Finite Group Databasebeta

← #25113149

Subgroups — #25113149

Order 11008.

1114 conjugacy classes of subgroups.

The subgroup lattice has 1034 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583603C211yesmaximal, characteristic
2#19137473C211yesmaximal, characteristic, complemented
3#19137467C211yesmaximal, characteristic, complemented
4#19135581C211yesmaximal, characteristic, complemented
5#19135578C211yesmaximal, characteristic, complemented
6#19135578C211yesmaximal, characteristic, complemented
7#19135578C211yesmaximal, characteristic, complemented
8#19135578C211yesmaximal, characteristic, complemented
9#19134582C211yesmaximal, characteristic
10#19134582C211yesmaximal, characteristic
11#19134580C211yesmaximal, characteristic
12C4×#13063239C211yesmaximal, characteristic
13#19134382C211yesmaximal, characteristic
14#19134382C211yesmaximal, characteristic
15C43×#1996C211yesmaximal, characteristic, complemented
16#14583603—21no—
17#14583603—21no—
18#14583603—21no—
19#14583603—21no—
20#14583603—21no—
21#14583603—21no—
22#14583603—21no—
23#14583603—21no—
24C2×#13063323C411yescharacteristic, complemented
25C2×#13063315C411yescharacteristic, complemented
26C2×#13063315C411yescharacteristic, complemented
27C2×#13063303C411yescharacteristic, complemented
28C2×#13063303C411yescharacteristic, complemented
29C2×#13063302C2211yescharacteristic
30C2×#13063302C2211yescharacteristic
31C2×#13063301C411yescharacteristic, complemented
32C2×#13063290C411yescharacteristic, complemented
33C2×C4×C22⋊D43C2211yescharacteristic
34C2×(C22⋊D43)⋊C4C2211yescharacteristic
35C2×(C22⋊D43)⋊C4C2211yescharacteristic
36C22×Dic43⋊C4C2211yescharacteristic
37C2×C4⋊C4×D43C411yescharacteristic, complemented
38C2×#13063239C2211yescharacteristic
39C2×#13063239C2211yescharacteristic
40C2×#13063239C2211yescharacteristic
41C2×#13063239C2211yescharacteristic
42#14582796—21no—
43#14582794—21no—
44#14582786—21no—
45#14582783—21no—
46#14582781—21no—
47#14582780—21no—
48#14582759C2211yescharacteristic
49#14582757C2211yescharacteristic
50#14582757C2211yescharacteristic
51#14582757C2211yescharacteristic
52#14582757C2211yescharacteristic
53C4×Dic43⋊C4—21no—
54#14582750—21no—
55C22⋊C4×Dic43C2211yescharacteristic
56C22⋊C4×Dic43C2211yescharacteristic
57C22⋊C4×Dic43C2211yescharacteristic
58C22⋊C4×Dic43C2211yescharacteristic
59C4×C22⋊Dic43C2211yescharacteristic
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
75C22×Dic86C2×C411yescharacteristic
76C22×Dic86C2×C411yescharacteristic
77C22×C22⋊D43C2311yescharacteristic
78C23×Dic43C2311yescharacteristic
79C23×Dic43C2311yescharacteristic
80C22×C4×D43C2×C411yescharacteristic
81C22×C4×D43C2×C411yescharacteristic
82C22×C4×D43C2×C411yescharacteristic
83#13063323—21no—
84#13063323—21no—
85#13063323—21no—
86#13063323—21no—
87#13063315—21no—
88#13063315—21no—
89#13063315—21no—
90#13063315—21no—
91#13063315—21no—
92#13063315—21no—
93#13063315—21no—
94#13063315—21no—
95#13063303—21no—
96#13063303—21no—
97#13063303—21no—
98#13063303—21no—
99#13063303—21no—
100#13063303—21no—
101#13063303—21no—
102#13063303—21no—
103#13063302—21no—
104#13063302—21no—
105#13063302—21no—
106#13063302—21no—
107#13063302—21no—
108#13063302—21no—
109#13063302—21no—
110#13063302—21no—
111#13063301—21no—
112#13063301—21no—
113#13063301—21no—
114#13063301—21no—
115#13063290—21no—
116#13063290—21no—
117#13063290—21no—
118#13063290—21no—
119C4×C22⋊D43—21no—
120C4×C22⋊D43—21no—
121C4×C22⋊D43—21no—
122C4×C22⋊D43—21no—
123(C22⋊D43)⋊C4—21no—
124(C22⋊D43)⋊C4—21no—
125(C22⋊D43)⋊C4—21no—
126(C22⋊D43)⋊C4—21no—
127(C22⋊D43)⋊C4—21no—
128(C22⋊D43)⋊C4—21no—
129(C22⋊D43)⋊C4—21no—
130(C22⋊D43)⋊C4—21no—
131C2×C4⋊Dic43—21no—
132C2×C4⋊Dic43C2×C411yescharacteristic
133C2×C4⋊Dic43C2×C411yescharacteristic
134C2×Dic43⋊C4—21no—
135C2×Dic43⋊C4—21no—
136C2×Dic43⋊C4—21no—
137C2×Dic43⋊C4—21no—
138C2×Dic43⋊C4C2×C411yescharacteristic
139C2×Dic43⋊C4C2×C411yescharacteristic
140C2×Dic43⋊C4C2×C411yescharacteristic
141C2×Dic43⋊C4C2×C411yescharacteristic
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
157C4⋊C4×D43—21no—
158C4⋊C4×D43—21no—
159C4⋊C4×D43—21no—
160C4⋊C4×D43—21no—
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#13063239—22no—
178#13063239—22no—
179#13063239—22no—
180#13063239Q814yescomplemented
181C43⋊#95—21no—
182C43⋊#95—21no—
183C43⋊#95—21no—
184C43⋊#95—21no—
185C43⋊#95—21no—
186C43⋊#95—21no—
187C43⋊#95—21no—
188C43⋊#95—21no—
189C43⋊#95—21no—
190C43⋊#95—21no—
191C22×Q8×C43C2×C411yescharacteristic
192C23×C4×C43C2311yescharacteristic
193C22⋊Q8×C43—21no—
194C22⋊Q8×C43—21no—
195C22⋊Q8×C43—21no—
196C22⋊Q8×C43—21no—
197C2×C4⋊C4×C43—21no—
198C2×C4⋊C4×C43C2×C411yescharacteristic
199C2×C4⋊C4×C43C2×C411yescharacteristic
200C2×C4⋊C4×C43C2×C411yescharacteristic
201C2×C22⋊C4×C43C2311yescharacteristic
202C2×C22⋊C4×C43C2311yescharacteristic
203C2×C22⋊C4×C43C2311yescharacteristic
204C2×C22⋊C4×C43C2311yescharacteristic
205C2×C22⋊C4×C43C2311yescharacteristic
206C2×C22⋊C4×C43C2311yescharacteristic
207C2×C42×C43—21no—
208#95×C43—21no—
209#95×C43—21no—
210C24×C43C2411yescharacteristic
211C23×D43C22×C411yescharacteristic
212C2×Q8×C43—21no—
213C2×Q8×C43—21no—
214C2×Q8×C43—81no—
215C22×C4×C43—21no—
216C22×C4×C43—21no—
217C22×C4×C43—21no—
218C22×C4×C43—21no—
219C22×C4×C43—81no—
220C22×C4×C43C22×C411yescharacteristic
221C22×C4×C43C22×C411yescharacteristic
222C22×C4×C43C22×C411yescharacteristic
223C22×C4×C43C22×C411yescharacteristic
224C22×C4×C43C22×C411yescharacteristic
225C22×C4×C43C22×C411yescharacteristic
226C22×C4×C43C2×D411yescharacteristic
227C22×C4×C43C2×D411yescharacteristic
228C22×C4×C43C2×D411yescharacteristic
229C22×C4×C43C2×D411yescharacteristic
230C2×C22⋊D43—21no—
231C2×C22⋊D43—21no—
232C2×C22⋊D43—21no—
233C2×C22⋊D43—21no—
234C2×C22⋊D43C2×Q812yes—
235C2×C22⋊D43#4112yes—
236C22×Dic43—21no—
237C22×Dic43—21no—
238C22×Dic43—21no—
239C22×Dic43—21no—
240C22×Dic43—42no—
241C22×Dic43—81no—
242C22×Dic43C22×C411yescharacteristic
243C22×Dic43C22×C411yescharacteristic
244C22×Dic43C22×C411yescharacteristic
245C22×Dic43C22×C411yescharacteristic
246C22×Dic43C22×C411yescharacteristic
247C22×Dic43C22×C411yescharacteristic
248C22×Dic43C22×C411yescharacteristic
249C22×Dic43C2×D411yescharacteristic
250C22×Dic43C2×D411yescharacteristic
251C22×Dic43C2×D411yescharacteristic
252C22×Dic43C2×D411yescharacteristic
253C22×Dic43C2×D411yescharacteristic
254C22×Dic43C2×D411yescharacteristic
255C22×Dic43C2×D411yescharacteristic
256C22×Dic43C2×D411yescharacteristic
257C2×C4×D43—21no—
258C2×C4×D43—21no—
259C2×C4×D43—21no—
260C2×C4×D43—21no—
261C2×C4×D43—21no—
262C2×C4×D43—21no—
263C2×C4×D43—42no—
264C2×C4×D43—81no—
265C2×C4×D43—81no—
266C2×Dic86—21no—
267C2×Dic86—21no—
268C2×Dic86—21no—
269C2×Dic86—21no—
270C2×Dic86—42no—
271C2×Dic86—81no—
272C4⋊C4×C43—21no—
273C4⋊C4×C43—21no—
274C4⋊C4×C43—21no—
275C4⋊C4×C43—21no—
276C4⋊C4×C43—21no—
277C4⋊C4×C43—21no—
278C4⋊C4×C43—81no—
279C22⋊C4×C43—21no—
280C22⋊C4×C43—21no—
281C22⋊C4×C43—21no—
282C22⋊C4×C43—21no—
283C22⋊C4×C43—21no—
284C22⋊C4×C43—21no—
285C22⋊C4×C43—21no—
286C22⋊C4×C43—21no—
287C22⋊C4×C43—21no—
288C22⋊C4×C43—21no—
289C22⋊C4×C43—21no—
290C22⋊C4×C43C2×Q812yes—
291C42×C43—81no—
292C22⋊Dic43—21no—
293C22⋊Dic43—21no—
294C22⋊Dic43—21no—
295C22⋊Dic43—21no—
296C22⋊Dic43—21no—
297C22⋊Dic43—21no—
298C22⋊Dic43—21no—
299C22⋊Dic43—21no—
300C22⋊Dic43—21no—
301C22⋊Dic43C2×Q812yes—
302(C2×D43)⋊C4—21no—
303(C2×D43)⋊C4—21no—
304(C2×D43)⋊C4—21no—
305(C2×D43)⋊C4—21no—
306(C2×D43)⋊C4—21no—
307(C2×D43)⋊C4—21no—
308C4⋊Dic43—21no—
309C4⋊Dic43—21no—
310C4⋊Dic43—21no—
311C4⋊Dic43—21no—
312C4⋊Dic43—81no—
313Dic43⋊C4—21no—
314Dic43⋊C4—21no—
315Dic43⋊C4—21no—
316Dic43⋊C4—21no—
317Dic43⋊C4—21no—
318Dic43⋊C4—21no—
319Dic43⋊C4—21no—
320Dic43⋊C4—21no—
321Dic43⋊C4—21no—
322Dic43⋊C4—21no—
323Dic43⋊C4—21no—
324Dic43⋊C4—21no—
325Dic43⋊C4—21no—
326Dic43⋊C4—21no—
327Dic43⋊C4—42no—
328Dic43⋊C4—42no—
329Dic43⋊C4—81no—
330Dic43⋊C4—81no—
331Dic43⋊C4C22⋊C411yescharacteristic
332Dic43⋊C4C22⋊C411yescharacteristic
333Dic43⋊C4C22⋊C411yescharacteristic
334Dic43⋊C4C22⋊C411yescharacteristic
335Dic43⋊C4C22⋊C411yescharacteristic
336Dic43⋊C4C22⋊C411yescharacteristic
337Dic43⋊C4C22⋊C411yescharacteristic
338Dic43⋊C4C22⋊C411yescharacteristic
339Dic43⋊C4C22⋊C411yescharacteristic
340Dic43⋊C4C22⋊C411yescharacteristic
341Dic43⋊C4C22⋊C411yescharacteristic
342Dic43⋊C4C22⋊C411yescharacteristic
343Dic43⋊C4C22⋊C411yescharacteristic
344Dic43⋊C4C22⋊C411yescharacteristic
345Dic43⋊C4C22⋊C411yescharacteristic
346Dic43⋊C4C22⋊C411yescharacteristic
347C4×Dic43—21no—
348C4×Dic43—21no—
349C4×Dic43—21no—
350C4×Dic43—21no—
351C4×Dic43—21no—
352C4×Dic43—21no—
353C4×Dic43—42no—
354C4×Dic43—42no—
355C4×Dic43—81no—
356C4×Dic43—81no—
357C4×Dic43—81no—
358C23×C43—41no—
359C23×C43—41no—
360C23×C43C23×C411yescharacteristic
361C23×C43C22×D411yescharacteristic
362C23×C43C22×D411yescharacteristic
363C23×C43C22×Q811yescharacteristic
364C23×C43C2×#4111yescharacteristic
365C23×C432−1+411yescharacteristic
366C23×C432−1+411yescharacteristic
367C22×D43—21no—
368C22×D43—21no—
369C22×D43—41no—
370C22×D43—41no—
371C22×D43C4×Q812yes—
372Q8×C43—81no—
373Q8×C43—81no—
374C2×C4×C43—21no—
375C2×C4×C43—21no—
376C2×C4×C43—21no—
377C2×C4×C43—21no—
378C2×C4×C43—22no—
379C2×C4×C43—41no—
380C2×C4×C43—41no—
381C2×C4×C43—41no—
382C2×C4×C43—41no—
383C2×C4×C43—41no—
384C2×C4×C43—41no—
385C2×C4×C43—41no—
386C2×C4×C43—41no—
387C2×C4×C43—41no—
388C2×C4×C43—41no—
389C2×C4×C43—41no—
390C2×C4×C43—41no—
391C2×C4×C43—41no—
392C2×C4×C43—41no—
393C2×C4×C43—41no—
394C2×C4×C43—41no—
395C2×C4×C43—41no—
396C2×C4×C43—41no—
397C2×C4×C43—41no—
398C2×C4×C43—41no—
399C2×C4×C43—41no—
400C2×C4×C43C2×C22⋊C411yescharacteristic
401C2×C4×C43C2×C22⋊C411yescharacteristic
402C2×C4×C43C2×C22⋊C411yescharacteristic
403C2×C4×C43C2×C22⋊C411yescharacteristic
404C22⋊D43—22no—
405C22⋊D43—22no—
406C22⋊D43—22no—
407C22⋊D43—22no—
408C2×Dic43—21no—
409C2×Dic43—21no—
410C2×Dic43—22no—
411C2×Dic43—22no—
412C2×Dic43—22no—
413C2×Dic43—21no—
414C2×Dic43—21no—
415C2×Dic43—22no—
416C2×Dic43—41no—
417C2×Dic43—41no—
418C2×Dic43—41no—
419C2×Dic43—41no—
420C2×Dic43—41no—
421C2×Dic43—41no—
422C2×Dic43—41no—
423C2×Dic43—41no—
424C2×Dic43—41no—
425C2×Dic43—41no—
426C2×Dic43—41no—
427C2×Dic43—41no—
428C2×Dic43—41no—
429C2×Dic43—41no—
430C2×Dic43—41no—
431C2×Dic43—41no—
432C2×Dic43—41no—
433C2×Dic43—41no—
434C2×Dic43—41no—
435C2×Dic43—41no—
436C2×Dic43—41no—
437C2×Dic43—41no—
438C2×Dic43C2×C22⋊C411yescharacteristic
439C2×Dic43C2×C22⋊C411yescharacteristic
440C2×Dic43C2×C22⋊C411yescharacteristic
441C2×Dic43C2×C22⋊C411yescharacteristic
442C2×Dic43C2×C22⋊C411yescharacteristic
443C2×Dic43C2×C22⋊C411yescharacteristic
444C2×Dic43C2×C22⋊C411yescharacteristic
445C2×Dic43C2×C22⋊C411yescharacteristic
446C2×Dic43C4×Q812yes—
447C4×D43—42no—
448C4×D43—42no—
449C4×D43—81no—
450C4×D43—81no—
451C4×D43—81no—
452C4×D43—81no—
453Dic86—42no—
454Dic86—42no—
455Dic86—81no—
456Dic86—81no—
457#22513—431nomaximal, Sylow
458C22×C43—21no—
459C22×C43—21no—
460C22×C43—21no—
461C22×C43—21no—
462C22×C43—21no—
463C22×C43—21no—
464C22×C43—41no—
465C22×C43—41no—
466C22×C43—41no—
467C22×C43—41no—
468C22×C43C22×C22⋊C411yescharacteristic
469C22×C43C2×C4×Q811yescharacteristic
470C22×C43#51911yescharacteristic
471C22×C43#54811yescharacteristic
472C22×C43#54811yescharacteristic
473C22×C43D4×Q811yescharacteristic
474C22×C43D4×Q811yescharacteristic
475C2×D43—22no—
476C2×D43—42no—
477C2×D43—41no—
478C2×D43—41no—
479C2×D43—42no—
480C4×C43—21no—
481C4×C43—21no—
482C4×C43—21no—
483C4×C43—21no—
484C4×C43—42no—
485C4×C43—41no—
486C4×C43—41no—
487C4×C43—41no—
488C4×C43—41no—
489C4×C43—81no—
490C4×C43—81no—
491C4×C43—81no—
492Dic43—22no—
493Dic43—21no—
494Dic43—21no—
495Dic43—21no—
496Dic43—21no—
497Dic43—21no—
498Dic43—21no—
499Dic43—21no—
500Dic43—42no—
501Dic43—41no—
502Dic43—41no—
503Dic43—81no—
504Dic43—81no—
505Dic43—81no—
506Dic43#41012yes—
507C2×#554—431no—
508#2345—431no—
509#2345—431no—
510#1996—431no—
511#1996—431no—
512#1996—431no—
513#1996—431no—
514#1996—431no—
515#1996D4311yescharacteristic, complemented
516#1799—431no—
517#1799—431no—
518#1799—431no—
519C4×#99—431no—
520C4×#99—431no—
521C4×#99—431no—
522C2×C43—21no—
523C2×C43—21no—
524C2×C43—21no—
525C2×C43—21no—
526C2×C43—21no—
527C2×C43—21no—
528C2×C43Q8×C22⋊C411yescharacteristic
529C2×C43C2×#41011yescharacteristic
530C2×C43#288311yescharacteristic
531D43—42no—
532#554—861no—
533#554—861no—
534#554—861no—
535#554—861no—
536#554—861no—
537#554—861no—
538#554—861no—
539#554—861no—
540C2×C4⋊Q8—431no—
541C2×#125—431no—
542C2×#125—431no—
543C2×C22⋊Q8—431no—
544C2×C22⋊Q8—431no—
545C2×C22⋊Q8—431no—
546C2×C22⋊Q8—431no—
547C2×C22⋊Q8—431no—
548C2×C22⋊Q8C2×D4311yescharacteristic
549C2×C4×Q8—431no—
550C2×C4×D4—431no—
551C2×C4×D4—431no—
552C2×C4×D4—431no—
553C22×C4⋊C4—431no—
554C22×C4⋊C4—431no—
555C2×#99—431no—
556C2×#99—431no—
557C2×#99—431no—
558C2×#99—431no—
559#389—861no—
560#389—861no—
561#387—861no—
562#387—861no—
563#387—861no—
564#387—861no—
565#380—431no—
566#380—431no—
567#380—431no—
568#380—431no—
569#380—431no—
570#380C2×D4311yescharacteristic
571C4×C4⋊C4—861no—
572C4×C4⋊C4—861no—
573C4×C22⋊C4—431no—
574C4×C22⋊C4—431no—
575C4×C22⋊C4—431no—
576C4×C22⋊C4—431no—
577C4×C22⋊C4—431no—
578C4×C22⋊C4C2×D4311yescharacteristic
579#342—431no—
580#342—431no—
581#342—431no—
582#342—431no—
583#342—431no—
584#342—431no—
585#342—431no—
586#342—431no—
587#342C2×D4311yescharacteristic
588#342C2×D4311yescharacteristic
589#342C2×D4311yescharacteristic
590#342C2×D4311yescharacteristic
591C43#2251311yescharacteristic, complemented, Sylow
592C22×Q8—431no—
593C22×Q8—431no—
594C22×Q8C4×D4311yescharacteristic
595C22×D4—431no—
596C23×C4—431no—
597C23×C4—431no—
598C23×C4—431no—
599C23×C4—431no—
600C23×C4—431no—
601C23×C4C22×D4311yescharacteristic
602C4⋊Q8—861no—
603C4⋊Q8—861no—
604C4⋊Q8—861no—
605C4⋊Q8—861no—
606#125—861no—
607#125—861no—
608#125—861no—
609#125—861no—
610#125—861no—
611#125—861no—
612#125—861no—
613#125—861no—
614C22⋊Q8—21no—
615C22⋊Q8—21no—
616C22⋊Q8—21no—
617C22⋊Q8—21no—
618C22⋊Q8—861no—
619C22⋊Q8—861no—
620C22⋊Q8—861no—
621C22⋊Q8—861no—
622C22⋊Q8—861no—
623C22⋊Q8—861no—
624C22⋊Q8—861no—
625C22⋊Q8—861no—
626C22⋊Q8—861no—
627C22⋊Q8—861no—
628C22⋊Q8—861no—
629C22⋊Q8—861no—
630C22⋊Q8—861no—
631C22⋊Q8—861no—
632C22⋊Q8—861no—
633C22⋊Q8—861no—
634C22⋊Q8—861no—
635C22⋊Q8—861no—
636C22⋊Q8—861no—
637C22⋊Q8—861no—
638C4×Q8—861no—
639C4×Q8—861no—
640C4×Q8—861no—
641C4×Q8—861no—
642C4×D4—861no—
643C4×D4—861no—
644C4×D4—861no—
645C4×D4—861no—
646C4×D4—861no—
647C4×D4—861no—
648C4×D4—861no—
649C4×D4—861no—
650C4×D4—861no—
651C4×D4—861no—
652C4×D4—861no—
653C4×D4—861no—
654C2×C4⋊C4—21no—
655C2×C4⋊C4—431no—
656C2×C4⋊C4—431no—
657C2×C4⋊C4—431no—
658C2×C4⋊C4—431no—
659C2×C4⋊C4—431no—
660C2×C4⋊C4—431no—
661C2×C4⋊C4—431no—
662C2×C4⋊C4—431no—
663C2×C4⋊C4—431no—
664C2×C4⋊C4—431no—
665C2×C4⋊C4—431no—
666C2×C4⋊C4—431no—
667C2×C4⋊C4—431no—
668C2×C4⋊C4—431no—
669C2×C4⋊C4—431no—
670C2×C4⋊C4—431no—
671C2×C4⋊C4—431no—
672C2×C4⋊C4—431no—
673C2×C4⋊C4—431no—
674C2×C4⋊C4—431no—
675C2×C4⋊C4—431no—
676C2×C4⋊C4—861no—
677C2×C4⋊C4—861no—
678C2×C4⋊C4—861no—
679C2×C4⋊C4—861no—
680C2×C4⋊C4—861no—
681C2×C4⋊C4—861no—
682C2×C4⋊C4—861no—
683C2×C4⋊C4—861no—
684C2×C4⋊C4—861no—
685C2×C4⋊C4C4×D4311yescharacteristic
686C2×C4⋊C4C4×D4311yescharacteristic
687C2×C4⋊C4C4×D4311yescharacteristic
688C2×C22⋊C4—431no—
689C2×C22⋊C4—431no—
690C2×C22⋊C4—431no—
691C2×C22⋊C4—431no—
692C2×C22⋊C4—431no—
693C2×C22⋊C4—431no—
694C2×C22⋊C4—431no—
695C2×C22⋊C4—431no—
696C2×C22⋊C4C22×D4311yescharacteristic
697C2×C22⋊C4C22×D4311yescharacteristic
698C2×C22⋊C4C22×D4311yescharacteristic
699C2×C22⋊C4C22×D4311yescharacteristic
700C2×C22⋊C4C22×D4311yescharacteristic
701C2×C22⋊C4C22×D4311yescharacteristic
702C2×C42—21no—
703C2×C42—431no—
704C2×C42—431no—
705C2×C42—431no—
706C2×C42—861no—
707C2×C42—861no—
708C2×C42—861no—
709C2×C42—861no—
710C2×C42—861no—
711#99—434no—
712#99—862no—
713#99—862no—
714#99—862no—
715#95—21no—
716#95—21no—
717#95—861no—
718#95—861no—
719#95—861no—
720#95—861no—
721#95—861no—
722#95—861no—
723#95—861no—
724#95—861no—
725#95—861no—
726#95—861no—
727C24—431no—
728C24C23×D4311yescharacteristic
729C2×Q8—21no—
730C2×Q8—21no—
731C2×Q8—81no—
732C2×Q8—861no—
733C2×Q8—861no—
734C2×Q8—861no—
735C2×Q8—861no—
736C2×Q8—3441no—
737C2×Q8—1722no—
738C2×D4—432no—
739C2×D4—432no—
740C2×D4—861no—
741C2×D4—861no—
742C2×D4—861no—
743C2×D4—861no—
744C22×C4—21no—
745C22×C4—21no—
746C22×C4—21no—
747C22×C4—21no—
748C22×C4—81no—
749C22×C4—431no—
750C22×C4—431no—
751C22×C4—431no—
752C22×C4—431no—
753C22×C4—431no—
754C22×C4—431no—
755C22×C4—431no—
756C22×C4—431no—
757C22×C4—431no—
758C22×C4—431no—
759C22×C4—431no—
760C22×C4—431no—
761C22×C4—431no—
762C22×C4—431no—
763C22×C4—431no—
764C22×C4—861no—
765C22×C4—861no—
766C22×C4—861no—
767C22×C4—861no—
768C22×C4—861no—
769C22×C4—861no—
770C22×C4—861no—
771C22×C4—861no—
772C22×C4—861no—
773C22×C4—861no—
774C22×C4—3441no—
775C22×C4—3441no—
776C22×C4—3441no—
777C22×C4—1722no—
778C22×C4—1722no—
779C22×C4C2×C4×D4311yescharacteristic
780C22×C4C2×C4×D4311yescharacteristic
781C22×C4C2×C4×D4311yescharacteristic
782C22×C4C2×C4×D4311yescharacteristic
783C22×C4C2×C4×D4311yescharacteristic
784C22×C4C2×C4×D4311yescharacteristic
785C22×C4D4×D4311yescharacteristic
786C22×C4D4×D4311yescharacteristic
787C22×C4D4×D4311yescharacteristic
788C22×C4D4×D4311yescharacteristic
789C4⋊C4—21no—
790C4⋊C4—21no—
791C4⋊C4—21no—
792C4⋊C4—21no—
793C4⋊C4—21no—
794C4⋊C4—21no—
795C4⋊C4—81no—
796C4⋊C4—431no—
797C4⋊C4—431no—
798C4⋊C4—431no—
799C4⋊C4—431no—
800C4⋊C4—431no—
801C4⋊C4—431no—
802C4⋊C4—431no—
803C4⋊C4—431no—
804C4⋊C4—431no—
805C4⋊C4—431no—
806C4⋊C4—431no—
807C4⋊C4—431no—
808C4⋊C4—431no—
809C4⋊C4—431no—
810C4⋊C4—431no—
811C4⋊C4—431no—
812C4⋊C4—861no—
813C4⋊C4—861no—
814C4⋊C4—861no—
815C4⋊C4—861no—
816C4⋊C4—861no—
817C4⋊C4—861no—
818C4⋊C4—861no—
819C4⋊C4—861no—
820C4⋊C4—861no—
821C4⋊C4—861no—
822C4⋊C4—861no—
823C4⋊C4—861no—
824C4⋊C4—861no—
825C4⋊C4—861no—
826C4⋊C4—861no—
827C4⋊C4—861no—
828C4⋊C4—861no—
829C4⋊C4—861no—
830C4⋊C4—3441no—
831C4⋊C4—3441no—
832C4⋊C4—3441no—
833C4⋊C4—1722no—
834C4⋊C4—1722no—
835C22⋊C4—21no—
836C22⋊C4—21no—
837C22⋊C4—21no—
838C22⋊C4—21no—
839C22⋊C4—21no—
840C22⋊C4—21no—
841C22⋊C4—21no—
842C22⋊C4—21no—
843C22⋊C4—21no—
844C22⋊C4—21no—
845C22⋊C4—21no—
846C22⋊C4—432no—
847C22⋊C4—861no—
848C22⋊C4—861no—
849C22⋊C4—861no—
850C22⋊C4—861no—
851C22⋊C4—861no—
852C22⋊C4—861no—
853C22⋊C4—861no—
854C22⋊C4—861no—
855C22⋊C4—861no—
856C22⋊C4—861no—
857C22⋊C4—861no—
858C22⋊C4—861no—
859C22⋊C4—861no—
860C22⋊C4—861no—
861C22⋊C4—861no—
862C22⋊C4Q8×D4312yes—
863C42—81no—
864C42—861no—
865C42—861no—
866C42—861no—
867C42—861no—
868C42—861no—
869C42—861no—
870C42—3441no—
871C42—3441no—
872C42—3441no—
873C42—1722no—
874C42—1722no—
875C23—41no—
876C23—41no—
877C23—432no—
878C23—861no—
879C23—861no—
880C23—1721no—
881C23—1721no—
882C23C22×C4×D4311yescharacteristic
883C23C2×D4×D4311yescharacteristic
884C23C2×D4×D4311yescharacteristic
885C23C2×Q8×D4311yescharacteristic
886C23#41×D4311yescharacteristic
887C23#1306337211yescharacteristic
888C23#1306337311yescharacteristic
889Q8—81no—
890Q8—81no—
891Q8—3441no—
892Q8—3441no—
893Q8—1722no—
894Q8—1722no—
895D4—862no—
896D4—862no—
897D4—862no—
898D4—862no—
899C2×C4—22no—
900C2×C4—21no—
901C2×C4—21no—
902C2×C4—21no—
903C2×C4—21no—
904C2×C4—41no—
905C2×C4—41no—
906C2×C4—41no—
907C2×C4—41no—
908C2×C4—41no—
909C2×C4—41no—
910C2×C4—41no—
911C2×C4—41no—
912C2×C4—41no—
913C2×C4—41no—
914C2×C4—41no—
915C2×C4—41no—
916C2×C4—41no—
917C2×C4—41no—
918C2×C4—41no—
919C2×C4—41no—
920C2×C4—41no—
921C2×C4—41no—
922C2×C4—41no—
923C2×C4—41no—
924C2×C4—41no—
925C2×C4—431no—
926C2×C4—431no—
927C2×C4—431no—
928C2×C4—431no—
929C2×C4—431no—
930C2×C4—431no—
931C2×C4—431no—
932C2×C4—431no—
933C2×C4—432no—
934C2×C4—862no—
935C2×C4—862no—
936C2×C4—862no—
937C2×C4—861no—
938C2×C4—861no—
939C2×C4—862no—
940C2×C4—861no—
941C2×C4—861no—
942C2×C4—3441no—
943C2×C4—3441no—
944C2×C4—3441no—
945C2×C4—3441no—
946C2×C4—1722no—
947C2×C4—1722no—
948C2×C4—1721no—
949C2×C4—1721no—
950C2×C4—1721no—
951C2×C4—1721no—
952C2×C4—1721no—
953C2×C4—1721no—
954C2×C4—1721no—
955C2×C4—1721no—
956C2×C4—1721no—
957C2×C4—1721no—
958C2×C4—1721no—
959C2×C4—1721no—
960C2×C4—1721no—
961C2×C4—1721no—
962C2×C4—1721no—
963C2×C4—1721no—
964C2×C4—1721no—
965C2×C4—1721no—
966C2×C4—1721no—
967C2×C4—1721no—
968C2×C4—1721no—
969C2×C4—1721no—
970C2×C4C22⋊C4×D4311yescharacteristic
971C2×C4C22⋊C4×D4311yescharacteristic
972C2×C4C22⋊C4×D4311yescharacteristic
973C2×C4C22⋊C4×D4311yescharacteristic
974C22—21no—
975C22—21no—
976C22—21no—
977C22—21no—
978C22—21no—
979C22—21no—
980C22—41no—
981C22—41no—
982C22—41no—
983C22—41no—
984C22—862no—
985C22—1722no—
986C22—1722no—
987C22—1721no—
988C22—1721no—
989C22C2×C22⋊C4×D4311yescharacteristic
990C22C4×Q8×D4311yescharacteristic
991C22#1458337511yescharacteristic
992C22#1458355711yescharacteristic
993C22#1458355911yescharacteristic
994C22#1458356211yescharacteristic
995C22#1458356411yescharacteristic
996C4—21no—
997C4—21no—
998C4—21no—
999C4—21no—
1000C4—42no—
1001C4—41no—
1002C4—41no—
1003C4—41no—
1004C4—41no—
1005C4—81no—
1006C4—81no—
1007C4—81no—
1008C4—432no—
1009C4—861no—
1010C4—861no—
1011C4—861no—
1012C4—861no—
1013C4—861no—
1014C4—861no—
1015C4—861no—
1016C4—862no—
1017C4—3441no—
1018C4—3441no—
1019C4—3441no—
1020C4—1722no—
1021C4—1721no—
1022C4—1721no—
1023C2—21no—
1024C2—21no—
1025C2—21no—
1026C2—21no—
1027C2—21no—
1028C2—21no—
1029C2—1722no—
1030C2#1913742911yescharacteristic
1031C2#410×D4311yescharacteristic
1032C2#1914305311yescharacteristic
subgroupG/H
centerC22C2×C22⋊C4×D43
commutatorC23×C43C23×C4
FrattiniC24C23×D43
FittingC43×#1996C2
socleC22×C43C22×C22⋊C4
prime radicalC22×C22⋊D43C23
cosocleC24×C43C24
hypercenter#1996D43
hypocenterC43#22513
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. #19137473C2semidirect
3. #19137467C2semidirect
4. #19135581C2semidirect
5. #19135578C2semidirect
6. #19135578C2semidirect
7. #19135578C2semidirect
8. #19135578C2semidirect
15. C43×#1996C2semidirect
24. C2×#13063323C4semidirect
25. C2×#13063315C4semidirect
26. C2×#13063315C4semidirect
27. C2×#13063303C4semidirect
28. C2×#13063303C4semidirect
31. C2×#13063301C4semidirect
32. C2×#13063290C4semidirect
37. C2×C4⋊C4×D43C4semidirect
180. #13063239Q8semidirect
515. #1996D43semidirect
591. C43#22513semidirect

Maximal subgroups

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

subgroupindex
C2×#145836032
#191374732
#191374672
#191355812
#191355782
#191345822
#191345802
C4×#130632392
#191343822
C43×#19962
#2251343