Finite Group Databasebeta

← #11778306

Subgroups — #11778306

Order 1152.

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

normal subgroups only

This group has 533 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
2C3×#4739C211yesmaximal, characteristic, complemented
3#10591344C211yesmaximal, characteristic, complemented
4#10591174C211yesmaximal, characteristic
5#10589336C211yesmaximal, characteristic
6C3×#4469C211yesmaximal, characteristic, complemented
7#10589152C211yesmaximal, characteristic, complemented
8#70982—31nomaximal
9#68132—31nomaximal
10C22×C3×Dic6C2211yescharacteristic
11#64139C2211yescharacteristic
12C3×#924C2211yescharacteristic
13C2×C3×Dic3⋊C4C2211yescharacteristic
14C2×C3×Dic12—21no—
15C2×#3724—21no—
16#63966—21no—
17#63952—21no—
18#63897—21no—
19#63888—21no—
20#63848—21no—
21#63845—21no—
22C2×#3717—21no—
23C32×C22⋊C8C2211yescharacteristic
24#63658C2211yescharacteristic
25C3×#830C2211yescharacteristic
26C3×#816—21no—
27#63579—21no—
28#63566—21no—
29#5645—31no—
30#5515—31no—
31C3×#451—31no—
32#5230—31no—
33#5227—31no—
34#4979—31no—
35#4739D311yescharacteristic, complemented
36#4738—31no—
37C3×#324—31no—
38#4538—31no—
39#4470—31no—
40#4470—31no—
41#4470—61no—
42#4469D311yescharacteristic, complemented
43#4467—31no—
44C22×C32×C4C2311yescharacteristic
45C2×#638—21no—
46C22×C3⋊Dic3—21no—
47C2×C4⋊(C3⋊D3)D411yescharacteristic
48C22×C3×Dic3—21no—
49C22×C3×Dic3D411yescharacteristic
50C22×C3×Dic3D411yescharacteristic
51C2×C3×Dic6—21no—
52C2×C3×Dic6—21no—
53C2×C3×Dic6—42no—
54C2×C3×Dic6D411yescharacteristic
55C2×#624—21no—
56C2×C32×C8—21no—
57#3752—21no—
58C4⋊(C3⋊Dic3)D411yescharacteristic
59C3×#217—21no—
60C3×C4⋊Dic3D411yescharacteristic
61C3×Dic3⋊C4—21no—
62C3×Dic3⋊C4—21no—
63C3×Dic3⋊C4—21no—
64C2×C3×C3⋊C8—21no—
65C3×Dic12—42no—
66#3724—21no—
67#3724—42no—
68Dic3⋊Dic3—21no—
69Dic3⋊Dic3—21no—
70#3722—21no—
71#3722—21no—
72#3722—21no—
73Dic32—21no—
74#3717—42no—
75#1603—91noSylow
76C22×C3×Q8—31no—
77C22×Dic6C2×D311yescharacteristic
78C2×C3×Q16—61no—
79C3×C22⋊Q8—31no—
80C2×C3×C4⋊C4—31no—
81#946—61no—
82C2×#215—61no—
83#930—31no—
84#930—31no—
85#930—61no—
86#929—61no—
87C4×#67—61no—
88#924C2×D311yescharacteristic
89C2×Dic3⋊C4—61no—
90C2×Dic3⋊C4—61no—
91C2×Dic3⋊C4C2×D311yescharacteristic
92C2×Dic12—21no—
93C2×#204—61no—
94#898—61no—
95#898—61no—
96#896—61no—
97#894—61no—
98#894—61no—
99#890—61no—
100#889—61no—
101#886—61no—
102#67⋊C4—61no—
103C3×#103—61no—
104C3×C22⋊C8—21no—
105C3×C22⋊C8—31no—
106C3×C22⋊C8C2×D311yescharacteristic
107C3×C22⋊C8C2×D311yescharacteristic
108#835—61no—
109C3⋊#95—31no—
110C3⋊#95—31no—
111C3⋊#95—61no—
112C3⋊#95—61no—
113C3⋊#95—61no—
114#830C2×D311yescharacteristic
115#816—21no—
116#816—61no—
117C23×C32C2×D411yescharacteristic
118C22×C3⋊D3—21no—
119C2×C32×C4—41no—
120C2×C32×C4C2×D411yescharacteristic
121C2×C32×C4C2×D411yescharacteristic
122#638—41no—
123#638—41no—
124C2×C3⋊Dic3—22no—
125C2×C3⋊Dic3—21no—
126C2×C3⋊Dic3—41no—
127C2×C3⋊Dic3—41no—
128C4⋊(C3⋊D3)—41no—
129C2×C3×Dic3—22no—
130C2×C3×Dic3—21no—
131C2×C3×Dic3—21no—
132C2×C3×Dic3—21no—
133C2×C3×Dic3—21no—
134C2×C3×Dic3—21no—
135C2×C3×Dic3—21no—
136C2×C3×Dic3—41no—
137C2×C3×Dic3—41no—
138C2×C3×Dic3—41no—
139C3×Dic6—22no—
140C3×Dic6—22no—
141C3×Dic6—41no—
142C3×Dic6—41no—
143C3×Dic6—41no—
144#624—81no—
145C32×C8—41no—
146C3×C3⋊C8—41no—
147#539—91no—
148#451—31no—
149#448—91no—
150#395—91no—
151#328—91no—
152#327—91no—
153#324—31no—
154C2×C3×Q8—31no—
155C2×C3×Q8—61no—
156C2×C3×Q8—61no—
157C2×C3×Q8—122no—
158C22×C3×C4—21no—
159C22×C3×C4—31no—
160C22×C3×C4—31no—
161C22×C3×C4—61no—
162C22×C3×C4C22×D311yescharacteristic
163C22×C3×C4C22×D311yescharacteristic
164C2×#67—61no—
165C2×#67—61no—
166C2×#67—121no—
167C22×Dic3—21no—
168C22×Dic3—61no—
169C22×Dic3—61no—
170C22×Dic3—121no—
171C22×Dic3D1211yescharacteristic
172C22×Dic3D1211yescharacteristic
173C2×D12—31no—
174C2×D12—31no—
175C2×D12—61no—
176C2×C4×D3—61no—
177C2×C4×D3—61no—
178C2×Dic6—21no—
179C2×Dic6—21no—
180C2×Dic6—42no—
181C2×Dic6#6711yescharacteristic
182C3×Q16—122no—
183C2×C3×C8—21no—
184C2×C3×C8—21no—
185C2×C3×C8—41no—
186C2×C3×C8—61no—
187C3×C4⋊C4—31no—
188C3×C4⋊C4—61no—
189C3×C4⋊C4—61no—
190C3×C4⋊C4—61no—
191C3×C22⋊C4—61no—
192#217—21no—
193#215—122no—
194(C2×D3)⋊C4—61no—
195(C2×D3)⋊C4—61no—
196(C2×D3)⋊C4—61no—
197(C2×D3)⋊C4—61no—
198(C2×D3)⋊C4—61no—
199(C2×D3)⋊C4—61no—
200(C2×D3)⋊C4—61no—
201(C2×D3)⋊C4—61no—
202(C2×D3)⋊C4—121no—
203C4⋊Dic3—31no—
204C4⋊Dic3—31no—
205C4⋊Dic3—61no—
206C4⋊Dic3—61no—
207C4⋊Dic3—61no—
208C4⋊Dic3#6711yescharacteristic
209Dic3⋊C4—21no—
210Dic3⋊C4—21no—
211Dic3⋊C4—21no—
212Dic3⋊C4—61no—
213Dic3⋊C4—61no—
214Dic3⋊C4—61no—
215Dic3⋊C4—61no—
216Dic3⋊C4—122no—
217Dic3⋊C4—122no—
218C4×Dic3—61no—
219C4×Dic3—61no—
220C2×C3⋊C8—21no—
221Dic12—42no—
222#204—122no—
223C22×C32—21no—
224C22×C32—21no—
225C22×C32#12011yescharacteristic
226C22×C32#13511yescharacteristic
227C22×C32#13711yescharacteristic
228C2×C3⋊D3—41no—
229C2×C3⋊D3—41no—
230C2×C3⋊D3—41no—
231C32×C4—21no—
232C32×C4—21no—
233C3⋊Dic3—42no—
234C3⋊Dic3—41no—
235C3×Dic3—41no—
236C3×Dic3—41no—
237C3×Dic3—41no—
238C3×Dic3—41no—
239C3×Dic3—42no—
240C22×Q8—31no—
241C2×Q16—61no—
242C2×SD16—181no—
243#126—181no—
244#125—181no—
245#123—181no—
246#123—181no—
247C22⋊Q8—31no—
248C22⋊Q8—181no—
249#121—91no—
250C4×D4—181no—
251C2×C4⋊C4—31no—
252C2×C4⋊C4—181no—
253#103—61no—
254#103—181no—
255C22⋊C8—31no—
256C22⋊C8D3211yescharacteristic
257#95—91no—
258#95—181no—
259C23×C3—21no—
260C23×C3C2×D1211yescharacteristic
261C23×C3D3×D411yescharacteristic
262C22×D3—61no—
263C22×D3—61no—
264C22×D3—121no—
265C3×Q8—62no—
266C3×Q8—62no—
267C3×Q8—121no—
268C3×Q8—121no—
269C3×Q8—121no—
270C2×C3×C4—21no—
271C2×C3×C4—21no—
272C2×C3×C4—41no—
273C2×C3×C4—41no—
274C2×C3×C4—62no—
275C2×C3×C4—61no—
276C2×C3×C4—61no—
277C2×C3×C4—61no—
278C2×C3×C4—61no—
279C2×C3×C4—61no—
280C2×C3×C4—61no—
281C2×C3×C4—81no—
282C2×C3×C4—121no—
283C2×C3×C4—121no—
284C2×C3×C4—121no—
285C2×C3×C4D3×D411yescharacteristic
286C2×C3×C4D3×D411yescharacteristic
287C2×C3×C4D3×D411yescharacteristic
288C2×C3×C4C2×#6711yescharacteristic
289#67—121no—
290#67—121no—
291#67—121no—
292#67—121no—
293#67—241no—
294#67—241no—
295C2×Dic3—22no—
296C2×Dic3—21no—
297C2×Dic3—21no—
298C2×Dic3—21no—
299C2×Dic3—21no—
300C2×Dic3—21no—
301C2×Dic3—21no—
302C2×Dic3—41no—
303C2×Dic3—41no—
304C2×Dic3—41no—
305C2×Dic3—62no—
306C2×Dic3—62no—
307C2×Dic3—61no—
308C2×Dic3—61no—
309C2×Dic3—121no—
310C2×Dic3—122no—
311C2×Dic3—121no—
312C2×Dic3—121no—
313C2×Dic3—121no—
314C2×Dic3—121no—
315C2×Dic3—241no—
316C2×Dic3—241no—
317D12—121no—
318D12—121no—
319D12—241no—
320C4×D3—241no—
321C4×D3—241no—
322Dic6—22no—
323Dic6—22no—
324Dic6—41no—
325Dic6—41no—
326Dic6—41no—
327C3×C8—41no—
328C3×C8—41no—
329C3×C8—81no—
330C3×C8—121no—
331C3⋊C8—41no—
332C2×C32—21no—
333C2×C32—21no—
334C2×C32#45211yescharacteristic
335C2×C32#45611yescharacteristic
336C2×C32B(4,𝔽2)11yescharacteristic
337C3⋊D3—81no—
338C2×Q8—31no—
339C2×Q8—61no—
340C2×Q8—61no—
341C2×Q8—122no—
342C2×D4—91no—
343C2×D4—181no—
344C22×C4—31no—
345C22×C4—31no—
346C22×C4—61no—
347C22×C4—181no—
348C22×C4—181no—
349C22×C4C2×D3211yescharacteristic
350Q16—122no—
351SD16—362no—
352C2×C8—21no—
353C2×C8—61no—
354C4⋊C4—31no—
355C4⋊C4—61no—
356C4⋊C4—61no—
357C4⋊C4—61no—
358C4⋊C4—91no—
359C4⋊C4—181no—
360C4⋊C4—181no—
361C4⋊C4—181no—
362C4⋊C4—362no—
363C22⋊C4—61no—
364C22⋊C4—181no—
365C22⋊C4—181no—
366C22⋊C4—181no—
367C22⋊C4—181no—
368C42—181no—
369C22×C3—21no—
370C22×C3—21no—
371C22×C3—21no—
372C22×C3—21no—
373C22×C3—21no—
374C22×C3—21no—
375C22×C3—21no—
376C22×C3—41no—
377C22×C3—41no—
378C22×C3#88211yescharacteristic
379C22×C3#90411yescharacteristic
380C22×C3#90911yescharacteristic
381C22×C3#91811yescharacteristic
382C22×C3#91911yescharacteristic
383C22×C3#93711yescharacteristic
384C2×D3—121no—
385C2×D3—121no—
386C2×D3—121no—
387C2×D3—121no—
388C2×D3—121no—
389C2×D3—121no—
390C2×D3—241no—
391C2×D3—241no—
392C2×D3—241no—
393C3×C4—21no—
394C3×C4—21no—
395C3×C4—21no—
396C3×C4—21no—
397C3×C4—41no—
398C3×C4—41no—
399C3×C4—121no—
400C3×C4—121no—
401C3×C4—122no—
402C3×C4—121no—
403C3×C4—121no—
404Dic3—41no—
405Dic3—41no—
406Dic3—41no—
407Dic3—42no—
408Dic3—41no—
409Dic3—122no—
410Dic3—122no—
411Dic3—121no—
412Dic3—121no—
413Dic3—241no—
414Dic3—242no—
415C32#160311yescharacteristic, complemented, Sylow
416C23—181no—
417C23D3×D1211yescharacteristic
418Q8—62no—
419Q8—62no—
420Q8—121no—
421Q8—121no—
422Q8—121no—
423D4—361no—
424D4—361no—
425D4—361no—
426C2×C4—41no—
427C2×C4—62no—
428C2×C4—61no—
429C2×C4—61no—
430C2×C4—61no—
431C2×C4—61no—
432C2×C4—61no—
433C2×C4—61no—
434C2×C4—121no—
435C2×C4—121no—
436C2×C4—121no—
437C2×C4—182no—
438C2×C4—181no—
439C2×C4—361no—
440C2×C4—361no—
441C2×C4—721no—
442C2×C4#380211yescharacteristic
443C2×C4D3×#6711yescharacteristic
444C8—41no—
445C8—121no—
446C2×C3—21no—
447C2×C3—21no—
448C2×C3—21no—
449C2×C3—21no—
450C2×C3—21no—
451C2×C3—21no—
452C2×C3—21no—
453C2×C3—41no—
454C2×C3—41no—
455C2×C3#473311yescharacteristic
456C2×C3#474111yescharacteristic
457C2×C3#475211yescharacteristic
458C2×C3#503211yescharacteristic
459C2×C3#518711yescharacteristic
460C2×C3#520511yescharacteristic
461D3—241no—
462D3—241no—
463D3—481no—
464C22—21no—
465C22—21no—
466C22—361no—
467C22—361no—
468C22—361no—
469C22#6380111yescharacteristic
470C22#6380811yescharacteristic
471C22#6392211yescharacteristic
472C4—21no—
473C4—21no—
474C4—121no—
475C4—122no—
476C4—121no—
477C4—121no—
478C4—121no—
479C4—362no—
480C4—361no—
481C3—21no—
482C3#6813211yescharacteristic, complemented
483C3#7098211yescharacteristic, complemented
484C2—21no—
485C2—21no—
486C2—721no—
487C2#1059040711yescharacteristic
488C2#1059096611yescharacteristic
489C2#1059101811yescharacteristic
subgroupG/H
centerC22#63922
commutator, cosocleC22×C32×C4C23
FrattiniC22×C4C2×D32
FittingC32×C22⋊C8C22
socleC22×C32#120
prime radical#64139C22
hypercenterC22⋊C8D32
hypocenterC32#1603
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. C3×#4739C2semidirect
3. #10591344C2semidirect
6. C3×#4469C2semidirect
7. #10589152C2semidirect
35. #4739D3semidirect
42. #4469D3semidirect
415. C32#1603semidirect
482. C3#68132semidirect
483. C3#70982semidirect

Maximal subgroups

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

subgroupindex
#105949802
C3×#47392
#105913442
#105911742
#105893362
C3×#44692
#105891522
#709823
#681323