Finite Group Databasebeta

← #11788206

Subgroups — #11788206

Order 1152.

811 conjugacy classes of subgroups.

The subgroup lattice has 572 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10595034C211yesmaximal, characteristic
2C2×#63874C211yesmaximal, characteristic, complemented
3#10592825C211yesmaximal, characteristic, complemented
4C2×C3×#825C211yesmaximal, characteristic, complemented
5C2×#63569C211yesmaximal, characteristic, complemented
6C3×#4555C211yesmaximal, characteristic, complemented
7#10589161C211yesmaximal, characteristic, complemented
8#70383—31nomaximal
9#68757—31nomaximal
10C22×C4×C3⋊D3C2211yescharacteristic
11C2×C3×#235C2211yescharacteristic
12C2×C32×M16C2211yescharacteristic
13C2×#3748C2211yescharacteristic
14C3×#926C2211yescharacteristic
15C2×C3×C4×Dic3C2211yescharacteristic
16C2×C3×C4×Dic3C2211yescharacteristic
17#63981—21no—
18C2×#3724—21no—
19C2×#3722—21no—
20#63962—21no—
21#63916C412yescomplemented
22C4×#626—22no—
23#63874—22no—
24#63874—22no—
25#63871C412yescomplemented
26#63647—22no—
27C3×#825—22no—
28#63569—22no—
29#5828—31no—
30#5524—31no—
31C2×#872—31no—
32C2×#872—31no—
33C2×C3×#104—31no—
34C2×#837—31no—
35C2×#825D311yescharacteristic, complemented
36#5126—31no—
37#5126—31no—
38#5126—61no—
39C2×#805—31no—
40C3×#339—31no—
41#4555D311yescharacteristic, complemented
42#4532—31no—
43#4523—31no—
44C23×C3⋊D3D411yescharacteristic
45C22×C32×C4C2311yescharacteristic
46C22×C3⋊Dic3D411yescharacteristic
47C2×C4×C3⋊D3—21no—
48C2×C4×C3⋊D3—21no—
49C2×C4×C3⋊D3—21no—
50C2×C4×C3⋊D3—21no—
51C2×C4×C3⋊D3C2×C412yes—
52C2×C4×C3⋊D3D412yes—
53C2×C3×#67—21no—
54C22×C3×Dic3—21no—
55C22×C3×Dic3—21no—
56C3×#235—21no—
57C3×#235—21no—
58C3×#235—21no—
59C3×#235—21no—
60C2×C3×D12C2×C411yescharacteristic
61C2×C3×C4×D3—21no—
62C2×C3×Dic6C2×C411yescharacteristic
63C2×#626—22no—
64C32×M16—21no—
65C32×M16—21no—
66C2×C32×C8—21no—
67#3748—21no—
68#3748—21no—
69C2×C3⋊(C3⋊C8)—21no—
70C3×#217—21no—
71C3×C4⋊Dic3C2×C412yes—
72C3×C4×Dic3—21no—
73C3×C4×Dic3—21no—
74C3×C4×Dic3—21no—
75C3×C4×Dic3D412yescomplemented
76C3×C4×Dic3D412yescomplemented
77#3724—24no—
78Dic3⋊Dic3—22no—
79#3722—24no—
80#3722—22no—
81(C2×D3)⋊Dic3—22no—
82#1897—91noSylow
83C2×C3×#41—31no—
84C2×#235C2×D311yescharacteristic
85C22×C4×D3—31no—
86C22×C4×D3—31no—
87C22×C4×D3—61no—
88C2×C3×M16—21no—
89C2×C3×M16C2×D311yescharacteristic
90C2×C3×M16C2×D311yescharacteristic
91C3×#117—31no—
92C2×C3×C42—31no—
93C2×C3×C42—31no—
94#946—32no—
95#938—32no—
96#937—61no—
97#935—61no—
98C4×#67—62no—
99C2×(C2×D3)⋊C4—61no—
100C2×(C2×D3)⋊C4—61no—
101#926C2×D311yescharacteristic
102C2×Dic3⋊C4—61no—
103C2×Dic3⋊C4—61no—
104C2×C4×Dic3C2×D311yescharacteristic
105C2×C4×Dic3C2×D311yescharacteristic
106C2×#208—31no—
107C2×#208—31no—
108C2×#208—61no—
109#897—32no—
110#895—32no—
111#886—61no—
112#882—61no—
113C4×D12—62no—
114#872—62no—
115#872—62no—
116#872—62no—
117#872—62no—
118C3×#104—62no—
119#837—62no—
120#825—22no—
121(C2×D3)⋊C8—62no—
122(C2×D3)⋊C8—62no—
123(C2×D3)⋊C8—64no—
124#805—62no—
125C23×C32C2×D411yescharacteristic
126C22×C3⋊D3—21no—
127C22×C3⋊D3—21no—
128C22×C3⋊D3—42no—
129C22×C3⋊D3C22⋊C412yes—
130C22×C3×D3—21no—
131C2×C32×C4C22×C411yescharacteristic
132C2×C32×C4C2×D411yescharacteristic
133C2×C32×C4C2×D411yescharacteristic
134C2×C32×C4C2×D411yescharacteristic
135C2×C32×C4#4111yescharacteristic
136C2×C32×C4#4111yescharacteristic
137C2×C3⋊Dic3—21no—
138C2×C3⋊Dic3—21no—
139C2×C3⋊Dic3C22⋊C412yes—
140C4×C3⋊D3—22no—
141C4×C3⋊D3—22no—
142C4×C3⋊D3—22no—
143C4×C3⋊D3—22no—
144C3×#67—41no—
145C3×#67—41no—
146C2×C3×Dic3—22no—
147C2×C3×Dic3—21no—
148C2×C3×Dic3—22no—
149C2×C3×Dic3—22no—
150C2×C3×Dic3—42no—
151C2×C3×Dic3—42no—
152C3×D12—21no—
153C3×D12—21no—
154C3×C4×D3—41no—
155C3×C4×D3—41no—
156C3×Dic6—21no—
157C3×Dic6—21no—
158#626—44no—
159C32×C8—41no—
160C3⋊(C3⋊C8)—41no—
161#525—91no—
162C2×#117—91no—
163C2×#104—31no—
164C2×#104—91no—
165#407—91no—
166#339—31no—
167#339—91no—
168C23×D3—31no—
169C23×D3—31no—
170C23×D3—61no—
171C3×#41—61no—
172C3×#41—61no—
173C3×#41—61no—
174C3×#41—61no—
175C2×C3×Q8—31no—
176C2×C3×D4—31no—
177C2×C3×D4—61no—
178C22×C3×C4—21no—
179C22×C3×C4—61no—
180C22×C3×C4—61no—
181C22×C3×C4—61no—
182C22×C3×C4C22×D311yescharacteristic
183C22×C3×C4C22×D311yescharacteristic
184C2×#67—21no—
185C2×#67—62no—
186C22×Dic3—21no—
187C22×Dic3—21no—
188C22×Dic3—31no—
189C22×Dic3—31no—
190C22×Dic3—61no—
191#235—21no—
192#235—21no—
193#235—21no—
194#235—21no—
195C2×D12—62no—
196C2×D12C4×D311yescharacteristic
197C2×C4×D3—21no—
198C2×C4×D3—32no—
199C2×C4×D3—32no—
200C2×C4×D3—32no—
201C2×C4×D3—32no—
202C2×C4×D3—62no—
203C2×C4×D3—62no—
204C2×C4×D3—61no—
205C2×C4×D3—61no—
206C2×C4×D3—61no—
207C2×C4×D3—61no—
208C2×C4×D3—61no—
209C2×C4×D3—61no—
210C2×C4×D3—61no—
211C2×C4×D3—61no—
212C2×C4×D3—121no—
213C2×C4×D3—121no—
214C2×C4×D3—121no—
215C2×C4×D3—121no—
216C2×Dic6C4×D311yescharacteristic
217C3×M16—21no—
218C3×M16—21no—
219C3×M16—21no—
220C3×M16—21no—
221C3×M16—41no—
222C3×M16—41no—
223C2×C3×C8—22no—
224C2×C3×C8—21no—
225C2×C3×C8—21no—
226C3×C4⋊C4—32no—
227C3×C22⋊C4—61no—
228C3×C42—32no—
229C3×C42—32no—
230C3×C42—61no—
231C3×C42—61no—
232C3×C42—61no—
233#217—21no—
234#217—62no—
235(C2×D3)⋊C4—62no—
236(C2×D3)⋊C4—62no—
237(C2×D3)⋊C4—64no—
238(C2×D3)⋊C4—64no—
239(C2×D3)⋊C4—62no—
240C4⋊Dic3—62no—
241C4⋊Dic3C4×D312yes—
242Dic3⋊C4—62no—
243Dic3⋊C4—64no—
244Dic3⋊C4—64no—
245C4×Dic3—21no—
246C4×Dic3—21no—
247C4×Dic3—21no—
248C4×Dic3D1212yescomplemented
249C4×Dic3#6712yescomplemented
250#208—61no—
251#208—61no—
252#208—61no—
253#208—61no—
254#208—121no—
255#208—121no—
256C2×C3⋊C8—62no—
257C2×C3⋊C8—61no—
258C2×C3⋊C8—61no—
259C22×C32—22no—
260C22×C32C2×C22⋊C411yescharacteristic
261C22×C32#12011yescharacteristic
262C22×C32#12311yescharacteristic
263C2×C3⋊D3—22no—
264C2×C3⋊D3—22no—
265C2×C3⋊D3—22no—
266C2×C3⋊D3—42no—
267C2×C3⋊D3—42no—
268C2×C3×D3—41no—
269C2×C3×D3—42no—
270C32×C4C4×D411yescharacteristic
271C32×C4C4×D411yescharacteristic
272C32×C4#12111yescharacteristic
273C32×C4#12111yescharacteristic
274C3⋊Dic3—22no—
275C3×Dic3—42no—
276C3×Dic3—42no—
277C3×Dic3—41no—
278C3×Dic3—42no—
279C2×#41—31no—
280C23×C4—91no—
281C2×M16—91no—
282C2×M16D3211yescharacteristic
283#123—181no—
284C22⋊Q8—92no—
285#121—92no—
286#120—181no—
287C4×D4—182no—
288#117—31no—
289#117—182no—
290#117—182no—
291C2×C4⋊C4—181no—
292C2×C22⋊C4—181no—
293C2×C42—31no—
294C2×C42—31no—
295#104—62no—
296#104—182no—
297C22⋊C8—182no—
298C23×C3—21no—
299C23×C3—61no—
300C23×C3D3×D411yescharacteristic
301C23×C3D3×D411yescharacteristic
302C22×D3—21no—
303C22×D3—32no—
304C22×D3—32no—
305C22×D3—62no—
306C22×D3—61no—
307C22×D3—61no—
308C22×D3—61no—
309C22×D3—61no—
310C22×D3—121no—
311C22×D3—121no—
312C22×D3—122no—
313C22×D3—122no—
314C22×D3—124no—
315C3×Q8—61no—
316C3×Q8—61no—
317C3×D4—61no—
318C3×D4—61no—
319C3×D4—121no—
320C3×D4—121no—
321C2×C3×C4—21no—
322C2×C3×C4—21no—
323C2×C3×C4—21no—
324C2×C3×C4—21no—
325C2×C3×C4—21no—
326C2×C3×C4—21no—
327C2×C3×C4—61no—
328C2×C3×C4—62no—
329C2×C3×C4—62no—
330C2×C3×C4—62no—
331C2×C3×C4—122no—
332C2×C3×C4—122no—
333C2×C3×C4—121no—
334C2×C3×C4—121no—
335C2×C3×C4C2×C4×D311yescharacteristic
336C2×C3×C4C2×C4×D311yescharacteristic
337C2×C3×C4C2×D1211yescharacteristic
338C2×C3×C4#23511yescharacteristic
339C2×C3×C4#23511yescharacteristic
340C2×C3×C4D3×D411yescharacteristic
341C2×C3×C4D3×D411yescharacteristic
342C2×C3×C4D3×D411yescharacteristic
343C2×C3×C4D3×D411yescharacteristic
344C2×C3×C4#23711yescharacteristic
345C2×C3×C4#23911yescharacteristic
346C2×C3×C4C2×#6711yescharacteristic
347#67—41no—
348#67—41no—
349#67—124no—
350C2×Dic3—22no—
351C2×Dic3—21no—
352C2×Dic3—22no—
353C2×Dic3—22no—
354C2×Dic3—32no—
355C2×Dic3—32no—
356C2×Dic3—42no—
357C2×Dic3—42no—
358C2×Dic3—62no—
359C2×Dic3—61no—
360C2×Dic3—61no—
361C2×Dic3—61no—
362C2×Dic3—61no—
363C2×Dic3—121no—
364C2×Dic3—121no—
365D12—21no—
366D12—21no—
367D12—124no—
368C4×D3—41no—
369C4×D3—41no—
370C4×D3—62no—
371C4×D3—62no—
372C4×D3—62no—
373C4×D3—62no—
374C4×D3—62no—
375C4×D3—62no—
376C4×D3—62no—
377C4×D3—62no—
378C4×D3—122no—
379C4×D3—122no—
380C4×D3—122no—
381C4×D3—122no—
382Dic6—21no—
383Dic6—21no—
384C3×C8—42no—
385C3×C8—41no—
386C3×C8—41no—
387C3⋊C8—122no—
388C3⋊C8—121no—
389C3⋊C8—121no—
390C2×C32—21no—
391C2×C32—21no—
392C2×C32#38611yescharacteristic
393C2×C32#42112yes—
394C3⋊D3—42no—
395C3×D3—81no—
396C24—91no—
397#41—61no—
398#41—61no—
399#41—61no—
400#41—61no—
401C2×Q8—31no—
402C2×D4—31no—
403C2×D4—61no—
404C2×D4—182no—
405C22×C4—61no—
406C22×C4—61no—
407C22×C4—61no—
408C22×C4—91no—
409C22×C4—92no—
410C22×C4—92no—
411C22×C4—181no—
412C22×C4—181no—
413C22×C4—181no—
414C22×C4—181no—
415C22×C4C2×D3211yescharacteristic
416M16—21no—
417M16—21no—
418M16—181no—
419M16—181no—
420C2×C8—21no—
421C2×C8—181no—
422C4⋊C4—32no—
423C4⋊C4—182no—
424C4⋊C4—184no—
425C22⋊C4—61no—
426C22⋊C4—182no—
427C22⋊C4—184no—
428C22⋊C4—182no—
429C42—32no—
430C42—32no—
431C42—61no—
432C42—61no—
433C42—61no—
434C22×C3—22no—
435C22×C3—22no—
436C22×C3—21no—
437C22×C3—21no—
438C22×C3—21no—
439C22×C3—42no—
440C22×C3—121no—
441C22×C3—122no—
442C22×C3D3×C22⋊C411yescharacteristic
443C22×C3D3×C22⋊C411yescharacteristic
444C22×C3#88211yescharacteristic
445C22×C3#88311yescharacteristic
446C22×C3#89411yescharacteristic
447C22×C3#93711yescharacteristic
448C2×D3—41no—
449C2×D3—42no—
450C2×D3—64no—
451C2×D3—62no—
452C2×D3—62no—
453C2×D3—62no—
454C2×D3—62no—
455C2×D3—62no—
456C2×D3—62no—
457C2×D3—122no—
458C2×D3—122no—
459C2×D3—122no—
460C2×D3—122no—
461C2×D3—122no—
462C2×D3—122no—
463C2×D3—124no—
464C2×D3—124no—
465C3×C4—21no—
466C3×C4—21no—
467C3×C4—21no—
468C3×C4—21no—
469C3×C4—122no—
470C3×C4—122no—
471C3×C4—121no—
472C3×C4—122no—
473C3×C4C4×D1211yescharacteristic
474C3×C4#67⋊C411yescharacteristic
475C3×C4#88411yescharacteristic
476C3×C4#88411yescharacteristic
477C3×C4#89311yescharacteristic
478C3×C4#89511yescharacteristic
479C3×C4C4×#6711yescharacteristic
480C3×C4#93811yescharacteristic
481Dic3—42no—
482Dic3—42no—
483Dic3—41no—
484Dic3—42no—
485Dic3—62no—
486Dic3—62no—
487Dic3—122no—
488C32#189711yescharacteristic, complemented, Sylow
489C23—61no—
490C23—92no—
491C23—181no—
492C23—181no—
493C23—362no—
494C23#380211yescharacteristic
495Q8—61no—
496Q8—61no—
497D4—61no—
498D4—61no—
499D4—121no—
500D4—121no—
501D4—364no—
502C2×C4—62no—
503C2×C4—61no—
504C2×C4—62no—
505C2×C4—62no—
506C2×C4—92no—
507C2×C4—122no—
508C2×C4—122no—
509C2×C4—121no—
510C2×C4—121no—
511C2×C4—181no—
512C2×C4—181no—
513C2×C4—182no—
514C2×C4—182no—
515C2×C4—182no—
516C2×C4—182no—
517C2×C4#379911yescharacteristic
518C2×C4C4×D3211yescharacteristic
519C2×C4D3×D1211yescharacteristic
520C2×C4#380411yescharacteristic
521C2×C4D3×#6711yescharacteristic
522C2×C4#381111yescharacteristic
523C8—41no—
524C8—361no—
525C2×C3—21no—
526C2×C3—21no—
527C2×C3—21no—
528C2×C3—21no—
529C2×C3—22no—
530C2×C3—21no—
531C2×C3—41no—
532C2×C3—41no—
533C2×C3—241no—
534C2×C3#466511yescharacteristic
535C2×C3#482112yes—
536C2×C3#482112yes—
537C2×C3#495611yescharacteristic
538D3—81no—
539D3—124no—
540D3—122no—
541D3—122no—
542C22—22no—
543C22—122no—
544C22—121no—
545C22—182no—
546C22—182no—
547C22—182no—
548C22—362no—
549C22—362no—
550C22#6385411yescharacteristic
551C22#6392111yescharacteristic
552C22#6392211yescharacteristic
553C4—122no—
554C4—122no—
555C4—122no—
556C4—121no—
557C4—182no—
558C4#6388011yescharacteristic
559C4#6390411yescharacteristic
560C4#6391011yescharacteristic
561C4#6395811yescharacteristic
562C3—21no—
563C3#6875711yescharacteristic, complemented
564C3#7038311yescharacteristic, complemented
565C2—21no—
566C2—21no—
567C2—241no—
568C2—362no—
569C2#1059100912yes—
570C2#1059127511yescharacteristic
subgroupG/H
centerC2×C4#3811
commutatorC2×C32×C4C22×C4
FrattiniC22×C4C2×D32
FittingC2×C32×M16C22
socleC22×C32C2×C22⋊C4
prime radical#10595034C2
cosocleC22×C32×C4C23
hypercenterC2×M16D32
hypocenterC32#1897
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C2×M16

Complements

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

NH ≅ G/Ntype
2. C2×#63874C2semidirect
3. #10592825C2semidirect
4. C2×C3×#825C2semidirect
5. C2×#63569C2semidirect
6. C3×#4555C2semidirect
7. #10589161C2semidirect
21. #63916C4semidirect
25. #63871C4semidirect
35. C2×#825D3semidirect
41. #4555D3semidirect
75. C3×C4×Dic3D4semidirect
76. C3×C4×Dic3D4semidirect
248. C4×Dic3D12semidirect
249. C4×Dic3#67semidirect
488. C32#1897semidirect
563. C3#68757semidirect
564. C3#70383semidirect

Maximal subgroups

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

subgroupindex
#105950342
C2×#638742
#105928252
C2×C3×#8252
C2×#635692
C3×#45552
#105891612
#703833
#687573