Finite Group Databasebeta

← #25101608

Subgroups — #25101608

Order 11008.

1184 conjugacy classes of subgroups.

The subgroup lattice has 800 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583427C211yesmaximal, characteristic
2C2×#14582855C211yesmaximal, characteristic, complemented
3#19135534C211yesmaximal, characteristic, complemented
4#19135530C211yesmaximal, characteristic, complemented
5#19135392C211yesmaximal, characteristic, complemented
6#19135388C211yesmaximal, characteristic, complemented
7#19134890C211yesmaximal, characteristic, complemented
8#19134890C211yesmaximal, characteristic, complemented
9#19134885C211yesmaximal, characteristic, complemented
10#19134885C211yesmaximal, characteristic, complemented
11#19134364C211yesmaximal, characteristic, complemented
12#19134362C211yesmaximal, characteristic, complemented
13#19134358C211yesmaximal, characteristic, complemented
14C4×(C2×D43)⋊C8C211yesmaximal, characteristic, complemented
15C2×C43×#433C211yesmaximal, characteristic, complemented
16C22×#10621877C2211yescharacteristic
17C23×C43⋊C8C2211yescharacteristic
18#14583427—24no—
19#14583427—24no—
20C2×#13063320C411yescharacteristic
21C2×#13063318C411yescharacteristic
22C2×#13063315C411yescharacteristic
23C2×#13063311C411yescharacteristic
24C2×#13063310C411yescharacteristic
25C2×#13063307C411yescharacteristic
26C2×#13063303C411yescharacteristic
27C2×#13063298C411yescharacteristic
28C2×C4×Dic86C2211yescharacteristic
29C2×C4×D172C2211yescharacteristic
30C2×C4×C22⋊D43C2211yescharacteristic
31C2×C4×C22⋊D43C2211yescharacteristic
32C2×#13063282C2211yescharacteristic
33C2×C42×D43C2211yescharacteristic
34C2×(C2×D43)⋊C8C2211yescharacteristic
35C2×(C2×D43)⋊C8C2211yescharacteristic
36C2×(C2×D43)⋊C8C2211yescharacteristic
37C2×(C2×D43)⋊C8C2211yescharacteristic
38C2×(C2×D43)⋊C8C2211yescharacteristic
39C2×(C2×D43)⋊C8C2211yescharacteristic
40C2×(C2×D43)⋊C8C2211yescharacteristic
41C2×(C2×D43)⋊C8C2211yescharacteristic
42#14582855—24no—
43C2×#13063236C2211yescharacteristic
44C2×#13063236C2211yescharacteristic
45C2×C4×C43⋊C8C2211yescharacteristic
46C2×C4×C43⋊C8C2211yescharacteristic
47#14582653C2211yescharacteristic
48#14582653C2211yescharacteristic
49#14582653C2211yescharacteristic
50#14582653C2211yescharacteristic
51#14582653C2211yescharacteristic
52#14582653C2211yescharacteristic
53#14582653C2211yescharacteristic
54#14582653C2211yescharacteristic
55C2×#117×C43C2211yescharacteristic
56C43×#433—24no—
57C2×C4⋊C8×C43C2211yescharacteristic
58C2×C4⋊C8×C43C2211yescharacteristic
59C2×C22⋊C8×C43C2211yescharacteristic
60C2×C22⋊C8×C43C2211yescharacteristic
61C2×#97×C43C2211yescharacteristic
62C2×C4×C8×C43C2211yescharacteristic
63C22×Dic86C2×C411yescharacteristic
64C22×D172C2×C411yescharacteristic
65C22×C22⋊D43C2×C411yescharacteristic
66C22×C22⋊D43C2×C411yescharacteristic
67C22×C4×D43C2×C411yescharacteristic
68C22×C4×D43C2×C411yescharacteristic
69C22×C4×D43C2311yescharacteristic
70C22×C4×D43C2311yescharacteristic
71C2×#10621877—22no—
72C2×#10621877—22no—
73C2×#10621877—22no—
74C22×C43⋊C8—22no—
75C22×C43⋊C8—22no—
76C22×C43⋊C8—22no—
77C22×C43⋊C8C2311yescharacteristic
78C22×C43⋊C8C2311yescharacteristic
79C22×C43⋊C8C2311yescharacteristic
80C22×C43⋊C8C2311yescharacteristic
81#13063320—24no—
82#13063318—24no—
83#13063315—24no—
84#13063311—24no—
85#13063310—24no—
86#13063307—24no—
87#13063303—24no—
88#13063298—24no—
89C4×Dic86—22no—
90C4×Dic86—22no—
91C4×D172—22no—
92C4×D172—22no—
93C4×C22⋊D43—22no—
94C4×C22⋊D43—22no—
95C4×C22⋊D43—22no—
96C4×C22⋊D43—22no—
97#13063282—22no—
98#13063282—22no—
99C2×C4⋊Dic43C2×C411yescharacteristic
100C2×C4⋊Dic43C2×C411yescharacteristic
101C2×Dic43⋊C4C2×C411yescharacteristic
102C2×Dic43⋊C4C2×C411yescharacteristic
103C2×Dic43⋊C4C2×C411yescharacteristic
104C2×Dic43⋊C4C2×C411yescharacteristic
105C2×Dic43⋊C4C2×C411yescharacteristic
106C2×Dic43⋊C4C2×C411yescharacteristic
107C2×C22⋊Dic43C2×C411yescharacteristic
108C2×C22⋊Dic43C2×C411yescharacteristic
109C2×(C2×D43)⋊C4C2×C411yescharacteristic
110C2×(C2×D43)⋊C4C2×C411yescharacteristic
111C2×(C2×D43)⋊C4C2×C411yescharacteristic
112C2×(C2×D43)⋊C4C2×C411yescharacteristic
113C2×(C2×D43)⋊C4C2×C411yescharacteristic
114C2×(C2×D43)⋊C4C2×C411yescharacteristic
115C2×C4×Dic43C2×C411yescharacteristic
116C2×C4×Dic43C2×C411yescharacteristic
117C2×C4×Dic43C2311yescharacteristic
118C2×C4×Dic43C2311yescharacteristic
119C42×D43—22no—
120C42×D43—22no—
121(C2×D43)⋊C8—22no—
122(C2×D43)⋊C8—22no—
123(C2×D43)⋊C8—22no—
124(C2×D43)⋊C8—22no—
125(C2×D43)⋊C8—22no—
126(C2×D43)⋊C8—22no—
127(C2×D43)⋊C8—22no—
128(C2×D43)⋊C8—22no—
129#13063236—22no—
130#13063236—22no—
131C4×C43⋊C8—22no—
132C4×C43⋊C8—22no—
133C23×C4×C43C2311yescharacteristic
134C22×C8×C43C2311yescharacteristic
135C22×C8×C43C2311yescharacteristic
136C22×C8×C43C2311yescharacteristic
137C22×C8×C43C2311yescharacteristic
138#117×C43D414yes—
139#117×C43D414yes—
140C2×C4⋊C4×C43C2×C411yescharacteristic
141C2×C4⋊C4×C43C2×C411yescharacteristic
142C2×C22⋊C4×C43C2×C411yescharacteristic
143C2×C22⋊C4×C43C2×C411yescharacteristic
144C2×C42×C43C2311yescharacteristic
145C2×C42×C43C2311yescharacteristic
146C4⋊C8×C43—22no—
147C4⋊C8×C43—22no—
148C22⋊C8×C43—22no—
149C22⋊C8×C43—22no—
150#97×C43—22no—
151C4×C8×C43—22no—
152C24×C43C22×C411yescharacteristic
153C23×D43C22×C411yescharacteristic
154C23×D43C22×C411yescharacteristic
155C22×C4×C43—21no—
156C22×C4×C43—21no—
157C22×C4×C43—21no—
158C22×C4×C43—21no—
159C22×C4×C43C22×C411yescharacteristic
160C22×C4×C43C22×C411yescharacteristic
161C22×C4×C43C22×C411yescharacteristic
162C22×C4×C43C22×C411yescharacteristic
163C22×C4×C43C22×C411yescharacteristic
164C22×C4×C43C2×D412yes—
165C22×C4×C43C2×D412yes—
166C22×C4×C43C2411yescharacteristic
167C2×C22⋊D43—22no—
168C2×C22⋊D43—22no—
169C2×C22⋊D43—22no—
170C2×C22⋊D43—22no—
171C2×C22⋊D43—41no—
172C2×C22⋊D43—41no—
173C22×Dic43C22×C411yescharacteristic
174C22×Dic43C22×C411yescharacteristic
175C22×Dic43C22×C411yescharacteristic
176C22×Dic43C22×C411yescharacteristic
177C22×Dic43C22×C411yescharacteristic
178C22×Dic43C22×C411yescharacteristic
179C2×D172—22no—
180C2×D172—22no—
181C2×D172—41no—
182C2×C4×D43—22no—
183C2×C4×D43—22no—
184C2×C4×D43—21no—
185C2×C4×D43—21no—
186C2×C4×D43—21no—
187C2×C4×D43—21no—
188C2×C4×D43—21no—
189C2×C4×D43—21no—
190C2×C4×D43—21no—
191C2×C4×D43—21no—
192C2×C4×D43—21no—
193C2×C4×D43—21no—
194C2×C4×D43—21no—
195C2×C4×D43—21no—
196C2×C4×D43—22no—
197C2×C4×D43—22no—
198C2×C4×D43—41no—
199C2×C4×D43—41no—
200C2×Dic86—22no—
201C2×Dic86—22no—
202C2×Dic86—41no—
203C2×C8×C43—21no—
204C2×C8×C43—21no—
205C2×C8×C43—21no—
206C2×C8×C43—21no—
207C2×C8×C43—21no—
208C2×C8×C43—21no—
209C2×C8×C43—21no—
210C2×C8×C43—21no—
211C2×C8×C43—21no—
212C2×C8×C43—21no—
213C2×C8×C43—21no—
214C2×C8×C43—21no—
215C4⋊C4×C43C22⋊C414yes—
216C4⋊C4×C43C22⋊C414yes—
217C22⋊C4×C43C22⋊C414yes—
218C22⋊C4×C43C22⋊C414yes—
219C42×C43C2×D412yes—
220C42×C43C2×D412yes—
221C42×C43C2×D412yes—
222C42×C43C2×D412yes—
223C22⋊Dic43—22no—
224C22⋊Dic43—22no—
225(C2×D43)⋊C4—22no—
226(C2×D43)⋊C4—22no—
227(C2×D43)⋊C4—22no—
228(C2×D43)⋊C4—22no—
229(C2×D43)⋊C4—22no—
230(C2×D43)⋊C4—22no—
231C4⋊Dic43—22no—
232C4⋊Dic43—22no—
233Dic43⋊C4—22no—
234Dic43⋊C4—22no—
235Dic43⋊C4—22no—
236Dic43⋊C4—22no—
237Dic43⋊C4—22no—
238Dic43⋊C4—22no—
239C4×Dic43—22no—
240C4×Dic43—22no—
241C4×Dic43—21no—
242C4×Dic43—21no—
243C4×Dic43—21no—
244C4×Dic43—21no—
245#10621877—28no—
246C2×C43⋊C8—28no—
247C2×C43⋊C8—21no—
248C2×C43⋊C8—21no—
249C2×C43⋊C8—21no—
250C2×C43⋊C8—21no—
251C2×C43⋊C8—21no—
252C2×C43⋊C8—21no—
253C2×C43⋊C8—21no—
254C2×C43⋊C8—21no—
255C2×C43⋊C8#4112yes—
256C2×C43⋊C8#4112yes—
257C2×C43⋊C8#4112yes—
258C2×C43⋊C8#4112yes—
259C23×C43—21no—
260C23×C43—21no—
261C23×C43—21no—
262C23×C43—21no—
263C23×C43—21no—
264C23×C43—21no—
265C23×C43C2×C22⋊C412yes—
266C23×C43C23×C411yescharacteristic
267C22×D43—21no—
268C22×D43—21no—
269C22×D43—21no—
270C22×D43—21no—
271C22×D43—21no—
272C22×D43—21no—
273C22×D43—21no—
274C22×D43—21no—
275C22×D43—21no—
276C22×D43—21no—
277C22×D43—21no—
278C22×D43—21no—
279C22×D43—21no—
280C22×D43#13112yes—
281C2×C4×C43—21no—
282C2×C4×C43—21no—
283C2×C4×C43—21no—
284C2×C4×C43—21no—
285C2×C4×C43—21no—
286C2×C4×C43—21no—
287C2×C4×C43—21no—
288C2×C4×C43—21no—
289C2×C4×C43—21no—
290C2×C4×C43—21no—
291C2×C4×C43—22no—
292C2×C4×C43—22no—
293C2×C4×C43—22no—
294C2×C4×C43—22no—
295C2×C4×C43C2×C22⋊C412yes—
296C2×C4×C43C2×C22⋊C412yes—
297C2×C4×C43C2×C22⋊C412yes—
298C2×C4×C43C2×C22⋊C412yes—
299C2×C4×C43C2×C22⋊C412yes—
300C2×C4×C43C22×D411yescharacteristic
301C2×C4×C43C22×D411yescharacteristic
302C2×C4×C43C2×#4111yescharacteristic
303C2×C4×C43C2×#4111yescharacteristic
304C2×C4×C43C2×#4111yescharacteristic
305C2×C4×C43C2×#4111yescharacteristic
306C22⋊D43—44no—
307C22⋊D43—44no—
308C2×Dic43—21no—
309C2×Dic43—21no—
310C2×Dic43—21no—
311C2×Dic43—21no—
312C2×Dic43—21no—
313C2×Dic43—21no—
314C2×Dic43—21no—
315C2×Dic43—21no—
316C2×Dic43—21no—
317C2×Dic43—21no—
318C2×Dic43—21no—
319C2×Dic43—21no—
320C2×Dic43—21no—
321C2×Dic43—21no—
322C2×Dic43—21no—
323C2×Dic43—21no—
324C2×Dic43—21no—
325C2×Dic43#13112yes—
326D172—44no—
327C4×D43—44no—
328C4×D43—44no—
329C4×D43—41no—
330C4×D43—41no—
331C4×D43—41no—
332C4×D43—41no—
333C4×D43—41no—
334C4×D43—41no—
335C4×D43—41no—
336C4×D43—41no—
337Dic86—44no—
338C8×C43—41no—
339C8×C43—41no—
340C8×C43—41no—
341C8×C43—41no—
342C43⋊C8—22no—
343C43⋊C8—22no—
344C43⋊C8—22no—
345C43⋊C8—22no—
346#21381—431nomaximal, Sylow
347C22×C43—22no—
348C22×C43—22no—
349C22×C43—22no—
350C22×C43—41no—
351C22×C43—41no—
352C22×C43—41no—
353C22×C43—41no—
354C22×C43C22×C22⋊C411yescharacteristic
355C22×C43C4×#4111yescharacteristic
356C22×C43C4×#4111yescharacteristic
357C22×C43C2×#13111yescharacteristic
358C22×C43C2×#13111yescharacteristic
359C22×C43#56811yescharacteristic
360C22×C43#56811yescharacteristic
361C2×D43—22no—
362C2×D43—22no—
363C2×D43—22no—
364C2×D43—41no—
365C2×D43—41no—
366C2×D43—41no—
367C2×D43—41no—
368C2×D43—41no—
369C2×D43—41no—
370C2×D43—41no—
371C2×D43—41no—
372C2×D43—41no—
373C2×D43—41no—
374C2×D43—41no—
375C4×C43—22no—
376C4×C43—22no—
377C4×C43—22no—
378C4×C43—22no—
379C4×C43—22no—
380C4×C43#52511yescharacteristic
381C4×C43#52511yescharacteristic
382C4×C43#53211yescharacteristic
383C4×C43#53211yescharacteristic
384Dic43—22no—
385Dic43—41no—
386Dic43—41no—
387Dic43—41no—
388Dic43—41no—
389Dic43—41no—
390C2×#529—431no—
391C2×#433D4311yescharacteristic, complemented
392C2×#405—431no—
393#1985—431no—
394#1984—431no—
395#1955—431no—
396#1954—431no—
397#1870—431no—
398#1870—431no—
399#1869—431no—
400#1869—431no—
401#1750—431no—
402#1750—431no—
403#1749—431no—
404C4×C22⋊C8—431no—
405C2×C43—42no—
406C2×C43#229711yescharacteristic
407C2×C43#288011yescharacteristic
408C2×C43#288011yescharacteristic
409C2×C43#296611yescharacteristic
410C2×C43#296711yescharacteristic
411C2×C43#296811yescharacteristic
412C2×C43#296911yescharacteristic
413D43—42no—
414D43—81no—
415C22×M16—431no—
416C23×C8—431no—
417#529—864no—
418#529—864no—
419C2×#126—431no—
420C2×#126—431no—
421C2×#125—431no—
422C2×#124—431no—
423C2×#123—431no—
424C2×#123—431no—
425C2×C22⋊Q8—431no—
426C2×#121—431no—
427C2×C4×Q8—431no—
428C2×C4×D4—431no—
429C2×C4×D4—431no—
430C2×C4×D4—431no—
431C2×#117—431no—
432C2×#117C2×D4311yescharacteristic
433C22×C42—431no—
434#433—24no—
435C2×C4⋊C8C2×D4311yescharacteristic
436C2×C4⋊C8C2×D4311yescharacteristic
437C2×C22⋊C8—431no—
438C2×C22⋊C8—431no—
439C2×C22⋊C8—431no—
440C2×C22⋊C8—431no—
441C2×C22⋊C8—431no—
442C2×C22⋊C8—431no—
443C2×C22⋊C8—431no—
444C2×C22⋊C8—431no—
445C2×C22⋊C8C2×D4311yescharacteristic
446C2×C22⋊C8C2×D4311yescharacteristic
447#405—864no—
448C2×#97—431no—
449C2×#97—431no—
450C2×#97C2×D4311yescharacteristic
451C2×C4×C8—431no—
452C2×C4×C8—431no—
453C2×C4×C8C2×D4311yescharacteristic
454#336—431no—
455#336—431no—
456#336—431no—
457#336—431no—
458#336—431no—
459#336—431no—
460#336—431no—
461#336—431no—
462C43#2138111yescharacteristic, complemented, Sylow
463C22×Q8—431no—
464C22×D4—431no—
465C22×D4—431no—
466C22×D4—431no—
467C23×C4—431no—
468C23×C4—431no—
469C23×C4—431no—
470C23×C4—431no—
471C23×C4C22×D4311yescharacteristic
472C2×M16—862no—
473C2×M16—862no—
474C2×M16—862no—
475C22×C8—431no—
476C22×C8—431no—
477C22×C8—431no—
478C22×C8—431no—
479C22×C8—862no—
480C22×C8—862no—
481C22×C8—862no—
482C22×C8C22×D4311yescharacteristic
483C22×C8C22×D4311yescharacteristic
484C22×C8C22×D4311yescharacteristic
485C22×C8C22×D4311yescharacteristic
486#126—864no—
487#126—864no—
488#125—864no—
489#124—864no—
490#123—864no—
491#123—864no—
492C22⋊Q8—864no—
493#121—864no—
494C4×Q8—862no—
495C4×Q8—862no—
496C4×D4—862no—
497C4×D4—862no—
498C4×D4—862no—
499C4×D4—862no—
500C4×D4—862no—
501C4×D4—862no—
502#117—862no—
503#117—862no—
504#117D17214yes—
505#117C22⋊D4314yes—
506C2×C4⋊C4—431no—
507C2×C4⋊C4—431no—
508C2×C4⋊C4—431no—
509C2×C4⋊C4—431no—
510C2×C4⋊C4—431no—
511C2×C4⋊C4—431no—
512C2×C4⋊C4—431no—
513C2×C4⋊C4—431no—
514C2×C4⋊C4C4×D4311yescharacteristic
515C2×C4⋊C4C4×D4311yescharacteristic
516C2×C22⋊C4—431no—
517C2×C22⋊C4—431no—
518C2×C22⋊C4—431no—
519C2×C22⋊C4—431no—
520C2×C22⋊C4—431no—
521C2×C22⋊C4—431no—
522C2×C22⋊C4—431no—
523C2×C22⋊C4—431no—
524C2×C22⋊C4C4×D4311yescharacteristic
525C2×C22⋊C4C4×D4311yescharacteristic
526C2×C42—431no—
527C2×C42—431no—
528C2×C42—431no—
529C2×C42—431no—
530C2×C42—862no—
531C2×C42—862no—
532C2×C42C22×D4311yescharacteristic
533C2×C42C22×D4311yescharacteristic
534C4⋊C8—22no—
535C4⋊C8—22no—
536C22⋊C8—22no—
537C22⋊C8—22no—
538C22⋊C8—862no—
539C22⋊C8—862no—
540C22⋊C8—862no—
541C22⋊C8—862no—
542C22⋊C8—862no—
543C22⋊C8—862no—
544C22⋊C8—862no—
545C22⋊C8—862no—
546#97—22no—
547#97—862no—
548#97—862no—
549C4×C8—22no—
550C4×C8—862no—
551C4×C8—862no—
552C24—431no—
553C24—431no—
554C24C2×C4×D4311yescharacteristic
555C2×Q8—862no—
556C2×Q8—862no—
557C2×Q8—1721no—
558C2×D4—862no—
559C2×D4—862no—
560C2×D4—862no—
561C2×D4—862no—
562C2×D4—862no—
563C2×D4—862no—
564C2×D4—1721no—
565C2×D4—1721no—
566C2×D4—1721no—
567C22×C4—21no—
568C22×C4—21no—
569C22×C4—21no—
570C22×C4—21no—
571C22×C4—431no—
572C22×C4—431no—
573C22×C4—431no—
574C22×C4—431no—
575C22×C4—431no—
576C22×C4—431no—
577C22×C4—862no—
578C22×C4—862no—
579C22×C4—862no—
580C22×C4—862no—
581C22×C4—861no—
582C22×C4—861no—
583C22×C4—861no—
584C22×C4—861no—
585C22×C4—861no—
586C22×C4—861no—
587C22×C4—861no—
588C22×C4—861no—
589C22×C4—861no—
590C22×C4—861no—
591C22×C4—861no—
592C22×C4—861no—
593C22×C4—1721no—
594C22×C4—1721no—
595C22×C4C2×C4×D4311yescharacteristic
596C22×C4C2×C4×D4311yescharacteristic
597C22×C4C2×C4×D4311yescharacteristic
598C22×C4C2×C4×D4311yescharacteristic
599C22×C4C2×C4×D4311yescharacteristic
600C22×C4C2×D17212yes—
601C22×C4C2×C22⋊D4312yes—
602C22×C4C23×D4311yescharacteristic
603M16—868no—
604C2×C8—21no—
605C2×C8—21no—
606C2×C8—21no—
607C2×C8—21no—
608C2×C8—21no—
609C2×C8—21no—
610C2×C8—21no—
611C2×C8—21no—
612C2×C8—21no—
613C2×C8—21no—
614C2×C8—21no—
615C2×C8—21no—
616C2×C8—432no—
617C2×C8—432no—
618C2×C8—432no—
619C2×C8—432no—
620C2×C8—868no—
621C2×C8—861no—
622C2×C8—861no—
623C2×C8—861no—
624C2×C8—861no—
625C2×C8—861no—
626C2×C8—861no—
627C2×C8—861no—
628C2×C8—861no—
629C4⋊C4—862no—
630C4⋊C4—862no—
631C4⋊C4—862no—
632C4⋊C4—862no—
633C4⋊C4—862no—
634C4⋊C4—862no—
635C4⋊C4—862no—
636C4⋊C4—862no—
637C4⋊C4(C2×D43)⋊C414yes—
638C4⋊C4(C2×D43)⋊C414yes—
639C22⋊C4—862no—
640C22⋊C4—862no—
641C22⋊C4—862no—
642C22⋊C4—862no—
643C22⋊C4—862no—
644C22⋊C4—862no—
645C22⋊C4—862no—
646C22⋊C4—862no—
647C22⋊C4(C2×D43)⋊C414yes—
648C22⋊C4(C2×D43)⋊C414yes—
649C42—862no—
650C42—862no—
651C42—861no—
652C42—861no—
653C42—861no—
654C42—861no—
655C42C2×D17212yes—
656C42C2×D17212yes—
657C42C2×C22⋊D4312yes—
658C42C2×C22⋊D4312yes—
659C23—21no—
660C23—21no—
661C23—21no—
662C23—21no—
663C23—21no—
664C23—21no—
665C23—432no—
666C23—861no—
667C23—861no—
668C23—861no—
669C23—861no—
670C23—861no—
671C23—861no—
672C23—861no—
673C23—861no—
674C23—861no—
675C23—861no—
676C23—861no—
677C23—861no—
678C23—861no—
679C23C2×(C2×D43)⋊C412yes—
680C23C22×C4×D4311yescharacteristic
681Q8—1724no—
682D4—1724no—
683D4—1724no—
684D4—1724no—
685C2×C4—21no—
686C2×C4—21no—
687C2×C4—21no—
688C2×C4—21no—
689C2×C4—21no—
690C2×C4—21no—
691C2×C4—21no—
692C2×C4—21no—
693C2×C4—21no—
694C2×C4—21no—
695C2×C4—22no—
696C2×C4—22no—
697C2×C4—22no—
698C2×C4—22no—
699C2×C4—432no—
700C2×C4—861no—
701C2×C4—861no—
702C2×C4—861no—
703C2×C4—861no—
704C2×C4—861no—
705C2×C4—861no—
706C2×C4—861no—
707C2×C4—861no—
708C2×C4—861no—
709C2×C4—861no—
710C2×C4—861no—
711C2×C4—861no—
712C2×C4—861no—
713C2×C4—861no—
714C2×C4—861no—
715C2×C4—861no—
716C2×C4—861no—
717C2×C4—1724no—
718C2×C4—1724no—
719C2×C4—1721no—
720C2×C4—1721no—
721C2×C4—1721no—
722C2×C4—1721no—
723C2×C4—1721no—
724C2×C4—1721no—
725C2×C4—1721no—
726C2×C4—1721no—
727C2×C4C2×(C2×D43)⋊C412yes—
728C2×C4C2×(C2×D43)⋊C412yes—
729C2×C4C2×(C2×D43)⋊C412yes—
730C2×C4C2×(C2×D43)⋊C412yes—
731C2×C4C2×(C2×D43)⋊C412yes—
732C2×C4C22×C22⋊D4311yescharacteristic
733C2×C4C22×D17211yescharacteristic
734C2×C4#41×D4311yescharacteristic
735C2×C4#41×D4311yescharacteristic
736C2×C4#41×D4311yescharacteristic
737C2×C4#41×D4311yescharacteristic
738C8—41no—
739C8—41no—
740C8—41no—
741C8—41no—
742C8—862no—
743C8—862no—
744C8—862no—
745C8—862no—
746C22—22no—
747C22—22no—
748C22—22no—
749C22—41no—
750C22—41no—
751C22—41no—
752C22—41no—
753C22—862no—
754C22—862no—
755C22—862no—
756C22—1721no—
757C22—1721no—
758C22—1721no—
759C22—1721no—
760C22—1721no—
761C22—1721no—
762C22—1721no—
763C22—1721no—
764C22—1721no—
765C22—1721no—
766C22—1721no—
767C22C22×(C2×D43)⋊C411yescharacteristic
768C22#1458336711yescharacteristic
769C22#1458336711yescharacteristic
770C22#131×D4311yescharacteristic
771C22#131×D4311yescharacteristic
772C22#1458366411yescharacteristic
773C22#1458366411yescharacteristic
774C4—22no—
775C4—22no—
776C4—22no—
777C4—22no—
778C4—22no—
779C4—862no—
780C4—1721no—
781C4—1721no—
782C4—1721no—
783C4—1721no—
784C4—1721no—
785C4#1458341111yescharacteristic
786C4#1458341111yescharacteristic
787C4#1458344511yescharacteristic
788C4#1458344511yescharacteristic
789C2—42no—
790C2—3441no—
791C2—1722no—
792C2#1913708311yescharacteristic
793C2#1914304211yescharacteristic
794C2#1914304211yescharacteristic
795C2#1914356811yescharacteristic
796C2#1914357811yescharacteristic
797C2#1914358711yescharacteristic
798C2#1914359711yescharacteristic
subgroupG/H
center, FrattiniC22×C4C23×D43
commutator, socleC23×C43C23×C4
FittingC2×C43×#433C2
prime radicalC2×#13063298C4
cosocleC22×C4×C43C24
hypercenterC2×#433D43
hypocenterC43#21381
LCSG ▷ C23×C43 ▷ C43
UCSC1 ◁ C22×C4 ◁ C2×#433

Complements

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

NH ≅ G/Ntype
2. C2×#14582855C2semidirect
3. #19135534C2semidirect
4. #19135530C2semidirect
5. #19135392C2semidirect
6. #19135388C2semidirect
7. #19134890C2semidirect
8. #19134890C2semidirect
9. #19134885C2semidirect
10. #19134885C2semidirect
11. #19134364C2semidirect
12. #19134362C2semidirect
13. #19134358C2semidirect
14. C4×(C2×D43)⋊C8C2semidirect
15. C2×C43×#433C2semidirect
391. C2×#433D43semidirect
462. C43#21381semidirect

Maximal subgroups

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

subgroupindex
C2×#145834272
C2×#145828552
#191355342
#191355302
#191353922
#191353882
#191348902
#191348852
#191343642
#191343622
#191343582
C4×(C2×D43)⋊C82
C2×C43×#4332
#2138143