Finite Group Databasebeta

← #69428

Subgroups — #69428

Order 384.

780 conjugacy classes of subgroups.

The subgroup lattice has 514 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×(C2×D3)⋊C4C211yesmaximal, characteristic
2C22×(C2×D3)⋊C4C211yesmaximal, characteristic
3C22×(C2×D3)⋊C4C211yesmaximal, characteristic
4C22×Dic3⋊C4C211yesmaximal, characteristic, complemented
5C2×C3×#95C211yesmaximal, characteristic, complemented
6C2×C3⋊#95C211yesmaximal, characteristic, complemented
7C2×C3⋊#95C211yesmaximal, characteristic, complemented
8#1439—31nomaximal, Sylow
9C24×D3C2211yescharacteristic
10C23×C3×C4C2211yescharacteristic
11C23×C3×C4C2211yescharacteristic
12C23×C3×C4C2211yescharacteristic
13C23×Dic3C2211yescharacteristic
14C23×Dic3C2211yescharacteristic
15C23×Dic3C2211yescharacteristic
16C2×(C2×D3)⋊C4—22no—
17C2×(C2×D3)⋊C4—22no—
18C2×(C2×D3)⋊C4—22no—
19C2×(C2×D3)⋊C4—22no—
20C2×(C2×D3)⋊C4—22no—
21C2×(C2×D3)⋊C4—22no—
22C2×(C2×D3)⋊C4—22no—
23C2×(C2×D3)⋊C4—22no—
24C2×(C2×D3)⋊C4C414yescomplemented
25C2×Dic3⋊C4—22no—
26C2×Dic3⋊C4—22no—
27C2×Dic3⋊C4—22no—
28C3×#95—22no—
29C3⋊#95—22no—
30C3⋊#95—22no—
31C22×C4⋊C4—31no—
32C22×C22⋊C4—31no—
33C22×C22⋊C4—31no—
34C22×C22⋊C4—31no—
35C2×#95—31no—
36C2×#95—31no—
37C2×#95D311yescharacteristic, complemented
38C24×C3C2311yescharacteristic
39C23×D3—21no—
40C23×D3—21no—
41C23×D3—21no—
42C23×D3—21no—
43C23×D3—21no—
44C23×D3—21no—
45C23×D3—21no—
46C23×D3—21no—
47C23×D3—21no—
48C23×D3—21no—
49C23×D3—21no—
50C23×D3—21no—
51C23×D3C2×C412yes—
52C23×D3D412yes—
53C23×D3Q812yes—
54C22×C3×C4—21no—
55C22×C3×C4—21no—
56C22×C3×C4—21no—
57C22×C3×C4—21no—
58C22×C3×C4—21no—
59C22×C3×C4—21no—
60C22×C3×C4—21no—
61C22×C3×C4—21no—
62C22×C3×C4—21no—
63C22×C3×C4—21no—
64C22×C3×C4—21no—
65C22×C3×C4—21no—
66C22×C3×C4—21no—
67C22×C3×C4—21no—
68C22×C3×C4—21no—
69C22×C3×C4—21no—
70C22×C3×C4—21no—
71C22×C3×C4—21no—
72C22×C3×C4C2×C412yes—
73C22×C3×C4D412yes—
74C22×C3×C4D412yes—
75C22×Dic3—21no—
76C22×Dic3—21no—
77C22×Dic3—21no—
78C22×Dic3—21no—
79C22×Dic3—21no—
80C22×Dic3—21no—
81C22×Dic3—21no—
82C22×Dic3—21no—
83C22×Dic3—21no—
84C22×Dic3—21no—
85C22×Dic3—21no—
86C22×Dic3—21no—
87C22×Dic3—21no—
88C22×Dic3—21no—
89C22×Dic3—21no—
90C22×Dic3—21no—
91C22×Dic3C2×C412yes—
92C22×Dic3D412yes—
93C22×Dic3D412yes—
94C22×Dic3D412yes—
95C22×Dic3D412yes—
96(C2×D3)⋊C4—28no—
97(C2×D3)⋊C4—28no—
98(C2×D3)⋊C4—28no—
99Dic3⋊C4—28no—
100C25—31no—
101C23×C4—31no—
102C23×C4—31no—
103C23×C4—31no—
104C23×C4C2×D311yescharacteristic
105C23×C4C2×D311yescharacteristic
106C23×C4C2×D311yescharacteristic
107C2×C4⋊C4—62no—
108C2×C4⋊C4—62no—
109C2×C4⋊C4—62no—
110C2×C22⋊C4—34no—
111C2×C22⋊C4—62no—
112C2×C22⋊C4—62no—
113C2×C22⋊C4—62no—
114C2×C22⋊C4—62no—
115C2×C22⋊C4—62no—
116C2×C22⋊C4—62no—
117C2×C22⋊C4—62no—
118C2×C22⋊C4—62no—
119#95—22no—
120#95—62no—
121#95—62no—
122C23×C3C22×C411yescharacteristic
123C23×C3C2×D411yescharacteristic
124C23×C3C2×D411yescharacteristic
125C23×C3C2×D411yescharacteristic
126C23×C3C2×D411yescharacteristic
127C23×C3C2×D411yescharacteristic
128C23×C3C2×D411yescharacteristic
129C23×C3C2×D411yescharacteristic
130C23×C3C2×Q811yescharacteristic
131C23×C3#4111yescharacteristic
132C23×C3#4111yescharacteristic
133C23×C3#4111yescharacteristic
134C23×C3#4111yescharacteristic
135C23×C3#4111yescharacteristic
136C23×C3#4111yescharacteristic
137C22×D3—22no—
138C22×D3—22no—
139C22×D3—22no—
140C22×D3—22no—
141C22×D3—22no—
142C22×D3—22no—
143C22×D3—22no—
144C22×D3—22no—
145C22×D3—22no—
146C22×D3—22no—
147C22×D3—22no—
148C22×D3—22no—
149C22×D3—22no—
150C22×D3—22no—
151C22×D3—22no—
152C22×D3—22no—
153C22×D3—22no—
154C22×D3—22no—
155C22×D3—41no—
156C22×D3—41no—
157C22×D3—41no—
158C22×D3—41no—
159C22×D3—41no—
160C22×D3—41no—
161C22×D3—41no—
162C22×D3—41no—
163C22×D3—41no—
164C22×D3—41no—
165C22×D3—41no—
166C22×D3—41no—
167C22×D3—41no—
168C22×D3—41no—
169C22×D3—41no—
170C22×D3—41no—
171C22×D3C4⋊C414yescomplemented
172C2×C3×C4—22no—
173C2×C3×C4—22no—
174C2×C3×C4—22no—
175C2×C3×C4—22no—
176C2×C3×C4—22no—
177C2×C3×C4—22no—
178C2×C3×C4—22no—
179C2×C3×C4—22no—
180C2×C3×C4—22no—
181C2×C3×C4—41no—
182C2×C3×C4—41no—
183C2×C3×C4—41no—
184C2×C3×C4—41no—
185C2×C3×C4—41no—
186C2×C3×C4—41no—
187C2×C3×C4—41no—
188C2×C3×C4—41no—
189C2×C3×C4—41no—
190C2×C3×C4—41no—
191C2×C3×C4—41no—
192C2×C3×C4—41no—
193C2×Dic3—22no—
194C2×Dic3—22no—
195C2×Dic3—22no—
196C2×Dic3—22no—
197C2×Dic3—22no—
198C2×Dic3—22no—
199C2×Dic3—22no—
200C2×Dic3—22no—
201C2×Dic3—22no—
202C2×Dic3—22no—
203C2×Dic3—22no—
204C2×Dic3—22no—
205C2×Dic3—41no—
206C2×Dic3—41no—
207C2×Dic3—41no—
208C2×Dic3—41no—
209C2×Dic3—41no—
210C2×Dic3—41no—
211C2×Dic3—41no—
212C2×Dic3—41no—
213C2×Dic3C22⋊C414yescomplemented
214C24—32no—
215C24—32no—
216C24—32no—
217C24—61no—
218C24—61no—
219C24—61no—
220C24—61no—
221C24—61no—
222C24—61no—
223C24—61no—
224C24—61no—
225C24—61no—
226C24—61no—
227C24—61no—
228C24—61no—
229C24C22×D311yescharacteristic
230C22×C4—21no—
231C22×C4—21no—
232C22×C4—21no—
233C22×C4—21no—
234C22×C4—21no—
235C22×C4—21no—
236C22×C4—21no—
237C22×C4—21no—
238C22×C4—21no—
239C22×C4—21no—
240C22×C4—21no—
241C22×C4—21no—
242C22×C4—21no—
243C22×C4—21no—
244C22×C4—21no—
245C22×C4—21no—
246C22×C4—21no—
247C22×C4—21no—
248C22×C4—32no—
249C22×C4—32no—
250C22×C4—32no—
251C22×C4—32no—
252C22×C4—32no—
253C22×C4—61no—
254C22×C4—61no—
255C22×C4—61no—
256C22×C4—61no—
257C22×C4—61no—
258C22×C4—61no—
259C22×C4—61no—
260C22×C4—61no—
261C22×C4—61no—
262C22×C4—61no—
263C22×C4—61no—
264C22×C4—61no—
265C22×C4—61no—
266C22×C4—61no—
267C22×C4—61no—
268C22×C4—61no—
269C22×C4C4×D312yes—
270C22×C4D1212yes—
271C22×C4#6712yes—
272C4⋊C4—68no—
273C22⋊C4—68no—
274C22⋊C4—68no—
275C22⋊C4—68no—
276C22×C3C2×C22⋊C411yescharacteristic
277C22×C3C2×C4⋊C411yescharacteristic
278C22×C3#11711yescharacteristic
279C22×C3C4×D411yescharacteristic
280C22×C3C4×D411yescharacteristic
281C22×C3C4×D411yescharacteristic
282C22×C3C4×D411yescharacteristic
283C22×C3#12011yescharacteristic
284C22×C3#12011yescharacteristic
285C22×C3#12011yescharacteristic
286C22×C3#12111yescharacteristic
287C22×C3#12111yescharacteristic
288C22×C3#12111yescharacteristic
289C22×C3#12111yescharacteristic
290C22×C3#12111yescharacteristic
291C22×C3#12111yescharacteristic
292C22×C3#12111yescharacteristic
293C22×C3#12111yescharacteristic
294C22×C3C22⋊Q811yescharacteristic
295C22×C3C22⋊Q811yescharacteristic
296C22×C3C22⋊Q811yescharacteristic
297C22×C3C22⋊Q811yescharacteristic
298C22×C3C22⋊Q811yescharacteristic
299C22×C3C22⋊Q811yescharacteristic
300C22×C3#12311yescharacteristic
301C22×C3#12311yescharacteristic
302C22×C3#12311yescharacteristic
303C22×C3#12311yescharacteristic
304C22×C3#12311yescharacteristic
305C22×C3#12411yescharacteristic
306C22×C3#12411yescharacteristic
307C22×C3#12411yescharacteristic
308C22×C3#12611yescharacteristic
309C22×C3#12611yescharacteristic
310C22×C3#12711yescharacteristic
311C2×D3—24no—
312C2×D3—24no—
313C2×D3—24no—
314C2×D3—42no—
315C2×D3—42no—
316C2×D3—42no—
317C2×D3—42no—
318C2×D3—42no—
319C2×D3—42no—
320C2×D3—42no—
321C2×D3—42no—
322C2×D3—42no—
323C2×D3—42no—
324C2×D3—42no—
325C2×D3—42no—
326C3×C4—42no—
327C3×C4—42no—
328C3×C4—42no—
329Dic3—24no—
330Dic3—42no—
331Dic3—42no—
332C23—34no—
333C23—62no—
334C23—62no—
335C23—62no—
336C23—62no—
337C23—62no—
338C23—62no—
339C23—62no—
340C23—62no—
341C23—62no—
342C23—62no—
343C23—62no—
344C23—62no—
345C23—62no—
346C23—62no—
347C23—62no—
348C23—62no—
349C23—62no—
350C23—62no—
351C23—121no—
352C23—121no—
353C23—121no—
354C23—121no—
355C23—121no—
356C23—121no—
357C23—121no—
358C23—121no—
359C23—121no—
360C23—121no—
361C23—121no—
362C23—121no—
363C23—121no—
364C23—121no—
365C23—121no—
366C23—121no—
367C23C2×C4×D311yescharacteristic
368C23C2×D1211yescharacteristic
369C23#23511yescharacteristic
370C23#23511yescharacteristic
371C23#23511yescharacteristic
372C23#23511yescharacteristic
373C23D3×D411yescharacteristic
374C23D3×D411yescharacteristic
375C23D3×D411yescharacteristic
376C23D3×D411yescharacteristic
377C23D3×D411yescharacteristic
378C23#23711yescharacteristic
379C23D3×Q811yescharacteristic
380C23#23911yescharacteristic
381C23C2×#6711yescharacteristic
382C2×C4—22no—
383C2×C4—22no—
384C2×C4—22no—
385C2×C4—22no—
386C2×C4—22no—
387C2×C4—22no—
388C2×C4—22no—
389C2×C4—22no—
390C2×C4—22no—
391C2×C4—34no—
392C2×C4—41no—
393C2×C4—41no—
394C2×C4—41no—
395C2×C4—41no—
396C2×C4—41no—
397C2×C4—41no—
398C2×C4—41no—
399C2×C4—41no—
400C2×C4—41no—
401C2×C4—41no—
402C2×C4—41no—
403C2×C4—41no—
404C2×C4—62no—
405C2×C4—62no—
406C2×C4—62no—
407C2×C4—62no—
408C2×C4—62no—
409C2×C4—62no—
410C2×C4—62no—
411C2×C4—62no—
412C2×C4—62no—
413C2×C4—62no—
414C2×C4—62no—
415C2×C4—62no—
416C2×C4—121no—
417C2×C4—121no—
418C2×C4—121no—
419C2×C4—121no—
420C2×C4—121no—
421C2×C4—121no—
422C2×C4—121no—
423C2×C4—121no—
424C2×C3#38011yescharacteristic
425C2×C3#38511yescharacteristic
426C2×C3#38511yescharacteristic
427C2×C3#38611yescharacteristic
428C2×C3#38811yescharacteristic
429C2×C3#38811yescharacteristic
430C2×C3#39011yescharacteristic
431C2×C3#39211yescharacteristic
432C2×C3#39311yescharacteristic
433C2×C3#39411yescharacteristic
434C2×C3#39411yescharacteristic
435C2×C3#39611yescharacteristic
436C2×C3#39611yescharacteristic
437C2×C3#39711yescharacteristic
438C2×C3#39911yescharacteristic
439D3—44no—
440C22—64no—
441C22—64no—
442C22—64no—
443C22—122no—
444C22—122no—
445C22—122no—
446C22—122no—
447C22—122no—
448C22—122no—
449C22—122no—
450C22—122no—
451C22—122no—
452C22—122no—
453C22—122no—
454C22—122no—
455C22#87211yescharacteristic
456C22C4×D1211yescharacteristic
457C22#87511yescharacteristic
458C22#87611yescharacteristic
459C22D3×C22⋊C411yescharacteristic
460C22#67⋊C411yescharacteristic
461C22#88211yescharacteristic
462C22#88211yescharacteristic
463C22#88311yescharacteristic
464C22#88411yescharacteristic
465C22#88411yescharacteristic
466C22#88411yescharacteristic
467C22#88411yescharacteristic
468C22#88411yescharacteristic
469C22#88511yescharacteristic
470C22#88511yescharacteristic
471C22D3×C4⋊C411yescharacteristic
472C22#89311yescharacteristic
473C22#89411yescharacteristic
474C22#89411yescharacteristic
475C22#89411yescharacteristic
476C22#89511yescharacteristic
477C22#89611yescharacteristic
478C22#89611yescharacteristic
479C22#89611yescharacteristic
480C22#89611yescharacteristic
481C22#89711yescharacteristic
482C22#89811yescharacteristic
483C22C4×#6711yescharacteristic
484C22#92911yescharacteristic
485C22#93011yescharacteristic
486C22#93711yescharacteristic
487C22#93911yescharacteristic
488C22#94011yescharacteristic
489C22#94611yescharacteristic
490C4—42no—
491C4—42no—
492C4—42no—
493C4—64no—
494C4—122no—
495C4—122no—
496C3#143911yescharacteristic, complemented, Sylow
497C2—124no—
498C2#466511yescharacteristic
499C2#466711yescharacteristic
500C2#466811yescharacteristic
501C2#466911yescharacteristic
502C2#467211yescharacteristic
503C2#467311yescharacteristic
504C2#467511yescharacteristic
505C2#467611yescharacteristic
506C2#494011yescharacteristic
507C2#495711yescharacteristic
508C2#495911yescharacteristic
509C2#496011yescharacteristic
510C2#498911yescharacteristic
511C2#499311yescharacteristic
512C2#499411yescharacteristic
subgroupG/H
center, FrattiniC24C22×D3
commutatorC23×C3C22×C4
FittingC2×C3×#95C2
socle, cosocleC24×C3C23
prime radicalC24×D3C22
hypercenterC2×#95D3
hypocenterC3#1439
LCSG ▷ C23×C3 ▷ C3
UCSC1 ◁ C24 ◁ C2×#95

Complements

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

NH ≅ G/Ntype
4. C22×Dic3⋊C4C2semidirect
5. C2×C3×#95C2semidirect
6. C2×C3⋊#95C2semidirect
7. C2×C3⋊#95C2semidirect
24. C2×(C2×D3)⋊C4C4semidirect
37. C2×#95D3semidirect
171. C22×D3C4⋊C4semidirect
213. C2×Dic3C22⋊C4semidirect
496. C3#1439semidirect

Maximal subgroups

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

subgroupindex
C22×(C2×D3)⋊C42
C22×Dic3⋊C42
C2×C3×#952
C2×C3⋊#952
#14393