Finite Group Databasebeta

← #11778363

Subgroups — #11778363

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#10592927C211yesmaximal, characteristic
3C3×#5230C211yesmaximal, characteristic
4C3×#5228C211yesmaximal, characteristic
5#10589154C211yesmaximal, characteristic
6#10589153C211yesmaximal, characteristic
7#10589147C211yesmaximal, characteristic
8#70983—31nomaximal
9#69707—31nomaximal
10C22×C32×Q8C2211yescharacteristic
11C2×#3756—21no—
12#64133C2211yescharacteristic
13C2×C3×#216—21no—
14C3×#924C2211yescharacteristic
15C2×C3×Dic3⋊C4—21no—
16C2×C3×Dic3⋊C4C2211yescharacteristic
17#63964—21no—
18#63955—21no—
19#63846—21no—
20#63845—21no—
21#63840—21no—
22#63839—21no—
23#63662—21no—
24#63657C2211yescharacteristic
25C3×#835—21no—
26C3×C3⋊#95—21no—
27C3×C3⋊#95C2211yescharacteristic
28C3×#830C2211yescharacteristic
29#5623—31no—
30#5500—31no—
31C3×#451—31no—
32C3×#395—31no—
33#5230D311yescharacteristic
34#5228—31no—
35#5228—31no—
36#5228—61no—
37#5228D311yescharacteristic
38#4538—31no—
39#4528—31no—
40#4469—31no—
41#4467—31no—
42#4452—31no—
43#4452—31no—
44C2×C32×Q8—21no—
45C2×C32×Q8—21no—
46C2×C32×Q8—42no—
47C22×C32×C4—21no—
48C22×C32×C4C2311yescharacteristic
49C2×#634D411yescharacteristic
50C22×C3×Dic3—21no—
51C22×C3×Dic3D411yescharacteristic
52C22×C3×Dic3D411yescharacteristic
53C2×C3×Dic6D411yescharacteristic
54C2×#627—21no—
55#3757—21no—
56#3756—42no—
57C4⋊(C3⋊Dic3)D411yescharacteristic
58#3750—21no—
59C2×C3⋊(C3⋊C8)—21no—
60C3×#217—21no—
61C3×#216—42no—
62C3×C4⋊Dic3D411yescharacteristic
63C3×Dic3⋊C4—21no—
64C3×Dic3⋊C4—21no—
65C3×Dic3⋊C4—21no—
66C3×Dic3⋊C4—42no—
67C2×C3×C3⋊C8—21no—
68#3724—21no—
69Dic3⋊Dic3—21no—
70Dic3⋊Dic3—21no—
71Dic3⋊Dic3—21no—
72Dic3⋊Dic3—21no—
73Dic32—21no—
74Dic32—21no—
75#1605—91noSylow
76C22×C3×Q8—21no—
77C22×C3×Q8C2×D311yescharacteristic
78C22×C3×Q8C2×D311yescharacteristic
79C2×C3×Q16—61no—
80C3×C22⋊Q8—31no—
81C2×C3×C4⋊C4—31no—
82C2×C3×C4⋊C4—61no—
83#944—61no—
84C2×#216—21no—
85C2×#216—61no—
86C2×#216—61no—
87C2×#216—62no—
88#926—61no—
89#924—31no—
90#924—31no—
91#924—61no—
92#924—61no—
93#924C2×D311yescharacteristic
94C2×Dic3⋊C4—21no—
95C2×Dic3⋊C4C2×D311yescharacteristic
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×#103—61no—
106C3×C22⋊C8—31no—
107C3×#95—31no—
108C3×#95—61no—
109#835—21no—
110#835—61no—
111#835—61no—
112#835—62no—
113C3⋊#95—21no—
114C3⋊#95C2×D311yescharacteristic
115#830—31no—
116#830—31no—
117#830—61no—
118#830C2×D311yescharacteristic
119C23×C32C2×D411yescharacteristic
120C32×Q8—22no—
121C32×Q8—22no—
122C32×Q8—41no—
123C32×Q8—41no—
124C2×C32×C4—22no—
125C2×C32×C4—41no—
126C2×C32×C4—41no—
127C2×C32×C4—41no—
128C2×C32×C4C2×D411yescharacteristic
129C2×C32×C4C2×D411yescharacteristic
130C2×C3⋊Dic3—21no—
131C2×C3⋊Dic3—21no—
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—
145C3⋊(C3⋊C8)—41no—
146C3×C3⋊C8—41no—
147#544—91no—
148#451—31no—
149#451—91no—
150#395—31no—
151#328—91no—
152#328—91no—
153#324—91no—
154C2×C3×Q8—22no—
155C2×C3×Q8—21no—
156C2×C3×Q8—21no—
157C2×C3×Q8—21no—
158C2×C3×Q8—21no—
159C2×C3×Q8—31no—
160C2×C3×Q8—41no—
161C2×C3×Q8—42no—
162C2×C3×Q8—42no—
163C2×C3×Q8—44no—
164C22×C3×C4—21no—
165C22×C3×C4—21no—
166C22×C3×C4—21no—
167C22×C3×C4—31no—
168C22×C3×C4—31no—
169C22×C3×C4—41no—
170C22×C3×C4—61no—
171C22×C3×C4C22×D311yescharacteristic
172C22×C3×C4C22×D311yescharacteristic
173C22×Dic3—21no—
174C22×Dic3#6711yescharacteristic
175C22×Dic3#6711yescharacteristic
176C2×Dic6—31no—
177C2×Dic6—31no—
178C2×Dic6—61no—
179C2×Dic6—61no—
180C2×Dic6—61no—
181C2×Dic6#6711yescharacteristic
182C3×Q16—122no—
183C2×C3×C8—61no—
184C3×C4⋊C4—31no—
185C3×C4⋊C4—61no—
186C3×C4⋊C4—61no—
187C3×C4⋊C4—61no—
188C3×C4⋊C4—122no—
189C3×C22⋊C4—61no—
190#217—21no—
191#217—61no—
192#217—61no—
193#217—121no—
194#216—42no—
195#216—122no—
196#216—122no—
197#216—124no—
198C4⋊Dic3—31no—
199C4⋊Dic3—31no—
200C4⋊Dic3—61no—
201C4⋊Dic3—61no—
202C4⋊Dic3—61no—
203C4⋊Dic3—61no—
204C4⋊Dic3—61no—
205C4⋊Dic3#6711yescharacteristic
206Dic3⋊C4—21no—
207Dic3⋊C4—21no—
208Dic3⋊C4—21no—
209Dic3⋊C4—42no—
210Dic3⋊C4—61no—
211Dic3⋊C4—61no—
212Dic3⋊C4—61no—
213Dic3⋊C4—61no—
214Dic3⋊C4—61no—
215Dic3⋊C4—61no—
216Dic3⋊C4—61no—
217Dic3⋊C4—61no—
218Dic3⋊C4—121no—
219C4×Dic3—61no—
220C4×Dic3—61no—
221C4×Dic3—61no—
222C4×Dic3—61no—
223C2×C3⋊C8—21no—
224C2×C3⋊C8—62no—
225C2×C3⋊C8—61no—
226C2×C3⋊C8—61no—
227C22×C32—21no—
228C22×C32—21no—
229C22×C32#12011yescharacteristic
230C22×C32C2×Q1611yescharacteristic
231C22×C32#13711yescharacteristic
232C32×C4—21no—
233C32×C4—21no—
234C32×C4—42no—
235C3⋊Dic3—41no—
236C3⋊Dic3—41no—
237C3×Dic3—22no—
238C3×Dic3—42no—
239C3×Dic3—41no—
240C3×Dic3—41no—
241C3×Dic3—41no—
242C22×Q8D3211yescharacteristic
243C2×Q16—61no—
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—61no—
255#103—61no—
256#103—181no—
257C22⋊C8—31no—
258C22⋊C8—91no—
259#95—31no—
260#95—61no—
261C23×C3—21no—
262C23×C3D3×D411yescharacteristic
263C23×C3C2×#6711yescharacteristic
264C3×Q8—22no—
265C3×Q8—24no—
266C3×Q8—22no—
267C3×Q8—22no—
268C3×Q8—22no—
269C3×Q8—42no—
270C3×Q8—42no—
271C3×Q8—41no—
272C3×Q8—41no—
273C3×Q8—41no—
274C3×Q8—41no—
275C3×Q8—42no—
276C3×Q8—121no—
277C2×C3×C4—22no—
278C2×C3×C4—22no—
279C2×C3×C4—21no—
280C2×C3×C4—21no—
281C2×C3×C4—32no—
282C2×C3×C4—42no—
283C2×C3×C4—41no—
284C2×C3×C4—41no—
285C2×C3×C4—42no—
286C2×C3×C4—41no—
287C2×C3×C4—41no—
288C2×C3×C4—42no—
289C2×C3×C4—42no—
290C2×C3×C4—41no—
291C2×C3×C4—41no—
292C2×C3×C4—61no—
293C2×C3×C4—61no—
294C2×C3×C4—62no—
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×C4D3×D411yescharacteristic
302C2×C3×C4D3×D411yescharacteristic
303C2×C3×C4D3×D411yescharacteristic
304C2×C3×C4C2×#6711yescharacteristic
305C2×Dic3—21no—
306C2×Dic3—21no—
307C2×Dic3—22no—
308C2×Dic3—21no—
309C2×Dic3—21no—
310C2×Dic3—21no—
311C2×Dic3—41no—
312C2×Dic3—41no—
313C2×Dic3—41no—
314C2×Dic3—61no—
315C2×Dic3—61no—
316C2×Dic3—61no—
317C2×Dic3—61no—
318C2×Dic3—121no—
319C2×Dic3—121no—
320C2×Dic3#21612yescomplemented
321Dic6—41no—
322Dic6—121no—
323Dic6—121no—
324Dic6—122no—
325Dic6—241no—
326Dic6—241no—
327C3×C8—121no—
328C3⋊C8—41no—
329C3⋊C8—122no—
330C3⋊C8—121no—
331C3⋊C8—121no—
332C2×C32—21no—
333C2×C32—21no—
334C2×C32#45111yescharacteristic
335C2×C32#45611yescharacteristic
336C2×C32B(4,𝔽2)11yescharacteristic
337C2×Q8—21no—
338C2×Q8—21no—
339C2×Q8—31no—
340C2×Q8—42no—
341C2×Q8—91no—
342C2×Q8—181no—
343C22×C4—21no—
344C22×C4—31no—
345C22×C4—31no—
346C22×C4—61no—
347C22×C4C2×D3211yescharacteristic
348Q16—122no—
349Q16—362no—
350C2×C8—61no—
351C2×C8—181no—
352C4⋊C4—31no—
353C4⋊C4—61no—
354C4⋊C4—61no—
355C4⋊C4—61no—
356C4⋊C4—91no—
357C4⋊C4—122no—
358C4⋊C4—181no—
359C4⋊C4—181no—
360C4⋊C4—181no—
361C4⋊C4—181no—
362C4⋊C4—181no—
363C4⋊C4—181no—
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×C3D3×Q1611yescharacteristic
378C22×C3#91811yescharacteristic
379C22×C3#93711yescharacteristic
380C22×C3#93711yescharacteristic
381C22×C3C2×#21611yescharacteristic
382C22×C3#95111yescharacteristic
383C3×C4—22no—
384C3×C4—21no—
385C3×C4—21no—
386C3×C4—21no—
387C3×C4—21no—
388C3×C4—41no—
389C3×C4—44no—
390C3×C4—42no—
391C3×C4—42no—
392C3×C4—62no—
393C3×C4—122no—
394C3×C4—121no—
395C3×C4—121no—
396C3×C4—121no—
397Dic3—22no—
398Dic3—42no—
399Dic3—41no—
400Dic3—41no—
401Dic3—41no—
402Dic3—121no—
403Dic3—121no—
404Dic3—121no—
405Dic3—121no—
406Dic3—241no—
407Dic3—241no—
408C32#160511yescharacteristic, complemented, Sylow
409C23D3×#6711yescharacteristic
410Q8—22no—
411Q8—22no—
412Q8—41no—
413Q8—41no—
414Q8—121no—
415Q8—361no—
416Q8—721no—
417C2×C4—22no—
418C2×C4—32no—
419C2×C4—41no—
420C2×C4—41no—
421C2×C4—41no—
422C2×C4—61no—
423C2×C4—61no—
424C2×C4—62no—
425C2×C4—61no—
426C2×C4—61no—
427C2×C4—61no—
428C2×C4—121no—
429C2×C4—121no—
430C2×C4—121no—
431C2×C4—181no—
432C2×C4—181no—
433C2×C4D3×#6711yescharacteristic
434C2×C4#381111yescharacteristic
435C8—121no—
436C8—361no—
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#503211yescharacteristic
447C2×C3#503211yescharacteristic
448C2×C3#505011yescharacteristic
449C2×C3#509511yescharacteristic
450C2×C3#518611yescharacteristic
451C2×C3#520511yescharacteristic
452C22—21no—
453C22—21no—
454C22D3×#21611yescharacteristic
455C22#6394311yescharacteristic
456C22#6398311yescharacteristic
457C4—21no—
458C4—21no—
459C4—42no—
460C4—62no—
461C4—122no—
462C4—121no—
463C4—121no—
464C4—121no—
465C4—361no—
466C4—361no—
467C3—21no—
468C3#6970711yescharacteristic, complemented
469C3#7098311yescharacteristic, complemented
470C2—21no—
471C2—21no—
472C2#1059165311yescharacteristic
473C2#1059166111yescharacteristic
474C2#1059172511yescharacteristic
subgroupG/H
centerC22#63983
commutator, cosocleC22×C32×C4C23
FrattiniC22×C4C2×D32
FittingC22×C32×Q8C22
socleC22×C32#120
prime radicalC23×C32C2×D4
hypercenterC22×Q8D32
hypocenterC32#1605
LCSG ▷ C22×C32×C4 ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×Q8

Complements

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

NH ≅ G/Ntype
142. C2×C3×Dic3Q16semidirect
320. C2×Dic3#216semidirect
408. C32#1605semidirect
468. C3#69707semidirect
469. C3#70983semidirect

Maximal subgroups

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

subgroupindex
#105948122
#105929272
C3×#52302
C3×#52282
#105891542
#105891532
#105891472
#709833
#697073