Finite Group Databasebeta

← #49161764

Subgroups — #49161764

Order 37504.

928 conjugacy classes of subgroups.

The subgroup lattice has 516 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#22627593C211yesmaximal, characteristic
2C2×C4×C22⋊D293C211yesmaximal, characteristic, complemented
3C2×#22627584C211yesmaximal, characteristic, complemented
4C22×C22⋊Dic293C211yesmaximal, characteristic, complemented
5#34036029C211yesmaximal, characteristic, complemented
6#34036023C211yesmaximal, characteristic, complemented
7#34036017C211yesmaximal, characteristic, complemented
8#34036008C211yesmaximal, characteristic, complemented
9#34036006C211yesmaximal, characteristic, complemented
10#34036005C211yesmaximal, characteristic, complemented
11#34036002C211yesmaximal, characteristic, complemented
12#34036001C211yesmaximal, characteristic, complemented
13C22⋊C4×Dic293C211yesmaximal, characteristic, complemented
14C4×C22⋊Dic293C211yesmaximal, characteristic, complemented
15C22×C22⋊C4×C293C211yesmaximal, characteristic, complemented
16C22×C22⋊D293C2211yescharacteristic
17C22×C22⋊D293C2211yescharacteristic
18C22×C22⋊D293C2211yescharacteristic
19C23×Dic293C2211yescharacteristic
20C23×Dic293C2211yescharacteristic
21C22×C4×D293C2211yescharacteristic, complemented
22#22627593C418yescomplemented
23C4×C22⋊D293—24no—
24#22627584—24no—
25C2×#17989781C2211yescharacteristic, complemented
26C2×#17989781C2211yescharacteristic, complemented
27C2×#17989781C2211yescharacteristic, complemented
28C2×C22⋊Dic293—24no—
29C2×C22⋊Dic293C2211yescharacteristic
30C2×C22⋊Dic293C2211yescharacteristic
31C2×C22⋊Dic293C2211yescharacteristic
32C2×C22⋊Dic293C2211yescharacteristic
33C2×C22⋊Dic293C2211yescharacteristic
34C2×C22⋊Dic293C2211yescharacteristic
35C2×C22⋊Dic293C2211yescharacteristic
36C2×#17989779C2211yescharacteristic, complemented
37C2×#17989779C2211yescharacteristic, complemented
38C2×#17989779C2211yescharacteristic, complemented
39C2×C4×Dic293C2211yescharacteristic, complemented
40C2×C4×Dic293C2211yescharacteristic, complemented
41C2×C4×Dic293C2211yescharacteristic, complemented
42#22627531C2211yescharacteristic, complemented
43#22627531C2211yescharacteristic, complemented
44#22627531C2211yescharacteristic, complemented
45#22627531C2211yescharacteristic, complemented
46#22627531C2211yescharacteristic, complemented
47#22627531C2211yescharacteristic, complemented
48C25×C293C2211yescharacteristic
49C23×C4×C293C2211yescharacteristic
50C23×C4×C293C2211yescharacteristic
51C2×C22⋊C4×C293—24no—
52C2×C22⋊C4×C293C2211yescharacteristic
53C2×C22⋊C4×C293C2211yescharacteristic
54C2×C22⋊C4×C293C2211yescharacteristic
55C2×C22⋊C4×C293C2211yescharacteristic
56C23×D293C2311yescharacteristic
57C2×C22⋊D293—22no—
58C2×C22⋊D293—22no—
59C2×C22⋊D293—22no—
60C2×C22⋊D293—22no—
61C2×C22⋊D293—41no—
62C2×C22⋊D293—41no—
63C2×C22⋊D293C2×C414yescomplemented
64C2×C22⋊D293C2×C414yescomplemented
65C2×C22⋊D293C2×C414yescomplemented
66C22×Dic293—22no—
67C22×Dic293—22no—
68C22×Dic293—22no—
69C22×Dic293—22no—
70C22×Dic293—41no—
71C22×Dic293—41no—
72C22×Dic293C2311yescharacteristic
73C22×Dic293C2311yescharacteristic
74C22×Dic293C2311yescharacteristic
75C22×Dic293C2311yescharacteristic
76C22×Dic293C2311yescharacteristic
77C22×Dic293C2311yescharacteristic
78C22×Dic293C2311yescharacteristic
79C2×C4×D293—22no—
80C2×C4×D293—22no—
81C2×C4×D293—41no—
82#17989781—22no—
83#17989781—22no—
84#17989781—41no—
85C22⋊Dic293—22no—
86C22⋊Dic293—22no—
87C22⋊Dic293—22no—
88C22⋊Dic293C2×C414yescomplemented
89C22⋊Dic293C2×C414yescomplemented
90C22⋊Dic293C2×C414yescomplemented
91C22⋊Dic293D414yescomplemented
92#17989779—22no—
93#17989779—22no—
94#17989779—41no—
95C4×Dic293—22no—
96C4×Dic293—22no—
97C4×Dic293—41no—
98C24×C293—22no—
99C24×C293—22no—
100C24×C293—22no—
101C24×C293—22no—
102C24×C293—41no—
103C24×C293—41no—
104C24×C293C2×C414yescomplemented
105C24×C293C2311yescharacteristic
106C24×C293C2311yescharacteristic
107C24×C293C2311yescharacteristic
108C22×C4×C293—22no—
109C22×C4×C293—22no—
110C22×C4×C293—22no—
111C22×C4×C293—22no—
112C22×C4×C293—41no—
113C22×C4×C293—41no—
114C22×C4×C293C2311yescharacteristic
115C22×C4×C293C2311yescharacteristic
116C22×C4×C293C2311yescharacteristic
117C22×C4×C293C2311yescharacteristic
118C22⋊C4×C293—22no—
119C22⋊C4×C293—22no—
120C22⋊C4×C293—22no—
121C22⋊C4×C293D414yescomplemented
122C22×D293—21no—
123C22×D293—21no—
124C22×D293—21no—
125C22×D293—21no—
126C22×D293—21no—
127C22×D293—21no—
128C22×D293C22×C412yes—
129C22⋊D293—28no—
130C22⋊D293—28no—
131C22⋊D293—44no—
132C2×Dic293—21no—
133C2×Dic293—21no—
134C2×Dic293—21no—
135C2×Dic293—21no—
136C2×Dic293—21no—
137C2×Dic293—21no—
138C2×Dic293—21no—
139C2×Dic293—21no—
140C2×Dic293—21no—
141C2×Dic293—21no—
142C2×Dic293—21no—
143C2×Dic293—21no—
144C2×Dic293—21no—
145C2×Dic293—21no—
146C2×Dic293—21no—
147C2×Dic293—21no—
148C2×Dic293—44no—
149C2×Dic293—44no—
150C2×Dic293C22×C412yes—
151C2×Dic293C22×C412yes—
152C2×Dic293C22×C412yes—
153C2×Dic293C2×D412yes—
154C2×Dic293C2×D412yes—
155C4×D293—44no—
156C23×C293—21no—
157C23×C293—21no—
158C23×C293—21no—
159C23×C293—21no—
160C23×C293—21no—
161C23×C293—21no—
162C23×C293—21no—
163C23×C293—21no—
164C23×C293—28no—
165C23×C293—28no—
166C23×C293—21no—
167C23×C293—21no—
168C23×C293—21no—
169C23×C293—21no—
170C23×C293—21no—
171C23×C293—21no—
172C23×C293—44no—
173C23×C293—44no—
174C23×C293—44no—
175C23×C293—44no—
176C23×C293—44no—
177C23×C293C22×C412yes—
178C23×C293C22×C412yes—
179C23×C293C22×C412yes—
180C23×C293C2×D412yes—
181C23×C293C2×D412yes—
182C23×C293#4112yes—
183C23×C293#4112yes—
184C23×C293C2411yescharacteristic
185C2×C4×C293—21no—
186C2×C4×C293—21no—
187C2×C4×C293—21no—
188C2×C4×C293—21no—
189C2×C4×C293—21no—
190C2×C4×C293—21no—
191C2×C4×C293—21no—
192C2×C4×C293—21no—
193C2×C4×C293—21no—
194C2×C4×C293—21no—
195C2×C4×C293—44no—
196C2×C4×C293—44no—
197C2×C4×C293C2×D412yes—
198C2×C4×C293C2×D412yes—
199C22×C293—22no—
200C22×C293—22no—
201C22×C293—22no—
202C22×C293—22no—
203C22×C293—22no—
204C22×C293—22no—
205C22×C293—22no—
206C22×C293—22no—
207C22×C293—22no—
208C22×C293—22no—
209C22×C293—22no—
210C22×C293—22no—
211C22×C293—22no—
212C22×C293—22no—
213C22×C293—22no—
214C22×C293—416no—
215C22×C293—41no—
216C22×C293—41no—
217C22×C293—41no—
218C22×C293—41no—
219C22×C293C4×D414yescomplemented
220C22×C293C4×D414yescomplemented
221C22×C293C23×C411yescharacteristic
222C22×C293C22×D411yescharacteristic
223C22×C293C22×D411yescharacteristic
224C22×C293C2×#4111yescharacteristic
225C22×C293C2×#4111yescharacteristic
226C22×C293H(5,𝔽2)11yescharacteristic
227C22×C293H(5,𝔽2)11yescharacteristic
228C2×D293—22no—
229C2×D293—22no—
230C2×D293—22no—
231C2×D293—41no—
232C2×D293—41no—
233C2×D293—41no—
234C2×D293—41no—
235C4×C293—22no—
236C4×C293—22no—
237C4×C293—41no—
238C4×C293—41no—
239Dic293—22no—
240Dic293—22no—
241Dic293—22no—
242Dic293—22no—
243Dic293—22no—
244Dic293—41no—
245Dic293—41no—
246C2×C293—24no—
247C2×C293—24no—
248C2×C293—42no—
249C2×C293C2×C4×D411yescharacteristic
250C2×C293C2×C4×D411yescharacteristic
251C2×C293#51811yescharacteristic
252C2×C293D4211yescharacteristic
253C2×C293#54611yescharacteristic
254C2×C293#54611yescharacteristic
255C2×C293#55111yescharacteristic
256D293—42no—
257C293#235811yescharacteristic, complemented, Sylow
258#2358—2931nomaximal, Sylow
259C2×#120—2931no—
260C2×C4×D4—2931no—
261C2×C4×D4—2931no—
262C22×C22⋊C4—2931no—
263C22×C22⋊C4D29311yescharacteristic, complemented
264#390—2931no—
265#388—2931no—
266#388—2931no—
267#386—2931no—
268#386—2931no—
269#386—2931no—
270#385—2931no—
271#385—2931no—
272C4×C22⋊C4—2931no—
273C4×C22⋊C4—2931no—
274C25C2×D29311yescharacteristic
275C22×D4—2931no—
276C22×D4—2931no—
277C22×D4—2931no—
278C23×C4—2931no—
279C23×C4—2931no—
280C23×C4—2931no—
281C23×C4C2×D29311yescharacteristic
282C23×C4C2×D29311yescharacteristic
283#120—2938no—
284C4×D4—5864no—
285C4×D4—5864no—
286C2×C4⋊C4—2931no—
287C2×C4⋊C4—2931no—
288C2×C4⋊C4—2931no—
289C2×C22⋊C4—24no—
290C2×C22⋊C4—2931no—
291C2×C22⋊C4—2931no—
292C2×C22⋊C4—2931no—
293C2×C22⋊C4—2931no—
294C2×C22⋊C4—2931no—
295C2×C22⋊C4—2931no—
296C2×C22⋊C4—2931no—
297C2×C22⋊C4—2931no—
298C2×C22⋊C4—2931no—
299C2×C22⋊C4—2931no—
300C2×C22⋊C4—5864no—
301C2×C22⋊C4C2×D29311yescharacteristic
302C2×C22⋊C4C2×D29311yescharacteristic
303C2×C22⋊C4C2×D29311yescharacteristic
304C2×C22⋊C4C2×D29311yescharacteristic
305C2×C42—2931no—
306C2×C42—2931no—
307C2×C42—2931no—
308#95—2931no—
309#95—2931no—
310#95—2931no—
311#95—2931no—
312#95—2931no—
313#95—2931no—
314C24—22no—
315C24—22no—
316C24—22no—
317C24—22no—
318C24—41no—
319C24—41no—
320C24—2931no—
321C24C4×D29314yescomplemented
322C24C22×D29311yescharacteristic
323C24C22×D29311yescharacteristic
324C24C22×D29311yescharacteristic
325C2×D4—2934no—
326C2×D4—2934no—
327C2×D4—2934no—
328C2×D4—5862no—
329C2×D4—5862no—
330C2×D4—5862no—
331C2×D4—5862no—
332C2×D4—11721no—
333C2×D4—11721no—
334C22×C4—22no—
335C22×C4—22no—
336C22×C4—22no—
337C22×C4—22no—
338C22×C4—41no—
339C22×C4—41no—
340C22×C4—2931no—
341C22×C4—2931no—
342C22×C4—2931no—
343C22×C4—2931no—
344C22×C4—2931no—
345C22×C4—2931no—
346C22×C4—2931no—
347C22×C4—5862no—
348C22×C4—5862no—
349C22×C4—5862no—
350C22×C4—5862no—
351C22×C4—5862no—
352C22×C4—5862no—
353C22×C4—11721no—
354C22×C4—11721no—
355C22×C4—11721no—
356C22×C4C22×D29311yescharacteristic
357C22×C4C22×D29311yescharacteristic
358C22×C4C22×D29311yescharacteristic
359C22×C4C22×D29311yescharacteristic
360C4⋊C4—5862no—
361C4⋊C4—5862no—
362C4⋊C4—11721no—
363C22⋊C4—22no—
364C22⋊C4—22no—
365C22⋊C4—22no—
366C22⋊C4—2934no—
367C22⋊C4—2934no—
368C22⋊C4—2934no—
369C22⋊C4—2934no—
370C22⋊C4—5862no—
371C22⋊C4—5862no—
372C22⋊C4—5862no—
373C22⋊C4—5862no—
374C22⋊C4—5862no—
375C22⋊C4—11721no—
376C22⋊C4C22⋊D29314yescomplemented
377C42—5862no—
378C42—5862no—
379C42—11721no—
380C23—21no—
381C23—21no—
382C23—21no—
383C23—21no—
384C23—21no—
385C23—21no—
386C23—21no—
387C23—21no—
388C23—28no—
389C23—28no—
390C23—21no—
391C23—21no—
392C23—21no—
393C23—21no—
394C23—21no—
395C23—21no—
396C23—44no—
397C23—44no—
398C23—44no—
399C23—44no—
400C23—44no—
401C23—2932no—
402C23—5861no—
403C23—5861no—
404C23—5861no—
405C23—5861no—
406C23—5861no—
407C23—5861no—
408C23C2×C4×D29312yes—
409C23C2×C4×D29312yes—
410C23C2×C4×D29312yes—
411C23D4×D29312yes—
412C23C2×C22⋊D29312yes—
413C23#1798980112yes—
414C23#1798980212yes—
415C23C23×D29311yescharacteristic
416D4—5868no—
417D4—5868no—
418D4—11724no—
419C2×C4—21no—
420C2×C4—21no—
421C2×C4—21no—
422C2×C4—21no—
423C2×C4—21no—
424C2×C4—21no—
425C2×C4—21no—
426C2×C4—21no—
427C2×C4—21no—
428C2×C4—21no—
429C2×C4—44no—
430C2×C4—44no—
431C2×C4—2932no—
432C2×C4—2932no—
433C2×C4—2932no—
434C2×C4—2932no—
435C2×C4—2932no—
436C2×C4—5861no—
437C2×C4—5861no—
438C2×C4—5861no—
439C2×C4—5861no—
440C2×C4—5861no—
441C2×C4—5861no—
442C2×C4—5861no—
443C2×C4—5861no—
444C2×C4—5861no—
445C2×C4—5861no—
446C2×C4—5861no—
447C2×C4—5861no—
448C2×C4—5861no—
449C2×C4—5861no—
450C2×C4—5861no—
451C2×C4—5861no—
452C2×C4—11724no—
453C2×C4—11724no—
454C2×C4—11724no—
455C2×C4C2×C22⋊D29312yes—
456C2×C4C2×C22⋊D29312yes—
457C22—22no—
458C22—22no—
459C22—22no—
460C22—22no—
461C22—22no—
462C22—22no—
463C22—22no—
464C22—22no—
465C22—22no—
466C22—22no—
467C22—22no—
468C22—22no—
469C22—22no—
470C22—22no—
471C22—22no—
472C22—416no—
473C22—41no—
474C22—41no—
475C22—41no—
476C22—41no—
477C22—5862no—
478C22—5862no—
479C22—5862no—
480C22—11721no—
481C22—11721no—
482C22—11721no—
483C22—11721no—
484C22#2262758414yescomplemented
485C22C4×C22⋊D29314yescomplemented
486C22C22×C4×D29311yescharacteristic
487C22C2×D4×D29311yescharacteristic
488C22C22×C22⋊D29311yescharacteristic
489C22C2×#1798980111yescharacteristic
490C22C2×#1798980211yescharacteristic
491C22#2262766911yescharacteristic
492C22#2262766911yescharacteristic
493C4—22no—
494C4—22no—
495C4—41no—
496C4—41no—
497C4—5862no—
498C4—5862no—
499C4—5862no—
500C4—5862no—
501C4—5862no—
502C4—11721no—
503C4—11721no—
504C2—24no—
505C2—24no—
506C2—42no—
507C2—11722no—
508C2C2×#2262758411yescharacteristic
509C2C2×C4×C22⋊D29311yescharacteristic
510C2#3403660211yescharacteristic
511C2D4×C22⋊D29311yescharacteristic
512C2#3403676911yescharacteristic
513C2#3403677311yescharacteristic
514C2#3403680511yescharacteristic
subgroupG/H
center, FrattiniC23C23×D293
commutatorC22×C293C23×C4
FittingC22×C22⋊C4×C293C2
socle, cosocleC23×C293C24
prime radicalC2×#22627593C2
hypercenterC22×C22⋊C4D293
hypocenterC293#2358
LCSG ▷ C22×C293 ▷ C293
UCSC1 ◁ C23 ◁ C22×C22⋊C4

Complements

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

NH ≅ G/Ntype
2. C2×C4×C22⋊D293C2semidirect
3. C2×#22627584C2semidirect
4. C22×C22⋊Dic293C2semidirect
5. #34036029C2semidirect
6. #34036023C2semidirect
7. #34036017C2semidirect
8. #34036008C2semidirect
9. #34036006C2semidirect
10. #34036005C2semidirect
11. #34036002C2semidirect
12. #34036001C2semidirect
13. C22⋊C4×Dic293C2semidirect
14. C4×C22⋊Dic293C2semidirect
15. C22×C22⋊C4×C293C2semidirect
21. C22×C4×D293C22semidirect
22. #22627593C4semidirect
25. C2×#17989781C22semidirect
26. C2×#17989781C22semidirect
27. C2×#17989781C22semidirect
36. C2×#17989779C22semidirect
37. C2×#17989779C22semidirect
38. C2×#17989779C22semidirect
39. C2×C4×Dic293C22semidirect
40. C2×C4×Dic293C22semidirect
41. C2×C4×Dic293C22semidirect
42. #22627531C22semidirect
43. #22627531C22semidirect
44. #22627531C22semidirect
45. #22627531C22semidirect
46. #22627531C22semidirect
47. #22627531C22semidirect
63. C2×C22⋊D293C2×C4semidirect
64. C2×C22⋊D293C2×C4semidirect
65. C2×C22⋊D293C2×C4semidirect
88. C22⋊Dic293C2×C4semidirect
89. C22⋊Dic293C2×C4semidirect
90. C22⋊Dic293C2×C4semidirect
91. C22⋊Dic293D4semidirect
104. C24×C293C2×C4semidirect
121. C22⋊C4×C293D4semidirect
219. C22×C293C4×D4semidirect
220. C22×C293C4×D4semidirect
257. C293#2358semidirect
263. C22×C22⋊C4D293semidirect
321. C24C4×D293semidirect
376. C22⋊C4C22⋊D293semidirect
484. C22#22627584semidirect
485. C22C4×C22⋊D293semidirect

Maximal subgroups

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

subgroupindex
C2×#226275932
C2×C4×C22⋊D2932
C2×#226275842
C22×C22⋊Dic2932
#340360292
#340360232
#340360172
#340360082
#340360062
#340360052
#340360022
#340360012
C22⋊C4×Dic2932
C4×C22⋊Dic2932
C22×C22⋊C4×C2932
#2358293