Finite Group Databasebeta

← C3×#70982 #11778275

Subgroups — C3×#70982 #11778275

Order 1152.

562 conjugacy classes of subgroups; only the 98 normal subgroups are shown.

normal subgroups only

This group has 562 conjugacy classes of subgroups — too many to draw. Only its 98 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×#5645C211yesmaximal, characteristic
2C32×#451C211yesmaximal, characteristic, complemented
3C3×#5230C211yesmaximal, characteristic, complemented
4C3×#5227C211yesmaximal, characteristic
5C3×#4538C211yesmaximal, characteristic, complemented
6C3×#4470C211yesmaximal, characteristic
7C3×#4469C211yesmaximal, characteristic, complemented
8C3×#1603—31nomaximal
9#70982C311yesmaximal, characteristic, direct product factor
10C22×C32×Q8C2211yescharacteristic
11C2×C32×Q16—21no—
12C32×C22⋊Q8C2211yescharacteristic
13C3×#946—21no—
14C2×C3×#215—21no—
15C3×#930C2211yescharacteristic
16C2×C3×Dic3⋊C4—21no—
17C2×C3×Dic3⋊C4C2211yescharacteristic
18C3×#898—21no—
19C3×#894—21no—
20C3×#890—21no—
21C3×#886—21no—
22C3×#67⋊C4—21no—
23C32×#103—21no—
24C32×C22⋊C8C2211yescharacteristic
25C3×#835—21no—
26C3×C3⋊#95—21no—
27C3×C3⋊#95C2211yescharacteristic
28C3×#830C2211yescharacteristic
29C3×#539—31no—
30#5645C2×C311yescharacteristic
31C3×#451—21no—
32C3×#451D311yescharacteristic, complemented
33C3×#451C2×C311yescharacteristic, complemented
34C3×#448—31no—
35C3×#395—31no—
36#5230C2×C311yescharacteristic, complemented
37#5227C2×C311yescharacteristic
38C3×#328—31no—
39C3×#327—31no—
40C3×#324—31no—
41#4538C2×C311yescharacteristic, complemented
42#4470C2×C311yescharacteristic
43#4469C2×C311yescharacteristic, complemented
44C2×C32×Q8—21no—
45C2×C32×Q8—21no—
46C2×C32×Q8—42no—
47C2×C32×Q8D411yescharacteristic
48C22×C32×C4—21no—
49C22×C32×C4C2311yescharacteristic
50C2×C3×#67—21no—
51C22×C3×Dic3—21no—
52C22×C3×Dic3D411yescharacteristic
53C22×C3×Dic3D411yescharacteristic
54C2×C3×D12D411yescharacteristic
55C2×C3×C4×D3—21no—
56C32×Q16—42no—
57C2×C32×C8—21no—
58C32×C4⋊C4—21no—
59C32×C4⋊C4D411yescharacteristic
60C32×C22⋊C4—21no—
61C3×#215—42no—
62C3×(C2×D3)⋊C4—21no—
63C3×(C2×D3)⋊C4—21no—
64C3×(C2×D3)⋊C4—21no—
65C3×(C2×D3)⋊C4—21no—
66C3×C4⋊Dic3—21no—
67C3×C4⋊Dic3—21no—
68C3×C4⋊Dic3D411yescharacteristic
69C3×Dic3⋊C4—21no—
70C3×Dic3⋊C4—21no—
71C3×Dic3⋊C4—21no—
72C3×Dic3⋊C4—42no—
73C3×C4×Dic3—21no—
74C2×C3×C3⋊C8—21no—
75#1603—31noSylow
76C22×C3×Q8—21no—
77C22×C3×Q8C2×D311yescharacteristic
78C22×C3×Q8C22×C311yescharacteristic
79C2×C3×Q16—22no—
80C2×C3×Q16—21no—
81C2×C3×Q16—21no—
82C2×C3×SD16—61no—
83C3×#126—61no—
84C3×#125—61no—
85C3×#123—61no—
86C3×#123—61no—
87C3×C22⋊Q8—21no—
88C3×C22⋊Q8—61no—
89C3×C22⋊Q8C2×D311yescharacteristic
90C3×C22⋊Q8C22×C311yescharacteristic
91C3×#121—31no—
92C3×C4×D4—61no—
93C2×C3×C4⋊C4—31no—
94C2×C3×C4⋊C4—61no—
95#946—21no—
96C2×#215—21no—
97#930C22×C311yescharacteristic
98C2×Dic3⋊C4—21no—
99C2×Dic3⋊C4C22×C311yescharacteristic
100#898—21no—
101#894—21no—
102#890—21no—
103#886—21no—
104#67⋊C4—21no—
105C3×#103—22no—
106C3×#103—21no—
107C3×#103—21no—
108C3×#103—61no—
109C3×C22⋊C8—21no—
110C3×C22⋊C8—31no—
111C3×C22⋊C8C2×D311yescharacteristic
112C3×C22⋊C8C22×C311yescharacteristic
113C3×#95—31no—
114C3×#95—61no—
115#835—21no—
116C3⋊#95—21no—
117C3⋊#95C22×C311yescharacteristic
118#830C22×C311yescharacteristic
119C23×C32C2×D411yescharacteristic
120C22×C3×D3—21no—
121C32×Q8—22no—
122C32×Q8—22no—
123C32×Q8—41no—
124C32×Q8—41no—
125C32×Q8—41no—
126C2×C32×C4—22no—
127C2×C32×C4—21no—
128C2×C32×C4—21no—
129C2×C32×C4—41no—
130C2×C32×C4—41no—
131C2×C32×C4—41no—
132C2×C32×C4C2×D411yescharacteristic
133C2×C32×C4C2×D411yescharacteristic
134C3×#67—41no—
135C3×#67—41no—
136C2×C3×Dic3—22no—
137C2×C3×Dic3—21no—
138C2×C3×Dic3—21no—
139C2×C3×Dic3—21no—
140C2×C3×Dic3—21no—
141C2×C3×Dic3—21no—
142C2×C3×Dic3—41no—
143C2×C3×Dic3—41no—
144C2×C3×Dic3—41no—
145C3×D12—41no—
146C3×C4×D3—81no—
147C32×C8—41no—
148C3×C3⋊C8—41no—
149#539—31no—
150#451C3×D311yescharacteristic, complemented
151#448—31no—
152#395—31no—
153#328—31no—
154#327—31no—
155#324—31no—
156C2×C3×Q8—22no—
157C2×C3×Q8—21no—
158C2×C3×Q8—21no—
159C2×C3×Q8—21no—
160C2×C3×Q8—21no—
161C2×C3×Q8—21no—
162C2×C3×Q8—41no—
163C2×C3×Q8—42no—
164C2×C3×Q8—42no—
165C2×C3×Q8—44no—
166C2×C3×Q8#6711yescharacteristic
167C2×C3×Q8C3×D411yescharacteristic
168C2×C3×D4—31no—
169C2×C3×D4—61no—
170C22×C3×C4—21no—
171C22×C3×C4—21no—
172C22×C3×C4—21no—
173C22×C3×C4—31no—
174C22×C3×C4—31no—
175C22×C3×C4—41no—
176C22×C3×C4—61no—
177C22×C3×C4—61no—
178C22×C3×C4C22×D311yescharacteristic
179C22×C3×C4C23×C311yescharacteristic
180C2×#67—21no—
181C22×Dic3—21no—
182C22×Dic3C3×D411yescharacteristic
183C22×Dic3C3×D411yescharacteristic
184C2×D12C3×D411yescharacteristic
185C2×C4×D3—21no—
186C3×Q16—42no—
187C3×Q16—42no—
188C3×Q16—44no—
189C3×SD16—122no—
190C2×C3×C8—22no—
191C2×C3×C8—21no—
192C2×C3×C8—21no—
193C2×C3×C8—61no—
194C3×C4⋊C4—21no—
195C3×C4⋊C4—21no—
196C3×C4⋊C4—21no—
197C3×C4⋊C4—31no—
198C3×C4⋊C4—41no—
199C3×C4⋊C4—61no—
200C3×C4⋊C4—61no—
201C3×C4⋊C4—61no—
202C3×C4⋊C4—61no—
203C3×C4⋊C4—61no—
204C3×C4⋊C4—122no—
205C3×C4⋊C4#6711yescharacteristic
206C3×C4⋊C4C3×D411yescharacteristic
207C3×C22⋊C4—21no—
208C3×C22⋊C4—21no—
209C3×C22⋊C4—41no—
210C3×C22⋊C4—61no—
211C3×C22⋊C4—61no—
212C3×C22⋊C4—61no—
213C3×C22⋊C4—61no—
214C3×C42—61no—
215#215—42no—
216(C2×D3)⋊C4—21no—
217(C2×D3)⋊C4—21no—
218(C2×D3)⋊C4—21no—
219(C2×D3)⋊C4—21no—
220C4⋊Dic3—21no—
221C4⋊Dic3—21no—
222C4⋊Dic3C3×D411yescharacteristic
223Dic3⋊C4—21no—
224Dic3⋊C4—21no—
225Dic3⋊C4—21no—
226Dic3⋊C4—42no—
227C4×Dic3—21no—
228C2×C3⋊C8—21no—
229C22×C32—21no—
230C22×C32—21no—
231C22×C32#12011yescharacteristic
232C22×C32#13511yescharacteristic
233C22×C32#13711yescharacteristic
234C2×C3×D3—41no—
235C2×C3×D3—41no—
236C2×C3×D3—41no—
237C32×C4—21no—
238C32×C4—21no—
239C32×C4—42no—
240C32×C4—41no—
241C32×C4—41no—
242C3×Dic3—42no—
243C3×Dic3—41no—
244C3×Dic3—41no—
245C3×Dic3—41no—
246C22×Q8C2×C3×D311yescharacteristic
247C2×Q16—21no—
248C2×SD16—61no—
249#126—61no—
250#125—61no—
251#123—61no—
252#123—61no—
253C22⋊Q8—61no—
254C22⋊Q8C2×C3×D311yescharacteristic
255#121—31no—
256C4×D4—61no—
257C2×C4⋊C4—31no—
258C2×C4⋊C4—61no—
259#103—21no—
260#103—61no—
261C22⋊C8—31no—
262C22⋊C8C2×C3×D311yescharacteristic
263#95—31no—
264#95—61no—
265C23×C3—21no—
266C23×C3—61no—
267C23×C3D3×D411yescharacteristic
268C23×C3C2×C3×D411yescharacteristic
269C22×D3—21no—
270C3×Q8—22no—
271C3×Q8—22no—
272C3×Q8—24no—
273C3×Q8—22no—
274C3×Q8—22no—
275C3×Q8—42no—
276C3×Q8—41no—
277C3×Q8—41no—
278C3×Q8—42no—
279C3×Q8—41no—
280C3×Q8—41no—
281C3×Q8—41no—
282C3×Q8—41no—
283C3×Q8—42no—
284C3×Q8—42no—
285C3×D4—121no—
286C3×D4—121no—
287C3×D4—121no—
288C2×C3×C4—22no—
289C2×C3×C4—22no—
290C2×C3×C4—21no—
291C2×C3×C4—21no—
292C2×C3×C4—21no—
293C2×C3×C4—21no—
294C2×C3×C4—21no—
295C2×C3×C4—21no—
296C2×C3×C4—42no—
297C2×C3×C4—41no—
298C2×C3×C4—41no—
299C2×C3×C4—41no—
300C2×C3×C4—41no—
301C2×C3×C4—42no—
302C2×C3×C4—41no—
303C2×C3×C4—41no—
304C2×C3×C4—42no—
305C2×C3×C4—42no—
306C2×C3×C4—41no—
307C2×C3×C4—41no—
308C2×C3×C4—62no—
309C2×C3×C4—61no—
310C2×C3×C4—61no—
311C2×C3×C4—61no—
312C2×C3×C4—61no—
313C2×C3×C4—61no—
314C2×C3×C4—121no—
315C2×C3×C4—121no—
316C2×C3×C4—121no—
317C2×C3×C4—241no—
318C2×C3×C4D3×D411yescharacteristic
319C2×C3×C4C2×#6711yescharacteristic
320C2×C3×C4C2×C3×D411yescharacteristic
321C2×C3×C4C2×C3×D411yescharacteristic
322#67—41no—
323#67—41no—
324C2×Dic3—22no—
325C2×Dic3—21no—
326C2×Dic3—21no—
327C2×Dic3—21no—
328C2×Dic3—21no—
329C2×Dic3—21no—
330C2×Dic3—41no—
331C2×Dic3—41no—
332C2×Dic3—41no—
333D12—41no—
334C4×D3—81no—
335C3×C8—42no—
336C3×C8—41no—
337C3×C8—41no—
338C3×C8—121no—
339C3⋊C8—41no—
340C2×C32—21no—
341C2×C32—21no—
342C2×C32#45211yescharacteristic
343C2×C32#45611yescharacteristic
344C2×C32B(4,𝔽2)11yescharacteristic
345C3×D3—81no—
346C2×Q8—21no—
347C2×Q8—21no—
348C2×Q8—42no—
349C2×Q8C3×#6711yescharacteristic
350C2×D4—31no—
351C2×D4—61no—
352C22×C4—21no—
353C22×C4—31no—
354C22×C4—31no—
355C22×C4—61no—
356C22×C4—61no—
357C22×C4C22×C3×D311yescharacteristic
358Q16—42no—
359SD16—122no—
360C2×C8—21no—
361C2×C8—61no—
362C4⋊C4—21no—
363C4⋊C4—31no—
364C4⋊C4—61no—
365C4⋊C4—61no—
366C4⋊C4—61no—
367C4⋊C4—61no—
368C4⋊C4—61no—
369C4⋊C4—122no—
370C4⋊C4C3×#6711yescharacteristic
371C22⋊C4—21no—
372C22⋊C4—61no—
373C22⋊C4—61no—
374C22⋊C4—61no—
375C22⋊C4—61no—
376C42—61no—
377C22×C3—21no—
378C22×C3—21no—
379C22×C3—21no—
380C22×C3—21no—
381C22×C3—21no—
382C22×C3—21no—
383C22×C3—21no—
384C22×C3—41no—
385C22×C3—41no—
386C22×C3—121no—
387C22×C3—121no—
388C22×C3—121no—
389C22×C3#91811yescharacteristic
390C22×C3#91911yescharacteristic
391C22×C3#93711yescharacteristic
392C22×C3C3×#12011yescharacteristic
393C22×C3C3×#13511yescharacteristic
394C22×C3C3×#13711yescharacteristic
395C2×D3—41no—
396C2×D3—41no—
397C2×D3—41no—
398C3×C4—22no—
399C3×C4—21no—
400C3×C4—21no—
401C3×C4—21no—
402C3×C4—21no—
403C3×C4—41no—
404C3×C4—44no—
405C3×C4—41no—
406C3×C4—42no—
407C3×C4—41no—
408C3×C4—41no—
409C3×C4—41no—
410C3×C4—42no—
411C3×C4—81no—
412C3×C4—81no—
413C3×C4—122no—
414C3×C4—121no—
415C3×C4—121no—
416C3×C4—121no—
417Dic3—42no—
418Dic3—41no—
419Dic3—41no—
420Dic3—41no—
421C32#160311yescharacteristic, complemented, Sylow
422C23—61no—
423C23C3×D3×D411yescharacteristic
424Q8—22no—
425Q8—22no—
426Q8—41no—
427Q8—41no—
428Q8—41no—
429D4—121no—
430D4—121no—
431D4—121no—
432C2×C4—22no—
433C2×C4—21no—
434C2×C4—21no—
435C2×C4—41no—
436C2×C4—41no—
437C2×C4—41no—
438C2×C4—62no—
439C2×C4—61no—
440C2×C4—61no—
441C2×C4—61no—
442C2×C4—61no—
443C2×C4—61no—
444C2×C4—121no—
445C2×C4—121no—
446C2×C4—121no—
447C2×C4—241no—
448C2×C4C3×D3×D411yescharacteristic
449C2×C4C2×C3×#6711yescharacteristic
450C8—41no—
451C8—121no—
452C2×C3—21no—
453C2×C3—21no—
454C2×C3—21no—
455C2×C3—21no—
456C2×C3—21no—
457C2×C3—21no—
458C2×C3—21no—
459C2×C3—41no—
460C2×C3—41no—
461C2×C3—241no—
462C2×C3#503211yescharacteristic
463C2×C3#518711yescharacteristic
464C2×C3#520511yescharacteristic
465C2×C3C3×#45211yescharacteristic
466C2×C3C3×#45611yescharacteristic
467C2×C3C3×B(4,𝔽2)11yescharacteristic
468D3—81no—
469C22—21no—
470C22—21no—
471C22—121no—
472C22—121no—
473C22—121no—
474C22C3×#91811yescharacteristic
475C22C3×#91911yescharacteristic
476C22C3×#93711yescharacteristic
477C4—21no—
478C4—21no—
479C4—41no—
480C4—42no—
481C4—41no—
482C4—122no—
483C4—121no—
484C4—121no—
485C4—121no—
486C3—21no—
487C3#7098211yescharacteristic, direct product factor
488C3C3×#160311yescharacteristic, complemented
489C2—21no—
490C2—21no—
491C2—241no—
492C2C3×#503211yescharacteristic
493C2C3×#518711yescharacteristic
494C2C3×#520511yescharacteristic
subgroupG/H
centerC22×C3#937
commutator, cosocleC22×C3×C4C23×C3
FrattiniC22×C4C22×C3×D3
FittingC32×#451C2
socleC22×C32#120
prime radicalC3×#930C22
hypercenterC3×#451D3
hypocenterC3C3×#1603
LCSG ▷ C22×C3×C4 ▷ C22×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C22×C3×C4 ◁ C3×#451

Complements

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

NH ≅ G/Ntype
2. C32×#451C2semidirect
3. C3×#5230C2semidirect
5. C3×#4538C2semidirect
7. C3×#4469C2semidirect
9. #70982C3direct (N × H)
32. C3×#451D3semidirect
33. C3×#451C2×C3semidirect
36. #5230C2×C3semidirect
41. #4538C2×C3semidirect
43. #4469C2×C3semidirect
150. #451C3×D3semidirect
421. C32#1603semidirect
487. C3#70982direct (N × H)
488. C3C3×#1603semidirect

Maximal subgroups

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

subgroupindex
C3×#56452
C32×#4512
C3×#52302
C3×#52272
C3×#45382
C3×#44702
C3×#44692
C3×#16033
#709823