Finite Group Databasebeta

← #13162010

Subgroups — #13162010

Order 1728.

552 conjugacy classes of subgroups.

The subgroup lattice has 494 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×Q8×C3⋊Dic3C211yesmaximal, characteristic
2#11723680C211yesmaximal, characteristic
3C3×#63662C211yesmaximal, characteristic
4C3×#63662C211yesmaximal, characteristic
5#11722080C211yesmaximal, characteristic
6#11722079C211yesmaximal, characteristic
7#11722078C211yesmaximal, characteristic
8#10591615—31nomaximal
9#10591547—31nomaximal
10#10591545—31nomaximal
11C2×C33×Q8C2211yescharacteristic
12C3×C4⋊(C3⋊Dic3)—21no—
13C3×C4⋊(C3⋊Dic3)C2211yescharacteristic
14C3×C4⋊(C3⋊Dic3)C2211yescharacteristic
15C3×C4⋊(C3⋊Dic3)C2211yescharacteristic
16C3×C4×C3⋊Dic3—21no—
17C3×C4×C3⋊Dic3C2211yescharacteristic
18C2×C3×C3⋊(C3⋊C8)C2211yescharacteristic
19C2×C3×C3⋊(C3⋊C8)C2211yescharacteristic
20#88815—21no—
21#88815—21no—
22Q8×C3⋊Dic3D311yescharacteristic
23C3×Q8×Dic3—31no—
24C3×Q8×Dic3—31no—
25C3×Q8×Dic3—61no—
26#63872—31no—
27#63869—31no—
28#63869—31no—
29#63662D311yescharacteristic
30#63662D311yescharacteristic
31C3×#835—31no—
32C3×#835—31no—
33C3×#835—31no—
34C3×#835—31no—
35C3×#835—61no—
36C3×#835—61no—
37#63576—31no—
38#63575—31no—
39#63575—31no—
40#63574—31no—
41#63573—31no—
42#63573—31no—
43#63572—31no—
44Dic3⋊(C3⋊C8)—31no—
45Dic3⋊(C3⋊C8)—31no—
46C33×Q8—21no—
47C33×Q8Q812yes—
48C2×C33×C4—21no—
49C2×C33×C4C2311yescharacteristic
50C2×C3×C3⋊Dic3—21no—
51C2×C3×C3⋊Dic3—21no—
52C2×C3×C3⋊Dic3—21no—
53C2×C3×C3⋊Dic3D411yescharacteristic
54C2×C3×C3⋊Dic3D411yescharacteristic
55C3×C3⋊(C3⋊C8)—21no—
56C3×C3⋊(C3⋊C8)—21no—
57#5022—91no—
58#4799—91no—
59#4796—91no—
60C2×C32×Q8—21no—
61C2×C32×Q8—21no—
62C2×C32×Q8—21no—
63C2×C32×Q8—41no—
64C2×C32×Q8C2×D311yescharacteristic
65C2×C32×Q8C2×D311yescharacteristic
66C2×C32×Q8C2×D311yescharacteristic
67C4⋊(C3⋊Dic3)—21no—
68C4⋊(C3⋊Dic3)C2×D311yescharacteristic
69C4⋊(C3⋊Dic3)C2×D311yescharacteristic
70C4⋊(C3⋊Dic3)C2×D311yescharacteristic
71C4×C3⋊Dic3—21no—
72C4×C3⋊Dic3C2×D311yescharacteristic
73C2×C3⋊(C3⋊C8)C2×D311yescharacteristic
74C2×C3⋊(C3⋊C8)C2×D311yescharacteristic
75C3×C4⋊Dic3—31no—
76C3×C4⋊Dic3—31no—
77C3×C4⋊Dic3—31no—
78C3×C4⋊Dic3—31no—
79C3×C4⋊Dic3—31no—
80C3×C4⋊Dic3—31no—
81C3×C4⋊Dic3—61no—
82C3×C4⋊Dic3—61no—
83C3×C4⋊Dic3—61no—
84C3×C4⋊Dic3—62no—
85C3×C4⋊Dic3—61no—
86C3×C4⋊Dic3—61no—
87C3×C4×Dic3—31no—
88C3×C4×Dic3—31no—
89C3×C4×Dic3—61no—
90C3×C4×Dic3—61no—
91C3×C4×Dic3—61no—
92C3×C4×Dic3—62no—
93C2×C3×C3⋊C8—31no—
94C2×C3×C3⋊C8—31no—
95C2×C3×C3⋊C8—31no—
96C2×C3×C3⋊C8—31no—
97C2×C3×C3⋊C8—61no—
98C2×C3×C3⋊C8—61no—
99#3724—61no—
100#3724—61no—
101Dic3⋊Dic3—61no—
102Dic3⋊Dic3—61no—
103Dic3⋊Dic3—61no—
104Dic3⋊Dic3—61no—
105C22×C33C2×D411yescharacteristic
106C33×C4—22no—
107C33×C4C2×Q811yescharacteristic
108C33×C4#4111yescharacteristic
109C3×C3⋊Dic3—21no—
110C3×C3⋊Dic3—21no—
111C3×C3⋊Dic3—41no—
112C3×C3⋊Dic3—41no—
113C3×C3⋊Dic3—41no—
114C3×C4×Q8—91no—
115Q8×Dic3—31no—
116Q8×Dic3—31no—
117Q8×Dic3—61no—
118#890—91no—
119#890—91no—
120#870—91no—
121C3×#103—91no—
122C3×#103—91no—
123#835—31no—
124#835—31no—
125#835—31no—
126#835—31no—
127#835—61no—
128#835—61no—
129#818—91no—
130#817—91no—
131Dic3⋊C8—91no—
132Dic3⋊C8—91no—
133#808—91no—
134#808—91no—
135#807—91no—
136#807—91no—
137C4⋊(C3⋊C8)—91no—
138C32×Q8—21no—
139C32×Q8—22no—
140C32×Q8—21no—
141C32×Q8—21no—
142C32×Q8—22no—
143C32×Q8—22no—
144C32×Q8—22no—
145C32×Q8—42no—
146C32×Q8—41no—
147C32×Q8—41no—
148C32×Q8—42no—
149C32×Q8Dic612yes—
150C32×Q8Dic612yes—
151C32×Q8Dic612yes—
152C2×C32×C4—21no—
153C2×C32×C4—22no—
154C2×C32×C4—21no—
155C2×C32×C4—21no—
156C2×C32×C4—21no—
157C2×C32×C4—21no—
158C2×C32×C4—21no—
159C2×C32×C4—41no—
160C2×C32×C4—41no—
161C2×C32×C4—41no—
162C2×C32×C4—42no—
163C2×C32×C4C22×D311yescharacteristic
164C2×C32×C4C22×D311yescharacteristic
165C2×C32×C4C22×D311yescharacteristic
166C2×C3⋊Dic3—21no—
167C2×C3⋊Dic3—21no—
168C2×C3⋊Dic3—21no—
169C2×C3⋊Dic3#6711yescharacteristic
170C2×C3⋊Dic3#6711yescharacteristic
171C2×C3×Dic3—31no—
172C2×C3×Dic3—31no—
173C2×C3×Dic3—31no—
174C2×C3×Dic3—31no—
175C2×C3×Dic3—61no—
176C2×C3×Dic3—61no—
177C2×C3×Dic3—62no—
178C2×C3×Dic3—61no—
179C2×C3×Dic3—61no—
180C2×C3×Dic3—61no—
181C2×C3×Dic3—61no—
182C2×C3×Dic3—61no—
183C2×C3×Dic3—61no—
184C2×C3×Dic3—121no—
185C2×C3×Dic3—121no—
186C3⋊(C3⋊C8)—21no—
187C3⋊(C3⋊C8)—21no—
188C3×C3⋊C8—61no—
189C3×C3⋊C8—61no—
190C3×C3⋊C8—61no—
191C3×C3⋊C8—61no—
192C3×C3⋊C8—121no—
193C3×C3⋊C8—121no—
194#479—271noSylow
195C2×C33C22⋊Q811yescharacteristic
196C2×C33#13511yescharacteristic
197C2×C33#13711yescharacteristic
198C2×C3×Q8—21no—
199C2×C3×Q8—21no—
200C2×C3×Q8—21no—
201C2×C3×Q8—41no—
202C2×C3×Q8D3211yescharacteristic
203C2×C3×Q8D3211yescharacteristic
204C2×C3×Q8D3211yescharacteristic
205C2×C3×C8—91no—
206C2×C3×C8—91no—
207C3×C4⋊C4—91no—
208C3×C4⋊C4—91no—
209C3×C4⋊C4—91no—
210C3×C4⋊C4—181no—
211C3×C42—91no—
212C3×C42—181no—
213C4⋊Dic3—31no—
214C4⋊Dic3—31no—
215C4⋊Dic3—31no—
216C4⋊Dic3—31no—
217C4⋊Dic3—31no—
218C4⋊Dic3—31no—
219C4⋊Dic3—61no—
220C4⋊Dic3—61no—
221C4⋊Dic3—61no—
222C4⋊Dic3—61no—
223C4⋊Dic3—61no—
224C4⋊Dic3—62no—
225C4⋊Dic3—181no—
226C4⋊Dic3—181no—
227Dic3⋊C4—181no—
228Dic3⋊C4—181no—
229Dic3⋊C4—181no—
230Dic3⋊C4—181no—
231C4×Dic3—31no—
232C4×Dic3—31no—
233C4×Dic3—61no—
234C4×Dic3—61no—
235C4×Dic3—61no—
236C4×Dic3—62no—
237C2×C3⋊C8—31no—
238C2×C3⋊C8—31no—
239C2×C3⋊C8—31no—
240C2×C3⋊C8—31no—
241C2×C3⋊C8—61no—
242C2×C3⋊C8—61no—
243C22×C32—21no—
244C22×C32—21no—
245C22×C32—21no—
246C22×C32—41no—
247C22×C32D3×D411yescharacteristic
248C22×C32D3×D411yescharacteristic
249C22×C32C2×#6711yescharacteristic
250C32×C4—22no—
251C32×C4—24no—
252C32×C4—22no—
253C32×C4—22no—
254C32×C4—21no—
255C32×C4—21no—
256C32×C4—21no—
257C32×C4—21no—
258C32×C4—21no—
259C32×C4—21no—
260C32×C4—41no—
261C32×C4—41no—
262C32×C4—42no—
263C32×C4—42no—
264C32×C4—44no—
265C32×C4C2×Dic611yescharacteristic
266C32×C4C2×Dic611yescharacteristic
267C32×C4C2×Dic611yescharacteristic
268C32×C4#23511yescharacteristic
269C32×C4#23711yescharacteristic
270C32×C4#23711yescharacteristic
271C3⋊Dic3—21no—
272C3⋊Dic3—21no—
273C3⋊Dic3—41no—
274C3⋊Dic3—41no—
275C3⋊Dic3—41no—
276C3×Dic3—62no—
277C3×Dic3—61no—
278C3×Dic3—61no—
279C3×Dic3—61no—
280C3×Dic3—61no—
281C3×Dic3—121no—
282C3×Dic3—122no—
283C3×Dic3—121no—
284C3×Dic3—121no—
285C3×Dic3—121no—
286C3×Dic3—121no—
287C3×Dic3—121no—
288C3×Dic3—121no—
289C3×Dic3—241no—
290C3×Dic3—241no—
291#125—271no—
292C4×Q8—91no—
293#107—271no—
294#106—271no—
295C4⋊C8—271no—
296#103—91no—
297#103—91no—
298C33#47911yescharacteristic, complemented, Sylow
299C3×Q8—22no—
300C3×Q8—21no—
301C3×Q8—21no—
302C3×Q8—21no—
303C3×Q8—22no—
304C3×Q8—22no—
305C3×Q8—22no—
306C3×Q8—41no—
307C3×Q8—41no—
308C3×Q8—42no—
309C3×Q8—42no—
310C3×Q8#62712yes—
311C3×Q8#62712yes—
312C3×Q8#62712yes—
313C2×C3×C4—22no—
314C2×C3×C4—21no—
315C2×C3×C4—21no—
316C2×C3×C4—21no—
317C2×C3×C4—21no—
318C2×C3×C4—21no—
319C2×C3×C4—21no—
320C2×C3×C4—41no—
321C2×C3×C4—41no—
322C2×C3×C4—42no—
323C2×C3×C4—41no—
324C2×C3×C4—91no—
325C2×C3×C4—91no—
326C2×C3×C4—181no—
327C2×C3×C4—181no—
328C2×C3×C4—181no—
329C2×C3×C4C2×D3211yescharacteristic
330C2×C3×C4C2×D3211yescharacteristic
331C2×C3×C4C2×D3211yescharacteristic
332C2×Dic3—31no—
333C2×Dic3—31no—
334C2×Dic3—31no—
335C2×Dic3—31no—
336C2×Dic3—61no—
337C2×Dic3—61no—
338C2×Dic3—62no—
339C2×Dic3—61no—
340C2×Dic3—61no—
341C2×Dic3—61no—
342C2×Dic3—61no—
343C2×Dic3—61no—
344C2×Dic3—61no—
345C2×Dic3—121no—
346C2×Dic3—121no—
347C3×C8—181no—
348C3×C8—181no—
349C3⋊C8—61no—
350C3⋊C8—61no—
351C3⋊C8—61no—
352C3⋊C8—61no—
353C3⋊C8—121no—
354C3⋊C8—121no—
355C2×C32—21no—
356C2×C32—21no—
357C2×C32—21no—
358C2×C32—21no—
359C2×C32—21no—
360C2×C32—21no—
361C2×C32—21no—
362C2×C32—21no—
363C2×C32—21no—
364C2×C32—41no—
365C2×C32—41no—
366C2×C32—41no—
367C2×C32#87811yescharacteristic
368C2×C32#87811yescharacteristic
369C2×C32#91511yescharacteristic
370C2×C32#91611yescharacteristic
371C2×C32#91811yescharacteristic
372C2×C32#91911yescharacteristic
373C2×C32#92411yescharacteristic
374C2×C32#94211yescharacteristic
375C2×C32#95011yescharacteristic
376C2×Q8#111311yescharacteristic
377C2×C8—91no—
378C2×C8—91no—
379C4⋊C4—91no—
380C4⋊C4—91no—
381C4⋊C4—91no—
382C4⋊C4—181no—
383C4⋊C4—541no—
384C4⋊C4—541no—
385C42—91no—
386C42—181no—
387C22×C3—21no—
388C22×C3—21no—
389C22×C3—21no—
390C22×C3—41no—
391C22×C3D3×#6711yescharacteristic
392C22×C3D3×#6711yescharacteristic
393C22×C3#381111yescharacteristic
394C3×C4—24no—
395C3×C4—22no—
396C3×C4—22no—
397C3×C4—22no—
398C3×C4—21no—
399C3×C4—21no—
400C3×C4—21no—
401C3×C4—21no—
402C3×C4—21no—
403C3×C4—21no—
404C3×C4—42no—
405C3×C4—42no—
406C3×C4—44no—
407C3×C4—41no—
408C3×C4—41no—
409C3×C4—181no—
410C3×C4—181no—
411C3×C4—361no—
412C3×C4—361no—
413C3×C4—361no—
414C3×C4#380411yescharacteristic
415C3×C4#380411yescharacteristic
416C3×C4#380511yescharacteristic
417C3×C4C2×#62711yescharacteristic
418C3×C4C2×#62711yescharacteristic
419C3×C4C2×#62711yescharacteristic
420Dic3—62no—
421Dic3—61no—
422Dic3—61no—
423Dic3—61no—
424Dic3—61no—
425Dic3—121no—
426Dic3—122no—
427Dic3—121no—
428Dic3—121no—
429Dic3—121no—
430Dic3—121no—
431Dic3—121no—
432Dic3—121no—
433Dic3—241no—
434Dic3—241no—
435C32—21no—
436C32—21no—
437C32—21no—
438C32—41no—
439C32#479611yescharacteristic, complemented
440C32#479911yescharacteristic, complemented
441C32#502211yescharacteristic, complemented
442Q8—21no—
443Q8#629612yes—
444C2×C4—21no—
445C2×C4—91no—
446C2×C4—91no—
447C2×C4—181no—
448C2×C4—181no—
449C2×C4—181no—
450C2×C4C2×#111311yescharacteristic
451C8—181no—
452C8—181no—
453C2×C3—21no—
454C2×C3—21no—
455C2×C3—21no—
456C2×C3—21no—
457C2×C3—21no—
458C2×C3—21no—
459C2×C3—21no—
460C2×C3—21no—
461C2×C3—21no—
462C2×C3—41no—
463C2×C3—41no—
464C2×C3—41no—
465C2×C3#6394611yescharacteristic
466C2×C3#6394711yescharacteristic
467C2×C3#6394811yescharacteristic
468C2×C3#6394911yescharacteristic
469C2×C3#6395011yescharacteristic
470C2×C3#6395111yescharacteristic
471C2×C3#6396411yescharacteristic
472C2×C3#6396411yescharacteristic
473C2×C3#6398211yescharacteristic
474C22#8904911yescharacteristic
475C4—22no—
476C4—181no—
477C4—181no—
478C4—361no—
479C4—361no—
480C4—361no—
481C4#8904611yescharacteristic
482C4C2×#629611yescharacteristic
483C3—21no—
484C3—21no—
485C3—21no—
486C3—41no—
487C3#1059154511yescharacteristic, complemented
488C3#1059154711yescharacteristic, complemented
489C3#1059161511yescharacteristic, complemented
490C2#1172371211yescharacteristic
491C2#1172371311yescharacteristic
492C2#1172372111yescharacteristic
subgroupG/H
centerC22#89049
commutator, cosocleC2×C33×C4C23
FrattiniC2×C4C2×#1113
FittingC2×C33×Q8C22
socle, prime radicalC22×C33C2×D4
hypercenterC2×Q8#1113
hypocenterC33#479
LCSG ▷ C2×C33×C4 ▷ C2×C33 ▷ C33
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×Q8

Complements

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

NH ≅ G/Ntype
298. C33#479semidirect
439. C32#4796semidirect
440. C32#4799semidirect
441. C32#5022semidirect
487. C3#10591545semidirect
488. C3#10591547semidirect
489. C3#10591615semidirect

Maximal subgroups

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

subgroupindex
C3×Q8×C3⋊Dic32
#117236802
C3×#636622
#117220802
#117220792
#117220782
#105916153
#105915473
#105915453