Finite Group Databasebeta

← C149×#7694 #49186643

Subgroups — C149×#7694 #49186643

Order 38144.

556 conjugacy classes of subgroups.

The subgroup lattice has 394 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#2854×C149C211yesmaximal, characteristic
2#1817×C149C211yesmaximal, characteristic, complemented
3#1728×C149C211yesmaximal, characteristic, complemented
4#1271×C149C212yesmaximal, complemented
5#1270×C149C212yesmaximal, complemented
6C22×M16×C149—21no—
7C2×#123×C149—21no—
8C2×#121×C149C411yescharacteristic
9C22×C42×C149C2211yescharacteristic
10C2×C22⋊C8×C149—21no—
11#390×C149C411yescharacteristic
12#390×C149C2211yescharacteristic
13#389×C149C411yescharacteristic
14#389×C149C2211yescharacteristic
15#388×C149—21no—
16#388×C149—21no—
17#386×C149—21no—
18#380×C149C411yescharacteristic
19#336×C149—21no—
20#336×C149—21no—
21#336×C149C2212yes—
22#336×C149C2212yes—
23C22×D4×C149—21no—
24C22×D4×C149C2×C411yescharacteristic
25C23×C4×C149C2×C411yescharacteristic
26C23×C4×C149D411yescharacteristic
27C23×C4×C149D411yescharacteristic
28C2×M16×C149—24no—
29C2×M16×C149—42no—
30C2×M16×C149—42no—
31C22×C8×C149—22no—
32C22×C8×C149—22no—
33#123×C149—44no—
34#121×C149—42no—
35C2×C4⋊C4×C149—21no—
36C2×C4⋊C4×C149—21no—
37C2×C4⋊C4×C149C2×C411yescharacteristic
38C2×C4⋊C4×C149C2×C411yescharacteristic
39C2×C4⋊C4×C149C2×C411yescharacteristic
40C2×C22⋊C4×C149—21no—
41C2×C22⋊C4×C149—21no—
42C2×C22⋊C4×C149—21no—
43C2×C22⋊C4×C149—21no—
44C2×C22⋊C4×C149—21no—
45C2×C22⋊C4×C149—21no—
46C2×C42×C149—42no—
47C2×C42×C149C2×C411yescharacteristic
48C2×C42×C149D411yescharacteristic
49C2×C42×C149D411yescharacteristic
50C2×C42×C149C2311yescharacteristic
51C22⋊C8×C149—42no—
52#95×C149—21no—
53#95×C149—21no—
54#95×C149—21no—
55C24×C149—21no—
56C24×C149C22⋊C411yescharacteristic
57C2×D4×C149—22no—
58C2×D4×C149—41no—
59C2×D4×C149—41no—
60C2×D4×C149—42no—
61C2×D4×C149—42no—
62C2×D4×C149—42no—
63C22×C4×C149—22no—
64C22×C4×C149—22no—
65C22×C4×C149—21no—
66C22×C4×C149—21no—
67C22×C4×C149—22no—
68C22×C4×C149—22no—
69C22×C4×C149—22no—
70C22×C4×C149—22no—
71C22×C4×C149—21no—
72C22×C4×C149—21no—
73C22×C4×C149—21no—
74C22×C4×C149—41no—
75C22×C4×C149—41no—
76C22×C4×C149C22⋊C411yescharacteristic
77C22×C4×C149C22⋊C411yescharacteristic
78C22×C4×C149C22⋊C411yescharacteristic
79C22×C4×C149C22×C411yescharacteristic
80C22×C4×C149C2×D411yescharacteristic
81C22×C4×C149C2×D411yescharacteristic
82M16×C149—48no—
83C2×C8×C149—24no—
84C2×C8×C149—42no—
85C2×C8×C149—42no—
86C2×C8×C149—42no—
87C2×C8×C149—42no—
88C2×C8×C149—42no—
89C4⋊C4×C149—22no—
90C4⋊C4×C149—42no—
91C4⋊C4×C149—41no—
92C4⋊C4×C149—41no—
93C4⋊C4×C149—42no—
94C22⋊C4×C149—42no—
95C22⋊C4×C149—42no—
96C22⋊C4×C149—42no—
97C22⋊C4×C149—42no—
98C22⋊C4×C149—41no—
99C22⋊C4×C149—42no—
100C22⋊C4×C149—41no—
101C42×C149—41no—
102C42×C149—41no—
103C42×C149—41no—
104C42×C149—41no—
105C23×C149—21no—
106C23×C149—21no—
107C23×C149—21no—
108C23×C149—21no—
109C23×C149—21no—
110C23×C149—21no—
111C23×C149—41no—
112C23×C149—41no—
113C23×C149—41no—
114C23×C149—41no—
115C23×C149—41no—
116C23×C149—41no—
117C23×C149—41no—
118C23×C149#9912yes—
119C23×C149C2×C22⋊C411yescharacteristic
120D4×C149—82no—
121D4×C149—84no—
122C2×C4×C149—24no—
123C2×C4×C149—24no—
124C2×C4×C149—21no—
125C2×C4×C149—21no—
126C2×C4×C149—21no—
127C2×C4×C149—21no—
128C2×C4×C149—21no—
129C2×C4×C149—21no—
130C2×C4×C149—21no—
131C2×C4×C149—21no—
132C2×C4×C149—21no—
133C2×C4×C149—21no—
134C2×C4×C149—21no—
135C2×C4×C149—21no—
136C2×C4×C149—21no—
137C2×C4×C149—21no—
138C2×C4×C149—44no—
139C2×C4×C149—44no—
140C2×C4×C149—41no—
141C2×C4×C149—41no—
142C2×C4×C149—41no—
143C2×C4×C149—41no—
144C2×C4×C149—41no—
145C2×C4×C149—41no—
146C2×C4×C149—41no—
147C2×C4×C149—41no—
148C2×C4×C149—41no—
149C2×C4×C149#10412yes—
150C2×C4×C149#13112yes—
151C2×C4×C149AGL(1,ℤ/8)11yescharacteristic
152C2×C4×C149AGL(1,ℤ/8)12yes—
153C2×C4×C149#13711yescharacteristic
154C8×C149—44no—
155C8×C149—82no—
156C22×C149—22no—
157C22×C149—22no—
158C22×C149—22no—
159C22×C149—41no—
160C22×C149—41no—
161C22×C149—41no—
162C22×C149—41no—
163C22×C149—81no—
164C22×C149—81no—
165C22×C149—81no—
166C22×C149—81no—
167C22×C149—81no—
168C22×C149—81no—
169C22×C149—81no—
170C22×C149#40811yescharacteristic
171C22×C149C2×#9911yescharacteristic
172C22×C149#41311yescharacteristic
173C22×C149#41711yescharacteristic
174C22×C149#41811yescharacteristic
175C22×C149C2×#10411yescharacteristic
176C22×C149#42111yescharacteristic
177C4×C149—22no—
178C4×C149—21no—
179C4×C149—22no—
180C4×C149—21no—
181C4×C149—22no—
182C4×C149—41no—
183C4×C149—41no—
184C4×C149—81no—
185C4×C149—81no—
186C4×C149—81no—
187C2×C149—42no—
188C2×C149—161no—
189C2×C149#146811yescharacteristic
190C2×C149#148411yescharacteristic
191C2×C149#149511yescharacteristic
192C2×C149#150411yescharacteristic
193C2×C149#151011yescharacteristic
194C2×C149#152911yescharacteristic
195C2×C149#155711yescharacteristic
196#7694C14911yesmaximal, characteristic, direct product factor, Sylow
197C149#769411yescharacteristic, direct product factor, Sylow
198#2854C2×C14911yescharacteristic
199#1817C2×C14911yescharacteristic, complemented
200#1728C2×C14911yescharacteristic, complemented
201#1271C2×C14912yescomplemented
202#1270C2×C14912yescomplemented
203C22×M16—21no—
204C2×#123—21no—
205C2×#121C4×C14911yescharacteristic
206C22×C42C22×C14911yescharacteristic
207C2×C22⋊C8—21no—
208#390C4×C14911yescharacteristic
209#390C22×C14911yescharacteristic
210#389C4×C14911yescharacteristic
211#389C22×C14911yescharacteristic
212#388—21no—
213#388—21no—
214#386—21no—
215#380C4×C14911yescharacteristic
216#336—21no—
217#336—21no—
218#336C22×C14912yes—
219#336C22×C14912yes—
220C22×D4—21no—
221C22×D4C2×C4×C14911yescharacteristic
222C23×C4C2×C4×C14911yescharacteristic
223C23×C4D4×C14911yescharacteristic
224C23×C4D4×C14911yescharacteristic
225C2×M16—24no—
226C2×M16—42no—
227C2×M16—42no—
228C22×C8—22no—
229C22×C8—22no—
230#123—44no—
231#121—42no—
232C2×C4⋊C4—21no—
233C2×C4⋊C4—21no—
234C2×C4⋊C4C2×C4×C14911yescharacteristic
235C2×C4⋊C4C2×C4×C14911yescharacteristic
236C2×C4⋊C4C2×C4×C14911yescharacteristic
237C2×C22⋊C4—21no—
238C2×C22⋊C4—21no—
239C2×C22⋊C4—21no—
240C2×C22⋊C4—21no—
241C2×C22⋊C4—21no—
242C2×C22⋊C4—21no—
243C2×C42—42no—
244C2×C42C2×C4×C14911yescharacteristic
245C2×C42D4×C14911yescharacteristic
246C2×C42D4×C14911yescharacteristic
247C2×C42C23×C14911yescharacteristic
248C22⋊C8—42no—
249#95—21no—
250#95—21no—
251#95—21no—
252C24—21no—
253C24C22⋊C4×C14911yescharacteristic
254C2×D4—22no—
255C2×D4—41no—
256C2×D4—41no—
257C2×D4—42no—
258C2×D4—42no—
259C2×D4—42no—
260C22×C4—22no—
261C22×C4—22no—
262C22×C4—21no—
263C22×C4—21no—
264C22×C4—22no—
265C22×C4—22no—
266C22×C4—22no—
267C22×C4—22no—
268C22×C4—21no—
269C22×C4—21no—
270C22×C4—21no—
271C22×C4—41no—
272C22×C4—41no—
273C22×C4C22⋊C4×C14911yescharacteristic
274C22×C4C22⋊C4×C14911yescharacteristic
275C22×C4C22⋊C4×C14911yescharacteristic
276C22×C4C22×C4×C14911yescharacteristic
277C22×C4C2×D4×C14911yescharacteristic
278C22×C4C2×D4×C14911yescharacteristic
279M16—48no—
280C2×C8—24no—
281C2×C8—42no—
282C2×C8—42no—
283C2×C8—42no—
284C2×C8—42no—
285C2×C8—42no—
286C4⋊C4—22no—
287C4⋊C4—41no—
288C4⋊C4—41no—
289C4⋊C4—42no—
290C4⋊C4—42no—
291C22⋊C4—42no—
292C22⋊C4—42no—
293C22⋊C4—42no—
294C22⋊C4—42no—
295C22⋊C4—42no—
296C22⋊C4—41no—
297C22⋊C4—41no—
298C42—41no—
299C42—41no—
300C42—41no—
301C42—41no—
302C23—21no—
303C23—21no—
304C23—21no—
305C23—21no—
306C23—21no—
307C23—21no—
308C23—41no—
309C23—41no—
310C23—41no—
311C23—41no—
312C23—41no—
313C23—41no—
314C23—41no—
315C23#99×C14912yes—
316C23C2×C22⋊C4×C14911yescharacteristic
317D4—82no—
318D4—84no—
319C2×C4—24no—
320C2×C4—24no—
321C2×C4—21no—
322C2×C4—21no—
323C2×C4—21no—
324C2×C4—21no—
325C2×C4—21no—
326C2×C4—21no—
327C2×C4—21no—
328C2×C4—21no—
329C2×C4—21no—
330C2×C4—21no—
331C2×C4—21no—
332C2×C4—21no—
333C2×C4—21no—
334C2×C4—21no—
335C2×C4—44no—
336C2×C4—44no—
337C2×C4—41no—
338C2×C4—41no—
339C2×C4—41no—
340C2×C4—41no—
341C2×C4—41no—
342C2×C4—41no—
343C2×C4—41no—
344C2×C4—41no—
345C2×C4—41no—
346C2×C4#104×C14912yes—
347C2×C4#131×C14912yes—
348C2×C4AGL(1,ℤ/8)×C14911yescharacteristic
349C2×C4AGL(1,ℤ/8)×C14912yes—
350C2×C4#137×C14911yescharacteristic
351C8—44no—
352C8—82no—
353C22—22no—
354C22—22no—
355C22—22no—
356C22—41no—
357C22—41no—
358C22—41no—
359C22—41no—
360C22—81no—
361C22—81no—
362C22—81no—
363C22—81no—
364C22—81no—
365C22—81no—
366C22—81no—
367C22#408×C14911yescharacteristic
368C22C2×#99×C14911yescharacteristic
369C22#413×C14911yescharacteristic
370C22#417×C14911yescharacteristic
371C22#418×C14911yescharacteristic
372C22C2×#104×C14911yescharacteristic
373C22#421×C14911yescharacteristic
374C4—22no—
375C4—21no—
376C4—22no—
377C4—21no—
378C4—22no—
379C4—41no—
380C4—41no—
381C4—81no—
382C4—81no—
383C4—81no—
384C2—42no—
385C2—161no—
386C2#1468×C14911yescharacteristic
387C2#1484×C14911yescharacteristic
388C2#1495×C14911yescharacteristic
389C2#1504×C14911yescharacteristic
390C2#1510×C14911yescharacteristic
391C2#1529×C14911yescharacteristic
392C2#1557×C14911yescharacteristic
subgroupG/H
center, socleC23×C149C2×C22⋊C4
commutatorC22×C4C22×C4×C149
Frattini, cosocleC2×C42C23×C149
prime radicalC2×#121×C149C4
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C23×C149 ◁ C22×C42×C149 ◁ G

Complements

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

NH ≅ G/Ntype
2. #1817×C149C2semidirect
3. #1728×C149C2semidirect
4. #1271×C149C2semidirect
5. #1270×C149C2semidirect
196. #7694C149direct (N × H)
197. C149#7694direct (N × H)
199. #1817C2×C149semidirect
200. #1728C2×C149semidirect
201. #1271C2×C149semidirect
202. #1270C2×C149semidirect

Maximal subgroups

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

subgroupindex
#2854×C1492
#1817×C1492
#1728×C1492
#1271×C1492
#1270×C1492
#7694149