Finite Group Databasebeta

← #69429

Subgroups — #69429

Order 384.

736 conjugacy classes of subgroups.

The subgroup lattice has 508 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
4C2×C3×#95C211yesmaximal, characteristic, complemented
5C2×C3⋊#95C211yesmaximal, characteristic, complemented
6C2×C3⋊#95C211yesmaximal, characteristic, complemented
7C2×C3⋊#95C211yesmaximal, characteristic, complemented
8#1440—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
25C3×#95—22no—
26C3⋊#95—22no—
27C3⋊#95—22no—
28C3⋊#95—22no—
29C22×C22⋊C4—31no—
30C22×C22⋊C4—31no—
31C22×C22⋊C4—31no—
32C2×#95—31no—
33C2×#95—31no—
34C2×#95—31no—
35C2×#95D311yescharacteristic, complemented
36C24×C3C2311yescharacteristic
37C23×D3—21no—
38C23×D3—21no—
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×D3C2×C412yes—
50C23×D3D412yes—
51C23×D3D412yes—
52C22×C3×C4—21no—
53C22×C3×C4—21no—
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×C4C2×C412yes—
71C22×C3×C4D412yes—
72C22×C3×C4D412yes—
73C22×Dic3—21no—
74C22×Dic3—21no—
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—
94(C2×D3)⋊C4—28no—
95(C2×D3)⋊C4—28no—
96(C2×D3)⋊C4—28no—
97C25—31no—
98C23×C4—31no—
99C23×C4—31no—
100C23×C4—31no—
101C23×C4C2×D311yescharacteristic
102C23×C4C2×D311yescharacteristic
103C23×C4C2×D311yescharacteristic
104C2×C22⋊C4—34no—
105C2×C22⋊C4—62no—
106C2×C22⋊C4—62no—
107C2×C22⋊C4—62no—
108C2×C22⋊C4—62no—
109C2×C22⋊C4—62no—
110C2×C22⋊C4—62no—
111C2×C22⋊C4—62no—
112C2×C22⋊C4—62no—
113#95—22no—
114#95—62no—
115#95—62no—
116#95—62no—
117C23×C3C22×C411yescharacteristic
118C23×C3C2×D411yescharacteristic
119C23×C3C2×D411yescharacteristic
120C23×C3C2×D411yescharacteristic
121C23×C3C2×D411yescharacteristic
122C23×C3C2×D411yescharacteristic
123C23×C3C2×D411yescharacteristic
124C23×C3#4111yescharacteristic
125C23×C3#4111yescharacteristic
126C23×C3#4111yescharacteristic
127C23×C3#4111yescharacteristic
128C23×C3#4111yescharacteristic
129C23×C3#4111yescharacteristic
130C23×C3#4111yescharacteristic
131C23×C3#4111yescharacteristic
132C22×D3—22no—
133C22×D3—22no—
134C22×D3—22no—
135C22×D3—22no—
136C22×D3—22no—
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—41no—
151C22×D3—41no—
152C22×D3—41no—
153C22×D3—41no—
154C22×D3—41no—
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×D3C22⋊C414yes—
167C2×C3×C4—22no—
168C2×C3×C4—22no—
169C2×C3×C4—22no—
170C2×C3×C4—22no—
171C2×C3×C4—22no—
172C2×C3×C4—22no—
173C2×C3×C4—22no—
174C2×C3×C4—22no—
175C2×C3×C4—22no—
176C2×C3×C4—41no—
177C2×C3×C4—41no—
178C2×C3×C4—41no—
179C2×C3×C4—41no—
180C2×C3×C4—41no—
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×Dic3—22no—
189C2×Dic3—22no—
190C2×Dic3—22no—
191C2×Dic3—22no—
192C2×Dic3—22no—
193C2×Dic3—22no—
194C2×Dic3—22no—
195C2×Dic3—22no—
196C2×Dic3—22no—
197C2×Dic3—41no—
198C2×Dic3—41no—
199C2×Dic3—41no—
200C2×Dic3—41no—
201C2×Dic3—41no—
202C2×Dic3—41no—
203C2×Dic3—41no—
204C2×Dic3—41no—
205C2×Dic3—41no—
206C2×Dic3—41no—
207C2×Dic3—41no—
208C2×Dic3—41no—
209C24—32no—
210C24—32no—
211C24—32no—
212C24—61no—
213C24—61no—
214C24—61no—
215C24—61no—
216C24—61no—
217C24—61no—
218C24—61no—
219C24—61no—
220C24—61no—
221C24—61no—
222C24—61no—
223C24—61no—
224C24C22×D311yescharacteristic
225C22×C4—21no—
226C22×C4—21no—
227C22×C4—21no—
228C22×C4—21no—
229C22×C4—21no—
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—32no—
244C22×C4—32no—
245C22×C4—32no—
246C22×C4—61no—
247C22×C4—61no—
248C22×C4—61no—
249C22×C4—61no—
250C22×C4—61no—
251C22×C4—61no—
252C22×C4—61no—
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×C4C4×D312yes—
265C22×C4D1212yes—
266C22×C4#6712yes—
267C22⋊C4—68no—
268C22⋊C4—68no—
269C22⋊C4—68no—
270C22×C3C2×C22⋊C411yescharacteristic
271C22×C3#11711yescharacteristic
272C22×C3#11711yescharacteristic
273C22×C3C4×D411yescharacteristic
274C22×C3C4×D411yescharacteristic
275C22×C3C4×D411yescharacteristic
276C22×C3C4×D411yescharacteristic
277C22×C3#12011yescharacteristic
278C22×C3#12011yescharacteristic
279C22×C3#12111yescharacteristic
280C22×C3#12111yescharacteristic
281C22×C3#12111yescharacteristic
282C22×C3#12111yescharacteristic
283C22×C3#12111yescharacteristic
284C22×C3#12111yescharacteristic
285C22×C3#12111yescharacteristic
286C22×C3#12111yescharacteristic
287C22×C3#12311yescharacteristic
288C22×C3#12311yescharacteristic
289C22×C3#12311yescharacteristic
290C22×C3#12311yescharacteristic
291C22×C3#12311yescharacteristic
292C22×C3#12311yescharacteristic
293C22×C3#12311yescharacteristic
294C22×C3#12311yescharacteristic
295C22×C3#12311yescharacteristic
296C22×C3#12311yescharacteristic
297C22×C3#12411yescharacteristic
298C22×C3#12411yescharacteristic
299C22×C3#12411yescharacteristic
300C22×C3#12411yescharacteristic
301C22×C3#12611yescharacteristic
302C22×C3#12611yescharacteristic
303C22×C3#12611yescharacteristic
304C22×C3#12611yescharacteristic
305C2×D3—24no—
306C2×D3—24no—
307C2×D3—24no—
308C2×D3—42no—
309C2×D3—42no—
310C2×D3—42no—
311C2×D3—42no—
312C2×D3—42no—
313C2×D3—42no—
314C2×D3—42no—
315C2×D3—42no—
316C2×D3—42no—
317C2×D3—42no—
318C2×D3—42no—
319C2×D3—42no—
320C3×C4—42no—
321C3×C4—42no—
322C3×C4—42no—
323Dic3—42no—
324Dic3—42no—
325Dic3—42no—
326C23—34no—
327C23—62no—
328C23—62no—
329C23—62no—
330C23—62no—
331C23—62no—
332C23—62no—
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—121no—
346C23—121no—
347C23—121no—
348C23—121no—
349C23—121no—
350C23—121no—
351C23—121no—
352C23—121no—
353C23—121no—
354C23—121no—
355C23—121no—
356C23—121no—
357C23—121no—
358C23—121no—
359C23—121no—
360C23—121no—
361C23C2×C4×D311yescharacteristic
362C23C2×D1211yescharacteristic
363C23#23511yescharacteristic
364C23#23511yescharacteristic
365C23#23511yescharacteristic
366C23#23511yescharacteristic
367C23D3×D411yescharacteristic
368C23D3×D411yescharacteristic
369C23D3×D411yescharacteristic
370C23D3×D411yescharacteristic
371C23#23711yescharacteristic
372C23#23711yescharacteristic
373C23#23911yescharacteristic
374C23#23911yescharacteristic
375C23C2×#6711yescharacteristic
376C2×C4—22no—
377C2×C4—22no—
378C2×C4—22no—
379C2×C4—22no—
380C2×C4—22no—
381C2×C4—22no—
382C2×C4—22no—
383C2×C4—22no—
384C2×C4—22no—
385C2×C4—41no—
386C2×C4—41no—
387C2×C4—41no—
388C2×C4—41no—
389C2×C4—41no—
390C2×C4—41no—
391C2×C4—41no—
392C2×C4—41no—
393C2×C4—41no—
394C2×C4—41no—
395C2×C4—41no—
396C2×C4—41no—
397C2×C4—62no—
398C2×C4—62no—
399C2×C4—62no—
400C2×C4—62no—
401C2×C4—62no—
402C2×C4—62no—
403C2×C4—62no—
404C2×C4—62no—
405C2×C4—62no—
406C2×C4—121no—
407C2×C4—121no—
408C2×C4—121no—
409C2×C4—121no—
410C2×C4—121no—
411C2×C4—121no—
412C2×C4—121no—
413C2×C4—121no—
414C2×C4—121no—
415C2×C4—121no—
416C2×C4—121no—
417C2×C4—121no—
418C2×C3#38111yescharacteristic
419C2×C3#38611yescharacteristic
420C2×C3#38611yescharacteristic
421C2×C3#38811yescharacteristic
422C2×C3#38811yescharacteristic
423C2×C3#38811yescharacteristic
424C2×C3#38811yescharacteristic
425C2×C3#39411yescharacteristic
426C2×C3#39411yescharacteristic
427C2×C3#39411yescharacteristic
428C2×C3#39411yescharacteristic
429C2×C3#39711yescharacteristic
430C2×C3#39711yescharacteristic
431C2×C3#39711yescharacteristic
432C2×C3#39711yescharacteristic
433D3—44no—
434C22—64no—
435C22—64no—
436C22—64no—
437C22—122no—
438C22—122no—
439C22—122no—
440C22—122no—
441C22—122no—
442C22—122no—
443C22—122no—
444C22—122no—
445C22—122no—
446C22—122no—
447C22—122no—
448C22—122no—
449C22#87211yescharacteristic
450C22C4×D1211yescharacteristic
451C22#87511yescharacteristic
452C22#87611yescharacteristic
453C22D3×C22⋊C411yescharacteristic
454C22#67⋊C411yescharacteristic
455C22#88211yescharacteristic
456C22#88311yescharacteristic
457C22#88311yescharacteristic
458C22#88311yescharacteristic
459C22#88411yescharacteristic
460C22#88411yescharacteristic
461C22#88411yescharacteristic
462C22#88511yescharacteristic
463C22#88511yescharacteristic
464C22#88611yescharacteristic
465C22#89211yescharacteristic
466C22#89311yescharacteristic
467C22#89411yescharacteristic
468C22#89411yescharacteristic
469C22#89411yescharacteristic
470C22#89411yescharacteristic
471C22#89411yescharacteristic
472C22#89511yescharacteristic
473C22#89511yescharacteristic
474C22#89811yescharacteristic
475C22#89811yescharacteristic
476C22#89811yescharacteristic
477C22C4×#6711yescharacteristic
478C22#92911yescharacteristic
479C22#93011yescharacteristic
480C22#93711yescharacteristic
481C22#93811yescharacteristic
482C22#93911yescharacteristic
483C22#94711yescharacteristic
484C4—42no—
485C4—42no—
486C4—42no—
487C4—122no—
488C4—122no—
489C4—122no—
490C3#144011yescharacteristic, complemented, Sylow
491C2—124no—
492C2#466411yescharacteristic
493C2#466511yescharacteristic
494C2#466911yescharacteristic
495C2#467011yescharacteristic
496C2#467211yescharacteristic
497C2#467411yescharacteristic
498C2#467511yescharacteristic
499C2#467511yescharacteristic
500C2#494011yescharacteristic
501C2#495611yescharacteristic
502C2#495911yescharacteristic
503C2#496111yescharacteristic
504C2#499011yescharacteristic
505C2#499111yescharacteristic
506C2#499211yescharacteristic
subgroupG/H
center, FrattiniC24C22×D3
commutatorC23×C3C22×C4
FittingC2×C3×#95C2
socle, cosocleC24×C3C23
prime radicalC24×D3C22
hypercenterC2×#95D3
hypocenterC3#1440
LCSG ▷ C23×C3 ▷ C3
UCSC1 ◁ C24 ◁ C2×#95

Complements

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

NH ≅ G/Ntype
4. C2×C3×#95C2semidirect
5. C2×C3⋊#95C2semidirect
6. C2×C3⋊#95C2semidirect
7. C2×C3⋊#95C2semidirect
24. C2×(C2×D3)⋊C4C4semidirect
35. C2×#95D3semidirect
490. C3#1440semidirect

Maximal subgroups

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

subgroupindex
C22×(C2×D3)⋊C42
C2×C3×#952
C2×C3⋊#952
#14403