Finite Group Databasebeta

← C3×#70075 #11794321

Subgroups — C3×#70075 #11794321

Order 1152.

549 conjugacy classes of subgroups.

The subgroup lattice has 450 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C32×#100C211yesmaximal, characteristic
2C3×#5215C211yesmaximal, characteristic
3C2×C3×#832C211yesmaximal, characteristic
4C2×C3×#822C211yesmaximal, characteristic, complemented
5C3×#5121C211yesmaximal, characteristic, complemented
6C3×#5119C211yesmaximal, characteristic, complemented
7C3×#4554C211yesmaximal, characteristic, complemented
8C3×#2063—31nomaximal
9#70075C311yesmaximal, characteristic, direct product factor
10C22×C32×D4C2211yescharacteristic
11C2×C32×M16C2211yescharacteristic
12C2×C32×M16C2211yescharacteristic
13C3×#926C2211yescharacteristic
14C2×C3×C4⋊Dic3C2211yescharacteristic
15C2×C3×#208C2211yescharacteristic
16C22×C3×C3⋊C8C2211yescharacteristic
17C32×#100—22no—
18C3×#832—21no—
19C3×#832—21no—
20C3×#832—22no—
21C3×#822—22no—
22C3×#818—21no—
23C3×#817—21no—
24C3×Dic3⋊C8—22no—
25C2×C3×#108—31no—
26C3×#428—31no—
27C3×#424—31no—
28C3×#418—31no—
29C2×C3×#102—31no—
30C2×C3×#100—21no—
31C2×C3×#100D311yescharacteristic
32C2×C3×#100C2×C311yescharacteristic
33#5215C2×C311yescharacteristic
34C2×#832C2×C311yescharacteristic
35C2×#822C2×C311yescharacteristic, complemented
36#5121C2×C311yescharacteristic, complemented
37#5119C2×C311yescharacteristic, complemented
38C3×#343—31no—
39#4554C2×C311yescharacteristic, complemented
40C24×C32—21no—
41C2×C32×D4—21no—
42C2×C32×D4—21no—
43C2×C32×D4—21no—
44C2×C32×D4—21no—
45C2×C32×D4—21no—
46C2×C32×D4Q812yes—
47C22×C32×C4C2311yescharacteristic
48C22×C3×Dic3—21no—
49C32×M16—21no—
50C32×M16—21no—
51C32×M16—21no—
52C32×M16D412yes—
53C2×C32×C8—21no—
54C2×C32×C8—21no—
55C3×#217—21no—
56C3×C4⋊Dic3—21no—
57C3×C4⋊Dic3—21no—
58C3×C4⋊Dic3D411yescharacteristic
59C3×C4⋊Dic3D411yescharacteristic
60C3×C4×Dic3—21no—
61C3×#208—21no—
62C3×#208—21no—
63C2×C3×C3⋊C8—21no—
64C2×C3×C3⋊C8—21no—
65C2×C3×C3⋊C8—21no—
66C2×C3×C3⋊C8D412yes—
67#2063—31noSylow
68C22×C3×D4—21no—
69C22×C3×D4C2×D311yescharacteristic
70C22×C3×D4C22×C311yescharacteristic
71C2×C3×M16—21no—
72C2×C3×M16—21no—
73C2×C3×M16—31no—
74C2×C3×M16C2×D311yescharacteristic
75C2×C3×M16C2×D311yescharacteristic
76C2×C3×M16C22×C311yescharacteristic
77C2×C3×M16C22×C311yescharacteristic
78C22×C3×C8—31no—
79C3×#117—31no—
80C2×C3×C4⋊C4—31no—
81#926C22×C311yescharacteristic
82C2×C4⋊Dic3C22×C311yescharacteristic
83C2×#208C22×C311yescharacteristic
84C22×C3⋊C8C22×C311yescharacteristic
85C3×#108—62no—
86C3×#107—61no—
87C3×#106—61no—
88C3×C4⋊C8—62no—
89C3×#102—61no—
90C3×#102—61no—
91C3×#102—62no—
92C3×#100—24no—
93C3×#100—22no—
94C3×#100—22no—
95#832—21no—
96#832—21no—
97#832—22no—
98#822—22no—
99#818—21no—
100#817—21no—
101Dic3⋊C8—22no—
102C23×C32—22no—
103C23×C32—41no—
104C23×C32—41no—
105C23×C32—81no—
106C23×C32—81no—
107C23×C32#4111yescharacteristic
108C32×D4—22no—
109C32×D4—22no—
110C32×D4—41no—
111C32×D4—41no—
112C2×C32×C4C2×D411yescharacteristic
113C2×C32×C4C2×D411yescharacteristic
114C2×C32×C4C2×D411yescharacteristic
115C2×C32×C4C2×Q811yescharacteristic
116C2×C32×C4#4111yescharacteristic
117C2×C32×C4#4111yescharacteristic
118C2×C3×Dic3—21no—
119C2×C3×Dic3—21no—
120C2×C3×Dic3—41no—
121C2×C3×Dic3—81no—
122C32×C8—22no—
123C32×C8—41no—
124C3×C3⋊C8—22no—
125C3×C3⋊C8—41no—
126C2×#108—31no—
127#428—31no—
128#424—31no—
129#418—31no—
130C2×#102—31no—
131C2×#100C3×D311yescharacteristic
132#343—31no—
133C24×C3—22no—
134C24×C3—21no—
135C24×C3—21no—
136C2×C3×D4—22no—
137C2×C3×D4—21no—
138C2×C3×D4—21no—
139C2×C3×D4—21no—
140C2×C3×D4—21no—
141C2×C3×D4—21no—
142C2×C3×D4—21no—
143C2×C3×D4—21no—
144C2×C3×D4—21no—
145C2×C3×D4—21no—
146C2×C3×D4—21no—
147C2×C3×D4—22no—
148C2×C3×D4—41no—
149C2×C3×D4—41no—
150C2×C3×D4—41no—
151C2×C3×D4—41no—
152C2×C3×D4Dic612yes—
153C2×C3×D4C3×Q812yes—
154C22×C3×C4—21no—
155C22×C3×C4—61no—
156C22×C3×C4C22×D311yescharacteristic
157C22×C3×C4C23×C311yescharacteristic
158C22×Dic3—21no—
159C3×M16—21no—
160C3×M16—21no—
161C3×M16—22no—
162C3×M16—21no—
163C3×M16—21no—
164C3×M16—21no—
165C3×M16—21no—
166C3×M16—22no—
167C3×M16—41no—
168C3×M16—41no—
169C3×M16—61no—
170C3×M16—61no—
171C3×M16#6712yes—
172C3×M16C3×D412yes—
173C2×C3×C8—21no—
174C2×C3×C8—21no—
175C2×C3×C8—21no—
176C2×C3×C8—21no—
177C2×C3×C8—32no—
178C2×C3×C8—41no—
179C2×C3×C8—41no—
180C2×C3×C8—61no—
181C2×C3×C8—61no—
182C2×C3×C8—61no—
183C3×C4⋊C4—31no—
184C3×C4⋊C4—31no—
185C3×C4⋊C4—61no—
186C3×C4⋊C4—61no—
187C3×C22⋊C4—61no—
188C3×C42—61no—
189#217—21no—
190C4⋊Dic3—21no—
191C4⋊Dic3—21no—
192C4⋊Dic3C3×D411yescharacteristic
193C4⋊Dic3C3×D411yescharacteristic
194C4×Dic3—21no—
195#208—21no—
196#208—21no—
197C2×C3⋊C8—21no—
198C2×C3⋊C8—21no—
199C2×C3⋊C8—21no—
200C2×C3⋊C8C3×D412yes—
201C22×C32—21no—
202C22×C32—21no—
203C22×C32—42no—
204C22×C32—82no—
205C22×C32—82no—
206C22×C32—81no—
207C22×C32—81no—
208C22×C32#12111yescharacteristic
209C22×C32C22⋊Q811yescharacteristic
210C22×C32#12611yescharacteristic
211C32×C4#12111yescharacteristic
212C32×C4#12111yescharacteristic
213C32×C4C22⋊Q811yescharacteristic
214C32×C4C22⋊Q811yescharacteristic
215C3×Dic3—41no—
216C3×Dic3—41no—
217C3×Dic3—81no—
218C22×D4C2×C3×D311yescharacteristic
219C2×M16—31no—
220C2×M16C2×C3×D311yescharacteristic
221C2×M16C2×C3×D311yescharacteristic
222C22×C8—31no—
223#117—31no—
224C2×C4⋊C4—31no—
225#108—62no—
226#107—61no—
227#106—61no—
228C4⋊C8—62no—
229#102—61no—
230#102—61no—
231#102—62no—
232#100—22no—
233C23×C3—24no—
234C23×C3—22no—
235C23×C3—22no—
236C23×C3—21no—
237C23×C3—42no—
238C23×C3—42no—
239C23×C3—41no—
240C23×C3—41no—
241C23×C3—41no—
242C23×C3—41no—
243C23×C3—81no—
244C23×C3—81no—
245C23×C3—81no—
246C23×C3—81no—
247C23×C3—82no—
248C23×C3—82no—
249C23×C3#23511yescharacteristic
250C23×C3C3×#4111yescharacteristic
251C3×D4—22no—
252C3×D4—22no—
253C3×D4—22no—
254C3×D4—22no—
255C3×D4—42no—
256C3×D4—42no—
257C3×D4—42no—
258C3×D4—42no—
259C3×D4—41no—
260C3×D4—41no—
261C3×D4—41no—
262C3×D4—41no—
263C2×C3×C4—21no—
264C2×C3×C4—21no—
265C2×C3×C4—21no—
266C2×C3×C4—21no—
267C2×C3×C4—21no—
268C2×C3×C4—21no—
269C2×C3×C4—61no—
270C2×C3×C4—61no—
271C2×C3×C4—121no—
272C2×C3×C4—241no—
273C2×C3×C4C2×Dic611yescharacteristic
274C2×C3×C4D3×D411yescharacteristic
275C2×C3×C4D3×D411yescharacteristic
276C2×C3×C4#23711yescharacteristic
277C2×C3×C4#23711yescharacteristic
278C2×C3×C4C2×#6711yescharacteristic
279C2×C3×C4C2×C3×D411yescharacteristic
280C2×C3×C4C2×C3×D411yescharacteristic
281C2×C3×C4C2×C3×D411yescharacteristic
282C2×C3×C4C2×C3×Q811yescharacteristic
283C2×C3×C4C3×#4111yescharacteristic
284C2×C3×C4C3×#4111yescharacteristic
285C2×Dic3—21no—
286C2×Dic3—21no—
287C2×Dic3—41no—
288C2×Dic3—81no—
289C3×C8—22no—
290C3×C8—22no—
291C3×C8—42no—
292C3×C8—42no—
293C3×C8—41no—
294C3×C8—41no—
295C3×C8—62no—
296C3×C8—121no—
297C3⋊C8—22no—
298C3⋊C8—41no—
299C2×C32—21no—
300C2×C32—21no—
301C2×C32—82no—
302C2×C32#39611yescharacteristic
303C2×C32#47111yescharacteristic
304C2×C32#47211yescharacteristic
305C24—21no—
306C2×D4—21no—
307C2×D4—21no—
308C2×D4—21no—
309C2×D4—21no—
310C2×D4—21no—
311C2×D4C3×Dic612yes—
312C22×C4—61no—
313C22×C4C22×C3×D311yescharacteristic
314M16—21no—
315M16—21no—
316M16—21no—
317M16—61no—
318M16—61no—
319M16C3×#6712yes—
320C2×C8—21no—
321C2×C8—21no—
322C2×C8—32no—
323C2×C8—61no—
324C2×C8—61no—
325C2×C8—61no—
326C4⋊C4—31no—
327C4⋊C4—31no—
328C4⋊C4—61no—
329C4⋊C4—61no—
330C22⋊C4—61no—
331C42—61no—
332C22×C3—21no—
333C22×C3—21no—
334C22×C3—21no—
335C22×C3—21no—
336C22×C3—21no—
337C22×C3—21no—
338C22×C3—21no—
339C22×C3—41no—
340C22×C3—41no—
341C22×C3—44no—
342C22×C3—42no—
343C22×C3—42no—
344C22×C3—82no—
345C22×C3—82no—
346C22×C3—82no—
347C22×C3—82no—
348C22×C3—82no—
349C22×C3—82no—
350C22×C3—84no—
351C22×C3—84no—
352C22×C3—81no—
353C22×C3—81no—
354C22×C3—81no—
355C22×C3—81no—
356C22×C3#87911yescharacteristic
357C22×C3#88411yescharacteristic
358C22×C3#92411yescharacteristic
359C22×C3C3×#12111yescharacteristic
360C22×C3C3×C22⋊Q811yescharacteristic
361C22×C3C3×#12611yescharacteristic
362C3×C4—21no—
363C3×C4—21no—
364C3×C4—21no—
365C3×C4—21no—
366C3×C4—121no—
367C3×C4—121no—
368C3×C4—241no—
369C3×C4#87811yescharacteristic
370C3×C4#87811yescharacteristic
371C3×C4#93811yescharacteristic
372C3×C4#93911yescharacteristic
373C3×C4C3×#12111yescharacteristic
374C3×C4C3×#12111yescharacteristic
375C3×C4C3×C22⋊Q811yescharacteristic
376C3×C4C3×C22⋊Q811yescharacteristic
377Dic3—41no—
378Dic3—41no—
379Dic3—81no—
380C32#206311yescharacteristic, complemented, Sylow
381C23—22no—
382C23—41no—
383C23—41no—
384C23—81no—
385C23—81no—
386C23C3×#23511yescharacteristic
387D4—22no—
388D4—22no—
389D4—41no—
390D4—41no—
391C2×C4—61no—
392C2×C4—61no—
393C2×C4—121no—
394C2×C4—241no—
395C2×C4C2×C3×Dic611yescharacteristic
396C2×C4C3×D3×D411yescharacteristic
397C2×C4C3×D3×D411yescharacteristic
398C2×C4C3×#23711yescharacteristic
399C2×C4C3×#23711yescharacteristic
400C2×C4C2×C3×#6711yescharacteristic
401C8—22no—
402C8—41no—
403C8—62no—
404C8—121no—
405C2×C3—21no—
406C2×C3—21no—
407C2×C3—21no—
408C2×C3—21no—
409C2×C3—21no—
410C2×C3—21no—
411C2×C3—21no—
412C2×C3—41no—
413C2×C3—41no—
414C2×C3—84no—
415C2×C3—82no—
416C2×C3—82no—
417C2×C3#474811yescharacteristic
418C2×C3#474911yescharacteristic
419C2×C3#494811yescharacteristic
420C2×C3C3×#39611yescharacteristic
421C2×C3C3×#47111yescharacteristic
422C2×C3C3×#47211yescharacteristic
423C22—21no—
424C22—21no—
425C22—42no—
426C22—82no—
427C22—82no—
428C22—81no—
429C22—81no—
430C22C3×#87911yescharacteristic
431C22C3×#88411yescharacteristic
432C22C3×#92411yescharacteristic
433C4—121no—
434C4—121no—
435C4—241no—
436C4C3×#87811yescharacteristic
437C4C3×#87811yescharacteristic
438C4C3×#93811yescharacteristic
439C4C3×#93911yescharacteristic
440C3—21no—
441C3#7007511yescharacteristic, direct product factor
442C3C3×#206311yescharacteristic, complemented
443C2—21no—
444C2—21no—
445C2—82no—
446C2C3×#474811yescharacteristic
447C2C3×#474911yescharacteristic
448C2C3×#494811yescharacteristic
subgroupG/H
centerC22×C3#884
commutator, cosocleC22×C3×C4C23×C3
FrattiniC22×C4C22×C3×D3
FittingC2×C32×#100C2
socleC22×C32#121
prime radicalC22×C32×D4C22
hypercenterC2×C3×#100D3
hypocenterC3C3×#2063
LCSG ▷ C22×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C22×C3×C4 ◁ C2×C3×#100

Complements

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

NH ≅ G/Ntype
4. C2×C3×#822C2semidirect
5. C3×#5121C2semidirect
6. C3×#5119C2semidirect
7. C3×#4554C2semidirect
9. #70075C3direct (N × H)
35. C2×#822C2×C3semidirect
36. #5121C2×C3semidirect
37. #5119C2×C3semidirect
39. #4554C2×C3semidirect
380. C32#2063semidirect
441. C3#70075direct (N × H)
442. C3C3×#2063semidirect

Maximal subgroups

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

subgroupindex
C2×C32×#1002
C3×#52152
C2×C3×#8322
C2×C3×#8222
C3×#51212
C3×#51192
C3×#45542
C3×#20633
#700753