Finite Group Databasebeta

← #11873277

Subgroups — #11873277

Order 1152.

1074 conjugacy classes of subgroups.

The subgroup lattice has 489 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10596054C211yesmaximal, characteristic
2#10596043C211yesmaximal, characteristic
3C32×#441C211yesmaximal, characteristic, complemented
4#10592885C211yesmaximal, characteristic
5#10592881C211yesmaximal, characteristic, complemented
6C4×#3756C211yesmaximal, characteristic, complemented
7C4×#3756C211yesmaximal, characteristic, complemented
8#10592567C211yesmaximal, characteristic
9#10592556C211yesmaximal, characteristic, complemented
10#10592514C211yesmaximal, characteristic
11#10592508C211yesmaximal, characteristic
12#10592498C211yesmaximal, characteristic, complemented
13#10592494C211yesmaximal, characteristic, complemented
14#10592415C211yesmaximal, characteristic, complemented
15#10592408C211yesmaximal, characteristic
16#79836—34nomaximal
17C2×Q8×C3⋊D3C2211yescharacteristic
18C2×C32×Q16C2211yescharacteristic
19C32×C4×Q8C2211yescharacteristic
20C32×C4×Q8C2211yescharacteristic
21#64155C2211yescharacteristic
22Q8×C3⋊Dic3C2211yescharacteristic
23#64153C2211yescharacteristic
24C2×#3756C2211yescharacteristic
25C2×#3756C2211yescharacteristic
26C2×#3746C2211yescharacteristic
27#64107—21no—
28#64106C2211yescharacteristic
29#64101—21no—
30#64101C2211yescharacteristic
31#64099C2211yescharacteristic
32#64098—21no—
33#64096—21no—
34#64096C2211yescharacteristic
35#64085—21no—
36#64081—21no—
37#64081C2211yescharacteristic
38#64079—21no—
39C4×#634—21no—
40C4×#634C2211yescharacteristic
41C4×#634C2211yescharacteristic
42C32×#106C2211yescharacteristic
43C32×#103C2211yescharacteristic
44C32×#103C2211yescharacteristic
45C32×#97C2211yescharacteristic
46#63662C2211yescharacteristic
47#63662C2211yescharacteristic
48#63647C2211yescharacteristic
49#63647C2211yescharacteristic
50#63644C2211yescharacteristic
51#63643C2211yescharacteristic
52#63643C2211yescharacteristic
53#63641C2211yescharacteristic
54#63641C2211yescharacteristic
55#63637C2211yescharacteristic
56#63637C2211yescharacteristic
57#63634C2211yescharacteristic
58#63634C2211yescharacteristic
59C4×C3⋊(C3⋊C8)C2211yescharacteristic
60#5583—34no—
61#5572—34no—
62C3×#441D314yescomplemented
63#5186—34no—
64#5182—34no—
65C4×#216—34no—
66C4×#216—34no—
67#4868—34no—
68#4857—34no—
69#4815—34no—
70#4809—34no—
71#4799—34no—
72#4795—34no—
73#4716—34no—
74#4709—34no—
75C2×C32×Q8C2311yescharacteristic
76C2×C32×Q8C2311yescharacteristic
77Q8×C3⋊D3—22no—
78Q8×C3⋊D3—22no—
79C2×C4×C3⋊D3—21no—
80C2×C4×C3⋊D3C2311yescharacteristic
81C2×#634—21no—
82C2×#634C2311yescharacteristic
83C2×#634C2311yescharacteristic
84C32×Q16—22no—
85C2×C32×C8C2311yescharacteristic
86C2×C32×C8C2311yescharacteristic
87C32×C4⋊C4—21no—
88C32×C4⋊C4—21no—
89C32×C4⋊C4C2311yescharacteristic
90C32×C4⋊C4C2311yescharacteristic
91C32×C42—21no—
92C32×C42—21no—
93C32×C42C2311yescharacteristic
94#3756—22no—
95#3756—22no—
96#3752—21no—
97#3752—21no—
98#3752—21no—
99#3752D411yescharacteristic
100#3752D411yescharacteristic
101C4⋊(C3⋊Dic3)—21no—
102C4⋊(C3⋊Dic3)—21no—
103C4⋊(C3⋊Dic3)—21no—
104C4⋊(C3⋊Dic3)C2311yescharacteristic
105C4⋊(C3⋊Dic3)C2311yescharacteristic
106#3750—21no—
107#3750—21no—
108#3750—21no—
109#3750—21no—
110#3750—21no—
111#3750—21no—
112#3750—21no—
113#3750D411yescharacteristic
114#3750D411yescharacteristic
115C4×C3⋊Dic3—21no—
116C4×C3⋊Dic3—21no—
117C4×C3⋊Dic3—21no—
118C4×C3⋊Dic3—21no—
119C4×C3⋊Dic3—21no—
120C4×C3⋊Dic3C2311yescharacteristic
121C2×C3⋊(C3⋊C8)C2311yescharacteristic
122C2×C3⋊(C3⋊C8)C2311yescharacteristic
123#3746—22no—
124#3127—91noSylow
125C2×D3×Q8—34no—
126C2×C3×Q16C2×D314yes—
127C3×C4×Q8C2×D314yes—
128C3×C4×Q8C2×D314yes—
129#946—34no—
130Q8×Dic3—34no—
131#944—34no—
132C2×#216—34no—
133C2×#216—34no—
134C2×Dic12—34no—
135#898—64no—
136#897—34no—
137#892—34no—
138#892—64no—
139#890—34no—
140#889—64no—
141#887—34no—
142#887—64no—
143#876—64no—
144#872—34no—
145#872—64no—
146#870—64no—
147C4×Dic6—34no—
148C4×Dic6—34no—
149C4×Dic6—64no—
150C3×#106C2×D314yes—
151C3×#103C2×D314yes—
152C3×#103C2×D314yes—
153C3×#97C2×D314yes—
154#835—34no—
155#835—34no—
156(C2×D3)⋊C8—34no—
157(C2×D3)⋊C8—34no—
158#817—34no—
159#816—34no—
160#816—34no—
161Dic3⋊C8—34no—
162Dic3⋊C8—34no—
163#810—34no—
164#810—34no—
165#807—34no—
166#807—34no—
167C4×C3⋊C8—34no—
168C22×C3⋊D3C2×D411yescharacteristic
169C32×Q8—21no—
170C32×Q8—21no—
171C32×Q8—21no—
172C32×Q8#4112yes—
173C2×C32×C4—21no—
174C2×C32×C4—21no—
175C2×C32×C4—21no—
176C2×C32×C4—21no—
177C2×C32×C4C2×D411yescharacteristic
178C2×C32×C4C2×D411yescharacteristic
179C2×C32×C4C2411yescharacteristic
180C2×C3⋊Dic3—21no—
181C2×C3⋊Dic3—21no—
182C2×C3⋊Dic3—21no—
183C2×C3⋊Dic3—21no—
184C2×C3⋊Dic3C2×D411yescharacteristic
185C2×C3⋊Dic3C2×D411yescharacteristic
186C2×C3⋊Dic3C2×D411yescharacteristic
187C4×C3⋊D3—24no—
188C4×C3⋊D3—21no—
189C4×C3⋊D3—21no—
190#634—24no—
191#634—21no—
192#634—21no—
193#634—21no—
194#634#4112yes—
195C32×C8—21no—
196C32×C8—21no—
197C3⋊(C3⋊C8)—21no—
198C3⋊(C3⋊C8)—21no—
199#541—91no—
200#519—91no—
201#485—91no—
202#485—91no—
203#479—91no—
204#479—91no—
205#462—91no—
206#462—91no—
207#451—91no—
208#451—91no—
209#441—91no—
210#441C3⋊D311yescharacteristic, complemented
211C4×Q16—91no—
212C4×Q16—91no—
213#433—91no—
214C2×C3×Q8C22×D314yes—
215C2×C3×Q8C22×D314yes—
216D3×Q8—68no—
217D3×Q8—68no—
218C2×C4×D3—34no—
219C2×C4×D3—64no—
220C2×Dic6—34no—
221C2×Dic6—34no—
222C2×Dic6—64no—
223C3×Q16—28no—
224C2×C3×C8C22×D314yes—
225C2×C3×C8C22×D314yes—
226C3×C4⋊C4—24no—
227C3×C4⋊C4—24no—
228C3×C4⋊C4C22×D314yes—
229C3×C4⋊C4C22×D314yes—
230C3×C42—24no—
231C3×C42—24no—
232C3×C42C22×D314yes—
233#216—68no—
234#216—68no—
235(C2×D3)⋊C4—34no—
236(C2×D3)⋊C4—34no—
237(C2×D3)⋊C4—64no—
238(C2×D3)⋊C4—64no—
239(C2×D3)⋊C4—64no—
240C4⋊Dic3—34no—
241C4⋊Dic3—34no—
242C4⋊Dic3—64no—
243C4⋊Dic3—64no—
244C4⋊Dic3—64no—
245Dic3⋊C4—34no—
246Dic3⋊C4—34no—
247Dic3⋊C4—64no—
248Dic3⋊C4—64no—
249Dic3⋊C4—64no—
250Dic3⋊C4—64no—
251Dic3⋊C4—64no—
252Dic3⋊C4—64no—
253Dic3⋊C4—64no—
254C4×Dic3—34no—
255C4×Dic3—64no—
256C4×Dic3—64no—
257C4×Dic3—64no—
258C4×Dic3—64no—
259C4×Dic3—64no—
260C2×C3⋊C8—34no—
261C2×C3⋊C8—34no—
262Dic12—68no—
263C22×C32C22×D411yescharacteristic
264C2×C3⋊D3—21no—
265C2×C3⋊D3—21no—
266C2×C3⋊D3—21no—
267C32×C4—22no—
268C32×C4—21no—
269C32×C4—21no—
270C32×C4—41no—
271C32×C4—41no—
272C32×C4—41no—
273C32×C4C2×#4111yescharacteristic
274C32×C4C2×#4111yescharacteristic
275C3⋊Dic3—21no—
276C3⋊Dic3—22no—
277C3⋊Dic3—21no—
278C3⋊Dic3—21no—
279C3⋊Dic3—41no—
280C3⋊Dic3—41no—
281C3⋊Dic3—41no—
282C22×Q8—91no—
283C2×Q16—91no—
284C2×Q16—91no—
285C2×Q16—91no—
286C2×Q16C2×C3⋊D311yescharacteristic
287C4⋊Q8—91no—
288#126—181no—
289#126—181no—
290#125—91no—
291#125—181no—
292#125—181no—
293C22⋊Q8—91no—
294C22⋊Q8—91no—
295C4×Q8—91no—
296C4×Q8—91no—
297C4×Q8—91no—
298C4×Q8—91no—
299C4×Q8—181no—
300C4×Q8—181no—
301C4×Q8C2×C3⋊D311yescharacteristic
302C4×Q8C2×C3⋊D311yescharacteristic
303#117—91no—
304#117—91no—
305#117—181no—
306#117—181no—
307#107—91no—
308#107—91no—
309#106—91no—
310#106C2×C3⋊D311yescharacteristic
311C4⋊C8—91no—
312C4⋊C8—91no—
313#103—91no—
314#103—91no—
315#103—91no—
316#103—91no—
317#103—91no—
318#103—91no—
319#103C2×C3⋊D311yescharacteristic
320#103C2×C3⋊D311yescharacteristic
321C22⋊C8—91no—
322C22⋊C8—91no—
323#97C2×C3⋊D311yescharacteristic
324C4×C8—91no—
325C22×D3—34no—
326C3×Q8—24no—
327C3×Q8—24no—
328C3×Q8—24no—
329C3×Q8#23518yes—
330C2×C3×C4—24no—
331C2×C3×C4—24no—
332C2×C3×C4—24no—
333C2×C3×C4—24no—
334C2×C3×C4D3×D414yes—
335C2×C3×C4D3×D414yes—
336C2×C3×C4C23×D314yes—
337C2×Dic3—34no—
338C2×Dic3—34no—
339C2×Dic3—34no—
340C2×Dic3—64no—
341C2×Dic3—64no—
342C2×Dic3—64no—
343C2×Dic3—64no—
344C4×D3—616no—
345C4×D3—64no—
346C4×D3—64no—
347Dic6—38no—
348Dic6—616no—
349Dic6—64no—
350Dic6—64no—
351Dic6—64no—
352C3×C8—24no—
353C3×C8—24no—
354C3⋊C8—64no—
355C3⋊C8—64no—
356C2×C32#52511yescharacteristic
357C2×C32#57811yescharacteristic
358C2×C32#57811yescharacteristic
359C3⋊D3—41no—
360C2×Q8—91no—
361C2×Q8—91no—
362C2×Q8—181no—
363C2×Q8—182no—
364C2×Q8—182no—
365C2×Q8C22×C3⋊D311yescharacteristic
366C2×Q8C22×C3⋊D311yescharacteristic
367C22×C4—91no—
368C22×C4—181no—
369Q16—22no—
370Q16—182no—
371Q16—182no—
372Q16—182no—
373C2×C8—91no—
374C2×C8—91no—
375C2×C8C22×C3⋊D311yescharacteristic
376C2×C8C22×C3⋊D311yescharacteristic
377C4⋊C4—21no—
378C4⋊C4—21no—
379C4⋊C4—91no—
380C4⋊C4—91no—
381C4⋊C4—91no—
382C4⋊C4—91no—
383C4⋊C4—181no—
384C4⋊C4—181no—
385C4⋊C4—181no—
386C4⋊C4—181no—
387C4⋊C4—181no—
388C4⋊C4—181no—
389C4⋊C4—181no—
390C4⋊C4—181no—
391C4⋊C4—181no—
392C4⋊C4—181no—
393C4⋊C4C22×C3⋊D311yescharacteristic
394C4⋊C4C22×C3⋊D311yescharacteristic
395C22⋊C4—91no—
396C22⋊C4—91no—
397C22⋊C4—181no—
398C22⋊C4—181no—
399C22⋊C4—181no—
400C42—21no—
401C42—21no—
402C42—91no—
403C42—181no—
404C42—181no—
405C42—181no—
406C42—181no—
407C42—181no—
408C42C22×C3⋊D311yescharacteristic
409C22×C3C2×D3×D414yes—
410C2×D3—64no—
411C2×D3—64no—
412C2×D3—64no—
413C3×C4—24no—
414C3×C4—24no—
415C3×C4—28no—
416C3×C4—44no—
417C3×C4—44no—
418C3×C4—44no—
419C3×C4C2×#23514yes—
420C3×C4D3×#4114yes—
421Dic3—64no—
422Dic3—64no—
423Dic3—68no—
424Dic3—64no—
425Dic3—124no—
426Dic3—124no—
427Dic3—124no—
428C32#312711yescharacteristic, complemented, Sylow
429C23—91no—
430Q8—21no—
431Q8—21no—
432Q8—21no—
433Q8—92no—
434Q8—184no—
435Q8—181no—
436Q8—181no—
437Q8—181no—
438Q8#382812yes—
439C2×C4—21no—
440C2×C4—21no—
441C2×C4—21no—
442C2×C4—21no—
443C2×C4—91no—
444C2×C4—91no—
445C2×C4—91no—
446C2×C4—184no—
447C2×C4—181no—
448C2×C4—181no—
449C2×C4—181no—
450C2×C4—181no—
451C2×C4—181no—
452C2×C4—181no—
453C2×C4D4×C3⋊D311yescharacteristic
454C2×C4D4×C3⋊D311yescharacteristic
455C2×C4C23×C3⋊D311yescharacteristic
456C8—21no—
457C8—21no—
458C8—181no—
459C8—181no—
460C2×C3#554714yes—
461C2×C3#577914yes—
462C2×C3#577914yes—
463D3—124no—
464C22—181no—
465C22—181no—
466C22—181no—
467C22C2×D4×C3⋊D311yescharacteristic
468C4—21no—
469C4—21no—
470C4—22no—
471C4—41no—
472C4—41no—
473C4—41no—
474C4—181no—
475C4—181no—
476C4—181no—
477C4—182no—
478C4—361no—
479C4—361no—
480C4—361no—
481C4C2×#382811yescharacteristic
482C4#41×C3⋊D311yescharacteristic
483C3#7983614yescomplemented
484C2—361no—
485C2#1059601811yescharacteristic
486C2#1059625011yescharacteristic
487C2#1059625011yescharacteristic
subgroupG/H
centerC22C2×D4×C3⋊D3
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C23×C3⋊D3
FittingC32×#441C2
socleC22×C32C22×D4
prime radicalC22×C3⋊D3C2×D4
hypercenter#441C3⋊D3
hypocenterC32#3127
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ #441

Complements

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

NH ≅ G/Ntype
3. C32×#441C2semidirect
5. #10592881C2semidirect
6. C4×#3756C2semidirect
7. C4×#3756C2semidirect
9. #10592556C2semidirect
12. #10592498C2semidirect
13. #10592494C2semidirect
14. #10592415C2semidirect
62. C3×#441D3semidirect
210. #441C3⋊D3semidirect
428. C32#3127semidirect
483. C3#79836semidirect

Maximal subgroups

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

subgroupindex
#105960542
#105960432
C32×#4412
#105928852
#105928812
C4×#37562
#105925672
#105925562
#105925142
#105925082
#105924982
#105924942
#105924152
#105924082
#798363