Finite Group Databasebeta

← #25112737

Subgroups — #25112737

Order 11008.

1294 conjugacy classes of subgroups.

The subgroup lattice has 1190 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583576C211yesmaximal, characteristic
2#19137447C211yesmaximal, characteristic, complemented
3#19137441C211yesmaximal, characteristic, complemented
4#19135581C211yesmaximal, characteristic, complemented
5#19135052C211yesmaximal, characteristic, complemented
6#19135052C211yesmaximal, characteristic, complemented
7#19135047C211yesmaximal, characteristic
8#19135047C211yesmaximal, characteristic
9#19134671C211yesmaximal, characteristic, complemented
10#19134668C211yesmaximal, characteristic, complemented
11#19134580C211yesmaximal, characteristic, complemented
12C4×#13063239C211yesmaximal, characteristic, complemented
13#19134326C211yesmaximal, characteristic, complemented
14#342×D43C211yesmaximal, characteristic, complemented
15C43×#1996C211yesmaximal, characteristic, complemented
16#14583576—21no—
17#14583576—21no—
18#14583576—21no—
19#14583576—21no—
20#14583576—21no—
21#14583576—21no—
22#14583576—21no—
23#14583576—21no—
24C2×#13063320C411yescharacteristic, complemented
25C2×#13063320C411yescharacteristic, complemented
26C2×#13063314C411yescharacteristic, complemented
27C2×#13063310C411yescharacteristic, complemented
28C2×#13063310C411yescharacteristic, complemented
29C2×#13063309C2211yescharacteristic
30C2×#13063301C411yescharacteristic, complemented
31C2×#13063295C2211yescharacteristic
32C2×#13063287C411yescharacteristic, complemented
33C2×C4×C22⋊D43C2211yescharacteristic
34C2×#13063283C411yescharacteristic, complemented
35C2×#13063281C2211yescharacteristic
36C2×#13063281C2211yescharacteristic
37C2×#13063281C2211yescharacteristic
38C22×(C2×D43)⋊C4C2211yescharacteristic
39C2×C22⋊C4×D43C2211yescharacteristic
40C2×C22⋊C4×D43C2211yescharacteristic
41C2×C22⋊C4×D43C2211yescharacteristic
42C2×#13063239C2211yescharacteristic
43C2×#13063239C2211yescharacteristic
44C2×#13063239C2211yescharacteristic
45C2×#13063239C2211yescharacteristic
46#14582791—21no—
47#14582790—21no—
48#14582789—21no—
49#14582788—21no—
50#14582773—21no—
51#14582770—21no—
52#14582760C2211yescharacteristic
53#14582760C2211yescharacteristic
54#14582759C2211yescharacteristic
55#14582754C2211yescharacteristic
56#14582754C2211yescharacteristic
57C4×(C2×D43)⋊C4—21no—
58C4×C22⋊Dic43C2211yescharacteristic
59#14582746—21no—
60#14582666C2211yescharacteristic
61#14582666C2211yescharacteristic
62#14582666C2211yescharacteristic
63#14582666C2211yescharacteristic
64#14582665C2211yescharacteristic
65#14582665C2211yescharacteristic
66#14582665C2211yescharacteristic
67#14582665C2211yescharacteristic
68C2×C22⋊Q8×C43C2211yescharacteristic
69C43×#380C2211yescharacteristic
70C4×C22⋊C4×C43C2211yescharacteristic
71C43×#342C2211yescharacteristic
72C43×#342C2211yescharacteristic
73C43×#342C2211yescharacteristic
74C43×#342C2211yescharacteristic
75C24×D43C2311yescharacteristic
76C22×D172C2×C411yescharacteristic
77C22×D172C2×C411yescharacteristic
78C22×C22⋊D43C2311yescharacteristic
79C23×Dic43C2311yescharacteristic
80C22×C4×D43—21no—
81C22×C4×D43—21no—
82C22×C4×D43C2×C411yescharacteristic
83C22×C4×D43C2×C411yescharacteristic
84C22×C4×D43C2×C411yescharacteristic, complemented
85#13063320—21no—
86#13063320—21no—
87#13063320—21no—
88#13063320—21no—
89#13063320—21no—
90#13063320—21no—
91#13063320—21no—
92#13063320—21no—
93#13063314—21no—
94#13063314—21no—
95#13063314—21no—
96#13063314—21no—
97#13063310—21no—
98#13063310—21no—
99#13063310—21no—
100#13063310—21no—
101#13063310—21no—
102#13063310—21no—
103#13063310—21no—
104#13063310—21no—
105#13063309—21no—
106#13063309—21no—
107#13063309—21no—
108#13063309—21no—
109#13063301—21no—
110#13063301—21no—
111#13063301—21no—
112#13063301—21no—
113#13063295—21no—
114#13063295—21no—
115#13063295—21no—
116#13063295—21no—
117#13063287—21no—
118#13063287—21no—
119#13063287—21no—
120#13063287—21no—
121C4×C22⋊D43—21no—
122C4×C22⋊D43—21no—
123C4×C22⋊D43—21no—
124C4×C22⋊D43—21no—
125#13063283—21no—
126#13063283—21no—
127#13063283—21no—
128#13063283—21no—
129#13063281—21no—
130#13063281—21no—
131#13063281—21no—
132#13063281—21no—
133#13063281—22no—
134#13063281—22no—
135#13063281—41no—
136#13063281—41no—
137C2×C4⋊Dic43—21no—
138C2×C4⋊Dic43C2×C411yescharacteristic, complemented
139C2×C4⋊Dic43C2×C411yescharacteristic, complemented
140C2×Dic43⋊C4—21no—
141C2×Dic43⋊C4—21no—
142C2×Dic43⋊C4C2×C411yescharacteristic, complemented
143C2×Dic43⋊C4C2×C411yescharacteristic, complemented
144C2×Dic43⋊C4C2×C411yescharacteristic, complemented
145C2×C22⋊Dic43C2311yescharacteristic
146C2×C22⋊Dic43C2311yescharacteristic
147C2×C22⋊Dic43C2311yescharacteristic
148C2×C22⋊Dic43C2311yescharacteristic
149C2×C22⋊Dic43C2311yescharacteristic
150C2×(C2×D43)⋊C4—21no—
151C2×(C2×D43)⋊C4—21no—
152C2×(C2×D43)⋊C4—21no—
153C2×(C2×D43)⋊C4—21no—
154C2×(C2×D43)⋊C4—21no—
155C2×(C2×D43)⋊C4—21no—
156C2×(C2×D43)⋊C4C2×C411yescharacteristic
157C2×(C2×D43)⋊C4C2×C411yescharacteristic
158C2×(C2×D43)⋊C4C2×C411yescharacteristic
159C2×(C2×D43)⋊C4C2×C411yescharacteristic
160C2×(C2×D43)⋊C4C2×C411yescharacteristic
161C2×(C2×D43)⋊C4C2×C411yescharacteristic
162C2×(C2×D43)⋊C4C2×C411yescharacteristic
163C2×(C2×D43)⋊C4C2×C411yescharacteristic
164C2×(C2×D43)⋊C4C2×C411yescharacteristic, complemented
165C2×(C2×D43)⋊C4C2×C411yescharacteristic, complemented
166C2×(C2×D43)⋊C4C2×C411yescharacteristic, complemented
167C2×(C2×D43)⋊C4D411yescharacteristic
168C2×(C2×D43)⋊C4D411yescharacteristic
169C2×(C2×D43)⋊C4D411yescharacteristic
170C2×(C2×D43)⋊C4D411yescharacteristic
171C2×(C2×D43)⋊C4D411yescharacteristic
172C2×(C2×D43)⋊C4D411yescharacteristic
173C2×(C2×D43)⋊C4D411yescharacteristic
174C2×(C2×D43)⋊C4D411yescharacteristic
175C22⋊C4×D43—21no—
176C22⋊C4×D43—21no—
177C22⋊C4×D43—21no—
178C22⋊C4×D43—21no—
179C22⋊C4×D43—22no—
180C22⋊C4×D43—22no—
181C22⋊C4×D43—41no—
182C22⋊C4×D43—41no—
183C2×C4×Dic43—21no—
184C2×C4×Dic43—21no—
185C2×C4×Dic43—21no—
186C2×C4×Dic43C2×C411yescharacteristic, complemented
187C2×C4×Dic43C2×C411yescharacteristic, complemented
188C2×C4×Dic43C2×C411yescharacteristic, complemented
189#13063239—22no—
190#13063239—22no—
191#13063239—41no—
192#13063239—41no—
193C43⋊#95—21no—
194C43⋊#95—21no—
195C43⋊#95—21no—
196C43⋊#95—21no—
197C43⋊#95—21no—
198C43⋊#95—21no—
199C22×Q8×C43C2×C411yescharacteristic, complemented
200C23×C4×C43C2311yescharacteristic
201C22⋊Q8×C43—21no—
202C22⋊Q8×C43—21no—
203C22⋊Q8×C43—21no—
204C22⋊Q8×C43—21no—
205C2×C4⋊C4×C43—21no—
206C2×C4⋊C4×C43C2×C411yescharacteristic, complemented
207C2×C4⋊C4×C43C2×C411yescharacteristic, complemented
208C2×C4⋊C4×C43C2×C411yescharacteristic, complemented
209C2×C22⋊C4×C43C2311yescharacteristic
210C2×C22⋊C4×C43C2311yescharacteristic
211C2×C22⋊C4×C43C2311yescharacteristic
212C2×C22⋊C4×C43C2311yescharacteristic
213C2×C22⋊C4×C43C2311yescharacteristic
214C2×C22⋊C4×C43C2311yescharacteristic
215C2×C42×C43—21no—
216#95×C43—21no—
217#95×C43—21no—
218C24×C43C2411yescharacteristic
219C23×D43—21no—
220C23×D43—21no—
221C23×D43—21no—
222C23×D43—21no—
223C23×D43—42no—
224C23×D43—81no—
225C23×D43C22×C411yescharacteristic
226C23×D43C22×C411yescharacteristic
227C23×D43C22×C411yescharacteristic
228C23×D43C2×D411yescharacteristic
229C23×D43C2×D411yescharacteristic
230C23×D43C2×D411yescharacteristic
231C23×D43C2×D411yescharacteristic
232C2×Q8×C43—21no—
233C2×Q8×C43—21no—
234C2×Q8×C43—81no—
235C22×C4×C43—21no—
236C22×C4×C43—21no—
237C22×C4×C43—21no—
238C22×C4×C43—21no—
239C22×C4×C43—81no—
240C22×C4×C43C22×C411yescharacteristic
241C22×C4×C43C22×C411yescharacteristic
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—
256C22×Dic43—21no—
257C22×Dic43—21no—
258C22×Dic43—21no—
259C22×Dic43—21no—
260C22×Dic43—21no—
261C22×Dic43—21no—
262C22×Dic43—21no—
263C22×Dic43—21no—
264C22×Dic43C22×C411yescharacteristic
265C22×Dic43C22×C411yescharacteristic
266C22×Dic43C22×C411yescharacteristic
267C22×Dic43C22×C411yescharacteristic
268C22×Dic43C22×C411yescharacteristic
269C22×Dic43C2×D411yescharacteristic
270C22×Dic43C2×D411yescharacteristic
271C22×Dic43C2×D411yescharacteristic
272C22×Dic43C2×D411yescharacteristic
273C2×D172—21no—
274C2×D172—21no—
275C2×D172—21no—
276C2×D172—21no—
277C2×D172—42no—
278C2×D172—81no—
279C2×C4×D43—21no—
280C2×C4×D43—21no—
281C2×C4×D43—21no—
282C2×C4×D43—21no—
283C2×C4×D43—21no—
284C2×C4×D43—21no—
285C2×C4×D43—42no—
286C2×C4×D43—42no—
287C2×C4×D43—42no—
288C2×C4×D43—42no—
289C2×C4×D43—42no—
290C2×C4×D43—81no—
291C2×C4×D43—81no—
292C2×C4×D43—81no—
293C2×C4×D43—81no—
294C4⋊C4×C43—21no—
295C4⋊C4×C43—21no—
296C4⋊C4×C43—21no—
297C4⋊C4×C43—21no—
298C4⋊C4×C43—21no—
299C4⋊C4×C43—21no—
300C4⋊C4×C43—81no—
301C22⋊C4×C43—21no—
302C22⋊C4×C43—21no—
303C22⋊C4×C43—21no—
304C22⋊C4×C43—21no—
305C22⋊C4×C43—21no—
306C22⋊C4×C43—21no—
307C22⋊C4×C43—21no—
308C22⋊C4×C43—21no—
309C22⋊C4×C43—21no—
310C22⋊C4×C43—21no—
311C22⋊C4×C43—21no—
312C22⋊C4×C43#4112yes—
313C42×C43—81no—
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#4112yes—
324(C2×D43)⋊C4—21no—
325(C2×D43)⋊C4—21no—
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—
332(C2×D43)⋊C4—21no—
333(C2×D43)⋊C4—21no—
334(C2×D43)⋊C4—21no—
335(C2×D43)⋊C4—21no—
336(C2×D43)⋊C4—21no—
337(C2×D43)⋊C4—21no—
338(C2×D43)⋊C4—42no—
339(C2×D43)⋊C4—42no—
340(C2×D43)⋊C4—42no—
341(C2×D43)⋊C4—42no—
342(C2×D43)⋊C4—81no—
343(C2×D43)⋊C4—81no—
344(C2×D43)⋊C4C22⋊C411yescharacteristic
345(C2×D43)⋊C4C22⋊C411yescharacteristic
346(C2×D43)⋊C4C22⋊C411yescharacteristic
347(C2×D43)⋊C4C22⋊C411yescharacteristic
348(C2×D43)⋊C4C22⋊C411yescharacteristic
349(C2×D43)⋊C4C22⋊C411yescharacteristic
350(C2×D43)⋊C4C22⋊C411yescharacteristic
351(C2×D43)⋊C4C22⋊C411yescharacteristic
352(C2×D43)⋊C4C22⋊C411yescharacteristic
353(C2×D43)⋊C4C22⋊C411yescharacteristic
354(C2×D43)⋊C4C22⋊C411yescharacteristic
355(C2×D43)⋊C4C22⋊C411yescharacteristic
356(C2×D43)⋊C4C22⋊C411yescharacteristic
357(C2×D43)⋊C4C22⋊C411yescharacteristic
358(C2×D43)⋊C4C22⋊C411yescharacteristic
359(C2×D43)⋊C4C22⋊C411yescharacteristic
360C4⋊Dic43—21no—
361C4⋊Dic43—21no—
362C4⋊Dic43—21no—
363C4⋊Dic43—21no—
364C4⋊Dic43—81no—
365Dic43⋊C4—21no—
366Dic43⋊C4—21no—
367Dic43⋊C4—21no—
368Dic43⋊C4—21no—
369Dic43⋊C4—21no—
370Dic43⋊C4—21no—
371Dic43⋊C4—42no—
372Dic43⋊C4—42no—
373C4×Dic43—21no—
374C4×Dic43—21no—
375C4×Dic43—21no—
376C4×Dic43—21no—
377C4×Dic43—21no—
378C4×Dic43—21no—
379C4×Dic43—42no—
380C4×Dic43—42no—
381C4×Dic43—81no—
382C23×C43—41no—
383C23×C43—41no—
384C23×C43C23×C411yescharacteristic
385C23×C43C22×D411yescharacteristic
386C23×C43C22×D411yescharacteristic
387C23×C43C2×#4111yescharacteristic
388C23×C43C2×#4111yescharacteristic
389C23×C43H(5,𝔽2)11yescharacteristic
390C23×C432−1+411yescharacteristic
391C22×D43—21no—
392C22×D43—21no—
393C22×D43—21no—
394C22×D43—21no—
395C22×D43—21no—
396C22×D43—21no—
397C22×D43—21no—
398C22×D43—21no—
399C22×D43—21no—
400C22×D43—21no—
401C22×D43—21no—
402C22×D43—21no—
403C22×D43—22no—
404C22×D43—22no—
405C22×D43—22no—
406C22×D43—21no—
407C22×D43—21no—
408C22×D43—21no—
409C22×D43—41no—
410C22×D43—41no—
411C22×D43—41no—
412C22×D43—41no—
413C22×D43—41no—
414C22×D43—41no—
415C22×D43—41no—
416C22×D43—41no—
417C22×D43—41no—
418C22×D43—41no—
419C22×D43—41no—
420C22×D43—82no—
421C22×D43—82no—
422C22×D43—82no—
423C22×D43—82no—
424C22×D43C2×C22⋊C411yescharacteristic
425C22×D43C2×C22⋊C411yescharacteristic
426C22×D43C2×C22⋊C411yescharacteristic
427C22×D43C2×C22⋊C411yescharacteristic
428Q8×C43—81no—
429Q8×C43—81no—
430C2×C4×C43—21no—
431C2×C4×C43—21no—
432C2×C4×C43—21no—
433C2×C4×C43—21no—
434C2×C4×C43—22no—
435C2×C4×C43—41no—
436C2×C4×C43—41no—
437C2×C4×C43—41no—
438C2×C4×C43—41no—
439C2×C4×C43—41no—
440C2×C4×C43—41no—
441C2×C4×C43—41no—
442C2×C4×C43—41no—
443C2×C4×C43—41no—
444C2×C4×C43—41no—
445C2×C4×C43—41no—
446C2×C4×C43—41no—
447C2×C4×C43—41no—
448C2×C4×C43—41no—
449C2×C4×C43—41no—
450C2×C4×C43—41no—
451C2×C4×C43—41no—
452C2×C4×C43—41no—
453C2×C4×C43—41no—
454C2×C4×C43—41no—
455C2×C4×C43—41no—
456C2×C4×C43C2×C22⋊C411yescharacteristic
457C2×C4×C43C2×C22⋊C411yescharacteristic
458C2×C4×C43C2×C22⋊C411yescharacteristic
459C2×C4×C43C2×C22⋊C411yescharacteristic
460C22⋊D43—41no—
461C22⋊D43—41no—
462C22⋊D43—41no—
463C22⋊D43—41no—
464C2×Dic43—21no—
465C2×Dic43—21no—
466C2×Dic43—21no—
467C2×Dic43—21no—
468C2×Dic43—21no—
469C2×Dic43—21no—
470C2×Dic43—21no—
471C2×Dic43—21no—
472C2×Dic43—21no—
473C2×Dic43—21no—
474C2×Dic43—21no—
475C2×Dic43—21no—
476C2×Dic43—21no—
477C2×Dic43—21no—
478C2×Dic43—21no—
479C2×Dic43—21no—
480C2×Dic43—21no—
481C2×Dic43—22no—
482C2×Dic43—41no—
483C2×Dic43—41no—
484C2×Dic43—41no—
485C2×Dic43—41no—
486C2×Dic43—41no—
487C2×Dic43—41no—
488C2×Dic43—41no—
489C2×Dic43—41no—
490C2×Dic43—41no—
491C2×Dic43—41no—
492C2×Dic43—41no—
493C2×Dic43—41no—
494C2×Dic43—41no—
495C2×Dic43C2×C22⋊C411yescharacteristic
496C2×Dic43C2×C22⋊C411yescharacteristic
497C2×Dic43C2×C22⋊C411yescharacteristic
498C2×Dic43C2×C22⋊C411yescharacteristic
499D172—42no—
500D172—42no—
501D172—81no—
502D172—81no—
503C4×D43—42no—
504C4×D43—42no—
505C4×D43—81no—
506C4×D43—81no—
507C4×D43—81no—
508C4×D43—81no—
509C4×D43—84no—
510C4×D43—84no—
511#22477—431nomaximal, Sylow
512C22×C43—21no—
513C22×C43—21no—
514C22×C43—21no—
515C22×C43—21no—
516C22×C43—21no—
517C22×C43—21no—
518C22×C43—41no—
519C22×C43—41no—
520C22×C43—41no—
521C22×C43—41no—
522C22×C43C22×C22⋊C411yescharacteristic
523C22×C43C4×#4111yescharacteristic
524C22×C43#52011yescharacteristic
525C22×C43#54611yescharacteristic
526C22×C43#54611yescharacteristic
527C22×C43#54711yescharacteristic
528C22×C43#54711yescharacteristic
529C2×D43—21no—
530C2×D43—21no—
531C2×D43—21no—
532C2×D43—21no—
533C2×D43—21no—
534C2×D43—21no—
535C2×D43—21no—
536C2×D43—21no—
537C2×D43—21no—
538C2×D43—21no—
539C2×D43—21no—
540C2×D43—42no—
541C2×D43—42no—
542C2×D43—42no—
543C2×D43—42no—
544C2×D43—42no—
545C2×D43—42no—
546C2×D43—41no—
547C2×D43—41no—
548C2×D43—41no—
549C2×D43—81no—
550C2×D43—81no—
551C2×D43—81no—
552C2×D43—81no—
553C2×D43—81no—
554C2×D43—81no—
555C2×D43—81no—
556C2×D43—81no—
557C2×D43#41012yes—
558C4×C43—21no—
559C4×C43—21no—
560C4×C43—21no—
561C4×C43—21no—
562C4×C43—42no—
563C4×C43—41no—
564C4×C43—41no—
565C4×C43—41no—
566C4×C43—41no—
567C4×C43—81no—
568C4×C43—81no—
569C4×C43—81no—
570Dic43—21no—
571Dic43—21no—
572Dic43—21no—
573Dic43—21no—
574Dic43—42no—
575Dic43—41no—
576Dic43—41no—
577Dic43—41no—
578Dic43—81no—
579Dic43—81no—
580Dic43—81no—
581C2×#551—431no—
582#2342—431no—
583#2342—431no—
584#1996—431no—
585#1996D4311yescharacteristic, complemented
586#1899—431no—
587#1899—431no—
588#1898—431no—
589#1898—431no—
590#1820—431no—
591#1819—431no—
592#1799—431no—
593C4×#99—431no—
594#1740—431no—
595C2×#342—431no—
596C2×C43—21no—
597C2×C43—21no—
598C2×C43—21no—
599C2×C43—21no—
600C2×C43—21no—
601C2×C43—21no—
602C2×C43#233911yescharacteristic
603C2×C43C2×#41011yescharacteristic
604C2×C43#288311yescharacteristic
605D43—22no—
606D43—41no—
607D43—41no—
608D43—41no—
609D43—81no—
610#551—861no—
611#551—861no—
612#551—861no—
613#551—861no—
614#551—861no—
615#551—861no—
616#551—861no—
617#551—861no—
618C2×#126—431no—
619C2×#126—431no—
620C2×#124—431no—
621C2×#123—431no—
622C2×#123—431no—
623C2×#123—431no—
624C2×C22⋊Q8—431no—
625C2×C22⋊Q8C2×D4311yescharacteristic
626C2×#120—431no—
627C2×C4×D4—431no—
628C2×C4×D4—431no—
629C2×#117—431no—
630C2×#117—431no—
631C2×#117—431no—
632C2×#117—431no—
633C22×C22⋊C4—431no—
634C22×C22⋊C4—431no—
635C22×C22⋊C4—431no—
636C22×C22⋊C4—431no—
637C2×#99—431no—
638C2×#99—431no—
639C2×#99—431no—
640C2×#99—431no—
641#388—861no—
642#388—861no—
643#388—861no—
644#388—861no—
645#385—861no—
646#385—861no—
647#381—431no—
648#381—431no—
649#380—431no—
650#380C2×D4311yescharacteristic
651#379—431no—
652#379—431no—
653C4×C22⋊C4—431no—
654C4×C22⋊C4—861no—
655C4×C22⋊C4—861no—
656C4×C22⋊C4C2×D4311yescharacteristic
657#342—431no—
658#342—431no—
659#342—431no—
660#342—431no—
661#342—431no—
662#342—431no—
663#342—431no—
664#342—431no—
665#342C2×D4311yescharacteristic
666#342C2×D4311yescharacteristic
667#342C2×D4311yescharacteristic
668#342C2×D4311yescharacteristic
669C43#2247711yescharacteristic, complemented, Sylow
670C25—431no—
671C22×Q8C4×D4311yescharacteristic, complemented
672C22×D4—431no—
673C22×D4—431no—
674C22×D4—431no—
675C23×C4—431no—
676C23×C4—431no—
677C23×C4—431no—
678C23×C4—431no—
679C23×C4—861no—
680C23×C4—861no—
681C23×C4C22×D4311yescharacteristic
682#126—861no—
683#126—861no—
684#126—861no—
685#126—861no—
686#126—861no—
687#126—861no—
688#126—861no—
689#126—861no—
690#124—861no—
691#124—861no—
692#124—861no—
693#124—861no—
694#123—861no—
695#123—861no—
696#123—861no—
697#123—861no—
698#123—861no—
699#123—861no—
700#123—861no—
701#123—861no—
702#123—861no—
703#123—861no—
704#123—861no—
705#123—861no—
706C22⋊Q8—21no—
707C22⋊Q8—21no—
708C22⋊Q8—21no—
709C22⋊Q8—21no—
710C22⋊Q8—861no—
711C22⋊Q8—861no—
712C22⋊Q8—861no—
713C22⋊Q8—861no—
714#120—861no—
715#120—861no—
716#120—861no—
717#120—861no—
718C4×D4—861no—
719C4×D4—861no—
720C4×D4—861no—
721C4×D4—861no—
722C4×D4—861no—
723C4×D4—861no—
724C4×D4—861no—
725C4×D4—861no—
726#117—861no—
727#117—861no—
728#117—861no—
729#117—861no—
730#117—861no—
731#117—861no—
732#117—861no—
733#117—861no—
734#117—862no—
735#117—862no—
736#117—1721no—
737#117—1721no—
738C2×C4⋊C4—21no—
739C2×C4⋊C4—431no—
740C2×C4⋊C4—431no—
741C2×C4⋊C4—431no—
742C2×C4⋊C4—431no—
743C2×C4⋊C4—431no—
744C2×C4⋊C4—861no—
745C2×C4⋊C4—861no—
746C2×C4⋊C4—861no—
747C2×C4⋊C4C4×D4311yescharacteristic, complemented
748C2×C4⋊C4C4×D4311yescharacteristic, complemented
749C2×C4⋊C4C4×D4311yescharacteristic, complemented
750C2×C22⋊C4—431no—
751C2×C22⋊C4—431no—
752C2×C22⋊C4—431no—
753C2×C22⋊C4—431no—
754C2×C22⋊C4—431no—
755C2×C22⋊C4—431no—
756C2×C22⋊C4—431no—
757C2×C22⋊C4—431no—
758C2×C22⋊C4—431no—
759C2×C22⋊C4—431no—
760C2×C22⋊C4—431no—
761C2×C22⋊C4—431no—
762C2×C22⋊C4—431no—
763C2×C22⋊C4—431no—
764C2×C22⋊C4—431no—
765C2×C22⋊C4—431no—
766C2×C22⋊C4—431no—
767C2×C22⋊C4—431no—
768C2×C22⋊C4—431no—
769C2×C22⋊C4—431no—
770C2×C22⋊C4—431no—
771C2×C22⋊C4—431no—
772C2×C22⋊C4—431no—
773C2×C22⋊C4—431no—
774C2×C22⋊C4—862no—
775C2×C22⋊C4—861no—
776C2×C22⋊C4—861no—
777C2×C22⋊C4—861no—
778C2×C22⋊C4—861no—
779C2×C22⋊C4—862no—
780C2×C22⋊C4—861no—
781C2×C22⋊C4—861no—
782C2×C22⋊C4—861no—
783C2×C22⋊C4—861no—
784C2×C22⋊C4—861no—
785C2×C22⋊C4—861no—
786C2×C22⋊C4—1721no—
787C2×C22⋊C4—1721no—
788C2×C22⋊C4C22×D4311yescharacteristic
789C2×C22⋊C4C22×D4311yescharacteristic
790C2×C22⋊C4C22×D4311yescharacteristic
791C2×C22⋊C4C22×D4311yescharacteristic
792C2×C22⋊C4C22×D4311yescharacteristic
793C2×C22⋊C4C22×D4311yescharacteristic
794C2×C42—21no—
795C2×C42—431no—
796C2×C42—431no—
797C2×C42—431no—
798C2×C42—861no—
799C2×C42—861no—
800C2×C42—861no—
801#99—862no—
802#99—862no—
803#99—1721no—
804#99—1721no—
805#95—21no—
806#95—21no—
807#95—861no—
808#95—861no—
809#95—861no—
810#95—861no—
811#95—861no—
812#95—861no—
813C24—431no—
814C24—431no—
815C24—431no—
816C24—431no—
817C24—431no—
818C24—431no—
819C24—431no—
820C24—861no—
821C24—861no—
822C24—861no—
823C24—861no—
824C24—3441no—
825C24—1722no—
826C24C23×D4311yescharacteristic
827C2×Q8—21no—
828C2×Q8—21no—
829C2×Q8—81no—
830C2×D4—861no—
831C2×D4—861no—
832C2×D4—861no—
833C2×D4—861no—
834C2×D4—861no—
835C2×D4—861no—
836C2×D4—861no—
837C2×D4—861no—
838C2×D4—861no—
839C2×D4—861no—
840C2×D4—3441no—
841C2×D4—1722no—
842C22×C4—21no—
843C22×C4—21no—
844C22×C4—21no—
845C22×C4—21no—
846C22×C4—81no—
847C22×C4—431no—
848C22×C4—431no—
849C22×C4—431no—
850C22×C4—431no—
851C22×C4—431no—
852C22×C4—431no—
853C22×C4—431no—
854C22×C4—431no—
855C22×C4—431no—
856C22×C4—861no—
857C22×C4—861no—
858C22×C4—861no—
859C22×C4—861no—
860C22×C4—861no—
861C22×C4—861no—
862C22×C4—861no—
863C22×C4—861no—
864C22×C4—861no—
865C22×C4—861no—
866C22×C4—861no—
867C22×C4—861no—
868C22×C4—861no—
869C22×C4—861no—
870C22×C4—3441no—
871C22×C4—3441no—
872C22×C4—3441no—
873C22×C4—3441no—
874C22×C4—1722no—
875C22×C4—1722no—
876C22×C4—1722no—
877C22×C4—1722no—
878C22×C4—1722no—
879C22×C4C2×C4×D4311yescharacteristic
880C22×C4C2×C4×D4311yescharacteristic
881C22×C4C2×C4×D4311yescharacteristic
882C22×C4C2×C4×D4311yescharacteristic
883C22×C4C2×C4×D4311yescharacteristic
884C22×C4C2×C4×D4311yescharacteristic
885C22×C4D4×D4311yescharacteristic
886C22×C4D4×D4311yescharacteristic
887C22×C4D4×D4311yescharacteristic
888C22×C4D4×D4311yescharacteristic
889C4⋊C4—21no—
890C4⋊C4—21no—
891C4⋊C4—21no—
892C4⋊C4—21no—
893C4⋊C4—21no—
894C4⋊C4—21no—
895C4⋊C4—81no—
896C4⋊C4—861no—
897C4⋊C4—861no—
898C4⋊C4—861no—
899C4⋊C4—861no—
900C4⋊C4—861no—
901C4⋊C4—861no—
902C4⋊C4—861no—
903C4⋊C4—861no—
904C4⋊C4—861no—
905C4⋊C4—861no—
906C4⋊C4—3441no—
907C4⋊C4—1722no—
908C4⋊C4—1722no—
909C22⋊C4—21no—
910C22⋊C4—21no—
911C22⋊C4—21no—
912C22⋊C4—21no—
913C22⋊C4—21no—
914C22⋊C4—21no—
915C22⋊C4—21no—
916C22⋊C4—21no—
917C22⋊C4—21no—
918C22⋊C4—21no—
919C22⋊C4—21no—
920C22⋊C4—431no—
921C22⋊C4—431no—
922C22⋊C4—431no—
923C22⋊C4—431no—
924C22⋊C4—431no—
925C22⋊C4—431no—
926C22⋊C4—431no—
927C22⋊C4—431no—
928C22⋊C4—431no—
929C22⋊C4—431no—
930C22⋊C4—431no—
931C22⋊C4—431no—
932C22⋊C4—431no—
933C22⋊C4—431no—
934C22⋊C4—431no—
935C22⋊C4—431no—
936C22⋊C4—432no—
937C22⋊C4—861no—
938C22⋊C4—861no—
939C22⋊C4—861no—
940C22⋊C4—861no—
941C22⋊C4—861no—
942C22⋊C4—861no—
943C22⋊C4—861no—
944C22⋊C4—861no—
945C22⋊C4—861no—
946C22⋊C4—861no—
947C22⋊C4—861no—
948C22⋊C4—861no—
949C22⋊C4—861no—
950C22⋊C4—861no—
951C22⋊C4—861no—
952C22⋊C4—861no—
953C22⋊C4—861no—
954C22⋊C4—861no—
955C22⋊C4—861no—
956C22⋊C4—861no—
957C22⋊C4—861no—
958C22⋊C4—861no—
959C22⋊C4—861no—
960C22⋊C4—3441no—
961C22⋊C4—3441no—
962C22⋊C4—1722no—
963C22⋊C4—1722no—
964C22⋊C4—1722no—
965C22⋊C4—1722no—
966C22⋊C4#1062190212yes—
967C42—81no—
968C42—861no—
969C42—861no—
970C42—861no—
971C42—861no—
972C42—861no—
973C42—861no—
974C42—3441no—
975C42—1722no—
976C42—1722no—
977C23—41no—
978C23—41no—
979C23—431no—
980C23—431no—
981C23—431no—
982C23—431no—
983C23—862no—
984C23—862no—
985C23—862no—
986C23—861no—
987C23—861no—
988C23—861no—
989C23—861no—
990C23—861no—
991C23—861no—
992C23—861no—
993C23—861no—
994C23—861no—
995C23—861no—
996C23—861no—
997C23—861no—
998C23—861no—
999C23—861no—
1000C23—861no—
1001C23—3442no—
1002C23—3442no—
1003C23—3442no—
1004C23—3442no—
1005C23—1721no—
1006C23—1721no—
1007C23—1721no—
1008C23—1721no—
1009C23—1721no—
1010C23—1721no—
1011C23—1721no—
1012C23—1721no—
1013C23—1721no—
1014C23—1721no—
1015C23—1721no—
1016C23C22×C4×D4311yescharacteristic
1017C23C2×D4×D4311yescharacteristic
1018C23C2×D4×D4311yescharacteristic
1019C23#41×D4311yescharacteristic
1020C23C2×#1062190211yescharacteristic
1021C23#1306337111yescharacteristic
1022C23#1306337311yescharacteristic
1023Q8—81no—
1024Q8—81no—
1025D4—3441no—
1026D4—3441no—
1027D4—1722no—
1028D4—1722no—
1029D4—1721no—
1030D4—1721no—
1031D4—1721no—
1032D4—1721no—
1033C2×C4—21no—
1034C2×C4—21no—
1035C2×C4—21no—
1036C2×C4—21no—
1037C2×C4—22no—
1038C2×C4—41no—
1039C2×C4—41no—
1040C2×C4—41no—
1041C2×C4—41no—
1042C2×C4—41no—
1043C2×C4—41no—
1044C2×C4—41no—
1045C2×C4—41no—
1046C2×C4—41no—
1047C2×C4—41no—
1048C2×C4—41no—
1049C2×C4—41no—
1050C2×C4—41no—
1051C2×C4—41no—
1052C2×C4—41no—
1053C2×C4—41no—
1054C2×C4—41no—
1055C2×C4—41no—
1056C2×C4—41no—
1057C2×C4—41no—
1058C2×C4—41no—
1059C2×C4—431no—
1060C2×C4—431no—
1061C2×C4—431no—
1062C2×C4—431no—
1063C2×C4—861no—
1064C2×C4—861no—
1065C2×C4—861no—
1066C2×C4—861no—
1067C2×C4—861no—
1068C2×C4—861no—
1069C2×C4—861no—
1070C2×C4—861no—
1071C2×C4—861no—
1072C2×C4—861no—
1073C2×C4—861no—
1074C2×C4—861no—
1075C2×C4—861no—
1076C2×C4—861no—
1077C2×C4—861no—
1078C2×C4—861no—
1079C2×C4—861no—
1080C2×C4—862no—
1081C2×C4—3441no—
1082C2×C4—3441no—
1083C2×C4—3444no—
1084C2×C4—3441no—
1085C2×C4—3441no—
1086C2×C4—3444no—
1087C2×C4—1722no—
1088C2×C4—1722no—
1089C2×C4—1721no—
1090C2×C4—1721no—
1091C2×C4—1721no—
1092C2×C4—1721no—
1093C2×C4—1721no—
1094C2×C4—1721no—
1095C2×C4—1721no—
1096C2×C4—1721no—
1097C2×C4—1721no—
1098C2×C4—1721no—
1099C2×C4—1721no—
1100C2×C4—1721no—
1101C2×C4—1721no—
1102C2×C4C22⋊C4×D4311yescharacteristic
1103C2×C4C22⋊C4×D4311yescharacteristic
1104C2×C4C22⋊C4×D4311yescharacteristic
1105C2×C4C22⋊C4×D4311yescharacteristic
1106C22—21no—
1107C22—21no—
1108C22—21no—
1109C22—21no—
1110C22—21no—
1111C22—21no—
1112C22—41no—
1113C22—41no—
1114C22—41no—
1115C22—41no—
1116C22—432no—
1117C22—861no—
1118C22—861no—
1119C22—861no—
1120C22—861no—
1121C22—861no—
1122C22—861no—
1123C22—861no—
1124C22—861no—
1125C22—861no—
1126C22—861no—
1127C22—861no—
1128C22—3441no—
1129C22—3441no—
1130C22—3441no—
1131C22—3441no—
1132C22—3441no—
1133C22—3441no—
1134C22—3441no—
1135C22—3441no—
1136C22—1722no—
1137C22—1722no—
1138C22—1722no—
1139C22—1722no—
1140C22—1722no—
1141C22—1722no—
1142C22—1721no—
1143C22—1721no—
1144C22—1721no—
1145C22C2×C22⋊C4×D4311yescharacteristic
1146C22C4×#1062190211yescharacteristic
1147C22#1458338111yescharacteristic
1148C22#1458354011yescharacteristic
1149C22#1458354211yescharacteristic
1150C22#1458355111yescharacteristic
1151C22#1458355211yescharacteristic
1152C4—21no—
1153C4—21no—
1154C4—21no—
1155C4—21no—
1156C4—42no—
1157C4—41no—
1158C4—41no—
1159C4—41no—
1160C4—41no—
1161C4—81no—
1162C4—81no—
1163C4—81no—
1164C4—861no—
1165C4—861no—
1166C4—861no—
1167C4—861no—
1168C4—3441no—
1169C4—3441no—
1170C4—3441no—
1171C4—1722no—
1172C4—1721no—
1173C4—1721no—
1174C4—1721no—
1175C2—21no—
1176C2—21no—
1177C2—21no—
1178C2—21no—
1179C2—21no—
1180C2—21no—
1181C2—862no—
1182C2—3441no—
1183C2—1721no—
1184C2—1721no—
1185C2—1721no—
1186C2#1913742411yescharacteristic
1187C2#410×D4311yescharacteristic
1188C2#1914305311yescharacteristic
subgroupG/H
centerC22C2×C22⋊C4×D43
commutatorC23×C43C23×C4
FrattiniC24C23×D43
FittingC43×#1996C2
socleC22×C43C22×C22⋊C4
prime radicalC2×#13063295C22
cosocleC24×C43C24
hypercenter#1996D43
hypocenterC43#22477
LCSG ▷ C23×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1996

Complements

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

NH ≅ G/Ntype
2. #19137447C2semidirect
3. #19137441C2semidirect
4. #19135581C2semidirect
5. #19135052C2semidirect
6. #19135052C2semidirect
9. #19134671C2semidirect
10. #19134668C2semidirect
11. #19134580C2semidirect
12. C4×#13063239C2semidirect
13. #19134326C2semidirect
14. #342×D43C2semidirect
15. C43×#1996C2semidirect
24. C2×#13063320C4semidirect
25. C2×#13063320C4semidirect
26. C2×#13063314C4semidirect
27. C2×#13063310C4semidirect
28. C2×#13063310C4semidirect
30. C2×#13063301C4semidirect
32. C2×#13063287C4semidirect
34. C2×#13063283C4semidirect
84. C22×C4×D43C2×C4semidirect
138. C2×C4⋊Dic43C2×C4semidirect
139. C2×C4⋊Dic43C2×C4semidirect
142. C2×Dic43⋊C4C2×C4semidirect
143. C2×Dic43⋊C4C2×C4semidirect
144. C2×Dic43⋊C4C2×C4semidirect
164. C2×(C2×D43)⋊C4C2×C4semidirect
165. C2×(C2×D43)⋊C4C2×C4semidirect
166. C2×(C2×D43)⋊C4C2×C4semidirect
186. C2×C4×Dic43C2×C4semidirect
187. C2×C4×Dic43C2×C4semidirect
188. C2×C4×Dic43C2×C4semidirect
199. C22×Q8×C43C2×C4semidirect
206. C2×C4⋊C4×C43C2×C4semidirect
207. C2×C4⋊C4×C43C2×C4semidirect
208. C2×C4⋊C4×C43C2×C4semidirect
585. #1996D43semidirect
669. C43#22477semidirect
671. C22×Q8C4×D43semidirect
747. C2×C4⋊C4C4×D43semidirect
748. C2×C4⋊C4C4×D43semidirect
749. C2×C4⋊C4C4×D43semidirect

Maximal subgroups

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

subgroupindex
C2×#145835762
#191374472
#191374412
#191355812
#191350522
#191350472
#191346712
#191346682
#191345802
C4×#130632392
#191343262
#342×D432
C43×#19962
#2247743