Finite Group Databasebeta

← #27139984

Subgroups — #27139984

Order 12416.

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×#13095488C211yesmaximal, characteristic
2C22×#13095488C211yesmaximal, characteristic
3C22×#13095488C211yesmaximal, characteristic
4C2×#15690717C211yesmaximal, characteristic, complemented
5C2×#15690717C211yesmaximal, characteristic, complemented
6C2×#15690717C211yesmaximal, characteristic, complemented
7C2×#95×C97C211yesmaximal, characteristic, complemented
8C24×D97C2211yescharacteristic
9C23×Dic97C2211yescharacteristic
10C23×Dic97C2211yescharacteristic
11C23×Dic97C2211yescharacteristic
12C2×#13095488—22no—
13C2×#13095488—22no—
14C2×#13095488—22no—
15C2×#13095488—22no—
16C2×#13095488—22no—
17C2×#13095488—22no—
18C2×#13095488—22no—
19C2×#13095488—22no—
20C2×#13095488C414yescomplemented
21#15690717—22no—
22#15690717—22no—
23#15690717—22no—
24C23×C4×C97C2211yescharacteristic
25C23×C4×C97C2211yescharacteristic
26C23×C4×C97C2211yescharacteristic
27#95×C97—22no—
28C23×D97—21no—
29C23×D97—21no—
30C23×D97—21no—
31C23×D97—21no—
32C23×D97—21no—
33C23×D97—21no—
34C23×D97—21no—
35C23×D97—21no—
36C23×D97—21no—
37C23×D97—21no—
38C23×D97—21no—
39C23×D97—21no—
40C23×D97C2×C412yes—
41C23×D97D412yes—
42C23×D97D412yes—
43C22×Dic97—21no—
44C22×Dic97—21no—
45C22×Dic97—21no—
46C22×Dic97—21no—
47C22×Dic97—21no—
48C22×Dic97—21no—
49C22×Dic97—21no—
50C22×Dic97—21no—
51C22×Dic97—21no—
52C22×Dic97—21no—
53C22×Dic97—21no—
54C22×Dic97—21no—
55C22×Dic97—21no—
56C22×Dic97—21no—
57C22×Dic97—21no—
58C22×Dic97—21no—
59C22×Dic97—21no—
60C22×Dic97—21no—
61C22×Dic97C2×C412yes—
62C22×Dic97D412yes—
63C22×Dic97D412yes—
64#13095488—28no—
65#13095488—28no—
66#13095488—28no—
67C24×C97C2311yescharacteristic
68C22×C4×C97—21no—
69C22×C4×C97—21no—
70C22×C4×C97—21no—
71C22×C4×C97—21no—
72C22×C4×C97—21no—
73C22×C4×C97—21no—
74C22×C4×C97—21no—
75C22×C4×C97—21no—
76C22×C4×C97—21no—
77C22×C4×C97—21no—
78C22×C4×C97—21no—
79C22×C4×C97—21no—
80C22×C4×C97—21no—
81C22×C4×C97—21no—
82C22×C4×C97—21no—
83C22×C4×C97—21no—
84C22×C4×C97—21no—
85C22×C4×C97—21no—
86C22×C4×C97C2×C412yes—
87C22×C4×C97D412yes—
88C22×C4×C97D412yes—
89C23×C97C22×C411yescharacteristic
90C23×C97C2×D411yescharacteristic
91C23×C97C2×D411yescharacteristic
92C23×C97C2×D411yescharacteristic
93C23×C97C2×D411yescharacteristic
94C23×C97C2×D411yescharacteristic
95C23×C97C2×D411yescharacteristic
96C23×C97#4111yescharacteristic
97C23×C97#4111yescharacteristic
98C23×C97#4111yescharacteristic
99C23×C97#4111yescharacteristic
100C23×C97#4111yescharacteristic
101C23×C97#4111yescharacteristic
102C23×C97#4111yescharacteristic
103C23×C97#4111yescharacteristic
104C22×D97—22no—
105C22×D97—22no—
106C22×D97—22no—
107C22×D97—22no—
108C22×D97—22no—
109C22×D97—22no—
110C22×D97—22no—
111C22×D97—22no—
112C22×D97—22no—
113C22×D97—22no—
114C22×D97—22no—
115C22×D97—22no—
116C22×D97—22no—
117C22×D97—22no—
118C22×D97—22no—
119C22×D97—22no—
120C22×D97—22no—
121C22×D97—22no—
122C22×D97—41no—
123C22×D97—41no—
124C22×D97—41no—
125C22×D97—41no—
126C22×D97—41no—
127C22×D97—41no—
128C22×D97—41no—
129C22×D97—41no—
130C22×D97—41no—
131C22×D97—41no—
132C22×D97—41no—
133C22×D97—41no—
134C22×D97—41no—
135C22×D97—41no—
136C22×D97—41no—
137C22×D97—41no—
138C22×D97C22⋊C414yes—
139C2×C4×C97—22no—
140C2×C4×C97—22no—
141C2×C4×C97—22no—
142C2×C4×C97—22no—
143C2×C4×C97—22no—
144C2×C4×C97—22no—
145C2×C4×C97—22no—
146C2×C4×C97—22no—
147C2×C4×C97—22no—
148C2×C4×C97—41no—
149C2×C4×C97—41no—
150C2×C4×C97—41no—
151C2×C4×C97—41no—
152C2×C4×C97—41no—
153C2×C4×C97—41no—
154C2×C4×C97—41no—
155C2×C4×C97—41no—
156C2×C4×C97—41no—
157C2×C4×C97—41no—
158C2×C4×C97—41no—
159C2×C4×C97—41no—
160C2×Dic97—22no—
161C2×Dic97—22no—
162C2×Dic97—22no—
163C2×Dic97—22no—
164C2×Dic97—22no—
165C2×Dic97—22no—
166C2×Dic97—22no—
167C2×Dic97—22no—
168C2×Dic97—22no—
169C2×Dic97—41no—
170C2×Dic97—41no—
171C2×Dic97—41no—
172C2×Dic97—41no—
173C2×Dic97—41no—
174C2×Dic97—41no—
175C2×Dic97—41no—
176C2×Dic97—41no—
177C2×Dic97—41no—
178C2×Dic97—41no—
179C2×Dic97—41no—
180C2×Dic97—41no—
181C22×C97C2×C22⋊C411yescharacteristic
182C22×C97#11711yescharacteristic
183C22×C97#11711yescharacteristic
184C22×C97C4×D411yescharacteristic
185C22×C97C4×D411yescharacteristic
186C22×C97C4×D411yescharacteristic
187C22×C97C4×D411yescharacteristic
188C22×C97#12011yescharacteristic
189C22×C97#12011yescharacteristic
190C22×C97#12111yescharacteristic
191C22×C97#12111yescharacteristic
192C22×C97#12111yescharacteristic
193C22×C97#12111yescharacteristic
194C22×C97#12111yescharacteristic
195C22×C97#12111yescharacteristic
196C22×C97#12111yescharacteristic
197C22×C97#12111yescharacteristic
198C22×C97#12311yescharacteristic
199C22×C97#12311yescharacteristic
200C22×C97#12311yescharacteristic
201C22×C97#12311yescharacteristic
202C22×C97#12311yescharacteristic
203C22×C97#12311yescharacteristic
204C22×C97#12311yescharacteristic
205C22×C97#12311yescharacteristic
206C22×C97#12311yescharacteristic
207C22×C97#12311yescharacteristic
208C22×C97#12411yescharacteristic
209C22×C97#12411yescharacteristic
210C22×C97#12411yescharacteristic
211C22×C97#12411yescharacteristic
212C22×C97#12611yescharacteristic
213C22×C97#12611yescharacteristic
214C22×C97#12611yescharacteristic
215C22×C97#12611yescharacteristic
216C2×D97—24no—
217C2×D97—24no—
218C2×D97—24no—
219C2×D97—42no—
220C2×D97—42no—
221C2×D97—42no—
222C2×D97—42no—
223C2×D97—42no—
224C2×D97—42no—
225C2×D97—42no—
226C2×D97—42no—
227C2×D97—42no—
228C2×D97—42no—
229C2×D97—42no—
230C2×D97—42no—
231C4×C97—42no—
232C4×C97—42no—
233C4×C97—42no—
234Dic97—42no—
235Dic97—42no—
236Dic97—42no—
237C2×C97#38111yescharacteristic
238C2×C97#38611yescharacteristic
239C2×C97#38611yescharacteristic
240C2×C97#38811yescharacteristic
241C2×C97#38811yescharacteristic
242C2×C97#38811yescharacteristic
243C2×C97#38811yescharacteristic
244C2×C97#39411yescharacteristic
245C2×C97#39411yescharacteristic
246C2×C97#39411yescharacteristic
247C2×C97#39411yescharacteristic
248C2×C97#39711yescharacteristic
249C2×C97#39711yescharacteristic
250C2×C97#39711yescharacteristic
251C2×C97#39711yescharacteristic
252D97—44no—
253#1440—971nomaximal, Sylow
254C97#144011yescharacteristic, complemented, Sylow
255C22×C22⋊C4—971no—
256C22×C22⋊C4—971no—
257C22×C22⋊C4—971no—
258C2×#95—971no—
259C2×#95—971no—
260C2×#95—971no—
261C2×#95D9711yescharacteristic, complemented
262C25—971no—
263C23×C4—971no—
264C23×C4—971no—
265C23×C4—971no—
266C23×C4C2×D9711yescharacteristic
267C23×C4C2×D9711yescharacteristic
268C23×C4C2×D9711yescharacteristic
269C2×C22⋊C4—974no—
270C2×C22⋊C4—1942no—
271C2×C22⋊C4—1942no—
272C2×C22⋊C4—1942no—
273C2×C22⋊C4—1942no—
274C2×C22⋊C4—1942no—
275C2×C22⋊C4—1942no—
276C2×C22⋊C4—1942no—
277C2×C22⋊C4—1942no—
278#95—22no—
279#95—1942no—
280#95—1942no—
281#95—1942no—
282C24—972no—
283C24—972no—
284C24—972no—
285C24—1941no—
286C24—1941no—
287C24—1941no—
288C24—1941no—
289C24—1941no—
290C24—1941no—
291C24—1941no—
292C24—1941no—
293C24—1941no—
294C24—1941no—
295C24—1941no—
296C24—1941no—
297C24C22×D9711yescharacteristic
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—972no—
317C22×C4—972no—
318C22×C4—972no—
319C22×C4—1941no—
320C22×C4—1941no—
321C22×C4—1941no—
322C22×C4—1941no—
323C22×C4—1941no—
324C22×C4—1941no—
325C22×C4—1941no—
326C22×C4—1941no—
327C22×C4—1941no—
328C22×C4—1941no—
329C22×C4—1941no—
330C22×C4—1941no—
331C22×C4—1941no—
332C22×C4—1941no—
333C22×C4—1941no—
334C22×C4—1941no—
335C22×C4—1941no—
336C22×C4—1941no—
337C22×C4C4×D9712yes—
338C22×C4D38812yes—
339C22×C4C22⋊D9712yes—
340C22⋊C4—1948no—
341C22⋊C4—1948no—
342C22⋊C4—1948no—
343C23—974no—
344C23—3881no—
345C23—3881no—
346C23—3881no—
347C23—3881no—
348C23—3881no—
349C23—3881no—
350C23—3881no—
351C23—3881no—
352C23—3881no—
353C23—3881no—
354C23—3881no—
355C23—3881no—
356C23—3881no—
357C23—3881no—
358C23—3881no—
359C23—3881no—
360C23—1942no—
361C23—1942no—
362C23—1942no—
363C23—1942no—
364C23—1942no—
365C23—1942no—
366C23—1942no—
367C23—1942no—
368C23—1942no—
369C23—1942no—
370C23—1942no—
371C23—1942no—
372C23—1942no—
373C23—1942no—
374C23—1942no—
375C23—1942no—
376C23—1942no—
377C23—1942no—
378C23C2×C4×D9711yescharacteristic
379C23D4×D9711yescharacteristic
380C23D4×D9711yescharacteristic
381C23D4×D9711yescharacteristic
382C23D4×D9711yescharacteristic
383C23C2×C22⋊D9711yescharacteristic
384C23C2×D38811yescharacteristic
385C23#1309551011yescharacteristic
386C23#1309551011yescharacteristic
387C23#1309551111yescharacteristic
388C23#1309551111yescharacteristic
389C23#1309551111yescharacteristic
390C23#1309551111yescharacteristic
391C23#1309551211yescharacteristic
392C23#1309551211yescharacteristic
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—3881no—
415C2×C4—3881no—
416C2×C4—3881no—
417C2×C4—3881no—
418C2×C4—3881no—
419C2×C4—3881no—
420C2×C4—3881no—
421C2×C4—3881no—
422C2×C4—3881no—
423C2×C4—3881no—
424C2×C4—3881no—
425C2×C4—3881no—
426C2×C4—1942no—
427C2×C4—1942no—
428C2×C4—1942no—
429C2×C4—1942no—
430C2×C4—1942no—
431C2×C4—1942no—
432C2×C4—1942no—
433C2×C4—1942no—
434C2×C4—1942no—
435C22—3882no—
436C22—3882no—
437C22—3882no—
438C22—3882no—
439C22—3882no—
440C22—3882no—
441C22—3882no—
442C22—3882no—
443C22—3882no—
444C22—3882no—
445C22—3882no—
446C22—3882no—
447C22—1944no—
448C22—1944no—
449C22—1944no—
450C22C22⋊C4×D9711yescharacteristic
451C22#1569076711yescharacteristic
452C22#1569076811yescharacteristic
453C22#1569077011yescharacteristic
454C22C4×C22⋊D9711yescharacteristic
455C22#1569077211yescharacteristic
456C22C4×D38811yescharacteristic
457C22#1569077811yescharacteristic
458C22#1569078011yescharacteristic
459C22#1569078111yescharacteristic
460C22#1569078211yescharacteristic
461C22#1569078311yescharacteristic
462C22#1569078311yescharacteristic
463C22#1569078311yescharacteristic
464C22#1569078411yescharacteristic
465C22#1569078511yescharacteristic
466C22#1569078511yescharacteristic
467C22#1569079211yescharacteristic
468C22#1569079211yescharacteristic
469C22#1569079211yescharacteristic
470C22#1569079311yescharacteristic
471C22#1569079411yescharacteristic
472C22#1569079511yescharacteristic
473C22#1569079511yescharacteristic
474C22#1569079511yescharacteristic
475C22#1569079511yescharacteristic
476C22#1569079511yescharacteristic
477C22#1569079611yescharacteristic
478C22#1569079611yescharacteristic
479C22#1569079811yescharacteristic
480C22#1569079911yescharacteristic
481C22#1569080411yescharacteristic
482C22#1569080511yescharacteristic
483C22#1569080511yescharacteristic
484C22#1569080511yescharacteristic
485C4—42no—
486C4—42no—
487C4—42no—
488C4—3882no—
489C4—3882no—
490C4—3882no—
491C2—3884no—
492C2#2026059711yescharacteristic
493C2#2026061111yescharacteristic
494C2#2026061311yescharacteristic
495C2#2026062411yescharacteristic
496C2#2026062511yescharacteristic
497C2#2026062611yescharacteristic
498C2#2026062711yescharacteristic
499C2#2026065011yescharacteristic
500C2#2026065111yescharacteristic
501C2#2026065211yescharacteristic
502C2#2026065311yescharacteristic
503C2#2026066111yescharacteristic
504C2#2026066211yescharacteristic
505C2#2026066411yescharacteristic
506C2#2026066411yescharacteristic
subgroupG/H
center, FrattiniC24C22×D97
commutatorC23×C97C22×C4
FittingC2×#95×C97C2
socle, cosocleC24×C97C23
prime radicalC24×D97C22
hypercenterC2×#95D97
hypocenterC97#1440
LCSG ▷ C23×C97 ▷ C97
UCSC1 ◁ C24 ◁ C2×#95

Complements

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

NH ≅ G/Ntype
4. C2×#15690717C2semidirect
5. C2×#15690717C2semidirect
6. C2×#15690717C2semidirect
7. C2×#95×C97C2semidirect
20. C2×#13095488C4semidirect
254. C97#1440semidirect
261. C2×#95D97semidirect

Maximal subgroups

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

subgroupindex
C22×#130954882
C2×#156907172
C2×#95×C972
#144097