Finite Group Databasebeta

← C149×#7756 #49186705

Subgroups — C149×#7756 #49186705

Order 38144.

504 conjugacy classes of subgroups; only the 102 normal subgroups are shown.

normal subgroups only

This group has 504 conjugacy classes of subgroups — too many to draw. Only its 102 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#2732×C149C211yesmaximal, characteristic
2#2057×C149C211yesmaximal, characteristic, complemented
3#2023×C149C211yesmaximal, characteristic
4#2016×C149C211yesmaximal, characteristic, complemented
5#1272×C149C211yesmaximal, characteristic, complemented
6#1271×C149C211yesmaximal, characteristic, complemented
7#1270×C149C211yesmaximal, characteristic
8C22×Q16×C149—21no—
9C2×C4⋊Q8×C149C2211yescharacteristic
10C2×C22⋊Q8×C149—21no—
11C2×#107×C149—21no—
12C2×#103×C149—21no—
13C2×#102×C149—21no—
14#399×C149—21no—
15#398×C149—21no—
16#396×C149—21no—
17#391×C149C2211yescharacteristic
18#390×C149C2211yescharacteristic
19#389×C149C2211yescharacteristic
20#386×C149—21no—
21#385×C149—21no—
22#340×C149—21no—
23#340×C149—21no—
24#336×C149C2211yescharacteristic
25#336×C149C2211yescharacteristic
26#336×C149C2211yescharacteristic
27C22×Q8×C149—21no—
28C22×Q8×C149D411yescharacteristic
29C22×D4×C149D411yescharacteristic
30C23×C4×C149—21no—
31C2×Q16×C149—42no—
32C2×Q16×C149—42no—
33C2×Q16×C149—42no—
34C22×C8×C149—21no—
35C22×C8×C149—21no—
36C22×C8×C149—21no—
37C4⋊Q8×C149—42no—
38C22⋊Q8×C149—42no—
39C22⋊Q8×C149—42no—
40C2×C4⋊C4×C149—21no—
41C2×C4⋊C4×C149—21no—
42C2×C4⋊C4×C149—21no—
43C2×C4⋊C4×C149—21no—
44C2×C4⋊C4×C149—21no—
45C2×C4⋊C4×C149—21no—
46C2×C4⋊C4×C149D411yescharacteristic
47C2×C4⋊C4×C149D411yescharacteristic
48C2×C4⋊C4×C149D411yescharacteristic
49C2×C4⋊C4×C149D411yescharacteristic
50C2×C22⋊C4×C149—21no—
51C2×C22⋊C4×C149—21no—
52C2×C22⋊C4×C149—21no—
53C2×C22⋊C4×C149—21no—
54C2×C22⋊C4×C149—21no—
55C2×C42×C149C2311yescharacteristic
56#107×C149—42no—
57#103×C149—42no—
58#102×C149—42no—
59#95×C149—21no—
60#95×C149—21no—
61#95×C149—21no—
62#95×C149—21no—
63C24×C149—21no—
64C2×Q8×C149—21no—
65C2×Q8×C149—22no—
66C2×Q8×C149—41no—
67C2×Q8×C149—41no—
68C2×Q8×C149—41no—
69C2×Q8×C149—41no—
70C2×Q8×C149—41no—
71C2×Q8×C149—41no—
72C2×Q8×C149—41no—
73C2×Q8×C149D812yes—
74C2×D4×C149—21no—
75C2×D4×C149—41no—
76C2×D4×C149—41no—
77C2×D4×C149Q1612yescomplemented
78C22×C4×C149—21no—
79C22×C4×C149—21no—
80C22×C4×C149—21no—
81C22×C4×C149—21no—
82C22×C4×C149—21no—
83C22×C4×C149—42no—
84C22×C4×C149—41no—
85C22×C4×C149—81no—
86C22×C4×C149—81no—
87C22×C4×C149C2×D411yescharacteristic
88C22×C4×C149C2×D411yescharacteristic
89C22×C4×C149C2×D411yescharacteristic
90Q16×C149—48no—
91C2×C8×C149—22no—
92C2×C8×C149—22no—
93C2×C8×C149—41no—
94C2×C8×C149—41no—
95C2×C8×C149—41no—
96C2×C8×C149—41no—
97C2×C8×C149—41no—
98C2×C8×C149—41no—
99C2×C8×C149—41no—
100C4⋊C4×C149—22no—
101C4⋊C4×C149—22no—
102C4⋊C4×C149—21no—
103C4⋊C4×C149—21no—
104C4⋊C4×C149—42no—
105C4⋊C4×C149—42no—
106C4⋊C4×C149—41no—
107C4⋊C4×C149—41no—
108C4⋊C4×C149—41no—
109C4⋊C4×C149—41no—
110C4⋊C4×C149—41no—
111C4⋊C4×C149—41no—
112C4⋊C4×C149—41no—
113C4⋊C4×C149—81no—
114C22⋊C4×C149—42no—
115C22⋊C4×C149—41no—
116C22⋊C4×C149—41no—
117C22⋊C4×C149—41no—
118C22⋊C4×C149—41no—
119C22⋊C4×C149—81no—
120C22⋊C4×C149—81no—
121C42×C149—41no—
122C23×C149—22no—
123C23×C149—41no—
124C23×C149—41no—
125C23×C149—41no—
126C23×C149—41no—
127C23×C149—41no—
128C23×C149—41no—
129C23×C149#12011yescharacteristic
130Q8×C149—42no—
131Q8×C149—42no—
132Q8×C149—42no—
133Q8×C149—81no—
134Q8×C149—81no—
135Q8×C149—81no—
136D4×C149—42no—
137D4×C149—81no—
138C2×C4×C149—21no—
139C2×C4×C149—21no—
140C2×C4×C149—21no—
141C2×C4×C149—21no—
142C2×C4×C149—21no—
143C2×C4×C149—21no—
144C2×C4×C149—22no—
145C2×C4×C149—41no—
146C2×C4×C149—41no—
147C2×C4×C149—41no—
148C2×C4×C149—41no—
149C2×C4×C149—41no—
150C2×C4×C149—41no—
151C2×C4×C149—41no—
152C2×C4×C149—41no—
153C2×C4×C149—41no—
154C2×C4×C149—41no—
155C2×C4×C149—41no—
156C2×C4×C149—41no—
157C2×C4×C149—41no—
158C2×C4×C149—42no—
159C2×C4×C149—41no—
160C2×C4×C149—84no—
161C2×C4×C149—81no—
162C2×C4×C149—81no—
163C2×C4×C149C2×D811yescharacteristic
164C2×C4×C149C2×Q1611yescharacteristic
165C2×C4×C149#13511yescharacteristic
166C2×C4×C149AGL(1,ℤ/8)11yescharacteristic
167C2×C4×C149#13711yescharacteristic
168C2×C4×C149#13711yescharacteristic
169C8×C149—42no—
170C8×C149—42no—
171C8×C149—81no—
172C22×C149—42no—
173C22×C149—42no—
174C22×C149—42no—
175C22×C149—81no—
176C22×C149—81no—
177C22×C149—81no—
178C22×C149—81no—
179C22×C149#44711yescharacteristic
180C22×C149#45111yescharacteristic
181C22×C149#45211yescharacteristic
182C22×C149#45311yescharacteristic
183C22×C149#45511yescharacteristic
184C22×C149#45611yescharacteristic
185C22×C149B(4,𝔽2)11yescharacteristic
186C4×C149—21no—
187C4×C149—21no—
188C4×C149—21no—
189C4×C149—21no—
190C4×C149—21no—
191C4×C149—21no—
192C4×C149—42no—
193C4×C149—81no—
194C4×C149—82no—
195C4×C149—81no—
196C4×C149—81no—
197C4×C149—81no—
198C2×C149—82no—
199C2×C149#159511yescharacteristic
200C2×C149#160211yescharacteristic
201C2×C149#160311yescharacteristic
202C2×C149#163211yescharacteristic
203C2×C149#164111yescharacteristic
204C2×C149#164911yescharacteristic
205C2×C149#166111yescharacteristic
206#7756C14911yesmaximal, characteristic, direct product factor, Sylow
207C149#775611yescharacteristic, direct product factor, Sylow
208#2732C2×C14911yescharacteristic
209#2057C2×C14911yescharacteristic, complemented
210#2023C2×C14911yescharacteristic
211#2016C2×C14911yescharacteristic, complemented
212#1272C2×C14911yescharacteristic, complemented
213#1271C2×C14911yescharacteristic, complemented
214#1270C2×C14911yescharacteristic
215C22×Q16—21no—
216C2×C4⋊Q8C22×C14911yescharacteristic
217C2×C22⋊Q8—21no—
218C2×#107—21no—
219C2×#103—21no—
220C2×#102—21no—
221#399—21no—
222#398—21no—
223#396—21no—
224#391C22×C14911yescharacteristic
225#390C22×C14911yescharacteristic
226#389C22×C14911yescharacteristic
227#386—21no—
228#385—21no—
229#340—21no—
230#340—21no—
231#336C22×C14911yescharacteristic
232#336C22×C14911yescharacteristic
233#336C22×C14911yescharacteristic
234C22×Q8—21no—
235C22×Q8D4×C14911yescharacteristic
236C22×D4D4×C14911yescharacteristic
237C23×C4—21no—
238C2×Q16—42no—
239C2×Q16—42no—
240C2×Q16—42no—
241C22×C8—21no—
242C22×C8—21no—
243C22×C8—21no—
244C4⋊Q8—42no—
245C22⋊Q8—42no—
246C22⋊Q8—42no—
247C2×C4⋊C4—21no—
248C2×C4⋊C4—21no—
249C2×C4⋊C4—21no—
250C2×C4⋊C4—21no—
251C2×C4⋊C4—21no—
252C2×C4⋊C4—21no—
253C2×C4⋊C4D4×C14911yescharacteristic
254C2×C4⋊C4D4×C14911yescharacteristic
255C2×C4⋊C4D4×C14911yescharacteristic
256C2×C4⋊C4D4×C14911yescharacteristic
257C2×C22⋊C4—21no—
258C2×C22⋊C4—21no—
259C2×C22⋊C4—21no—
260C2×C22⋊C4—21no—
261C2×C22⋊C4—21no—
262C2×C42C23×C14911yescharacteristic
263#107—42no—
264#103—42no—
265#102—42no—
266#95—21no—
267#95—21no—
268#95—21no—
269#95—21no—
270C24—21no—
271C2×Q8—21no—
272C2×Q8—22no—
273C2×Q8—41no—
274C2×Q8—41no—
275C2×Q8—41no—
276C2×Q8—41no—
277C2×Q8—41no—
278C2×Q8—41no—
279C2×Q8—41no—
280C2×Q8D8×C14912yes—
281C2×D4—21no—
282C2×D4—41no—
283C2×D4—41no—
284C2×D4Q16×C14912yescomplemented
285C22×C4—21no—
286C22×C4—21no—
287C22×C4—21no—
288C22×C4—21no—
289C22×C4—21no—
290C22×C4—42no—
291C22×C4—41no—
292C22×C4—81no—
293C22×C4—81no—
294C22×C4C2×D4×C14911yescharacteristic
295C22×C4C2×D4×C14911yescharacteristic
296C22×C4C2×D4×C14911yescharacteristic
297Q16—48no—
298C2×C8—22no—
299C2×C8—22no—
300C2×C8—41no—
301C2×C8—41no—
302C2×C8—41no—
303C2×C8—41no—
304C2×C8—41no—
305C2×C8—41no—
306C2×C8—41no—
307C4⋊C4—22no—
308C4⋊C4—22no—
309C4⋊C4—21no—
310C4⋊C4—21no—
311C4⋊C4—41no—
312C4⋊C4—41no—
313C4⋊C4—41no—
314C4⋊C4—42no—
315C4⋊C4—42no—
316C4⋊C4—41no—
317C4⋊C4—41no—
318C4⋊C4—41no—
319C4⋊C4—41no—
320C4⋊C4—81no—
321C22⋊C4—42no—
322C22⋊C4—41no—
323C22⋊C4—41no—
324C22⋊C4—41no—
325C22⋊C4—41no—
326C22⋊C4—81no—
327C22⋊C4—81no—
328C42—41no—
329C23—22no—
330C23—41no—
331C23—41no—
332C23—41no—
333C23—41no—
334C23—41no—
335C23—41no—
336C23#120×C14911yescharacteristic
337Q8—42no—
338Q8—42no—
339Q8—42no—
340Q8—81no—
341Q8—81no—
342Q8—81no—
343D4—42no—
344D4—81no—
345C2×C4—21no—
346C2×C4—21no—
347C2×C4—21no—
348C2×C4—21no—
349C2×C4—21no—
350C2×C4—21no—
351C2×C4—22no—
352C2×C4—41no—
353C2×C4—41no—
354C2×C4—41no—
355C2×C4—41no—
356C2×C4—41no—
357C2×C4—41no—
358C2×C4—41no—
359C2×C4—41no—
360C2×C4—41no—
361C2×C4—41no—
362C2×C4—41no—
363C2×C4—41no—
364C2×C4—41no—
365C2×C4—42no—
366C2×C4—41no—
367C2×C4—84no—
368C2×C4—81no—
369C2×C4—81no—
370C2×C4C2×D8×C14911yescharacteristic
371C2×C4C2×Q16×C14911yescharacteristic
372C2×C4#135×C14911yescharacteristic
373C2×C4AGL(1,ℤ/8)×C14911yescharacteristic
374C2×C4#137×C14911yescharacteristic
375C2×C4#137×C14911yescharacteristic
376C8—42no—
377C8—42no—
378C8—81no—
379C22—42no—
380C22—42no—
381C22—42no—
382C22—81no—
383C22—81no—
384C22—81no—
385C22—81no—
386C22#447×C14911yescharacteristic
387C22#451×C14911yescharacteristic
388C22#452×C14911yescharacteristic
389C22#453×C14911yescharacteristic
390C22#455×C14911yescharacteristic
391C22#456×C14911yescharacteristic
392C22B(4,𝔽2)×C14911yescharacteristic
393C4—21no—
394C4—21no—
395C4—21no—
396C4—21no—
397C4—21no—
398C4—21no—
399C4—42no—
400C4—81no—
401C4—82no—
402C4—81no—
403C4—81no—
404C4—81no—
405C2—82no—
406C2#1595×C14911yescharacteristic
407C2#1602×C14911yescharacteristic
408C2#1603×C14911yescharacteristic
409C2#1632×C14911yescharacteristic
410C2#1641×C14911yescharacteristic
411C2#1649×C14911yescharacteristic
412C2#1661×C14911yescharacteristic
subgroupG/H
center, socleC23×C149#120
commutator, Frattini, cosocleC2×C42C23×C149
prime radicalC22×D4×C149D4
LCSG ▷ C2×C42 ▷ C23 ▷ C1
UCSC1 ◁ C23×C149 ◁ C2×C42×C149 ◁ G

Complements

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

NH ≅ G/Ntype
2. #2057×C149C2semidirect
4. #2016×C149C2semidirect
5. #1272×C149C2semidirect
6. #1271×C149C2semidirect
77. C2×D4×C149Q16semidirect
206. #7756C149direct (N × H)
207. C149#7756direct (N × H)
209. #2057C2×C149semidirect
211. #2016C2×C149semidirect
212. #1272C2×C149semidirect
213. #1271C2×C149semidirect
284. C2×D4Q16×C149semidirect

Maximal subgroups

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

subgroupindex
#2732×C1492
#2057×C1492
#2023×C1492
#2016×C1492
#1272×C1492
#1271×C1492
#1270×C1492
#7756149