Finite Group Databasebeta

← #11789713

Subgroups — #11789713

Order 1152.

517 conjugacy classes of subgroups.

The subgroup lattice has 446 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#63652C211yesmaximal, characteristic
2C3×#5124C211yesmaximal, characteristic, complemented
3#10591113C211yesmaximal, characteristic
4#10591078C211yesmaximal, characteristic
5#10591060C211yesmaximal, characteristic, complemented
6C3×#4556C211yesmaximal, characteristic, complemented
7#10589160C211yesmaximal, characteristic, complemented
8#70727—31nomaximal
9#69012—31nomaximal
10C2×#3828C2211yescharacteristic
11C2×C32×M16C2211yescharacteristic
12C2×C4×C3⋊Dic3C2211yescharacteristic
13C3×#926C2211yescharacteristic
14C2×C3×#208C2211yescharacteristic
15C2×C3×#208C2211yescharacteristic
16C2×C3×#208C2211yescharacteristic
17#63652—21no—
18#63652—21no—
19C3×#822—22no—
20#63570—22no—
21#63561C412yescomplemented
22#63559C412yescomplemented
23#63555—21no—
24#63553—21no—
25C3×#430—31no—
26#5139—31no—
27C2×#825—31no—
28C2×#825—31no—
29C2×#825—61no—
30#5132—31no—
31#5132—31no—
32#5124D311yescharacteristic, complemented
33Dic3×M16—31no—
34Dic3×M16—31no—
35#5005—31no—
36C3×#344—31no—
37#4556D311yescharacteristic, complemented
38#4555—31no—
39#4532—31no—
40C22×C32×C4C2311yescharacteristic
41C2×#638—21no—
42C22×C3⋊Dic3—21no—
43#3828—21no—
44#3828—21no—
45#3828—21no—
46#3828—21no—
47C2×C4⋊(C3⋊D3)C2×C411yescharacteristic
48C2×C4×C3⋊D3—21no—
49C2×#634C2×C411yescharacteristic
50C32×M16—21no—
51C32×M16—21no—
52C2×C32×C8—21no—
53C4×C3⋊Dic3—21no—
54C4×C3⋊Dic3D411yescharacteristic
55C4×C3⋊Dic3D411yescharacteristic
56C3×#217—21no—
57C3×C4⋊Dic3—21no—
58C3×C4×Dic3—21no—
59C3×#208—21no—
60C3×#208—21no—
61C3×#208—21no—
62C3×#208C2×C412yes—
63C3×#208C2×C412yes—
64C3×#208D412yes—
65C2×C3×C3⋊C8—21no—
66C2×C3×C3⋊C8—21no—
67C2×C3×C3⋊C8—21no—
68#1932—91noSylow
69C2×#235—31no—
70C2×#235—31no—
71C2×#235—61no—
72C2×C3×M16—21no—
73C2×C3×M16—31no—
74C2×C3×M16—31no—
75C2×C3×M16—31no—
76C2×C3×M16C2×D311yescharacteristic
77C2×C3×M16C2×D311yescharacteristic
78C3×#117—31no—
79#926C2×D311yescharacteristic
80C2×C4×Dic3—31no—
81C2×C4×Dic3—31no—
82C2×C4×Dic3—61no—
83C2×#208C2×D311yescharacteristic
84C2×#208C2×D311yescharacteristic
85C2×#208C2×D311yescharacteristic
86C3×#108—62no—
87#825—62no—
88#825—61no—
89#825—61no—
90#825—61no—
91#825—61no—
92#825—62no—
93#825—62no—
94#824—32no—
95#824—32no—
96#823—32no—
97#823—32no—
98#822—22no—
99#815—61no—
100#815—61no—
101C8×Dic3—61no—
102C8×Dic3—61no—
103#805—62no—
104C23×C32#4111yescharacteristic
105C22×C3⋊D3—21no—
106C2×C32×C4C22×C411yescharacteristic
107C2×C32×C4C2×D411yescharacteristic
108C2×C32×C4C2×D411yescharacteristic
109C2×C32×C4#4111yescharacteristic
110C2×C32×C4#4111yescharacteristic
111C2×C32×C4#4111yescharacteristic
112#638—41no—
113#638—41no—
114C2×C3⋊Dic3—21no—
115C2×C3⋊Dic3—21no—
116C2×C3⋊Dic3—21no—
117C2×C3⋊Dic3—42no—
118C4⋊(C3⋊D3)—21no—
119C4⋊(C3⋊D3)—21no—
120C4×C3⋊D3—41no—
121C4×C3⋊D3—41no—
122#634—21no—
123#634—21no—
124C2×C3×Dic3—41no—
125C32×C8—41no—
126C3×C3⋊C8—22no—
127C3×C3⋊C8—22no—
128C3×C3⋊C8—22no—
129#430—31no—
130#421—91no—
131C2×#104—91no—
132#413—91no—
133C4×M16—91no—
134#344—31no—
135#339—91no—
136C22×C3×C4—21no—
137C22×C3×C4C22×D311yescharacteristic
138C22×C3×C4C22×D311yescharacteristic
139C2×#67—61no—
140C2×#67—61no—
141C2×#67—121no—
142C22×Dic3—61no—
143C22×Dic3—61no—
144C22×Dic3—121no—
145#235—62no—
146#235—62no—
147#235—61no—
148#235—61no—
149#235—61no—
150#235—61no—
151#235—61no—
152#235—61no—
153#235—61no—
154#235—61no—
155#235—121no—
156#235—121no—
157C2×D12—31no—
158C2×D12—31no—
159C2×D12—61no—
160C2×C4×D3—61no—
161C2×C4×D3—61no—
162C2×C4×D3—121no—
163C2×Dic6—31no—
164C2×Dic6—31no—
165C2×Dic6—61no—
166C3×M16—22no—
167C3×M16—21no—
168C3×M16—21no—
169C3×M16—21no—
170C3×M16—21no—
171C3×M16—32no—
172C3×M16—32no—
173C3×M16—32no—
174C3×M16—41no—
175C3×M16—61no—
176C3×M16—61no—
177C3×M16—61no—
178C2×C3×C8—21no—
179C2×C3×C8—21no—
180C2×C3×C8—41no—
181C2×C3×C8—61no—
182C2×C3×C8—61no—
183C2×C3×C8—61no—
184C3×C4⋊C4—61no—
185C3×C22⋊C4—61no—
186C3×C42—61no—
187#217—21no—
188C4⋊Dic3—21no—
189C4×Dic3—21no—
190C4×Dic3—31no—
191C4×Dic3—31no—
192C4×Dic3—31no—
193C4×Dic3—31no—
194C4×Dic3—61no—
195C4×Dic3—61no—
196C4×Dic3—61no—
197C4×Dic3—61no—
198C4×Dic3—121no—
199#208—21no—
200#208—21no—
201#208—21no—
202#208C4×D312yes—
203#208C4×D312yes—
204#208#6712yes—
205C2×C3⋊C8—21no—
206C2×C3⋊C8—21no—
207C2×C3⋊C8—21no—
208C22×C32—41no—
209C22×C32#11711yescharacteristic
210C22×C32#12311yescharacteristic
211C22×C32#12411yescharacteristic
212C2×C3⋊D3—41no—
213C2×C3⋊D3—81no—
214C32×C4C4×D411yescharacteristic
215C32×C4C4×D411yescharacteristic
216C32×C4#12111yescharacteristic
217C32×C4#12611yescharacteristic
218C3⋊Dic3—22no—
219C3⋊Dic3—41no—
220C3⋊Dic3—41no—
221C3×Dic3—81no—
222C2×#41—91no—
223C2×M16—31no—
224C2×M16—31no—
225C2×M16—31no—
226C2×M16D3211yescharacteristic
227#117—31no—
228C2×C42—91no—
229#108—62no—
230#104—182no—
231#104—181no—
232#104—181no—
233#101—92no—
234#100—92no—
235#97—181no—
236C4×C8—181no—
237C23×C3—21no—
238C23×C3#23511yescharacteristic
239C23×C3#23911yescharacteristic
240C22×D3—61no—
241C22×D3—61no—
242C22×D3—121no—
243C2×C3×C4—21no—
244C2×C3×C4—21no—
245C2×C3×C4—21no—
246C2×C3×C4—21no—
247C2×C3×C4—21no—
248C2×C3×C4—21no—
249C2×C3×C4—121no—
250C2×C3×C4C2×C4×D311yescharacteristic
251C2×C3×C4C2×C4×D311yescharacteristic
252C2×C3×C4#23511yescharacteristic
253C2×C3×C4#23511yescharacteristic
254C2×C3×C4D3×D411yescharacteristic
255C2×C3×C4D3×D411yescharacteristic
256C2×C3×C4D3×D411yescharacteristic
257C2×C3×C4#23711yescharacteristic
258C2×C3×C4#23711yescharacteristic
259C2×C3×C4#23911yescharacteristic
260C2×C3×C4#23911yescharacteristic
261C2×C3×C4C2×#6711yescharacteristic
262#67—122no—
263#67—122no—
264#67—121no—
265#67—121no—
266#67—121no—
267#67—121no—
268C2×Dic3—41no—
269C2×Dic3—61no—
270C2×Dic3—61no—
271C2×Dic3—61no—
272C2×Dic3—61no—
273C2×Dic3—61no—
274C2×Dic3—61no—
275C2×Dic3—121no—
276C2×Dic3—121no—
277C2×Dic3—121no—
278C2×Dic3—122no—
279C2×Dic3—122no—
280C2×Dic3—124no—
281D12—62no—
282D12—61no—
283D12—61no—
284D12—61no—
285D12—61no—
286D12—121no—
287C4×D3—122no—
288C4×D3—122no—
289C4×D3—121no—
290C4×D3—121no—
291C4×D3—121no—
292C4×D3—121no—
293Dic6—62no—
294Dic6—61no—
295Dic6—61no—
296Dic6—61no—
297Dic6—61no—
298Dic6—121no—
299C3×C8—42no—
300C3×C8—41no—
301C3×C8—41no—
302C3×C8—62no—
303C3×C8—62no—
304C3×C8—62no—
305C3⋊C8—22no—
306C3⋊C8—22no—
307C3⋊C8—22no—
308C2×C32—21no—
309C2×C32—21no—
310C2×C32—21no—
311C2×C32#38811yescharacteristic
312C3⋊D3—81no—
313#41—181no—
314#41—181no—
315#41—181no—
316#41—181no—
317C2×Q8—91no—
318C2×D4—91no—
319C2×D4—181no—
320C22×C4—181no—
321C22×C4—181no—
322C22×C4C2×D3211yescharacteristic
323M16—21no—
324M16—21no—
325M16—32no—
326M16—32no—
327M16—32no—
328M16—61no—
329M16—61no—
330M16—61no—
331C2×C8—21no—
332C2×C8—61no—
333C2×C8—61no—
334C2×C8—61no—
335C4⋊C4—61no—
336C22⋊C4—61no—
337C42—61no—
338C42—91no—
339C42—91no—
340C42—181no—
341C22×C3—21no—
342C22×C3—21no—
343C22×C3—21no—
344C22×C3—41no—
345C22×C3—41no—
346C22×C3—42no—
347C22×C3#87211yescharacteristic
348C22×C3#88511yescharacteristic
349C22×C3#89211yescharacteristic
350C22×C3#89411yescharacteristic
351C22×C3#89411yescharacteristic
352C22×C3#94711yescharacteristic
353C2×D3—122no—
354C2×D3—121no—
355C2×D3—121no—
356C2×D3—242no—
357C2×D3—241no—
358C2×D3—241no—
359C3×C4—21no—
360C3×C4—21no—
361C3×C4—21no—
362C3×C4—21no—
363C3×C4—241no—
364C3×C4#67⋊C411yescharacteristic
365C3×C4#88411yescharacteristic
366C3×C4#89311yescharacteristic
367C3×C4#89311yescharacteristic
368C3×C4#89811yescharacteristic
369C3×C4#89811yescharacteristic
370C3×C4C4×#6711yescharacteristic
371C3×C4#93911yescharacteristic
372Dic3—62no—
373Dic3—62no—
374Dic3—81no—
375Dic3—122no—
376Dic3—122no—
377Dic3—121no—
378Dic3—121no—
379Dic3—122no—
380Dic3—121no—
381Dic3—121no—
382C32#193211yescharacteristic, complemented, Sylow
383C23—181no—
384C23#379911yescharacteristic
385Q8—181no—
386Q8—181no—
387D4—181no—
388D4—181no—
389D4—361no—
390D4—361no—
391C2×C4—121no—
392C2×C4—181no—
393C2×C4—181no—
394C2×C4—181no—
395C2×C4—362no—
396C2×C4—361no—
397C2×C4—361no—
398C2×C4#379611yescharacteristic
399C2×C4#379911yescharacteristic
400C2×C4C4×D3211yescharacteristic
401C2×C4#380411yescharacteristic
402C2×C4D3×#6711yescharacteristic
403C2×C4#381111yescharacteristic
404C8—41no—
405C8—62no—
406C8—62no—
407C8—62no—
408C2×C3—22no—
409C2×C3—21no—
410C2×C3—21no—
411C2×C3—21no—
412C2×C3—21no—
413C2×C3—21no—
414C2×C3—21no—
415C2×C3—21no—
416C2×C3—41no—
417C2×C3—41no—
418C2×C3#466911yescharacteristic
419C2×C3#499011yescharacteristic
420D3—242no—
421D3—241no—
422D3—241no—
423C22—41no—
424C22—361no—
425C22—721no—
426C22#6383611yescharacteristic
427C22#6389711yescharacteristic
428C22#6390711yescharacteristic
429C4—182no—
430C4—241no—
431C4—361no—
432C4—361no—
433C4#6384811yescharacteristic
434C4#6388111yescharacteristic
435C4#6390411yescharacteristic
436C4#6397111yescharacteristic
437C3—21no—
438C3#6901211yescharacteristic, complemented
439C3#7072711yescharacteristic, complemented
440C2—21no—
441C2—21no—
442C2—21no—
443C2—721no—
444C2#1059125811yescharacteristic
subgroupG/H
centerC4#63971
commutatorC2×C32×C4C22×C4
FrattiniC22×C4C2×D32
FittingC2×C32×M16C22
socleC2×C32#388
prime radicalC2×#3828C22
cosocleC22×C32×C4C23
hypercenterC2×M16D32
hypocenterC32#1932
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C4 ◁ C22×C4 ◁ C2×M16

Complements

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

NH ≅ G/Ntype
2. C3×#5124C2semidirect
5. #10591060C2semidirect
6. C3×#4556C2semidirect
7. #10589160C2semidirect
21. #63561C4semidirect
22. #63559C4semidirect
32. #5124D3semidirect
37. #4556D3semidirect
382. C32#1932semidirect
438. C3#69012semidirect
439. C3#70727semidirect

Maximal subgroups

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

subgroupindex
C2×#636522
C3×#51242
#105911132
#105910782
#105910602
C3×#45562
#105891602
#707273
#690123