Finite Group Databasebeta

← C3×#70379 #11793850

Subgroups — C3×#70379 #11793850

Order 1152.

617 conjugacy classes of subgroups.

The subgroup lattice has 554 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5822C211yesmaximal, characteristic
2C2×C32×#104C211yesmaximal, characteristic, complemented
3C3×#5237C211yesmaximal, characteristic, complemented
4C3×#5132C211yesmaximal, characteristic, complemented
5C2×C3×#805C211yesmaximal, characteristic, complemented
6C3×#4924C211yesmaximal, characteristic, complemented
7C3×C3⋊#338C211yesmaximal, characteristic, complemented
8C3×#2050—31nomaximal
9#70379C311yesmaximal, characteristic, direct product factor
10C2×C32×#41C2211yescharacteristic
11C2×C3×#235C2211yescharacteristic
12C2×C32×M16C2211yescharacteristic
13C2×C32×C42C2211yescharacteristic
14C3×#951—21no—
15C3×#950—22no—
16C3×#949—21no—
17C3×#942—21no—
18C3×#932—21no—
19C2×C3×#208C2211yescharacteristic
20C2×C3×#208C2211yescharacteristic
21C2×C3×#208C2211yescharacteristic
22C32×#104—21no—
23C32×#104—21no—
24C3×#836—21no—
25C3×#833—21no—
26C3×#824—21no—
27C3×#823—21no—
28C3×#805—21no—
29C3×#805—21no—
30C3×C4⋊(C3⋊C8)—22no—
31C3×#575—31no—
32#5822C2×C311yescharacteristic
33C3×#423—31no—
34C2×C3×#104—21no—
35C2×C3×#104—31no—
36C2×C3×#104D311yescharacteristic, complemented
37C2×C3×#104C2×C311yescharacteristic, complemented
38C3×#413—31no—
39C3×#413—31no—
40#5237C2×C311yescharacteristic, complemented
41#5132C2×C311yescharacteristic, complemented
42C2×#805C2×C311yescharacteristic, complemented
43#4924C2×C311yescharacteristic, complemented
44C3×#338—31no—
45C3⋊#338C2×C311yescharacteristic, complemented
46C32×#41—21no—
47C32×#41—21no—
48C32×#41—21no—
49C32×#41—21no—
50C2×C32×Q8D411yescharacteristic
51C2×C32×D4—21no—
52C2×C32×D4D411yescharacteristic
53C22×C32×C4—21no—
54C22×C32×C4—21no—
55C22×C32×C4C2311yescharacteristic
56C2×C3×#67—21no—
57C3×#235—21no—
58C3×#235—21no—
59C3×#235—21no—
60C3×#235—21no—
61C2×C3×D12D411yescharacteristic
62C2×C3×C4×D3—21no—
63C2×C3×Dic6D411yescharacteristic
64C32×M16—21no—
65C32×M16—21no—
66C2×C32×C8—21no—
67C32×C42—21no—
68C32×C42D411yescharacteristic
69C32×C42D411yescharacteristic
70C3×#216—22no—
71C3×#215—22no—
72C3×#214—22no—
73C3×#213—22no—
74C3×#208—21no—
75C3×#208—21no—
76C3×#208—21no—
77C3×#208—21no—
78C3×#208—21no—
79C3×#208—21no—
80C2×C3×C3⋊C8—21no—
81C2×C3×C3⋊C8—21no—
82C2×C3×C3⋊C8D412yes—
83#2050—31noSylow
84C2×C3×#41—21no—
85C2×C3×#41—31no—
86C2×C3×#41C2×D311yescharacteristic
87C2×C3×#41C22×C311yescharacteristic
88C2×#235C22×C311yescharacteristic
89C3×#137—61no—
90C3×#137—61no—
91C3×AGL(1,ℤ/8)—61no—
92C3×AGL(1,ℤ/8)—61no—
93C3×#135—62no—
94C2×C3×M16—21no—
95C2×C3×M16—31no—
96C2×C3×M16—31no—
97C2×C3×M16—31no—
98C2×C3×M16C2×D311yescharacteristic
99C2×C3×M16C22×C311yescharacteristic
100C2×C3×C42—21no—
101C2×C3×C42C2×D311yescharacteristic
102C2×C3×C42C22×C311yescharacteristic
103#951—21no—
104#950—22no—
105#949—21no—
106#942—21no—
107#932—21no—
108C2×#208C22×C311yescharacteristic
109C2×#208C22×C311yescharacteristic
110C2×#208C22×C311yescharacteristic
111C3×C4⋊C8—62no—
112C3×#104—22no—
113C3×#104—22no—
114C3×#104—21no—
115C3×#104—21no—
116C3×#104—21no—
117C3×#104—21no—
118C3×#104—61no—
119C3×#104—61no—
120C3×#101—61no—
121C3×#101—61no—
122C3×#100—61no—
123C3×#100—61no—
124#836—21no—
125#833—21no—
126#824—21no—
127#823—21no—
128#805—21no—
129#805—21no—
130C4⋊(C3⋊C8)—22no—
131C23×C32—21no—
132C23×C32#4111yescharacteristic
133C22×C3×D3—21no—
134C32×Q8—21no—
135C32×Q8—21no—
136C32×D4—21no—
137C32×D4—21no—
138C32×D4—41no—
139C32×D4—41no—
140C2×C32×C4—21no—
141C2×C32×C4—21no—
142C2×C32×C4—21no—
143C2×C32×C4—42no—
144C2×C32×C4—41no—
145C2×C32×C4—41no—
146C2×C32×C4C2×D411yescharacteristic
147C2×C32×C4C2×D411yescharacteristic
148C2×C32×C4C2×D411yescharacteristic
149C2×C32×C4C2×D411yescharacteristic
150C2×C32×C4#4111yescharacteristic
151C2×C32×C4#4111yescharacteristic
152C3×#67—41no—
153C3×#67—41no—
154C2×C3×Dic3—21no—
155C3×D12—21no—
156C3×D12—21no—
157C3×C4×D3—41no—
158C3×C4×D3—41no—
159C3×Dic6—21no—
160C3×Dic6—21no—
161C32×C8—41no—
162C3×C3⋊C8—22no—
163C3×C3⋊C8—41no—
164C3×C3⋊C8—41no—
165#575—31no—
166#423—31no—
167C2×#104—31no—
168C2×#104C3×D311yescharacteristic, complemented
169#413—31no—
170#413—31no—
171#338—31no—
172C3×#41—22no—
173C3×#41—22no—
174C3×#41—21no—
175C3×#41—21no—
176C3×#41—21no—
177C3×#41—21no—
178C3×#41—21no—
179C3×#41—21no—
180C3×#41—21no—
181C3×#41—21no—
182C3×#41—41no—
183C3×#41—41no—
184C3×#41—61no—
185C3×#41—61no—
186C3×#41—61no—
187C3×#41—61no—
188C2×C3×Q8—21no—
189C2×C3×Q8—31no—
190C2×C3×Q8D1211yescharacteristic
191C2×C3×Q8C3×D411yescharacteristic
192C2×C3×D4—21no—
193C2×C3×D4—21no—
194C2×C3×D4—21no—
195C2×C3×D4—31no—
196C2×C3×D4—41no—
197C2×C3×D4—61no—
198C2×C3×D4D1211yescharacteristic
199C2×C3×D4C3×D411yescharacteristic
200C22×C3×C4—21no—
201C22×C3×C4—21no—
202C22×C3×C4—21no—
203C22×C3×C4—21no—
204C22×C3×C4—21no—
205C22×C3×C4—41no—
206C22×C3×C4—41no—
207C22×C3×C4—61no—
208C22×C3×C4C22×D311yescharacteristic
209C22×C3×C4C23×C311yescharacteristic
210C2×#67—21no—
211#235—21no—
212#235—21no—
213#235—21no—
214#235—21no—
215C2×D12C3×D411yescharacteristic
216C2×C4×D3—21no—
217C2×Dic6C3×D411yescharacteristic
218C3×Q16—62no—
219C3×SD16—62no—
220C3×SD16—62no—
221C3×D8—62no—
222C3×M16—22no—
223C3×M16—21no—
224C3×M16—21no—
225C3×M16—21no—
226C3×M16—21no—
227C3×M16—41no—
228C3×M16—61no—
229C3×M16—61no—
230C3×M16—61no—
231C3×M16—61no—
232C3×M16—61no—
233C3×M16—61no—
234C2×C3×C8—21no—
235C2×C3×C8—21no—
236C2×C3×C8—32no—
237C2×C3×C8—41no—
238C2×C3×C8—61no—
239C2×C3×C8—61no—
240C3×C42—21no—
241C3×C42—21no—
242C3×C42—21no—
243C3×C42—21no—
244C3×C42—41no—
245C3×C42#6711yescharacteristic
246C3×C42#6711yescharacteristic
247C3×C42C3×D411yescharacteristic
248C3×C42C3×D411yescharacteristic
249#216—22no—
250#215—22no—
251#214—22no—
252#213—22no—
253#208—21no—
254#208—21no—
255#208—21no—
256#208—21no—
257#208—21no—
258#208—21no—
259C2×C3⋊C8—21no—
260C2×C3⋊C8—21no—
261C2×C3⋊C8C3×D412yes—
262C22×C32—41no—
263C22×C32—41no—
264C22×C32—81no—
265C22×C32#12111yescharacteristic
266C22×C32#12311yescharacteristic
267C22×C32#12311yescharacteristic
268C2×C3×D3—41no—
269C2×C3×D3—81no—
270C32×C4—22no—
271C32×C4—41no—
272C32×C4—41no—
273C32×C4#12011yescharacteristic
274C32×C4#12111yescharacteristic
275C32×C4#12111yescharacteristic
276C32×C4#12411yescharacteristic
277C3×Dic3—41no—
278C2×#41—31no—
279C2×#41C2×C3×D311yescharacteristic
280#137—61no—
281#137—61no—
282AGL(1,ℤ/8)—61no—
283AGL(1,ℤ/8)—61no—
284#135—62no—
285C2×M16—31no—
286C2×M16—31no—
287C2×M16—31no—
288C2×M16C2×C3×D311yescharacteristic
289C2×C42C2×C3×D311yescharacteristic
290C4⋊C8—62no—
291#104—21no—
292#104—21no—
293#104—61no—
294#104—61no—
295#101—61no—
296#101—61no—
297#100—61no—
298#100—61no—
299C23×C3—21no—
300C23×C3—21no—
301C23×C3—21no—
302C23×C3—41no—
303C23×C3—61no—
304C23×C3#23711yescharacteristic
305C23×C3C3×#4111yescharacteristic
306C22×D3—21no—
307C3×Q8—22no—
308C3×Q8—21no—
309C3×Q8—21no—
310C3×Q8—21no—
311C3×Q8—21no—
312C3×Q8—41no—
313C3×Q8—61no—
314C3×Q8—61no—
315C3×D4—22no—
316C3×D4—21no—
317C3×D4—21no—
318C3×D4—21no—
319C3×D4—21no—
320C3×D4—41no—
321C3×D4—42no—
322C3×D4—42no—
323C3×D4—41no—
324C3×D4—41no—
325C3×D4—41no—
326C3×D4—41no—
327C3×D4—61no—
328C3×D4—61no—
329C3×D4—121no—
330C3×D4—121no—
331C2×C3×C4—21no—
332C2×C3×C4—21no—
333C2×C3×C4—21no—
334C2×C3×C4—21no—
335C2×C3×C4—21no—
336C2×C3×C4—21no—
337C2×C3×C4—21no—
338C2×C3×C4—21no—
339C2×C3×C4—21no—
340C2×C3×C4—21no—
341C2×C3×C4—21no—
342C2×C3×C4—21no—
343C2×C3×C4—41no—
344C2×C3×C4—41no—
345C2×C3×C4—41no—
346C2×C3×C4—42no—
347C2×C3×C4—42no—
348C2×C3×C4—42no—
349C2×C3×C4—42no—
350C2×C3×C4—44no—
351C2×C3×C4—41no—
352C2×C3×C4—41no—
353C2×C3×C4—41no—
354C2×C3×C4—41no—
355C2×C3×C4—61no—
356C2×C3×C4—121no—
357C2×C3×C4—121no—
358C2×C3×C4C2×D1211yescharacteristic
359C2×C3×C4#23511yescharacteristic
360C2×C3×C4D3×D411yescharacteristic
361C2×C3×C4D3×D411yescharacteristic
362C2×C3×C4#23711yescharacteristic
363C2×C3×C4C2×#6711yescharacteristic
364C2×C3×C4C2×C3×D411yescharacteristic
365C2×C3×C4C2×C3×D411yescharacteristic
366C2×C3×C4C2×C3×D411yescharacteristic
367C2×C3×C4C2×C3×D411yescharacteristic
368C2×C3×C4C3×#4111yescharacteristic
369C2×C3×C4C3×#4111yescharacteristic
370#67—41no—
371#67—41no—
372C2×Dic3—21no—
373D12—21no—
374D12—21no—
375C4×D3—41no—
376C4×D3—41no—
377Dic6—21no—
378Dic6—21no—
379C3×C8—42no—
380C3×C8—41no—
381C3×C8—41no—
382C3×C8—62no—
383C3×C8—121no—
384C3×C8—121no—
385C3⋊C8—22no—
386C3⋊C8—41no—
387C3⋊C8—41no—
388C2×C32—21no—
389C2×C32—21no—
390C2×C32—21no—
391C2×C32—81no—
392C2×C32#39411yescharacteristic
393C3×D3—81no—
394#41—21no—
395#41—21no—
396#41—21no—
397#41—21no—
398#41—61no—
399#41—61no—
400#41—61no—
401#41—61no—
402C2×Q8—31no—
403C2×Q8C3×D1211yescharacteristic
404C2×D4—21no—
405C2×D4—31no—
406C2×D4—61no—
407C2×D4C3×D1211yescharacteristic
408C22×C4—21no—
409C22×C4—21no—
410C22×C4—61no—
411C22×C4C22×C3×D311yescharacteristic
412Q16—62no—
413SD16—62no—
414SD16—62no—
415D8—62no—
416M16—21no—
417M16—21no—
418M16—61no—
419M16—61no—
420M16—61no—
421M16—61no—
422M16—61no—
423M16—61no—
424C2×C8—21no—
425C2×C8—32no—
426C2×C8—61no—
427C2×C8—61no—
428C42—21no—
429C42C3×#6711yescharacteristic
430C42C3×#6711yescharacteristic
431C22×C3—21no—
432C22×C3—21no—
433C22×C3—21no—
434C22×C3—41no—
435C22×C3—41no—
436C22×C3—42no—
437C22×C3—42no—
438C22×C3—41no—
439C22×C3—41no—
440C22×C3—81no—
441C22×C3—81no—
442C22×C3—82no—
443C22×C3—121no—
444C22×C3—241no—
445C22×C3#88311yescharacteristic
446C22×C3#88611yescharacteristic
447C22×C3#93911yescharacteristic
448C22×C3C3×#12111yescharacteristic
449C22×C3C3×#12311yescharacteristic
450C22×C3C3×#12311yescharacteristic
451C2×D3—41no—
452C2×D3—81no—
453C3×C4—22no—
454C3×C4—22no—
455C3×C4—21no—
456C3×C4—21no—
457C3×C4—21no—
458C3×C4—21no—
459C3×C4—42no—
460C3×C4—41no—
461C3×C4—41no—
462C3×C4—42no—
463C3×C4—42no—
464C3×C4—41no—
465C3×C4—41no—
466C3×C4—121no—
467C3×C4#88211yescharacteristic
468C3×C4#88511yescharacteristic
469C3×C4#93011yescharacteristic
470C3×C4#93811yescharacteristic
471C3×C4C3×#12011yescharacteristic
472C3×C4C3×#12111yescharacteristic
473C3×C4C3×#12111yescharacteristic
474C3×C4C3×#12411yescharacteristic
475Dic3—41no—
476C32#205011yescharacteristic, complemented, Sylow
477C23—21no—
478C23—61no—
479C23C3×#23711yescharacteristic
480Q8—21no—
481Q8—21no—
482Q8—61no—
483Q8—61no—
484D4—21no—
485D4—21no—
486D4—41no—
487D4—41no—
488D4—61no—
489D4—61no—
490D4—121no—
491D4—121no—
492C2×C4—21no—
493C2×C4—21no—
494C2×C4—21no—
495C2×C4—42no—
496C2×C4—41no—
497C2×C4—41no—
498C2×C4—61no—
499C2×C4—121no—
500C2×C4—121no—
501C2×C4C2×C3×D1211yescharacteristic
502C2×C4C3×#23511yescharacteristic
503C2×C4C3×D3×D411yescharacteristic
504C2×C4C3×D3×D411yescharacteristic
505C2×C4C3×#23711yescharacteristic
506C2×C4C2×C3×#6711yescharacteristic
507C8—41no—
508C8—62no—
509C8—121no—
510C8—121no—
511C2×C3—22no—
512C2×C3—21no—
513C2×C3—21no—
514C2×C3—21no—
515C2×C3—21no—
516C2×C3—21no—
517C2×C3—21no—
518C2×C3—21no—
519C2×C3—41no—
520C2×C3—41no—
521C2×C3—82no—
522C2×C3—81no—
523C2×C3—81no—
524C2×C3—241no—
525C2×C3#496111yescharacteristic
526C2×C3C3×#39411yescharacteristic
527D3—81no—
528C22—41no—
529C22—41no—
530C22—81no—
531C22—121no—
532C22—241no—
533C22C3×#88311yescharacteristic
534C22C3×#88611yescharacteristic
535C22C3×#93911yescharacteristic
536C4—22no—
537C4—41no—
538C4—41no—
539C4—121no—
540C4C3×#88211yescharacteristic
541C4C3×#88511yescharacteristic
542C4C3×#93011yescharacteristic
543C4C3×#93811yescharacteristic
544C3—21no—
545C3#7037911yescharacteristic, direct product factor
546C3C3×#205011yescharacteristic, complemented
547C2—21no—
548C2—21no—
549C2—21no—
550C2—81no—
551C2—241no—
552C2C3×#496111yescharacteristic
subgroupG/H
centerC3×C4#885
commutator, cosocleC22×C3×C4C23×C3
FrattiniC22×C4C22×C3×D3
FittingC2×C32×#104C2
socleC2×C32#394
prime radicalC3×#5822C2
hypercenterC2×C3×#104D3
hypocenterC3C3×#2050
LCSG ▷ C22×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C3×C4 ◁ C22×C3×C4 ◁ C2×C3×#104

Complements

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

NH ≅ G/Ntype
2. C2×C32×#104C2semidirect
3. C3×#5237C2semidirect
4. C3×#5132C2semidirect
5. C2×C3×#805C2semidirect
6. C3×#4924C2semidirect
7. C3×C3⋊#338C2semidirect
9. #70379C3direct (N × H)
36. C2×C3×#104D3semidirect
37. C2×C3×#104C2×C3semidirect
40. #5237C2×C3semidirect
41. #5132C2×C3semidirect
42. C2×#805C2×C3semidirect
43. #4924C2×C3semidirect
45. C3⋊#338C2×C3semidirect
168. C2×#104C3×D3semidirect
476. C32#2050semidirect
545. C3#70379direct (N × H)
546. C3C3×#2050semidirect

Maximal subgroups

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

subgroupindex
C3×#58222
C2×C32×#1042
C3×#52372
C3×#51322
C2×C3×#8052
C3×#49242
C3×C3⋊#3382
C3×#20503
#703793