Finite Group Databasebeta

← #11859510

Subgroups — #11859510

Order 1152.

1452 conjugacy classes of subgroups.

The subgroup lattice has 609 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64116C211yesmaximal, characteristic, complemented
2C2×#64110C211yesmaximal, characteristic, complemented
3#10596019C211yesmaximal, characteristic
4C32×#435C211yesmaximal, characteristic, complemented
5#10592826C211yesmaximal, characteristic, complemented
6#10592810C211yesmaximal, characteristic, complemented
7#10592710C211yesmaximal, characteristic, complemented
8#10592536C211yesmaximal, characteristic, complemented
9#10592535C211yesmaximal, characteristic, complemented
10#10592429C211yesmaximal, characteristic, complemented
11#10592427C211yesmaximal, characteristic, complemented
12#10592426C211yesmaximal, characteristic, complemented
13#10592426C211yesmaximal, characteristic, complemented
14#10592405C211yesmaximal, characteristic, complemented
15C3⋊D3×#97C211yesmaximal, characteristic, complemented
16#79480—34nomaximal
17C2×#3828C2211yescharacteristic
18C2×#3828C2211yescharacteristic
19C2×C32×M16C2211yescharacteristic
20C22×C32×C8C2211yescharacteristic
21C32×C4×D4C2211yescharacteristic
22#64149C411yescharacteristic
23#64147C411yescharacteristic
24C4×#638C2211yescharacteristic
25C4×#638C2211yescharacteristic
26C2×#3748C2211yescharacteristic
27C22×C3⋊(C3⋊C8)C2211yescharacteristic
28#64116—24no—
29#64110—24no—
30C2×#3743C2211yescharacteristic
31C2×#3743C2211yescharacteristic
32C2×#3743C2211yescharacteristic
33C2×#3743C2211yescharacteristic
34C2×C8×C3⋊D3C2211yescharacteristic
35C2×C8×C3⋊D3C2211yescharacteristic
36C2×C8×C3⋊D3C2211yescharacteristic
37C2×C8×C3⋊D3C2211yescharacteristic
38#64104C411yescharacteristic
39#64097C411yescharacteristic
40#64094C411yescharacteristic
41#64094C411yescharacteristic
42#64093C411yescharacteristic
43#64093C411yescharacteristic
44C4×C4⋊(C3⋊D3)C2211yescharacteristic
45C42×C3⋊D3C2211yescharacteristic
46C32×C4⋊C8C2211yescharacteristic
47C32×C22⋊C8C2211yescharacteristic
48C32×C22⋊C8C2211yescharacteristic
49C32×#97C2211yescharacteristic
50#63657C2211yescharacteristic
51#63657C2211yescharacteristic
52#63647C2211yescharacteristic
53#63647C2211yescharacteristic
54#63647C2211yescharacteristic
55#63647C2211yescharacteristic
56#63642C2211yescharacteristic
57#63642C2211yescharacteristic
58#63641C2211yescharacteristic
59#63641C2211yescharacteristic
60C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic
61#63630C2211yescharacteristic
62C2×#907—34no—
63C2×#901—34no—
64#5548—34no—
65C3×#435D314yescomplemented
66#5127—34no—
67#5111—34no—
68#5011—34no—
69#4837—34no—
70#4836—34no—
71#4730—34no—
72#4728—34no—
73#4727—34no—
74#4727—34no—
75#4706—34no—
76D3×#97—34no—
77C2×C32×D4C2×C411yescharacteristic
78C22×C32×C4C2311yescharacteristic
79C22×C32×C4C2311yescharacteristic
80C2×#638C2×C411yescharacteristic
81C2×#638C2×C411yescharacteristic
82C2×#638C2×C411yescharacteristic
83C2×#638C2×C411yescharacteristic
84C2×#638C2×C411yescharacteristic
85C2×#638C2×C411yescharacteristic
86#3828—22no—
87#3828—22no—
88#3828—22no—
89#3828—22no—
90C2×C4⋊(C3⋊D3)C2×C411yescharacteristic
91C2×C4⋊(C3⋊D3)C2×C411yescharacteristic
92C2×C4⋊(C3⋊D3)C2×C411yescharacteristic
93C2×C4×C3⋊D3C2×C411yescharacteristic
94C2×C4×C3⋊D3C2×C411yescharacteristic
95C2×C4×C3⋊D3C2311yescharacteristic
96C2×C4×C3⋊D3C2311yescharacteristic
97C2×C4×C3⋊D3C2311yescharacteristic
98C2×#634C2×C411yescharacteristic
99C2×#634C2×C411yescharacteristic
100C32×M16—22no—
101C2×C32×C8—22no—
102C2×C32×C8C2311yescharacteristic
103C2×C32×C8C2311yescharacteristic
104C2×C32×C8C2311yescharacteristic
105C2×C32×C8C2311yescharacteristic
106C32×C4⋊C4C2×C411yescharacteristic
107C32×C22⋊C4C2×C411yescharacteristic
108C32×C22⋊C4C2×C411yescharacteristic
109C32×C42C2311yescharacteristic
110#3757C2×C411yescharacteristic
111#3757C2×C411yescharacteristic
112#3752C2×C411yescharacteristic
113#3752C2×C411yescharacteristic
114#3752C2×C411yescharacteristic
115#3752C2×C411yescharacteristic
116C4⋊(C3⋊Dic3)C2×C411yescharacteristic
117#3750C2×C411yescharacteristic
118#3750C2×C411yescharacteristic
119C4×C3⋊Dic3C2×C411yescharacteristic
120C4×C3⋊Dic3C2×C411yescharacteristic
121C4×C3⋊Dic3C2311yescharacteristic
122#3748—22no—
123C2×C3⋊(C3⋊C8)—22no—
124C2×C3⋊(C3⋊C8)C2311yescharacteristic
125C2×C3⋊(C3⋊C8)C2311yescharacteristic
126C2×C3⋊(C3⋊C8)C2311yescharacteristic
127C2×C3⋊(C3⋊C8)C2311yescharacteristic
128#3743—22no—
129#3743—22no—
130#3743—22no—
131#3743—22no—
132C8×C3⋊D3—22no—
133C8×C3⋊D3—22no—
134C8×C3⋊D3—22no—
135C8×C3⋊D3D414yescomplemented
136#2932—91noSylow
137C2×#235—34no—
138C2×#235—34no—
139C2×C3×M16C2×D314yes—
140C22×C3×C8C2×D314yes—
141C3×C4×D4C2×D314yes—
142#940—34no—
143#938—34no—
144C4×#67—34no—
145C4×#67—34no—
146C2×#208—34no—
147C22×C3⋊C8—34no—
148#907—616no—
149#901—616no—
150C2×ΓL(1,𝔽25)—34no—
151C2×ΓL(1,𝔽25)—34no—
152C2×ΓL(1,𝔽25)—34no—
153C2×ΓL(1,𝔽25)—34no—
154C2×D3×C8—34no—
155C2×D3×C8—34no—
156C2×D3×C8—34no—
157C2×D3×C8—34no—
158#895—34no—
159#888—34no—
160#885—34no—
161#885—34no—
162#884—34no—
163#884—34no—
164C4×D12—34no—
165C42×D3—34no—
166C3×C4⋊C8C2×D314yes—
167C3×C22⋊C8C2×D314yes—
168C3×C22⋊C8C2×D314yes—
169C3×#97C2×D314yes—
170#830—34no—
171#830—34no—
172(C2×D3)⋊C8—34no—
173(C2×D3)⋊C8—34no—
174(C2×D3)⋊C8—34no—
175(C2×D3)⋊C8—34no—
176#815—34no—
177#815—34no—
178Dic3⋊C8—34no—
179Dic3⋊C8—34no—
180C4⋊(C3⋊C8)—34no—
181#803—34no—
182C23×C32C22×C411yescharacteristic
183C23×C32C22×C411yescharacteristic
184C22×C3⋊D3C22×C411yescharacteristic
185C22×C3⋊D3C22×C411yescharacteristic
186C22×C3⋊D3C22×C411yescharacteristic
187C32×D4—41no—
188C2×C32×C4—21no—
189C2×C32×C4—21no—
190C2×C32×C4—21no—
191C2×C32×C4—21no—
192C2×C32×C4C22×C411yescharacteristic
193C2×C32×C4C22×C411yescharacteristic
194C2×C32×C4C22×C411yescharacteristic
195C2×C32×C4C22×C411yescharacteristic
196C2×C32×C4C2411yescharacteristic
197#638—22no—
198#638—22no—
199#638—22no—
200#638—22no—
201#638—41no—
202#638—41no—
203C2×C3⋊Dic3C22×C411yescharacteristic
204C2×C3⋊Dic3C22×C411yescharacteristic
205C2×C3⋊Dic3C22×C411yescharacteristic
206C2×C3⋊Dic3C22×C411yescharacteristic
207C2×C3⋊Dic3C22×C411yescharacteristic
208C4⋊(C3⋊D3)—22no—
209C4⋊(C3⋊D3)—22no—
210C4⋊(C3⋊D3)—41no—
211C4×C3⋊D3—21no—
212C4×C3⋊D3—21no—
213C4×C3⋊D3—21no—
214C4×C3⋊D3—21no—
215C4×C3⋊D3—41no—
216C4×C3⋊D3—41no—
217C4×C3⋊D3C2×D412yes—
218C4×C3⋊D3#4112yes—
219#634—22no—
220#634—22no—
221C32×C8—21no—
222C32×C8—21no—
223C32×C8—21no—
224C32×C8C2×D412yes—
225C3⋊(C3⋊C8)—21no—
226C3⋊(C3⋊C8)—21no—
227C3⋊(C3⋊C8)—21no—
228C3⋊(C3⋊C8)C2×D412yes—
229C2×#131—91no—
230C2×#131—91no—
231#532—91no—
232#435—91no—
233#435—91no—
234#435—91no—
235#435—91no—
236#435—91no—
237#435—91no—
238#435—91no—
239#435C3⋊D311yescharacteristic, complemented
240#423—91no—
241#408—91no—
242#408—91no—
243C2×#97—91no—
244C2×C3×D4C4×D314yes—
245C22×C3×C4C22×D314yes—
246C22×C3×C4C22×D314yes—
247C2×#67—34no—
248C2×#67—34no—
249C2×#67—34no—
250C2×#67—34no—
251C2×#67—34no—
252C2×#67—34no—
253#235—68no—
254#235—68no—
255#235—68no—
256#235—68no—
257C2×D12—34no—
258C2×D12—34no—
259C2×D12—34no—
260C2×C4×D3—34no—
261C2×C4×D3—34no—
262C2×C4×D3—34no—
263C2×C4×D3—34no—
264C2×C4×D3—34no—
265C2×Dic6—34no—
266C2×Dic6—34no—
267C3×M16—28no—
268C2×C3×C8—28no—
269C2×C3×C8C22×D314yes—
270C2×C3×C8C22×D314yes—
271C2×C3×C8C22×D314yes—
272C2×C3×C8C22×D314yes—
273C3×C4⋊C4C4×D314yes—
274C3×C22⋊C4C4×D314yes—
275C3×C22⋊C4C4×D314yes—
276C3×C42C22×D314yes—
277#217—34no—
278#217—34no—
279(C2×D3)⋊C4—34no—
280(C2×D3)⋊C4—34no—
281(C2×D3)⋊C4—34no—
282(C2×D3)⋊C4—34no—
283C4⋊Dic3—34no—
284Dic3⋊C4—34no—
285Dic3⋊C4—34no—
286C4×Dic3—34no—
287C4×Dic3—34no—
288C4×Dic3—34no—
289#208—68no—
290C2×C3⋊C8—34no—
291C2×C3⋊C8—34no—
292C2×C3⋊C8—34no—
293C2×C3⋊C8—34no—
294C2×C3⋊C8—68no—
295ΓL(1,𝔽25)—68no—
296ΓL(1,𝔽25)—68no—
297ΓL(1,𝔽25)—68no—
298ΓL(1,𝔽25)—68no—
299D3×C8—316no—
300D3×C8—68no—
301D3×C8—68no—
302D3×C8—68no—
303C22×C32—21no—
304C22×C32—21no—
305C22×C32—21no—
306C22×C32—21no—
307C22×C32—21no—
308C22×C32—21no—
309C22×C32C23×C411yescharacteristic
310C2×C3⋊D3—21no—
311C2×C3⋊D3—21no—
312C2×C3⋊D3—21no—
313C2×C3⋊D3—21no—
314C2×C3⋊D3—21no—
315C2×C3⋊D3—21no—
316C2×C3⋊D3—21no—
317C2×C3⋊D3—21no—
318C2×C3⋊D3C4×D412yes—
319C32×C4—21no—
320C32×C4—21no—
321C32×C4—21no—
322C32×C4—21no—
323C32×C4C22×D411yescharacteristic
324C32×C4C2×#4111yescharacteristic
325C3⋊Dic3—21no—
326C3⋊Dic3—21no—
327C3⋊Dic3—21no—
328C3⋊Dic3—21no—
329C3⋊Dic3C4×D412yes—
330C2×#41—91no—
331C2×#41—91no—
332#131—184no—
333#131—184no—
334C2×M16—91no—
335C2×M16—91no—
336C2×M16—91no—
337C2×M16—91no—
338C2×M16—91no—
339C2×M16C2×C3⋊D311yescharacteristic
340C22×C8—91no—
341C22×C8—91no—
342C22×C8—91no—
343C22×C8—91no—
344C22×C8—91no—
345C22×C8C2×C3⋊D311yescharacteristic
346C4⋊Q8—91no—
347#127—91no—
348#124—91no—
349#124—91no—
350#121—91no—
351#121—91no—
352#121—91no—
353#121—91no—
354C4×D4—91no—
355C4×D4—91no—
356C4×D4—91no—
357C4×D4C2×C3⋊D311yescharacteristic
358C2×C42—91no—
359C4⋊C8—91no—
360C4⋊C8—91no—
361C4⋊C8—91no—
362C4⋊C8C2×C3⋊D311yescharacteristic
363C22⋊C8—91no—
364C22⋊C8—91no—
365C22⋊C8—91no—
366C22⋊C8—91no—
367C22⋊C8—91no—
368C22⋊C8—91no—
369C22⋊C8C2×C3⋊D311yescharacteristic
370C22⋊C8C2×C3⋊D311yescharacteristic
371#97—91no—
372#97—91no—
373#97—91no—
374#97C2×C3⋊D311yescharacteristic
375C23×C3C2×C4×D314yes—
376C23×C3C2×C4×D314yes—
377C22×D3—34no—
378C22×D3—34no—
379C22×D3—34no—
380C3×D4—44no—
381C2×C3×C4—24no—
382C2×C3×C4—24no—
383C2×C3×C4—24no—
384C2×C3×C4—24no—
385C2×C3×C4C2×C4×D314yes—
386C2×C3×C4C2×C4×D314yes—
387C2×C3×C4C2×C4×D314yes—
388C2×C3×C4C2×C4×D314yes—
389C2×C3×C4C23×D314yes—
390#67—68no—
391#67—68no—
392#67—68no—
393#67—68no—
394#67—124no—
395#67—124no—
396C2×Dic3—34no—
397C2×Dic3—34no—
398C2×Dic3—34no—
399C2×Dic3—34no—
400C2×Dic3—34no—
401D12—68no—
402D12—68no—
403D12—124no—
404C4×D3—38no—
405C4×D3—38no—
406C4×D3—64no—
407C4×D3—64no—
408C4×D3—64no—
409C4×D3—64no—
410C4×D3—124no—
411C4×D3—124no—
412Dic6—68no—
413Dic6—68no—
414C3×C8—24no—
415C3×C8—24no—
416C3×C8—24no—
417C3×C8D3×D418yes—
418C3⋊C8—38no—
419C3⋊C8—64no—
420C3⋊C8—64no—
421C3⋊C8—64no—
422C2×C32—41no—
423C2×C32—41no—
424C2×C32C2×C4×D411yescharacteristic
425C2×C32#56811yescharacteristic
426C2×C32#56811yescharacteristic
427C3⋊D3—22no—
428C3⋊D3—41no—
429C3⋊D3—41no—
430#41—182no—
431#41—182no—
432#41—182no—
433#41—182no—
434C2×Q8—91no—
435C2×Q8—91no—
436C2×D4—91no—
437C2×D4—91no—
438C2×D4—91no—
439C2×D4—91no—
440C2×D4—91no—
441C2×D4—91no—
442C2×D4—91no—
443C2×D4—91no—
444C2×D4—91no—
445C2×D4C4×C3⋊D311yescharacteristic
446C22×C4—91no—
447C22×C4—91no—
448C22×C4—91no—
449C22×C4—91no—
450C22×C4—91no—
451C22×C4C22×C3⋊D311yescharacteristic
452C22×C4C22×C3⋊D311yescharacteristic
453M16—22no—
454M16—182no—
455M16—182no—
456M16—182no—
457M16—182no—
458M16—182no—
459C2×C8—22no—
460C2×C8—91no—
461C2×C8—94no—
462C2×C8—91no—
463C2×C8—91no—
464C2×C8—91no—
465C2×C8—182no—
466C2×C8—182no—
467C2×C8—182no—
468C2×C8—182no—
469C2×C8C22×C3⋊D311yescharacteristic
470C2×C8C22×C3⋊D311yescharacteristic
471C2×C8C22×C3⋊D311yescharacteristic
472C2×C8C22×C3⋊D311yescharacteristic
473C4⋊C4—91no—
474C4⋊C4—91no—
475C4⋊C4—91no—
476C4⋊C4C4×C3⋊D311yescharacteristic
477C22⋊C4—91no—
478C22⋊C4—91no—
479C22⋊C4—91no—
480C22⋊C4—91no—
481C22⋊C4—91no—
482C22⋊C4—91no—
483C22⋊C4C4×C3⋊D311yescharacteristic
484C22⋊C4C4×C3⋊D311yescharacteristic
485C42—91no—
486C42—91no—
487C42—91no—
488C42C22×C3⋊D311yescharacteristic
489C22×C3—24no—
490C22×C3—24no—
491C22×C3—24no—
492C22×C3—24no—
493C22×C3—24no—
494C22×C3—24no—
495C22×C3C22×C4×D314yes—
496C2×D3—38no—
497C2×D3—64no—
498C2×D3—64no—
499C2×D3—64no—
500C2×D3—64no—
501C2×D3—64no—
502C2×D3—64no—
503C2×D3—64no—
504C2×D3—64no—
505C3×C4—24no—
506C3×C4—24no—
507C3×C4—24no—
508C3×C4—24no—
509C3×C4C2×D3×D414yes—
510C3×C4D3×#4114yes—
511Dic3—38no—
512Dic3—64no—
513Dic3—64no—
514Dic3—64no—
515Dic3—64no—
516C32#293211yescharacteristic, complemented, Sylow
517C23—91no—
518C23—91no—
519C23—91no—
520C23C2×C4×C3⋊D311yescharacteristic
521C23C2×C4×C3⋊D311yescharacteristic
522Q8—182no—
523Q8—182no—
524D4—41no—
525D4—182no—
526D4—182no—
527D4—182no—
528D4—182no—
529D4—182no—
530D4—182no—
531D4—361no—
532D4—361no—
533D4—361no—
534C2×C4—21no—
535C2×C4—21no—
536C2×C4—21no—
537C2×C4—21no—
538C2×C4—91no—
539C2×C4—92no—
540C2×C4—92no—
541C2×C4—91no—
542C2×C4—91no—
543C2×C4—91no—
544C2×C4—91no—
545C2×C4—181no—
546C2×C4—181no—
547C2×C4—181no—
548C2×C4—181no—
549C2×C4—361no—
550C2×C4—361no—
551C2×C4C2×C4×C3⋊D311yescharacteristic
552C2×C4C2×C4×C3⋊D311yescharacteristic
553C2×C4C2×C4×C3⋊D311yescharacteristic
554C2×C4C2×C4×C3⋊D311yescharacteristic
555C2×C4C23×C3⋊D311yescharacteristic
556C8—21no—
557C8—21no—
558C8—21no—
559C8—92no—
560C8—181no—
561C8—181no—
562C8—181no—
563C8D4×C3⋊D312yes—
564C2×C3—44no—
565C2×C3—44no—
566C2×C3C4×D3×D414yes—
567C2×C3#574514yes—
568C2×C3#575014yes—
569D3—68no—
570D3—124no—
571D3—124no—
572C22—21no—
573C22—21no—
574C22—21no—
575C22—21no—
576C22—21no—
577C22—21no—
578C22—92no—
579C22—181no—
580C22—181no—
581C22—181no—
582C22—181no—
583C22—181no—
584C22—181no—
585C22—181no—
586C22—181no—
587C22C22×C4×C3⋊D311yescharacteristic
588C4—21no—
589C4—21no—
590C4—21no—
591C4—21no—
592C4—92no—
593C4—181no—
594C4—181no—
595C4—181no—
596C4—181no—
597C4C2×D4×C3⋊D311yescharacteristic
598C4#41×C3⋊D311yescharacteristic
599C3#7948014yescomplemented
600C2—41no—
601C2—41no—
602C2—182no—
603C2—361no—
604C2—361no—
605C2C4×D4×C3⋊D311yescharacteristic
606C2#1059621611yescharacteristic
607C2#1059622111yescharacteristic
subgroupG/H
center, FrattiniC2×C4C23×C3⋊D3
commutator, socleC22×C32C23×C4
FittingC32×#435C2
prime radical#10596019C2
cosocleC2×C32×C4C24
hypercenter#435C3⋊D3
hypocenterC32#2932
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C2×C4 ◁ #435

Complements

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

NH ≅ G/Ntype
1. C2×#64116C2semidirect
2. C2×#64110C2semidirect
4. C32×#435C2semidirect
5. #10592826C2semidirect
6. #10592810C2semidirect
7. #10592710C2semidirect
8. #10592536C2semidirect
9. #10592535C2semidirect
10. #10592429C2semidirect
11. #10592427C2semidirect
12. #10592426C2semidirect
13. #10592426C2semidirect
14. #10592405C2semidirect
15. C3⋊D3×#97C2semidirect
65. C3×#435D3semidirect
135. C8×C3⋊D3D4semidirect
239. #435C3⋊D3semidirect
516. C32#2932semidirect
599. C3#79480semidirect

Maximal subgroups

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

subgroupindex
C2×#641162
C2×#641102
#105960192
C32×#4352
#105928262
#105928102
#105927102
#105925362
#105925352
#105924292
#105924272
#105924262
#105924052
C3⋊D3×#972
#794803