Finite Group Databasebeta

← #11897672

Subgroups — #11897672

Order 1152.

741 conjugacy classes of subgroups.

The subgroup lattice has 514 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10593958C211yesmaximal, characteristic
2#10593856C211yesmaximal, characteristic, complemented
3C4×#3744C211yesmaximal, characteristic
4C3×#4682C211yesmaximal, characteristic, complemented
5C3×#4679C211yesmaximal, characteristic, complemented
6#10590894C212yesmaximal, complemented
7#10590814C212yesmaximal, complemented
8#10590773C212yesmaximal
9#10590764C212yesmaximal
10#10590300C211yesmaximal, characteristic
11#10590284C211yesmaximal, characteristic, complemented
12#81954—31nomaximal
13#79976—31nomaximal
14C2×#3744C2211yescharacteristic
15C4×C4⋊(C3⋊D3)C2211yescharacteristic
16C4×#634C2211yescharacteristic
17C3×#869C2211yescharacteristic
18C3×#869C2211yescharacteristic
19C3×C4×Dic6C2211yescharacteristic
20#63919—21no—
21#63918C2212yes—
22#63900—21no—
23#63894C2212yes—
24#63888—22no—
25#63871—21no—
26#63869C2212yes—
27#63844C2212yes—
28#63843—21no—
29#63839—22no—
30C32×C4×C8C2211yescharacteristic
31#63648C2211yescharacteristic
32#63644C2211yescharacteristic
33#63643C2211yescharacteristic
34C3×#818C2212yes—
35C3×#818C2212yes—
36C3×#815C2212yes—
37C3×Dic3⋊C8C2212yes—
38C3×C4⋊(C3⋊C8)C2211yescharacteristic
39#63575C2212yes—
40#63573C2212yes—
41#63567C2212yes—
42#63564C2212yes—
43#5730—31no—
44#5722—31no—
45#5579—31no—
46Q8×Dic6—31no—
47C3×#500—31no—
48C3×#446—31no—
49#5091—31no—
50#5084—31no—
51#4890—32no—
52#4889—32no—
53#4877—32no—
54#4876—32no—
55#4850—31no—
56#4846—32no—
57#4842—31no—
58#4829—32no—
59#4710—32no—
60#4702—32no—
61C4×#204—31no—
62C4×#204—31no—
63C4×#204—61no—
64#4682D311yescharacteristic, complemented
65#4679D311yescharacteristic, complemented
66C2×C4⋊(C3⋊D3)C2311yescharacteristic
67C2×C4×C3⋊D3—21no—
68C2×#634C2311yescharacteristic
69C2×C3×Dic6—21no—
70C2×C3×Dic6—21no—
71C2×C3×Dic6D411yescharacteristic
72C2×#627—22no—
73C2×#624—22no—
74C2×C32×C8C2311yescharacteristic
75C2×C32×C8C2311yescharacteristic
76C32×C42C2311yescharacteristic
77#3752—21no—
78C4⋊(C3⋊Dic3)C2311yescharacteristic
79C4⋊(C3⋊Dic3)C2311yescharacteristic
80#3750—21no—
81C4×C3⋊Dic3—21no—
82#3744Q814yescomplemented
83C3×C4⋊Dic3—21no—
84C3×C4⋊Dic3—21no—
85C3×C4⋊Dic3D411yescharacteristic
86C3×C4⋊Dic3C2312yes—
87C3×C4⋊Dic3C2312yes—
88C3×Dic3⋊C4D412yes—
89C3×C4×Dic3C2312yes—
90C2×C3×C3⋊C8C2312yes—
91#3724—22no—
92#3724—22no—
93Dic3⋊Dic3—22no—
94Dic3⋊Dic3—22no—
95#3722—22no—
96Dic32—22no—
97#3385—91noSylow
98C3×C4⋊Q8—31no—
99C3×C4⋊Q8—31no—
100C3×C4×Q8—31no—
101#946—61no—
102#946—62no—
103Q8×Dic3—61no—
104#944—62no—
105C2×#204—31no—
106C2×#204—31no—
107C2×#204—61no—
108#897—61no—
109#896—62no—
110#893—32no—
111D3×C4⋊C4—61no—
112D3×C4⋊C4—61no—
113#890—32no—
114#888—32no—
115#888—61no—
116#888—62no—
117#888—61no—
118#887—32no—
119#887—61no—
120C4×D12—31no—
121C4×D12—31no—
122C4×D12—32no—
123C4×D12—61no—
124#870—32no—
125#869—32no—
126#869C2×D311yescharacteristic
127#869C2×D311yescharacteristic
128C4×Dic6—31no—
129C4×Dic6—31no—
130C4×Dic6—32no—
131C4×Dic6—61no—
132C4×Dic6C2×D311yescharacteristic
133C3×#107—32no—
134C3×#107—32no—
135C3×C4⋊C8—32no—
136C3×C4⋊C8—31no—
137C3×#97—32no—
138C3×C4×C8—21no—
139C3×C4×C8C2×D311yescharacteristic
140C3×C4×C8C2×D311yescharacteristic
141#821—31no—
142#821—31no—
143#821—32no—
144#821—61no—
145#818—32no—
146#818C2×D312yes—
147#818C2×D312yes—
148#817—31no—
149#817—31no—
150#817—32no—
151#817—61no—
152#816—31no—
153#816—31no—
154#816—32no—
155#816—61no—
156#815C2×D312yes—
157Dic3⋊C8C2×D312yes—
158#810—32no—
159#809—32no—
160#808—32no—
161#807—32no—
162C4⋊(C3⋊C8)C2×D311yescharacteristic
163C22×C3⋊D3—21no—
164C2×C32×C4C2×D411yescharacteristic
165C2×C32×C4C2×D411yescharacteristic
166C2×C32×C4C2411yescharacteristic
167C2×C3⋊Dic3—21no—
168C2×C3⋊Dic3—21no—
169C2×C3⋊Dic3—21no—
170C4⋊(C3⋊D3)—21no—
171C4⋊(C3⋊D3)C2×Q812yes—
172C4×C3⋊D3—42no—
173#634—21no—
174#634C2×Q812yes—
175C2×C3×Dic3—22no—
176C2×C3×Dic3—22no—
177C2×C3×Dic3C2×D412yes—
178C2×C3×Dic3C2×D412yes—
179C3×Dic6—22no—
180C3×Dic6—81no—
181C3×Dic6—81no—
182#627—82no—
183#624—82no—
184C32×C8—21no—
185C32×C8C2×Q812yes—
186C3×C3⋊C8—22no—
187Q82—91no—
188#554—91no—
189#501—92no—
190#500—31no—
191#479—92no—
192#477—91no—
193#476—91no—
194#474—92no—
195#446—31no—
196#440—92no—
197C4×SD16—91no—
198C2×C3×Q8—31no—
199C2×C3×Q8—61no—
200C2×C3×Q8—61no—
201C2×D12—31no—
202C2×D12—31no—
203C2×D12—61no—
204C2×C4×D3—61no—
205C2×C4×D3—61no—
206C2×C4×D3—62no—
207C2×C4×D3—62no—
208C2×C4×D3—121no—
209C2×Dic6—21no—
210C2×Dic6—21no—
211C2×Dic6—31no—
212C2×Dic6—31no—
213C2×Dic6—61no—
214C2×Dic6—62no—
215C2×Dic6—62no—
216C2×Dic6D1211yescharacteristic
217C2×C3×C8—21no—
218C2×C3×C8—21no—
219C2×C3×C8—32no—
220C2×C3×C8C22×D311yescharacteristic
221C2×C3×C8C22×D311yescharacteristic
222C2×C3×C8C22×D311yescharacteristic
223C2×C3×C8C22×D311yescharacteristic
224C3×C4⋊C4—31no—
225C3×C4⋊C4—32no—
226C3×C4⋊C4—32no—
227C3×C4⋊C4—32no—
228C3×C4⋊C4—61no—
229C3×C4⋊C4—61no—
230C3×C42—21no—
231C3×C42—32no—
232C3×C42C22×D311yescharacteristic
233C3×C42C22×D311yescharacteristic
234(C2×D3)⋊C4—62no—
235(C2×D3)⋊C4—61no—
236(C2×D3)⋊C4—61no—
237(C2×D3)⋊C4—62no—
238(C2×D3)⋊C4—121no—
239C4⋊Dic3—21no—
240C4⋊Dic3—21no—
241C4⋊Dic3—31no—
242C4⋊Dic3—31no—
243C4⋊Dic3—31no—
244C4⋊Dic3—31no—
245C4⋊Dic3—61no—
246C4⋊Dic3—61no—
247C4⋊Dic3—62no—
248C4⋊Dic3—62no—
249C4⋊Dic3D1211yescharacteristic
250C4⋊Dic3C22×D312yes—
251C4⋊Dic3C22×D312yes—
252Dic3⋊C4—62no—
253Dic3⋊C4—62no—
254Dic3⋊C4—62no—
255Dic3⋊C4—61no—
256Dic3⋊C4—61no—
257Dic3⋊C4—62no—
258Dic3⋊C4—62no—
259Dic3⋊C4—62no—
260Dic3⋊C4—121no—
261Dic3⋊C4D1212yes—
262C4×Dic3—62no—
263C4×Dic3—61no—
264C4×Dic3—61no—
265C4×Dic3—62no—
266C4×Dic3—121no—
267C4×Dic3C22×D312yes—
268C2×C3⋊C8C22×D312yes—
269#204—34no—
270#204—34no—
271#204—64no—
272C22×C32C22×D411yescharacteristic
273C2×C3⋊D3—22no—
274C2×C3⋊D3—41no—
275C2×C3⋊D3—41no—
276C32×C4—21no—
277C32×C4#13712yes—
278C32×C4C22×Q811yescharacteristic
279C32×C42−1+411yescharacteristic
280C3⋊Dic3—22no—
281C3⋊Dic3—41no—
282C3⋊Dic3—41no—
283C3×Dic3—22no—
284C3×Dic3—22no—
285C3×Dic3—42no—
286C3×Dic3—42no—
287C2×SD16—91no—
288C4⋊Q8—31no—
289C4⋊Q8—31no—
290C4⋊Q8—92no—
291C4⋊Q8—181no—
292C4⋊Q8—182no—
293#125—92no—
294C22⋊Q8—182no—
295C22⋊Q8—181no—
296C4×Q8—31no—
297C4×Q8—92no—
298C4×Q8—91no—
299C4×Q8—181no—
300C4×D4—92no—
301C4×D4—91no—
302C2×C4⋊C4—181no—
303#107—32no—
304#107—32no—
305#107—92no—
306#106—92no—
307#106—91no—
308C4⋊C8—32no—
309C4⋊C8—31no—
310#103—92no—
311#103—91no—
312#102—92no—
313#102—91no—
314#97—32no—
315C4×C8D3211yescharacteristic
316C22×D3—61no—
317C22×D3—61no—
318C22×D3—121no—
319C3×Q8—62no—
320C3×Q8—241no—
321C3×Q8—241no—
322C2×C3×C4—21no—
323C2×C3×C4—21no—
324C2×C3×C4—21no—
325C2×C3×C4—32no—
326C2×C3×C4—32no—
327C2×C3×C4—62no—
328C2×C3×C4—62no—
329C2×C3×C4C2×D1211yescharacteristic
330C2×C3×C4C2×D1211yescharacteristic
331C2×C3×C4D3×D411yescharacteristic
332C2×C3×C4D3×D411yescharacteristic
333C2×C3×C4C23×D311yescharacteristic
334C2×C3×C4C23×D311yescharacteristic
335C2×Dic3—22no—
336C2×Dic3—22no—
337C2×Dic3—61no—
338C2×Dic3—61no—
339C2×Dic3—61no—
340C2×Dic3—61no—
341C2×Dic3—61no—
342C2×Dic3—61no—
343C2×Dic3—121no—
344C2×Dic3—121no—
345C2×Dic3—121no—
346C2×Dic3C2×D1212yes—
347C2×Dic3C2×D1212yes—
348D12—32no—
349D12—32no—
350D12—62no—
351D12—61no—
352D12—61no—
353D12—121no—
354C4×D3—122no—
355C4×D3—122no—
356C4×D3—242no—
357C4×D3—242no—
358C4×D3—242no—
359Dic6—22no—
360Dic6—32no—
361Dic6—32no—
362Dic6—62no—
363Dic6—61no—
364Dic6—61no—
365Dic6—81no—
366Dic6—81no—
367Dic6—121no—
368Dic6—242no—
369Dic6—242no—
370C3×C8—21no—
371C3×C8—21no—
372C3×C8—22no—
373C3×C8—41no—
374C3×C8—62no—
375C3×C8D3×Q812yes—
376C3×C8D3×Q812yes—
377C3⋊C8—22no—
378C2×C32D4×Q811yescharacteristic
379C2×C32C2×#13711yescharacteristic
380C2×C32#57611yescharacteristic
381C3⋊D3—42no—
382C2×Q8—31no—
383C2×Q8—61no—
384C2×Q8—61no—
385C2×Q8—91no—
386C2×Q8—182no—
387C2×D4—91no—
388C22×C4—182no—
389C22×C4—181no—
390SD16—94no—
391C2×C8—32no—
392C2×C8C2×D3211yescharacteristic
393C2×C8C2×D3211yescharacteristic
394C4⋊C4—31no—
395C4⋊C4—32no—
396C4⋊C4—32no—
397C4⋊C4—32no—
398C4⋊C4—61no—
399C4⋊C4—61no—
400C4⋊C4—91no—
401C4⋊C4—91no—
402C4⋊C4—182no—
403C4⋊C4—182no—
404C4⋊C4—182no—
405C4⋊C4—182no—
406C4⋊C4—181no—
407C22⋊C4—182no—
408C22⋊C4—181no—
409C42—32no—
410C42—182no—
411C42—181no—
412C42C2×D3211yescharacteristic
413C22×C3—21no—
414C22×C3C22×D1211yescharacteristic
415C22×C3C2×D3×D411yescharacteristic
416C2×D3—62no—
417C2×D3—62no—
418C2×D3—122no—
419C2×D3—121no—
420C2×D3—121no—
421C2×D3—121no—
422C2×D3—121no—
423C2×D3—241no—
424C2×D3—241no—
425C3×C4—21no—
426C3×C4—21no—
427C3×C4—21no—
428C3×C4—21no—
429C3×C4—22no—
430C3×C4—41no—
431C3×C4—62no—
432C3×C4—62no—
433C3×C4—122no—
434C3×C4—122no—
435C3×C4#90912yes—
436C3×C4#91812yes—
437C3×C4C2×D3×Q811yescharacteristic
438C3×C4C2×D3×Q811yescharacteristic
439C3×C4#100711yescharacteristic
440C3×C4#101011yescharacteristic
441Dic3—22no—
442Dic3—22no—
443Dic3—42no—
444Dic3—42no—
445Dic3—62no—
446Dic3—62no—
447Dic3—122no—
448Dic3—121no—
449Dic3—121no—
450Dic3—121no—
451Dic3—121no—
452Dic3—241no—
453Dic3—241no—
454C32#338511yescharacteristic, complemented, Sylow
455C23—181no—
456Q8—62no—
457Q8—92no—
458Q8—181no—
459Q8—241no—
460Q8—241no—
461Q8—722no—
462D4—92no—
463D4—181no—
464C2×C4—32no—
465C2×C4—32no—
466C2×C4—62no—
467C2×C4—62no—
468C2×C4—181no—
469C2×C4—181no—
470C2×C4—181no—
471C2×C4—362no—
472C2×C4—722no—
473C2×C4D3×D1211yescharacteristic
474C2×C4D3×D1211yescharacteristic
475C2×C4C22×D3211yescharacteristic
476C8—21no—
477C8—62no—
478C8#379712yes—
479C2×C3—21no—
480C2×C3—21no—
481C2×C3—21no—
482C2×C3Q8×D1211yescharacteristic
483C2×C3#572711yescharacteristic
484C2×C3C2×#90911yescharacteristic
485C2×C3#575211yescharacteristic
486C2×C3#575711yescharacteristic
487C2×C3C2×#91811yescharacteristic
488D3—122no—
489D3—122no—
490D3—242no—
491C22—182no—
492C22—361no—
493C22—361no—
494C22C2×D3×D1211yescharacteristic
495C4—21no—
496C4—62no—
497C4—62no—
498C4—122no—
499C4—122no—
500C4—182no—
501C4—361no—
502C4—361no—
503C4#6380112yes—
504C4#6429711yescharacteristic
505C4C2×#379711yescharacteristic
506C3—21no—
507C3#7997611yescharacteristic, complemented
508C3#8195411yescharacteristic, complemented
509C2—362no—
510C2#1059390311yescharacteristic
511C2#1059467811yescharacteristic
512C2C2×#6380111yescharacteristic
subgroupG/H
centerC22C2×D3×D12
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C4×C8C22
socleC22×C32C22×D4
prime radicalC2×C4⋊(C3⋊D3)C23
hypercenterC4×C8D32
hypocenterC32#3385
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8

Complements

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

NH ≅ G/Ntype
2. #10593856C2semidirect
4. C3×#4682C2semidirect
5. C3×#4679C2semidirect
6. #10590894C2semidirect
7. #10590814C2semidirect
11. #10590284C2semidirect
64. #4682D3semidirect
65. #4679D3semidirect
82. #3744Q8semidirect
454. C32#3385semidirect
507. C3#79976semidirect
508. C3#81954semidirect

Maximal subgroups

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

subgroupindex
#105939582
#105938562
C4×#37442
C3×#46822
C3×#46792
#105908942
#105908142
#105907732
#105907642
#105903002
#105902842
#819543
#799763