Finite Group Databasebeta

← #11896075

Subgroups — #11896075

Order 1152.

725 conjugacy classes of subgroups.

The subgroup lattice has 504 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5732C211yesmaximal, characteristic
2Dic62C211yesmaximal, characteristic, complemented
3#10592778C211yesmaximal, characteristic, complemented
4C3×#5090C211yesmaximal, characteristic, complemented
5#10591624C212yesmaximal
6#10591578C212yesmaximal
7#10591576C212yesmaximal, complemented
8#10591544C212yesmaximal, complemented
9C4×#3715C211yesmaximal, characteristic
10#10590268C211yesmaximal, characteristic
11#10590259C211yesmaximal, characteristic, complemented
12#83677—31nomaximal
13#80464—31nomaximal
14C32×C4⋊Q8C2211yescharacteristic
15#64078C2211yescharacteristic
16C3×#947C2212yes—
17C3×Q8×Dic3C2212yes—
18C2×C3×#216C2212yes—
19C3×#898—22no—
20C3×#897—21no—
21C3×#892—21no—
22C3×C4×D12C2211yescharacteristic
23C3×C4×Dic6C2211yescharacteristic
24C3×C4×Dic6C2211yescharacteristic
25#63918—21no—
26#63918C2212yes—
27Dic3×Dic6—21no—
28Dic3×Dic6C2212yes—
29#63840—22no—
30C2×#3715C2211yescharacteristic
31#63662C2212yes—
32#63662C2212yes—
33C4×C3⋊(C3⋊C8)C2211yescharacteristic
34C3×#835C2212yes—
35C3×C4⋊(C3⋊C8)C2211yescharacteristic
36#63574C2211yescharacteristic
37#63573C2212yes—
38Dic3⋊(C3⋊C8)C2212yes—
39#63565C2211yescharacteristic
40#63563C2212yes—
41#63562C2211yescharacteristic
42#63554C2212yes—
43C3×#556—31no—
44#5732D311yescharacteristic
45Q8×Dic6—31no—
46Q8×Dic6—31no—
47C3×#462—31no—
48#5185—32no—
49#5184—32no—
50#5090D311yescharacteristic, complemented
51#5079—31no—
52#5079—31no—
53#5079—61no—
54#5055—32no—
55#5054—32no—
56#5030—32no—
57C4×#215—31no—
58#5024—31no—
59#5020—32no—
60C4×#214—31no—
61#5008—31no—
62#4842—31no—
63#4831—31no—
64#4794—32no—
65#4791—32no—
66C2×C32×Q8C2312yes—
67C2×#634—21no—
68C2×C3×D12C2311yescharacteristic
69C2×C3×C4×D3—21no—
70C2×C3×Dic6D411yescharacteristic
71C2×C3×Dic6C2311yescharacteristic
72C2×#627—22no—
73C32×C4⋊C4—21no—
74C32×C4⋊C4—21no—
75C32×C42C2311yescharacteristic
76C4⋊(C3⋊Dic3)—21no—
77C4⋊(C3⋊Dic3)C2312yes—
78C2×C3⋊(C3⋊C8)C2311yescharacteristic
79C2×C3⋊(C3⋊C8)C2311yescharacteristic
80C3×#216—24no—
81C3×(C2×D3)⋊C4—21no—
82C3×(C2×D3)⋊C4—22no—
83C3×(C2×D3)⋊C4—22no—
84C3×C4⋊Dic3—22no—
85C3×C4⋊Dic3D411yescharacteristic
86C3×C4⋊Dic3C2311yescharacteristic
87C3×C4⋊Dic3C2311yescharacteristic
88C3×Dic3⋊C4—21no—
89C3×Dic3⋊C4D412yes—
90C3×C4×Dic3—21no—
91C3×C4×Dic3—22no—
92C3×C4×Dic3C2312yes—
93C2×C3×C3⋊C8C2312yes—
94Dic3⋊Dic3—22no—
95Dic3⋊Dic3—22no—
96Dic32—22no—
97#3715—22no—
98#3369—91noSylow
99C2×C3×Q16—32no—
100C3×C4⋊Q8—21no—
101C3×C4⋊Q8C2×D311yescharacteristic
102C3×C4⋊Q8C2×D311yescharacteristic
103C3×#126—62no—
104C3×#124—32no—
105C3×C22⋊Q8—61no—
106C3×C4×Q8—31no—
107C3×C4×Q8—32no—
108C3×C4×Q8—31no—
109C3×C4×D4—31no—
110C3×#117—61no—
111#947C2×D312yes—
112Q8×Dic3—32no—
113Q8×Dic3—61no—
114Q8×Dic3C2×D312yes—
115C2×#216C2×D312yes—
116C2×#215—31no—
117C2×#214—31no—
118#898—22no—
119#897—21no—
120#892—21no—
121#888—32no—
122#888—61no—
123#888—62no—
124#888—62no—
125C4×D12C2×D311yescharacteristic
126#869—31no—
127#869—31no—
128#869—32no—
129#869—61no—
130#869—61no—
131C4×Dic6—32no—
132C4×Dic6—61no—
133C4×Dic6C2×D311yescharacteristic
134C4×Dic6C2×D311yescharacteristic
135C3×C4⋊C8—31no—
136C3×#103—32no—
137#835—32no—
138#835—32no—
139#835—32no—
140#835—32no—
141#835—31no—
142#835—62no—
143#835—62no—
144#835C2×D312yes—
145#832—31no—
146#832—32no—
147#821—32no—
148#817—32no—
149#815—32no—
150Dic3⋊C8—32no—
151#810—31no—
152#809—31no—
153#808—31no—
154#808—31no—
155#808—32no—
156C4⋊(C3⋊C8)—32no—
157C4⋊(C3⋊C8)C2×D311yescharacteristic
158#803—32no—
159C4×C3⋊C8—31no—
160C4×C3⋊C8—31no—
161C4×C3⋊C8—61no—
162C22×C3×D3—21no—
163C32×Q8—22no—
164C32×Q8—22no—
165C2×C32×C4—22no—
166C2×C32×C4C2×D411yescharacteristic
167C2×C32×C4C2×D411yescharacteristic
168C2×C32×C4C2411yescharacteristic
169C2×C3⋊Dic3—22no—
170#634—81no—
171C2×C3×Dic3—21no—
172C2×C3×Dic3—21no—
173C2×C3×Dic3—21no—
174C2×C3×Dic3C2×D412yes—
175C2×C3×Dic3C2×D412yes—
176C3×D12—21no—
177C3×D12—21no—
178C3×C4×D3—42no—
179C3×Dic6—22no—
180C3×Dic6—21no—
181C3×Dic6#4112yes—
182#627—82no—
183C3⋊(C3⋊C8)—21no—
184C3⋊(C3⋊C8)—21no—
185C3×C3⋊C8—22no—
186Q82—91no—
187#556—31no—
188#489—92no—
189#487—91no—
190#476—91no—
191#475—92no—
192#464—92no—
193#462—31no—
194#446—91no—
195#441—92no—
196C4×SD16—91no—
197C2×C3×Q8—22no—
198C2×C3×Q8—31no—
199C2×C3×Q8—31no—
200C2×C3×Q8C22×D312yes—
201C2×C3×Q8C22×D312yes—
202C2×C3×D4—31no—
203C22×C3×C4—61no—
204C2×D12C22×D311yescharacteristic
205C2×C4×D3—21no—
206C2×Dic6—62no—
207C2×Dic6—61no—
208C2×Dic6—61no—
209C2×Dic6—62no—
210C2×Dic6—121no—
211C2×Dic6#6711yescharacteristic
212C2×Dic6C22×D311yescharacteristic
213C3×Q16—64no—
214C2×C3×C8—32no—
215C3×C4⋊C4—21no—
216C3×C4⋊C4—21no—
217C3×C4⋊C4—21no—
218C3×C4⋊C4—21no—
219C3×C4⋊C4—32no—
220C3×C4⋊C4—31no—
221C3×C4⋊C4—31no—
222C3×C4⋊C4—31no—
223C3×C4⋊C4—41no—
224C3×C4⋊C4—41no—
225C3×C4⋊C4—62no—
226C3×C4⋊C4—61no—
227C3×C22⋊C4—62no—
228C3×C22⋊C4—62no—
229C3×C22⋊C4—61no—
230C3×C42—21no—
231C3×C42—32no—
232C3×C42—62no—
233C3×C42—61no—
234C3×C42C22×D311yescharacteristic
235C3×C42C22×D311yescharacteristic
236#216—24no—
237#215—62no—
238#214—62no—
239(C2×D3)⋊C4—21no—
240(C2×D3)⋊C4—22no—
241(C2×D3)⋊C4—22no—
242C4⋊Dic3—22no—
243C4⋊Dic3—32no—
244C4⋊Dic3—32no—
245C4⋊Dic3—62no—
246C4⋊Dic3—62no—
247C4⋊Dic3—61no—
248C4⋊Dic3—61no—
249C4⋊Dic3—62no—
250C4⋊Dic3—121no—
251C4⋊Dic3#6711yescharacteristic
252C4⋊Dic3C22×D311yescharacteristic
253C4⋊Dic3C22×D311yescharacteristic
254Dic3⋊C4—21no—
255Dic3⋊C4—62no—
256Dic3⋊C4—62no—
257Dic3⋊C4#6712yes—
258C4×Dic3—21no—
259C4×Dic3—22no—
260C4×Dic3—62no—
261C4×Dic3—62no—
262C4×Dic3C22×D312yes—
263C2×C3⋊C8—31no—
264C2×C3⋊C8—31no—
265C2×C3⋊C8—31no—
266C2×C3⋊C8—31no—
267C2×C3⋊C8—61no—
268C2×C3⋊C8—61no—
269C2×C3⋊C8C22×D312yes—
270C22×C32C22×D411yescharacteristic
271C2×C3×D3—41no—
272C2×C3×D3—41no—
273C2×C3×D3—41no—
274C32×C4—21no—
275C32×C4—42no—
276C32×C4#13712yes—
277C32×C4C2×#4111yescharacteristic
278C32×C42−1+411yescharacteristic
279C3⋊Dic3—42no—
280C3×Dic3—22no—
281C3×Dic3—22no—
282C3×Dic3—22no—
283C3×Dic3—41no—
284C3×Dic3—41no—
285C2×Q16—32no—
286C2×SD16—91no—
287C4⋊Q8—92no—
288C4⋊Q8—91no—
289C4⋊Q8—181no—
290C4⋊Q8—182no—
291C4⋊Q8D3211yescharacteristic
292#126—62no—
293#124—32no—
294C22⋊Q8—61no—
295C4×Q8—31no—
296C4×Q8—32no—
297C4×Q8—31no—
298C4×Q8—92no—
299C4×Q8—181no—
300C4×D4—31no—
301#117—61no—
302#106—91no—
303#106—92no—
304C4⋊C8—31no—
305C4⋊C8—92no—
306#103—32no—
307#103—91no—
308#103—92no—
309#103—92no—
310#102—91no—
311#102—92no—
312#97—92no—
313C4×C8—91no—
314C23×C3—61no—
315C22×D3—21no—
316C3×Q8—22no—
317C3×Q8—22no—
318C3×Q8—22no—
319C3×Q8—22no—
320C3×Q8—32no—
321C3×Q8—42no—
322C3×Q8—42no—
323C3×Q8—62no—
324C3×Q8—61no—
325C3×D4—61no—
326C3×D4—61no—
327C2×C3×C4—22no—
328C2×C3×C4—22no—
329C2×C3×C4—21no—
330C2×C3×C4—21no—
331C2×C3×C4—21no—
332C2×C3×C4—32no—
333C2×C3×C4—32no—
334C2×C3×C4—42no—
335C2×C3×C4—61no—
336C2×C3×C4—61no—
337C2×C3×C4—61no—
338C2×C3×C4—122no—
339C2×C3×C4D3×D411yescharacteristic
340C2×C3×C4D3×D411yescharacteristic
341C2×C3×C4C2×#6711yescharacteristic
342C2×C3×C4C2×#6711yescharacteristic
343C2×C3×C4C23×D311yescharacteristic
344C2×C3×C4C23×D311yescharacteristic
345C2×Dic3—21no—
346C2×Dic3—21no—
347C2×Dic3—21no—
348C2×Dic3—62no—
349C2×Dic3—62no—
350C2×Dic3—122no—
351C2×Dic3C2×#6712yes—
352C2×Dic3C2×#6712yes—
353D12—21no—
354D12—21no—
355C4×D3—42no—
356Dic6—22no—
357Dic6—21no—
358Dic6—242no—
359Dic6—242no—
360Dic6—241no—
361Dic6—241no—
362Dic6—242no—
363Dic6#23712yes—
364C3×C8—62no—
365C3⋊C8—22no—
366C3⋊C8—61no—
367C3⋊C8—61no—
368C3⋊C8—61no—
369C3⋊C8—61no—
370C3⋊C8—121no—
371C3⋊C8—121no—
372C2×C32#54811yescharacteristic
373C2×C32C2×#13711yescharacteristic
374C2×C32#57711yescharacteristic
375C3×D3—81no—
376C2×Q8—31no—
377C2×Q8—31no—
378C2×Q8—182no—
379C2×Q8—181no—
380C2×Q8C2×D3212yes—
381C2×D4—31no—
382C22×C4—61no—
383Q16—64no—
384SD16—182no—
385C2×C8—32no—
386C2×C8—91no—
387C2×C8—91no—
388C4⋊C4—21no—
389C4⋊C4—21no—
390C4⋊C4—31no—
391C4⋊C4—32no—
392C4⋊C4—31no—
393C4⋊C4—31no—
394C4⋊C4—62no—
395C4⋊C4—61no—
396C4⋊C4—92no—
397C4⋊C4—182no—
398C4⋊C4—182no—
399C4⋊C4—181no—
400C22⋊C4—62no—
401C22⋊C4—62no—
402C22⋊C4—61no—
403C42—32no—
404C42—62no—
405C42—61no—
406C42—182no—
407C42C2×D3211yescharacteristic
408C22×C3—21no—
409C22×C3—121no—
410C22×C3—121no—
411C22×C3—121no—
412C22×C3C2×D3×D411yescharacteristic
413C22×C3C22×#6711yescharacteristic
414C2×D3—41no—
415C2×D3—41no—
416C2×D3—41no—
417C3×C4—22no—
418C3×C4—21no—
419C3×C4—21no—
420C3×C4—21no—
421C3×C4—21no—
422C3×C4—22no—
423C3×C4—42no—
424C3×C4—42no—
425C3×C4—62no—
426C3×C4—62no—
427C3×C4—62no—
428C3×C4—82no—
429C3×C4—121no—
430C3×C4—121no—
431C3×C4#91812yes—
432C3×C4#95112yes—
433C3×C4C2×#23711yescharacteristic
434C3×C4D3×#4111yescharacteristic
435C3×C4#101011yescharacteristic
436C3×C4#101011yescharacteristic
437Dic3—22no—
438Dic3—22no—
439Dic3—22no—
440Dic3—41no—
441Dic3—41no—
442Dic3—122no—
443Dic3—122no—
444Dic3—242no—
445C32#336911yescharacteristic, complemented, Sylow
446C23—61no—
447Q8—22no—
448Q8—22no—
449Q8—32no—
450Q8—61no—
451Q8—62no—
452Q8—721no—
453Q8—722no—
454D4—61no—
455D4—61no—
456C2×C4—22no—
457C2×C4—32no—
458C2×C4—32no—
459C2×C4—61no—
460C2×C4—61no—
461C2×C4—61no—
462C2×C4—122no—
463C2×C4—182no—
464C2×C4D3×#6711yescharacteristic
465C2×C4D3×#6711yescharacteristic
466C2×C4C22×D3211yescharacteristic
467C8—62no—
468C8—181no—
469C8—181no—
470C2×C3—21no—
471C2×C3—21no—
472C2×C3—21no—
473C2×C3—241no—
474C2×C3#559811yescharacteristic
475C2×C3C2×#91811yescharacteristic
476C2×C3#577811yescharacteristic
477C2×C3C2×#95111yescharacteristic
478C2×C3#583111yescharacteristic
479C2×C3#583711yescharacteristic
480D3—81no—
481C22—121no—
482C22—121no—
483C22—121no—
484C22C2×D3×#6711yescharacteristic
485C4—21no—
486C4—42no—
487C4—62no—
488C4—62no—
489C4—62no—
490C4—121no—
491C4—121no—
492C4—362no—
493C4#6394312yes—
494C4#6430911yescharacteristic
495C4D3×#23711yescharacteristic
496C3—21no—
497C3#8046411yescharacteristic, complemented
498C3#8367711yescharacteristic, complemented
499C2—241no—
500C2#1059515711yescharacteristic
501C2#1059531911yescharacteristic
502C2C2×#6394311yescharacteristic
subgroupG/H
centerC22C2×D3×#67
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C4⋊Q8C22
socleC22×C32C22×D4
prime radicalC2×C3×D12C23
hypercenterC4⋊Q8D32
hypocenterC32#3369
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ C4⋊Q8

Complements

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

NH ≅ G/Ntype
2. Dic62C2semidirect
3. #10592778C2semidirect
4. C3×#5090C2semidirect
7. #10591576C2semidirect
8. #10591544C2semidirect
11. #10590259C2semidirect
50. #5090D3semidirect
445. C32#3369semidirect
497. C3#80464semidirect
498. C3#83677semidirect

Maximal subgroups

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

subgroupindex
C3×#57322
Dic622
#105927782
C3×#50902
#105916242
#105915782
#105915762
#105915442
C4×#37152
#105902682
#105902592
#836773
#804643