Finite Group Databasebeta

← #11920413

Subgroups — #11920413

Order 1152.

556 conjugacy classes of subgroups; only the 56 normal subgroups are shown.

normal subgroups only

This group has 556 conjugacy classes of subgroups — too many to draw. Only its 56 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#41×C22⋊C9C211yesmaximal, characteristic, complemented
2#10593087C211yesmaximal, characteristic, complemented
3#10589519C211yesmaximal, characteristic, complemented
4#10589518C211yesmaximal, characteristic, complemented
5#10589517C211yesmaximal, characteristic, complemented
6#10589516C211yesmaximal, characteristic, complemented
7C2×(C22⋊C9)⋊C8C211yesmaximal, characteristic, complemented
8#84080—31nomaximal
9Q8×C22⋊C9C2211yescharacteristic
10D4×C22⋊C9—21no—
11D4×C22⋊C9C2211yescharacteristic
12C2×C4×C22⋊C9—21no—
13C2×C4×C22⋊C9C2211yescharacteristic
14#63694—21no—
15C4⋊((C22⋊C9)⋊C2)C2211yescharacteristic
16C4×(C22⋊C9)⋊C2—21no—
17(C22⋊C9)⋊Q8C2211yescharacteristic
18#63513—41nomaximal
19(C22⋊C9)⋊C8C2211yescharacteristic
20(C22⋊C9)⋊C8C2211yescharacteristic
21C22×C3×#41D311yescharacteristic
22C2×#950—31no—
23C2×#950—31no—
24#5791—31no—
25#5239—31no—
26#5239—31no—
27#5238—31no—
28#5238—31no—
29#5233—31no—
30#5233—31no—
31#5228—31no—
32#5227—31no—
33#5218—31no—
34#5217—31no—
35C2×#830—31no—
36C22×C22⋊C9—21no—
37C22×C22⋊C9D411yescharacteristic
38C2×(C22⋊C9)⋊C2—21no—
39C9×#41—41no—
40#3697—41no—
41C4×C22⋊C9—21no—
42C4×C22⋊C9D411yescharacteristic
43C4×C22⋊C9C2311yescharacteristic
44(C22⋊C9)⋊C4—21no—
45#3675—41no—
46#3674—41no—
47#3673—41no—
48#3672—41no—
49C2×C9⋊C8—41no—
50#3002—91noSylow
51C2×C3×#41—31no—
52C2×C3×#41—31no—
53C2×C3×#41—31no—
54C2×C3×#41—31no—
55C2×C3×#41—61no—
56C2×C3×#41—61no—
57C22×C3×Q8C2×D311yescharacteristic
58C22×C3×D4—21no—
59C22×C3×D4C2×D311yescharacteristic
60C23×C3×C4—21no—
61C23×C3×C4C2×D311yescharacteristic
62C2×#235—31no—
63#953—61no—
64#950—62no—
65#950—62no—
66#950—61no—
67#950—61no—
68#950—61no—
69#950—61no—
70C2×#216—31no—
71C2×#216—31no—
72C2×#215—31no—
73C2×#215—31no—
74C2×#214—31no—
75C2×#214—31no—
76C2×#213—31no—
77C2×#213—31no—
78#930—31no—
79#930—31no—
80#929—61no—
81C4×#67—61no—
82C4×#67—61no—
83#926—31no—
84#924—31no—
85#924—31no—
86C22×C3⋊C8—31no—
87C22×C3⋊C8—31no—
88#835—31no—
89#835—31no—
90#835—31no—
91#835—31no—
92#832—31no—
93#832—31no—
94#832—31no—
95#832—31no—
96#830—31no—
97#830—31no—
98#830—31no—
99#830—31no—
100C2×C22⋊C9—21no—
101C2×C22⋊C9—41no—
102C2×C22⋊C9C2×D411yescharacteristic
103(C22⋊C9)⋊C2—41no—
104Q8×C9—41no—
105D4×C9—41no—
106D4×C9—81no—
107C2×C4×C9—41no—
108C2×C4×C9—81no—
109#611—81no—
110D36—41no—
111C4×D9—81no—
112Dic18—41no—
113C9⋊C8—41no—
114C9⋊C8—41no—
115C22×#41D911yescharacteristic, complemented
116C2×#135—91no—
117C2×#135—91no—
118#525—91no—
119#452—91no—
120#452—91no—
121#451—91no—
122#450—91no—
123#449—91no—
124#449—91no—
125#448—91no—
126#447—91no—
127#416—91no—
128#416—91no—
129C2×C22⋊C8—91no—
130C24×C3—21no—
131C24×C3#6711yescharacteristic
132C3×#41—32no—
133C3×#41—32no—
134C3×#41—31no—
135C3×#41—31no—
136C3×#41—31no—
137C3×#41—61no—
138C3×#41—61no—
139C3×#41—61no—
140C3×#41—62no—
141C3×#41—62no—
142C3×#41S411yescharacteristic
143C2×C3×Q8—31no—
144C2×C3×Q8—31no—
145C2×C3×Q8—61no—
146C2×C3×D4—31no—
147C2×C3×D4—31no—
148C2×C3×D4—61no—
149C2×C3×D4—61no—
150C2×C3×D4—61no—
151C2×C3×D4—61no—
152C2×C3×D4—61no—
153C22×C3×C4—21no—
154C22×C3×C4—31no—
155C22×C3×C4—31no—
156C22×C3×C4—31no—
157C22×C3×C4—31no—
158C22×C3×C4—61no—
159C22×C3×C4—61no—
160C22×C3×C4—61no—
161C22×C3×C4—61no—
162C22×C3×C4#6711yescharacteristic
163C22×C3×C4C22×D311yescharacteristic
164C2×#67—61no—
165C2×#67—61no—
166C2×#67—61no—
167#235—61no—
168#235—61no—
169#235—61no—
170#235—61no—
171C2×D12—31no—
172C2×C4×D3—61no—
173C2×Dic6—31no—
174#217—61no—
175#217—61no—
176#217—61no—
177#216—62no—
178#216—61no—
179#216—61no—
180#215—62no—
181#215—61no—
182#215—61no—
183#214—62no—
184#214—61no—
185#214—61no—
186#213—62no—
187#213—61no—
188#213—61no—
189(C2×D3)⋊C4—61no—
190(C2×D3)⋊C4—61no—
191C4⋊Dic3—31no—
192C4⋊Dic3—31no—
193Dic3⋊C4—61no—
194Dic3⋊C4—61no—
195C4×Dic3—61no—
196C2×C3⋊C8—31no—
197C2×C3⋊C8—31no—
198C2×C3⋊C8—31no—
199C2×C3⋊C8—31no—
200C2×C3⋊C8—61no—
201C2×C3⋊C8—61no—
202C2×C3⋊C8—61no—
203C2×C3⋊C8—61no—
204C22×C9—41no—
205C22×C9—81no—
206C2×D9—81no—
207C22⋊C9#13511yescharacteristic, complemented
208C4×C9—41no—
209C4×C9—41no—
210C4×C9—81no—
211Dic9—81no—
212C2×#41—31no—
213C2×#41—31no—
214C2×#41—31no—
215C2×#41—31no—
216C2×#41—61no—
217C2×#41—61no—
218C2×#41—91no—
219C22×Q8C2×D911yescharacteristic
220C22×D4—21no—
221C22×D4C2×D911yescharacteristic
222C23×C4—21no—
223C23×C4C2×D911yescharacteristic
224#135—182no—
225#135—182no—
226#135—181no—
227#135—181no—
228#135—181no—
229#135—181no—
230C2×Q16—91no—
231C2×Q16—91no—
232C2×SD16—91no—
233C2×SD16—91no—
234C2×SD16—91no—
235C2×SD16—91no—
236C2×D8—91no—
237C2×D8—91no—
238C22×C8—91no—
239C22×C8—91no—
240#123—181no—
241C22⋊Q8—91no—
242C22⋊Q8—91no—
243#121—91no—
244#121—91no—
245#120—181no—
246C4×D4—181no—
247C4×D4—181no—
248#117—91no—
249#103—91no—
250#103—91no—
251#103—91no—
252#103—91no—
253#102—91no—
254#102—91no—
255#102—91no—
256#102—91no—
257C22⋊C8—91no—
258C22⋊C8—91no—
259C22⋊C8—91no—
260C22⋊C8—91no—
261C23×C3—21no—
262C23×C3—31no—
263C23×C3—31no—
264C23×C3—41no—
265C23×C3—61no—
266C23×C3—61no—
267C23×C3—61no—
268C23×C3—121no—
269C23×C3C2×#6711yescharacteristic
270C22×D3—61no—
271C3×Q8—32no—
272C3×Q8—31no—
273C3×Q8—61no—
274C3×Q8C2×S411yescharacteristic
275C3×D4—21no—
276C3×D4—32no—
277C3×D4—31no—
278C3×D4—61no—
279C3×D4—61no—
280C3×D4—61no—
281C3×D4—62no—
282C3×D4—61no—
283C3×D4C2×S411yescharacteristic
284C2×C3×C4—21no—
285C2×C3×C4—31no—
286C2×C3×C4—31no—
287C2×C3×C4—31no—
288C2×C3×C4—31no—
289C2×C3×C4—31no—
290C2×C3×C4—31no—
291C2×C3×C4—31no—
292C2×C3×C4—61no—
293C2×C3×C4—61no—
294C2×C3×C4—61no—
295C2×C3×C4—61no—
296C2×C3×C4—62no—
297C2×C3×C4—61no—
298C2×C3×C4—61no—
299C2×C3×C4C2×S411yescharacteristic
300#67—121no—
301#67—121no—
302#67—122no—
303#67—121no—
304#67—121no—
305C2×Dic3—61no—
306C2×Dic3—61no—
307C2×Dic3—61no—
308D12—61no—
309D12—61no—
310C4×D3—121no—
311C4×D3—121no—
312Dic6—61no—
313Dic6—61no—
314C3⋊C8—61no—
315C3⋊C8—61no—
316C3⋊C8—61no—
317C3⋊C8—61no—
318C2×C9—41no—
319C2×C9—81no—
320C2×C9—161no—
321D9—161no—
322C24—21no—
323C24#61111yescharacteristic
324#41—32no—
325#41—32no—
326#41—31no—
327#41—31no—
328#41—31no—
329#41—61no—
330#41—61no—
331#41—61no—
332#41—62no—
333#41—62no—
334#41—181no—
335#41—181no—
336#41—181no—
337#41—181no—
338#41(C22⋊C9)⋊C211yescharacteristic, complemented
339C2×Q8—31no—
340C2×Q8—31no—
341C2×Q8—61no—
342C2×Q8—91no—
343C2×D4—31no—
344C2×D4—31no—
345C2×D4—61no—
346C2×D4—61no—
347C2×D4—61no—
348C2×D4—61no—
349C2×D4—61no—
350C2×D4—91no—
351C2×D4—181no—
352C2×D4—181no—
353C2×D4—181no—
354C22×C4—21no—
355C22×C4—31no—
356C22×C4—31no—
357C22×C4—31no—
358C22×C4—31no—
359C22×C4—61no—
360C22×C4—61no—
361C22×C4—61no—
362C22×C4—61no—
363C22×C4—181no—
364C22×C4#61111yescharacteristic
365C22×C4C22×D911yescharacteristic
366Q16—182no—
367Q16—181no—
368Q16—181no—
369SD16—182no—
370SD16—181no—
371SD16—182no—
372SD16—181no—
373SD16—181no—
374SD16—181no—
375D8—182no—
376D8—181no—
377D8—181no—
378C2×C8—91no—
379C2×C8—91no—
380C2×C8—91no—
381C2×C8—91no—
382C2×C8—181no—
383C2×C8—181no—
384C2×C8—181no—
385C2×C8—181no—
386C4⋊C4—91no—
387C4⋊C4—91no—
388C4⋊C4—181no—
389C4⋊C4—181no—
390C22⋊C4—181no—
391C22⋊C4—181no—
392C22⋊C4—181no—
393C22⋊C4—181no—
394C22⋊C4—181no—
395C42—181no—
396C22×C3—21no—
397C22×C3—31no—
398C22×C3—31no—
399C22×C3—31no—
400C22×C3—61no—
401C22×C3—61no—
402C22×C3—61no—
403C22×C3—61no—
404C22×C3—61no—
405C22×C3—121no—
406C22×C3—121no—
407C22×C3—121no—
408C22×C3—121no—
409C22×C3#95011yescharacteristic
410C22×C3GL(2,ℤ/4)11yescharacteristic
411C2×D3—121no—
412C2×D3—121no—
413C2×D3—121no—
414C3×C4—21no—
415C3×C4—31no—
416C3×C4—31no—
417C3×C4—61no—
418C3×C4GL(2,ℤ/4)11yescharacteristic
419C3×C4C22×S411yescharacteristic
420Dic3—121no—
421Dic3—121no—
422Dic3—121no—
423C9—41noSylow
424C23—21no—
425C23—31no—
426C23—31no—
427C23—41no—
428C23—61no—
429C23—61no—
430C23—61no—
431C23—121no—
432C23—181no—
433C23C2×#61111yescharacteristic
434Q8—32no—
435Q8—31no—
436Q8—61no—
437Q8—181no—
438Q8—181no—
439Q8C2×(C22⋊C9)⋊C211yescharacteristic
440D4—21no—
441D4—32no—
442D4—31no—
443D4—61no—
444D4—61no—
445D4—61no—
446D4—62no—
447D4—61no—
448D4—181no—
449D4—181no—
450D4—361no—
451D4—361no—
452D4—362no—
453D4—361no—
454D4—361no—
455D4C2×(C22⋊C9)⋊C211yescharacteristic
456C2×C4—21no—
457C2×C4—31no—
458C2×C4—31no—
459C2×C4—31no—
460C2×C4—31no—
461C2×C4—31no—
462C2×C4—31no—
463C2×C4—31no—
464C2×C4—61no—
465C2×C4—61no—
466C2×C4—61no—
467C2×C4—61no—
468C2×C4—62no—
469C2×C4—61no—
470C2×C4—61no—
471C2×C4—181no—
472C2×C4—181no—
473C2×C4—181no—
474C2×C4—361no—
475C2×C4—361no—
476C2×C4C2×(C22⋊C9)⋊C211yescharacteristic
477C8—181no—
478C8—181no—
479C8—181no—
480C8—181no—
481C2×C3—21no—
482C2×C3—31no—
483C2×C3—31no—
484C2×C3—41no—
485C2×C3—61no—
486C2×C3—121no—
487C2×C3C2×GL(2,ℤ/4)11yescharacteristic
488D3—241no—
489C22—21no—
490C22—31no—
491C22—31no—
492C22—31no—
493C22—61no—
494C22—61no—
495C22—61no—
496C22—61no—
497C22—61no—
498C22—121no—
499C22—121no—
500C22—121no—
501C22—121no—
502C22—361no—
503C22—361no—
504C22—361no—
505C22#6351311yescharacteristic, complemented
506C22#6369411yescharacteristic
507C4—21no—
508C4—31no—
509C4—31no—
510C4—61no—
511C4—361no—
512C4—361no—
513C4—361no—
514C4#6369411yescharacteristic
515C4C22×(C22⋊C9)⋊C211yescharacteristic
516C3#8551411yescharacteristic
517C2—21no—
518C2—31no—
519C2—31no—
520C2—41no—
521C2—61no—
522C2—121no—
523C2—721no—
524C2C2×#6369411yescharacteristic
subgroupG/H
centerC4#63694
commutator, cosocleC4×C22⋊C9C23
FrattiniC3×C4C22×S4
FittingC22×C3×#41D3
socleC23×C3C2×#67
hypercenter#41(C22⋊C9)⋊C2
hypocenterC22⋊C9#135
LCSG ▷ C4×C22⋊C9 ▷ C2×C22⋊C9 ▷ C22⋊C9
UCSC1 ◁ C4 ◁ C2×C4 ◁ #41

Complements

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

NH ≅ G/Ntype
1. #41×C22⋊C9C2semidirect
2. #10593087C2semidirect
3. #10589519C2semidirect
4. #10589518C2semidirect
5. #10589517C2semidirect
6. #10589516C2semidirect
7. C2×(C22⋊C9)⋊C8C2semidirect
115. C22×#41D9semidirect
207. C22⋊C9#135semidirect
338. #41(C22⋊C9)⋊C2semidirect
505. C22#63513semidirect

Maximal subgroups

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

subgroupindex
#41×C22⋊C92
#105930872
#105895192
#105895182
#105895172
#105895162
C2×(C22⋊C9)⋊C82
#840803
#635134