Finite Group Databasebeta

← #25004179

Subgroups — #25004179

Order 11008.

818 conjugacy classes of subgroups.

The subgroup lattice has 598 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14582915C211yesmaximal, characteristic
2C2×#14582893C211yesmaximal, characteristic
3C2×#14582881C211yesmaximal, characteristic
4C2×#14582663C211yesmaximal, characteristic, complemented
5C2×#14582655C211yesmaximal, characteristic, complemented
6#19134293C211yesmaximal, characteristic, complemented
7C2×C43×#344C211yesmaximal, characteristic, complemented
8C22×#10621898C2211yescharacteristic
9C22×#10621877C2211yescharacteristic
10C23×C43⋊C8C2211yescharacteristic
11C2×#13063284C2211yescharacteristic
12#14582915—22no—
13#14582915—22no—
14C2×#13063251—22no—
15#14582893—22no—
16#14582893—22no—
17C2×#13063248—21no—
18C2×#13063245—21no—
19#14582881—22no—
20#14582881C414yescomplemented
21C2×#13063243—21no—
22C2×#13063241—21no—
23#14582663—22no—
24#14582655—22no—
25#14582653—22no—
26C22×M16×C43C2211yescharacteristic
27C22×M16×C43C2211yescharacteristic
28C2×#117×C43C2211yescharacteristic
29C43×#344—22no—
30C2×#10621898—21no—
31C2×#10621898—21no—
32C2×#10621898—21no—
33C2×#10621898—21no—
34C2×#10621898—21no—
35C2×#10621898—21no—
36C2×#10621898—21no—
37C2×#10621898—21no—
38C2×#10621898—21no—
39C2×#10621898—21no—
40C2×#10621898C2×C412yes—
41C2×#10621898D412yes—
42C22×Dic86D411yescharacteristic
43C22×D172D411yescharacteristic
44C22×C22⋊D43—21no—
45C22×C4×D43—21no—
46C2×#10621877—21no—
47C2×#10621877—21no—
48C2×#10621877—21no—
49C2×#10621877—21no—
50C2×#10621877—21no—
51C2×#10621877C2×C412yes—
52C22×C43⋊C8—21no—
53C22×C43⋊C8—21no—
54C22×C43⋊C8—21no—
55C22×C43⋊C8—21no—
56C22×C43⋊C8—21no—
57C22×C43⋊C8—21no—
58C22×C43⋊C8—21no—
59C22×C43⋊C8D412yes—
60#13063284—21no—
61#13063284—21no—
62#13063284—21no—
63#13063284—21no—
64C2×C4⋊Dic43—21no—
65C2×C22⋊Dic43—21no—
66C2×C4×Dic43D412yes—
67#13063251—28no—
68#13063248—24no—
69#13063245—24no—
70#13063243—24no—
71#13063241—24no—
72C23×C4×C43C2311yescharacteristic
73C2×M16×C43—21no—
74C2×M16×C43—21no—
75C2×M16×C43—21no—
76C2×M16×C43—21no—
77C2×M16×C43—21no—
78C2×M16×C43—21no—
79C2×M16×C43—21no—
80C2×M16×C43—21no—
81C2×M16×C43—21no—
82C2×M16×C43—21no—
83C2×M16×C43C2×C412yes—
84C2×M16×C43D412yes—
85C22×C8×C43—21no—
86C22×C8×C43—21no—
87#117×C43—21no—
88#117×C43—21no—
89#117×C43—21no—
90#117×C43D412yes—
91C2×C4⋊C4×C43—21no—
92C2×C22⋊C4×C43—21no—
93C2×C42×C43—21no—
94C24×C43#4111yescharacteristic
95C23×D43—21no—
96C22×C4×C43—41no—
97C22×C4×C43C22×C411yescharacteristic
98C22×C4×C43C2×D411yescharacteristic
99C22×C4×C43C2×D411yescharacteristic
100C22×C4×C43C2×D411yescharacteristic
101C22×C4×C43C2×D411yescharacteristic
102C22×C4×C43C2×D411yescharacteristic
103C22×C4×C43C2×D411yescharacteristic
104C22×C4×C43#4111yescharacteristic
105C22×C4×C43#4111yescharacteristic
106C22×C4×C43#4111yescharacteristic
107C22×C4×C43#4111yescharacteristic
108C22×C4×C43#4111yescharacteristic
109C22×C4×C43#4111yescharacteristic
110C22×C4×C43#4111yescharacteristic
111C2×C22⋊D43—22no—
112C2×C22⋊D43—22no—
113C2×C22⋊D43—41no—
114C2×C22⋊D43—41no—
115C2×C22⋊D43—41no—
116C2×C22⋊D43—41no—
117C22×Dic43—21no—
118C22×Dic43—22no—
119#10621898—22no—
120#10621898—22no—
121#10621898—22no—
122#10621898—22no—
123#10621898—22no—
124#10621898—22no—
125#10621898—22no—
126#10621898—22no—
127#10621898—41no—
128#10621898—41no—
129#10621898—41no—
130#10621898—41no—
131#10621898—41no—
132#10621898—41no—
133#10621898—41no—
134#10621898—41no—
135C2×D172—21no—
136C2×D172—21no—
137C2×D172—21no—
138C2×D172—21no—
139C2×D172—21no—
140C2×D172C22⋊C412yes—
141C2×C4×D43—22no—
142C2×C4×D43—22no—
143C2×C4×D43—41no—
144C2×C4×D43—41no—
145C2×C4×D43—41no—
146C2×C4×D43—41no—
147C2×Dic86—21no—
148C2×Dic86—21no—
149C2×Dic86—21no—
150C2×Dic86—21no—
151C2×Dic86—21no—
152C2×Dic86C22⋊C412yes—
153M16×C43—22no—
154M16×C43—22no—
155M16×C43—22no—
156M16×C43—22no—
157M16×C43—41no—
158M16×C43—41no—
159M16×C43—41no—
160M16×C43—41no—
161C2×C8×C43—22no—
162C2×C8×C43—22no—
163C2×C8×C43—41no—
164C2×C8×C43—41no—
165C2×C8×C43—41no—
166C2×C8×C43—41no—
167C4⋊C4×C43—22no—
168C4⋊C4×C43—41no—
169C22⋊C4×C43—22no—
170C22⋊C4×C43—41no—
171C42×C43—22no—
172C42×C43—41no—
173C22⋊Dic43—41no—
174C22⋊Dic43—41no—
175C4⋊Dic43—41no—
176C4⋊Dic43—41no—
177C4×Dic43—22no—
178C4×Dic43—22no—
179#10621877—22no—
180#10621877—22no—
181#10621877—41no—
182#10621877—41no—
183C2×C43⋊C8—22no—
184C2×C43⋊C8—22no—
185C2×C43⋊C8—22no—
186C2×C43⋊C8—22no—
187C2×C43⋊C8—41no—
188C2×C43⋊C8—41no—
189C2×C43⋊C8—41no—
190C2×C43⋊C8—41no—
191C2×C43⋊C8—41no—
192C2×C43⋊C8—41no—
193C23×C43—42no—
194C23×C43#11711yescharacteristic
195C23×C43#12111yescharacteristic
196C23×C43#12311yescharacteristic
197C23×C43#12311yescharacteristic
198C23×C43#12311yescharacteristic
199C23×C43#12411yescharacteristic
200C23×C43#12611yescharacteristic
201C22×D43—22no—
202C22×D43—41no—
203C22×D43—41no—
204C22×D43—82no—
205C2×C4×C43—42no—
206C2×C4×C43—82no—
207C2×C4×C43C2×C22⋊C411yescharacteristic
208C2×C4×C43#11711yescharacteristic
209C2×C4×C43C4×D411yescharacteristic
210C2×C4×C43C4×D411yescharacteristic
211C2×C4×C43C4×D411yescharacteristic
212C2×C4×C43C4×D411yescharacteristic
213C2×C4×C43#12011yescharacteristic
214C2×C4×C43#12011yescharacteristic
215C2×C4×C43#12111yescharacteristic
216C2×C4×C43#12111yescharacteristic
217C2×C4×C43#12111yescharacteristic
218C2×C4×C43#12111yescharacteristic
219C2×C4×C43#12111yescharacteristic
220C2×C4×C43#12111yescharacteristic
221C2×C4×C43#12111yescharacteristic
222C2×C4×C43#12311yescharacteristic
223C2×C4×C43#12311yescharacteristic
224C2×C4×C43#12311yescharacteristic
225C2×C4×C43#12311yescharacteristic
226C2×C4×C43#12311yescharacteristic
227C2×C4×C43#12311yescharacteristic
228C2×C4×C43#12311yescharacteristic
229C2×C4×C43#12411yescharacteristic
230C2×C4×C43#12411yescharacteristic
231C2×C4×C43#12411yescharacteristic
232C2×C4×C43#12611yescharacteristic
233C2×C4×C43#12611yescharacteristic
234C2×C4×C43#12611yescharacteristic
235C22⋊D43—42no—
236C22⋊D43—42no—
237C22⋊D43—42no—
238C22⋊D43—42no—
239C2×Dic43—22no—
240C2×Dic43—41no—
241C2×Dic43—41no—
242C2×Dic43—44no—
243C2×Dic43—42no—
244D172—22no—
245D172—22no—
246D172—41no—
247D172—41no—
248C4×D43—42no—
249C4×D43—42no—
250C4×D43—42no—
251C4×D43—42no—
252Dic86—22no—
253Dic86—22no—
254Dic86—41no—
255Dic86—41no—
256C8×C43—42no—
257C8×C43—42no—
258C43⋊C8—42no—
259C43⋊C8—42no—
260#11150—431nomaximal, Sylow
261C22×C43—22no—
262C22×C43—22no—
263C22×C43—22no—
264C22×C43—41no—
265C22×C43—41no—
266C22×C43—41no—
267C22×C43—41no—
268C22×C43#38111yescharacteristic
269C22×C43#38811yescharacteristic
270C22×C43#38811yescharacteristic
271C22×C43#39411yescharacteristic
272C22×C43#39411yescharacteristic
273C22×C43#39711yescharacteristic
274C22×C43#39711yescharacteristic
275C2×D43—42no—
276C2×D43—82no—
277C2×D43—82no—
278C2×D43—82no—
279C4×C43—82no—
280C4×C43#38611yescharacteristic
281C4×C43#38611yescharacteristic
282C4×C43#38811yescharacteristic
283C4×C43#38811yescharacteristic
284C4×C43#39411yescharacteristic
285C4×C43#39411yescharacteristic
286C4×C43#39711yescharacteristic
287C4×C43#39711yescharacteristic
288Dic43—42no—
289Dic43—82no—
290C2×#421—431no—
291C2×#416—431no—
292C2×#413—431no—
293C2×#344D4311yescharacteristic, complemented
294C2×#341—431no—
295C2×H(3,ℤ/4)—431no—
296#1729—431no—
297C2×C43—21no—
298C2×C43—21no—
299C2×C43—21no—
300C2×C43—21no—
301C2×C43—21no—
302C2×C43—21no—
303C2×C43#144011yescharacteristic
304C2×C43#208012yes—
305D43—82no—
306C22×#41—431no—
307C22×M16—431no—
308C22×M16C2×D4311yescharacteristic
309C22×M16C2×D4311yescharacteristic
310C23×C8—431no—
311C2×#117—431no—
312C2×#117C2×D4311yescharacteristic
313#421—862no—
314#421—862no—
315C2×#104—862no—
316#416—862no—
317#416—862no—
318C2×#103—861no—
319C2×#102—861no—
320#413—434no—
321#413—862no—
322C2×#101—861no—
323C2×#100—861no—
324#344—22no—
325#341—862no—
326H(3,ℤ/4)—862no—
327#336—862no—
328C43#1115011yescharacteristic, complemented, Sylow
329C2×#41—432no—
330C2×#41—432no—
331C2×#41—861no—
332C2×#41—861no—
333C2×#41—861no—
334C2×#41—861no—
335C2×#41—861no—
336C2×#41—861no—
337C2×#41—861no—
338C2×#41—861no—
339C2×#41—861no—
340C2×#41—861no—
341C22×Q8—431no—
342C22×D4—431no—
343C22×D4—861no—
344C23×C4—861no—
345C23×C4C22×D4311yescharacteristic
346C2×M16—21no—
347C2×M16—21no—
348C2×M16—21no—
349C2×M16—21no—
350C2×M16—21no—
351C2×M16—21no—
352C2×M16—21no—
353C2×M16—21no—
354C2×M16—21no—
355C2×M16—21no—
356C2×M16—432no—
357C2×M16—861no—
358C2×M16—861no—
359C2×M16—861no—
360C2×M16—861no—
361C2×M16—861no—
362C2×M16C4×D4312yes—
363C2×M16C22⋊D4312yes—
364C22×C8—21no—
365C22×C8—21no—
366C22×C8—432no—
367C22×C8—861no—
368C22×C8—861no—
369C22×C8—861no—
370C22×C8—861no—
371C22×C8—861no—
372C22×C8—861no—
373C22×C8—861no—
374#117—21no—
375#117—21no—
376#117—21no—
377#117—861no—
378#117—861no—
379#117—861no—
380#117—861no—
381#117D17212yes—
382C2×C4⋊C4—21no—
383C2×C4⋊C4—861no—
384C2×C22⋊C4—21no—
385C2×C22⋊C4—861no—
386C2×C42—21no—
387C2×C42—432no—
388#104—868no—
389#103—864no—
390#102—864no—
391#101—864no—
392#100—864no—
393C24—861no—
394C24#1062189811yescharacteristic
395#41—862no—
396#41—862no—
397#41—862no—
398#41—862no—
399#41—862no—
400#41—862no—
401#41—862no—
402#41—862no—
403#41—1721no—
404#41—1721no—
405#41—1721no—
406#41—1721no—
407#41—1721no—
408#41—1721no—
409#41—1721no—
410#41—1721no—
411C2×Q8—432no—
412C2×Q8—861no—
413C2×Q8—861no—
414C2×Q8—861no—
415C2×Q8—861no—
416C2×Q8—861no—
417C2×D4—432no—
418C2×D4—862no—
419C2×D4—862no—
420C2×D4—861no—
421C2×D4—861no—
422C2×D4—861no—
423C2×D4—861no—
424C2×D4—861no—
425C2×D4—1721no—
426C2×D4—1721no—
427C2×D4—1721no—
428C2×D4—1721no—
429C22×C4—41no—
430C22×C4—861no—
431C22×C4—862no—
432C22×C4—862no—
433C22×C4—862no—
434C22×C4—1721no—
435C22×C4—1721no—
436C22×C4—1721no—
437C22×C4—1721no—
438C22×C4C2×C4×D4311yescharacteristic
439C22×C4C2×D17211yescharacteristic
440C22×C4#1062189811yescharacteristic
441C22×C4#1062189811yescharacteristic
442C22×C4#1062189811yescharacteristic
443C22×C4D4×D4311yescharacteristic
444C22×C4D4×D4311yescharacteristic
445C22×C4D4×D4311yescharacteristic
446C22×C4D4×D4311yescharacteristic
447C22×C4#1062190011yescharacteristic
448C22×C4#1062190011yescharacteristic
449C22×C4#1062190211yescharacteristic
450C22×C4#1062190211yescharacteristic
451C22×C4C2×C22⋊D4311yescharacteristic
452M16—22no—
453M16—22no—
454M16—22no—
455M16—22no—
456M16—41no—
457M16—41no—
458M16—41no—
459M16—41no—
460M16—862no—
461M16—862no—
462M16—1721no—
463M16—1721no—
464C2×C8—22no—
465C2×C8—22no—
466C2×C8—41no—
467C2×C8—41no—
468C2×C8—41no—
469C2×C8—41no—
470C2×C8—862no—
471C2×C8—862no—
472C2×C8—862no—
473C2×C8—862no—
474C2×C8—1721no—
475C2×C8—1721no—
476C2×C8—1721no—
477C2×C8—1721no—
478C2×C8—1721no—
479C2×C8—1721no—
480C4⋊C4—22no—
481C4⋊C4—41no—
482C4⋊C4—1721no—
483C4⋊C4—1721no—
484C22⋊C4—22no—
485C22⋊C4—41no—
486C22⋊C4—1721no—
487C22⋊C4—1721no—
488C42—22no—
489C42—41no—
490C42—862no—
491C42—862no—
492C23—42no—
493C23—862no—
494C23—3442no—
495C23—1721no—
496C23—1721no—
497C23#1306328211yescharacteristic
498C23#1306329911yescharacteristic
499C23#1306330711yescharacteristic
500C23#1306331011yescharacteristic
501C23#1306331011yescharacteristic
502C23#1306331111yescharacteristic
503C23#1306331911yescharacteristic
504Q8—862no—
505Q8—862no—
506Q8—1721no—
507Q8—1721no—
508D4—862no—
509D4—862no—
510D4—1722no—
511D4—1722no—
512D4—1722no—
513D4—1722no—
514D4—1721no—
515D4—1721no—
516C2×C4—42no—
517C2×C4—82no—
518C2×C4—862no—
519C2×C4—1724no—
520C2×C4—1722no—
521C2×C4—1721no—
522C2×C4—1721no—
523C2×C4—1722no—
524C2×C4—1722no—
525C2×C4—1722no—
526C2×C4—1722no—
527C2×C4C22⋊C4×D4311yescharacteristic
528C2×C4#1306328311yescharacteristic
529C2×C4(C22⋊D43)⋊C411yescharacteristic
530C2×C4C4×C22⋊D4311yescharacteristic
531C2×C4#1306328711yescharacteristic
532C2×C4C4×D17211yescharacteristic
533C2×C4#1306329311yescharacteristic
534C2×C4#1306329511yescharacteristic
535C2×C4#1306329611yescharacteristic
536C2×C4#1306329711yescharacteristic
537C2×C4#1306329811yescharacteristic
538C2×C4#1306329811yescharacteristic
539C2×C4#1306329811yescharacteristic
540C2×C4#1306330011yescharacteristic
541C2×C4#1306330011yescharacteristic
542C2×C4#1306330711yescharacteristic
543C2×C4#1306330711yescharacteristic
544C2×C4#1306330811yescharacteristic
545C2×C4#1306330911yescharacteristic
546C2×C4#1306331011yescharacteristic
547C2×C4#1306331011yescharacteristic
548C2×C4#1306331011yescharacteristic
549C2×C4#1306331111yescharacteristic
550C2×C4#1306331311yescharacteristic
551C2×C4#1306331411yescharacteristic
552C2×C4#1306332011yescharacteristic
553C2×C4#1306332011yescharacteristic
554C2×C4#1306332011yescharacteristic
555C8—42no—
556C8—42no—
557C8—1722no—
558C8—1722no—
559C22—22no—
560C22—22no—
561C22—22no—
562C22—41no—
563C22—41no—
564C22—41no—
565C22—41no—
566C22—3442no—
567C22—3442no—
568C22—3442no—
569C22—1722no—
570C22#1458276111yescharacteristic
571C22#1458278811yescharacteristic
572C22#1458279011yescharacteristic
573C22#1458281511yescharacteristic
574C22#1458281611yescharacteristic
575C22#1458282811yescharacteristic
576C22#1458282811yescharacteristic
577C4—82no—
578C4—3442no—
579C4—1722no—
580C4#1458277511yescharacteristic
581C4#1458277711yescharacteristic
582C4#1458278911yescharacteristic
583C4#1458279111yescharacteristic
584C4#1458281411yescharacteristic
585C4#1458281711yescharacteristic
586C4#1458282511yescharacteristic
587C4#1458282611yescharacteristic
588C2—21no—
589C2—21no—
590C2—21no—
591C2—21no—
592C2—21no—
593C2—21no—
594C2—3442no—
595C2#1913284311yescharacteristic
596C2#1913605012yes—
subgroupG/H
centerC2×C4#13063311
commutatorC22×C4×C43C22×C4
FrattiniC23×C4C22×D43
FittingC2×C43×#344C2
socleC22×C43#397
prime radicalC22×#10621898C22
cosocleC23×C4×C43C23
hypercenterC2×#344D43
hypocenterC43#11150
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ C2×#344

Complements

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

NH ≅ G/Ntype
4. C2×#14582663C2semidirect
5. C2×#14582655C2semidirect
6. #19134293C2semidirect
7. C2×C43×#344C2semidirect
20. #14582881C4semidirect
293. C2×#344D43semidirect
328. C43#11150semidirect

Maximal subgroups

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

subgroupindex
C2×#145829152
C2×#145828932
C2×#145828812
C2×#145826632
C2×#145826552
#191342932
C2×C43×#3442
#1115043