacteristic
486C2×Dic43C2×C22⋊C411yescharacteristic
487C4×D43—81no—
488C4×D43—81no—
489#22535—431nomaximal, Sylow
490C22×C43—21no—
491C22×C43—21no—
492C22×C43—21no—
493C22×C43—21no—
494C22×C43—21no—
495C22×C43—21no—
496C22×C43—41no—
497C22×C43—41no—
498C22×C43—41no—
499C22×C43—41no—
500C22×C43—41no—
501C22×C43—41no—
502C22×C43—41no—
503C22×C43—41no—
504C22×C43—41no—
505C22×C43—41no—
506C22×C43—81no—
507C22×C43—81no—
508C22×C43—81no—
509C22×C43—81no—
510C22×C43C22×C22⋊C411yescharacteristic
511C22×C43C4×#4111yescharacteristic
512C22×C43#52011yescharacteristic
513C22×C43#54811yescharacteristic
514C22×C43#54811yescharacteristic
515C22×C43#55011yescharacteristic
516C22×C43#55011yescharacteristic
517C2×D43—41no—
518C2×D43—41no—
519C2×D43—41no—
520C2×D43—81no—
521C2×D43—81no—
522C4×C43—21no—
523C4×C43—21no—
524C4×C43—21no—
525C4×C43—21no—
526C4×C43—42no—
527C4×C43—41no—
528C4×C43—41no—
529C4×C43—81no—
530C4×C43—81no—
531C4×C43—81no—
532Dic43—21no—
533Dic43—21no—
534Dic43—21no—
535Dic43—21no—
536Dic43—21no—
537Dic43—21no—
538Dic43—21no—
539Dic43—42no—
540Dic43—41no—
541Dic43—41no—
542Dic43—41no—
543Dic43—81no—
544Dic43—81no—
545Dic43—81no—
546Dic43#41012yes—
547C2×#553—431no—
548#2345—431no—
549#2345—431no—
550#1964—431no—
551#1964—431no—
552#1964—431no—
553#1964—431no—
554#1964—431no—
555#1964D4311yescharacteristic, complemented
556#1799—431no—
557#1799—431no—
558#1799—431no—
559C4×#99—431no—
560C4×#99—431no—
561C4×#99—431no—
562C2×C43—21no—
563C2×C43—21no—
564C2×C43—21no—
565C2×C43—21no—
566C2×C43—21no—
567C2×C43—21no—
568C2×C43—81no—
569C2×C43—81no—
570C2×C43#234111yescharacteristic
571C2×C43C2×#41011yescharacteristic
572C2×C43#288311yescharacteristic
573D43—81no—
574#553—861no—
575#553—861no—
576#553—861no—
577#553—861no—
578#553—861no—
579#553—861no—
580#553—861no—
581#553—861no—
582C2×#126—431no—
583C2×#126—431no—
584C2×#125—431no—
585C2×#123—431no—
586C2×#123—431no—
587C2×#121—431no—
588C2×#121—431no—
589C2×#121—431no—
590C2×#121C2×D4311yescharacteristic
591C2×C4×D4—431no—
592C2×C4×D4—431no—
593C2×C4×D4—431no—
594C2×C4×D4—431no—
595C2×#117—431no—
596C22×C4⋊C4—431no—
597C2×#99—431no—
598C2×#99—431no—
599C2×#99—431no—
600C2×#99—431no—
601C2×#99—431no—
602C2×#99—431no—
603C2×#99—431no—
604C2×#99—431no—
605C2×#99C2×D4311yescharacteristic
606C2×#99C2×D4311yescharacteristic
607C2×#99C2×D4311yescharacteristic
608C2×#99C2×D4311yescharacteristic
609#389—861no—
610#389—861no—
611#387—861no—
612#387—861no—
613#387—861no—
614#387—861no—
615#380—431no—
616#380—431no—
617#380—431no—
618#380—431no—
619#380—431no—
620#380C2×D4311yescharacteristic
621C4×C4⋊C4—861no—
622C4×C4⋊C4—861no—
623C4×C22⋊C4—431no—
624C4×C22⋊C4—431no—
625C4×C22⋊C4—431no—
626C4×C22⋊C4—431no—
627C4×C22⋊C4—431no—
628C4×C22⋊C4C2×D4311yescharacteristic
629#342—431no—
630#342—431no—
631#342—431no—
632#342—431no—
633C43#2253511yescharacteristic, complemented, Sylow
634C22×D4—431no—
635C22×D4—431no—
636C22×D4—431no—
637C22×D4C4×D4311yescharacteristic
638C22×D4C22×D4311yescharacteristic
639C22×D4C22×D4311yescharacteristic
640C23×C4—431no—
641C23×C4—431no—
642C23×C4—431no—
643C23×C4—431no—
644C23×C4—431no—
645C23×C4C22×D4311yescharacteristic
646#126—861no—
647#126—861no—
648#126—861no—
649#126—861no—
650#126—861no—
651#126—861no—
652#126—861no—
653#126—861no—
654#125—861no—
655#125—861no—
656#125—861no—
657#125—861no—
658#123—861no—
659#123—861no—
660#123—861no—
661#123—861no—
662#123—861no—
663#123—861no—
664#123—861no—
665#123—861no—
666#121—21no—
667#121—21no—
668#121—21no—
669#121—21no—
670#121—861no—
671#121—861no—
672#121—861no—
673#121—861no—
674#121—861no—
675#121—861no—
676#121—861no—
677#121—861no—
678#121—861no—
679#121—861no—
680#121—861no—
681#121—861no—
682C4×D4—861no—
683C4×D4—861no—
684C4×D4—861no—
685C4×D4—861no—
686C4×D4—861no—
687C4×D4—861no—
688C4×D4—861no—
689C4×D4—861no—
690C4×D4—861no—
691C4×D4—861no—
692C4×D4—861no—
693C4×D4—861no—
694C4×D4—861no—
695C4×D4—861no—
696C4×D4—861no—
697C4×D4—861no—
698#117—861no—
699#117—861no—
700#117—861no—
701#117—861no—
702C2×C4⋊C4—21no—
703C2×C4⋊C4—431no—
704C2×C4⋊C4—431no—
705C2×C4⋊C4—431no—
706C2×C4⋊C4—431no—
707C2×C4⋊C4—431no—
708C2×C4⋊C4—431no—
709C2×C4⋊C4—431no—
710C2×C4⋊C4—431no—
711C2×C4⋊C4—431no—
712C2×C4⋊C4—431no—
713C2×C4⋊C4—431no—
714C2×C4⋊C4—431no—
715C2×C4⋊C4—431no—
716C2×C4⋊C4—431no—
717C2×C4⋊C4—431no—
718C2×C4⋊C4—431no—
719C2×C4⋊C4—431no—
720C2×C4⋊C4—861no—
721C2×C4⋊C4—861no—
722C2×C4⋊C4—861no—
723C2×C4⋊C4—861no—
724C2×C4⋊C4—861no—
725C2×C4⋊C4C4×D4311yescharacteristic
726C2×C22⋊C4—431no—
727C2×C22⋊C4—431no—
728C2×C22⋊C4—431no—
729C2×C22⋊C4—431no—
730C2×C22⋊C4—431no—
731C2×C22⋊C4—431no—
732C2×C22⋊C4—431no—
733C2×C22⋊C4—431no—
734C2×C22⋊C4—431no—
735C2×C22⋊C4—431no—
736C2×C22⋊C4—431no—
737C2×C22⋊C4—431no—
738C2×C22⋊C4C4×D4311yescharacteristic
739C2×C22⋊C4C4×D4311yescharacteristic
740C2×C22⋊C4C22×D4311yescharacteristic
741C2×C22⋊C4C22×D4311yescharacteristic
742C2×C22⋊C4C22×D4311yescharacteristic
743C2×C22⋊C4C22×D4311yescharacteristic
744C2×C42—21no—
745C2×C42—431no—
746C2×C42—431no—
747C2×C42—431no—
748C2×C42—861no—
749C2×C42—861no—
750C2×C42—861no—
751C2×C42—861no—
752C2×C42—861no—
753#99—22no—
754#99—22no—
755#99—41no—
756#99—41no—
757#99—862no—
758#99—862no—
759#99—862no—
760#99—862no—
761#99—1721no—
762#99—1721no—
763#99—1721no—
764#99—1721no—
765#95—21no—
766#95—21no—
767#95—861no—
768#95—861no—
769#95—861no—
770#95—861no—
771#95—861no—
772#95—861no—
773#95—861no—
774#95—861no—
775#95—861no—
776#95—861no—
777C24—431no—
778C24C2×C4×D4311yescharacteristic
779C24C2×C4×D4311yescharacteristic
780C24C23×D4311yescharacteristic
781C2×D4—21no—
782C2×D4—21no—
783C2×D4—21no—
784C2×D4—21no—
785C2×D4—21no—
786C2×D4—21no—
787C2×D4—21no—
788C2×D4—21no—
789C2×D4—21no—
790C2×D4—21no—
791C2×D4—21no—
792C2×D4—21no—
793C2×D4—21no—
794C2×D4—21no—
795C2×D4—81no—
796C2×D4—861no—
797C2×D4—861no—
798C2×D4—861no—
799C2×D4—861no—
800C2×D4—861no—
801C2×D4—861no—
802C2×D4—861no—
803C2×D4—861no—
804C2×D4—861no—
805C2×D4—861no—
806C2×D4—3441no—
807C2×D4—1722no—
808C22×C4—21no—
809C22×C4—21no—
810C22×C4—21no—
811C22×C4—21no—
812C22×C4—81no—
813C22×C4—431no—
814C22×C4—431no—
815C22×C4—431no—
816C22×C4—431no—
817C22×C4—431no—
818C22×C4—431no—
819C22×C4—431no—
820C22×C4—431no—
821C22×C4—431no—
822C22×C4—431no—
823C22×C4—431no—
824C22×C4—431no—
825C22×C4—431no—
826C22×C4—431no—
827C22×C4—431no—
828C22×C4—861no—
829C22×C4—861no—
830C22×C4—861no—
831C22×C4—861no—
832C22×C4—861no—
833C22×C4—861no—
834C22×C4—861no—
835C22×C4—861no—
836C22×C4—861no—
837C22×C4—861no—
838C22×C4—3441no—
839C22×C4—3441no—
840C22×C4—3441no—
841C22×C4—1722no—
842C22×C4—1722no—
843C22×C4C2×C4×D4311yescharacteristic
844C22×C4C2×C4×D4311yescharacteristic
845C22×C4C2×C4×D4311yescharacteristic
846C22×C4C2×C4×D4311yescharacteristic
847C22×C4D4×D4311yescharacteristic
848C22×C4D4×D4311yescharacteristic
849C22×C4D4×D4311yescharacteristic
850C22×C4D4×D4311yescharacteristic
851C4⋊C4—21no—
852C4⋊C4—21no—
853C4⋊C4—81no—
854C4⋊C4—431no—
855C4⋊C4—431no—
856C4⋊C4—431no—
857C4⋊C4—431no—
858C4⋊C4—431no—
859C4⋊C4—431no—
860C4⋊C4—431no—
861C4⋊C4—431no—
862C4⋊C4—431no—
863C4⋊C4—431no—
864C4⋊C4—431no—
865C4⋊C4—431no—
866C4⋊C4—431no—
867C4⋊C4—431no—
868C4⋊C4—431no—
869C4⋊C4—431no—
870C4⋊C4—861no—
871C4⋊C4—861no—
872C4⋊C4—861no—
873C4⋊C4—861no—
874C4⋊C4—861no—
875C4⋊C4—861no—
876C4⋊C4—861no—
877C4⋊C4—861no—
878C4⋊C4—861no—
879C4⋊C4—861no—
880C4⋊C4—3441no—
881C4⋊C4—3441no—
882C4⋊C4—3441no—
883C4⋊C4—1722no—
884C4⋊C4—1722no—
885C22⋊C4—21no—
886C22⋊C4—21no—
887C22⋊C4—21no—
888C22⋊C4—21no—
889C22⋊C4—21no—
890C22⋊C4—21no—
891C22⋊C4—21no—
892C22⋊C4—21no—
893C22⋊C4—21no—
894C22⋊C4—21no—
895C22⋊C4—21no—
896C22⋊C4—432no—
897C22⋊C4—861no—
898C22⋊C4—861no—
899C22⋊C4—861no—
900C22⋊C4—861no—
901C22⋊C4—861no—
902C22⋊C4—861no—
903C22⋊C4—861no—
904C22⋊C4—861no—
905C22⋊C4—861no—
906C22⋊C4—861no—
907C22⋊C4—861no—
908C22⋊C4—861no—
909C22⋊C4—861no—
910C22⋊C4—861no—
911C22⋊C4—861no—
912C22⋊C4—861no—
913C22⋊C4—861no—
914C22⋊C4—861no—
915C22⋊C4—861no—
916C22⋊C4—861no—
917C22⋊C4—861no—
918C22⋊C4—861no—
919C22⋊C4—861no—
920C22⋊C4#1062190012yes—
921C42—81no—
922C42—861no—
923C42—861no—
924C42—861no—
925C42—861no—
926C42—861no—
927C42—861no—
928C42—3441no—
929C42—3441no—
930C42—3441no—
931C42—1722no—
932C42—1722no—
933C23—21no—
934C23—21no—
935C23—21no—
936C23—21no—
937C23—21no—
938C23—21no—
939C23—41no—
940C23—41no—
941C23—41no—
942C23—41no—
943C23—41no—
944C23—41no—
945C23—861no—
946C23—861no—
947C23—861no—
948C23—1721no—
949C23—1721no—
950C23C22×C4×D4311yescharacteristic
951C23C2×D4×D4311yescharacteristic
952C23C2×D4×D4311yescharacteristic
953C23#41×D4311yescharacteristic
954C23C2×#1062190011yescharacteristic
955C23#1306337011yescharacteristic
956C23#1306337211yescharacteristic
957D4—41no—
958D4—41no—
959D4—41no—
960D4—41no—
961D4—41no—
962D4—41no—
963D4—41no—
964D4—41no—
965D4—81no—
966D4—81no—
967D4—3441no—
968D4—3441no—
969D4—1722no—
970D4—1722no—
971D4—1721no—
972D4—1721no—
973D4—1721no—
974D4—1721no—
975C2×C4—22no—
976C2×C4—21no—
977C2×C4—21no—
978C2×C4—21no—
979C2×C4—21no—
980C2×C4—21no—
981C2×C4—21no—
982C2×C4—41no—
983C2×C4—41no—
984C2×C4—41no—
985C2×C4—41no—
986C2×C4—41no—
987C2×C4—41no—
988C2×C4—41no—
989C2×C4—41no—
990C2×C4—41no—
991C2×C4—41no—
992C2×C4—41no—
993C2×C4—41no—
994C2×C4—41no—
995C2×C4—41no—
996C2×C4—41no—
997C2×C4—41no—
998C2×C4—41no—
999C2×C4—431no—
1000C2×C4—431no—
1001C2×C4—431no—
1002C2×C4—431no—
1003C2×C4—431no—
1004C2×C4—431no—
1005C2×C4—431no—
1006C2×C4—431no—
1007C2×C4—862no—
1008C2×C4—862no—
1009C2×C4—862no—
1010C2×C4—862no—
1011C2×C4—861no—
1012C2×C4—861no—
1013C2×C4—861no—
1014C2×C4—861no—
1015C2×C4—861no—
1016C2×C4—3441no—
1017C2×C4—3441no—
1018C2×C4—3441no—
1019C2×C4—3441no—
1020C2×C4—1722no—
1021C2×C4—1721no—
1022C2×C4—1721no—
1023C2×C4—1721no—
1024C2×C4—1721no—
1025C2×C4—1721no—
1026C2×C4—1721no—
1027C2×C4—1721no—
1028C2×C4—1721no—
1029C2×C4—1721no—
1030C2×C4—1722no—
1031C2×C4—1721no—
1032C2×C4—1721no—
1033C2×C4—1721no—
1034C2×C4—1721no—
1035C2×C4—1721no—
1036C2×C4—1721no—
1037C2×C4—1721no—
1038C2×C4—1721no—
1039C2×C4—1721no—
1040C2×C4—1721no—
1041C2×C4—1721no—
1042C2×C4—1721no—
1043C2×C4—1721no—
1044C2×C4C22⋊C4×D4311yescharacteristic
1045C2×C4C22⋊C4×D4311yescharacteristic
1046C2×C4C22⋊C4×D4311yescharacteristic
1047C2×C4C22⋊C4×D4311yescharacteristic
1048C22—21no—
1049C22—21no—
1050C22—21no—
1051C22—21no—
1052C22—21no—
1053C22—21no—
1054C22—41no—
1055C22—41no—
1056C22—41no—
1057C22—41no—
1058C22—41no—
1059C22—41no—
1060C22—41no—
1061C22—41no—
1062C22—41no—
1063C22—41no—
1064C22—81no—
1065C22—81no—
1066C22—81no—
1067C22—81no—
1068C22—3441no—
1069C22—3441no—
1070C22—1721no—
1071C22—1721no—
1072C22—1721no—
1073C22C2×C22⋊C4×D4311yescharacteristic
1074C22C4×#1062190011yescharacteristic
1075C22#1458337811yescharacteristic
1076C22#1458355511yescharacteristic
1077C22#1458355711yescharacteristic
1078C22#1458356711yescharacteristic
1079C22#1458356911yescharacteristic
1080C4—21no—
1081C4—21no—
1082C4—21no—
1083C4—21no—
1084C4—42no—
1085C4—41no—
1086C4—41no—
1087C4—81no—
1088C4—81no—
1089C4—81no—
1090C4—432no—
1091C4—861no—
1092C4—861no—
1093C4—861no—
1094C4—861no—
1095C4—861no—
1096C4—861no—
1097C4—861no—
1098C4—3441no—
1099C4—3441no—
1100C4—3441no—
1101C4—1722no—
1102C4—1721no—
1103C4—1721no—
1104C4—1721no—
1105C2—21no—
1106C2—21no—
1107C2—21no—
1108C2—21no—
1109C2—21no—
1110C2—21no—
1111C2—81no—
1112C2—81no—
1113C2—3441no—
1114C2#1913743411yescharacteristic
1115C2#410×D4311yescharacteristic
1116C2#1914305311yescharacteristic
subgroupG/H
centerC22C2×C22⋊C4×D43
commutatorC23×C43C23×C4
FrattiniC24C23×D43
FittingC43×#1964C2
socleC22×C43C22×C22⋊C4
prime radicalC2×#14583592C2
cosocleC24×C43C24
hypercenter#1964D43
hypocenterC43#22535
LCSG ▷ C23×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1964

Complements

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

NH ≅ G/Ntype
2. #19137473C2semidirect
3. #19137467C2semidirect
4. #19135432C2semidirect
5. #19135429C2semidirect
6. #19135429C2semidirect
7. #19135429C2semidirect
8. #19135429C2semidirect
9. #19134581C2semidirect
10. #19134581C2semidirect
11. #19134580C2semidirect
12. #99×Dic43C2semidirect
13. #99×Dic43C2semidirect
14. C4×#13063239C2semidirect
15. C43×#1964C2semidirect
24. C2×#13063320C4semidirect
25. C2×#13063318C4semidirect
26. C2×#13063315C4semidirect
27. C2×#13063307C4semidirect
28. C2×#13063306C4semidirect
29. C2×#13063297C4semidirect
35. C2×(C22⋊D43)⋊C4C4semidirect
36. C2×#13063281C4semidirect
555. #1964D43semidirect
633. C43#22535semidirect

Maximal subgroups

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

subgroupindex
C2×#145835922
#191374732
#191374672
#191354322
#191354292
#191345812
#191345802
#99×Dic432
C4×#130632392
C43×#19642
#2253543