Finite Group Databasebeta

← C3×#70119 #11792194

Subgroups — C3×#70119 #11792194

Order 1152.

797 conjugacy classes of subgroups.

The subgroup lattice has 553 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5816C211yesmaximal, characteristic
2C2×C3×#944C211yesmaximal, characteristic, complemented
3C2×C3×#909C211yesmaximal, characteristic
4C2×C32×#101C211yesmaximal, characteristic, complemented
5C2×C3×#825C211yesmaximal, characteristic
6C3×#5120C211yesmaximal, characteristic, complemented
7C3×#4555C211yesmaximal, characteristic, complemented
8C3×#2005—31nomaximal
9#70119C311yesmaximal, characteristic, direct product factor
10C22×C32×Q8C2211yescharacteristic
11C2×C3×#235C2211yescharacteristic
12C22×C3×Dic6C2211yescharacteristic
13C2×C32×M16C2211yescharacteristic
14C2×C32×M16C2211yescharacteristic
15C3×#947—21no—
16C3×#946—22no—
17C3×#944—22no—
18C3×#944—21no—
19C3×#944—22no—
20C3×#929—22no—
21C3×#926C2211yescharacteristic
22C2×C3×Dic3⋊C4—22no—
23C2×C3×C4×Dic3C2211yescharacteristic
24C3×#909—22no—
25C3×#909—22no—
26C2×C3×Dic12—21no—
27C2×C3×#204—21no—
28C32×#101—22no—
29C3×#825—22no—
30C3×#816—22no—
31C2×C3×#137—31no—
32C3×#536—31no—
33C2×C3×C4⋊Q8—31no—
34#5816C2×C311yescharacteristic
35C2×#944C2×C311yescharacteristic, complemented
36C2×#909C2×C311yescharacteristic
37C2×C3×#104—31no—
38C3×#419—31no—
39C2×C3×#101—21no—
40C2×C3×#101D311yescharacteristic, complemented
41C2×C3×#101C2×C311yescharacteristic, complemented
42C2×#825C2×C311yescharacteristic
43#5120C2×C311yescharacteristic, complemented
44C3×#339—31no—
45#4555C2×C311yescharacteristic, complemented
46C2×C32×Q8—21no—
47C2×C32×Q8—21no—
48C2×C32×Q8—21no—
49C2×C32×Q8—21no—
50C2×C32×Q8—21no—
51C2×C32×Q8—21no—
52C22×C32×C4D412yes—
53C22×C32×C4C2311yescharacteristic
54C2×C3×#67—21no—
55C22×C3×Dic3—21no—
56C22×C3×Dic3—21no—
57C3×#235—21no—
58C3×#235—21no—
59C3×#235—21no—
60C3×#235—21no—
61C2×C3×D12D411yescharacteristic
62C2×C3×C4×D3—21no—
63C2×C3×Dic6—21no—
64C2×C3×Dic6—21no—
65C2×C3×Dic6—21no—
66C2×C3×Dic6—21no—
67C2×C3×Dic6—21no—
68C2×C3×Dic6D411yescharacteristic
69C2×C3×Dic6D412yes—
70C32×M16—21no—
71C32×M16—21no—
72C32×M16—21no—
73C32×M16D412yes—
74C2×C32×C8—21no—
75C2×C32×C8—21no—
76C3×#217—21no—
77C3×(C2×D3)⋊C4—24no—
78C3×C4⋊Dic3D412yes—
79C3×Dic3⋊C4—28no—
80C3×Dic3⋊C4—24no—
81C3×C4×Dic3—21no—
82C3×C4×Dic3—21no—
83C3×C4×Dic3D412yes—
84C3×Dic12—24no—
85C3×#204—24no—
86#2005—31noSylow
87C2×C3×#41—31no—
88C22×C3×Q8—21no—
89C22×C3×Q8—31no—
90C22×C3×Q8C2×D311yescharacteristic
91C22×C3×Q8C22×C311yescharacteristic
92C2×#235C22×C311yescharacteristic
93C22×Dic6C22×C311yescharacteristic
94C3×#137—62no—
95C3×#137—62no—
96C2×C3×Q16—61no—
97C2×C3×SD16—61no—
98C2×C3×M16—21no—
99C2×C3×M16—21no—
100C2×C3×M16C2×D311yescharacteristic
101C2×C3×M16C2×D311yescharacteristic
102C2×C3×M16C22×C311yescharacteristic
103C2×C3×M16C22×C311yescharacteristic
104C3×C4⋊Q8—62no—
105C3×C4⋊Q8—62no—
106C3×C4⋊Q8—61no—
107C3×#124—61no—
108C3×#123—62no—
109C3×C22⋊Q8—62no—
110C3×#117—31no—
111C2×C3×C4⋊C4—62no—
112C2×C3×C42—31no—
113#947—21no—
114#946—22no—
115#944—22no—
116#944—21no—
117#944—22no—
118#929—22no—
119#926C22×C311yescharacteristic
120C2×Dic3⋊C4—22no—
121C2×C4×Dic3C22×C311yescharacteristic
122#909—22no—
123#909—22no—
124C2×Dic12—21no—
125C2×#204—21no—
126C3×#104—62no—
127C3×#103—62no—
128C3×#101—24no—
129C3×#101—22no—
130C3×#101—22no—
131#825—22no—
132#816—22no—
133C23×C32C2×D411yescharacteristic
134C22×C3×D3—21no—
135C32×Q8—41no—
136C32×Q8—41no—
137C32×Q8—41no—
138C32×Q8—41no—
139C2×C32×C4—22no—
140C2×C32×C4—22no—
141C2×C32×C4—22no—
142C2×C32×C4C2×D411yescharacteristic
143C2×C32×C4C2×D411yescharacteristic
144C2×C32×C4C2×D411yescharacteristic
145C2×C32×C4C2×D411yescharacteristic
146C2×C32×C4C2×D411yescharacteristic
147C2×C32×C4#4111yescharacteristic
148C3×#67—41no—
149C3×#67—41no—
150C2×C3×Dic3—24no—
151C2×C3×Dic3—22no—
152C2×C3×Dic3—22no—
153C2×C3×Dic3—22no—
154C2×C3×Dic3—21no—
155C2×C3×Dic3—41no—
156C2×C3×Dic3—41no—
157C3×D12—21no—
158C3×D12—21no—
159C3×C4×D3—41no—
160C3×C4×D3—41no—
161C3×Dic6—22no—
162C3×Dic6—21no—
163C3×Dic6—22no—
164C3×Dic6—21no—
165C3×Dic6—41no—
166C3×Dic6—41no—
167C32×C8—22no—
168C32×C8—41no—
169C2×#137—31no—
170#536—31no—
171C2×C4⋊Q8—31no—
172C2×#104—31no—
173#419—31no—
174C2×#101C3×D311yescharacteristic, complemented
175#339—31no—
176C3×#41—61no—
177C3×#41—61no—
178C3×#41—61no—
179C3×#41—61no—
180C2×C3×Q8—22no—
181C2×C3×Q8—22no—
182C2×C3×Q8—21no—
183C2×C3×Q8—21no—
184C2×C3×Q8—21no—
185C2×C3×Q8—21no—
186C2×C3×Q8—21no—
187C2×C3×Q8—21no—
188C2×C3×Q8—21no—
189C2×C3×Q8—21no—
190C2×C3×Q8—21no—
191C2×C3×Q8—21no—
192C2×C3×Q8—21no—
193C2×C3×Q8—21no—
194C2×C3×Q8—31no—
195C2×C3×Q8—32no—
196C2×C3×Q8—41no—
197C2×C3×Q8—41no—
198C2×C3×Q8—41no—
199C2×C3×Q8—41no—
200C2×C3×Q8—61no—
201C2×C3×Q8—61no—
202C2×C3×Q8—61no—
203C2×C3×Q8—61no—
204C2×C3×Q8—61no—
205C2×C3×D4—31no—
206C2×C3×D4—61no—
207C22×C3×C4—22no—
208C22×C3×C4—21no—
209C22×C3×C4—61no—
210C22×C3×C4—61no—
211C22×C3×C4—61no—
212C22×C3×C4D1212yes—
213C22×C3×C4C3×D412yes—
214C22×C3×C4C22×D311yescharacteristic
215C22×C3×C4C23×C311yescharacteristic
216C2×#67—21no—
217C22×Dic3—21no—
218C22×Dic3—21no—
219#235—21no—
220#235—21no—
221#235—21no—
222#235—21no—
223C2×D12C3×D411yescharacteristic
224C2×C4×D3—21no—
225C2×Dic6—21no—
226C2×Dic6—21no—
227C2×Dic6—21no—
228C2×Dic6—21no—
229C2×Dic6—21no—
230C2×Dic6C3×D411yescharacteristic
231C2×Dic6C3×D412yes—
232C3×Q16—64no—
233C3×SD16—64no—
234C3×M16—21no—
235C3×M16—21no—
236C3×M16—22no—
237C3×M16—21no—
238C3×M16—21no—
239C3×M16—21no—
240C3×M16—21no—
241C3×M16—22no—
242C3×M16—41no—
243C3×M16—41no—
244C3×M16#6712yes—
245C3×M16C3×D412yes—
246C2×C3×C8—21no—
247C2×C3×C8—21no—
248C2×C3×C8—21no—
249C2×C3×C8—21no—
250C2×C3×C8—41no—
251C2×C3×C8—41no—
252C3×C4⋊C4—32no—
253C3×C4⋊C4—68no—
254C3×C4⋊C4—64no—
255C3×C22⋊C4—64no—
256C3×C22⋊C4—61no—
257C3×C42—32no—
258C3×C42—61no—
259C3×C42—61no—
260#217—21no—
261(C2×D3)⋊C4—24no—
262C4⋊Dic3C3×D412yes—
263Dic3⋊C4—28no—
264Dic3⋊C4—24no—
265C4×Dic3—21no—
266C4×Dic3—21no—
267C4×Dic3C3×D412yes—
268Dic12—24no—
269#204—24no—
270C22×C32—22no—
271C22×C32#12011yescharacteristic
272C22×C32#12011yescharacteristic
273C22×C32#12111yescharacteristic
274C2×C3×D3—41no—
275C2×C3×D3—42no—
276C32×C4—42no—
277C32×C4#12011yescharacteristic
278C32×C4#12111yescharacteristic
279C32×C4#12111yescharacteristic
280C32×C4#12711yescharacteristic
281C3×Dic3—24no—
282C3×Dic3—42no—
283C3×Dic3—41no—
284C3×Dic3—42no—
285C2×#41—31no—
286C22×Q8—31no—
287C22×Q8C2×C3×D311yescharacteristic
288#137—62no—
289#137—62no—
290C2×Q16—61no—
291C2×SD16—61no—
292C2×M16C2×C3×D311yescharacteristic
293C2×M16C2×C3×D311yescharacteristic
294C4⋊Q8—62no—
295C4⋊Q8—62no—
296C4⋊Q8—61no—
297#124—61no—
298#123—62no—
299C22⋊Q8—62no—
300#117—31no—
301C2×C4⋊C4—62no—
302C2×C42—31no—
303#104—62no—
304#103—62no—
305#101—22no—
306C23×C3—21no—
307C23×C3—61no—
308C23×C3C2×D1211yescharacteristic
309C23×C3C2×C3×D411yescharacteristic
310C22×D3—21no—
311C3×Q8—42no—
312C3×Q8—42no—
313C3×Q8—42no—
314C3×Q8—42no—
315C3×Q8—41no—
316C3×Q8—41no—
317C3×Q8—41no—
318C3×Q8—41no—
319C3×Q8—41no—
320C3×Q8—41no—
321C3×Q8—41no—
322C3×Q8—41no—
323C3×Q8—62no—
324C3×Q8—61no—
325C3×Q8—62no—
326C3×Q8—61no—
327C3×Q8—121no—
328C3×Q8—121no—
329C3×D4—61no—
330C3×D4—61no—
331C3×D4—121no—
332C3×D4—121no—
333C2×C3×C4—24no—
334C2×C3×C4—22no—
335C2×C3×C4—22no—
336C2×C3×C4—22no—
337C2×C3×C4—22no—
338C2×C3×C4—22no—
339C2×C3×C4—22no—
340C2×C3×C4—21no—
341C2×C3×C4—21no—
342C2×C3×C4—21no—
343C2×C3×C4—21no—
344C2×C3×C4—21no—
345C2×C3×C4—21no—
346C2×C3×C4—42no—
347C2×C3×C4—42no—
348C2×C3×C4—64no—
349C2×C3×C4—62no—
350C2×C3×C4—62no—
351C2×C3×C4—62no—
352C2×C3×C4—61no—
353C2×C3×C4—121no—
354C2×C3×C4—121no—
355C2×C3×C4—121no—
356C2×C3×C4—121no—
357C2×C3×C4#23511yescharacteristic
358C2×C3×C4D3×D411yescharacteristic
359C2×C3×C4D3×D411yescharacteristic
360C2×C3×C4D3×D411yescharacteristic
361C2×C3×C4D3×D411yescharacteristic
362C2×C3×C4C2×#6711yescharacteristic
363C2×C3×C4C2×C3×D411yescharacteristic
364C2×C3×C4C2×C3×D411yescharacteristic
365C2×C3×C4C2×C3×D411yescharacteristic
366C2×C3×C4C2×C3×D411yescharacteristic
367C2×C3×C4C2×C3×D411yescharacteristic
368C2×C3×C4C3×#4111yescharacteristic
369#67—41no—
370#67—41no—
371C2×Dic3—24no—
372C2×Dic3—22no—
373C2×Dic3—22no—
374C2×Dic3—22no—
375C2×Dic3—21no—
376C2×Dic3—41no—
377C2×Dic3—41no—
378D12—21no—
379D12—21no—
380C4×D3—41no—
381C4×D3—41no—
382Dic6—22no—
383Dic6—21no—
384Dic6—22no—
385Dic6—21no—
386Dic6—41no—
387Dic6—41no—
388C3×C8—22no—
389C3×C8—22no—
390C3×C8—42no—
391C3×C8—42no—
392C3×C8—41no—
393C3×C8—41no—
394C2×C32—21no—
395C2×C32—21no—
396C2×C32#39211yescharacteristic
397C2×C32#45612yes—
398C3×D3—81no—
399#41—61no—
400#41—61no—
401#41—61no—
402#41—61no—
403C2×Q8—21no—
404C2×Q8—21no—
405C2×Q8—21no—
406C2×Q8—21no—
407C2×Q8—21no—
408C2×Q8—21no—
409C2×Q8—31no—
410C2×Q8—32no—
411C2×Q8—61no—
412C2×Q8—61no—
413C2×Q8—61no—
414C2×Q8—61no—
415C2×Q8—61no—
416C2×D4—31no—
417C2×D4—61no—
418C22×C4—61no—
419C22×C4—61no—
420C22×C4—61no—
421C22×C4C3×D1212yes—
422C22×C4C22×C3×D311yescharacteristic
423Q16—64no—
424SD16—64no—
425M16—21no—
426M16—21no—
427M16—21no—
428M16C3×#6712yes—
429C2×C8—21no—
430C2×C8—21no—
431C4⋊C4—32no—
432C4⋊C4—68no—
433C4⋊C4—64no—
434C22⋊C4—64no—
435C22⋊C4—61no—
436C42—32no—
437C42—61no—
438C42—61no—
439C22×C3—22no—
440C22×C3—22no—
441C22×C3—21no—
442C22×C3—21no—
443C22×C3—21no—
444C22×C3—42no—
445C22×C3—121no—
446C22×C3—122no—
447C22×C3#88211yescharacteristic
448C22×C3#88211yescharacteristic
449C22×C3#93011yescharacteristic
450C22×C3C3×#12011yescharacteristic
451C22×C3C3×#12011yescharacteristic
452C22×C3C3×#12111yescharacteristic
453C2×D3—41no—
454C2×D3—42no—
455C3×C4—21no—
456C3×C4—21no—
457C3×C4—21no—
458C3×C4—21no—
459C3×C4—44no—
460C3×C4—42no—
461C3×C4—42no—
462C3×C4—64no—
463C3×C4—121no—
464C3×C4—122no—
465C3×C4—122no—
466C3×C4#88411yescharacteristic
467C3×C4#88411yescharacteristic
468C3×C4#93711yescharacteristic
469C3×C4#94011yescharacteristic
470C3×C4C3×#12011yescharacteristic
471C3×C4C3×#12111yescharacteristic
472C3×C4C3×#12111yescharacteristic
473C3×C4C3×#12711yescharacteristic
474Dic3—24no—
475Dic3—42no—
476Dic3—41no—
477Dic3—42no—
478C32#200511yescharacteristic, complemented, Sylow
479C23—61no—
480C23C2×C3×D1211yescharacteristic
481Q8—41no—
482Q8—41no—
483Q8—41no—
484Q8—41no—
485Q8—62no—
486Q8—61no—
487Q8—62no—
488Q8—61no—
489Q8—121no—
490Q8—121no—
491D4—61no—
492D4—61no—
493D4—121no—
494D4—121no—
495C2×C4—22no—
496C2×C4—22no—
497C2×C4—22no—
498C2×C4—64no—
499C2×C4—62no—
500C2×C4—62no—
501C2×C4—61no—
502C2×C4—62no—
503C2×C4—121no—
504C2×C4—121no—
505C2×C4—121no—
506C2×C4—121no—
507C2×C4C3×#23511yescharacteristic
508C2×C4C3×D3×D411yescharacteristic
509C2×C4C3×D3×D411yescharacteristic
510C2×C4C3×D3×D411yescharacteristic
511C2×C4C3×D3×D411yescharacteristic
512C2×C4C2×C3×#6711yescharacteristic
513C8—22no—
514C8—41no—
515C2×C3—21no—
516C2×C3—21no—
517C2×C3—21no—
518C2×C3—21no—
519C2×C3—21no—
520C2×C3—22no—
521C2×C3—41no—
522C2×C3—41no—
523C2×C3—241no—
524C2×C3#475212yes—
525C2×C3#496011yescharacteristic
526C2×C3C3×#39211yescharacteristic
527C2×C3C3×#45612yes—
528D3—81no—
529C22—22no—
530C22—121no—
531C22—122no—
532C22C3×#88211yescharacteristic
533C22C3×#88211yescharacteristic
534C22C3×#93011yescharacteristic
535C4—42no—
536C4—64no—
537C4—121no—
538C4—122no—
539C4—122no—
540C4C3×#88411yescharacteristic
541C4C3×#88411yescharacteristic
542C4C3×#93711yescharacteristic
543C4C3×#94011yescharacteristic
544C3—21no—
545C3#7011911yescharacteristic, direct product factor
546C3C3×#200511yescharacteristic, complemented
547C2—21no—
548C2—21no—
549C2—241no—
550C2C3×#475212yes—
551C2C3×#496011yescharacteristic
subgroupG/H
centerC22×C3#882
commutator, cosocleC22×C3×C4C23×C3
FrattiniC22×C4C22×C3×D3
FittingC2×C32×#101C2
socleC22×C32#120
prime radicalC2×C3×#235C22
hypercenterC2×C3×#101D3
hypocenterC3C3×#2005
LCSG ▷ C22×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C22×C3×C4 ◁ C2×C3×#101

Complements

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

NH ≅ G/Ntype
2. C2×C3×#944C2semidirect
4. C2×C32×#101C2semidirect
6. C3×#5120C2semidirect
7. C3×#4555C2semidirect
9. #70119C3direct (N × H)
35. C2×#944C2×C3semidirect
40. C2×C3×#101D3semidirect
41. C2×C3×#101C2×C3semidirect
43. #5120C2×C3semidirect
45. #4555C2×C3semidirect
174. C2×#101C3×D3semidirect
478. C32#2005semidirect
545. C3#70119direct (N × H)
546. C3C3×#2005semidirect

Maximal subgroups

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

subgroupindex
C3×#58162
C2×C3×#9442
C2×C3×#9092
C2×C32×#1012
C2×C3×#8252
C3×#51202
C3×#45552
C3×#20053
#701193