Finite Group Databasebeta

← #34047201

Subgroups — #34047201

Order 19072.

824 conjugacy classes of subgroups.

The subgroup lattice has 466 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#18011883C211yesmaximal, characteristic
2C2×D4×Dic149C211yesmaximal, characteristic, complemented
3C2×#18011871C211yesmaximal, characteristic, complemented
4C2×#18011871C211yesmaximal, characteristic, complemented
5C22×C4×Dic149C211yesmaximal, characteristic, complemented
6#23749525C211yesmaximal, characteristic, complemented
7#23749522C211yesmaximal, characteristic, complemented
8#23749517C211yesmaximal, characteristic, complemented
9#23749513C211yesmaximal, characteristic, complemented
10#23749504C211yesmaximal, characteristic, complemented
11#23749483C211yesmaximal, characteristic, complemented
12#23749476C211yesmaximal, characteristic, complemented
13C22⋊C4×Dic149C211yesmaximal, characteristic, complemented
14#23749472C211yesmaximal, characteristic, complemented
15#386×C149C211yesmaximal, characteristic, complemented
16C22×C22⋊D149C2211yescharacteristic
17C22×C22⋊D149C2211yescharacteristic
18C23×Dic149C2211yescharacteristic
19C23×Dic149C2211yescharacteristic
20C23×Dic149C2211yescharacteristic
21C22×C4×D149C2211yescharacteristic
22#18011883C418yescomplemented
23D4×Dic149—24no—
24#18011871—24no—
25#18011871—24no—
26C2×C4⋊Dic149C2211yescharacteristic
27C2×#14558715C2211yescharacteristic
28C2×#14558715C2211yescharacteristic
29C2×#14558715C2211yescharacteristic
30C2×#14558715C2211yescharacteristic
31C2×C22⋊Dic149C2211yescharacteristic
32C2×C22⋊Dic149C2211yescharacteristic
33C2×C22⋊Dic149C2211yescharacteristic
34C2×#14558713C2211yescharacteristic
35C2×#14558713C2211yescharacteristic
36C2×#14558713C2211yescharacteristic
37C2×#14558713C2211yescharacteristic
38C2×C4×Dic149—24no—
39C2×C4×Dic149C2211yescharacteristic
40C2×C4×Dic149C2211yescharacteristic
41C2×C4×Dic149C2211yescharacteristic
42C2×C4×Dic149C2211yescharacteristic
43C2×C4×Dic149C2211yescharacteristic
44C2×C4×Dic149C2211yescharacteristic
45#18011818C2211yescharacteristic
46#18011818C2211yescharacteristic
47#18011818C2211yescharacteristic
48#18011818C2211yescharacteristic
49C22×D4×C149C2211yescharacteristic
50C23×C4×C149C2211yescharacteristic
51C2×C22⋊C4×C149C2211yescharacteristic
52C2×C22⋊C4×C149C2211yescharacteristic
53C2×C22⋊C4×C149C2211yescharacteristic
54#95×C149C2211yescharacteristic
55#95×C149C2211yescharacteristic
56C23×D149C2311yescharacteristic
57C2×C22⋊D149—22no—
58C2×C22⋊D149—22no—
59C2×C22⋊D149—22no—
60C2×C22⋊D149—22no—
61C2×C22⋊D149C2×C414yescomplemented
62C2×C22⋊D149C2×C414yescomplemented
63C22×Dic149—22no—
64C22×Dic149—22no—
65C22×Dic149—22no—
66C22×Dic149—22no—
67C22×Dic149—22no—
68C22×Dic149—22no—
69C22×Dic149—22no—
70C22×Dic149C2×C414yescomplemented
71C22×Dic149D414yescomplemented
72C22×Dic149C2311yescharacteristic
73C22×Dic149C2311yescharacteristic
74C22×Dic149C2311yescharacteristic
75C22×Dic149C2311yescharacteristic
76C22×Dic149C2311yescharacteristic
77C22×Dic149C2311yescharacteristic
78C22×Dic149C2311yescharacteristic
79C2×C4×D149—22no—
80C2×C4×D149—22no—
81C2×C4×D149—22no—
82C4⋊Dic149—22no—
83#14558715—22no—
84#14558715—22no—
85#14558715—22no—
86#14558715C2×C414yescomplemented
87C22⋊Dic149—22no—
88C22⋊Dic149—22no—
89C22⋊Dic149C2×C414yescomplemented
90#14558713—22no—
91#14558713—22no—
92#14558713—22no—
93#14558713C2×C414yescomplemented
94C4×Dic149—22no—
95C4×Dic149—22no—
96C4×Dic149—22no—
97C4×Dic149—22no—
98C4×Dic149—22no—
99C4×Dic149D414yescomplemented
100C24×C149C2311yescharacteristic
101C24×C149C2311yescharacteristic
102C2×D4×C149—22no—
103C2×D4×C149—22no—
104C2×D4×C149C2×C414yescomplemented
105C22×C4×C149—22no—
106C22×C4×C149—22no—
107C22×C4×C149—22no—
108C22×C4×C149C2311yescharacteristic
109C22×C4×C149C2311yescharacteristic
110C22×C4×C149C2311yescharacteristic
111C22×C4×C149C2311yescharacteristic
112C22×C4×C149C2311yescharacteristic
113C22⋊C4×C149—22no—
114C22⋊C4×C149—22no—
115C22⋊C4×C149—22no—
116C22×D149—21no—
117C22×D149—21no—
118C22×D149—21no—
119C22×D149—21no—
120C22×D149—21no—
121C22×D149—21no—
122C22×D149C22×C412yes—
123C22⋊D149—28no—
124C22⋊D149—28no—
125C2×Dic149—21no—
126C2×Dic149—21no—
127C2×Dic149—21no—
128C2×Dic149—21no—
129C2×Dic149—21no—
130C2×Dic149—21no—
131C2×Dic149—28no—
132C2×Dic149—28no—
133C2×Dic149—21no—
134C2×Dic149—21no—
135C2×Dic149—21no—
136C2×Dic149—21no—
137C2×Dic149—21no—
138C2×Dic149—21no—
139C2×Dic149—44no—
140C2×Dic149C22×C412yes—
141C2×Dic149C22×C412yes—
142C2×Dic149C22×C412yes—
143C2×Dic149C2×D412yes—
144C2×Dic149C2×D412yes—
145C2×Dic149C2×D412yes—
146C2×Dic149C2×D412yes—
147C2×Dic149#4112yes—
148C2×Dic149#4112yes—
149C4×D149—44no—
150C23×C149—21no—
151C23×C149—21no—
152C23×C149—21no—
153C23×C149—21no—
154C23×C149—21no—
155C23×C149—21no—
156C23×C149—21no—
157C23×C149—21no—
158C23×C149—21no—
159C23×C149—21no—
160C23×C149C22×C412yes—
161C23×C149C22×C412yes—
162C23×C149C2×D412yes—
163C23×C149#4112yes—
164C23×C149C2411yescharacteristic
165D4×C149—28no—
166C2×C4×C149—28no—
167C2×C4×C149—21no—
168C2×C4×C149—21no—
169C2×C4×C149—21no—
170C2×C4×C149—21no—
171C2×C4×C149—21no—
172C2×C4×C149—21no—
173C2×C4×C149—21no—
174C2×C4×C149—21no—
175C2×C4×C149—21no—
176C2×C4×C149—21no—
177C2×C4×C149—21no—
178C2×C4×C149—21no—
179C2×C4×C149C22×C412yes—
180C2×C4×C149C2×D412yes—
181C2×C4×C149#4112yes—
182C22×C149—22no—
183C22×C149—22no—
184C22×C149—22no—
185C22×C149—22no—
186C22×C149—22no—
187C22×C149—22no—
188C22×C149—22no—
189C22×C149—22no—
190C22×C149—22no—
191C22×C149—41no—
192C22×C149—41no—
193C22×C149—41no—
194C22×C149—41no—
195C22×C149C4×D414yescomplemented
196C22×C149C23×C411yescharacteristic
197C22×C149C22×D411yescharacteristic
198C22×C149C22×D411yescharacteristic
199C22×C149C2×#4111yescharacteristic
200C22×C149C2×#4111yescharacteristic
201C22×C149C2×#4111yescharacteristic
202C22×C149C2×#4111yescharacteristic
203C2×D149—22no—
204C2×D149—22no—
205C2×D149—22no—
206C2×D149—41no—
207C2×D149—41no—
208C2×D149—41no—
209C2×D149—41no—
210C4×C149—22no—
211C4×C149—22no—
212C4×C149—22no—
213C4×C149—41no—
214C4×C149—41no—
215Dic149—22no—
216Dic149—22no—
217Dic149—22no—
218Dic149—41no—
219Dic149—41no—
220Dic149C4×D414yescomplemented
221Dic149#12114yescomplemented
222C2×C149—24no—
223C2×C149—42no—
224C2×C149C2×C4×D411yescharacteristic
225C2×C149C2×C4×D411yescharacteristic
226C2×C149C4×#4111yescharacteristic
227C2×C149C2×#12111yescharacteristic
228C2×C149#52511yescharacteristic
229C2×C149#52911yescharacteristic
230C2×C149#53211yescharacteristic
231D149—42no—
232C149C4×#12111yescharacteristic, complemented, Sylow
233C4×#121—1491nomaximal, Sylow
234C2×#121—1491no—
235C2×C4×D4—1491no—
236C2×C4×D4—1491no—
237C2×C4×D4—1491no—
238C22×C42—1491no—
239#390—1491no—
240#389—1491no—
241#388—1491no—
242#388—1491no—
243#386—1491no—
244#386D14911yescharacteristic, complemented
245#380—1491no—
246C4×C4⋊C4—1491no—
247C4×C22⋊C4—1491no—
248C4×C22⋊C4—1491no—
249C22×D4—1491no—
250C22×D4—1491no—
251C22×D4C2×D14911yescharacteristic
252C23×C4—1491no—
253C23×C4—1491no—
254C23×C4—1491no—
255C23×C4—1491no—
256C23×C4C2×D14911yescharacteristic
257#121—1498no—
258C4×D4—2984no—
259C4×D4—2984no—
260C4×D4—2984no—
261C2×C4⋊C4—1491no—
262C2×C4⋊C4—1491no—
263C2×C4⋊C4—1491no—
264C2×C4⋊C4—1491no—
265C2×C4⋊C4—1491no—
266C2×C22⋊C4—1491no—
267C2×C22⋊C4—1491no—
268C2×C22⋊C4—1491no—
269C2×C22⋊C4—1491no—
270C2×C22⋊C4—1491no—
271C2×C22⋊C4—1491no—
272C2×C22⋊C4—1491no—
273C2×C22⋊C4C2×D14911yescharacteristic
274C2×C22⋊C4C2×D14911yescharacteristic
275C2×C22⋊C4C2×D14911yescharacteristic
276C2×C42—2984no—
277C2×C42—1491no—
278C2×C42—1491no—
279C2×C42—1491no—
280C2×C42—1491no—
281C2×C42—1491no—
282C2×C42—1491no—
283#95—1491no—
284#95—1491no—
285#95—1491no—
286#95—1491no—
287#95C2×D14911yescharacteristic
288#95C2×D14911yescharacteristic
289C24—1491no—
290C24C22×D14911yescharacteristic
291C24C22×D14911yescharacteristic
292C2×D4—22no—
293C2×D4—22no—
294C2×D4—2982no—
295C2×D4—2982no—
296C2×D4—2982no—
297C2×D4—2982no—
298C2×D4—1494no—
299C2×D4—1494no—
300C2×D4C4×D14914yescomplemented
301C22×C4—22no—
302C22×C4—22no—
303C22×C4—22no—
304C22×C4—2982no—
305C22×C4—2982no—
306C22×C4—2982no—
307C22×C4—2982no—
308C22×C4—2982no—
309C22×C4—2982no—
310C22×C4—2982no—
311C22×C4—2982no—
312C22×C4—2982no—
313C22×C4—2982no—
314C22×C4—1491no—
315C22×C4—1491no—
316C22×C4—1494no—
317C22×C4—1494no—
318C22×C4—1491no—
319C22×C4—1491no—
320C22×C4—1491no—
321C22×C4—1491no—
322C22×C4—1491no—
323C22×C4C22×D14911yescharacteristic
324C22×C4C22×D14911yescharacteristic
325C22×C4C22×D14911yescharacteristic
326C22×C4C22×D14911yescharacteristic
327C22×C4C22×D14911yescharacteristic
328C4⋊C4—2982no—
329C4⋊C4—2982no—
330C4⋊C4—2982no—
331C4⋊C4—2982no—
332C4⋊C4—1494no—
333C22⋊C4—22no—
334C22⋊C4—22no—
335C22⋊C4—22no—
336C22⋊C4—2982no—
337C22⋊C4—2982no—
338C22⋊C4—2982no—
339C22⋊C4—2982no—
340C22⋊C4—2982no—
341C22⋊C4—1494no—
342C22⋊C4—1494no—
343C42—2982no—
344C42—2982no—
345C42—2982no—
346C42—2982no—
347C42—2982no—
348C42—1494no—
349C23—21no—
350C23—21no—
351C23—21no—
352C23—21no—
353C23—21no—
354C23—21no—
355C23—21no—
356C23—21no—
357C23—21no—
358C23—21no—
359C23—2981no—
360C23—2981no—
361C23—2981no—
362C23—2981no—
363C23—2981no—
364C23—2981no—
365C23—1492no—
366C23C2×C4×D14912yes—
367C23C2×C4×D14912yes—
368C23D4×D14912yes—
369C23#1455873512yes—
370C23C23×D14911yescharacteristic
371D4—28no—
372D4—2988no—
373D4—2988no—
374C2×C4—28no—
375C2×C4—21no—
376C2×C4—21no—
377C2×C4—21no—
378C2×C4—21no—
379C2×C4—21no—
380C2×C4—21no—
381C2×C4—21no—
382C2×C4—21no—
383C2×C4—21no—
384C2×C4—21no—
385C2×C4—21no—
386C2×C4—21no—
387C2×C4—2981no—
388C2×C4—2981no—
389C2×C4—2981no—
390C2×C4—2981no—
391C2×C4—2981no—
392C2×C4—2981no—
393C2×C4—2988no—
394C2×C4—2988no—
395C2×C4—2981no—
396C2×C4—2981no—
397C2×C4—2981no—
398C2×C4—2981no—
399C2×C4—2981no—
400C2×C4—2981no—
401C2×C4—5964no—
402C2×C4—5964no—
403C2×C4—1492no—
404C2×C4—1492no—
405C2×C4—1492no—
406C2×C4—1492no—
407C2×C4—1492no—
408C2×C4—1492no—
409C2×C4—1492no—
410C2×C4—1492no—
411C2×C4—1492no—
412C2×C4C2×C4×D14912yes—
413C2×C4D4×D14912yes—
414C2×C4#1455873512yes—
415C22—22no—
416C22—22no—
417C22—22no—
418C22—22no—
419C22—22no—
420C22—22no—
421C22—22no—
422C22—22no—
423C22—22no—
424C22—41no—
425C22—41no—
426C22—41no—
427C22—41no—
428C22—2982no—
429C22—2982no—
430C22—2982no—
431C22—5961no—
432C22—5961no—
433C22—5961no—
434C22—5961no—
435C22#1801187114yescomplemented
436C22C22×C4×D14911yescharacteristic
437C22C2×D4×D14911yescharacteristic
438C22C2×D4×D14911yescharacteristic
439C22#41×D14911yescharacteristic
440C22#41×D14911yescharacteristic
441C22C2×#1455873511yescharacteristic
442C22C2×#1455873511yescharacteristic
443C4—22no—
444C4—22no—
445C4—22no—
446C4—41no—
447C4—41no—
448C4—2982no—
449C4—2982no—
450C4—2982no—
451C4—5961no—
452C4—5961no—
453C4—1494no—
454C4—1494no—
455C2—24no—
456C2—42no—
457C2—5962no—
458C2C4×D4×D14911yescharacteristic
459C2C2×#1801187111yescharacteristic
460C2C4×#1455873511yescharacteristic
461C2#121×D14911yescharacteristic
462C2#2375013111yescharacteristic
463C2#2375015211yescharacteristic
464C2#2375017011yescharacteristic
subgroupG/H
center, FrattiniC23C23×D149
commutatorC22×C149C23×C4
Fitting#386×C149C2
socle, cosocleC23×C149C24
prime radicalC2×#18011883C2
hypercenter#386D149
hypocenterC149C4×#121
LCSG ▷ C22×C149 ▷ C149
UCSC1 ◁ C23 ◁ #386

Complements

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

NH ≅ G/Ntype
2. C2×D4×Dic149C2semidirect
3. C2×#18011871C2semidirect
4. C2×#18011871C2semidirect
5. C22×C4×Dic149C2semidirect
6. #23749525C2semidirect
7. #23749522C2semidirect
8. #23749517C2semidirect
9. #23749513C2semidirect
10. #23749504C2semidirect
11. #23749483C2semidirect
12. #23749476C2semidirect
13. C22⋊C4×Dic149C2semidirect
14. #23749472C2semidirect
15. #386×C149C2semidirect
22. #18011883C4semidirect
61. C2×C22⋊D149C2×C4semidirect
62. C2×C22⋊D149C2×C4semidirect
70. C22×Dic149C2×C4semidirect
71. C22×Dic149D4semidirect
86. #14558715C2×C4semidirect
89. C22⋊Dic149C2×C4semidirect
93. #14558713C2×C4semidirect
99. C4×Dic149D4semidirect
104. C2×D4×C149C2×C4semidirect
195. C22×C149C4×D4semidirect
220. Dic149C4×D4semidirect
221. Dic149#121semidirect
232. C149C4×#121semidirect
244. #386D149semidirect
300. C2×D4C4×D149semidirect
435. C22#18011871semidirect

Maximal subgroups

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

subgroupindex
C2×#180118832
C2×D4×Dic1492
C2×#180118712
C22×C4×Dic1492
#237495252
#237495222
#237495172
#237495132
#237495042
#237494832
#237494762
C22⋊C4×Dic1492
#237494722
#386×C1492
C4×#121149