Finite Group Databasebeta

← #25011554

Subgroups — #25011554

Order 11008.

768 conjugacy classes of subgroups.

The subgroup lattice has 606 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14582873C211yesmaximal, characteristic
2#19143040C211yesmaximal, characteristic
3#19132715C214yesmaximal, complemented
4C2×C43×#410C211yesmaximal, characteristic
5C22×#10621877C411yescharacteristic, complemented
6C22×#10621877C411yescharacteristic, complemented
7C2×#13063284—21no—
8#14582873—21no—
9#14582873—21no—
10#14582873C412yescomplemented
11#14582873C2212yes—
12C2×#13063240—21no—
13C2×#13063240C412yescomplemented
14#14582866—21no—
15#14582866—21no—
16#14582866C412yescomplemented
17#14582866C2212yes—
18#14582863—21no—
19#14582863—21no—
20C22×#41×C43C2211yescharacteristic
21C2×#117×C43—21no—
22C43×#410—21no—
23C43×#410—21no—
24C43×#410C412yescomplemented
25C43×#410C2212yes—
26C2×#99×C43—21no—
27C2×#99×C43C412yescomplemented
28C2×#10621877—21no—
29C2×#10621877—21no—
30C2×#10621877—21no—
31C2×#10621877—41no—
32C2×#10621877—41no—
33C2×#10621877—41no—
34C2×#10621877—41no—
35C2×#10621877C2×C412yescomplemented
36C22×C43⋊C8—21no—
37C22×C43⋊C8C2×C412yescomplemented
38#13063284—22no—
39#13063284—22no—
40#13063284—41no—
41#13063284—41no—
42C2×C4⋊Dic43—41no—
43C2×C22⋊Dic43—22no—
44C2×C4×Dic43—41no—
45#13063240—22no—
46#13063240—22no—
47#13063240—22no—
48#13063240C2×C414yescomplemented
49C22⋊(C43⋊C8)—22no—
50C22⋊(C43⋊C8)—22no—
51C22⋊(C43⋊C8)—22no—
52C22⋊(C43⋊C8)—22no—
53C2×#41×C43—41no—
54C2×#41×C43—41no—
55C2×#41×C43—41no—
56C2×#41×C43—41no—
57C2×#41×C43C2×C411yescharacteristic
58C2×#41×C43C2×C411yescharacteristic
59C2×#41×C43C2×C411yescharacteristic
60C2×#41×C43D411yescharacteristic
61C2×#41×C43D411yescharacteristic
62C2×#41×C43D411yescharacteristic
63C2×#41×C43Q811yescharacteristic
64C2×#41×C43C2311yescharacteristic
65C22×Q8×C43Q811yescharacteristic
66C22×D4×C43C2×C411yescharacteristic
67C22×D4×C43C2×C411yescharacteristic
68C22×D4×C43D411yescharacteristic
69C23×C4×C43C2×C411yescharacteristic
70C23×C4×C43D411yescharacteristic
71C23×C4×C43D411yescharacteristic
72#117×C43—22no—
73#117×C43—22no—
74#117×C43—41no—
75#117×C43—41no—
76C2×C4⋊C4×C43—41no—
77C2×C22⋊C4×C43—22no—
78C2×C42×C43—41no—
79#99×C43—22no—
80#99×C43—22no—
81#99×C43—22no—
82#99×C43C2×C414yescomplemented
83C24×C43C4211yescharacteristic
84C24×C43C22⋊C411yescharacteristic
85C24×C43C22⋊C411yescharacteristic
86#41×C43—41no—
87#41×C43—41no—
88#41×C43—41no—
89#41×C43—41no—
90#41×C43—41no—
91#41×C43—41no—
92#41×C43—41no—
93#41×C43—41no—
94#41×C43—41no—
95#41×C43—41no—
96#41×C43—41no—
97#41×C43—41no—
98#41×C43—41no—
99#41×C43—41no—
100#41×C43—41no—
101#41×C43—41no—
102C2×Q8×C43—41no—
103C2×Q8×C43—41no—
104C2×Q8×C43C4⋊C411yescharacteristic
105C2×Q8×C43C4⋊C411yescharacteristic
106C2×Q8×C43C4⋊C411yescharacteristic
107C2×Q8×C43C2×Q811yescharacteristic
108C2×D4×C43—41no—
109C2×D4×C43—41no—
110C2×D4×C43—41no—
111C2×D4×C43—41no—
112C2×D4×C43—41no—
113C2×D4×C43—41no—
114C2×D4×C43C4211yescharacteristic
115C2×D4×C43C4211yescharacteristic
116C2×D4×C43C22⋊C411yescharacteristic
117C2×D4×C43C22⋊C411yescharacteristic
118C2×D4×C43C22⋊C411yescharacteristic
119C2×D4×C43C22⋊C411yescharacteristic
120C2×D4×C43C4⋊C411yescharacteristic
121C2×D4×C43C4⋊C411yescharacteristic
122C2×D4×C43C4⋊C411yescharacteristic
123C2×D4×C43C22×C411yescharacteristic
124C2×D4×C43C22×C411yescharacteristic
125C2×D4×C43C2×D411yescharacteristic
126C22×C4×C43—21no—
127C22×C4×C43—21no—
128C22×C4×C43—21no—
129C22×C4×C43—21no—
130C22×C4×C43—21no—
131C22×C4×C43—21no—
132C22×C4×C43—21no—
133C22×C4×C43—21no—
134C22×C4×C43—21no—
135C22×C4×C43—21no—
136C22×C4×C43—21no—
137C22×C4×C43—21no—
138C22×C4×C43—42no—
139C22×C4×C43C4211yescharacteristic
140C22×C4×C43C22⋊C411yescharacteristic
141C22×C4×C43C22⋊C411yescharacteristic
142C22×C4×C43C22⋊C411yescharacteristic
143C22×C4×C43C22⋊C411yescharacteristic
144C22×C4×C43C22⋊C411yescharacteristic
145C22×C4×C43C22⋊C411yescharacteristic
146C22×C4×C43C4⋊C411yescharacteristic
147C22×C4×C43C4⋊C411yescharacteristic
148C22×C4×C43C4⋊C411yescharacteristic
149C22×C4×C43C4⋊C411yescharacteristic
150C22×C4×C43C4⋊C411yescharacteristic
151C22×C4×C43C4⋊C411yescharacteristic
152C22×C4×C43C22×C411yescharacteristic
153C22×C4×C43C2×D411yescharacteristic
154C22×C4×C43C2×D411yescharacteristic
155C22×Dic43—42no—
156C4⋊C4×C43—42no—
157C4⋊C4×C43—42no—
158C22⋊C4×C43—24no—
159C22⋊C4×C43—42no—
160C42×C43—42no—
161C42×C43—42no—
162C22⋊Dic43—24no—
163C22⋊Dic43—42no—
164C4⋊Dic43—42no—
165C4⋊Dic43—42no—
166C4×Dic43—42no—
167C4×Dic43—42no—
168#10621877—42no—
169#10621877—41no—
170#10621877—41no—
171#10621877—41no—
172#10621877—41no—
173#10621877—42no—
174C2×C43⋊C8—22no—
175C2×C43⋊C8—22no—
176C2×C43⋊C8—42no—
177C2×C43⋊C8—42no—
178C23×C43—21no—
179C23×C43—21no—
180C23×C43—21no—
181C23×C43—21no—
182C23×C43—21no—
183C23×C43—21no—
184C23×C43—81no—
185C23×C43—81no—
186C23×C43—81no—
187C23×C43#9511yescharacteristic
188C23×C43#9511yescharacteristic
189C23×C43#9511yescharacteristic
190C23×C43#9511yescharacteristic
191C23×C43C2×C4211yescharacteristic
192C23×C43C2×C22⋊C411yescharacteristic
193C23×C43C2×C22⋊C411yescharacteristic
194Q8×C43—41no—
195Q8×C43—41no—
196Q8×C43—41no—
197Q8×C43—41no—
198D4×C43—41no—
199D4×C43—41no—
200D4×C43—41no—
201D4×C43—41no—
202D4×C43—41no—
203D4×C43—41no—
204D4×C43—41no—
205D4×C43—41no—
206D4×C43—41no—
207D4×C43—41no—
208D4×C43—41no—
209D4×C43—41no—
210C2×C4×C43—21no—
211C2×C4×C43—21no—
212C2×C4×C43—21no—
213C2×C4×C43—21no—
214C2×C4×C43—21no—
215C2×C4×C43—21no—
216C2×C4×C43—21no—
217C2×C4×C43—21no—
218C2×C4×C43—21no—
219C2×C4×C43—21no—
220C2×C4×C43—21no—
221C2×C4×C43—21no—
222C2×C4×C43—21no—
223C2×C4×C43—21no—
224C2×C4×C43—21no—
225C2×C4×C43—21no—
226C2×C4×C43—21no—
227C2×C4×C43—21no—
228C2×C4×C43—21no—
229C2×C4×C43—21no—
230C2×C4×C43—21no—
231C2×C4×C43—21no—
232C2×C4×C43—21no—
233C2×C4×C43—21no—
234C2×C4×C43—21no—
235C2×C4×C43—21no—
236C2×C4×C43—21no—
237C2×C4×C43—21no—
238C2×C4×C43—21no—
239C2×C4×C43—21no—
240C2×C4×C43—44no—
241C2×C4×C43—84no—
242C2×C4×C43#9511yescharacteristic
243C2×C4×C43#9511yescharacteristic
244C2×C4×C43#9511yescharacteristic
245C2×C4×C43#9511yescharacteristic
246C2×C4×C43#9911yescharacteristic
247C2×C4×C43#9911yescharacteristic
248C2×C4×C43#9911yescharacteristic
249C2×C4×C43#9911yescharacteristic
250C2×C4×C43C2×C22⋊C411yescharacteristic
251C2×C4×C43C2×C4⋊C411yescharacteristic
252C2×C4×C43C2×C4⋊C411yescharacteristic
253C2×C4×C43C2×C4⋊C411yescharacteristic
254C2×Dic43—44no—
255C2×Dic43—84no—
256C43⋊C8—42no—
257C43⋊C8—42no—
258#12577—431nomaximal, Sylow
259C22×C43—21no—
260C22×C43—21no—
261C22×C43—21no—
262C22×C43—21no—
263C22×C43—21no—
264C22×C43—21no—
265C22×C43—41no—
266C22×C43—41no—
267C22×C43—41no—
268C22×C43—41no—
269C22×C43—41no—
270C22×C43—41no—
271C22×C43—41no—
272C22×C43—42no—
273C22×C43—42no—
274C22×C43—81no—
275C22×C43—81no—
276C22×C43—81no—
277C22×C43—81no—
278C22×C43#34211yescharacteristic
279C22×C43#34211yescharacteristic
280C22×C43C2×#9511yescharacteristic
281C4×C43—21no—
282C4×C43—21no—
283C4×C43—21no—
284C4×C43—21no—
285C4×C43—21no—
286C4×C43—21no—
287C4×C43—84no—
288C4×C43#34211yescharacteristic
289C4×C43#34211yescharacteristic
290C4×C43C2×#9911yescharacteristic
291C4×C43C2×#9911yescharacteristic
292Dic43—84no—
293C2×#410—431no—
294C2×#410D4311yescharacteristic
295#2879—431no—
296#1391—434no—
297C2×C43—21no—
298C2×C43—21no—
299C2×C43—21no—
300C2×C43—41no—
301C2×C43—41no—
302C2×C43—41no—
303C2×C43—41no—
304C2×C43—41no—
305C2×C43—41no—
306C2×C43C2×#34211yescharacteristic
307C22×#41C2×D4311yescharacteristic
308C22×M16—431no—
309C22×M16—431no—
310C2×#117—21no—
311C2×#117—861no—
312#410—21no—
313#410—21no—
314#410—432no—
315#410—432no—
316#410—861no—
317#410—861no—
318#410Dic4312yescomplemented
319#410C2×D4312yes—
320C2×#99—21no—
321C2×#99—432no—
322C2×#99—861no—
323C2×#99Dic4312yescomplemented
324#408—432no—
325#408—432no—
326#408—861no—
327#408—861no—
328#407—861no—
329#407—861no—
330C43#1257711yescharacteristic, complemented, Sylow
331C2×#41—41no—
332C2×#41—41no—
333C2×#41—41no—
334C2×#41—41no—
335C2×#41Dic8611yescharacteristic
336C2×#41C4×D4311yescharacteristic
337C2×#41C4×D4311yescharacteristic
338C2×#41D17211yescharacteristic
339C2×#41C2×Dic4311yescharacteristic
340C2×#41C22⋊D4311yescharacteristic
341C2×#41C22⋊D4311yescharacteristic
342C2×#41C22×D4311yescharacteristic
343C22×Q8Dic8611yescharacteristic
344C22×D4C4×D4311yescharacteristic
345C22×D4C2×Dic4311yescharacteristic
346C22×D4C22⋊D4311yescharacteristic
347C23×C4C4×D4311yescharacteristic
348C23×C4D17211yescharacteristic
349C23×C4C22⋊D4311yescharacteristic
350C2×M16—432no—
351C2×M16—861no—
352C2×M16—861no—
353C2×M16—861no—
354C2×M16—1721no—
355C2×M16—1721no—
356C2×M16—1721no—
357C2×M16—1721no—
358C22×C8—432no—
359C22×C8—861no—
360#117—22no—
361#117—22no—
362#117—41no—
363#117—41no—
364#117—862no—
365#117—862no—
366#117—1721no—
367#117—1721no—
368C2×C4⋊C4—41no—
369C2×C4⋊C4—1721no—
370C2×C22⋊C4—22no—
371C2×C22⋊C4—862no—
372C2×C42—41no—
373C2×C42—1721no—
374#99—22no—
375#99—22no—
376#99—22no—
377#99—434no—
378#99—862no—
379#99—862no—
380#99—862no—
381#99C2×Dic4314yescomplemented
382C22⋊C8—862no—
383C22⋊C8—862no—
384C22⋊C8—862no—
385C22⋊C8—862no—
386C24C4×Dic4311yescharacteristic
387C24(C2×D43)⋊C411yescharacteristic
388C24C22⋊Dic4311yescharacteristic
389#41—41no—
390#41—41no—
391#41—41no—
392#41—41no—
393#41—41no—
394#41—41no—
395#41—41no—
396#41—41no—
397#41—41no—
398#41—41no—
399#41—41no—
400#41—41no—
401#41—41no—
402#41—41no—
403#41—41no—
404#41—41no—
405C2×Q8—41no—
406C2×Q8—41no—
407C2×Q8Dic43⋊C411yescharacteristic
408C2×Q8Dic43⋊C411yescharacteristic
409C2×Q8C4⋊Dic4311yescharacteristic
410C2×Q8C2×Dic8611yescharacteristic
411C2×D4—41no—
412C2×D4—41no—
413C2×D4—41no—
414C2×D4—41no—
415C2×D4—41no—
416C2×D4—41no—
417C2×D4C4×Dic4311yescharacteristic
418C2×D4C4×Dic4311yescharacteristic
419C2×D4Dic43⋊C411yescharacteristic
420C2×D4Dic43⋊C411yescharacteristic
421C2×D4C4⋊Dic4311yescharacteristic
422C2×D4(C2×D43)⋊C411yescharacteristic
423C2×D4(C2×D43)⋊C411yescharacteristic
424C2×D4C22⋊Dic4311yescharacteristic
425C2×D4C22⋊Dic4311yescharacteristic
426C2×D4C2×C4×D4311yescharacteristic
427C2×D4C22×Dic4311yescharacteristic
428C2×D4C2×C22⋊D4311yescharacteristic
429C22×C4—21no—
430C22×C4—21no—
431C22×C4—21no—
432C22×C4—21no—
433C22×C4—21no—
434C22×C4—21no—
435C22×C4—21no—
436C22×C4—21no—
437C22×C4—21no—
438C22×C4—21no—
439C22×C4—21no—
440C22×C4—21no—
441C22×C4—42no—
442C22×C4—1722no—
443C22×C4C4×Dic4311yescharacteristic
444C22×C4Dic43⋊C411yescharacteristic
445C22×C4Dic43⋊C411yescharacteristic
446C22×C4Dic43⋊C411yescharacteristic
447C22×C4Dic43⋊C411yescharacteristic
448C22×C4C4⋊Dic4311yescharacteristic
449C22×C4C4⋊Dic4311yescharacteristic
450C22×C4(C2×D43)⋊C411yescharacteristic
451C22×C4(C2×D43)⋊C411yescharacteristic
452C22×C4(C2×D43)⋊C411yescharacteristic
453C22×C4(C2×D43)⋊C411yescharacteristic
454C22×C4(C2×D43)⋊C411yescharacteristic
455C22×C4C22⋊Dic4311yescharacteristic
456C22×C4C2×C4×D4311yescharacteristic
457C22×C4C2×D17211yescharacteristic
458C22×C4C2×C22⋊D4311yescharacteristic
459M16—1722no—
460M16—1721no—
461M16—1721no—
462M16—1721no—
463M16—1721no—
464M16—1722no—
465C2×C8—862no—
466C2×C8—862no—
467C2×C8—1722no—
468C2×C8—1722no—
469C4⋊C4—42no—
470C4⋊C4—42no—
471C4⋊C4—1722no—
472C4⋊C4—1722no—
473C22⋊C4—24no—
474C22⋊C4—42no—
475C22⋊C4—864no—
476C22⋊C4—1722no—
477C42—42no—
478C42—42no—
479C42—1722no—
480C42—1722no—
481C23—21no—
482C23—21no—
483C23—21no—
484C23—21no—
485C23—21no—
486C23—21no—
487C23—81no—
488C23—81no—
489C23—81no—
490C23C43⋊#9511yescharacteristic
491C23C43⋊#9511yescharacteristic
492C23C43⋊#9511yescharacteristic
493C23C43⋊#9511yescharacteristic
494C23C2×C4×Dic4311yescharacteristic
495C23C2×(C2×D43)⋊C411yescharacteristic
496C23C2×C22⋊Dic4311yescharacteristic
497Q8—41no—
498Q8—41no—
499Q8—41no—
500Q8—41no—
501D4—41no—
502D4—41no—
503D4—41no—
504D4—41no—
505D4—41no—
506D4—41no—
507D4—41no—
508D4—41no—
509D4—41no—
510D4—41no—
511D4—41no—
512D4—41no—
513C2×C4—21no—
514C2×C4—21no—
515C2×C4—21no—
516C2×C4—21no—
517C2×C4—21no—
518C2×C4—21no—
519C2×C4—21no—
520C2×C4—21no—
521C2×C4—21no—
522C2×C4—21no—
523C2×C4—21no—
524C2×C4—21no—
525C2×C4—21no—
526C2×C4—21no—
527C2×C4—21no—
528C2×C4—21no—
529C2×C4—21no—
530C2×C4—21no—
531C2×C4—21no—
532C2×C4—21no—
533C2×C4—21no—
534C2×C4—21no—
535C2×C4—21no—
536C2×C4—21no—
537C2×C4—21no—
538C2×C4—21no—
539C2×C4—21no—
540C2×C4—21no—
541C2×C4—21no—
542C2×C4—21no—
543C2×C4—44no—
544C2×C4—84no—
545C2×C4—3444no—
546C2×C4—1724no—
547C2×C4C43⋊#9511yescharacteristic
548C2×C4C43⋊#9511yescharacteristic
549C2×C4C43⋊#9511yescharacteristic
550C2×C4C43⋊#9511yescharacteristic
551C2×C4#1306323911yescharacteristic
552C2×C4#1306323911yescharacteristic
553C2×C4#1306323911yescharacteristic
554C2×C4#1306323911yescharacteristic
555C2×C4C2×(C2×D43)⋊C411yescharacteristic
556C2×C4C2×Dic43⋊C411yescharacteristic
557C2×C4C2×Dic43⋊C411yescharacteristic
558C2×C4C2×C4⋊Dic4311yescharacteristic
559C8—1722no—
560C8—1722no—
561C22—21no—
562C22—21no—
563C22—21no—
564C22—21no—
565C22—21no—
566C22—21no—
567C22—41no—
568C22—41no—
569C22—41no—
570C22—41no—
571C22—41no—
572C22—41no—
573C22—41no—
574C22—42no—
575C22—42no—
576C22—81no—
577C22—81no—
578C22—81no—
579C22—81no—
580C22#1458266511yescharacteristic
581C22#1458266511yescharacteristic
582C22C2×C43⋊#9511yescharacteristic
583C4—21no—
584C4—21no—
585C4—21no—
586C4—21no—
587C4—21no—
588C4—21no—
589C4—84no—
590C4—3444no—
591C4#1458266511yescharacteristic
592C4#1458266511yescharacteristic
593C4C2×#1306323911yescharacteristic
594C4C2×#1306323911yescharacteristic
595C2—21no—
596C2—21no—
597C2—21no—
598C2—41no—
599C2—41no—
600C2—41no—
601C2—41no—
602C2—41no—
603C2—41no—
604C2C2×#1458266511yescharacteristic
subgroupG/H
centerC4C2×#13063239
commutatorC23×C43C2×C42
FrattiniC2×#41C22×D43
FittingC2×C43×#410C2
socleC2×C43C2×#342
prime radicalC22×#41×C43C22
cosocleC2×#41×C43C23
hypercenterC2×#410D43
hypocenterC43#12577
LCSG ▷ C23×C43 ▷ C22×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C4 ◁ C22×C4 ◁ C22×#41 ◁ C2×#410

Complements

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

NH ≅ G/Ntype
3. #19132715C2semidirect
5. C22×#10621877C4semidirect
6. C22×#10621877C4semidirect
10. #14582873C4semidirect
13. C2×#13063240C4semidirect
16. #14582866C4semidirect
24. C43×#410C4semidirect
27. C2×#99×C43C4semidirect
35. C2×#10621877C2×C4semidirect
37. C22×C43⋊C8C2×C4semidirect
48. #13063240C2×C4semidirect
82. #99×C43C2×C4semidirect
318. #410Dic43semidirect
323. C2×#99Dic43semidirect
330. C43#12577semidirect
381. #99C2×Dic43semidirect

Maximal subgroups

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

subgroupindex
C2×#145828732
#191430402
#191327152
C2×C43×#4102
#1257743