Finite Group Databasebeta

← #15671645

Subgroups — #15671645

Order 2944.

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×D23)⋊C4C211yesmaximal, characteristic
2C22×(C2×D23)⋊C4C211yesmaximal, characteristic
3C22×(C2×D23)⋊C4C211yesmaximal, characteristic
4C2×C23⋊#95C211yesmaximal, characteristic, complemented
5C2×C23⋊#95C211yesmaximal, characteristic, complemented
6C2×C23⋊#95C211yesmaximal, characteristic, complemented
7C2×C23×#95C211yesmaximal, characteristic, complemented
8C24×D23C2211yescharacteristic
9C23×C4×C23C2211yescharacteristic
10C23×C4×C23C2211yescharacteristic
11C23×C4×C23C2211yescharacteristic
12C23×Dic23C2211yescharacteristic
13C23×Dic23C2211yescharacteristic
14C23×Dic23C2211yescharacteristic
15C2×(C2×D23)⋊C4—22no—
16C2×(C2×D23)⋊C4—22no—
17C2×(C2×D23)⋊C4—22no—
18C2×(C2×D23)⋊C4—22no—
19C2×(C2×D23)⋊C4—22no—
20C2×(C2×D23)⋊C4—22no—
21C2×(C2×D23)⋊C4—22no—
22C2×(C2×D23)⋊C4—22no—
23C2×(C2×D23)⋊C4C414yescomplemented
24C23×#95—22no—
25C23⋊#95—22no—
26C23⋊#95—22no—
27C23⋊#95—22no—
28C24×C23C2311yescharacteristic
29C23×D23—21no—
30C23×D23—21no—
31C23×D23—21no—
32C23×D23—21no—
33C23×D23—21no—
34C23×D23—21no—
35C23×D23—21no—
36C23×D23—21no—
37C23×D23—21no—
38C23×D23—21no—
39C23×D23—21no—
40C23×D23—21no—
41C23×D23C2×C412yes—
42C23×D23D412yes—
43C23×D23D412yes—
44C22×C4×C23—21no—
45C22×C4×C23—21no—
46C22×C4×C23—21no—
47C22×C4×C23—21no—
48C22×C4×C23—21no—
49C22×C4×C23—21no—
50C22×C4×C23—21no—
51C22×C4×C23—21no—
52C22×C4×C23—21no—
53C22×C4×C23—21no—
54C22×C4×C23—21no—
55C22×C4×C23—21no—
56C22×C4×C23—21no—
57C22×C4×C23—21no—
58C22×C4×C23—21no—
59C22×C4×C23—21no—
60C22×C4×C23—21no—
61C22×C4×C23—21no—
62C22×C4×C23C2×C412yes—
63C22×C4×C23D412yes—
64C22×C4×C23D412yes—
65C22×Dic23—21no—
66C22×Dic23—21no—
67C22×Dic23—21no—
68C22×Dic23—21no—
69C22×Dic23—21no—
70C22×Dic23—21no—
71C22×Dic23—21no—
72C22×Dic23—21no—
73C22×Dic23—21no—
74C22×Dic23—21no—
75C22×Dic23—21no—
76C22×Dic23—21no—
77C22×Dic23—21no—
78C22×Dic23—21no—
79C22×Dic23—21no—
80C22×Dic23—21no—
81C22×Dic23—21no—
82C22×Dic23—21no—
83C22×Dic23C2×C412yes—
84C22×Dic23D412yes—
85C22×Dic23D412yes—
86(C2×D23)⋊C4—28no—
87(C2×D23)⋊C4—28no—
88(C2×D23)⋊C4—28no—
89C23×C23C22×C411yescharacteristic
90C23×C23C2×D411yescharacteristic
91C23×C23C2×D411yescharacteristic
92C23×C23C2×D411yescharacteristic
93C23×C23C2×D411yescharacteristic
94C23×C23C2×D411yescharacteristic
95C23×C23C2×D411yescharacteristic
96C23×C23#4111yescharacteristic
97C23×C23#4111yescharacteristic
98C23×C23#4111yescharacteristic
99C23×C23#4111yescharacteristic
100C23×C23#4111yescharacteristic
101C23×C23#4111yescharacteristic
102C23×C23#4111yescharacteristic
103C23×C23#4111yescharacteristic
104C22×D23—22no—
105C22×D23—22no—
106C22×D23—22no—
107C22×D23—22no—
108C22×D23—22no—
109C22×D23—22no—
110C22×D23—22no—
111C22×D23—22no—
112C22×D23—22no—
113C22×D23—22no—
114C22×D23—22no—
115C22×D23—22no—
116C22×D23—22no—
117C22×D23—22no—
118C22×D23—22no—
119C22×D23—22no—
120C22×D23—22no—
121C22×D23—22no—
122C22×D23—41no—
123C22×D23—41no—
124C22×D23—41no—
125C22×D23—41no—
126C22×D23—41no—
127C22×D23—41no—
128C22×D23—41no—
129C22×D23—41no—
130C22×D23—41no—
131C22×D23—41no—
132C22×D23—41no—
133C22×D23—41no—
134C22×D23—41no—
135C22×D23—41no—
136C22×D23—41no—
137C22×D23—41no—
138C22×D23C22⋊C414yes—
139C2×C4×C23—22no—
140C2×C4×C23—22no—
141C2×C4×C23—22no—
142C2×C4×C23—22no—
143C2×C4×C23—22no—
144C2×C4×C23—22no—
145C2×C4×C23—22no—
146C2×C4×C23—22no—
147C2×C4×C23—22no—
148C2×C4×C23—41no—
149C2×C4×C23—41no—
150C2×C4×C23—41no—
151C2×C4×C23—41no—
152C2×C4×C23—41no—
153C2×C4×C23—41no—
154C2×C4×C23—41no—
155C2×C4×C23—41no—
156C2×C4×C23—41no—
157C2×C4×C23—41no—
158C2×C4×C23—41no—
159C2×C4×C23—41no—
160C2×Dic23—22no—
161C2×Dic23—22no—
162C2×Dic23—22no—
163C2×Dic23—22no—
164C2×Dic23—22no—
165C2×Dic23—22no—
166C2×Dic23—22no—
167C2×Dic23—22no—
168C2×Dic23—22no—
169C2×Dic23—41no—
170C2×Dic23—41no—
171C2×Dic23—41no—
172C2×Dic23—41no—
173C2×Dic23—41no—
174C2×Dic23—41no—
175C2×Dic23—41no—
176C2×Dic23—41no—
177C2×Dic23—41no—
178C2×Dic23—41no—
179C2×Dic23—41no—
180C2×Dic23—41no—
181#1440—231nomaximal, Sylow
182C22×C23C2×C22⋊C411yescharacteristic
183C22×C23#11711yescharacteristic
184C22×C23#11711yescharacteristic
185C22×C23C4×D411yescharacteristic
186C22×C23C4×D411yescharacteristic
187C22×C23C4×D411yescharacteristic
188C22×C23C4×D411yescharacteristic
189C22×C23#12011yescharacteristic
190C22×C23#12011yescharacteristic
191C22×C23#12111yescharacteristic
192C22×C23#12111yescharacteristic
193C22×C23#12111yescharacteristic
194C22×C23#12111yescharacteristic
195C22×C23#12111yescharacteristic
196C22×C23#12111yescharacteristic
197C22×C23#12111yescharacteristic
198C22×C23#12111yescharacteristic
199C22×C23#12311yescharacteristic
200C22×C23#12311yescharacteristic
201C22×C23#12311yescharacteristic
202C22×C23#12311yescharacteristic
203C22×C23#12311yescharacteristic
204C22×C23#12311yescharacteristic
205C22×C23#12311yescharacteristic
206C22×C23#12311yescharacteristic
207C22×C23#12311yescharacteristic
208C22×C23#12311yescharacteristic
209C22×C23#12411yescharacteristic
210C22×C23#12411yescharacteristic
211C22×C23#12411yescharacteristic
212C22×C23#12411yescharacteristic
213C22×C23#12611yescharacteristic
214C22×C23#12611yescharacteristic
215C22×C23#12611yescharacteristic
216C22×C23#12611yescharacteristic
217C2×D23—24no—
218C2×D23—24no—
219C2×D23—24no—
220C2×D23—42no—
221C2×D23—42no—
222C2×D23—42no—
223C2×D23—42no—
224C2×D23—42no—
225C2×D23—42no—
226C2×D23—42no—
227C2×D23—42no—
228C2×D23—42no—
229C2×D23—42no—
230C2×D23—42no—
231C2×D23—42no—
232C4×C23—42no—
233C4×C23—42no—
234C4×C23—42no—
235Dic23—42no—
236Dic23—42no—
237Dic23—42no—
238C22×C22⋊C4—231no—
239C22×C22⋊C4—231no—
240C22×C22⋊C4—231no—
241C2×#95—231no—
242C2×#95—231no—
243C2×#95—231no—
244C2×#95D2311yescharacteristic, complemented
245C2×C23#38111yescharacteristic
246C2×C23#38611yescharacteristic
247C2×C23#38611yescharacteristic
248C2×C23#38811yescharacteristic
249C2×C23#38811yescharacteristic
250C2×C23#38811yescharacteristic
251C2×C23#38811yescharacteristic
252C2×C23#39411yescharacteristic
253C2×C23#39411yescharacteristic
254C2×C23#39411yescharacteristic
255C2×C23#39411yescharacteristic
256C2×C23#39711yescharacteristic
257C2×C23#39711yescharacteristic
258C2×C23#39711yescharacteristic
259C2×C23#39711yescharacteristic
260D23—44no—
261C25—231no—
262C23×C4—231no—
263C23×C4—231no—
264C23×C4—231no—
265C23×C4C2×D2311yescharacteristic
266C23×C4C2×D2311yescharacteristic
267C23×C4C2×D2311yescharacteristic
268C2×C22⋊C4—234no—
269C2×C22⋊C4—462no—
270C2×C22⋊C4—462no—
271C2×C22⋊C4—462no—
272C2×C22⋊C4—462no—
273C2×C22⋊C4—462no—
274C2×C22⋊C4—462no—
275C2×C22⋊C4—462no—
276C2×C22⋊C4—462no—
277#95—22no—
278#95—462no—
279#95—462no—
280#95—462no—
281C23#144011yescharacteristic, complemented, Sylow
282C24—232no—
283C24—232no—
284C24—232no—
285C24—461no—
286C24—461no—
287C24—461no—
288C24—461no—
289C24—461no—
290C24—461no—
291C24—461no—
292C24—461no—
293C24—461no—
294C24—461no—
295C24—461no—
296C24—461no—
297C24C22×D2311yescharacteristic
298C22×C4—21no—
299C22×C4—21no—
300C22×C4—21no—
301C22×C4—21no—
302C22×C4—21no—
303C22×C4—21no—
304C22×C4—21no—
305C22×C4—21no—
306C22×C4—21no—
307C22×C4—21no—
308C22×C4—21no—
309C22×C4—21no—
310C22×C4—21no—
311C22×C4—21no—
312C22×C4—21no—
313C22×C4—21no—
314C22×C4—21no—
315C22×C4—21no—
316C22×C4—232no—
317C22×C4—232no—
318C22×C4—232no—
319C22×C4—461no—
320C22×C4—461no—
321C22×C4—461no—
322C22×C4—461no—
323C22×C4—461no—
324C22×C4—461no—
325C22×C4—461no—
326C22×C4—461no—
327C22×C4—461no—
328C22×C4—461no—
329C22×C4—461no—
330C22×C4—461no—
331C22×C4—461no—
332C22×C4—461no—
333C22×C4—461no—
334C22×C4—461no—
335C22×C4—461no—
336C22×C4—461no—
337C22×C4C4×D2312yes—
338C22×C4D9212yes—
339C22×C4C22⋊D2312yes—
340C22⋊C4—468no—
341C22⋊C4—468no—
342C22⋊C4—468no—
343C23—234no—
344C23—462no—
345C23—462no—
346C23—462no—
347C23—462no—
348C23—462no—
349C23—462no—
350C23—462no—
351C23—462no—
352C23—462no—
353C23—462no—
354C23—462no—
355C23—462no—
356C23—462no—
357C23—462no—
358C23—462no—
359C23—462no—
360C23—462no—
361C23—462no—
362C23—921no—
363C23—921no—
364C23—921no—
365C23—921no—
366C23—921no—
367C23—921no—
368C23—921no—
369C23—921no—
370C23—921no—
371C23—921no—
372C23—921no—
373C23—921no—
374C23—921no—
375C23—921no—
376C23—921no—
377C23—921no—
378C23C2×C4×D2311yescharacteristic
379C23C2×D9211yescharacteristic
380C23#6728811yescharacteristic
381C23#6728811yescharacteristic
382C23#6728811yescharacteristic
383C23#6728811yescharacteristic
384C23D4×D2311yescharacteristic
385C23D4×D2311yescharacteristic
386C23D4×D2311yescharacteristic
387C23D4×D2311yescharacteristic
388C23#6729011yescharacteristic
389C23#6729011yescharacteristic
390C23#6729211yescharacteristic
391C23#6729211yescharacteristic
392C23C2×C22⋊D2311yescharacteristic
393C2×C4—22no—
394C2×C4—22no—
395C2×C4—22no—
396C2×C4—22no—
397C2×C4—22no—
398C2×C4—22no—
399C2×C4—22no—
400C2×C4—22no—
401C2×C4—22no—
402C2×C4—41no—
403C2×C4—41no—
404C2×C4—41no—
405C2×C4—41no—
406C2×C4—41no—
407C2×C4—41no—
408C2×C4—41no—
409C2×C4—41no—
410C2×C4—41no—
411C2×C4—41no—
412C2×C4—41no—
413C2×C4—41no—
414C2×C4—462no—
415C2×C4—462no—
416C2×C4—462no—
417C2×C4—462no—
418C2×C4—462no—
419C2×C4—462no—
420C2×C4—462no—
421C2×C4—462no—
422C2×C4—462no—
423C2×C4—921no—
424C2×C4—921no—
425C2×C4—921no—
426C2×C4—921no—
427C2×C4—921no—
428C2×C4—921no—
429C2×C4—921no—
430C2×C4—921no—
431C2×C4—921no—
432C2×C4—921no—
433C2×C4—921no—
434C2×C4—921no—
435C22—464no—
436C22—464no—
437C22—464no—
438C22—922no—
439C22—922no—
440C22—922no—
441C22—922no—
442C22—922no—
443C22—922no—
444C22—922no—
445C22—922no—
446C22—922no—
447C22—922no—
448C22—922no—
449C22—922no—
450C22#1062504311yescharacteristic
451C22C4×D9211yescharacteristic
452C22#1062504611yescharacteristic
453C22#1062504711yescharacteristic
454C22C22⋊C4×D2311yescharacteristic
455C22(C22⋊D23)⋊C411yescharacteristic
456C22#1062505311yescharacteristic
457C22#1062505411yescharacteristic
458C22#1062505411yescharacteristic
459C22#1062505411yescharacteristic
460C22#1062505511yescharacteristic
461C22#1062505511yescharacteristic
462C22#1062505511yescharacteristic
463C22#1062505611yescharacteristic
464C22#1062505611yescharacteristic
465C22#1062505711yescharacteristic
466C22#1062506311yescharacteristic
467C22#1062506411yescharacteristic
468C22#1062506511yescharacteristic
469C22#1062506511yescharacteristic
470C22#1062506511yescharacteristic
471C22#1062506511yescharacteristic
472C22#1062506511yescharacteristic
473C22#1062506611yescharacteristic
474C22#1062506611yescharacteristic
475C22#1062506911yescharacteristic
476C22#1062506911yescharacteristic
477C22#1062506911yescharacteristic
478C22C4×C22⋊D2311yescharacteristic
479C22#1062510011yescharacteristic
480C22#1062510111yescharacteristic
481C22#1062510811yescharacteristic
482C22#1062510911yescharacteristic
483C22#1062511011yescharacteristic
484C22#1062511811yescharacteristic
485C4—42no—
486C4—42no—
487C4—42no—
488C4—922no—
489C4—922no—
490C4—922no—
491C2—924no—
492C2#1309227911yescharacteristic
493C2#1309229311yescharacteristic
494C2#1309229511yescharacteristic
495C2#1309230611yescharacteristic
496C2#1309230711yescharacteristic
497C2#1309230811yescharacteristic
498C2#1309230911yescharacteristic
499C2#1309233211yescharacteristic
500C2#1309233311yescharacteristic
501C2#1309233411yescharacteristic
502C2#1309233511yescharacteristic
503C2#1309234311yescharacteristic
504C2#1309234411yescharacteristic
505C2#1309234611yescharacteristic
506C2#1309234611yescharacteristic
subgroupG/H
center, FrattiniC24C22×D23
commutatorC23×C23C22×C4
FittingC2×C23×#95C2
socle, cosocleC24×C23C23
prime radicalC24×D23C22
hypercenterC2×#95D23
hypocenterC23#1440
LCSG ▷ C23×C23 ▷ C23
UCSC1 ◁ C24 ◁ C2×#95

Complements

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

NH ≅ G/Ntype
4. C2×C23⋊#95C2semidirect
5. C2×C23⋊#95C2semidirect
6. C2×C23⋊#95C2semidirect
7. C2×C23×#95C2semidirect
23. C2×(C2×D23)⋊C4C4semidirect
244. C2×#95D23semidirect
281. C23#1440semidirect

Maximal subgroups

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

subgroupindex
C22×(C2×D23)⋊C42
C2×C23⋊#952
C2×C23×#952
#144023