Finite Group Databasebeta

← #11778074

Subgroups — #11778074

Order 1152.

589 conjugacy classes of subgroups; only the 78 normal subgroups are shown.

normal subgroups only

This group has 589 conjugacy classes of subgroups — too many to draw. Only its 78 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#10594980C211yesmaximal, characteristic, complemented
2C3×#4672C211yesmaximal, characteristic, complemented
3#10591169C211yesmaximal, characteristic, complemented
4#10591162C211yesmaximal, characteristic
5#10589317C211yesmaximal, characteristic, complemented
6C3×#4452C211yesmaximal, characteristic, complemented
7#10589147C211yesmaximal, characteristic, complemented
8#69702—31nomaximal
9#68324—31nomaximal
10C22×C3×D12C2211yescharacteristic
11#64139C2211yescharacteristic
12C2×C3×(C2×D3)⋊C4—21no—
13C2×C3×(C2×D3)⋊C4—21no—
14C3×#924C2211yescharacteristic
15C2×C3×Dic3⋊C4C2211yescharacteristic
16#63966—21no—
17#63952—21no—
18#63897—21no—
19#63888—21no—
20#63848—21no—
21#63845—21no—
22C2×#3715—21no—
23C2×#3714—21no—
24C32×#95C2211yescharacteristic
25#63657C2211yescharacteristic
26C3×#830C2211yescharacteristic
27#63563—21no—
28#63562—21no—
29#5645—31no—
30#5515—31no—
31C3×#394—31no—
32#5218—31no—
33#5217—31no—
34#5046—31no—
35#4732—31no—
36#4672D311yescharacteristic, complemented
37C3×#328—31no—
38#4528—31no—
39#4469—31no—
40#4452D311yescharacteristic, complemented
41#4451—31no—
42#4451—31no—
43#4451—61no—
44C23×C3×D3—21no—
45C22×C32×C4—21no—
46C22×C32×C4C2311yescharacteristic
47C2×#638—21no—
48C2×C4⋊(C3⋊D3)D411yescharacteristic
49C22×C3×Dic3D411yescharacteristic
50C22×C3×Dic3D411yescharacteristic
51C2×C3×D12—21no—
52C2×C3×D12—21no—
53C2×C3×D12—42no—
54C2×C3×Dic6D411yescharacteristic
55C2×#624—21no—
56#3752—21no—
57C4⋊(C3⋊Dic3)D411yescharacteristic
58C2×C3⋊(C3⋊C8)—21no—
59C3×#217—21no—
60C3×(C2×D3)⋊C4—42no—
61C3×(C2×D3)⋊C4—42no—
62C3×C4⋊Dic3D411yescharacteristic
63C3×Dic3⋊C4—21no—
64C3×Dic3⋊C4—21no—
65C3×Dic3⋊C4—21no—
66C2×C3×C3⋊C8—21no—
67#3724—21no—
68Dic3⋊Dic3—21no—
69Dic3⋊Dic3—21no—
70#3722—21no—
71#3722—21no—
72#3722—21no—
73Dic32—21no—
74#3715—42no—
75#3714—42no—
76#1597—91noSylow
77C22×C3×D4—31no—
78C22×D12C2×D311yescharacteristic
79C3×C22⋊Q8—31no—
80C2×C3×C4⋊C4—31no—
81C2×C3×C22⋊C4—61no—
82C2×C3×C22⋊C4—61no—
83#946—61no—
84C2×#215—61no—
85C2×#214—61no—
86C2×#213—61no—
87#930—31no—
88#930—31no—
89#930—61no—
90#929—61no—
91C4×#67—61no—
92C2×(C2×D3)⋊C4—21no—
93C2×(C2×D3)⋊C4—21no—
94#924C2×D311yescharacteristic
95C2×Dic3⋊C4C2×D311yescharacteristic
96C2×D24—61no—
97#898—61no—
98#898—61no—
99#896—61no—
100#894—61no—
101#894—61no—
102#890—61no—
103#889—61no—
104#886—61no—
105#67⋊C4—61no—
106C3×C22⋊C8—31no—
107C3×#95—21no—
108C3×#95C2×D311yescharacteristic
109C3×#95C2×D311yescharacteristic
110#832—61no—
111#832—61no—
112#830—31no—
113#830—31no—
114#830—61no—
115#830C2×D311yescharacteristic
116#821—61no—
117#809—61no—
118C23×C32C2×D411yescharacteristic
119C22×C3⋊D3—21no—
120C22×C3×D3—22no—
121C22×C3×D3—41no—
122C22×C3×D3—41no—
123C22×C3×D3—41no—
124C22×C3×D3—41no—
125C22×C3×D3—41no—
126C22×C3×D3—41no—
127C2×C32×C4—41no—
128C2×C32×C4—41no—
129C2×C32×C4—41no—
130C2×C32×C4—41no—
131C2×C32×C4C2×D411yescharacteristic
132C2×C32×C4C2×D411yescharacteristic
133#638—41no—
134#638—41no—
135C2×C3⋊Dic3—21no—
136C4⋊(C3⋊D3)—41no—
137C2×C3×Dic3—21no—
138C2×C3×Dic3—21no—
139C2×C3×Dic3—21no—
140C2×C3×Dic3—21no—
141C2×C3×Dic3—21no—
142C2×C3×Dic3—21no—
143C2×C3×Dic3—41no—
144C3×D12—22no—
145C3×D12—22no—
146C3×D12—41no—
147C3×D12—41no—
148C3×Dic6—41no—
149#624—81no—
150C3⋊(C3⋊C8)—41no—
151C3×C3⋊C8—41no—
152#539—91no—
153#450—91no—
154#447—91no—
155#394—31no—
156#328—31no—
157#327—91no—
158#324—91no—
159C24×C3—61no—
160C23×D3—21no—
161C2×C3×Q8—31no—
162C2×C3×D4—61no—
163C2×C3×D4—61no—
164C2×C3×D4—122no—
165C22×C3×C4—21no—
166C22×C3×C4—21no—
167C22×C3×C4—21no—
168C22×C3×C4—31no—
169C22×C3×C4—31no—
170C22×C3×C4—41no—
171C22×C3×C4C22×D311yescharacteristic
172C22×C3×C4C22×D311yescharacteristic
173C2×#67—61no—
174C2×#67—61no—
175C2×#67—121no—
176C22×Dic3#6711yescharacteristic
177C22×Dic3#6711yescharacteristic
178C2×D12—21no—
179C2×D12—21no—
180C2×D12—31no—
181C2×D12—31no—
182C2×D12—42no—
183C2×D12—61no—
184C2×C4×D3—61no—
185C2×C4×D3—61no—
186C2×Dic6D1211yescharacteristic
187C2×C3×C8—61no—
188C3×C4⋊C4—31no—
189C3×C4⋊C4—61no—
190C3×C4⋊C4—61no—
191C3×C4⋊C4—61no—
192C3×C22⋊C4—61no—
193C3×C22⋊C4—122no—
194C3×C22⋊C4—122no—
195#217—21no—
196#215—122no—
197#214—122no—
198#213—122no—
199(C2×D3)⋊C4—42no—
200(C2×D3)⋊C4—42no—
201(C2×D3)⋊C4—61no—
202(C2×D3)⋊C4—61no—
203(C2×D3)⋊C4—61no—
204(C2×D3)⋊C4—61no—
205(C2×D3)⋊C4—61no—
206(C2×D3)⋊C4—61no—
207(C2×D3)⋊C4—61no—
208(C2×D3)⋊C4—61no—
209(C2×D3)⋊C4—121no—
210C4⋊Dic3—31no—
211C4⋊Dic3—31no—
212C4⋊Dic3—61no—
213C4⋊Dic3—61no—
214C4⋊Dic3—61no—
215C4⋊Dic3D1211yescharacteristic
216Dic3⋊C4—21no—
217Dic3⋊C4—21no—
218Dic3⋊C4—21no—
219Dic3⋊C4—61no—
220Dic3⋊C4—61no—
221Dic3⋊C4—61no—
222Dic3⋊C4—61no—
223C4×Dic3—61no—
224C4×Dic3—61no—
225C2×C3⋊C8—21no—
226C2×C3⋊C8—61no—
227C2×C3⋊C8—61no—
228C2×C3⋊C8—121no—
229D24—122no—
230C22×C32—21no—
231C22×C32—21no—
232C22×C32#12011yescharacteristic
233C22×C32#13511yescharacteristic
234C22×C32AGL(1,ℤ/8)11yescharacteristic
235C2×C3⋊D3—41no—
236C2×C3⋊D3—41no—
237C2×C3⋊D3—41no—
238C2×C3×D3—42no—
239C2×C3×D3—42no—
240C2×C3×D3—42no—
241C2×C3×D3—81no—
242C2×C3×D3—81no—
243C2×C3×D3—81no—
244C2×C3×D3—81no—
245C32×C4—21no—
246C32×C4—21no—
247C32×C4—81no—
248C3⋊Dic3—41no—
249C3×Dic3—41no—
250C3×Dic3—41no—
251C3×Dic3—41no—
252C3×Dic3—41no—
253C22×D4—31no—
254C2×SD16—181no—
255C2×D8—181no—
256#126—181no—
257#125—181no—
258#123—181no—
259#123—181no—
260C22⋊Q8—31no—
261C22⋊Q8—181no—
262#121—91no—
263C4×D4—181no—
264C2×C4⋊C4—31no—
265C2×C22⋊C4—61no—
266C2×C22⋊C4—61no—
267#102—181no—
268#102—181no—
269C22⋊C8—31no—
270C22⋊C8—91no—
271#95D3211yescharacteristic
272C23×C3—21no—
273C23×C3—62no—
274C23×C3—121no—
275C23×C3—121no—
276C23×C3—121no—
277C23×C3—121no—
278C23×C3—121no—
279C23×C3—121no—
280C23×C3D3×D411yescharacteristic
281C23×C3C2×#6711yescharacteristic
282C22×D3—22no—
283C22×D3—41no—
284C22×D3—41no—
285C22×D3—41no—
286C22×D3—41no—
287C22×D3—41no—
288C22×D3—41no—
289C22×D3—61no—
290C22×D3—61no—
291C22×D3—121no—
292C3×Q8—121no—
293C3×D4—62no—
294C3×D4—62no—
295C3×D4—121no—
296C3×D4—121no—
297C2×C3×C4—21no—
298C2×C3×C4—21no—
299C2×C3×C4—41no—
300C2×C3×C4—41no—
301C2×C3×C4—41no—
302C2×C3×C4—41no—
303C2×C3×C4—41no—
304C2×C3×C4—41no—
305C2×C3×C4—42no—
306C2×C3×C4—41no—
307C2×C3×C4—41no—
308C2×C3×C4—61no—
309C2×C3×C4—61no—
310C2×C3×C4—61no—
311C2×C3×C4—61no—
312C2×C3×C4—61no—
313C2×C3×C4—61no—
314C2×C3×C4—81no—
315C2×C3×C4—81no—
316C2×C3×C4—81no—
317C2×C3×C4—121no—
318C2×C3×C4C2×D1211yescharacteristic
319C2×C3×C4D3×D411yescharacteristic
320C2×C3×C4D3×D411yescharacteristic
321C2×C3×C4D3×D411yescharacteristic
322#67—121no—
323#67—121no—
324#67—121no—
325#67—121no—
326#67—241no—
327#67—241no—
328C2×Dic3—21no—
329C2×Dic3—21no—
330C2×Dic3—21no—
331C2×Dic3—21no—
332C2×Dic3—21no—
333C2×Dic3—21no—
334C2×Dic3—41no—
335C2×Dic3—61no—
336C2×Dic3—61no—
337C2×Dic3—121no—
338D12—22no—
339D12—22no—
340D12—41no—
341D12—41no—
342D12—121no—
343D12—121no—
344D12—241no—
345C4×D3—241no—
346C4×D3—241no—
347Dic6—41no—
348C3×C8—121no—
349C3⋊C8—41no—
350C3⋊C8—121no—
351C3⋊C8—121no—
352C3⋊C8—241no—
353C2×C32—21no—
354C2×C32—21no—
355C2×C32#44911yescharacteristic
356C2×C32#45411yescharacteristic
357C2×C32B(4,𝔽2)11yescharacteristic
358C3⋊D3—81no—
359C3×D3—82no—
360C24—61no—
361C2×Q8—31no—
362C2×D4—61no—
363C2×D4—61no—
364C2×D4—91no—
365C2×D4—122no—
366C2×D4—181no—
367C22×C4—21no—
368C22×C4—31no—
369C22×C4—31no—
370C22×C4—181no—
371C22×C4C2×D3211yescharacteristic
372SD16—362no—
373D8—362no—
374C2×C8—61no—
375C2×C8—181no—
376C4⋊C4—31no—
377C4⋊C4—61no—
378C4⋊C4—61no—
379C4⋊C4—61no—
380C4⋊C4—91no—
381C4⋊C4—181no—
382C4⋊C4—181no—
383C4⋊C4—181no—
384C22⋊C4—61no—
385C22⋊C4—122no—
386C22⋊C4—122no—
387C22⋊C4—181no—
388C22⋊C4—181no—
389C22⋊C4—181no—
390C22⋊C4—181no—
391C42—181no—
392C22×C3—21no—
393C22×C3—21no—
394C22×C3—21no—
395C22×C3—21no—
396C22×C3—21no—
397C22×C3—21no—
398C22×C3—21no—
399C22×C3—41no—
400C22×C3—41no—
401C22×C3—122no—
402C22×C3—122no—
403C22×C3—122no—
404C22×C3—241no—
405C22×C3—241no—
406C22×C3—241no—
407C22×C3—241no—
408C22×C3#88211yescharacteristic
409C22×C3#91411yescharacteristic
410C22×C3#91911yescharacteristic
411C22×C3#93211yescharacteristic
412C22×C3#93711yescharacteristic
413C22×C3#95011yescharacteristic
414C2×D3—42no—
415C2×D3—42no—
416C2×D3—42no—
417C2×D3—81no—
418C2×D3—81no—
419C2×D3—81no—
420C2×D3—81no—
421C2×D3—121no—
422C2×D3—121no—
423C2×D3—121no—
424C2×D3—121no—
425C2×D3—121no—
426C2×D3—121no—
427C2×D3—241no—
428C2×D3—241no—
429C2×D3—241no—
430C3×C4—21no—
431C3×C4—21no—
432C3×C4—21no—
433C3×C4—21no—
434C3×C4—41no—
435C3×C4—41no—
436C3×C4—81no—
437C3×C4—81no—
438C3×C4—82no—
439C3×C4—121no—
440C3×C4—121no—
441C3×C4—121no—
442C3×C4—121no—
443Dic3—41no—
444Dic3—41no—
445Dic3—41no—
446Dic3—41no—
447Dic3—121no—
448Dic3—121no—
449Dic3—241no—
450C32#159711yescharacteristic, complemented, Sylow
451C23—62no—
452C23—121no—
453C23—121no—
454C23—121no—
455C23—121no—
456C23—121no—
457C23—121no—
458C23—181no—
459C23D3×#6711yescharacteristic
460Q8—121no—
461D4—62no—
462D4—62no—
463D4—121no—
464D4—121no—
465D4—361no—
466D4—361no—
467D4—361no—
468C2×C4—41no—
469C2×C4—41no—
470C2×C4—41no—
471C2×C4—41no—
472C2×C4—61no—
473C2×C4—61no—
474C2×C4—61no—
475C2×C4—61no—
476C2×C4—61no—
477C2×C4—61no—
478C2×C4—121no—
479C2×C4—181no—
480C2×C4—721no—
481C2×C4D3×D1211yescharacteristic
482C2×C4#380211yescharacteristic
483C8—121no—
484C8—361no—
485C2×C3—21no—
486C2×C3—21no—
487C2×C3—21no—
488C2×C3—21no—
489C2×C3—21no—
490C2×C3—21no—
491C2×C3—21no—
492C2×C3—41no—
493C2×C3—41no—
494C2×C3—242no—
495C2×C3#474111yescharacteristic
496C2×C3#481011yescharacteristic
497C2×C3#482711yescharacteristic
498C2×C3#503211yescharacteristic
499C2×C3#503711yescharacteristic
500C2×C3#506211yescharacteristic
501D3—82no—
502D3—241no—
503D3—241no—
504D3—481no—
505C22—21no—
506C22—21no—
507C22—122no—
508C22—122no—
509C22—122no—
510C22—241no—
511C22—241no—
512C22—241no—
513C22—241no—
514C22—361no—
515C22—361no—
516C22—361no—
517C22#6392211yescharacteristic
518C22#6393411yescharacteristic
519C22#6394911yescharacteristic
520C4—21no—
521C4—21no—
522C4—81no—
523C4—121no—
524C4—121no—
525C4—121no—
526C4—121no—
527C4—361no—
528C3—21no—
529C3#6832411yescharacteristic, complemented
530C3#6970211yescharacteristic, complemented
531C2—21no—
532C2—21no—
533C2—242no—
534C2—721no—
535C2#1059040011yescharacteristic
536C2#1059040711yescharacteristic
537C2#1059061511yescharacteristic
subgroupG/H
centerC22#63922
commutator, cosocleC22×C32×C4C23
FrattiniC22×C4C2×D32
FittingC32×#95C22
socleC22×C32#120
prime radical#10591162C2
hypercenter#95D32
hypocenterC32#1597
LCSG ▷ C22×C32×C4 ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ #95

Complements

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

NH ≅ G/Ntype
1. #10594980C2semidirect
2. C3×#4672C2semidirect
3. #10591169C2semidirect
5. #10589317C2semidirect
6. C3×#4452C2semidirect
7. #10589147C2semidirect
36. #4672D3semidirect
40. #4452D3semidirect
450. C32#1597semidirect
529. C3#68324semidirect
530. C3#69702semidirect

Maximal subgroups

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

subgroupindex
#105949802
C3×#46722
#105911692
#105911622
#105893172
C3×#44522
#105891472
#697023
#683243