Finite Group Databasebeta

← C3×#68352 #11780570

Subgroups — C3×#68352 #11780570

Order 1152.

491 conjugacy classes of subgroups; only the 90 normal subgroups are shown.

normal subgroups only

This group has 491 conjugacy classes of subgroups — too many to draw. Only its 90 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5683C211yesmaximal, characteristic
2C3×#5055C211yesmaximal, characteristic, complemented
3C3×#4715C211yesmaximal, characteristic, complemented
4C3×#4714C211yesmaximal, characteristic, complemented
5C32×#329C211yesmaximal, characteristic, complemented
6C3×#4464C211yesmaximal, characteristic, complemented
7C3×#4464C211yesmaximal, characteristic, complemented
8C3×#1659—31nomaximal
9#68352C311yesmaximal, characteristic, direct product factor
10C32×#124C2211yescharacteristic
11C3×#947—21no—
12C3×#937—21no—
13C2×C3×Dic12—21no—
14C2×C3×#204—21no—
15C3×#885—21no—
16C3×#885—21no—
17C3×#882—21no—
18C3×#882—21no—
19C3×#875C2211yescharacteristic
20C3×#875C2211yescharacteristic
21C3×#869C2211yescharacteristic, complemented
22C32×#97C2211yescharacteristic, complemented
23C32×#97C2211yescharacteristic, complemented
24C3×#835—21no—
25C3×#832—21no—
26C3×#821—21no—
27C3×#816—21no—
28C3×#803C2211yescharacteristic, complemented
29C3×H(3,𝔽4)—31no—
30#5683C2×C311yescharacteristic
31C3×#497—31no—
32C3×#489—31no—
33C3×#489—31no—
34#5055C2×C311yescharacteristic, complemented
35#4715C2×C311yescharacteristic, complemented
36#4714C2×C311yescharacteristic, complemented
37C3×#329—21no—
38C3×#329—31no—
39C3×#329—31no—
40C3×#329D311yescharacteristic, complemented
41C3×#329C2×C311yescharacteristic, complemented
42#4464C2×C311yescharacteristic, complemented
43#4464C2×C311yescharacteristic, complemented
44C23×C3×D3—21no—
45C2×C32×Q8D411yescharacteristic
46C2×C32×D4D411yescharacteristic
47C2×C3×#67—21no—
48C2×C3×#67—21no—
49C2×C3×D12—21no—
50C2×C3×D12D411yescharacteristic
51C2×C3×D12D411yescharacteristic
52C2×C3×Dic6—21no—
53C2×C3×Dic6D411yescharacteristic
54C2×C3×Dic6D411yescharacteristic
55C2×C32×C8—21no—
56C2×C32×C8—21no—
57C32×C22⋊C4—21no—
58C32×C22⋊C4—21no—
59C32×C42C2311yescharacteristic
60C3×#217—21no—
61C3×(C2×D3)⋊C4—21no—
62C3×(C2×D3)⋊C4—21no—
63C3×(C2×D3)⋊C4—21no—
64C3×(C2×D3)⋊C4—21no—
65C3×(C2×D3)⋊C4—21no—
66C3×(C2×D3)⋊C4—21no—
67C3×C4⋊Dic3—21no—
68C3×C4⋊Dic3—21no—
69C3×C4×Dic3—21no—
70C2×C3×C3⋊C8—21no—
71C3×Dic12—42no—
72C3×#204—42no—
73#1659—31noSylow
74C2×C3×Q16—61no—
75C2×C3×SD16—61no—
76C3×C4⋊Q8—31no—
77C3×#124—21no—
78C3×#124—31no—
79C3×#124—31no—
80C3×#124—61no—
81C3×#124—61no—
82C3×#124—61no—
83C3×#124C2×D311yescharacteristic
84C3×#124C22×C311yescharacteristic
85C3×#120—61no—
86C3×#120—61no—
87C3×#120—61no—
88#947—21no—
89#937—21no—
90C2×Dic12—21no—
91C2×#204—21no—
92#885—21no—
93#885—21no—
94#882—21no—
95#882—21no—
96#875C22×C311yescharacteristic
97#875C22×C311yescharacteristic
98#869C22×C311yescharacteristic, complemented
99C3×#103—61no—
100C3×#103—61no—
101C3×#102—61no—
102C3×#102—61no—
103C3×#97—21no—
104C3×#97—21no—
105C3×#97—31no—
106C3×#97C2×D311yescharacteristic, complemented
107C3×#97C2×D311yescharacteristic, complemented
108C3×#97C22×C311yescharacteristic, complemented
109C3×#97C22×C311yescharacteristic, complemented
110#835—21no—
111#832—21no—
112#821—21no—
113#816—21no—
114#803C22×C311yescharacteristic, complemented
115C23×C32—21no—
116C22×C3×D3—21no—
117C22×C3×D3—21no—
118C22×C3×D3—81no—
119C22×C3×D3—81no—
120C22×C3×D3—81no—
121C32×Q8—41no—
122C32×D4—41no—
123C2×C32×C4—21no—
124C2×C32×C4C2×D411yescharacteristic
125C2×C32×C4C2×D411yescharacteristic
126C2×C32×C4C2×D411yescharacteristic
127C3×#67—81no—
128C3×#67—81no—
129C2×C3×Dic3—21no—
130C2×C3×Dic3—21no—
131C2×C3×Dic3—41no—
132C3×D12—41no—
133C3×D12—41no—
134C3×D12—81no—
135C3×Dic6—41no—
136C3×Dic6—41no—
137C3×Dic6—41no—
138C3×Dic6—41no—
139C32×C8—22no—
140C32×C8—41no—
141C3×C3⋊C8—41no—
142H(3,𝔽4)—31no—
143#497—31no—
144#489—31no—
145#489—31no—
146#329—31no—
147#329—31no—
148#329C3×D311yescharacteristic, complemented
149C24×C3—61no—
150C23×D3—21no—
151C2×C3×Q8—21no—
152C2×C3×Q8—31no—
153C2×C3×Q8—31no—
154C2×C3×Q8—61no—
155C2×C3×Q8D1211yescharacteristic
156C2×C3×Q8C3×D411yescharacteristic
157C2×C3×D4—21no—
158C2×C3×D4—31no—
159C2×C3×D4—31no—
160C2×C3×D4—61no—
161C2×C3×D4—61no—
162C2×C3×D4—61no—
163C2×C3×D4D1211yescharacteristic
164C2×C3×D4C3×D411yescharacteristic
165C2×#67—21no—
166C2×#67—21no—
167C2×D12—21no—
168C2×D12C3×D411yescharacteristic
169C2×D12C3×D411yescharacteristic
170C2×Dic6—21no—
171C2×Dic6C3×D411yescharacteristic
172C2×Dic6C3×D411yescharacteristic
173C3×Q16—122no—
174C3×SD16—122no—
175C2×C3×C8—21no—
176C2×C3×C8—21no—
177C2×C3×C8—21no—
178C2×C3×C8—21no—
179C2×C3×C8—41no—
180C2×C3×C8—41no—
181C2×C3×C8—61no—
182C3×C4⋊C4—61no—
183C3×C4⋊C4—61no—
184C3×C22⋊C4—21no—
185C3×C22⋊C4—21no—
186C3×C22⋊C4—21no—
187C3×C22⋊C4—21no—
188C3×C22⋊C4—41no—
189C3×C22⋊C4—41no—
190C3×C22⋊C4—61no—
191C3×C22⋊C4—61no—
192C3×C22⋊C4—61no—
193C3×C22⋊C4—61no—
194C3×C22⋊C4—61no—
195C3×C22⋊C4—61no—
196C3×C22⋊C4—61no—
197C3×C42—21no—
198C3×C42—61no—
199C3×C42C22×D311yescharacteristic
200C3×C42C23×C311yescharacteristic
201#217—21no—
202(C2×D3)⋊C4—21no—
203(C2×D3)⋊C4—21no—
204(C2×D3)⋊C4—21no—
205(C2×D3)⋊C4—21no—
206(C2×D3)⋊C4—21no—
207(C2×D3)⋊C4—21no—
208C4⋊Dic3—21no—
209C4⋊Dic3—21no—
210C4×Dic3—21no—
211C2×C3⋊C8—21no—
212Dic12—42no—
213#204—42no—
214C22×C32—41no—
215C22×C32—41no—
216C22×C32—41no—
217C22×C32#12011yescharacteristic
218C2×C3×D3—41no—
219C2×C3×D3—41no—
220C2×C3×D3—41no—
221C2×C3×D3—41no—
222C2×C3×D3—41no—
223C2×C3×D3—41no—
224C2×C3×D3—84no—
225C32×C4—21no—
226C32×C4—21no—
227C32×C4—21no—
228C32×C4—41no—
229C3×Dic3—41no—
230C3×Dic3—41no—
231C3×Dic3—81no—
232C2×Q16—61no—
233C2×SD16—61no—
234C4⋊Q8—31no—
235#124—31no—
236#124—31no—
237#124—61no—
238#124—61no—
239#124—61no—
240#124C2×C3×D311yescharacteristic
241#120—61no—
242#120—61no—
243#120—61no—
244#103—61no—
245#103—61no—
246#102—61no—
247#102—61no—
248#97—31no—
249#97C2×C3×D311yescharacteristic, complemented
250#97C2×C3×D311yescharacteristic, complemented
251C23×C3—21no—
252C23×C3—21no—
253C23×C3—41no—
254C23×C3—61no—
255C23×C3—61no—
256C23×C3—241no—
257C23×C3—241no—
258C23×C3—241no—
259C22×D3—21no—
260C22×D3—21no—
261C22×D3—81no—
262C22×D3—81no—
263C22×D3—81no—
264C3×Q8—41no—
265C3×Q8—41no—
266C3×Q8—81no—
267C3×Q8—121no—
268C3×Q8—121no—
269C3×Q8—121no—
270C3×Q8—121no—
271C3×D4—41no—
272C3×D4—41no—
273C3×D4—81no—
274C3×D4—121no—
275C3×D4—121no—
276C3×D4—241no—
277C3×D4—241no—
278C3×D4—241no—
279C2×C3×C4—21no—
280C2×C3×C4—21no—
281C2×C3×C4—21no—
282C2×C3×C4—21no—
283C2×C3×C4—21no—
284C2×C3×C4—41no—
285C2×C3×C4—61no—
286C2×C3×C4—61no—
287C2×C3×C4—121no—
288C2×C3×C4C2×D1211yescharacteristic
289C2×C3×C4D3×D411yescharacteristic
290C2×C3×C4D3×D411yescharacteristic
291C2×C3×C4C2×C3×D411yescharacteristic
292C2×C3×C4C2×C3×D411yescharacteristic
293C2×C3×C4C2×C3×D411yescharacteristic
294#67—81no—
295#67—81no—
296C2×Dic3—21no—
297C2×Dic3—21no—
298C2×Dic3—41no—
299D12—41no—
300D12—41no—
301D12—81no—
302Dic6—41no—
303Dic6—41no—
304Dic6—41no—
305Dic6—41no—
306C3×C8—22no—
307C3×C8—22no—
308C3×C8—42no—
309C3×C8—41no—
310C3×C8—41no—
311C3×C8—42no—
312C3×C8—121no—
313C3⋊C8—41no—
314C2×C32—81no—
315C2×C32#45311yescharacteristic
316C2×C32#45511yescharacteristic
317C2×C32#45511yescharacteristic
318C3×D3—81no—
319C3×D3—81no—
320C24—61no—
321C2×Q8—31no—
322C2×Q8—31no—
323C2×Q8—61no—
324C2×Q8C3×D1211yescharacteristic
325C2×D4—31no—
326C2×D4—31no—
327C2×D4—61no—
328C2×D4—61no—
329C2×D4—61no—
330C2×D4C3×D1211yescharacteristic
331Q16—122no—
332SD16—122no—
333C2×C8—21no—
334C2×C8—21no—
335C2×C8—61no—
336C4⋊C4—61no—
337C4⋊C4—61no—
338C22⋊C4—21no—
339C22⋊C4—21no—
340C22⋊C4—61no—
341C22⋊C4—61no—
342C22⋊C4—61no—
343C22⋊C4—61no—
344C22⋊C4—61no—
345C22⋊C4—61no—
346C22⋊C4—61no—
347C42—61no—
348C42C22×C3×D311yescharacteristic
349C22×C3—21no—
350C22×C3—41no—
351C22×C3—41no—
352C22×C3—41no—
353C22×C3—41no—
354C22×C3—41no—
355C22×C3—41no—
356C22×C3—81no—
357C22×C3—81no—
358C22×C3—81no—
359C22×C3—121no—
360C22×C3—121no—
361C22×C3—121no—
362C22×C3—121no—
363C22×C3—121no—
364C22×C3—121no—
365C22×C3—244no—
366C22×C3#88211yescharacteristic
367C22×C3C3×#12011yescharacteristic
368C2×D3—41no—
369C2×D3—41no—
370C2×D3—41no—
371C2×D3—41no—
372C2×D3—41no—
373C2×D3—41no—
374C2×D3—84no—
375C3×C4—21no—
376C3×C4—21no—
377C3×C4—21no—
378C3×C4—21no—
379C3×C4—21no—
380C3×C4—21no—
381C3×C4—41no—
382C3×C4—41no—
383C3×C4—41no—
384C3×C4—41no—
385C3×C4—41no—
386C3×C4—81no—
387C3×C4—121no—
388C3×C4—121no—
389C3×C4—241no—
390Dic3—41no—
391Dic3—41no—
392Dic3—81no—
393C32#165911yescharacteristic, complemented, Sylow
394C23—21no—
395C23—61no—
396C23—61no—
397C23—241no—
398C23—241no—
399C23—241no—
400Q8—41no—
401Q8—121no—
402Q8—121no—
403Q8—121no—
404Q8—121no—
405D4—41no—
406D4—121no—
407D4—121no—
408D4—241no—
409D4—241no—
410D4—241no—
411C2×C4—21no—
412C2×C4—61no—
413C2×C4—61no—
414C2×C4—121no—
415C2×C4C2×C3×D1211yescharacteristic
416C2×C4C3×D3×D411yescharacteristic
417C2×C4C3×D3×D411yescharacteristic
418C8—22no—
419C8—41no—
420C8—121no—
421C2×C3—21no—
422C2×C3—21no—
423C2×C3—21no—
424C2×C3—81no—
425C2×C3—81no—
426C2×C3—161no—
427C2×C3—241no—
428C2×C3—241no—
429C2×C3#474611yescharacteristic
430C2×C3#482211yescharacteristic
431C2×C3#482511yescharacteristic
432C2×C3C3×#45311yescharacteristic
433C2×C3C3×#45511yescharacteristic
434C2×C3C3×#45511yescharacteristic
435D3—81no—
436D3—81no—
437C22—41no—
438C22—41no—
439C22—41no—
440C22—121no—
441C22—121no—
442C22—121no—
443C22—121no—
444C22—121no—
445C22—121no—
446C22—244no—
447C22C3×#88211yescharacteristic
448C4—21no—
449C4—21no—
450C4—21no—
451C4—41no—
452C4—121no—
453C4—121no—
454C4—241no—
455C3—21no—
456C3#6835211yescharacteristic, direct product factor
457C3C3×#165911yescharacteristic, complemented
458C2—81no—
459C2—241no—
460C2—241no—
461C2C3×#474611yescharacteristic
462C2C3×#482211yescharacteristic
463C2C3×#482511yescharacteristic
subgroupG/H
centerC22×C3#882
commutator, cosocleC3×C42C23×C3
FrattiniC42C22×C3×D3
FittingC32×#329C2
socleC22×C32#120
prime radicalC3×#5683C2
hypercenterC3×#329D3
hypocenterC3C3×#1659
LCSG ▷ C3×C42 ▷ C22×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C3×C42 ◁ C3×#329

Complements

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

NH ≅ G/Ntype
2. C3×#5055C2semidirect
3. C3×#4715C2semidirect
4. C3×#4714C2semidirect
5. C32×#329C2semidirect
6. C3×#4464C2semidirect
7. C3×#4464C2semidirect
9. #68352C3direct (N × H)
21. C3×#869C22semidirect
22. C32×#97C22semidirect
23. C32×#97C22semidirect
28. C3×#803C22semidirect
34. #5055C2×C3semidirect
35. #4715C2×C3semidirect
36. #4714C2×C3semidirect
40. C3×#329D3semidirect
41. C3×#329C2×C3semidirect
42. #4464C2×C3semidirect
43. #4464C2×C3semidirect
98. #869C22×C3semidirect
106. C3×#97C2×D3semidirect
107. C3×#97C2×D3semidirect
108. C3×#97C22×C3semidirect
109. C3×#97C22×C3semidirect
114. #803C22×C3semidirect
148. #329C3×D3semidirect
249. #97C2×C3×D3semidirect
250. #97C2×C3×D3semidirect
393. C32#1659semidirect
456. C3#68352direct (N × H)
457. C3C3×#1659semidirect

Maximal subgroups

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

subgroupindex
C3×#56832
C3×#50552
C3×#47152
C3×#47142
C32×#3292
C3×#44642
C3×#16593
#683523