Finite Group Databasebeta

← #11808657

Subgroups — #11808657

Order 1152.

1584 conjugacy classes of subgroups.

The subgroup lattice has 558 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64135C211yesmaximal, characteristic
2C2×C4×#634C211yesmaximal, characteristic, complemented
3C32×C4×C22⋊C4C211yesmaximal, characteristic
4C4×#3757C211yesmaximal, characteristic
5#10592648C211yesmaximal, characteristic
6#10592647C211yesmaximal, characteristic
7#10592647C211yesmaximal, characteristic
8#10592646C211yesmaximal, characteristic
9C4×C4⋊(C3⋊Dic3)C211yesmaximal, characteristic, complemented
10C4×#3750C211yesmaximal, characteristic, complemented
11C4×#3750C211yesmaximal, characteristic, complemented
12#10592360C211yesmaximal, characteristic, complemented
13#10592359C211yesmaximal, characteristic, complemented
14#10592356C211yesmaximal, characteristic, complemented
15#10592355C211yesmaximal, characteristic, complemented
16#73480—34nomaximal
17C23×C32×C4C2211yescharacteristic
18C22×#634C2211yescharacteristic
19C2×C32×C22⋊C4C2211yescharacteristic
20C2×C32×C22⋊C4C2211yescharacteristic
21C2×C32×C42C2211yescharacteristic
22C2×C32×C42C2211yescharacteristic
23C2×#3757C2211yescharacteristic
24C2×#3757C2211yescharacteristic
25C2×#3757C2211yescharacteristic
26C2×#3757C2211yescharacteristic
27#64135—24no—
28C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
29C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
30C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
31C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
32C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
33C2×#3750C2211yescharacteristic
34C2×#3750C2211yescharacteristic
35C2×#3750C2211yescharacteristic
36C2×#3750C2211yescharacteristic
37C2×#3750C2211yescharacteristic
38C2×#3750C2211yescharacteristic
39C2×C4×C3⋊Dic3C2211yescharacteristic
40C2×C4×C3⋊Dic3C2211yescharacteristic
41C2×C4×C3⋊Dic3C2211yescharacteristic
42C2×C4×C3⋊Dic3C2211yescharacteristic
43C4×#634—24no—
44C32×#95C2211yescharacteristic
45C32×#95C2211yescharacteristic
46#63658C2211yescharacteristic
47#63658C2211yescharacteristic
48#63658C2211yescharacteristic
49#63658C2211yescharacteristic
50#63658C2211yescharacteristic
51#63658C2211yescharacteristic
52#63658C2211yescharacteristic
53#63658C2211yescharacteristic
54C2×#926—34no—
55C2×C4×Dic6—34no—
56C3×C4×C22⋊C4D314yes—
57C4×#217—34no—
58#4949—34no—
59#4948—34no—
60#4948—34no—
61#4947—34no—
62C4×C4⋊Dic3—34no—
63C4×Dic3⋊C4—34no—
64C4×Dic3⋊C4—34no—
65#4661—34no—
66#4660—34no—
67#4657—34no—
68#4656—34no—
69C24×C32C2311yescharacteristic
70C22×C32×C4—22no—
71C22×C32×C4—22no—
72C22×C32×C4Q814yescomplemented
73C22×C32×C4C2311yescharacteristic
74C22×C32×C4C2311yescharacteristic
75C22×C32×C4C2311yescharacteristic
76C22×C32×C4C2311yescharacteristic
77C22×C32×C4C2311yescharacteristic
78C22×C32×C4C2311yescharacteristic
79C22×C3⋊Dic3C2311yescharacteristic
80C22×C3⋊Dic3C2311yescharacteristic
81C22×C3⋊Dic3C2311yescharacteristic
82C22×C3⋊Dic3C2311yescharacteristic
83C22×C3⋊Dic3C2311yescharacteristic
84C22×C3⋊Dic3C2311yescharacteristic
85C22×C3⋊Dic3C2311yescharacteristic
86C22×C3⋊Dic3C2311yescharacteristic
87C2×#634—22no—
88C2×#634—22no—
89C2×#634—22no—
90C32×C22⋊C4—22no—
91C32×C22⋊C4—22no—
92C32×C42—22no—
93C32×C42—22no—
94#3757—22no—
95#3757—22no—
96#3757—22no—
97#3757—22no—
98C4⋊(C3⋊Dic3)—22no—
99C4⋊(C3⋊Dic3)—22no—
100C4⋊(C3⋊Dic3)—22no—
101C4⋊(C3⋊Dic3)—22no—
102C4⋊(C3⋊Dic3)—22no—
103#3750—22no—
104#3750—22no—
105#3750—22no—
106#3750—22no—
107#3750—22no—
108#3750—22no—
109C4×C3⋊Dic3—22no—
110C4×C3⋊Dic3—22no—
111C4×C3⋊Dic3—22no—
112C4×C3⋊Dic3D414yes—
113#2396—91noSylow
114C23×C3×C4C2×D314yes—
115C22×Dic6—34no—
116C2×C3×C22⋊C4C2×D314yes—
117C2×C3×C22⋊C4C2×D314yes—
118C2×C3×C42C2×D314yes—
119C2×C3×C42C2×D314yes—
120C2×#217—34no—
121C2×#217—34no—
122C2×#217—34no—
123C2×#217—34no—
124#926—616no—
125C2×C4⋊Dic3—34no—
126C2×C4⋊Dic3—34no—
127C2×C4⋊Dic3—34no—
128C2×C4⋊Dic3—34no—
129C2×C4⋊Dic3—34no—
130C2×Dic3⋊C4—34no—
131C2×Dic3⋊C4—34no—
132C2×Dic3⋊C4—34no—
133C2×Dic3⋊C4—34no—
134C2×Dic3⋊C4—34no—
135C2×Dic3⋊C4—34no—
136C2×C4×Dic3—34no—
137C2×C4×Dic3—34no—
138C2×C4×Dic3—34no—
139C2×C4×Dic3—34no—
140C4×Dic6—616no—
141C3×#95C2×D314yes—
142C3×#95C2×D314yes—
143C3⋊#95—34no—
144C3⋊#95—34no—
145C3⋊#95—34no—
146C3⋊#95—34no—
147C3⋊#95—34no—
148C3⋊#95—34no—
149C3⋊#95—34no—
150C3⋊#95—34no—
151C23×C32—21no—
152C23×C32—21no—
153C23×C32—21no—
154C23×C32—21no—
155C23×C32—21no—
156C23×C32—21no—
157C23×C32C2×Q812yes—
158C23×C32C2411yescharacteristic
159C2×C32×C4—21no—
160C2×C32×C4—21no—
161C2×C32×C4—21no—
162C2×C32×C4—21no—
163C2×C32×C4—21no—
164C2×C32×C4—21no—
165C2×C32×C4—28no—
166C2×C32×C4—21no—
167C2×C32×C4—21no—
168C2×C32×C4—21no—
169C2×C32×C4—21no—
170C2×C32×C4—21no—
171C2×C32×C4—21no—
172C2×C32×C4C2×D412yes—
173C2×C32×C4C2×Q812yes—
174C2×C32×C4C2×Q812yes—
175C2×C32×C4#4112yes—
176C2×C32×C4#4112yes—
177C2×C32×C4#4112yes—
178C2×C3⋊Dic3—21no—
179C2×C3⋊Dic3—21no—
180C2×C3⋊Dic3—21no—
181C2×C3⋊Dic3—21no—
182C2×C3⋊Dic3—21no—
183C2×C3⋊Dic3—21no—
184C2×C3⋊Dic3—21no—
185C2×C3⋊Dic3—21no—
186C2×C3⋊Dic3—21no—
187C2×C3⋊Dic3—21no—
188C2×C3⋊Dic3—21no—
189C2×C3⋊Dic3—21no—
190C2×C3⋊Dic3—21no—
191C2×C3⋊Dic3—21no—
192C2×C3⋊Dic3—21no—
193C2×C3⋊Dic3—21no—
194C2×C3⋊Dic3—21no—
195C2×C3⋊Dic3—21no—
196C2×C3⋊Dic3—21no—
197C2×C3⋊Dic3—21no—
198C2×C3⋊Dic3C2×D412yes—
199C2×C3⋊Dic3C2×D412yes—
200C2×C3⋊Dic3#4112yes—
201C2×C3⋊Dic3#4112yes—
202#634—28no—
203C2×C4×Q8—91no—
204C2×#117—91no—
205#400—91no—
206#399—91no—
207#398—91no—
208#398—91no—
209#396—91no—
210#396—91no—
211#395—91no—
212#393—91no—
213C4×C4⋊C4—91no—
214C4×C4⋊C4—91no—
215C4×C4⋊C4—91no—
216C4×C22⋊C4—91no—
217C4×C22⋊C4C3⋊D311yescharacteristic
218C24×C3C22×D314yes—
219C22×C3×C4—28no—
220C22×C3×C4—28no—
221C22×C3×C4Dic6116yescomplemented
222C22×C3×C4C22×D314yes—
223C22×C3×C4C22×D314yes—
224C22×C3×C4C22×D314yes—
225C22×C3×C4C22×D314yes—
226C22×C3×C4C22×D314yes—
227C22×C3×C4C22×D314yes—
228C22×Dic3—34no—
229C22×Dic3—34no—
230C22×Dic3—34no—
231C22×Dic3—34no—
232C22×Dic3—34no—
233C22×Dic3—34no—
234C22×Dic3—34no—
235C22×Dic3—34no—
236C2×Dic6—68no—
237C2×Dic6—68no—
238C2×Dic6—68no—
239C3×C22⋊C4—28no—
240C3×C22⋊C4—28no—
241C3×C42—28no—
242C3×C42—28no—
243#217—68no—
244#217—68no—
245#217—68no—
246#217—68no—
247C4⋊Dic3—68no—
248C4⋊Dic3—68no—
249C4⋊Dic3—68no—
250C4⋊Dic3—68no—
251C4⋊Dic3—68no—
252Dic3⋊C4—68no—
253Dic3⋊C4—68no—
254Dic3⋊C4—68no—
255Dic3⋊C4—68no—
256Dic3⋊C4—68no—
257Dic3⋊C4—68no—
258C4×Dic3—316no—
259C4×Dic3—68no—
260C4×Dic3—68no—
261C4×Dic3—68no—
262C22×C32—22no—
263C22×C32—22no—
264C22×C32—22no—
265C22×C32—41no—
266C22×C32—41no—
267C22×C32—41no—
268C22×C32—41no—
269C22×C32C22×D411yescharacteristic
270C22×C32C22×Q811yescharacteristic
271C22×C32C2×#4111yescharacteristic
272C22×C32C2×#4111yescharacteristic
273C22×C32C2×#4111yescharacteristic
274C22×C32C2×#4111yescharacteristic
275C22×C32C2×#4111yescharacteristic
276C32×C4—22no—
277C32×C4—22no—
278C32×C4—22no—
279C32×C4—41no—
280C32×C4—41no—
281C32×C4C22⋊Q814yes—
282C3⋊Dic3—22no—
283C3⋊Dic3—22no—
284C3⋊Dic3—22no—
285C3⋊Dic3—22no—
286C3⋊Dic3—41no—
287C3⋊Dic3—41no—
288C3⋊Dic3—41no—
289C3⋊Dic3—41no—
290C22×Q8—91no—
291C23×C4C2×C3⋊D311yescharacteristic
292C4×Q8—184no—
293#117—184no—
294C2×C4⋊C4—91no—
295C2×C4⋊C4—91no—
296C2×C4⋊C4—91no—
297C2×C4⋊C4—91no—
298C2×C4⋊C4—91no—
299C2×C4⋊C4—91no—
300C2×C4⋊C4—91no—
301C2×C4⋊C4—91no—
302C2×C4⋊C4—91no—
303C2×C4⋊C4—91no—
304C2×C4⋊C4—91no—
305C2×C22⋊C4—91no—
306C2×C22⋊C4—91no—
307C2×C22⋊C4—91no—
308C2×C22⋊C4—91no—
309C2×C22⋊C4C2×C3⋊D311yescharacteristic
310C2×C22⋊C4C2×C3⋊D311yescharacteristic
311C2×C42—91no—
312C2×C42—91no—
313C2×C42—91no—
314C2×C42—91no—
315C2×C42C2×C3⋊D311yescharacteristic
316C2×C42C2×C3⋊D311yescharacteristic
317#95—91no—
318#95—91no—
319#95—91no—
320#95—91no—
321#95—91no—
322#95—91no—
323#95—91no—
324#95—91no—
325#95C2×C3⋊D311yescharacteristic
326#95C2×C3⋊D311yescharacteristic
327C23×C3—24no—
328C23×C3—24no—
329C23×C3—24no—
330C23×C3—24no—
331C23×C3—24no—
332C23×C3—24no—
333C23×C3C2×Dic618yes—
334C23×C3C23×D314yes—
335C2×C3×C4—24no—
336C2×C3×C4—24no—
337C2×C3×C4—24no—
338C2×C3×C4—24no—
339C2×C3×C4—24no—
340C2×C3×C4—24no—
341C2×C3×C4—232no—
342C2×C3×C4—24no—
343C2×C3×C4—24no—
344C2×C3×C4—24no—
345C2×C3×C4—24no—
346C2×C3×C4—24no—
347C2×C3×C4—24no—
348C2×C3×C4C2×Dic618yes—
349C2×C3×C4C2×Dic618yes—
350C2×C3×C4#23518yes—
351C2×C3×C4#23518yes—
352C2×C3×C4D3×D418yes—
353C2×C3×C4#23718yes—
354C2×Dic3—38no—
355C2×Dic3—38no—
356C2×Dic3—38no—
357C2×Dic3—38no—
358C2×Dic3—64no—
359C2×Dic3—64no—
360C2×Dic3—64no—
361C2×Dic3—64no—
362C2×Dic3—64no—
363C2×Dic3—64no—
364C2×Dic3—64no—
365C2×Dic3—64no—
366C2×Dic3—64no—
367C2×Dic3—64no—
368C2×Dic3—64no—
369C2×Dic3—64no—
370C2×Dic3—64no—
371C2×Dic3—64no—
372C2×Dic3—64no—
373C2×Dic3—64no—
374C2×Dic3—64no—
375C2×Dic3—64no—
376C2×Dic3—64no—
377C2×Dic3—64no—
378Dic6—632no—
379C2×C32—42no—
380C2×C32C2×C22⋊Q811yescharacteristic
381C2×C32#52511yescharacteristic
382C2×C32#52911yescharacteristic
383C2×C32#52911yescharacteristic
384C2×C32#53211yescharacteristic
385C2×C32#53311yescharacteristic
386C2×C32#53311yescharacteristic
387C24C22×C3⋊D311yescharacteristic
388C2×Q8—182no—
389C2×Q8—182no—
390C2×Q8—182no—
391C22×C4—22no—
392C22×C4—22no—
393C22×C4—91no—
394C22×C4—91no—
395C22×C4—91no—
396C22×C4—91no—
397C22×C4—91no—
398C22×C4—91no—
399C22×C4—91no—
400C22×C4—91no—
401C22×C4#63414yescomplemented
402C22×C4C22×C3⋊D311yescharacteristic
403C22×C4C22×C3⋊D311yescharacteristic
404C22×C4C22×C3⋊D311yescharacteristic
405C22×C4C22×C3⋊D311yescharacteristic
406C22×C4C22×C3⋊D311yescharacteristic
407C22×C4C22×C3⋊D311yescharacteristic
408C4⋊C4—182no—
409C4⋊C4—182no—
410C4⋊C4—182no—
411C4⋊C4—182no—
412C4⋊C4—182no—
413C4⋊C4—182no—
414C4⋊C4—182no—
415C4⋊C4—182no—
416C4⋊C4—182no—
417C4⋊C4—182no—
418C4⋊C4—182no—
419C22⋊C4—22no—
420C22⋊C4—22no—
421C22⋊C4—182no—
422C22⋊C4—182no—
423C22⋊C4—182no—
424C22⋊C4—182no—
425C42—22no—
426C42—22no—
427C42—94no—
428C42—182no—
429C42—182no—
430C42—182no—
431C22×C3—28no—
432C22×C3—28no—
433C22×C3—28no—
434C22×C3—44no—
435C22×C3—44no—
436C22×C3—44no—
437C22×C3—44no—
438C22×C3C22×Dic614yes—
439C22×C3C2×#23514yes—
440C22×C3C2×#23514yes—
441C22×C3C2×D3×D414yes—
442C22×C3C2×#23714yes—
443C22×C3D3×#4114yes—
444C22×C3D3×#4114yes—
445C3×C4—28no—
446C3×C4—28no—
447C3×C4—28no—
448C3×C4—44no—
449C3×C4—44no—
450C3×C4#878116yes—
451Dic3—68no—
452Dic3—68no—
453Dic3—68no—
454Dic3—68no—
455Dic3—124no—
456Dic3—124no—
457Dic3—124no—
458Dic3—124no—
459C32#239611yescharacteristic, complemented, Sylow
460C23—21no—
461C23—21no—
462C23—21no—
463C23—21no—
464C23—21no—
465C23—21no—
466C23C2×#63412yes—
467C23C23×C3⋊D311yescharacteristic
468Q8—188no—
469C2×C4—21no—
470C2×C4—21no—
471C2×C4—21no—
472C2×C4—21no—
473C2×C4—21no—
474C2×C4—21no—
475C2×C4—28no—
476C2×C4—21no—
477C2×C4—21no—
478C2×C4—21no—
479C2×C4—21no—
480C2×C4—21no—
481C2×C4—21no—
482C2×C4—92no—
483C2×C4—92no—
484C2×C4—92no—
485C2×C4—92no—
486C2×C4—181no—
487C2×C4—181no—
488C2×C4—181no—
489C2×C4—181no—
490C2×C4—181no—
491C2×C4—181no—
492C2×C4—181no—
493C2×C4—181no—
494C2×C4—181no—
495C2×C4—181no—
496C2×C4—181no—
497C2×C4—181no—
498C2×C4—181no—
499C2×C4—181no—
500C2×C4—181no—
501C2×C4—181no—
502C2×C4—181no—
503C2×C4—181no—
504C2×C4—181no—
505C2×C4—181no—
506C2×C4C2×#63412yes—
507C2×C4C2×#63412yes—
508C2×C4#382812yes—
509C2×C4#382812yes—
510C2×C4D4×C3⋊D312yes—
511C2×C4#383012yes—
512C2×C3—48no—
513C2×C3#547014yes—
514C2×C3C2×#87814yes—
515C2×C3#551714yes—
516C2×C3#553814yes—
517C2×C3#554714yes—
518C2×C3#554814yes—
519C2×C3#555714yes—
520C22—22no—
521C22—22no—
522C22—22no—
523C22—41no—
524C22—41no—
525C22—41no—
526C22—41no—
527C22C22×#63411yescharacteristic
528C22C2×#382811yescharacteristic
529C22C2×#382811yescharacteristic
530C22C2×D4×C3⋊D311yescharacteristic
531C22C2×#383011yescharacteristic
532C22#41×C3⋊D311yescharacteristic
533C22#41×C3⋊D311yescharacteristic
534C4—22no—
535C4—22no—
536C4—22no—
537C4—41no—
538C4—41no—
539C4—182no—
540C4—182no—
541C4—182no—
542C4—182no—
543C4—361no—
544C4—361no—
545C4—361no—
546C4—361no—
547C4#6408714yes—
548C3#7348014yescomplemented
549C2—42no—
550C2#1059594111yescharacteristic
551C2C2×#6408711yescharacteristic
552C2#1059598811yescharacteristic
553C2#1059600911yescharacteristic
554C2#1059601811yescharacteristic
555C2#1059601911yescharacteristic
556C2#1059602811yescharacteristic
subgroupG/H
centerC22×C4C22×C3⋊D3
commutator, socle, cosocleC23×C32C24
FrattiniC23C23×C3⋊D3
FittingC32×C4×C22⋊C4C2
prime radicalC24×C32C23
hypercenterC4×C22⋊C4C3⋊D3
hypocenterC32#2396
LCSG ▷ C23×C32 ▷ C32
UCSC1 ◁ C22×C4 ◁ C4×C22⋊C4

Complements

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

NH ≅ G/Ntype
2. C2×C4×#634C2semidirect
9. C4×C4⋊(C3⋊Dic3)C2semidirect
10. C4×#3750C2semidirect
11. C4×#3750C2semidirect
12. #10592360C2semidirect
13. #10592359C2semidirect
14. #10592356C2semidirect
15. #10592355C2semidirect
72. C22×C32×C4Q8semidirect
221. C22×C3×C4Dic6semidirect
401. C22×C4#634semidirect
459. C32#2396semidirect
548. C3#73480semidirect

Maximal subgroups

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

subgroupindex
C2×#641352
C2×C4×#6342
C32×C4×C22⋊C42
C4×#37572
#105926482
#105926472
#105926462
C4×C4⋊(C3⋊Dic3)2
C4×#37502
#105923602
#105923592
#105923562
#105923552
#734803