Finite Group Databasebeta

← C3×#70197 #11794327

Subgroups — C3×#70197 #11794327

Order 1152.

557 conjugacy classes of subgroups.

The subgroup lattice has 452 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C32×#102C211yesmaximal, characteristic
2C2×C3×#833C211yesmaximal, characteristic
3C3×#5215C211yesmaximal, characteristic
4C2×C3×#819C211yesmaximal, characteristic, complemented
5C3×#5102C211yesmaximal, characteristic, complemented
6C3×#4964C211yesmaximal, characteristic, complemented
7C3×#4530C211yesmaximal, characteristic, complemented
8C3×#2063—31nomaximal
9#70197C311yesmaximal, characteristic, direct product factor
10C22×C32×D4C2211yescharacteristic
11C22×C32×C8C2211yescharacteristic
12C2×C32×C4⋊C4C2211yescharacteristic
13C3×#926C2211yescharacteristic
14C2×C3×#208C2211yescharacteristic
15C2×C3×#208C2211yescharacteristic
16C2×C3×#208C2211yescharacteristic
17C32×#102—22no—
18C3×#833—22no—
19C3×#832—21no—
20C3×#832—21no—
21C3×#819—22no—
22C3×Dic3⋊C8—22no—
23C3×#808—21no—
24C3×#807—21no—
25C2×C3×#108—31no—
26C3×#428—31no—
27C3×#424—31no—
28C3×#418—31no—
29C2×C3×#102—21no—
30C2×C3×#102D311yescharacteristic
31C2×C3×#102C2×C311yescharacteristic
32C2×C3×#100—31no—
33C2×#833C2×C311yescharacteristic
34#5215C2×C311yescharacteristic
35C2×#819C2×C311yescharacteristic, complemented
36#5102C2×C311yescharacteristic, complemented
37#4964C2×C311yescharacteristic, complemented
38C3×#343—31no—
39#4530C2×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×C4—21no—
48C22×C32×C4C2311yescharacteristic
49C2×C32×C8—21no—
50C2×C32×C8—21no—
51C2×C32×C8D412yes—
52C32×C4⋊C4—21no—
53C32×C4⋊C4—21no—
54C3×#217—21no—
55C3×C4⋊Dic3D411yescharacteristic
56C3×C4⋊Dic3D411yescharacteristic
57C3×C4×Dic3—21no—
58C3×#208—21no—
59C3×#208—21no—
60C3×#208—21no—
61C3×#208—21no—
62C3×#208—21no—
63C3×#208D412yes—
64C2×C3×C3⋊C8—21no—
65C2×C3×C3⋊C8—21no—
66C2×C3×C3⋊C8—21no—
67#2063—31noSylow
68C22×C3×D4—21no—
69C22×C3×D4C2×D311yescharacteristic
70C22×C3×D4C22×C311yescharacteristic
71C2×C3×M16—31no—
72C2×C3×M16—31no—
73C2×C3×M16—31no—
74C22×C3×C8—21no—
75C22×C3×C8C2×D311yescharacteristic
76C22×C3×C8C22×C311yescharacteristic
77C3×#117—31no—
78C2×C3×C4⋊C4—21no—
79C2×C3×C4⋊C4C2×D311yescharacteristic
80C2×C3×C4⋊C4C22×C311yescharacteristic
81#926C22×C311yescharacteristic
82C2×#208C22×C311yescharacteristic
83C2×#208C22×C311yescharacteristic
84C2×#208C22×C311yescharacteristic
85C3×#108—62no—
86C3×#107—61no—
87C3×#106—61no—
88C3×C4⋊C8—62no—
89C3×#102—24no—
90C3×#102—22no—
91C3×#102—22no—
92C3×#102—61no—
93C3×#102—61no—
94C3×#100—62no—
95#833—22no—
96#832—21no—
97#832—21no—
98#819—22no—
99Dic3⋊C8—22no—
100#808—21no—
101#807—21no—
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×C4—41no—
113C2×C32×C4—81no—
114C2×C32×C4C2×D411yescharacteristic
115C2×C32×C4C2×D411yescharacteristic
116C2×C32×C4C2×D411yescharacteristic
117C2×C32×C4C2×Q811yescharacteristic
118C2×C32×C4#4111yescharacteristic
119C2×C32×C4#4111yescharacteristic
120C2×C3×Dic3—21no—
121C2×C3×Dic3—21no—
122C32×C8—22no—
123C3×C3⋊C8—22no—
124C3×C3⋊C8—41no—
125C3×C3⋊C8—41no—
126C2×#108—31no—
127#428—31no—
128#424—31no—
129#418—31no—
130C2×#102C3×D311yescharacteristic
131C2×#100—31no—
132#343—31no—
133C24×C3—21no—
134C24×C3—21no—
135C24×C3—41no—
136C2×C3×D4—22no—
137C2×C3×D4—22no—
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—21no—
148C2×C3×D4—22no—
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—21no—
156C22×C3×C4—21no—
157C22×C3×C4—41no—
158C22×C3×C4C22×D311yescharacteristic
159C22×C3×C4C23×C311yescharacteristic
160C3×M16—32no—
161C3×M16—61no—
162C3×M16—61no—
163C3×M16—61no—
164C3×M16—61no—
165C3×M16—61no—
166C2×C3×C8—21no—
167C2×C3×C8—21no—
168C2×C3×C8—21no—
169C2×C3×C8—21no—
170C2×C3×C8—22no—
171C2×C3×C8—41no—
172C2×C3×C8—41no—
173C2×C3×C8—61no—
174C2×C3×C8—61no—
175C2×C3×C8—61no—
176C2×C3×C8#6712yes—
177C2×C3×C8C3×D412yes—
178C3×C4⋊C4—22no—
179C3×C4⋊C4—21no—
180C3×C4⋊C4—21no—
181C3×C4⋊C4—21no—
182C3×C4⋊C4—21no—
183C3×C4⋊C4—31no—
184C3×C4⋊C4—31no—
185C3×C4⋊C4—41no—
186C3×C22⋊C4—61no—
187C3×C42—61no—
188#217—21no—
189C4⋊Dic3C3×D411yescharacteristic
190C4⋊Dic3C3×D411yescharacteristic
191C4×Dic3—21no—
192#208—21no—
193#208—21no—
194#208—21no—
195#208—21no—
196#208—21no—
197#208C3×D412yes—
198C2×C3⋊C8—21no—
199C2×C3⋊C8—21no—
200C2×C3⋊C8—21no—
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—81no—
212C32×C4#12111yescharacteristic
213C32×C4#12111yescharacteristic
214C32×C4C22⋊Q811yescharacteristic
215C32×C4C22⋊Q811yescharacteristic
216C3×Dic3—41no—
217C3×Dic3—41no—
218C22×D4C2×C3×D311yescharacteristic
219C2×M16—31no—
220C2×M16—31no—
221C2×M16—31no—
222C22×C8C2×C3×D311yescharacteristic
223#117—31no—
224C2×C4⋊C4C2×C3×D311yescharacteristic
225#108—62no—
226#107—61no—
227#106—61no—
228C4⋊C8—62no—
229#102—22no—
230#102—61no—
231#102—61no—
232#100—62no—
233C23×C3—22no—
234C23×C3—22no—
235C23×C3—21no—
236C23×C3—42no—
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#23711yescharacteristic
250C23×C3C3×#4111yescharacteristic
251C3×D4—24no—
252C3×D4—22no—
253C3×D4—22no—
254C3×D4—22no—
255C3×D4—22no—
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—42no—
270C2×C3×C4—41no—
271C2×C3×C4—41no—
272C2×C3×C4—61no—
273C2×C3×C4—61no—
274C2×C3×C4—82no—
275C2×C3×C4—81no—
276C2×C3×C4—81no—
277C2×C3×C4C2×Dic611yescharacteristic
278C2×C3×C4#23511yescharacteristic
279C2×C3×C4D3×D411yescharacteristic
280C2×C3×C4D3×D411yescharacteristic
281C2×C3×C4#23711yescharacteristic
282C2×C3×C4C2×#6711yescharacteristic
283C2×C3×C4C2×C3×D411yescharacteristic
284C2×C3×C4C2×C3×D411yescharacteristic
285C2×C3×C4C2×C3×D411yescharacteristic
286C2×C3×C4C2×C3×Q811yescharacteristic
287C2×C3×C4C3×#4111yescharacteristic
288C2×C3×C4C3×#4111yescharacteristic
289C2×Dic3—21no—
290C2×Dic3—21no—
291C3×C8—22no—
292C3×C8—22no—
293C3×C8—42no—
294C3×C8—62no—
295C3×C8—121no—
296C3×C8—121no—
297C3⋊C8—22no—
298C3⋊C8—41no—
299C3⋊C8—41no—
300C2×C32—21no—
301C2×C32—21no—
302C2×C32—82no—
303C2×C32#39611yescharacteristic
304C2×C32#47111yescharacteristic
305C2×C32#47211yescharacteristic
306C24—21no—
307C2×D4—21no—
308C2×D4—21no—
309C2×D4—21no—
310C2×D4—21no—
311C2×D4—21no—
312C2×D4C3×Dic612yes—
313C22×C4—21no—
314C22×C4C22×C3×D311yescharacteristic
315M16—32no—
316M16—61no—
317M16—61no—
318M16—61no—
319M16—61no—
320M16—61no—
321C2×C8—21no—
322C2×C8—21no—
323C2×C8—61no—
324C2×C8—61no—
325C2×C8—61no—
326C2×C8C3×#6712yes—
327C4⋊C4—21no—
328C4⋊C4—21no—
329C4⋊C4—31no—
330C4⋊C4—31no—
331C22⋊C4—61no—
332C42—61no—
333C22×C3—22no—
334C22×C3—22no—
335C22×C3—21no—
336C22×C3—21no—
337C22×C3—21no—
338C22×C3—21no—
339C22×C3—21no—
340C22×C3—21no—
341C22×C3—21no—
342C22×C3—44no—
343C22×C3—42no—
344C22×C3—42no—
345C22×C3—82no—
346C22×C3—82no—
347C22×C3—84no—
348C22×C3—84no—
349C22×C3—82no—
350C22×C3—82no—
351C22×C3—82no—
352C22×C3—82no—
353C22×C3—81no—
354C22×C3—81no—
355C22×C3—81no—
356C22×C3—81no—
357C22×C3#87811yescharacteristic
358C22×C3#87911yescharacteristic
359C22×C3#93811yescharacteristic
360C22×C3C3×#12111yescharacteristic
361C22×C3C3×C22⋊Q811yescharacteristic
362C22×C3C3×#12611yescharacteristic
363C3×C4—21no—
364C3×C4—21no—
365C3×C4—21no—
366C3×C4—21no—
367C3×C4—82no—
368C3×C4—81no—
369C3×C4—81no—
370C3×C4—121no—
371C3×C4—121no—
372C3×C4#87811yescharacteristic
373C3×C4#88411yescharacteristic
374C3×C4#92411yescharacteristic
375C3×C4#93911yescharacteristic
376C3×C4C3×#12111yescharacteristic
377C3×C4C3×#12111yescharacteristic
378C3×C4C3×C22⋊Q811yescharacteristic
379C3×C4C3×C22⋊Q811yescharacteristic
380Dic3—41no—
381Dic3—41no—
382C32#206311yescharacteristic, complemented, Sylow
383C23—22no—
384C23—41no—
385C23—41no—
386C23—81no—
387C23—81no—
388C23C3×#23711yescharacteristic
389D4—22no—
390D4—22no—
391D4—41no—
392D4—41no—
393C2×C4—41no—
394C2×C4—61no—
395C2×C4—61no—
396C2×C4—81no—
397C2×C4C2×C3×Dic611yescharacteristic
398C2×C4C3×#23511yescharacteristic
399C2×C4C3×D3×D411yescharacteristic
400C2×C4C3×D3×D411yescharacteristic
401C2×C4C3×#23711yescharacteristic
402C2×C4C2×C3×#6711yescharacteristic
403C8—22no—
404C8—62no—
405C8—121no—
406C8—121no—
407C2×C3—22no—
408C2×C3—22no—
409C2×C3—21no—
410C2×C3—21no—
411C2×C3—21no—
412C2×C3—21no—
413C2×C3—21no—
414C2×C3—21no—
415C2×C3—21no—
416C2×C3—84no—
417C2×C3—82no—
418C2×C3—82no—
419C2×C3#494811yescharacteristic
420C2×C3#516011yescharacteristic
421C2×C3#517711yescharacteristic
422C2×C3C3×#39611yescharacteristic
423C2×C3C3×#47111yescharacteristic
424C2×C3C3×#47211yescharacteristic
425C22—21no—
426C22—21no—
427C22—42no—
428C22—82no—
429C22—82no—
430C22—81no—
431C22—81no—
432C22C3×#87811yescharacteristic
433C22C3×#87911yescharacteristic
434C22C3×#93811yescharacteristic
435C4—81no—
436C4—121no—
437C4—121no—
438C4C3×#87811yescharacteristic
439C4C3×#88411yescharacteristic
440C4C3×#92411yescharacteristic
441C4C3×#93911yescharacteristic
442C3—21no—
443C3#7019711yescharacteristic, direct product factor
444C3C3×#206311yescharacteristic, complemented
445C2—21no—
446C2—21no—
447C2—82no—
448C2C3×#494811yescharacteristic
449C2C3×#516011yescharacteristic
450C2C3×#517711yescharacteristic
subgroupG/H
centerC22×C3#938
commutator, cosocleC22×C3×C4C23×C3
FrattiniC22×C4C22×C3×D3
FittingC2×C32×#102C2
socleC22×C32#121
prime radicalC22×C32×D4C22
hypercenterC2×C3×#102D3
hypocenterC3C3×#2063
LCSG ▷ C22×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C22×C3×C4 ◁ C2×C3×#102

Complements

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

NH ≅ G/Ntype
4. C2×C3×#819C2semidirect
5. C3×#5102C2semidirect
6. C3×#4964C2semidirect
7. C3×#4530C2semidirect
9. #70197C3direct (N × H)
35. C2×#819C2×C3semidirect
36. #5102C2×C3semidirect
37. #4964C2×C3semidirect
39. #4530C2×C3semidirect
382. C32#2063semidirect
443. C3#70197direct (N × H)
444. C3C3×#2063semidirect

Maximal subgroups

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

subgroupindex
C2×C32×#1022
C2×C3×#8332
C3×#52152
C2×C3×#8192
C3×#51022
C3×#49642
C3×#45302
C3×#20633
#701973