Finite Group Databasebeta

← #25004236

Subgroups — #25004236

Order 11008.

804 conjugacy classes of subgroups.

The subgroup lattice has 594 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14582917C211yesmaximal, characteristic
2C2×#14582915C211yesmaximal, characteristic
3C2×#14582881C211yesmaximal, characteristic
4#19134333C211yesmaximal, characteristic, complemented
5#19134304C211yesmaximal, characteristic, complemented
6C2×C43⋊#338C211yesmaximal, characteristic, complemented
7C2×C43×#344C211yesmaximal, characteristic, complemented
8C22×#10621898C2211yescharacteristic
9C22×#10621877C2211yescharacteristic
10C22×#10621877C2211yescharacteristic
11C2×#13063284C2211yescharacteristic
12#14582917—22no—
13#14582917—22no—
14#14582915—22no—
15#14582915—22no—
16C2×#13063253—22no—
17C2×#13063251—22no—
18#14582881—22no—
19#14582881—22no—
20C2×#13063243C412yescomplemented
21C2×#13063241C412yescomplemented
22#14582667—22no—
23#14582658—22no—
24C43⋊#338—22no—
25C22×M16×C43C2211yescharacteristic
26C22×M16×C43C2211yescharacteristic
27C2×#117×C43C2211yescharacteristic
28C43×#344—22no—
29C2×#10621898—21no—
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×#10621898D412yes—
40C2×#10621898D412yes—
41C22×Dic86C2×C411yescharacteristic
42C22×D172C2×C411yescharacteristic
43C22×C22⋊D43—21no—
44C22×C4×D43—21no—
45C2×#10621877—21no—
46C2×#10621877—21no—
47C2×#10621877—21no—
48C2×#10621877—21no—
49C2×#10621877—21no—
50C2×#10621877—21no—
51C2×#10621877—21no—
52C2×#10621877—21no—
53C2×#10621877—21no—
54C2×#10621877—21no—
55C2×#10621877C2×C412yes—
56C2×#10621877D412yes—
57C22×C43⋊C8—21no—
58C22×C43⋊C8—21no—
59#13063284—21no—
60#13063284—21no—
61#13063284—21no—
62#13063284—21no—
63C2×C4⋊Dic43—21no—
64C2×C22⋊Dic43—21no—
65C2×C4×Dic43D412yes—
66#13063253—28no—
67#13063251—28no—
68#13063243—24no—
69#13063241—24no—
70C23×C4×C43C2311yescharacteristic
71C2×M16×C43—21no—
72C2×M16×C43—21no—
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×C43C2×C412yes—
82C2×M16×C43D412yes—
83C22×C8×C43—21no—
84C22×C8×C43—21no—
85#117×C43—21no—
86#117×C43—21no—
87#117×C43—21no—
88#117×C43D412yes—
89C2×C4⋊C4×C43—21no—
90C2×C22⋊C4×C43—21no—
91C2×C42×C43—21no—
92C24×C43#4111yescharacteristic
93C23×D43—21no—
94C22×C4×C43—41no—
95C22×C4×C43C22×C411yescharacteristic
96C22×C4×C43C2×D411yescharacteristic
97C22×C4×C43C2×D411yescharacteristic
98C22×C4×C43C2×D411yescharacteristic
99C22×C4×C43C2×D411yescharacteristic
100C22×C4×C43C2×D411yescharacteristic
101C22×C4×C43C2×D411yescharacteristic
102C22×C4×C43#4111yescharacteristic
103C22×C4×C43#4111yescharacteristic
104C22×C4×C43#4111yescharacteristic
105C22×C4×C43#4111yescharacteristic
106C22×C4×C43#4111yescharacteristic
107C22×C4×C43#4111yescharacteristic
108C22×C4×C43#4111yescharacteristic
109C2×C22⋊D43—22no—
110C2×C22⋊D43—22no—
111C2×C22⋊D43—41no—
112C2×C22⋊D43—41no—
113C2×C22⋊D43—41no—
114C2×C22⋊D43—41no—
115C22×Dic43—21no—
116C22×Dic43—22no—
117#10621898—22no—
118#10621898—22no—
119#10621898—22no—
120#10621898—22no—
121#10621898—22no—
122#10621898—22no—
123#10621898—22no—
124#10621898—22no—
125#10621898—41no—
126#10621898—41no—
127#10621898—41no—
128#10621898—41no—
129#10621898—41no—
130#10621898—41no—
131#10621898—41no—
132#10621898—41no—
133C2×D172—21no—
134C2×D172—21no—
135C2×D172—21no—
136C2×D172—21no—
137C2×D172—21no—
138C2×D172C22⋊C412yes—
139C2×C4×D43—22no—
140C2×C4×D43—22no—
141C2×C4×D43—41no—
142C2×C4×D43—41no—
143C2×C4×D43—41no—
144C2×C4×D43—41no—
145C2×Dic86—21no—
146C2×Dic86—21no—
147C2×Dic86—21no—
148C2×Dic86—21no—
149C2×Dic86—21no—
150C2×Dic86C22⋊C412yes—
151M16×C43—22no—
152M16×C43—22no—
153M16×C43—22no—
154M16×C43—22no—
155M16×C43—41no—
156M16×C43—41no—
157M16×C43—41no—
158M16×C43—41no—
159C2×C8×C43—22no—
160C2×C8×C43—22no—
161C2×C8×C43—41no—
162C2×C8×C43—41no—
163C2×C8×C43—41no—
164C2×C8×C43—41no—
165C4⋊C4×C43—22no—
166C4⋊C4×C43—41no—
167C22⋊C4×C43—22no—
168C22⋊C4×C43—41no—
169C42×C43—22no—
170C42×C43—41no—
171C22⋊Dic43—41no—
172C22⋊Dic43—41no—
173C4⋊Dic43—41no—
174C4⋊Dic43—41no—
175C4×Dic43—22no—
176C4×Dic43—22no—
177#10621877—22no—
178#10621877—22no—
179#10621877—22no—
180#10621877—22no—
181#10621877—41no—
182#10621877—41no—
183#10621877—41no—
184#10621877—41no—
185C2×C43⋊C8—22no—
186C2×C43⋊C8—22no—
187C2×C43⋊C8—41no—
188C2×C43⋊C8—41no—
189C2×C43⋊C8—41no—
190C2×C43⋊C8—41no—
191C23×C43—81no—
192C23×C43#11711yescharacteristic
193C23×C43#12111yescharacteristic
194C23×C43#12311yescharacteristic
195C23×C43#12311yescharacteristic
196C23×C43#12311yescharacteristic
197C23×C43#12411yescharacteristic
198C23×C43#12611yescharacteristic
199C22×D43—22no—
200C22×D43—41no—
201C22×D43—41no—
202C22×D43—82no—
203C2×C4×C43—42no—
204C2×C4×C43—82no—
205C2×C4×C43C2×C22⋊C411yescharacteristic
206C2×C4×C43#11711yescharacteristic
207C2×C4×C43C4×D411yescharacteristic
208C2×C4×C43C4×D411yescharacteristic
209C2×C4×C43C4×D411yescharacteristic
210C2×C4×C43C4×D411yescharacteristic
211C2×C4×C43#12011yescharacteristic
212C2×C4×C43#12011yescharacteristic
213C2×C4×C43#12111yescharacteristic
214C2×C4×C43#12111yescharacteristic
215C2×C4×C43#12111yescharacteristic
216C2×C4×C43#12111yescharacteristic
217C2×C4×C43#12111yescharacteristic
218C2×C4×C43#12111yescharacteristic
219C2×C4×C43#12111yescharacteristic
220C2×C4×C43#12311yescharacteristic
221C2×C4×C43#12311yescharacteristic
222C2×C4×C43#12311yescharacteristic
223C2×C4×C43#12311yescharacteristic
224C2×C4×C43#12311yescharacteristic
225C2×C4×C43#12311yescharacteristic
226C2×C4×C43#12311yescharacteristic
227C2×C4×C43#12411yescharacteristic
228C2×C4×C43#12411yescharacteristic
229C2×C4×C43#12411yescharacteristic
230C2×C4×C43#12611yescharacteristic
231C2×C4×C43#12611yescharacteristic
232C2×C4×C43#12611yescharacteristic
233C22⋊D43—42no—
234C22⋊D43—42no—
235C22⋊D43—42no—
236C22⋊D43—42no—
237C2×Dic43—22no—
238C2×Dic43—41no—
239C2×Dic43—41no—
240C2×Dic43—42no—
241C2×Dic43—82no—
242D172—22no—
243D172—22no—
244D172—41no—
245D172—41no—
246C4×D43—42no—
247C4×D43—42no—
248C4×D43—42no—
249C4×D43—42no—
250Dic86—22no—
251Dic86—22no—
252Dic86—41no—
253Dic86—41no—
254C8×C43—42no—
255C8×C43—42no—
256C43⋊C8—42no—
257C43⋊C8—42no—
258#11159—431nomaximal, Sylow
259C22×C43—41no—
260C22×C43—41no—
261C22×C43—41no—
262C22×C43—41no—
263C22×C43—41no—
264C22×C43—41no—
265C22×C43—41no—
266C22×C43#38111yescharacteristic
267C22×C43#38811yescharacteristic
268C22×C43#38811yescharacteristic
269C22×C43#39411yescharacteristic
270C22×C43#39411yescharacteristic
271C22×C43#39711yescharacteristic
272C22×C43#39711yescharacteristic
273C2×D43—42no—
274C2×D43—82no—
275C2×D43—82no—
276C2×D43—82no—
277C4×C43—82no—
278C4×C43#38611yescharacteristic
279C4×C43#38611yescharacteristic
280C4×C43#38811yescharacteristic
281C4×C43#38811yescharacteristic
282C4×C43#39411yescharacteristic
283C4×C43#39411yescharacteristic
284C4×C43#39711yescharacteristic
285C4×C43#39711yescharacteristic
286Dic43—42no—
287Dic43—82no—
288C2×#421—431no—
289C2×#421—431no—
290C2×#413—431no—
291C2×#344D4311yescharacteristic, complemented
292#1742—431no—
293#1733—431no—
294C2×#338—431no—
295C2×C43—21no—
296C2×C43—21no—
297C2×C43—21no—
298C2×C43—21no—
299C2×C43—21no—
300C2×C43—21no—
301C2×C43—21no—
302C2×C43#144011yescharacteristic
303D43—82no—
304C22×#41—431no—
305C22×M16—431no—
306C22×M16—431no—
307C22×M16C2×D4311yescharacteristic
308C22×M16C2×D4311yescharacteristic
309C2×#117—431no—
310C2×#117C2×D4311yescharacteristic
311#421—862no—
312#421—862no—
313#421—862no—
314#421—862no—
315C2×#104—862no—
316C2×#104—862no—
317#413—862no—
318#413—862no—
319C2×#101—432no—
320C2×#100—432no—
321#344—22no—
322#343—862no—
323#339—862no—
324#338—862no—
325C43#1115911yescharacteristic, complemented, Sylow
326C2×#41—432no—
327C2×#41—432no—
328C2×#41—861no—
329C2×#41—861no—
330C2×#41—861no—
331C2×#41—861no—
332C2×#41—861no—
333C2×#41—861no—
334C2×#41—861no—
335C2×#41—861no—
336C2×#41—861no—
337C2×#41—861no—
338C22×Q8—431no—
339C22×D4—431no—
340C22×D4—861no—
341C23×C4—861no—
342C23×C4C22×D4311yescharacteristic
343C2×M16—21no—
344C2×M16—21no—
345C2×M16—21no—
346C2×M16—21no—
347C2×M16—21no—
348C2×M16—21no—
349C2×M16—21no—
350C2×M16—21no—
351C2×M16—21no—
352C2×M16—21no—
353C2×M16—432no—
354C2×M16—432no—
355C2×M16—861no—
356C2×M16—861no—
357C2×M16—861no—
358C2×M16—861no—
359C2×M16—861no—
360C2×M16—861no—
361C2×M16—861no—
362C2×M16—861no—
363C2×M16—861no—
364C2×M16—861no—
365C2×M16C4×D4312yes—
366C2×M16D17212yes—
367C22×C8—21no—
368C22×C8—21no—
369C22×C8—861no—
370C22×C8—861no—
371#117—21no—
372#117—21no—
373#117—21no—
374#117—861no—
375#117—861no—
376#117—861no—
377#117—861no—
378#117C22⋊D4312yes—
379C2×C4⋊C4—21no—
380C2×C4⋊C4—861no—
381C2×C22⋊C4—21no—
382C2×C22⋊C4—861no—
383C2×C42—21no—
384C2×C42—432no—
385#104—868no—
386#104—868no—
387#101—864no—
388#100—864no—
389C24—861no—
390C24#1062189811yescharacteristic
391#41—862no—
392#41—862no—
393#41—862no—
394#41—862no—
395#41—862no—
396#41—862no—
397#41—862no—
398#41—862no—
399#41—1721no—
400#41—1721no—
401#41—1721no—
402#41—1721no—
403#41—1721no—
404#41—1721no—
405#41—1721no—
406#41—1721no—
407C2×Q8—432no—
408C2×Q8—861no—
409C2×Q8—861no—
410C2×Q8—861no—
411C2×Q8—861no—
412C2×Q8—861no—
413C2×D4—432no—
414C2×D4—862no—
415C2×D4—862no—
416C2×D4—861no—
417C2×D4—861no—
418C2×D4—861no—
419C2×D4—861no—
420C2×D4—861no—
421C2×D4—1721no—
422C2×D4—1721no—
423C2×D4—1721no—
424C2×D4—1721no—
425C22×C4—41no—
426C22×C4—861no—
427C22×C4—862no—
428C22×C4—862no—
429C22×C4—862no—
430C22×C4—1721no—
431C22×C4—1721no—
432C22×C4—1721no—
433C22×C4—1721no—
434C22×C4C2×C4×D4311yescharacteristic
435C22×C4C2×D17211yescharacteristic
436C22×C4#1062189811yescharacteristic
437C22×C4#1062189811yescharacteristic
438C22×C4#1062189811yescharacteristic
439C22×C4D4×D4311yescharacteristic
440C22×C4D4×D4311yescharacteristic
441C22×C4D4×D4311yescharacteristic
442C22×C4D4×D4311yescharacteristic
443C22×C4#1062190011yescharacteristic
444C22×C4#1062190011yescharacteristic
445C22×C4#1062190211yescharacteristic
446C22×C4#1062190211yescharacteristic
447C22×C4C2×C22⋊D4311yescharacteristic
448M16—22no—
449M16—22no—
450M16—22no—
451M16—22no—
452M16—41no—
453M16—41no—
454M16—41no—
455M16—41no—
456M16—862no—
457M16—862no—
458M16—862no—
459M16—862no—
460M16—1721no—
461M16—1721no—
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—1721no—
473C2×C8—1721no—
474C2×C8—1721no—
475C2×C8—1721no—
476C4⋊C4—22no—
477C4⋊C4—41no—
478C4⋊C4—1721no—
479C4⋊C4—1721no—
480C22⋊C4—22no—
481C22⋊C4—41no—
482C22⋊C4—1721no—
483C22⋊C4—1721no—
484C42—22no—
485C42—41no—
486C42—862no—
487C42—862no—
488C23—81no—
489C23—862no—
490C23—3442no—
491C23—1721no—
492C23—1721no—
493C23#1306328211yescharacteristic
494C23#1306329811yescharacteristic
495C23#1306330711yescharacteristic
496C23#1306330811yescharacteristic
497C23#1306331011yescharacteristic
498C23#1306331311yescharacteristic
499C23#1306332011yescharacteristic
500Q8—862no—
501Q8—862no—
502Q8—1721no—
503Q8—1721no—
504D4—862no—
505D4—862no—
506D4—1722no—
507D4—1722no—
508D4—1722no—
509D4—1722no—
510D4—1721no—
511D4—1721no—
512C2×C4—42no—
513C2×C4—82no—
514C2×C4—862no—
515C2×C4—3442no—
516C2×C4—1722no—
517C2×C4—1721no—
518C2×C4—1721no—
519C2×C4—1722no—
520C2×C4—1722no—
521C2×C4—1722no—
522C2×C4—1722no—
523C2×C4C22⋊C4×D4311yescharacteristic
524C2×C4#1306328311yescharacteristic
525C2×C4(C22⋊D43)⋊C411yescharacteristic
526C2×C4C4×C22⋊D4311yescharacteristic
527C2×C4#1306328711yescharacteristic
528C2×C4C4×D17211yescharacteristic
529C2×C4#1306329311yescharacteristic
530C2×C4#1306329511yescharacteristic
531C2×C4#1306329611yescharacteristic
532C2×C4#1306329711yescharacteristic
533C2×C4#1306329811yescharacteristic
534C2×C4#1306329811yescharacteristic
535C2×C4#1306329911yescharacteristic
536C2×C4#1306330011yescharacteristic
537C2×C4#1306330011yescharacteristic
538C2×C4#1306330711yescharacteristic
539C2×C4#1306330711yescharacteristic
540C2×C4#1306330911yescharacteristic
541C2×C4#1306331011yescharacteristic
542C2×C4#1306331011yescharacteristic
543C2×C4#1306331011yescharacteristic
544C2×C4#1306331011yescharacteristic
545C2×C4#1306331111yescharacteristic
546C2×C4#1306331111yescharacteristic
547C2×C4#1306331411yescharacteristic
548C2×C4#1306331911yescharacteristic
549C2×C4#1306332011yescharacteristic
550C2×C4#1306332011yescharacteristic
551C8—42no—
552C8—42no—
553C8—1722no—
554C8—1722no—
555C22—41no—
556C22—41no—
557C22—41no—
558C22—41no—
559C22—41no—
560C22—41no—
561C22—41no—
562C22—3442no—
563C22—3442no—
564C22—3442no—
565C22—1722no—
566C22#1458276111yescharacteristic
567C22#1458278811yescharacteristic
568C22#1458279011yescharacteristic
569C22#1458281411yescharacteristic
570C22#1458281711yescharacteristic
571C22#1458282511yescharacteristic
572C22#1458282611yescharacteristic
573C4—82no—
574C4—3442no—
575C4—1722no—
576C4#1458277511yescharacteristic
577C4#1458277711yescharacteristic
578C4#1458278911yescharacteristic
579C4#1458279111yescharacteristic
580C4#1458281511yescharacteristic
581C4#1458281611yescharacteristic
582C4#1458282811yescharacteristic
583C4#1458282811yescharacteristic
584C2—21no—
585C2—21no—
586C2—21no—
587C2—21no—
588C2—21no—
589C2—21no—
590C2—21no—
591C2—3442no—
592C2#1913284311yescharacteristic
subgroupG/H
centerC4#14582828
commutatorC22×C4×C43C22×C4
FrattiniC23×C4C22×D43
FittingC2×C43×#344C2
socleC2×C43#1440
prime radicalC22×#10621898C22
cosocleC23×C4×C43C23
hypercenterC2×#344D43
hypocenterC43#11159
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C4 ◁ C23×C4 ◁ C2×#344

Complements

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

NH ≅ G/Ntype
4. #19134333C2semidirect
5. #19134304C2semidirect
6. C2×C43⋊#338C2semidirect
7. C2×C43×#344C2semidirect
20. C2×#13063243C4semidirect
21. C2×#13063241C4semidirect
291. C2×#344D43semidirect
325. C43#11159semidirect

Maximal subgroups

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

subgroupindex
C2×#145829172
C2×#145829152
C2×#145828812
#191343332
#191343042
C2×C43⋊#3382
C2×C43×#3442
#1115943