Finite Group Databasebeta

← C3×#10913 #10629520

Subgroups — C3×#10913 #10629520

Order 768.

826 conjugacy classes of subgroups.

The subgroup lattice has 412 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×C4×M16C211yesmaximal, characteristic
2C2×C3×#389C211yesmaximal, characteristic
3C2×C3×#343C212yesmaximal
4C2×C3×#343C212yesmaximal
5C3×#1728C211yesmaximal, characteristic
6#10913C311yesmaximal, characteristic, direct product factor, Sylow
7C22×C3×M16C2212yes—
8C22×C3×M16C2212yes—
9C22×C3×C4⋊C4C412yes—
10C22×C3×C4⋊C4C2211yescharacteristic
11C22×C3×C4⋊C4C2211yescharacteristic
12C22×C3×C42C2211yescharacteristic
13C3×C4×M16—24no—
14C2×C3×#97—21no—
15C2×C3×C4×C8—21no—
16C3×#389—21no—
17C3×#389—21no—
18C3×#389—21no—
19C3×#389—21no—
20C2×C3×#95C412yes—
21C3×#343—24no—
22C3×#343C418yescomplemented
23C3×#336—21no—
24C3×#336—21no—
25C2×C4×M16C2×C311yescharacteristic
26C2×#389C2×C311yescharacteristic
27C2×#343C2×C312yes—
28C2×#343C2×C312yes—
29#1728C2×C311yescharacteristic
30C23×C3×C4C2×C411yescharacteristic
31C23×C3×C4C2×C411yescharacteristic
32C23×C3×C4C2×C412yes—
33C23×C3×C4C2×C412yes—
34C23×C3×C4C2311yescharacteristic
35C2×C3×M16—22no—
36C2×C3×M16—22no—
37C2×C3×M16—22no—
38C2×C3×M16—22no—
39C2×C3×M16—22no—
40C2×C3×M16—22no—
41C2×C3×M16—22no—
42C2×C3×M16—22no—
43C2×C3×M16C2×C414yes—
44C2×C3×M16C2×C414yes—
45C2×C3×M16D414yes—
46C2×C3×M16Q814yes—
47C22×C3×C8—22no—
48C22×C3×C8—22no—
49C2×C3×C4⋊C4—21no—
50C2×C3×C4⋊C4—21no—
51C2×C3×C4⋊C4—22no—
52C2×C3×C4⋊C4—22no—
53C2×C3×C4⋊C4—22no—
54C2×C3×C4⋊C4—21no—
55C2×C3×C4⋊C4—21no—
56C2×C3×C4⋊C4—22no—
57C2×C3×C4⋊C4—22no—
58C2×C3×C4⋊C4—44no—
59C2×C3×C4⋊C4C2×C414yes—
60C2×C3×C42—22no—
61C2×C3×C42—22no—
62C2×C3×C42D411yescharacteristic
63C2×C3×C42D411yescharacteristic
64C2×C3×C42D411yescharacteristic
65C2×C3×C42D411yescharacteristic
66C3×#97—24no—
67C3×C4×C8—24no—
68C3×#95—22no—
69C3×#95—22no—
70C22×M16C22×C312yes—
71C22×M16C22×C312yes—
72C22×C4⋊C4C3×C412yes—
73C22×C4⋊C4C22×C311yescharacteristic
74C22×C4⋊C4C22×C311yescharacteristic
75C22×C42C22×C311yescharacteristic
76C4×M16—24no—
77C2×#97—21no—
78C2×C4×C8—21no—
79#389—21no—
80#389—21no—
81#389—21no—
82#389—21no—
83C2×#95C3×C412yes—
84#343—24no—
85#343C3×C418yescomplemented
86#336—21no—
87#336—21no—
88C24×C3C22×C411yescharacteristic
89C22×C3×C4—22no—
90C22×C3×C4—22no—
91C22×C3×C4—22no—
92C22×C3×C4—22no—
93C22×C3×C4—22no—
94C22×C3×C4—22no—
95C22×C3×C4—22no—
96C22×C3×C4—24no—
97C22×C3×C4—41no—
98C22×C3×C4—41no—
99C22×C3×C4—42no—
100C22×C3×C4—42no—
101C22×C3×C4—42no—
102C22×C3×C4—42no—
103C22×C3×C4C4214yes—
104C22×C3×C4C22⋊C411yescharacteristic
105C22×C3×C4C22⋊C411yescharacteristic
106C22×C3×C4C22⋊C411yescharacteristic
107C22×C3×C4C22⋊C411yescharacteristic
108C22×C3×C4C22×C412yes—
109C22×C3×C4C2×D412yes—
110C22×C3×C4C2×D411yescharacteristic
111C22×C3×C4C2×D411yescharacteristic
112C22×C3×C4C2×Q812yes—
113C22×C3×C4#4112yes—
114C22×C3×C4#4112yes—
115C22×C3×C4#4112yes—
116C3×M16—24no—
117C3×M16—24no—
118C3×M16—24no—
119C3×M16—24no—
120C3×M16—24no—
121C3×M16—42no—
122C3×M16—42no—
123C3×M16C4⋊C418yescomplemented
124C2×C3×C8—24no—
125C2×C3×C8—24no—
126C2×C3×C8—24no—
127C2×C3×C8—24no—
128C2×C3×C8—42no—
129C2×C3×C8—42no—
130C3×C4⋊C4—24no—
131C3×C4⋊C4—24no—
132C3×C4⋊C4—44no—
133C3×C4⋊C4—44no—
134C3×C4⋊C4—41no—
135C3×C4⋊C4—42no—
136C3×C4⋊C4—41no—
137C3×C42—21no—
138C3×C42—21no—
139C3×C42—22no—
140C3×C42—22no—
141C3×C42—21no—
142C3×C42—21no—
143C23×C4C2×C3×C411yescharacteristic
144C23×C4C2×C3×C411yescharacteristic
145C23×C4C2×C3×C412yes—
146C23×C4C2×C3×C412yes—
147C23×C4C23×C311yescharacteristic
148C2×M16—22no—
149C2×M16—22no—
150C2×M16—22no—
151C2×M16—22no—
152C2×M16—22no—
153C2×M16—22no—
154C2×M16—22no—
155C2×M16—22no—
156C2×M16C2×C3×C414yes—
157C2×M16C2×C3×C414yes—
158C2×M16C3×D414yes—
159C2×M16C3×Q814yes—
160C22×C8—22no—
161C22×C8—22no—
162C2×C4⋊C4—21no—
163C2×C4⋊C4—21no—
164C2×C4⋊C4—22no—
165C2×C4⋊C4—22no—
166C2×C4⋊C4—22no—
167C2×C4⋊C4—22no—
168C2×C4⋊C4—21no—
169C2×C4⋊C4—21no—
170C2×C4⋊C4—22no—
171C2×C4⋊C4—44no—
172C2×C4⋊C4C2×C3×C414yes—
173C2×C42—22no—
174C2×C42—22no—
175C2×C42C3×D411yescharacteristic
176C2×C42C3×D411yescharacteristic
177C2×C42C3×D411yescharacteristic
178C2×C42C3×D411yescharacteristic
179#97—24no—
180C4×C8—24no—
181#95—22no—
182#95—22no—
183C23×C3—21no—
184C23×C3—21no—
185C23×C3—21no—
186C23×C3—21no—
187C23×C3C2×C4211yescharacteristic
188C23×C3C2×C22⋊C411yescharacteristic
189C23×C3#11711yescharacteristic
190C23×C3C4×D412yes—
191C23×C3C4×Q812yes—
192C2×C3×C4—21no—
193C2×C3×C4—21no—
194C2×C3×C4—21no—
195C2×C3×C4—21no—
196C2×C3×C4—24no—
197C2×C3×C4—21no—
198C2×C3×C4—21no—
199C2×C3×C4—21no—
200C2×C3×C4—21no—
201C2×C3×C4—21no—
202C2×C3×C4—21no—
203C2×C3×C4—44no—
204C2×C3×C4—44no—
205C2×C3×C4—44no—
206C2×C3×C4—42no—
207C2×C3×C4—42no—
208C2×C3×C4—44no—
209C2×C3×C4—42no—
210C2×C3×C4—42no—
211C2×C3×C4—42no—
212C2×C3×C4—84no—
213C2×C3×C4#10012yes—
214C2×C3×C4#10112yes—
215C2×C3×C4C2×C4⋊C412yes—
216C2×C3×C4#11712yes—
217C2×C3×C4C4×D412yes—
218C2×C3×C4C4×D412yes—
219C2×C3×C4C4×D412yes—
220C2×C3×C4C4×Q812yes—
221C2×C3×C4#12011yescharacteristic
222C2×C3×C4#12112yes—
223C2×C3×C4C22⋊Q812yes—
224C2×C3×C4C22⋊Q812yes—
225C2×C3×C4#12312yes—
226C2×C3×C4#12311yescharacteristic
227C2×C3×C4#12411yescharacteristic
228C2×C3×C4#12512yes—
229C2×C3×C4#12612yes—
230C2×C3×C4C4⋊Q811yescharacteristic
231C3×C8—28no—
232C3×C8—44no—
233C24C22×C3×C411yescharacteristic
234C22×C4—22no—
235C22×C4—22no—
236C22×C4—22no—
237C22×C4—22no—
238C22×C4—22no—
239C22×C4—22no—
240C22×C4—22no—
241C22×C4—24no—
242C22×C4—41no—
243C22×C4—41no—
244C22×C4—42no—
245C22×C4—42no—
246C22×C4—42no—
247C22×C4—42no—
248C22×C4C3×C4214yes—
249C22×C4C3×C22⋊C411yescharacteristic
250C22×C4C3×C22⋊C411yescharacteristic
251C22×C4C3×C22⋊C411yescharacteristic
252C22×C4C3×C22⋊C411yescharacteristic
253C22×C4C22×C3×C412yes—
254C22×C4C2×C3×D412yes—
255C22×C4C2×C3×D411yescharacteristic
256C22×C4C2×C3×D411yescharacteristic
257C22×C4C2×C3×Q812yes—
258C22×C4C3×#4112yes—
259C22×C4C3×#4112yes—
260C22×C4C3×#4112yes—
261M16—24no—
262M16—24no—
263M16—24no—
264M16—24no—
265M16—24no—
266M16—42no—
267M16—42no—
268M16C3×C4⋊C418yescomplemented
269C2×C8—24no—
270C2×C8—24no—
271C2×C8—24no—
272C2×C8—24no—
273C2×C8—42no—
274C2×C8—42no—
275C4⋊C4—24no—
276C4⋊C4—24no—
277C4⋊C4—44no—
278C4⋊C4—44no—
279C4⋊C4—41no—
280C4⋊C4—42no—
281C4⋊C4—41no—
282C42—21no—
283C42—21no—
284C42—22no—
285C42—22no—
286C42—21no—
287C42—21no—
288C22×C3—22no—
289C22×C3—22no—
290C22×C3—22no—
291C22×C3—22no—
292C22×C3—21no—
293C22×C3—21no—
294C22×C3—21no—
295C22×C3—21no—
296C22×C3C4×C22⋊C411yescharacteristic
297C22×C3C4×C4⋊C412yes—
298C22×C3#38611yescharacteristic
299C22×C3#38712yes—
300C22×C3#39111yescharacteristic
301C22×C3C2×#10011yescharacteristic
302C22×C3C2×#10111yescharacteristic
303C22×C3#41311yescharacteristic
304C22×C3#41311yescharacteristic
305C3×C4—22no—
306C3×C4—22no—
307C3×C4—41no—
308C3×C4—41no—
309C3×C4—44no—
310C3×C4—82no—
311C3×C4#38512yes—
312C3×C4#38712yes—
313C3×C4#38812yes—
314C3×C4#38912yes—
315C23—21no—
316C23—21no—
317C23—21no—
318C23—21no—
319C23C2×C3×C4211yescharacteristic
320C23C2×C3×C22⋊C411yescharacteristic
321C23C3×#11711yescharacteristic
322C23C3×C4×D412yes—
323C23C3×C4×Q812yes—
324C2×C4—21no—
325C2×C4—21no—
326C2×C4—21no—
327C2×C4—21no—
328C2×C4—24no—
329C2×C4—21no—
330C2×C4—21no—
331C2×C4—21no—
332C2×C4—21no—
333C2×C4—21no—
334C2×C4—21no—
335C2×C4—44no—
336C2×C4—44no—
337C2×C4—44no—
338C2×C4—42no—
339C2×C4—42no—
340C2×C4—44no—
341C2×C4—42no—
342C2×C4—42no—
343C2×C4—42no—
344C2×C4—84no—
345C2×C4C3×#10012yes—
346C2×C4C3×#10112yes—
347C2×C4C2×C3×C4⋊C412yes—
348C2×C4C3×#11712yes—
349C2×C4C3×C4×D412yes—
350C2×C4C3×C4×D412yes—
351C2×C4C3×C4×D412yes—
352C2×C4C3×C4×Q812yes—
353C2×C4C3×#12011yescharacteristic
354C2×C4C3×#12112yes—
355C2×C4C3×C22⋊Q812yes—
356C2×C4C3×C22⋊Q812yes—
357C2×C4C3×#12312yes—
358C2×C4C3×#12311yescharacteristic
359C2×C4C3×#12411yescharacteristic
360C2×C4C3×#12512yes—
361C2×C4C3×#12612yes—
362C2×C4C3×C4⋊Q811yescharacteristic
363C8—28no—
364C8—44no—
365C2×C3—22no—
366C2×C3—22no—
367C2×C3#143611yescharacteristic
368C2×C3C4×#10011yescharacteristic
369C2×C3C4×#10111yescharacteristic
370C2×C3#190011yescharacteristic
371C2×C3#190111yescharacteristic
372C2×C3#199711yescharacteristic
373C2×C3#199811yescharacteristic
374C22—22no—
375C22—22no—
376C22—21no—
377C22—21no—
378C22—21no—
379C22—21no—
380C22—22no—
381C22—22no—
382C22C3×C4×C22⋊C411yescharacteristic
383C22C3×C4×C4⋊C412yes—
384C22C3×#38611yescharacteristic
385C22C3×#38712yes—
386C22C3×#39111yescharacteristic
387C22C2×C3×#10011yescharacteristic
388C22C2×C3×#10111yescharacteristic
389C22C3×#41311yescharacteristic
390C22C3×#41311yescharacteristic
391C4—22no—
392C4—22no—
393C4—44no—
394C4—41no—
395C4—41no—
396C4—82no—
397C4C3×#38512yes—
398C4C3×#38712yes—
399C4C3×#38812yes—
400C4C3×#38912yes—
401C3#1091311yescharacteristic, direct product factor, Sylow
402C2—22no—
403C2—22no—
404C2C3×#143611yescharacteristic
405C2C3×C4×#10011yescharacteristic
406C2C3×C4×#10111yescharacteristic
407C2C3×#190011yescharacteristic
408C2C3×#190111yescharacteristic
409C2C3×#199711yescharacteristic
410C2C3×#199811yescharacteristic
subgroupG/H
center, socleC23×C3C2×C22⋊C4
commutatorC23C2×C3×C42
Frattini, cosocleC23×C4C23×C3
prime radicalC24×C3C22×C4
LCSG ▷ C23 ▷ C2 ▷ C1
UCSC1 ◁ C23×C3 ◁ C22×C3×C42 ◁ G

Complements

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

NH ≅ G/Ntype
6. #10913C3direct (N × H)
22. C3×#343C4semidirect
85. #343C3×C4semidirect
123. C3×M16C4⋊C4semidirect
268. M16C3×C4⋊C4semidirect
401. C3#10913direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×C4×M162
C2×C3×#3892
C2×C3×#3432
C3×#17282
#109133