Finite Group Databasebeta

← C149×#9225 #49188174

Subgroups — C149×#9225 #49188174

Order 38144.

578 conjugacy classes of subgroups.

The subgroup lattice has 428 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#461×C149C211yesmaximal, characteristic
2C2×#436×C149C211yesmaximal, characteristic
3#1990×C149C211yesmaximal, characteristic, complemented
4#1802×C149C211yesmaximal, characteristic
5C2×#332×C149C211yesmaximal, characteristic, complemented
6#1296×C149C211yesmaximal, characteristic, complemented
7#1277×C149C211yesmaximal, characteristic, complemented
8C22×SD16×C149—21no—
9C22×M16×C149—21no—
10C2×C4⋊Q8×C149C2211yescharacteristic
11C2×C4×D4×C149C2211yescharacteristic
12#461×C149—22no—
13#461×C149C414yescomplemented
14#436×C149—22no—
15#436×C149—22no—
16C2×C4⋊C8×C149C2211yescharacteristic
17C2×C4⋊C8×C149C2211yescharacteristic
18C2×C4⋊C8×C149C2211yescharacteristic
19C2×#103×C149—21no—
20C2×#102×C149—21no—
21C2×C22⋊C8×C149—21no—
22C2×C4×C8×C149C2211yescharacteristic
23#384×C149C2211yescharacteristic
24#340×C149—21no—
25#340×C149—21no—
26#340×C149—21no—
27#332×C149—22no—
28C22×Q8×C149—21no—
29C22×D4×C149D411yescharacteristic
30C23×C4×C149—21no—
31C2×SD16×C149—24no—
32C2×SD16×C149—42no—
33C2×SD16×C149—42no—
34C2×M16×C149—24no—
35C2×M16×C149—42no—
36C2×M16×C149—42no—
37C22×C8×C149—21no—
38C22×C8×C149—21no—
39C22×C8×C149—21no—
40C22×C8×C149D411yescharacteristic
41C22×C8×C149D411yescharacteristic
42C4⋊Q8×C149—21no—
43C4⋊Q8×C149—21no—
44C4⋊Q8×C149—21no—
45C4⋊Q8×C149C2×C412yes—
46C4×D4×C149—21no—
47C4×D4×C149—21no—
48C4×D4×C149C2×C412yes—
49C4×D4×C149D412yes—
50C2×C4⋊C4×C149—21no—
51C2×C4⋊C4×C149—21no—
52C2×C4⋊C4×C149—21no—
53C2×C4⋊C4×C149—21no—
54C2×C4⋊C4×C149—21no—
55C2×C4⋊C4×C149D411yescharacteristic
56C2×C22⋊C4×C149—21no—
57C2×C42×C149C2311yescharacteristic
58C4⋊C8×C149—21no—
59C4⋊C8×C149—21no—
60C4⋊C8×C149—21no—
61C4⋊C8×C149—21no—
62C4⋊C8×C149C2×C412yes—
63C4⋊C8×C149D412yes—
64#103×C149—24no—
65#102×C149—42no—
66C22⋊C8×C149—24no—
67C4×C8×C149—21no—
68C4×C8×C149—21no—
69C24×C149—21no—
70C2×Q8×C149—22no—
71C2×Q8×C149—41no—
72C2×Q8×C149—41no—
73C2×Q8×C149—41no—
74C2×Q8×C149—41no—
75C2×Q8×C149—41no—
76C2×D4×C149—21no—
77C2×D4×C149—21no—
78C2×D4×C149—21no—
79C2×D4×C149—21no—
80C2×D4×C149—21no—
81C2×D4×C149C22⋊C412yes—
82C22×C4×C149—21no—
83C22×C4×C149—22no—
84C22×C4×C149—22no—
85C22×C4×C149—41no—
86C22×C4×C149—41no—
87C22×C4×C149—41no—
88C22×C4×C149—41no—
89C22×C4×C149—41no—
90C22×C4×C149—41no—
91C22×C4×C149C2×D411yescharacteristic
92C22×C4×C149C2×D411yescharacteristic
93C22×C4×C149#4111yescharacteristic
94SD16×C149—48no—
95M16×C149—48no—
96C2×C8×C149—21no—
97C2×C8×C149—21no—
98C2×C8×C149—22no—
99C2×C8×C149—21no—
100C2×C8×C149—22no—
101C2×C8×C149—21no—
102C2×C8×C149—21no—
103C2×C8×C149—41no—
104C2×C8×C149—41no—
105C2×C8×C149—41no—
106C2×C8×C149—41no—
107C2×C8×C149—41no—
108C2×C8×C149—41no—
109C2×C8×C149—41no—
110C2×C8×C149SD1612yescomplemented
111C4⋊C4×C149—21no—
112C4⋊C4×C149—22no—
113C4⋊C4×C149—22no—
114C4⋊C4×C149—41no—
115C4⋊C4×C149—41no—
116C4⋊C4×C149—41no—
117C4⋊C4×C149—41no—
118C4⋊C4×C149—41no—
119C4⋊C4×C149—41no—
120C4⋊C4×C149—81no—
121C4⋊C4×C149C22⋊C412yes—
122C22⋊C4×C149—22no—
123C22⋊C4×C149—22no—
124C42×C149C22×C411yescharacteristic
125C42×C149C2×D411yescharacteristic
126C42×C149C2×D411yescharacteristic
127C42×C149#4111yescharacteristic
128C23×C149—22no—
129C23×C149—41no—
130C23×C149—41no—
131C23×C149—41no—
132C23×C149—41no—
133C23×C149—41no—
134C23×C149—41no—
135C23×C149#12111yescharacteristic
136Q8×C149—42no—
137Q8×C149—42no—
138Q8×C149—81no—
139Q8×C149—81no—
140D4×C149—22no—
141D4×C149—22no—
142D4×C149—41no—
143D4×C149—41no—
144C2×C4×C149—21no—
145C2×C4×C149—21no—
146C2×C4×C149—22no—
147C2×C4×C149—41no—
148C2×C4×C149—41no—
149C2×C4×C149—42no—
150C2×C4×C149—42no—
151C2×C4×C149—42no—
152C2×C4×C149—42no—
153C2×C4×C149—42no—
154C2×C4×C149—81no—
155C2×C4×C149—81no—
156C2×C4×C149—81no—
157C2×C4×C149—81no—
158C2×C4×C149—81no—
159C2×C4×C149C2×C22⋊C411yescharacteristic
160C2×C4×C149C4×D411yescharacteristic
161C2×C4×C149C4×D411yescharacteristic
162C2×C4×C149#12011yescharacteristic
163C2×C4×C149#12111yescharacteristic
164C2×C4×C149#12311yescharacteristic
165C2×C4×C149C2×SD1611yescharacteristic
166C2×C4×C149#13511yescharacteristic
167C2×C4×C149AGL(1,ℤ/8)11yescharacteristic
168C2×C4×C149AGL(1,ℤ/8)11yescharacteristic
169C2×C4×C149AGL(1,ℤ/8)11yescharacteristic
170C2×C4×C149AGL(1,ℤ/8)11yescharacteristic
171C2×C4×C149#13711yescharacteristic
172C2×C4×C149#13711yescharacteristic
173C8×C149—22no—
174C8×C149—42no—
175C8×C149—42no—
176C8×C149—41no—
177C8×C149—81no—
178C22×C149—42no—
179C22×C149—42no—
180C22×C149—42no—
181C22×C149—81no—
182C22×C149—81no—
183C22×C149—81no—
184C22×C149—81no—
185C22×C149#38611yescharacteristic
186C22×C149#46111yescharacteristic
187C22×C149#46311yescharacteristic
188C22×C149#46811yescharacteristic
189C22×C149#46911yescharacteristic
190C22×C149#47111yescharacteristic
191C22×C149#47311yescharacteristic
192C4×C149—21no—
193C4×C149—21no—
194C4×C149—42no—
195C4×C149—82no—
196C4×C149—161no—
197C4×C149#41711yescharacteristic
198C4×C149#41811yescharacteristic
199C4×C149C4×SD1611yescharacteristic
200C4×C149#44011yescharacteristic
201C4×C149#45011yescharacteristic
202C4×C149#45211yescharacteristic
203C4×C149#46811yescharacteristic
204C4×C149#46911yescharacteristic
205C2×C149—82no—
206C2×C149#169111yescharacteristic
207C2×C149#169311yescharacteristic
208C2×C149#169911yescharacteristic
209C2×C149#170111yescharacteristic
210C2×C149#187711yescharacteristic
211C2×C149#189511yescharacteristic
212C2×C149#190811yescharacteristic
213#9225C14911yesmaximal, characteristic, direct product factor, Sylow
214C149#922511yescharacteristic, direct product factor, Sylow
215C2×#461C2×C14911yescharacteristic
216C2×#436C2×C14911yescharacteristic
217#1990C2×C14911yescharacteristic, complemented
218#1802C2×C14911yescharacteristic
219C2×#332C2×C14911yescharacteristic, complemented
220#1296C2×C14911yescharacteristic, complemented
221#1277C2×C14911yescharacteristic, complemented
222C22×SD16—21no—
223C22×M16—21no—
224C2×C4⋊Q8C22×C14911yescharacteristic
225C2×C4×D4C22×C14911yescharacteristic
226#461—22no—
227#461C4×C14914yescomplemented
228#436—22no—
229#436—22no—
230C2×C4⋊C8C22×C14911yescharacteristic
231C2×C4⋊C8C22×C14911yescharacteristic
232C2×C4⋊C8C22×C14911yescharacteristic
233C2×#103—21no—
234C2×#102—21no—
235C2×C22⋊C8—21no—
236C2×C4×C8C22×C14911yescharacteristic
237#384C22×C14911yescharacteristic
238#340—21no—
239#340—21no—
240#340—21no—
241#332—22no—
242C22×Q8—21no—
243C22×D4D4×C14911yescharacteristic
244C23×C4—21no—
245C2×SD16—24no—
246C2×SD16—42no—
247C2×SD16—42no—
248C2×M16—24no—
249C2×M16—42no—
250C2×M16—42no—
251C22×C8—21no—
252C22×C8—21no—
253C22×C8—21no—
254C22×C8D4×C14911yescharacteristic
255C22×C8D4×C14911yescharacteristic
256C4⋊Q8—21no—
257C4⋊Q8—21no—
258C4⋊Q8—21no—
259C4⋊Q8C2×C4×C14912yes—
260C4×D4—21no—
261C4×D4—21no—
262C4×D4C2×C4×C14912yes—
263C4×D4D4×C14912yes—
264C2×C4⋊C4—21no—
265C2×C4⋊C4—21no—
266C2×C4⋊C4—21no—
267C2×C4⋊C4—21no—
268C2×C4⋊C4—21no—
269C2×C4⋊C4D4×C14911yescharacteristic
270C2×C22⋊C4—21no—
271C2×C42C23×C14911yescharacteristic
272C4⋊C8—21no—
273C4⋊C8—21no—
274C4⋊C8—21no—
275C4⋊C8—21no—
276C4⋊C8C2×C4×C14912yes—
277C4⋊C8D4×C14912yes—
278#103—24no—
279#102—42no—
280C22⋊C8—24no—
281C4×C8—21no—
282C4×C8—21no—
283C24—21no—
284C2×Q8—22no—
285C2×Q8—41no—
286C2×Q8—41no—
287C2×Q8—41no—
288C2×Q8—41no—
289C2×Q8—41no—
290C2×D4—21no—
291C2×D4—21no—
292C2×D4—21no—
293C2×D4—21no—
294C2×D4—21no—
295C2×D4C22⋊C4×C14912yes—
296C22×C4—21no—
297C22×C4—22no—
298C22×C4—22no—
299C22×C4—41no—
300C22×C4—41no—
301C22×C4—41no—
302C22×C4—41no—
303C22×C4—41no—
304C22×C4—41no—
305C22×C4C2×D4×C14911yescharacteristic
306C22×C4C2×D4×C14911yescharacteristic
307C22×C4#41×C14911yescharacteristic
308SD16—48no—
309M16—48no—
310C2×C8—21no—
311C2×C8—21no—
312C2×C8—22no—
313C2×C8—21no—
314C2×C8—22no—
315C2×C8—21no—
316C2×C8—21no—
317C2×C8—41no—
318C2×C8—41no—
319C2×C8—41no—
320C2×C8—41no—
321C2×C8—41no—
322C2×C8—41no—
323C2×C8—41no—
324C2×C8SD16×C14912yescomplemented
325C4⋊C4—21no—
326C4⋊C4—22no—
327C4⋊C4—22no—
328C4⋊C4—41no—
329C4⋊C4—41no—
330C4⋊C4—41no—
331C4⋊C4—41no—
332C4⋊C4—41no—
333C4⋊C4—41no—
334C4⋊C4—81no—
335C4⋊C4C22⋊C4×C14912yes—
336C22⋊C4—22no—
337C22⋊C4—22no—
338C42C22×C4×C14911yescharacteristic
339C42C2×D4×C14911yescharacteristic
340C42C2×D4×C14911yescharacteristic
341C42#41×C14911yescharacteristic
342C23—22no—
343C23—41no—
344C23—41no—
345C23—41no—
346C23—41no—
347C23—41no—
348C23—41no—
349C23#121×C14911yescharacteristic
350Q8—42no—
351Q8—42no—
352Q8—81no—
353Q8—81no—
354D4—22no—
355D4—22no—
356D4—41no—
357D4—41no—
358C2×C4—21no—
359C2×C4—21no—
360C2×C4—22no—
361C2×C4—41no—
362C2×C4—41no—
363C2×C4—42no—
364C2×C4—42no—
365C2×C4—42no—
366C2×C4—42no—
367C2×C4—42no—
368C2×C4—81no—
369C2×C4—81no—
370C2×C4—81no—
371C2×C4—81no—
372C2×C4—81no—
373C2×C4C2×C22⋊C4×C14911yescharacteristic
374C2×C4C4×D4×C14911yescharacteristic
375C2×C4C4×D4×C14911yescharacteristic
376C2×C4#120×C14911yescharacteristic
377C2×C4#121×C14911yescharacteristic
378C2×C4#123×C14911yescharacteristic
379C2×C4C2×SD16×C14911yescharacteristic
380C2×C4#135×C14911yescharacteristic
381C2×C4AGL(1,ℤ/8)×C14911yescharacteristic
382C2×C4AGL(1,ℤ/8)×C14911yescharacteristic
383C2×C4AGL(1,ℤ/8)×C14911yescharacteristic
384C2×C4AGL(1,ℤ/8)×C14911yescharacteristic
385C2×C4#137×C14911yescharacteristic
386C2×C4#137×C14911yescharacteristic
387C8—22no—
388C8—42no—
389C8—42no—
390C8—41no—
391C8—81no—
392C22—42no—
393C22—42no—
394C22—42no—
395C22—81no—
396C22—81no—
397C22—81no—
398C22—81no—
399C22#386×C14911yescharacteristic
400C22#461×C14911yescharacteristic
401C22#463×C14911yescharacteristic
402C22#468×C14911yescharacteristic
403C22#469×C14911yescharacteristic
404C22#471×C14911yescharacteristic
405C22#473×C14911yescharacteristic
406C4—21no—
407C4—21no—
408C4—42no—
409C4—82no—
410C4—161no—
411C4#417×C14911yescharacteristic
412C4#418×C14911yescharacteristic
413C4C4×SD16×C14911yescharacteristic
414C4#440×C14911yescharacteristic
415C4#450×C14911yescharacteristic
416C4#452×C14911yescharacteristic
417C4#468×C14911yescharacteristic
418C4#469×C14911yescharacteristic
419C2—82no—
420C2#1691×C14911yescharacteristic
421C2#1693×C14911yescharacteristic
422C2#1699×C14911yescharacteristic
423C2#1701×C14911yescharacteristic
424C2#1877×C14911yescharacteristic
425C2#1895×C14911yescharacteristic
426C2#1908×C14911yescharacteristic
subgroupG/H
center, socleC23×C149#121
commutatorC42C22×C4×C149
Frattini, cosocleC2×C42C23×C149
prime radicalC22×D4×C149D4
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C23×C149 ◁ C2×C42×C149 ◁ G

Complements

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

NH ≅ G/Ntype
3. #1990×C149C2semidirect
5. C2×#332×C149C2semidirect
6. #1296×C149C2semidirect
7. #1277×C149C2semidirect
13. #461×C149C4semidirect
110. C2×C8×C149SD16semidirect
213. #9225C149direct (N × H)
214. C149#9225direct (N × H)
217. #1990C2×C149semidirect
219. C2×#332C2×C149semidirect
220. #1296C2×C149semidirect
221. #1277C2×C149semidirect
227. #461C4×C149semidirect
324. C2×C8SD16×C149semidirect

Maximal subgroups

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

subgroupindex
C2×#461×C1492
C2×#436×C1492
#1990×C1492
#1802×C1492
C2×#332×C1492
#1296×C1492
#1277×C1492
#9225149