Finite Group Databasebeta

← #11791141

Subgroups — #11791141

Order 1152.

745 conjugacy classes of subgroups.

The subgroup lattice has 496 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#3715C211yesmaximal, characteristic
2C2×#63634C211yesmaximal, characteristic, complemented
3C3×#4988C211yesmaximal, characteristic
4C2×C3×#810C211yesmaximal, characteristic, complemented
5#10591220C211yesmaximal, characteristic, complemented
6C2×#63563C211yesmaximal, characteristic
7C2×#63554C211yesmaximal, characteristic, complemented
8#70260—31nomaximal
9#69649—31nomaximal
10C22×C3×D12C2211yescharacteristic
11C22×C3×Dic6C2211yescharacteristic
12C2×C32×C4⋊C4C2211yescharacteristic
13C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
14C22×C3⋊(C3⋊C8)C2211yescharacteristic
15C2×C3×(C2×D3)⋊C4—22no—
16C2×C3×C4×Dic3C2211yescharacteristic
17C22×C3×C3⋊C8C2211yescharacteristic
18C2×#3715—22no—
19C2×#3715—22no—
20C2×#3715C414yescomplemented
21#63634—22no—
22C3×#810—22no—
23#63579—22no—
24#63563—22no—
25#63554—22no—
26C22×#215—31no—
27C22×#214—31no—
28C2×C3×#103—31no—
29C3×#390—31no—
30#5229—31no—
31C2×#832—31no—
32C2×#821—31no—
33C2×#815—31no—
34#4988D311yescharacteristic
35C2×#810D311yescharacteristic, complemented
36C2×#807—31no—
37C2×#807—31no—
38C2×#807—61no—
39#4929—31no—
40C2×#803—31no—
41C23×C3×D3—21no—
42C22×C32×C4—21no—
43C22×C32×C4C2311yescharacteristic
44C22×C3⋊Dic3—21no—
45C22×C3×Dic3—21no—
46C22×C3×Dic3D412yes—
47C2×C3×D12—21no—
48C2×C3×D12—21no—
49C2×C3×D12—21no—
50C2×C3×D12—21no—
51C2×C3×D12—21no—
52C2×C3×D12C2×C412yes—
53C2×C3×Dic6—21no—
54C2×C3×Dic6—21no—
55C2×C3×Dic6—21no—
56C2×C3×Dic6—21no—
57C2×C3×Dic6—21no—
58C2×C3×Dic6C2×C412yes—
59C32×C4⋊C4—21no—
60C32×C4⋊C4—21no—
61C4⋊(C3⋊Dic3)—21no—
62C4⋊(C3⋊Dic3)—21no—
63C2×C3⋊(C3⋊C8)C2×C412yes—
64C2×C3⋊(C3⋊C8)D412yes—
65C2×C3⋊(C3⋊C8)D412yes—
66C3×(C2×D3)⋊C4—44no—
67C3×C4×Dic3—21no—
68C3×C4×Dic3—21no—
69C2×C3×C3⋊C8—21no—
70C2×C3×C3⋊C8—21no—
71C2×C3×C3⋊C8D412yes—
72#3715—28no—
73#1973—91noSylow
74C22×C3×Q8—31no—
75C22×C3×D4—31no—
76C22×D12C2×D311yescharacteristic
77C22×Dic6C2×D311yescharacteristic
78C22×C3×C8—31no—
79C2×C3×C4⋊C4—21no—
80C2×C3×C4⋊C4C2×D311yescharacteristic
81C2×C3×C4⋊C4C2×D311yescharacteristic
82C2×C3×C22⋊C4—62no—
83C2×C3×C42—31no—
84C2×#215—34no—
85C2×#215—62no—
86C2×#215—62no—
87C2×#214—34no—
88C2×#214—62no—
89C2×#214—62no—
90C2×(C2×D3)⋊C4—22no—
91C2×C4⋊Dic3—31no—
92C2×C4⋊Dic3—31no—
93C2×C4⋊Dic3—61no—
94C2×C4×Dic3C2×D311yescharacteristic
95C22×C3⋊C8—31no—
96C22×C3⋊C8—31no—
97C22×C3⋊C8—61no—
98C22×C3⋊C8C2×D311yescharacteristic
99C3×#103—62no—
100#832—62no—
101C3⋊#95—62no—
102C3⋊#95—62no—
103#821—62no—
104#815—62no—
105#810—22no—
106#807—62no—
107#807—62no—
108#807—64no—
109#803—62no—
110C23×C32C2×D411yescharacteristic
111C22×C3×D3—22no—
112C22×C3×D3—41no—
113C22×C3×D3—41no—
114C22×C3×D3—42no—
115C22×C3×D3—42no—
116C2×C32×C4—41no—
117C2×C32×C4—42no—
118C2×C32×C4C22×C411yescharacteristic
119C2×C32×C4C2×D411yescharacteristic
120C2×C32×C4C2×D411yescharacteristic
121C2×C32×C4C2×D411yescharacteristic
122C2×C32×C4#4111yescharacteristic
123C2×C32×C4#4111yescharacteristic
124C2×C3⋊Dic3—41no—
125C2×C3⋊Dic3—42no—
126C2×C3×Dic3—22no—
127C2×C3×Dic3—22no—
128C2×C3×Dic3—22no—
129C2×C3×Dic3—22no—
130C2×C3×Dic3—41no—
131C2×C3×Dic3—41no—
132C3×D12—22no—
133C3×D12—22no—
134C3×D12—41no—
135C3×D12—41no—
136C3×Dic6—22no—
137C3×Dic6—22no—
138C3×Dic6—41no—
139C3×Dic6—41no—
140C3⋊(C3⋊C8)C22⋊C414yescomplemented
141C3×C3⋊C8—22no—
142C22×SD16—91no—
143C2×#107—91no—
144C2×#103—31no—
145C2×#102—91no—
146C2×#97—91no—
147#391—91no—
148#390—31no—
149C24×C3—61no—
150C23×D3—21no—
151C2×C3×Q8—32no—
152C2×C3×Q8—61no—
153C2×C3×Q8—61no—
154C2×C3×Q8—61no—
155C2×C3×Q8—61no—
156C2×C3×Q8—61no—
157C2×C3×D4—32no—
158C2×C3×D4—61no—
159C2×C3×D4—61no—
160C2×C3×D4—61no—
161C2×C3×D4—61no—
162C2×C3×D4—61no—
163C22×C3×C4—21no—
164C22×C3×C4—21no—
165C22×C3×C4—21no—
166C22×C3×C4—32no—
167C22×C3×C4—41no—
168C22×C3×C4—61no—
169C22×C3×C4C22×D311yescharacteristic
170C22×C3×C4C22×D311yescharacteristic
171C22×Dic3—21no—
172C22×Dic3—61no—
173C22×Dic3—61no—
174C22×Dic3—121no—
175C22×Dic3#6712yes—
176C2×D12—21no—
177C2×D12—21no—
178C2×D12—21no—
179C2×D12—21no—
180C2×D12—21no—
181C2×D12C4×D312yes—
182C2×Dic6—21no—
183C2×Dic6—21no—
184C2×Dic6—21no—
185C2×Dic6—21no—
186C2×Dic6—21no—
187C2×Dic6C4×D312yes—
188C2×C3×C8—32no—
189C2×C3×C8—61no—
190C2×C3×C8—61no—
191C3×C4⋊C4—22no—
192C3×C4⋊C4—21no—
193C3×C4⋊C4—21no—
194C3×C4⋊C4—21no—
195C3×C4⋊C4—21no—
196C3×C4⋊C4—41no—
197C3×C22⋊C4—124no—
198C3×C42—61no—
199C3×C42—61no—
200#215—68no—
201#214—68no—
202(C2×D3)⋊C4—44no—
203C4⋊Dic3—62no—
204C4⋊Dic3—61no—
205C4⋊Dic3—61no—
206C4⋊Dic3—61no—
207C4⋊Dic3—61no—
208C4⋊Dic3—121no—
209C4×Dic3—21no—
210C4×Dic3—21no—
211C2×C3⋊C8—21no—
212C2×C3⋊C8—21no—
213C2×C3⋊C8—32no—
214C2×C3⋊C8—32no—
215C2×C3⋊C8—32no—
216C2×C3⋊C8—32no—
217C2×C3⋊C8—32no—
218C2×C3⋊C8—32no—
219C2×C3⋊C8—62no—
220C2×C3⋊C8—62no—
221C2×C3⋊C8—62no—
222C2×C3⋊C8#6712yes—
223C22×C32C4×D411yescharacteristic
224C22×C32#12111yescharacteristic
225C22×C32#12711yescharacteristic
226C22×C32AGL(1,ℤ/8)12yes—
227C22×C32#13712yes—
228C2×C3×D3—42no—
229C2×C3×D3—44no—
230C2×C3×D3—82no—
231C2×C3×D3—81no—
232C2×C3×D3—81no—
233C32×C4—81no—
234C32×C4C2×C22⋊C411yescharacteristic
235C32×C4C4×D411yescharacteristic
236C32×C4#12111yescharacteristic
237C32×C4#12411yescharacteristic
238C3⋊Dic3—81no—
239C3×Dic3—42no—
240C3×Dic3—42no—
241C22×Q8—31no—
242C22×D4—31no—
243C2×SD16—94no—
244C2×SD16—182no—
245C2×SD16—182no—
246C22×C8—31no—
247C22×C8—91no—
248C2×C4⋊C4—91no—
249C2×C4⋊C4D3211yescharacteristic
250C2×C22⋊C4—62no—
251C2×C42—31no—
252#107—182no—
253#103—62no—
254#102—182no—
255#97—182no—
256#95—182no—
257C23×C3—21no—
258C23×C3—62no—
259C23×C3—121no—
260C23×C3—122no—
261C23×C3—122no—
262C23×C3—121no—
263C23×C3D3×D411yescharacteristic
264C23×C3C2×#6711yescharacteristic
265C22×D3—22no—
266C22×D3—42no—
267C22×D3—41no—
268C22×D3—41no—
269C22×D3—42no—
270C3×Q8—62no—
271C3×Q8—62no—
272C3×Q8—121no—
273C3×Q8—121no—
274C3×D4—62no—
275C3×D4—62no—
276C3×D4—121no—
277C3×D4—121no—
278C2×C3×C4—21no—
279C2×C3×C4—21no—
280C2×C3×C4—21no—
281C2×C3×C4—21no—
282C2×C3×C4—21no—
283C2×C3×C4—21no—
284C2×C3×C4—42no—
285C2×C3×C4—42no—
286C2×C3×C4—42no—
287C2×C3×C4—41no—
288C2×C3×C4—41no—
289C2×C3×C4—62no—
290C2×C3×C4—62no—
291C2×C3×C4—62no—
292C2×C3×C4—62no—
293C2×C3×C4—82no—
294C2×C3×C4—121no—
295C2×C3×C4—121no—
296C2×C3×C4C2×C4×D311yescharacteristic
297C2×C3×C4C2×C4×D311yescharacteristic
298C2×C3×C4#23511yescharacteristic
299C2×C3×C4#23511yescharacteristic
300C2×C3×C4D3×D411yescharacteristic
301C2×C3×C4D3×D411yescharacteristic
302C2×C3×C4D3×D411yescharacteristic
303C2×C3×C4D3×D411yescharacteristic
304C2×C3×C4D3×D411yescharacteristic
305C2×C3×C4#23711yescharacteristic
306C2×C3×C4#23711yescharacteristic
307C2×C3×C4C2×#6711yescharacteristic
308C2×Dic3—22no—
309C2×Dic3—22no—
310C2×Dic3—22no—
311C2×Dic3—22no—
312C2×Dic3—41no—
313C2×Dic3—41no—
314C2×Dic3—122no—
315C2×Dic3—122no—
316C2×Dic3—122no—
317C2×Dic3—121no—
318C2×Dic3—121no—
319C2×Dic3—242no—
320D12—22no—
321D12—22no—
322D12—41no—
323D12—41no—
324Dic6—22no—
325Dic6—22no—
326Dic6—41no—
327Dic6—41no—
328C3×C8—62no—
329C3⋊C8—22no—
330C3⋊C8—34no—
331C3⋊C8—34no—
332C3⋊C8—64no—
333C2×C32#39011yescharacteristic
334C2×C32#44012yes—
335C2×C32#46812yes—
336C2×C32#49611yescharacteristic
337C2×C32#49711yescharacteristic
338C3×D3—82no—
339C24—61no—
340C2×Q8—32no—
341C2×Q8—61no—
342C2×Q8—61no—
343C2×Q8—61no—
344C2×Q8—61no—
345C2×Q8—61no—
346C2×D4—32no—
347C2×D4—61no—
348C2×D4—61no—
349C2×D4—61no—
350C2×D4—61no—
351C2×D4—61no—
352C22×C4—21no—
353C22×C4—32no—
354C22×C4—61no—
355C22×C4—181no—
356C22×C4C2×D3211yescharacteristic
357SD16—188no—
358C2×C8—32no—
359C2×C8—61no—
360C2×C8—61no—
361C2×C8—92no—
362C2×C8—92no—
363C2×C8—92no—
364C4⋊C4—21no—
365C4⋊C4—21no—
366C4⋊C4—181no—
367C4⋊C4—181no—
368C22⋊C4—124no—
369C42—61no—
370C42—61no—
371C22×C3—21no—
372C22×C3—21no—
373C22×C3—22no—
374C22×C3—22no—
375C22×C3—21no—
376C22×C3—122no—
377C22×C3—124no—
378C22×C3—241no—
379C22×C3—241no—
380C22×C3—242no—
381C22×C3#67⋊C411yescharacteristic
382C22×C3#88411yescharacteristic
383C22×C3#91412yes—
384C22×C3#91812yes—
385C22×C3C4×#6711yescharacteristic
386C22×C3#93212yes—
387C22×C3#93911yescharacteristic
388C22×C3#94011yescharacteristic
389C22×C3#94011yescharacteristic
390C22×C3#95112yes—
391C2×D3—42no—
392C2×D3—44no—
393C2×D3—82no—
394C2×D3—81no—
395C2×D3—81no—
396C3×C4—21no—
397C3×C4—21no—
398C3×C4—21no—
399C3×C4—21no—
400C3×C4—82no—
401C3×C4—81no—
402C3×C4—81no—
403C3×C4—122no—
404C3×C4—122no—
405C3×C4D3×C22⋊C411yescharacteristic
406C3×C4D3×C22⋊C411yescharacteristic
407C3×C4#67⋊C411yescharacteristic
408C3×C4#88411yescharacteristic
409C3×C4#88511yescharacteristic
410C3×C4#88511yescharacteristic
411C3×C4C4×#6711yescharacteristic
412C3×C4#93911yescharacteristic
413Dic3—42no—
414Dic3—42no—
415Dic3—242no—
416Dic3—241no—
417Dic3—241no—
418C32#197311yescharacteristic, complemented, Sylow
419C23—62no—
420C23—121no—
421C23—122no—
422C23—122no—
423C23—121no—
424C23D3×#6711yescharacteristic
425Q8—62no—
426Q8—62no—
427Q8—121no—
428Q8—121no—
429D4—62no—
430D4—62no—
431D4—121no—
432D4—121no—
433C2×C4—42no—
434C2×C4—41no—
435C2×C4—62no—
436C2×C4—62no—
437C2×C4—62no—
438C2×C4—62no—
439C2×C4—121no—
440C2×C4—121no—
441C2×C4—362no—
442C2×C4—361no—
443C2×C4#379511yescharacteristic
444C2×C4#379511yescharacteristic
445C2×C4C4×D3211yescharacteristic
446C2×C4#380211yescharacteristic
447C2×C4D3×#6711yescharacteristic
448C2×C4#381111yescharacteristic
449C8—62no—
450C8—94no—
451C2×C3—22no—
452C2×C3—22no—
453C2×C3—21no—
454C2×C3—21no—
455C2×C3—21no—
456C2×C3—242no—
457C2×C3#481212yes—
458C2×C3#481712yes—
459C2×C3#495711yescharacteristic
460C2×C3#495711yescharacteristic
461C2×C3#501812yes—
462C2×C3#504212yes—
463C2×C3#506011yescharacteristic
464C2×C3#507411yescharacteristic
465C2×C3#517611yescharacteristic
466C2×C3#519011yescharacteristic
467D3—82no—
468C22—124no—
469C22—122no—
470C22—242no—
471C22—241no—
472C22—241no—
473C22#6387911yescharacteristic
474C22#6388511yescharacteristic
475C22#6393412yes—
476C22#6394312yes—
477C22#6397911yescharacteristic
478C4—81no—
479C4—122no—
480C4—122no—
481C4—721no—
482C4#6387911yescharacteristic
483C4#6388511yescharacteristic
484C4#6391311yescharacteristic
485C4#6392111yescharacteristic
486C3—21no—
487C3#6964911yescharacteristic, complemented
488C3#7026011yescharacteristic, complemented
489C2—242no—
490C2#1059047812yes—
491C2#1059051512yes—
492C2#1059138611yescharacteristic
493C2#1059147211yescharacteristic
494C2#1059162711yescharacteristic
subgroupG/H
centerC23D3×#67
commutatorC2×C32×C4C22×C4
FrattiniC22×C4C2×D32
FittingC2×C32×C4⋊C4C22
socleC23×C32C2×D4
prime radicalC22×C3×D12C22
cosocleC22×C32×C4C23
hypercenterC2×C4⋊C4D32
hypocenterC32#1973
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C23 ◁ C22×C4 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
2. C2×#63634C2semidirect
4. C2×C3×#810C2semidirect
5. #10591220C2semidirect
7. C2×#63554C2semidirect
20. C2×#3715C4semidirect
35. C2×#810D3semidirect
140. C3⋊(C3⋊C8)C22⋊C4semidirect
418. C32#1973semidirect
487. C3#69649semidirect
488. C3#70260semidirect

Maximal subgroups

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

subgroupindex
C22×#37152
C2×#636342
C3×#49882
C2×C3×#8102
#105912202
C2×#635632
C2×#635542
#702603
#696493