Finite Group Databasebeta

← #27197865

Subgroups — #27197865

Order 13184.

740 conjugacy classes of subgroups.

The subgroup lattice has 492 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#15693017C211yesmaximal, characteristic
2C2×C4×C22⋊D103C211yesmaximal, characteristic, complemented
3C2×(C22⋊D103)⋊C4C211yesmaximal, characteristic, complemented
4#20267691C211yesmaximal, characteristic, complemented
5#20267691C211yesmaximal, characteristic, complemented
6#20267671C211yesmaximal, characteristic, complemented
7#20267670C211yesmaximal, characteristic, complemented
8#20267669C211yesmaximal, characteristic, complemented
9#20267669C211yesmaximal, characteristic, complemented
10#20267668C211yesmaximal, characteristic, complemented
11#20267667C211yesmaximal, characteristic, complemented
12#20267667C211yesmaximal, characteristic, complemented
13#20267655C211yesmaximal, characteristic, complemented
14#20267636C211yesmaximal, characteristic, complemented
15#386×C103C211yesmaximal, characteristic, complemented
16C22×D412C2211yescharacteristic
17C22×C22⋊D103C2211yescharacteristic
18C22×C22⋊D103C2211yescharacteristic
19C22×C22⋊D103C2211yescharacteristic
20C22×C22⋊D103C2211yescharacteristic
21C23×Dic103C2211yescharacteristic
22C22×C4×D103C2211yescharacteristic
23C22×C4×D103C2211yescharacteristic
24#15693017C418yescomplemented
25C4×C22⋊D103—24no—
26(C22⋊D103)⋊C4—24no—
27C2×Dic103⋊C4C2211yescharacteristic
28C2×Dic103⋊C4C2211yescharacteristic
29C2×C22⋊Dic103C2211yescharacteristic
30C2×C22⋊Dic103C2211yescharacteristic
31C2×C22⋊Dic103C2211yescharacteristic
32C2×(C2×D103)⋊C4C2211yescharacteristic
33C2×(C2×D103)⋊C4C2211yescharacteristic
34C2×(C2×D103)⋊C4C2211yescharacteristic
35C2×(C2×D103)⋊C4C2211yescharacteristic
36C2×(C2×D103)⋊C4C2211yescharacteristic
37C2×(C2×D103)⋊C4C2211yescharacteristic
38C2×C4×Dic103C2211yescharacteristic
39C2×C4×Dic103C2211yescharacteristic
40C2×C4×Dic103C2211yescharacteristic
41C103⋊#95C2211yescharacteristic
42C103⋊#95C2211yescharacteristic
43C103⋊#95C2211yescharacteristic
44C103⋊#95C2211yescharacteristic
45C103⋊#95C2211yescharacteristic
46C103⋊#95C2211yescharacteristic
47C22×D4×C103C2211yescharacteristic
48C23×C4×C103C2211yescharacteristic
49C2×C22⋊C4×C103C2211yescharacteristic
50C2×C22⋊C4×C103C2211yescharacteristic
51C2×C22⋊C4×C103C2211yescharacteristic
52#95×C103C2211yescharacteristic
53#95×C103C2211yescharacteristic
54C23×D103C2311yescharacteristic
55C23×D103C2311yescharacteristic
56C2×D412—41no—
57C2×D412—41no—
58C2×D412C2×C414yescomplemented
59C2×C22⋊D103—22no—
60C2×C22⋊D103—22no—
61C2×C22⋊D103—22no—
62C2×C22⋊D103—22no—
63C2×C22⋊D103—41no—
64C2×C22⋊D103—41no—
65C2×C22⋊D103—41no—
66C2×C22⋊D103—41no—
67C2×C22⋊D103C2×C414yescomplemented
68C2×C22⋊D103C2×C414yescomplemented
69C2×C22⋊D103C2×C414yescomplemented
70C2×C22⋊D103C2×C414yescomplemented
71C22×Dic103—22no—
72C22×Dic103—41no—
73C22×Dic103—41no—
74C22×Dic103C2311yescharacteristic
75C22×Dic103C2311yescharacteristic
76C22×Dic103C2311yescharacteristic
77C22×Dic103C2311yescharacteristic
78C22×Dic103C2311yescharacteristic
79C22×Dic103C2311yescharacteristic
80C2×C4×D103—22no—
81C2×C4×D103—22no—
82C2×C4×D103—41no—
83C2×C4×D103—41no—
84C2×C4×D103—41no—
85C2×C4×D103—41no—
86Dic103⋊C4—22no—
87Dic103⋊C4—22no—
88C22⋊Dic103—22no—
89C22⋊Dic103—41no—
90C22⋊Dic103—41no—
91(C2×D103)⋊C4—22no—
92(C2×D103)⋊C4—22no—
93(C2×D103)⋊C4—41no—
94(C2×D103)⋊C4—41no—
95(C2×D103)⋊C4—41no—
96(C2×D103)⋊C4—41no—
97C4×Dic103—22no—
98C4×Dic103C2×C414yescomplemented
99C4×Dic103D414yescomplemented
100C24×C103C2311yescharacteristic
101C24×C103C2311yescharacteristic
102C2×D4×C103—41no—
103C2×D4×C103—41no—
104C2×D4×C103C2×C414yescomplemented
105C22×C4×C103—22no—
106C22×C4×C103—41no—
107C22×C4×C103—41no—
108C22×C4×C103C2311yescharacteristic
109C22×C4×C103C2311yescharacteristic
110C22×C4×C103C2311yescharacteristic
111C22×C4×C103C2311yescharacteristic
112C22×C4×C103C2311yescharacteristic
113C22⋊C4×C103—22no—
114C22⋊C4×C103—41no—
115C22⋊C4×C103—41no—
116C23×C103—21no—
117C23×C103—21no—
118C23×C103—21no—
119C23×C103—21no—
120C23×C103—21no—
121C23×C103—21no—
122C23×C103—21no—
123C23×C103—21no—
124C23×C103—21no—
125C23×C103—21no—
126C23×C103—21no—
127C23×C103—21no—
128C23×C103C22×C412yes—
129C23×C103C22×C412yes—
130C23×C103C2411yescharacteristic
131C22×D103—21no—
132C22×D103—21no—
133C22×D103—21no—
134C22×D103—21no—
135C22×D103—21no—
136C22×D103—21no—
137C22×D103—21no—
138C22×D103—21no—
139C22×D103—21no—
140C22×D103—21no—
141C22×D103—21no—
142C22×D103—21no—
143C22×D103C22×C412yes—
144C22×D103C22×C412yes—
145D4×C103—44no—
146C2×C4×C103—21no—
147C2×C4×C103—21no—
148C2×C4×C103—21no—
149C2×C4×C103—21no—
150C2×C4×C103—21no—
151C2×C4×C103—21no—
152C2×C4×C103—21no—
153C2×C4×C103—21no—
154C2×C4×C103—21no—
155C2×C4×C103—21no—
156C2×C4×C103—21no—
157C2×C4×C103—21no—
158C2×C4×C103—21no—
159C2×C4×C103—44no—
160C2×C4×C103C22×C412yes—
161C2×C4×C103C2×D412yes—
162C22⋊D103—28no—
163C22⋊D103—28no—
164C22⋊D103—44no—
165C22⋊D103—44no—
166C2×Dic103—21no—
167C2×Dic103—21no—
168C2×Dic103—21no—
169C2×Dic103—21no—
170C2×Dic103—21no—
171C2×Dic103—21no—
172C2×Dic103—21no—
173C2×Dic103—21no—
174C2×Dic103—21no—
175C2×Dic103—21no—
176C2×Dic103—21no—
177C2×Dic103—21no—
178C2×Dic103—21no—
179C2×Dic103—44no—
180C2×Dic103C22×C412yes—
181C2×Dic103C22×C412yes—
182C2×Dic103C2×D412yes—
183C2×Dic103C2×D412yes—
184C2×Dic103#4112yes—
185D412—44no—
186C4×D103—44no—
187C4×D103—44no—
188C22×C103—22no—
189C22×C103—22no—
190C22×C103—22no—
191C22×C103—22no—
192C22×C103—22no—
193C22×C103—22no—
194C22×C103—41no—
195C22×C103—41no—
196C22×C103—41no—
197C22×C103—41no—
198C22×C103—41no—
199C22×C103—41no—
200C22×C103—41no—
201C22×C103—41no—
202C22×C103C23×C411yescharacteristic
203C22×C103C22×D411yescharacteristic
204C22×C103C2×#4111yescharacteristic
205C22×C103H(5,𝔽2)11yescharacteristic
206C22×C103H(5,𝔽2)11yescharacteristic
207C22×C103H(5,𝔽2)11yescharacteristic
208C22×C103H(5,𝔽2)11yescharacteristic
209C2×D103—22no—
210C2×D103—22no—
211C2×D103—22no—
212C2×D103—22no—
213C2×D103—22no—
214C2×D103—22no—
215C2×D103—41no—
216C2×D103—41no—
217C2×D103—41no—
218C2×D103—41no—
219C2×D103—41no—
220C2×D103—41no—
221C2×D103—41no—
222C2×D103—41no—
223C4×C103—22no—
224C4×C103—22no—
225C4×C103—41no—
226C4×C103—41no—
227C4×C103—41no—
228Dic103—22no—
229Dic103—22no—
230Dic103—41no—
231Dic103—41no—
232Dic103—41no—
233Dic103C4×D414yes—
234C2×C103—42no—
235C2×C103—42no—
236C2×C103C2×C4×D411yescharacteristic
237C2×C103#51811yescharacteristic
238C2×C103#51811yescharacteristic
239C2×C103#53511yescharacteristic
240C2×C103#53511yescharacteristic
241C2×C103#54011yescharacteristic
242C2×C103#54011yescharacteristic
243D103—42no—
244D103—42no—
245#2328—1031nomaximal, Sylow
246C103#232811yescharacteristic, complemented, Sylow
247C2×#127—1031no—
248C2×C4×D4—1031no—
249C2×C4×D4—1031no—
250#390—1031no—
251#390—1031no—
252#386—1031no—
253#386—1031no—
254#386—1031no—
255#386—1031no—
256#386—1031no—
257#386—1031no—
258#386—1031no—
259#386D10311yescharacteristic, complemented
260#382—1031no—
261#376—1031no—
262C22×D4—1031no—
263C22×D4—1031no—
264C22×D4—1031no—
265C22×D4—1031no—
266C22×D4—1031no—
267C22×D4C2×D10311yescharacteristic
268C23×C4—1031no—
269C23×C4—1031no—
270C23×C4—1031no—
271C23×C4C2×D10311yescharacteristic
272#127—1038no—
273C4×D4—2064no—
274C4×D4—2064no—
275C2×C4⋊C4—1031no—
276C2×C4⋊C4—1031no—
277C2×C22⋊C4—1031no—
278C2×C22⋊C4—1031no—
279C2×C22⋊C4—1031no—
280C2×C22⋊C4—1031no—
281C2×C22⋊C4—1031no—
282C2×C22⋊C4—1031no—
283C2×C22⋊C4—1031no—
284C2×C22⋊C4—1031no—
285C2×C22⋊C4—1031no—
286C2×C22⋊C4C2×D10311yescharacteristic
287C2×C22⋊C4C2×D10311yescharacteristic
288C2×C22⋊C4C2×D10311yescharacteristic
289C2×C42—1031no—
290C2×C42—1031no—
291C2×C42—1031no—
292#95—1031no—
293#95—1031no—
294#95—1031no—
295#95—1031no—
296#95—1031no—
297#95—1031no—
298#95C2×D10311yescharacteristic
299#95C2×D10311yescharacteristic
300C24—1031no—
301C24—1031no—
302C24C22×D10311yescharacteristic
303C24C22×D10311yescharacteristic
304C2×D4—41no—
305C2×D4—41no—
306C2×D4—1034no—
307C2×D4—1034no—
308C2×D4—1034no—
309C2×D4—1034no—
310C2×D4—1034no—
311C2×D4—4121no—
312C2×D4—4121no—
313C2×D4—4121no—
314C2×D4—4121no—
315C2×D4—4121no—
316C2×D4—4121no—
317C2×D4—2062no—
318C2×D4—2062no—
319C2×D4—2062no—
320C2×D4—2062no—
321C2×D4C4×D10314yescomplemented
322C22×C4—22no—
323C22×C4—41no—
324C22×C4—41no—
325C22×C4—1031no—
326C22×C4—1031no—
327C22×C4—1031no—
328C22×C4—1031no—
329C22×C4—1031no—
330C22×C4—1031no—
331C22×C4—4121no—
332C22×C4—4121no—
333C22×C4—4121no—
334C22×C4—4121no—
335C22×C4—4121no—
336C22×C4—4121no—
337C22×C4—2062no—
338C22×C4—2062no—
339C22×C4—2062no—
340C22×C4C22×D10311yescharacteristic
341C22×C4C22×D10311yescharacteristic
342C22×C4C22×D10311yescharacteristic
343C22×C4C22×D10311yescharacteristic
344C22×C4C22×D10311yescharacteristic
345C4⋊C4—2062no—
346C4⋊C4—2062no—
347C22⋊C4—22no—
348C22⋊C4—41no—
349C22⋊C4—41no—
350C22⋊C4—4121no—
351C22⋊C4—4121no—
352C22⋊C4—4121no—
353C22⋊C4—4121no—
354C22⋊C4—4121no—
355C22⋊C4—4121no—
356C22⋊C4—2062no—
357C22⋊C4—2062no—
358C22⋊C4—2062no—
359C42—1034no—
360C42—1034no—
361C42—2062no—
362C23—21no—
363C23—21no—
364C23—21no—
365C23—21no—
366C23—21no—
367C23—21no—
368C23—21no—
369C23—21no—
370C23—21no—
371C23—21no—
372C23—21no—
373C23—21no—
374C23—1032no—
375C23—1032no—
376C23—2061no—
377C23—2061no—
378C23—2061no—
379C23—2061no—
380C23—2061no—
381C23—2061no—
382C23—2061no—
383C23—2061no—
384C23—2061no—
385C23—2061no—
386C23—2061no—
387C23—2061no—
388C23C2×C4×D10312yes—
389C23C2×C4×D10312yes—
390C23C23×D10311yescharacteristic
391D4—44no—
392D4—4124no—
393D4—4124no—
394D4—4124no—
395D4—2068no—
396D4—2068no—
397C2×C4—21no—
398C2×C4—21no—
399C2×C4—21no—
400C2×C4—21no—
401C2×C4—21no—
402C2×C4—21no—
403C2×C4—21no—
404C2×C4—21no—
405C2×C4—21no—
406C2×C4—21no—
407C2×C4—21no—
408C2×C4—21no—
409C2×C4—21no—
410C2×C4—44no—
411C2×C4—1032no—
412C2×C4—1032no—
413C2×C4—1032no—
414C2×C4—1032no—
415C2×C4—1032no—
416C2×C4—4124no—
417C2×C4—4124no—
418C2×C4—4124no—
419C2×C4—2061no—
420C2×C4—2061no—
421C2×C4—2061no—
422C2×C4—2061no—
423C2×C4—2061no—
424C2×C4—2061no—
425C2×C4—2061no—
426C2×C4—2061no—
427C2×C4—2061no—
428C2×C4—2061no—
429C2×C4—2061no—
430C2×C4—2061no—
431C2×C4—2061no—
432C2×C4C2×C4×D10312yes—
433C2×C4D4×D10312yes—
434C22—22no—
435C22—22no—
436C22—22no—
437C22—22no—
438C22—22no—
439C22—22no—
440C22—41no—
441C22—41no—
442C22—41no—
443C22—41no—
444C22—41no—
445C22—41no—
446C22—41no—
447C22—41no—
448C22—4121no—
449C22—4121no—
450C22—4121no—
451C22—4121no—
452C22—4121no—
453C22—4121no—
454C22—4121no—
455C22—4121no—
456C22—2062no—
457C22—2062no—
458C22—2062no—
459C22—2062no—
460C22—2062no—
461C22—2062no—
462C22C22×C4×D10311yescharacteristic
463C22C2×D4×D10311yescharacteristic
464C22#41×D10311yescharacteristic
465C22#1569306611yescharacteristic
466C22#1569306611yescharacteristic
467C22#1569306611yescharacteristic
468C22#1569306711yescharacteristic
469C4—22no—
470C4—22no—
471C4—41no—
472C4—41no—
473C4—41no—
474C4—1034no—
475C4—4121no—
476C4—4121no—
477C4—4121no—
478C4—2062no—
479C4—2062no—
480C2—42no—
481C2—42no—
482C2—4122no—
483C2—4122no—
484C2C4×D4×D10311yescharacteristic
485C2#2026826311yescharacteristic
486C2#2026826411yescharacteristic
487C2#2026835611yescharacteristic
488C2#2026835711yescharacteristic
489C2#2026839111yescharacteristic
490C2#2026839311yescharacteristic
subgroupG/H
center, FrattiniC23C23×D103
commutatorC22×C103C23×C4
Fitting#386×C103C2
socle, cosocleC23×C103C24
prime radicalC2×#15693017C2
hypercenter#386D103
hypocenterC103#2328
LCSG ▷ C22×C103 ▷ C103
UCSC1 ◁ C23 ◁ #386

Complements

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

NH ≅ G/Ntype
2. C2×C4×C22⋊D103C2semidirect
3. C2×(C22⋊D103)⋊C4C2semidirect
4. #20267691C2semidirect
5. #20267691C2semidirect
6. #20267671C2semidirect
7. #20267670C2semidirect
8. #20267669C2semidirect
9. #20267669C2semidirect
10. #20267668C2semidirect
11. #20267667C2semidirect
12. #20267667C2semidirect
13. #20267655C2semidirect
14. #20267636C2semidirect
15. #386×C103C2semidirect
24. #15693017C4semidirect
58. C2×D412C2×C4semidirect
67. C2×C22⋊D103C2×C4semidirect
68. C2×C22⋊D103C2×C4semidirect
69. C2×C22⋊D103C2×C4semidirect
70. C2×C22⋊D103C2×C4semidirect
98. C4×Dic103C2×C4semidirect
99. C4×Dic103D4semidirect
104. C2×D4×C103C2×C4semidirect
246. C103#2328semidirect
259. #386D103semidirect
321. C2×D4C4×D103semidirect

Maximal subgroups

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

subgroupindex
C2×#156930172
C2×C4×C22⋊D1032
C2×(C22⋊D103)⋊C42
#202676912
#202676712
#202676702
#202676692
#202676682
#202676672
#202676552
#202676362
#386×C1032
#2328103