Finite Group Databasebeta

← #11778410

Subgroups — #11778410

Order 1152.

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

normal subgroups only

This group has 599 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#10595038C211yesmaximal, characteristic
2#10592437C211yesmaximal, characteristic, complemented
3#10591322C211yesmaximal, characteristic, complemented
4#10591190C211yesmaximal, characteristic, complemented
5C3×#4468C211yesmaximal, characteristic, complemented
6C3×#4467C211yesmaximal, characteristic, complemented
7#10589151C211yesmaximal, characteristic, complemented
8#68319—31nomaximal
9#68109—31nomaximal
10C22×#634C2211yescharacteristic
11#64139C2211yescharacteristic
12C2×#3744—21no—
13C2×C3×(C2×D3)⋊C4C2211yescharacteristic
14C3×#924C2211yescharacteristic
15#63977—21no—
16C2×(C2×D3)⋊Dic3—21no—
17#63952—21no—
18#63910—21no—
19#63907—21no—
20#63861—21no—
21#63854—21no—
22C2×#3719—21no—
23C32×C22⋊C8C2211yescharacteristic
24#63643—21no—
25C3×C3⋊#95C2211yescharacteristic
26C3×#830C2211yescharacteristic
27#63579—21no—
28#63567—21no—
29#5644—31no—
30#5494—31no—
31#5050—31no—
32#4947—31no—
33#4739—31no—
34#4738—31no—
35#4738—31no—
36#4738—61no—
37#4673—31no—
38C3×#328—31no—
39C3×#323—31no—
40#4470—31no—
41#4468D311yescharacteristic, complemented
42#4467D311yescharacteristic, complemented
43#4451—31no—
44C23×C3×D3D411yescharacteristic
45C22×C32×C4C2311yescharacteristic
46C2×#638—21no—
47C22×C3⋊Dic3—21no—
48C2×C4⋊(C3⋊D3)D411yescharacteristic
49C2×#634—21no—
50C2×#634—21no—
51C2×#634—42no—
52C22×C3×Dic3—21no—
53C22×C3×Dic3D411yescharacteristic
54C2×C3×Dic6D411yescharacteristic
55C2×#626—21no—
56C2×#626—21no—
57C2×#624—21no—
58C2×C32×C8—21no—
59#3752—21no—
60C4⋊(C3⋊Dic3)D411yescharacteristic
61#3744—42no—
62C3×#217—21no—
63C3×(C2×D3)⋊C4—21no—
64C3×(C2×D3)⋊C4—21no—
65C3×C4⋊Dic3D411yescharacteristic
66C3×Dic3⋊C4—21no—
67C2×C3×C3⋊C8—21no—
68#3724—21no—
69#3722—21no—
70(C2×D3)⋊Dic3—21no—
71(C2×D3)⋊Dic3—21no—
72(C2×D3)⋊Dic3—42no—
73Dic32—21no—
74#3719—42no—
75#1606—91noSylow
76C22×Dic6—31no—
77C22×Dic6—31no—
78C22×Dic6—61no—
79C3×C22⋊Q8—31no—
80C2×C3×C22⋊C4—31no—
81#953—61no—
82C2×#217—61no—
83#947—61no—
84C2×#216—61no—
85#930—31no—
86#930—31no—
87#930—61no—
88C4×#67—61no—
89C2×(C2×D3)⋊C4—61no—
90C2×(C2×D3)⋊C4C2×D311yescharacteristic
91#924C2×D311yescharacteristic
92C2×Dic12—61no—
93C2×#204—61no—
94C2×#204—61no—
95C2×#204—62no—
96#898—61no—
97#895—61no—
98#894—61no—
99#885—61no—
100#884—61no—
101#883—61no—
102#882—61no—
103#67⋊C4—61no—
104#879—61no—
105C3×C22⋊C8—21no—
106C3×C22⋊C8—31no—
107C3×C22⋊C8C2×D311yescharacteristic
108C3×C22⋊C8C2×D311yescharacteristic
109C3×#95—31no—
110C3⋊#95—61no—
111C3⋊#95—61no—
112C3⋊#95C2×D311yescharacteristic
113#830C2×D311yescharacteristic
114#816—61no—
115#816—61no—
116#816—62no—
117#816—61no—
118#810—61no—
119C23×C32C2×D411yescharacteristic
120C22×C3⋊D3—21no—
121C22×C3×D3—21no—
122C22×C3×D3—21no—
123C22×C3×D3—21no—
124C22×C3×D3—41no—
125C22×C3×D3—41no—
126C2×C32×C4—41no—
127C2×C32×C4C2×D411yescharacteristic
128C2×C32×C4C2×D411yescharacteristic
129#638—41no—
130#638—41no—
131C2×C3⋊Dic3—22no—
132C2×C3⋊Dic3—21no—
133C2×C3⋊Dic3—41no—
134C2×C3⋊Dic3—41no—
135C4⋊(C3⋊D3)—41no—
136#634—22no—
137#634—22no—
138#634—41no—
139#634—41no—
140C2×C3×Dic3—21no—
141C2×C3×Dic3—21no—
142C2×C3×Dic3—21no—
143C2×C3×Dic3—41no—
144C2×C3×Dic3—41no—
145C2×C3×Dic3—41no—
146C2×C3×Dic3—41no—
147C3×Dic6—41no—
148#626—81no—
149#626—81no—
150#624—81no—
151C32×C8—41no—
152C3×C3⋊C8—41no—
153#538—91no—
154#451—91no—
155#448—91no—
156#393—91no—
157#328—31no—
158#327—91no—
159#323—31no—
160C24×C3—31no—
161C23×D3D1211yescharacteristic
162C2×C3×Q8—31no—
163C22×C3×C4—21no—
164C22×C3×C4—31no—
165C22×C3×C4—61no—
166C22×C3×C4C22×D311yescharacteristic
167C22×C3×C4C22×D311yescharacteristic
168C2×#67—61no—
169C2×#67—61no—
170C2×#67—61no—
171C2×#67—61no—
172C2×#67—121no—
173C22×Dic3—21no—
174C22×Dic3—61no—
175C22×Dic3—61no—
176C22×Dic3—121no—
177C22×Dic3D1211yescharacteristic
178C2×D12—31no—
179C2×D12—31no—
180C2×D12—61no—
181C2×D12—61no—
182C2×D12—61no—
183C2×C4×D3—61no—
184C2×C4×D3—61no—
185C2×Dic6—62no—
186C2×Dic6—61no—
187C2×Dic6—61no—
188C2×Dic6—61no—
189C2×Dic6—61no—
190C2×Dic6—121no—
191C2×Dic6—122no—
192C2×Dic6—122no—
193C2×Dic6—124no—
194C2×Dic6D1211yescharacteristic
195C2×C3×C8—22no—
196C2×C3×C8—21no—
197C2×C3×C8—21no—
198C2×C3×C8—61no—
199C3×C4⋊C4—31no—
200C3×C4⋊C4—61no—
201C3×C22⋊C4—61no—
202C3×C22⋊C4—61no—
203C3×C22⋊C4—61no—
204#217—21no—
205#217—61no—
206#217—61no—
207#217—122no—
208#216—122no—
209(C2×D3)⋊C4—21no—
210(C2×D3)⋊C4—21no—
211(C2×D3)⋊C4—61no—
212(C2×D3)⋊C4—61no—
213(C2×D3)⋊C4—61no—
214(C2×D3)⋊C4—61no—
215(C2×D3)⋊C4—61no—
216(C2×D3)⋊C4—61no—
217(C2×D3)⋊C4—121no—
218(C2×D3)⋊C4—122no—
219C4⋊Dic3—31no—
220C4⋊Dic3—31no—
221C4⋊Dic3—61no—
222C4⋊Dic3D1211yescharacteristic
223Dic3⋊C4—21no—
224Dic3⋊C4—61no—
225Dic3⋊C4—61no—
226C4×Dic3—61no—
227C4×Dic3—61no—
228C2×C3⋊C8—21no—
229Dic12—122no—
230#204—122no—
231#204—122no—
232#204—124no—
233C22×C32—21no—
234C22×C32—21no—
235C22×C32#12011yescharacteristic
236C22×C32#13511yescharacteristic
237C22×C32#13711yescharacteristic
238C2×C3⋊D3—41no—
239C2×C3⋊D3—41no—
240C2×C3⋊D3—41no—
241C2×C3×D3—42no—
242C2×C3×D3—41no—
243C2×C3×D3—41no—
244C2×C3×D3—41no—
245C2×C3×D3—81no—
246C32×C4—21no—
247C32×C4—21no—
248C3⋊Dic3—42no—
249C3⋊Dic3—41no—
250C3×Dic3—41no—
251C3×Dic3—41no—
252C3×Dic3—41no—
253C3×Dic3—81no—
254C22×Q8—91no—
255C2×Q16—181no—
256C2×SD16—181no—
257#126—181no—
258#124—181no—
259#123—181no—
260C22⋊Q8—31no—
261#121—91no—
262#121—181no—
263#120—181no—
264C4×D4—181no—
265C2×C22⋊C4—31no—
266C2×C22⋊C4—181no—
267#103—181no—
268#103—181no—
269C22⋊C8—31no—
270C22⋊C8D3211yescharacteristic
271#95—31no—
272#95—181no—
273C23×C3—21no—
274C23×C3—61no—
275C23×C3—61no—
276C23×C3—61no—
277C23×C3—121no—
278C23×C3—121no—
279C23×C3C2×D1211yescharacteristic
280C23×C3D3×D411yescharacteristic
281C22×D3—21no—
282C22×D3—21no—
283C22×D3—21no—
284C22×D3—41no—
285C22×D3—41no—
286C22×D3—61no—
287C22×D3—61no—
288C22×D3—121no—
289C3×Q8—121no—
290C2×C3×C4—21no—
291C2×C3×C4—21no—
292C2×C3×C4—41no—
293C2×C3×C4—41no—
294C2×C3×C4—42no—
295C2×C3×C4—61no—
296C2×C3×C4—61no—
297C2×C3×C4—61no—
298C2×C3×C4—121no—
299C2×C3×C4—121no—
300C2×C3×C4—121no—
301C2×C3×C4—121no—
302C2×C3×C4C2×D1211yescharacteristic
303C2×C3×C4D3×D411yescharacteristic
304C2×C3×C4D3×D411yescharacteristic
305C2×C3×C4D3×D411yescharacteristic
306#67—121no—
307#67—121no—
308#67—121no—
309#67—121no—
310#67—241no—
311#67—241no—
312#67—241no—
313#67—241no—
314C2×Dic3—21no—
315C2×Dic3—21no—
316C2×Dic3—21no—
317C2×Dic3—41no—
318C2×Dic3—41no—
319C2×Dic3—41no—
320C2×Dic3—41no—
321C2×Dic3—62no—
322C2×Dic3—62no—
323C2×Dic3—61no—
324C2×Dic3—61no—
325C2×Dic3—122no—
326C2×Dic3—121no—
327C2×Dic3—122no—
328C2×Dic3—121no—
329C2×Dic3—121no—
330C2×Dic3—122no—
331C2×Dic3—121no—
332C2×Dic3—121no—
333D12—121no—
334D12—121no—
335D12—122no—
336D12—241no—
337D12—241no—
338C4×D3—241no—
339C4×D3—241no—
340Dic6—41no—
341Dic6—64no—
342Dic6—62no—
343Dic6—62no—
344Dic6—62no—
345Dic6—62no—
346Dic6—122no—
347Dic6—122no—
348Dic6—121no—
349Dic6—121no—
350Dic6—121no—
351Dic6—121no—
352Dic6—122no—
353C3×C8—42no—
354C3×C8—41no—
355C3×C8—41no—
356C3×C8—121no—
357C3⋊C8—41no—
358C2×C32—21no—
359C2×C32—21no—
360C2×C32#45211yescharacteristic
361C2×C32#45511yescharacteristic
362C2×C32B(4,𝔽2)11yescharacteristic
363C3⋊D3—81no—
364C3×D3—81no—
365C24—31no—
366C2×Q8—31no—
367C2×Q8—181no—
368C2×Q8—181no—
369C2×Q8—362no—
370C2×D4—91no—
371C2×D4—181no—
372C2×D4—181no—
373C2×D4—181no—
374C22×C4—31no—
375C22×C4—61no—
376C22×C4—181no—
377C22×C4—181no—
378C22×C4C2×D3211yescharacteristic
379Q16—362no—
380SD16—362no—
381C2×C8—21no—
382C2×C8—61no—
383C4⋊C4—31no—
384C4⋊C4—61no—
385C4⋊C4—91no—
386C4⋊C4—181no—
387C22⋊C4—61no—
388C22⋊C4—61no—
389C22⋊C4—61no—
390C22⋊C4—181no—
391C22⋊C4—181no—
392C22⋊C4—181no—
393C22⋊C4—181no—
394C22⋊C4—362no—
395C42—181no—
396C22×C3—21no—
397C22×C3—21no—
398C22×C3—21no—
399C22×C3—21no—
400C22×C3—21no—
401C22×C3—21no—
402C22×C3—21no—
403C22×C3—41no—
404C22×C3—41no—
405C22×C3—122no—
406C22×C3—121no—
407C22×C3—121no—
408C22×C3—121no—
409C22×C3—241no—
410C22×C3#88211yescharacteristic
411C22×C3#88211yescharacteristic
412C22×C3#90411yescharacteristic
413C22×C3#90911yescharacteristic
414C22×C3#91611yescharacteristic
415C22×C3#91811yescharacteristic
416C2×D3—42no—
417C2×D3—41no—
418C2×D3—41no—
419C2×D3—41no—
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—22no—
431C3×C4—21no—
432C3×C4—21no—
433C3×C4—21no—
434C3×C4—21no—
435C3×C4—41no—
436C3×C4—121no—
437C3×C4—121no—
438C3×C4—121no—
439C3×C4—241no—
440Dic3—41no—
441Dic3—41no—
442Dic3—41no—
443Dic3—81no—
444Dic3—124no—
445Dic3—121no—
446Dic3—122no—
447Dic3—122no—
448Dic3—121no—
449Dic3—241no—
450C32#160611yescharacteristic, complemented, Sylow
451C23—61no—
452C23—61no—
453C23—61no—
454C23—121no—
455C23—121no—
456C23—181no—
457C23D3×D1211yescharacteristic
458Q8—121no—
459Q8—182no—
460Q8—182no—
461Q8—361no—
462Q8—361no—
463D4—361no—
464D4—361no—
465D4—361no—
466D4—721no—
467D4—721no—
468C2×C4—41no—
469C2×C4—61no—
470C2×C4—61no—
471C2×C4—61no—
472C2×C4—121no—
473C2×C4—121no—
474C2×C4—121no—
475C2×C4—121no—
476C2×C4—182no—
477C2×C4—181no—
478C2×C4—361no—
479C2×C4—361no—
480C2×C4—721no—
481C2×C4D3×D1211yescharacteristic
482C2×C4#381111yescharacteristic
483C8—41no—
484C8—121no—
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—241no—
495C2×C3#473311yescharacteristic
496C2×C3#474111yescharacteristic
497C2×C3#474111yescharacteristic
498C2×C3#474611yescharacteristic
499C2×C3#480811yescharacteristic
500C2×C3#482511yescharacteristic
501D3—81no—
502D3—241no—
503D3—241no—
504D3—481no—
505C22—21no—
506C22—21no—
507C22—122no—
508C22—121no—
509C22—121no—
510C22—121no—
511C22—241no—
512C22—361no—
513C22—361no—
514C22—361no—
515C22#6380111yescharacteristic
516C22#6380611yescharacteristic
517C22#6392311yescharacteristic
518C4—21no—
519C4—21no—
520C4—121no—
521C4—121no—
522C4—121no—
523C4—241no—
524C4—362no—
525C4—361no—
526C3—21no—
527C3#6810911yescharacteristic, complemented
528C3#6831911yescharacteristic, complemented
529C2—21no—
530C2—21no—
531C2—241no—
532C2—721no—
533C2#1059041011yescharacteristic
534C2#1059097011yescharacteristic
535C2#1059101611yescharacteristic
subgroupG/H
centerC22#63923
commutator, cosocleC22×C32×C4C23
FrattiniC22×C4C2×D32
FittingC32×C22⋊C8C22
socleC22×C32#120
prime radical#10595038C2
hypercenterC22⋊C8D32
hypocenterC32#1606
LCSG ▷ C22×C32×C4 ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22⋊C8

Complements

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

NH ≅ G/Ntype
2. #10592437C2semidirect
3. #10591322C2semidirect
4. #10591190C2semidirect
5. C3×#4468C2semidirect
6. C3×#4467C2semidirect
7. #10589151C2semidirect
41. #4468D3semidirect
42. #4467D3semidirect
450. C32#1606semidirect
527. C3#68109semidirect
528. C3#68319semidirect

Maximal subgroups

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

subgroupindex
#105950382
#105924372
#105913222
#105911902
C3×#44682
C3×#44672
#105891512
#683193
#681093