Finite Group Databasebeta

← #11897602

Subgroups — #11897602

Order 1152.

628 conjugacy classes of subgroups; only the 105 normal subgroups are shown.

normal subgroups only

This group has 628 conjugacy classes of subgroups — too many to draw. Only its 105 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#10594534C211yesmaximal, characteristic, complemented
2#10594526C211yesmaximal, characteristic, complemented
3#10593754C211yesmaximal, characteristic, complemented
4#10593420C211yesmaximal, characteristic
5#10593419C211yesmaximal, characteristic
6#10593419C211yesmaximal, characteristic
7#10593392C211yesmaximal, characteristic, complemented
8#10593384C211yesmaximal, characteristic, complemented
9#10593383C211yesmaximal, characteristic, complemented
10#10593367C211yesmaximal, characteristic, complemented
11#10593364C211yesmaximal, characteristic, complemented
12#10593359C211yesmaximal, characteristic, complemented
13#10593357C211yesmaximal, characteristic, complemented
14#10593357C211yesmaximal, characteristic, complemented
15#10593350C211yesmaximal, characteristic, complemented
16C2×D3×Dic6—21no—
17C2×#3774C2211yescharacteristic
18#64096C2211yescharacteristic
19C3×#897—21no—
20C3×#896—21no—
21#63919C2211yescharacteristic
22#63919C2211yescharacteristic
23#63902C2211yescharacteristic
24#63902C2211yescharacteristic
25#63902C2211yescharacteristic
26#63902C2211yescharacteristic
27C4×#625C2211yescharacteristic
28C4×#625C2211yescharacteristic
29#63899—21no—
30#63899—21no—
31#63896—21no—
32#63887—21no—
33D3×Dic3⋊C4—21no—
34#63873C2211yescharacteristic
35#63873C2211yescharacteristic
36#63870C2211yescharacteristic
37#63870C2211yescharacteristic
38#63779C2211yescharacteristic
39#63779C2211yescharacteristic
40#63777C2211yescharacteristic
41#63777C2211yescharacteristic
42C4⋊#622C2211yescharacteristic
43C4×#622C2211yescharacteristic
44#63743C2211yescharacteristic
45#63743C2211yescharacteristic
46#63743C2211yescharacteristic
47#63742C2211yescharacteristic
48#63742C2211yescharacteristic
49#63742C2211yescharacteristic
50#63742C2211yescharacteristic
51#63742C2211yescharacteristic
52#63742C2211yescharacteristic
53#63739C2211yescharacteristic
54#63739C2211yescharacteristic
55#63739C2211yescharacteristic
56#63739C2211yescharacteristic
57#63739C2211yescharacteristic
58#63739C2211yescharacteristic
59#5636—61no—
60#5632—61no—
61C2×#634D411yescharacteristic
62C2×C3×C4×D3—21no—
63C2×C3×C4×D3—21no—
64C2×C3×Dic6—21no—
65C2×C3×Dic6—21no—
66C2×#627—21no—
67C2×#627—21no—
68C2×#625C2311yescharacteristic
69C2×#625C2311yescharacteristic
70C2×D3×Dic3—21no—
71C2×D3×Dic3—21no—
72C2×D3×Dic3—21no—
73C2×D3×Dic3—21no—
74D3×Dic6—44no—
75C2×#622C2311yescharacteristic
76C2×#622C2311yescharacteristic
77C2×#622C2311yescharacteristic
78C2×#622C2311yescharacteristic
79#3774Q814yescomplemented
80C32×C4⋊C4D411yescharacteristic
81#3750D411yescharacteristic
82#3750D411yescharacteristic
83C4×C3⋊Dic3C2311yescharacteristic
84C4×C3⋊Dic3C2311yescharacteristic
85C4×C3⋊Dic3C2311yescharacteristic
86C3×(C2×D3)⋊C4—21no—
87C3×(C2×D3)⋊C4—21no—
88C3×(C2×D3)⋊C4—21no—
89C3×(C2×D3)⋊C4—21no—
90C3×C4⋊Dic3—21no—
91C3×C4⋊Dic3—21no—
92C3×Dic3⋊C4—21no—
93C3×Dic3⋊C4—21no—
94#3724—21no—
95#3724—21no—
96#3724C2311yescharacteristic
97#3724C2311yescharacteristic
98#3724C2311yescharacteristic
99#3724C2311yescharacteristic
100#3724C2311yescharacteristic
101#3724C2311yescharacteristic
102Dic3⋊Dic3—21no—
103Dic3⋊Dic3—21no—
104(C2×D3)⋊Dic3—21no—
105(C2×D3)⋊Dic3—21no—
106#3384—91nomaximal, Sylow
107C2×D3×Q8—61no—
108C22×Dic6—61no—
109C3×C22⋊Q8—61no—
110C3×C22⋊Q8—61no—
111#946—61no—
112#944—61no—
113#944—61no—
114C4×#67—61no—
115C4×#67—61no—
116C2×Dic3⋊C4—61no—
117#897—21no—
118#896—21no—
119#896—61no—
120#896—61no—
121#896—61no—
122D3×C4⋊C4—61no—
123#889—61no—
124#889—61no—
125#888—61no—
126#888—61no—
127#887—61no—
128#887—61no—
129#67⋊C4—61no—
130#67⋊C4—61no—
131#67⋊C4—61no—
132#67⋊C4—61no—
133#878—61no—
134#878—61no—
135#878—61no—
136#878—61no—
137C22×C3×D3—21no—
138C22×C3×D3—21no—
139C2×C32×C4C2×D411yescharacteristic
140C2×C32×C4C2×D411yescharacteristic
141C2×C32×C4C2×D411yescharacteristic
142C2×C3⋊Dic3C2×D411yescharacteristic
143C2×C3⋊Dic3C2×D411yescharacteristic
144C2×C3⋊Dic3C2×D411yescharacteristic
145C2×C3⋊Dic3C2411yescharacteristic
146#634—22no—
147C2×C3×Dic3—21no—
148C2×C3×Dic3—21no—
149C2×C3×Dic3—21no—
150C2×C3×Dic3—21no—
151C2×C3×Dic3—21no—
152C2×C3×Dic3—21no—
153C3×C4×D3—42no—
154C3×C4×D3—81no—
155C3×Dic6—42no—
156C3×Dic6—81no—
157#627—42no—
158#627—42no—
159#625—21no—
160#625—21no—
161#625C2×Q812yes—
162#625C2×Q812yescomplemented
163D3×Dic3—42no—
164D3×Dic3—42no—
165D3×Dic3—42no—
166D3×Dic3—81no—
167#622—21no—
168#622—21no—
169#622—21no—
170#622C2×Q812yescomplemented
171#554—91no—
172D4×Q8—91no—
173#501—91no—
174#501—91no—
175#498—91no—
176#478—91no—
177#478—91no—
178#476—91no—
179#476—91no—
180#476—91no—
181#474—91no—
182#446—91no—
183#442—91no—
184#442—91no—
185C4×D8—91no—
186C2×C3×Q8—61no—
187C2×C3×Q8—61no—
188C22×C3×C4—61no—
189C22×C3×C4—61no—
190C2×#67—61no—
191C2×#67—61no—
192C22×Dic3—61no—
193C22×Dic3—61no—
194C22×Dic3—61no—
195C22×Dic3—61no—
196D3×Q8—124no—
197C2×C4×D3—21no—
198C2×C4×D3—21no—
199C2×C4×D3—61no—
200C2×C4×D3—61no—
201C2×C4×D3—61no—
202C2×C4×D3—61no—
203C2×Dic6—21no—
204C2×Dic6—21no—
205C2×Dic6—61no—
206C2×Dic6—61no—
207C2×Dic6—61no—
208C2×Dic6—61no—
209C2×Dic6—61no—
210C2×Dic6—61no—
211C2×Dic6—124no—
212C3×C4⋊C4—21no—
213C3×C4⋊C4—21no—
214C3×C4⋊C4—61no—
215C3×C4⋊C4—61no—
216C3×C4⋊C4—61no—
217C3×C4⋊C4—61no—
218C3×C22⋊C4—61no—
219C3×C22⋊C4—61no—
220C3×C22⋊C4—61no—
221C3×C22⋊C4—61no—
222#217—61no—
223#217—61no—
224(C2×D3)⋊C4—21no—
225(C2×D3)⋊C4—21no—
226(C2×D3)⋊C4—21no—
227(C2×D3)⋊C4—21no—
228(C2×D3)⋊C4—61no—
229(C2×D3)⋊C4—61no—
230C4⋊Dic3—21no—
231C4⋊Dic3—21no—
232C4⋊Dic3—61no—
233C4⋊Dic3—61no—
234Dic3⋊C4—21no—
235Dic3⋊C4—21no—
236Dic3⋊C4—61no—
237Dic3⋊C4—61no—
238Dic3⋊C4—61no—
239Dic3⋊C4—61no—
240Dic3⋊C4—61no—
241Dic3⋊C4—61no—
242Dic3⋊C4—61no—
243Dic3⋊C4—61no—
244Dic3⋊C4—61no—
245Dic3⋊C4—61no—
246Dic3⋊C4—61no—
247Dic3⋊C4—61no—
248Dic3⋊C4—61no—
249Dic3⋊C4—61no—
250Dic3⋊C4—61no—
251Dic3⋊C4—61no—
252C4×Dic3—61no—
253C4×Dic3—61no—
254C4×Dic3—61no—
255C4×Dic3—61no—
256C4×Dic3—61no—
257C4×Dic3—61no—
258C22×C32C22×D411yescharacteristic
259C2×C3×D3—22no—
260C2×C3×D3—22no—
261C2×C3×D3—41no—
262C2×C3×D3—41no—
263C2×C3×D3—41no—
264C2×C3×D3—41no—
265C32×C4—21no—
266C32×C4—21no—
267C32×C4—21no—
268C3⋊Dic3—21no—
269C3⋊Dic3—21no—
270C3⋊Dic3AGL(1,ℤ/8)12yes—
271C3⋊Dic3C22×Q811yescharacteristic
272C3⋊Dic32−1+411yescharacteristic
273C3×Dic3—41no—
274C3×Dic3—41no—
275C3×Dic3—41no—
276C3×Dic3—41no—
277C3×Dic3—41no—
278C3×Dic3—41no—
279C22×Q8—181no—
280C2×D8—91no—
281C4⋊Q8—91no—
282C4⋊Q8—91no—
283C4⋊Q8—91no—
284C4⋊Q8—91no—
285#125—91no—
286#125—91no—
287C22⋊Q8—61no—
288C22⋊Q8—61no—
289C22⋊Q8—181no—
290C22⋊Q8—181no—
291C22⋊Q8—181no—
292C22⋊Q8—181no—
293C4×Q8—91no—
294C4×D4—91no—
295C4×D4—91no—
296C4×D4—91no—
297C4×D4—91no—
298C4×D4—91no—
299C4×D4—91no—
300C2×C4⋊C4—181no—
301#107—91no—
302#107—91no—
303#107—91no—
304#106—91no—
305#106—91no—
306#106—91no—
307#106—91no—
308#106—91no—
309#106—91no—
310C4⋊C8—91no—
311C4⋊C8—91no—
312C4⋊C8—91no—
313#102—91no—
314#102—91no—
315#102—91no—
316#102—91no—
317#102—91no—
318#102—91no—
319#97—91no—
320#97—91no—
321C4×C8—91no—
322C23×C3—61no—
323C23×C3—61no—
324C22×D3—21no—
325C22×D3—21no—
326C3×Q8—122no—
327C3×Q8—241no—
328C2×C3×C4—21no—
329C2×C3×C4—21no—
330C2×C3×C4—21no—
331C2×C3×C4—21no—
332C2×C3×C4—21no—
333C2×C3×C4—21no—
334C2×C3×C4—61no—
335C2×C3×C4—61no—
336C2×C3×C4—61no—
337C2×C3×C4—61no—
338C2×C3×C4—61no—
339C2×C3×C4—61no—
340C2×C3×C4—122no—
341C2×C3×C4—241no—
342#67—62no—
343#67—62no—
344#67—62no—
345#67—62no—
346C2×Dic3—21no—
347C2×Dic3—21no—
348C2×Dic3—21no—
349C2×Dic3—21no—
350C2×Dic3—21no—
351C2×Dic3—21no—
352C2×Dic3—61no—
353C2×Dic3—61no—
354C2×Dic3—61no—
355C2×Dic3—61no—
356C2×Dic3—61no—
357C2×Dic3—61no—
358C2×Dic3—61no—
359C2×Dic3—61no—
360C2×Dic3—122no—
361C2×Dic3—122no—
362C2×Dic3—122no—
363C2×Dic3—241no—
364C4×D3—42no—
365C4×D3—81no—
366C4×D3—122no—
367C4×D3—122no—
368C4×D3—122no—
369C4×D3—241no—
370Dic6—42no—
371Dic6—64no—
372Dic6—81no—
373Dic6—122no—
374Dic6—122no—
375Dic6—122no—
376Dic6—122no—
377Dic6—122no—
378C2×C32D4×Q811yescharacteristic
379C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
380C2×C32#57711yescharacteristic
381C3×D3—42no—
382C3×D3—42no—
383C2×Q8—61no—
384C2×Q8—61no—
385C2×Q8—91no—
386C2×Q8—181no—
387C2×Q8—181no—
388C2×Q8—364no—
389C2×D4—91no—
390C2×D4—91no—
391C22×C4—61no—
392C22×C4—61no—
393C22×C4—181no—
394C22×C4—181no—
395C22×C4—181no—
396C22×C4—181no—
397D8—94no—
398C2×C8—91no—
399C2×C8—91no—
400C2×C8—91no—
401C2×C8—91no—
402C4⋊C4—61no—
403C4⋊C4—61no—
404C4⋊C4—61no—
405C4⋊C4—61no—
406C4⋊C4—91no—
407C4⋊C4—91no—
408C4⋊C4—91no—
409C4⋊C4—91no—
410C4⋊C4—91no—
411C4⋊C4—91no—
412C4⋊C4—91no—
413C4⋊C4—91no—
414C4⋊C4—181no—
415C4⋊C4—181no—
416C4⋊C4—181no—
417C4⋊C4—181no—
418C4⋊C4GO+(4,𝔽2)11yescharacteristic
419C22⋊C4—61no—
420C22⋊C4—61no—
421C22⋊C4—61no—
422C22⋊C4—61no—
423C22⋊C4—181no—
424C22⋊C4—181no—
425C42—91no—
426C42—91no—
427C42—91no—
428C22×C3—21no—
429C22×C3—21no—
430C22×C3—62no—
431C22×C3—62no—
432C22×C3—121no—
433C22×C3—121no—
434C22×C3—121no—
435C22×C3—121no—
436C2×D3—22no—
437C2×D3—22no—
438C2×D3—41no—
439C2×D3—41no—
440C2×D3—41no—
441C2×D3—41no—
442C3×C4—22no—
443C3×C4—41no—
444C3×C4—41no—
445C3×C4—41no—
446C3×C4—41no—
447C3×C4—41no—
448C3×C4—121no—
449C3×C4—121no—
450C3×C4—121no—
451C3×C4—121no—
452C3×C4—121no—
453C3×C4—121no—
454Dic3—41no—
455Dic3—41no—
456Dic3—41no—
457Dic3—41no—
458Dic3—41no—
459Dic3—41no—
460Dic3—62no—
461Dic3—62no—
462Dic3—61no—
463Dic3—61no—
464Dic3—61no—
465Dic3—61no—
466Dic3—62no—
467Dic3—121no—
468Dic3—121no—
469Dic3—121no—
470C32#338411yescharacteristic, complemented, Sylow
471C23—61no—
472C23—61no—
473Q8—122no—
474Q8—182no—
475Q8—241no—
476Q8—362no—
477Q8—362no—
478D4—92no—
479D4—92no—
480D4—181no—
481D4—181no—
482C2×C4—61no—
483C2×C4—61no—
484C2×C4—61no—
485C2×C4—61no—
486C2×C4—61no—
487C2×C4—61no—
488C2×C4—91no—
489C2×C4—91no—
490C2×C4—91no—
491C2×C4—91no—
492C2×C4—122no—
493C2×C4—241no—
494C2×C4—362no—
495C2×C4—362no—
496C2×C4—362no—
497C2×C4—721no—
498C2×C4C2×GO+(4,𝔽2)11yescharacteristic
499C2×C4C2×GO+(4,𝔽2)11yescharacteristic
500C2×C4C2×GO+(4,𝔽2)11yescharacteristic
501C8—92no—
502C8—181no—
503C8—181no—
504C8—181no—
505C2×C3—21no—
506C2×C3—21no—
507C2×C3—21no—
508C2×C3—21no—
509C2×C3—21no—
510C2×C3—21no—
511C2×C3—122no—
512C2×C3—122no—
513D3—42no—
514D3—42no—
515C22—62no—
516C22—62no—
517C22—121no—
518C22—121no—
519C22—121no—
520C22—121no—
521C22C22×GO+(4,𝔽2)11yescharacteristic
522C4—21no—
523C4—21no—
524C4—21no—
525C4—92no—
526C4—91no—
527C4—91no—
528C4—121no—
529C4—121no—
530C4—121no—
531C4—121no—
532C4—121no—
533C4—121no—
534C4—181no—
535C4—181no—
536C3—21no—
537C3—21no—
538C2—122no—
539C2—122no—
540C2#1059650111yescharacteristic
541C2#1059651511yescharacteristic
542C2Q8×GO+(4,𝔽2)11yescharacteristic
subgroupG/H
center, FrattiniC22C22×GO+(4,𝔽2)
commutator, cosocleC2×C3⋊Dic3C24
FittingC32×C4⋊C4D4
socleC22×C32C22×D4
prime radicalC2×#3774C22
hypercenterC4⋊C4GO+(4,𝔽2)
hypocenterC32#3384
LCSG ▷ C2×C3⋊Dic3 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C4⋊C4

Complements

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

NH ≅ G/Ntype
1. #10594534C2semidirect
2. #10594526C2semidirect
3. #10593754C2semidirect
7. #10593392C2semidirect
8. #10593384C2semidirect
9. #10593383C2semidirect
10. #10593367C2semidirect
11. #10593364C2semidirect
12. #10593359C2semidirect
13. #10593357C2semidirect
14. #10593357C2semidirect
15. #10593350C2semidirect
79. #3774Q8semidirect
162. #625C2×Q8semidirect
170. #622C2×Q8semidirect
470. C32#3384semidirect

Maximal subgroups

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

subgroupindex
#105945342
#105945262
#105937542
#105934202
#105934192
#105933922
#105933842
#105933832
#105933672
#105933642
#105933592
#105933572
#105933502
#33849