Finite Group Databasebeta

← C3×#70973 #11778382

Subgroups — C3×#70973 #11778382

Order 1152.

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

normal subgroups only

This group has 599 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×#5617C211yesmaximal, characteristic
2C32×#448C211yesmaximal, characteristic, complemented
3C3×#5231C211yesmaximal, characteristic, complemented
4C3×#5228C211yesmaximal, characteristic, complemented
5C3×#4537C211yesmaximal, characteristic, complemented
6C3×#4468C211yesmaximal, characteristic, complemented
7C3×#4467C211yesmaximal, characteristic, complemented
8C3×#1606—31nomaximal
9#70973C311yesmaximal, characteristic, direct product factor
10C22×C32×Q8C2211yescharacteristic
11C2×C32×SD16—21no—
12C32×#121C2211yescharacteristic
13C2×C3×#216—21no—
14C3×#939—21no—
15C3×#937—21no—
16C3×D4×Dic3—21no—
17C2×C3×(C2×D3)⋊C4—21no—
18C2×C3×(C2×D3)⋊C4C2211yescharacteristic
19C3×#924C2211yescharacteristic
20C3×#898—21no—
21C3×#886—21no—
22C3×#885—21no—
23C32×#103—21no—
24C32×C22⋊C8C2211yescharacteristic
25C3×#835—21no—
26C3×C3⋊#95—21no—
27C3×C3⋊#95C2211yescharacteristic
28C3×#830C2211yescharacteristic
29C3×#538—31no—
30#5617C2×C311yescharacteristic
31C3×#451—31no—
32C3×#448—21no—
33C3×#448D311yescharacteristic, complemented
34C3×#448C2×C311yescharacteristic, complemented
35C3×#393—31no—
36#5231C2×C311yescharacteristic, complemented
37#5228C2×C311yescharacteristic, complemented
38C3×#328—31no—
39C3×#327—31no—
40C3×#323—31no—
41#4537C2×C311yescharacteristic, complemented
42#4468C2×C311yescharacteristic, complemented
43#4467C2×C311yescharacteristic, complemented
44C23×C3×D3D411yescharacteristic
45C2×C32×Q8—21no—
46C2×C32×Q8—21no—
47C2×C32×Q8—42no—
48C2×C32×D4—21no—
49C2×C32×D4D411yescharacteristic
50C22×C32×C4—21no—
51C22×C32×C4C2311yescharacteristic
52C2×C3×#67—21no—
53C2×C3×#67—21no—
54C22×C3×Dic3—21no—
55C22×C3×Dic3—21no—
56C22×C3×Dic3D411yescharacteristic
57C2×C3×Dic6D411yescharacteristic
58C32×SD16—42no—
59C2×C32×C8—21no—
60C32×C4⋊C4D411yescharacteristic
61C32×C22⋊C4—21no—
62C3×#217—21no—
63C3×#217—21no—
64C3×#216—42no—
65C3×(C2×D3)⋊C4—21no—
66C3×(C2×D3)⋊C4—21no—
67C3×(C2×D3)⋊C4—21no—
68C3×(C2×D3)⋊C4—21no—
69C3×(C2×D3)⋊C4—42no—
70C3×C4⋊Dic3—21no—
71C3×C4⋊Dic3D411yescharacteristic
72C3×Dic3⋊C4—21no—
73C3×C4×Dic3—21no—
74C2×C3×C3⋊C8—21no—
75#1606—31noSylow
76C22×C3×Q8—21no—
77C22×C3×Q8C2×D311yescharacteristic
78C22×C3×Q8C22×C311yescharacteristic
79C2×C3×Q16—61no—
80C2×C3×SD16—22no—
81C2×C3×SD16—21no—
82C2×C3×SD16—21no—
83C3×#126—61no—
84C3×#124—61no—
85C3×#123—61no—
86C3×C22⋊Q8—31no—
87C3×#121—21no—
88C3×#121—61no—
89C3×#121C2×D311yescharacteristic
90C3×#121C22×C311yescharacteristic
91C3×#120—61no—
92C3×C4×D4—61no—
93C2×C3×C22⋊C4—31no—
94C2×C3×C22⋊C4—61no—
95C2×#216—21no—
96#939—21no—
97#937—21no—
98D4×Dic3—21no—
99C2×(C2×D3)⋊C4—21no—
100C2×(C2×D3)⋊C4C22×C311yescharacteristic
101#924C22×C311yescharacteristic
102#898—21no—
103#886—21no—
104#885—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×C32—21no—
120C23×C32C2×D411yescharacteristic
121C22×C3×D3—21no—
122C22×C3×D3—21no—
123C22×C3×D3—21no—
124C22×C3×D3—41no—
125C22×C3×D3—41no—
126C32×Q8—22no—
127C32×Q8—22no—
128C32×Q8—41no—
129C32×Q8—41no—
130C32×D4—41no—
131C32×D4—41no—
132C32×D4—41no—
133C2×C32×C4—22no—
134C2×C32×C4—21no—
135C2×C32×C4—41no—
136C2×C32×C4—41no—
137C2×C32×C4—41no—
138C2×C32×C4C2×D411yescharacteristic
139C2×C32×C4C2×D411yescharacteristic
140C3×#67—81no—
141C3×#67—81no—
142C2×C3×Dic3—21no—
143C2×C3×Dic3—21no—
144C2×C3×Dic3—21no—
145C2×C3×Dic3—41no—
146C2×C3×Dic3—41no—
147C2×C3×Dic3—41no—
148C2×C3×Dic3—41no—
149C2×C3×Dic3—81no—
150C3×Dic6—41no—
151C32×C8—41no—
152C3×C3⋊C8—41no—
153#538—31no—
154#451—31no—
155#448C3×D311yescharacteristic, complemented
156#393—31no—
157#328—31no—
158#327—31no—
159#323—31no—
160C24×C3—31no—
161C23×D3C3×D411yescharacteristic
162C2×C3×Q8—22no—
163C2×C3×Q8—21no—
164C2×C3×Q8—21no—
165C2×C3×Q8—21no—
166C2×C3×Q8—21no—
167C2×C3×Q8—31no—
168C2×C3×Q8—41no—
169C2×C3×Q8—42no—
170C2×C3×Q8—42no—
171C2×C3×Q8—44no—
172C2×C3×D4—21no—
173C2×C3×D4—21no—
174C2×C3×D4—21no—
175C2×C3×D4—41no—
176C2×C3×D4—61no—
177C2×C3×D4—61no—
178C2×C3×D4#6711yescharacteristic
179C2×C3×D4C3×D411yescharacteristic
180C22×C3×C4—21no—
181C22×C3×C4—21no—
182C22×C3×C4—21no—
183C22×C3×C4—31no—
184C22×C3×C4—41no—
185C22×C3×C4—61no—
186C22×C3×C4—61no—
187C22×C3×C4C22×D311yescharacteristic
188C22×C3×C4C23×C311yescharacteristic
189C2×#67—21no—
190C2×#67—21no—
191C22×Dic3—21no—
192C22×Dic3—21no—
193C22×Dic3C3×D411yescharacteristic
194C2×Dic6C3×D411yescharacteristic
195C3×Q16—122no—
196C3×SD16—42no—
197C3×SD16—42no—
198C3×SD16—44no—
199C2×C3×C8—22no—
200C2×C3×C8—21no—
201C2×C3×C8—21no—
202C2×C3×C8—61no—
203C3×C4⋊C4—21no—
204C3×C4⋊C4—31no—
205C3×C4⋊C4—61no—
206C3×C4⋊C4—61no—
207C3×C4⋊C4#6711yescharacteristic
208C3×C4⋊C4C3×D411yescharacteristic
209C3×C22⋊C4—21no—
210C3×C22⋊C4—21no—
211C3×C22⋊C4—41no—
212C3×C22⋊C4—61no—
213C3×C22⋊C4—61no—
214C3×C22⋊C4—61no—
215C3×C22⋊C4—61no—
216C3×C22⋊C4—61no—
217C3×C22⋊C4—61no—
218C3×C22⋊C4—122no—
219C3×C42—61no—
220#217—21no—
221#217—21no—
222#216—42no—
223(C2×D3)⋊C4—21no—
224(C2×D3)⋊C4—21no—
225(C2×D3)⋊C4—21no—
226(C2×D3)⋊C4—21no—
227(C2×D3)⋊C4—42no—
228C4⋊Dic3—21no—
229C4⋊Dic3C3×D411yescharacteristic
230Dic3⋊C4—21no—
231C4×Dic3—21no—
232C2×C3⋊C8—21no—
233C22×C32—21no—
234C22×C32—21no—
235C22×C32—41no—
236C22×C32—41no—
237C22×C32—41no—
238C22×C32#12011yescharacteristic
239C22×C32#13511yescharacteristic
240C22×C32#13711yescharacteristic
241C2×C3×D3—42no—
242C2×C3×D3—41no—
243C2×C3×D3—41no—
244C2×C3×D3—41no—
245C2×C3×D3—81no—
246C32×C4—21no—
247C32×C4—21no—
248C32×C4—42no—
249C32×C4—41no—
250C3×Dic3—41no—
251C3×Dic3—41no—
252C3×Dic3—41no—
253C3×Dic3—81no—
254C22×Q8C2×C3×D311yescharacteristic
255C2×Q16—61no—
256C2×SD16—21no—
257#126—61no—
258#124—61no—
259#123—61no—
260C22⋊Q8—31no—
261#121—61no—
262#121C2×C3×D311yescharacteristic
263#120—61no—
264C4×D4—61no—
265C2×C22⋊C4—31no—
266C2×C22⋊C4—61no—
267#103—21no—
268#103—61no—
269C22⋊C8—31no—
270C22⋊C8C2×C3×D311yescharacteristic
271#95—31no—
272#95—61no—
273C23×C3—21no—
274C23×C3—21no—
275C23×C3—21no—
276C23×C3—41no—
277C23×C3—61no—
278C23×C3—61no—
279C23×C3—61no—
280C23×C3—121no—
281C23×C3—121no—
282C23×C3D3×D411yescharacteristic
283C23×C3C2×C3×D411yescharacteristic
284C22×D3—21no—
285C22×D3—21no—
286C22×D3—21no—
287C22×D3—41no—
288C22×D3—41no—
289C3×Q8—22no—
290C3×Q8—24no—
291C3×Q8—22no—
292C3×Q8—22no—
293C3×Q8—22no—
294C3×Q8—42no—
295C3×Q8—42no—
296C3×Q8—41no—
297C3×Q8—41no—
298C3×Q8—41no—
299C3×Q8—41no—
300C3×Q8—42no—
301C3×Q8—121no—
302C3×D4—41no—
303C3×D4—41no—
304C3×D4—42no—
305C3×D4—41no—
306C3×D4—41no—
307C3×D4—41no—
308C3×D4—41no—
309C3×D4—81no—
310C3×D4—81no—
311C3×D4—241no—
312C3×D4—241no—
313C2×C3×C4—22no—
314C2×C3×C4—22no—
315C2×C3×C4—21no—
316C2×C3×C4—21no—
317C2×C3×C4—21no—
318C2×C3×C4—21no—
319C2×C3×C4—42no—
320C2×C3×C4—41no—
321C2×C3×C4—41no—
322C2×C3×C4—41no—
323C2×C3×C4—42no—
324C2×C3×C4—41no—
325C2×C3×C4—41no—
326C2×C3×C4—42no—
327C2×C3×C4—42no—
328C2×C3×C4—41no—
329C2×C3×C4—41no—
330C2×C3×C4—61no—
331C2×C3×C4—61no—
332C2×C3×C4—61no—
333C2×C3×C4—121no—
334C2×C3×C4—121no—
335C2×C3×C4—121no—
336C2×C3×C4—121no—
337C2×C3×C4—241no—
338C2×C3×C4D3×D411yescharacteristic
339C2×C3×C4C2×#6711yescharacteristic
340C2×C3×C4C2×C3×D411yescharacteristic
341C2×C3×C4C2×C3×D411yescharacteristic
342#67—81no—
343#67—81no—
344C2×Dic3—21no—
345C2×Dic3—21no—
346C2×Dic3—21no—
347C2×Dic3—41no—
348C2×Dic3—41no—
349C2×Dic3—41no—
350C2×Dic3—41no—
351C2×Dic3—81no—
352Dic6—41no—
353C3×C8—42no—
354C3×C8—41no—
355C3×C8—41no—
356C3×C8—121no—
357C3⋊C8—41no—
358C2×C32—21no—
359C2×C32—21no—
360C2×C32—81no—
361C2×C32#45211yescharacteristic
362C2×C32#45511yescharacteristic
363C2×C32B(4,𝔽2)11yescharacteristic
364C3×D3—81no—
365C24—31no—
366C2×Q8—21no—
367C2×Q8—21no—
368C2×Q8—31no—
369C2×Q8—42no—
370C2×D4—21no—
371C2×D4—61no—
372C2×D4—61no—
373C2×D4C3×#6711yescharacteristic
374C22×C4—21no—
375C22×C4—31no—
376C22×C4—61no—
377C22×C4—61no—
378C22×C4C22×C3×D311yescharacteristic
379Q16—122no—
380SD16—42no—
381C2×C8—21no—
382C2×C8—61no—
383C4⋊C4—31no—
384C4⋊C4—61no—
385C4⋊C4—61no—
386C4⋊C4C3×#6711yescharacteristic
387C22⋊C4—21no—
388C22⋊C4—61no—
389C22⋊C4—61no—
390C22⋊C4—61no—
391C22⋊C4—61no—
392C22⋊C4—61no—
393C22⋊C4—61no—
394C22⋊C4—122no—
395C42—61no—
396C22×C3—21no—
397C22×C3—21no—
398C22×C3—21no—
399C22×C3—21no—
400C22×C3—21no—
401C22×C3—21no—
402C22×C3—21no—
403C22×C3—41no—
404C22×C3—41no—
405C22×C3—41no—
406C22×C3—41no—
407C22×C3—41no—
408C22×C3—41no—
409C22×C3—41no—
410C22×C3—41no—
411C22×C3—81no—
412C22×C3—81no—
413C22×C3—81no—
414C22×C3—122no—
415C22×C3—121no—
416C22×C3—121no—
417C22×C3—121no—
418C22×C3—241no—
419C22×C3#91511yescharacteristic
420C22×C3#91611yescharacteristic
421C22×C3#93711yescharacteristic
422C22×C3C3×#12011yescharacteristic
423C22×C3C3×#13511yescharacteristic
424C22×C3C3×#13711yescharacteristic
425C2×D3—42no—
426C2×D3—41no—
427C2×D3—41no—
428C2×D3—41no—
429C2×D3—81no—
430C3×C4—22no—
431C3×C4—21no—
432C3×C4—21no—
433C3×C4—21no—
434C3×C4—21no—
435C3×C4—41no—
436C3×C4—44no—
437C3×C4—41no—
438C3×C4—42no—
439C3×C4—41no—
440C3×C4—42no—
441C3×C4—81no—
442C3×C4—121no—
443C3×C4—121no—
444C3×C4—121no—
445C3×C4—241no—
446Dic3—41no—
447Dic3—41no—
448Dic3—41no—
449Dic3—81no—
450C32#160611yescharacteristic, complemented, Sylow
451C23—21no—
452C23—61no—
453C23—61no—
454C23—61no—
455C23—121no—
456C23—121no—
457C23C3×D3×D411yescharacteristic
458Q8—22no—
459Q8—22no—
460Q8—41no—
461Q8—41no—
462Q8—121no—
463D4—41no—
464D4—41no—
465D4—41no—
466D4—241no—
467D4—241no—
468C2×C4—22no—
469C2×C4—21no—
470C2×C4—41no—
471C2×C4—41no—
472C2×C4—41no—
473C2×C4—61no—
474C2×C4—61no—
475C2×C4—61no—
476C2×C4—121no—
477C2×C4—121no—
478C2×C4—121no—
479C2×C4—121no—
480C2×C4—241no—
481C2×C4C3×D3×D411yescharacteristic
482C2×C4C2×C3×#6711yescharacteristic
483C8—41no—
484C8—121no—
485C2×C3—21no—
486C2×C3—21no—
487C2×C3—21no—
488C2×C3—21no—
489C2×C3—21no—
490C2×C3—21no—
491C2×C3—21no—
492C2×C3—41no—
493C2×C3—41no—
494C2×C3—81no—
495C2×C3—81no—
496C2×C3—161no—
497C2×C3—241no—
498C2×C3#503211yescharacteristic
499C2×C3#517311yescharacteristic
500C2×C3#520211yescharacteristic
501C2×C3C3×#45211yescharacteristic
502C2×C3C3×#45511yescharacteristic
503C2×C3C3×B(4,𝔽2)11yescharacteristic
504D3—81no—
505C22—21no—
506C22—21no—
507C22—41no—
508C22—41no—
509C22—41no—
510C22—122no—
511C22—121no—
512C22—121no—
513C22—121no—
514C22—241no—
515C22C3×#91511yescharacteristic
516C22C3×#91611yescharacteristic
517C22C3×#93711yescharacteristic
518C4—21no—
519C4—21no—
520C4—41no—
521C4—42no—
522C4—121no—
523C4—121no—
524C4—121no—
525C4—241no—
526C3—21no—
527C3#7097311yescharacteristic, direct product factor
528C3C3×#160611yescharacteristic, complemented
529C2—21no—
530C2—21no—
531C2—81no—
532C2—241no—
533C2C3×#503211yescharacteristic
534C2C3×#517311yescharacteristic
535C2C3×#520211yescharacteristic
subgroupG/H
centerC22×C3#937
commutator, cosocleC22×C3×C4C23×C3
FrattiniC22×C4C22×C3×D3
FittingC32×#448C2
socleC22×C32#120
prime radicalC3×#5617C2
hypercenterC3×#448D3
hypocenterC3C3×#1606
LCSG ▷ C22×C3×C4 ▷ C22×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C22×C3×C4 ◁ C3×#448

Complements

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

NH ≅ G/Ntype
2. C32×#448C2semidirect
3. C3×#5231C2semidirect
4. C3×#5228C2semidirect
5. C3×#4537C2semidirect
6. C3×#4468C2semidirect
7. C3×#4467C2semidirect
9. #70973C3direct (N × H)
33. C3×#448D3semidirect
34. C3×#448C2×C3semidirect
36. #5231C2×C3semidirect
37. #5228C2×C3semidirect
41. #4537C2×C3semidirect
42. #4468C2×C3semidirect
43. #4467C2×C3semidirect
155. #448C3×D3semidirect
450. C32#1606semidirect
527. C3#70973direct (N × H)
528. C3C3×#1606semidirect

Maximal subgroups

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

subgroupindex
C3×#56172
C32×#4482
C3×#52312
C3×#52282
C3×#45372
C3×#44682
C3×#44672
C3×#16063
#709733