Finite Group Databasebeta

← C3×#11070 #10629677

Subgroups — C3×#11070 #10629677

Order 768.

1202 conjugacy classes of subgroups.

The subgroup lattice has 476 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#2315C211yesmaximal, characteristic
2C2×C3×#381C212yesmaximal
3C2×C3×#381C211yesmaximal, characteristic
4C2×C3×#342C212yesmaximal
5C2×C3×#342C211yesmaximal, characteristic
6#11070C311yesmaximal, characteristic, direct product factor, Sylow
7C24×C3×C4C2211yescharacteristic
8C22×C3×C22⋊C4C2212yes—
9C22×C3×C22⋊C4C2211yescharacteristic
10C22×C3×C22⋊C4C2212yes—
11C22×C3×C22⋊C4C2211yescharacteristic
12C3×#385—24no—
13C3×#381—24no—
14C3×#381—24no—
15C3×#381—22no—
16C3×#381C414yescomplemented
17C3×#380—22no—
18C2×C3×#95—24no—
19C2×C3×#95—22no—
20C3×#342—22no—
21C3×#342—24no—
22#2315C2×C311yescharacteristic
23C2×#381C2×C312yes—
24C2×#381C2×C311yescharacteristic
25C2×#342C2×C312yes—
26C2×#342C2×C311yescharacteristic
27C25×C3C2311yescharacteristic
28C23×C3×C4—21no—
29C23×C3×C4—22no—
30C23×C3×C4—21no—
31C23×C3×C4—22no—
32C23×C3×C4—21no—
33C23×C3×C4—21no—
34C23×C3×C4—22no—
35C23×C3×C4—22no—
36C23×C3×C4—21no—
37C23×C3×C4—22no—
38C23×C3×C4C2×C412yes—
39C23×C3×C4D412yes—
40C23×C3×C4D414yes—
41C23×C3×C4D412yes—
42C23×C3×C4Q812yes—
43C2×C3×C4⋊C4—24no—
44C2×C3×C22⋊C4—22no—
45C2×C3×C22⋊C4—22no—
46C2×C3×C22⋊C4—22no—
47C2×C3×C22⋊C4—22no—
48C2×C3×C22⋊C4—22no—
49C2×C3×C22⋊C4—22no—
50C2×C3×C22⋊C4—22no—
51C2×C3×C22⋊C4—22no—
52C2×C3×C22⋊C4—22no—
53C2×C3×C22⋊C4—22no—
54C2×C3×C22⋊C4—21no—
55C2×C3×C22⋊C4—22no—
56C2×C3×C22⋊C4—22no—
57C2×C3×C22⋊C4—22no—
58C2×C3×C22⋊C4—22no—
59C2×C3×C22⋊C4—22no—
60C2×C3×C22⋊C4C2×C412yes—
61C2×C3×C22⋊C4C2×C412yes—
62C2×C3×C22⋊C4D414yes—
63C2×C3×C22⋊C4D412yes—
64C3×#95—216no—
65C3×#95—24no—
66C3×#95—28no—
67C24×C4C22×C311yescharacteristic
68C22×C22⋊C4C22×C312yes—
69C22×C22⋊C4C22×C311yescharacteristic
70C22×C22⋊C4C22×C312yes—
71C22×C22⋊C4C22×C311yescharacteristic
72#385—24no—
73#381—24no—
74#381—24no—
75#381—22no—
76#381C3×C414yescomplemented
77#380—22no—
78C2×#95—24no—
79C2×#95—22no—
80#342—22no—
81#342—24no—
82C24×C3—44no—
83C24×C3C22×C411yescharacteristic
84C24×C3C2×D411yescharacteristic
85C24×C3C2×D412yes—
86C24×C3C2×D411yescharacteristic
87C24×C3C2×D411yescharacteristic
88C24×C3C2×D412yes—
89C24×C3C2×Q811yescharacteristic
90C24×C3#4111yescharacteristic
91C24×C3#4111yescharacteristic
92C24×C3#4112yes—
93C24×C3#4112yes—
94C22×C3×C4—22no—
95C22×C3×C4—22no—
96C22×C3×C4—24no—
97C22×C3×C4—24no—
98C22×C3×C4—24no—
99C22×C3×C4—22no—
100C22×C3×C4—22no—
101C22×C3×C4—22no—
102C22×C3×C4—22no—
103C22×C3×C4—22no—
104C22×C3×C4—24no—
105C22×C3×C4—24no—
106C22×C3×C4—24no—
107C22×C3×C4—22no—
108C22×C3×C4—22no—
109C22×C3×C4—24no—
110C22×C3×C4—24no—
111C22×C3×C4—24no—
112C22×C3×C4—24no—
113C22×C3×C4—41no—
114C22×C3×C4—42no—
115C22×C3×C4—42no—
116C22×C3×C4—42no—
117C22×C3×C4—41no—
118C22×C3×C4—42no—
119C22×C3×C4—42no—
120C22×C3×C4—41no—
121C22×C3×C4—42no—
122C22×C3×C4—41no—
123C22×C3×C4—44no—
124C22×C3×C4—48no—
125C22×C3×C4—44no—
126C22×C3×C4—48no—
127C22×C3×C4—42no—
128C22×C3×C4—41no—
129C22×C3×C4—42no—
130C22×C3×C4—41no—
131C22×C3×C4C22⋊C414yes—
132C22×C3×C4C4⋊C414yescomplemented
133C3×C4⋊C4—84no—
134C3×C22⋊C4—24no—
135C3×C22⋊C4—24no—
136C3×C22⋊C4—24no—
137C3×C22⋊C4—24no—
138C3×C22⋊C4—24no—
139C3×C22⋊C4—42no—
140C3×C22⋊C4—42no—
141C3×C22⋊C4—42no—
142C3×C22⋊C4—42no—
143C3×C22⋊C4—42no—
144C3×C22⋊C4—42no—
145C3×C22⋊C4—42no—
146C25C23×C311yescharacteristic
147C23×C4—21no—
148C23×C4—22no—
149C23×C4—21no—
150C23×C4—22no—
151C23×C4—21no—
152C23×C4—21no—
153C23×C4—22no—
154C23×C4—22no—
155C23×C4—21no—
156C23×C4—22no—
157C23×C4C2×C3×C412yes—
158C23×C4C3×D412yes—
159C23×C4C3×D414yes—
160C23×C4C3×D412yes—
161C23×C4C3×Q812yes—
162C2×C4⋊C4—24no—
163C2×C22⋊C4—22no—
164C2×C22⋊C4—22no—
165C2×C22⋊C4—22no—
166C2×C22⋊C4—22no—
167C2×C22⋊C4—22no—
168C2×C22⋊C4—22no—
169C2×C22⋊C4—22no—
170C2×C22⋊C4—22no—
171C2×C22⋊C4—22no—
172C2×C22⋊C4—22no—
173C2×C22⋊C4—22no—
174C2×C22⋊C4—21no—
175C2×C22⋊C4—22no—
176C2×C22⋊C4—22no—
177C2×C22⋊C4—22no—
178C2×C22⋊C4—22no—
179C2×C22⋊C4C2×C3×C412yes—
180C2×C22⋊C4C2×C3×C412yes—
181C2×C22⋊C4C3×D414yes—
182C2×C22⋊C4C3×D412yes—
183#95—216no—
184#95—24no—
185#95—28no—
186C23×C3—24no—
187C23×C3—28no—
188C23×C3—42no—
189C23×C3—42no—
190C23×C3—42no—
191C23×C3—44no—
192C23×C3—42no—
193C23×C3—44no—
194C23×C3—42no—
195C23×C3—42no—
196C23×C3—44no—
197C23×C3C2×C22⋊C411yescharacteristic
198C23×C3C2×C4⋊C411yescharacteristic
199C23×C3#11711yescharacteristic
200C23×C3C4×D412yes—
201C23×C3C4×D412yes—
202C23×C3#12012yes—
203C23×C3#12011yescharacteristic
204C23×C3#12111yescharacteristic
205C23×C3#12112yes—
206C23×C3#12112yes—
207C23×C3#12111yescharacteristic
208C23×C3#12112yes—
209C23×C3C22⋊Q811yescharacteristic
210C23×C3C22⋊Q812yes—
211C23×C3C22⋊Q811yescharacteristic
212C23×C3C22⋊Q812yes—
213C23×C3#12311yescharacteristic
214C23×C3#12312yes—
215C23×C3#12312yes—
216C23×C3#12412yes—
217C23×C3#12411yescharacteristic
218C23×C3#12612yes—
219C23×C3#12711yescharacteristic
220C2×C3×C4—24no—
221C2×C3×C4—28no—
222C2×C3×C4—24no—
223C2×C3×C4—42no—
224C2×C3×C4—44no—
225C2×C3×C4—42no—
226C2×C3×C4—42no—
227C2×C3×C4—42no—
228C2×C3×C4—44no—
229C2×C3×C4—44no—
230C2×C3×C4—42no—
231C2×C3×C4—42no—
232C2×C3×C4—44no—
233C2×C3×C4—44no—
234C2×C3×C4—44no—
235C2×C3×C4—48no—
236C2×C3×C4—48no—
237C2×C3×C4—42no—
238C2×C3×C4—44no—
239C2×C3×C4—44no—
240C2×C3×C4—48no—
241C2×C3×C4—82no—
242C2×C3×C4—84no—
243C2×C3×C4—82no—
244C2×C3×C4—82no—
245C2×C3×C4—84no—
246C2×C3×C4—84no—
247C24—44no—
248C24C22×C3×C411yescharacteristic
249C24C2×C3×D411yescharacteristic
250C24C2×C3×D412yes—
251C24C2×C3×D411yescharacteristic
252C24C2×C3×D411yescharacteristic
253C24C2×C3×D412yes—
254C24C2×C3×Q811yescharacteristic
255C24C3×#4111yescharacteristic
256C24C3×#4111yescharacteristic
257C24C3×#4112yes—
258C24C3×#4112yes—
259C22×C4—22no—
260C22×C4—22no—
261C22×C4—24no—
262C22×C4—24no—
263C22×C4—24no—
264C22×C4—22no—
265C22×C4—22no—
266C22×C4—22no—
267C22×C4—22no—
268C22×C4—22no—
269C22×C4—24no—
270C22×C4—24no—
271C22×C4—24no—
272C22×C4—22no—
273C22×C4—22no—
274C22×C4—24no—
275C22×C4—24no—
276C22×C4—24no—
277C22×C4—24no—
278C22×C4—41no—
279C22×C4—42no—
280C22×C4—42no—
281C22×C4—42no—
282C22×C4—41no—
283C22×C4—42no—
284C22×C4—42no—
285C22×C4—41no—
286C22×C4—42no—
287C22×C4—41no—
288C22×C4—44no—
289C22×C4—48no—
290C22×C4—48no—
291C22×C4—44no—
292C22×C4—42no—
293C22×C4—41no—
294C22×C4—42no—
295C22×C4—41no—
296C22×C4C3×C22⋊C414yes—
297C22×C4C3×C4⋊C414yescomplemented
298C4⋊C4—84no—
299C22⋊C4—24no—
300C22⋊C4—24no—
301C22⋊C4—24no—
302C22⋊C4—24no—
303C22⋊C4—24no—
304C22⋊C4—42no—
305C22⋊C4—42no—
306C22⋊C4—42no—
307C22⋊C4—42no—
308C22⋊C4—42no—
309C22⋊C4—42no—
310C22⋊C4—42no—
311C22×C3—22no—
312C22×C3—24no—
313C22×C3—22no—
314C22×C3—24no—
315C22×C3—24no—
316C22×C3—24no—
317C22×C3—22no—
318C22×C3—22no—
319C22×C3—22no—
320C22×C3—24no—
321C22×C3—22no—
322C22×C3—24no—
323C22×C3—41no—
324C22×C3—41no—
325C22×C3—42no—
326C22×C3—42no—
327C22×C3—41no—
328C22×C3—41no—
329C22×C3—42no—
330C22×C3—42no—
331C22×C3—42no—
332C22×C3—42no—
333C22×C3#38011yescharacteristic
334C22×C3#38512yes—
335C22×C3#38611yescharacteristic
336C22×C3#38812yes—
337C22×C3#39011yescharacteristic
338C22×C3#39211yescharacteristic
339C22×C3#39311yescharacteristic
340C22×C3#39412yes—
341C22×C3#39612yes—
342C22×C3#39711yescharacteristic
343C22×C3#39911yescharacteristic
344C22×C3#45814yes—
345C3×C4—44no—
346C3×C4—44no—
347C3×C4—82no—
348C3×C4—84no—
349C3×C4—84no—
350C23—28no—
351C23—24no—
352C23—42no—
353C23—42no—
354C23—44no—
355C23—42no—
356C23—42no—
357C23—42no—
358C23—42no—
359C23—44no—
360C23—44no—
361C23C2×C3×C22⋊C411yescharacteristic
362C23C2×C3×C4⋊C411yescharacteristic
363C23C3×#11711yescharacteristic
364C23C3×C4×D412yes—
365C23C3×C4×D412yes—
366C23C3×#12012yes—
367C23C3×#12011yescharacteristic
368C23C3×#12111yescharacteristic
369C23C3×#12112yes—
370C23C3×#12112yes—
371C23C3×#12111yescharacteristic
372C23C3×#12112yes—
373C23C3×C22⋊Q811yescharacteristic
374C23C3×C22⋊Q812yes—
375C23C3×C22⋊Q811yescharacteristic
376C23C3×C22⋊Q812yes—
377C23C3×#12311yescharacteristic
378C23C3×#12312yes—
379C23C3×#12312yes—
380C23C3×#12412yes—
381C23C3×#12411yescharacteristic
382C23C3×#12612yes—
383C23C3×#12711yescharacteristic
384C2×C4—24no—
385C2×C4—28no—
386C2×C4—24no—
387C2×C4—42no—
388C2×C4—44no—
389C2×C4—42no—
390C2×C4—42no—
391C2×C4—42no—
392C2×C4—44no—
393C2×C4—44no—
394C2×C4—42no—
395C2×C4—42no—
396C2×C4—44no—
397C2×C4—44no—
398C2×C4—48no—
399C2×C4—44no—
400C2×C4—48no—
401C2×C4—42no—
402C2×C4—44no—
403C2×C4—44no—
404C2×C4—48no—
405C2×C4—82no—
406C2×C4—82no—
407C2×C4—82no—
408C2×C4—84no—
409C2×C4—84no—
410C2×C4—84no—
411C2×C3—21no—
412C2×C3—22no—
413C2×C3—21no—
414C2×C3—22no—
415C2×C3—22no—
416C2×C3—22no—
417C2×C3—21no—
418C2×C3—21no—
419C2×C3#143911yescharacteristic
420C2×C3#189012yes—
421C2×C3#202212yes—
422C2×C3#203012yes—
423C22—24no—
424C22—24no—
425C22—22no—
426C22—22no—
427C22—22no—
428C22—24no—
429C22—22no—
430C22—24no—
431C22—22no—
432C22—24no—
433C22—22no—
434C22—24no—
435C22—41no—
436C22—41no—
437C22—42no—
438C22—42no—
439C22—41no—
440C22—41no—
441C22—42no—
442C22—42no—
443C22—42no—
444C22—42no—
445C22C3×#38011yescharacteristic
446C22C3×#38512yes—
447C22C3×#38611yescharacteristic
448C22C3×#38812yes—
449C22C3×#39011yescharacteristic
450C22C3×#39211yescharacteristic
451C22C3×#39311yescharacteristic
452C22C3×#39412yes—
453C22C3×#39612yes—
454C22C3×#39711yescharacteristic
455C22C3×#39911yescharacteristic
456C22C3×#45814yes—
457C4—44no—
458C4—44no—
459C4—82no—
460C4—84no—
461C4—84no—
462C3#1107011yescharacteristic, direct product factor, Sylow
463C2—21no—
464C2—22no—
465C2—21no—
466C2—22no—
467C2—22no—
468C2—22no—
469C2—21no—
470C2—21no—
471C2C3×#143911yescharacteristic
472C2C3×#189012yes—
473C2C3×#202212yes—
474C2C3×#203012yes—
subgroupG/H
center, socleC23×C3#120
commutatorC24C22×C3×C4
Frattini, cosocleC25C23×C3
prime radicalC25×C3C23
LCSG ▷ C24 ▷ C2 ▷ C1
UCSC1 ◁ C23×C3 ◁ C25×C3 ◁ G

Complements

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

NH ≅ G/Ntype
6. #11070C3direct (N × H)
16. C3×#381C4semidirect
76. #381C3×C4semidirect
132. C22×C3×C4C4⋊C4semidirect
297. C22×C4C3×C4⋊C4semidirect
462. C3#11070direct (N × H)

Maximal subgroups

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

subgroupindex
C3×#23152
C2×C3×#3812
C2×C3×#3422
#110703