Finite Group Databasebeta

← #11778371

Subgroups — #11778371

Order 1152.

550 conjugacy classes of subgroups; only the 82 normal subgroups are shown.

normal subgroups only

This group has 550 conjugacy classes of subgroups — too many to draw. Only its 82 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#10594812C211yesmaximal, characteristic
2#10592438C211yesmaximal, characteristic
3#10591354C211yesmaximal, characteristic
4#10591190C211yesmaximal, characteristic
5C3×#4469C211yesmaximal, characteristic
6C3×#4467C211yesmaximal, characteristic
7#10589154C211yesmaximal, characteristic
8#68327—31nomaximal
9#68139—31nomaximal
10C22×#634C2211yescharacteristic
11#64133C2211yescharacteristic
12C2×#3746—21no—
13C3×#924C2211yescharacteristic
14C2×C3×Dic3⋊C4C2211yescharacteristic
15C2×Dic3⋊Dic3—21no—
16#63964—21no—
17#63955—21no—
18#63846—21no—
19#63845—21no—
20#63840—21no—
21#63839—21no—
22C2×#3719—21no—
23C32×C22⋊C8C2211yescharacteristic
24#63643—21no—
25C3×C3⋊#95C2211yescharacteristic
26C3×#830C2211yescharacteristic
27#63579—21no—
28#63567—21no—
29#5623—31no—
30#5500—31no—
31#5050—31no—
32#4979—31no—
33#4739—31no—
34#4739—31no—
35#4739—31no—
36#4739—61no—
37#4656—31no—
38C3×#328—31no—
39C3×#324—31no—
40#4469D311yescharacteristic
41#4467—31no—
42#4467D311yescharacteristic
43#4452—31no—
44C22×C32×C4C2311yescharacteristic
45C22×C3⋊Dic3—21no—
46C2×#634—21no—
47C2×#634—21no—
48C2×#634—42no—
49C2×#634D411yescharacteristic
50C22×C3×Dic3—21no—
51C22×C3×Dic3D411yescharacteristic
52C22×C3×Dic3D411yescharacteristic
53C2×C3×Dic6D411yescharacteristic
54C2×#627—21no—
55C2×C32×C8—21no—
56#3757—21no—
57C4⋊(C3⋊Dic3)D411yescharacteristic
58#3750—21no—
59#3746—42no—
60C3×#217—21no—
61C3×C4⋊Dic3D411yescharacteristic
62C3×Dic3⋊C4—21no—
63C3×Dic3⋊C4—21no—
64C3×Dic3⋊C4—21no—
65C2×C3×C3⋊C8—21no—
66#3724—21no—
67Dic3⋊Dic3—21no—
68Dic3⋊Dic3—21no—
69Dic3⋊Dic3—21no—
70Dic3⋊Dic3—21no—
71Dic3⋊Dic3—42no—
72Dic32—21no—
73Dic32—21no—
74#3719—42no—
75#1605—91noSylow
76C22×Dic6—31no—
77C22×Dic6—31no—
78C22×Dic6—61no—
79C3×C22⋊Q8—31no—
80C2×C3×C4⋊C4—31no—
81#944—61no—
82C2×#216—61no—
83#926—61no—
84C2×C4⋊Dic3—61no—
85#924—31no—
86#924—31no—
87#924—61no—
88#924—61no—
89#924C2×D311yescharacteristic
90C2×Dic3⋊C4—61no—
91C2×Dic3⋊C4C2×D311yescharacteristic
92C2×Dic12—61no—
93C2×Dic12—61no—
94C2×Dic12—62no—
95C2×Dic12—61no—
96#890—61no—
97#890—61no—
98#889—61no—
99#889—61no—
100#888—61no—
101#888—61no—
102#888—61no—
103#878—61no—
104#877—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
120C2×C32×C4—41no—
121C2×C32×C4C2×D411yescharacteristic
122C2×C32×C4C2×D411yescharacteristic
123C2×C3⋊Dic3—22no—
124C2×C3⋊Dic3—21no—
125C2×C3⋊Dic3—21no—
126C2×C3⋊Dic3—41no—
127C2×C3⋊Dic3—41no—
128#634—22no—
129#634—22no—
130#634—41no—
131#634—41no—
132#634—41no—
133C2×C3×Dic3—21no—
134C2×C3×Dic3—21no—
135C2×C3×Dic3—22no—
136C2×C3×Dic3—21no—
137C2×C3×Dic3—21no—
138C2×C3×Dic3—21no—
139C2×C3×Dic3—41no—
140C2×C3×Dic3—41no—
141C2×C3×Dic3—41no—
142C2×C3×Dic3Q1612yescomplemented
143C3×Dic6—41no—
144#627—81no—
145C32×C8—41no—
146C3×C3⋊C8—41no—
147#544—91no—
148#451—91no—
149#451—91no—
150#395—91no—
151#328—31no—
152#328—91no—
153#324—31no—
154C2×C3×Q8—31no—
155C22×C3×C4—21no—
156C22×C3×C4—31no—
157C22×C3×C4—31no—
158C22×C3×C4—61no—
159C22×C3×C4C22×D311yescharacteristic
160C22×C3×C4C22×D311yescharacteristic
161C22×Dic3—21no—
162C22×Dic3—61no—
163C22×Dic3—61no—
164C22×Dic3—121no—
165C22×Dic3D1211yescharacteristic
166C22×Dic3D1211yescharacteristic
167C2×Dic6—31no—
168C2×Dic6—31no—
169C2×Dic6—61no—
170C2×Dic6—62no—
171C2×Dic6—61no—
172C2×Dic6—61no—
173C2×Dic6—61no—
174C2×Dic6—61no—
175C2×Dic6—61no—
176C2×Dic6—61no—
177C2×Dic6—121no—
178C2×Dic6—122no—
179C2×Dic6—122no—
180C2×Dic6—124no—
181C2×Dic6D1211yescharacteristic
182C2×C3×C8—22no—
183C2×C3×C8—21no—
184C2×C3×C8—21no—
185C2×C3×C8—61no—
186C3×C4⋊C4—31no—
187C3×C4⋊C4—61no—
188C3×C4⋊C4—61no—
189C3×C4⋊C4—61no—
190C3×C22⋊C4—61no—
191#217—21no—
192#217—61no—
193#217—61no—
194#217—121no—
195#216—122no—
196C4⋊Dic3—31no—
197C4⋊Dic3—31no—
198C4⋊Dic3—61no—
199C4⋊Dic3—61no—
200C4⋊Dic3—61no—
201C4⋊Dic3—61no—
202C4⋊Dic3—61no—
203C4⋊Dic3—122no—
204C4⋊Dic3D1211yescharacteristic
205Dic3⋊C4—21no—
206Dic3⋊C4—21no—
207Dic3⋊C4—21no—
208Dic3⋊C4—61no—
209Dic3⋊C4—61no—
210Dic3⋊C4—61no—
211Dic3⋊C4—61no—
212Dic3⋊C4—61no—
213Dic3⋊C4—61no—
214Dic3⋊C4—61no—
215Dic3⋊C4—61no—
216Dic3⋊C4—121no—
217Dic3⋊C4—122no—
218C4×Dic3—61no—
219C4×Dic3—61no—
220C4×Dic3—61no—
221C4×Dic3—61no—
222C2×C3⋊C8—21no—
223Dic12—122no—
224Dic12—122no—
225Dic12—124no—
226Dic12—122no—
227C22×C32—21no—
228C22×C32—21no—
229C22×C32#12011yescharacteristic
230C22×C32C2×Q1611yescharacteristic
231C22×C32#13711yescharacteristic
232C32×C4—21no—
233C32×C4—21no—
234C3⋊Dic3—42no—
235C3⋊Dic3—41no—
236C3⋊Dic3—41no—
237C3×Dic3—22no—
238C3×Dic3—42no—
239C3×Dic3—41no—
240C3×Dic3—41no—
241C3×Dic3—41no—
242C22×Q8—91no—
243C2×Q16—181no—
244C2×Q16—181no—
245C4⋊Q8—181no—
246C4⋊Q8—181no—
247#125—181no—
248#125—181no—
249C22⋊Q8—31no—
250C22⋊Q8—91no—
251C22⋊Q8—181no—
252#117—181no—
253C2×C4⋊C4—31no—
254C2×C4⋊C4—181no—
255#103—181no—
256#103—181no—
257C22⋊C8—31no—
258C22⋊C8D3211yescharacteristic
259#95—31no—
260#95—181no—
261C23×C3—21no—
262C23×C3C2×D1211yescharacteristic
263C23×C3D3×D411yescharacteristic
264C3×Q8—121no—
265C2×C3×C4—21no—
266C2×C3×C4—21no—
267C2×C3×C4—32no—
268C2×C3×C4—41no—
269C2×C3×C4—41no—
270C2×C3×C4—42no—
271C2×C3×C4—61no—
272C2×C3×C4—61no—
273C2×C3×C4—62no—
274C2×C3×C4—61no—
275C2×C3×C4—61no—
276C2×C3×C4—61no—
277C2×C3×C4—121no—
278C2×C3×C4—121no—
279C2×C3×C4—121no—
280C2×C3×C4C2×D1211yescharacteristic
281C2×C3×C4D3×D411yescharacteristic
282C2×C3×C4D3×D411yescharacteristic
283C2×C3×C4D3×D411yescharacteristic
284C2×Dic3—21no—
285C2×Dic3—21no—
286C2×Dic3—22no—
287C2×Dic3—21no—
288C2×Dic3—21no—
289C2×Dic3—21no—
290C2×Dic3—41no—
291C2×Dic3—41no—
292C2×Dic3—41no—
293C2×Dic3—62no—
294C2×Dic3—62no—
295C2×Dic3—61no—
296C2×Dic3—61no—
297C2×Dic3—61no—
298C2×Dic3—61no—
299C2×Dic3—122no—
300C2×Dic3—121no—
301C2×Dic3—121no—
302C2×Dic3—122no—
303C2×Dic3—121no—
304C2×Dic3—121no—
305C2×Dic3—122no—
306C2×Dic3—121no—
307C2×Dic3—121no—
308C2×Dic3Dic1212yescomplemented
309Dic6—41no—
310Dic6—64no—
311Dic6—62no—
312Dic6—62no—
313Dic6—62no—
314Dic6—62no—
315Dic6—122no—
316Dic6—122no—
317Dic6—121no—
318Dic6—121no—
319Dic6—121no—
320Dic6—121no—
321Dic6—122no—
322Dic6—121no—
323Dic6—121no—
324Dic6—122no—
325Dic6—241no—
326Dic6—241no—
327C3×C8—42no—
328C3×C8—41no—
329C3×C8—41no—
330C3×C8—121no—
331C3⋊C8—41no—
332C2×C32—21no—
333C2×C32—21no—
334C2×C32#45111yescharacteristic
335C2×C32#45611yescharacteristic
336C2×C32B(4,𝔽2)11yescharacteristic
337C2×Q8—31no—
338C2×Q8—91no—
339C2×Q8—181no—
340C2×Q8—181no—
341C2×Q8—181no—
342C2×Q8—362no—
343C22×C4—31no—
344C22×C4—31no—
345C22×C4—61no—
346C22×C4—181no—
347C22×C4C2×D3211yescharacteristic
348Q16—362no—
349Q16—362no—
350C2×C8—21no—
351C2×C8—61no—
352C4⋊C4—31no—
353C4⋊C4—61no—
354C4⋊C4—61no—
355C4⋊C4—61no—
356C4⋊C4—91no—
357C4⋊C4—181no—
358C4⋊C4—181no—
359C4⋊C4—181no—
360C4⋊C4—181no—
361C4⋊C4—181no—
362C4⋊C4—181no—
363C4⋊C4—362no—
364C22⋊C4—61no—
365C22⋊C4—181no—
366C42—181no—
367C42—181no—
368C22×C3—21no—
369C22×C3—21no—
370C22×C3—21no—
371C22×C3—21no—
372C22×C3—21no—
373C22×C3—21no—
374C22×C3—21no—
375C22×C3—41no—
376C22×C3—41no—
377C22×C3#88211yescharacteristic
378C22×C3#88211yescharacteristic
379C22×C3C2×Dic1211yescharacteristic
380C22×C3#90911yescharacteristic
381C22×C3#91511yescharacteristic
382C22×C3D3×Q1611yescharacteristic
383C3×C4—22no—
384C3×C4—21no—
385C3×C4—21no—
386C3×C4—21no—
387C3×C4—21no—
388C3×C4—41no—
389C3×C4—62no—
390C3×C4—122no—
391C3×C4—121no—
392C3×C4—121no—
393C3×C4—121no—
394Dic3—22no—
395Dic3—42no—
396Dic3—41no—
397Dic3—41no—
398Dic3—41no—
399Dic3—124no—
400Dic3—122no—
401Dic3—122no—
402Dic3—121no—
403Dic3—121no—
404Dic3—121no—
405Dic3—121no—
406Dic3—241no—
407Dic3—241no—
408C32#160511yescharacteristic, complemented, Sylow
409C23D3×D1211yescharacteristic
410Q8—121no—
411Q8—182no—
412Q8—182no—
413Q8—361no—
414Q8—361no—
415Q8—361no—
416Q8—721no—
417C2×C4—32no—
418C2×C4—41no—
419C2×C4—61no—
420C2×C4—61no—
421C2×C4—62no—
422C2×C4—61no—
423C2×C4—61no—
424C2×C4—61no—
425C2×C4—121no—
426C2×C4—121no—
427C2×C4—121no—
428C2×C4—182no—
429C2×C4—181no—
430C2×C4—181no—
431C2×C4—361no—
432C2×C4—361no—
433C2×C4D3×D1211yescharacteristic
434C2×C4#381111yescharacteristic
435C8—41no—
436C8—121no—
437C2×C3—21no—
438C2×C3—21no—
439C2×C3—21no—
440C2×C3—21no—
441C2×C3—21no—
442C2×C3—21no—
443C2×C3—21no—
444C2×C3—41no—
445C2×C3—41no—
446C2×C3#473911yescharacteristic
447C2×C3#474111yescharacteristic
448C2×C3#474111yescharacteristic
449C2×C3#475211yescharacteristic
450C2×C3#480911yescharacteristic
451C2×C3#482611yescharacteristic
452C22—21no—
453C22—21no—
454C22D3×Dic1211yescharacteristic
455C22#6380011yescharacteristic
456C22#6392311yescharacteristic
457C4—21no—
458C4—21no—
459C4—62no—
460C4—122no—
461C4—121no—
462C4—121no—
463C4—121no—
464C4—361no—
465C4—362no—
466C4—361no—
467C3—21no—
468C3#6813911yescharacteristic, complemented
469C3#6832711yescharacteristic, complemented
470C2—21no—
471C2—21no—
472C2#1059041011yescharacteristic
473C2#1059095211yescharacteristic
474C2#1059102111yescharacteristic
subgroupG/H
centerC22#63923
commutator, cosocleC22×C32×C4C23
FrattiniC22×C4C2×D32
FittingC32×C22⋊C8C22
socleC22×C32#120
prime radicalC23×C32C2×D4
hypercenterC22⋊C8D32
hypocenterC32#1605
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
142. C2×C3×Dic3Q16semidirect
308. C2×Dic3Dic12semidirect
408. C32#1605semidirect
468. C3#68139semidirect
469. C3#68327semidirect

Maximal subgroups

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

subgroupindex
#105948122
#105924382
#105913542
#105911902
C3×#44692
C3×#44672
#105891542
#683273
#681393