Finite Group Databasebeta

← C149×#10178 #49189127

Subgroups — C149×#10178 #49189127

Order 38144.

592 conjugacy classes of subgroups.

The subgroup lattice has 426 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#3208×C149C211yesmaximal, characteristic, complemented
2#3077×C149C211yesmaximal, characteristic, complemented
3C2×#459×C149C211yesmaximal, characteristic
4#1545×C149C211yesmaximal, characteristic, complemented
5#1481×C149C211yesmaximal, characteristic, complemented
6#1460×C149C211yesmaximal, characteristic, complemented
7#1301×C149C211yesmaximal, characteristic, complemented
8C22×D8×C149—21no—
9#533×C149C2211yescharacteristic
10C2×#127×C149C2211yescharacteristic
11C2×C4×D4×C149C2211yescharacteristic
12#492×C149—21no—
13#486×C149—21no—
14#478×C149—22no—
15#476×C149—21no—
16#474×C149—21no—
17#460×C149—22no—
18#459×C149—22no—
19#459×C149—22no—
20#450×C149—22no—
21#431×C149C2211yescharacteristic
22#431×C149C2211yescharacteristic
23#428×C149—21no—
24#423×C149C2211yescharacteristic
25C2×C4⋊C8×C149C2211yescharacteristic
26#418×C149—21no—
27C2×#102×C149—21no—
28#331×C149—22no—
29Q8⋊C8×C149—22no—
30#323×C149—22no—
31C22×D4×C149—21no—
32C22×D4×C149—21no—
33C22×D4×C149—21no—
34C22×D4×C149D411yescharacteristic
35C23×C4×C149—21no—
36C2×SD16×C149—24no—
37C2×D8×C149—24no—
38C2×D8×C149—42no—
39C2×D8×C149—42no—
40C2×M16×C149—21no—
41C22×C8×C149—21no—
42C4⋊Q8×C149D411yescharacteristic
43C4⋊Q8×C149D411yescharacteristic
44#127×C149—21no—
45#127×C149—21no—
46#127×C149—21no—
47#127×C149D412yes—
48#125×C149—21no—
49C22⋊Q8×C149—21no—
50C22⋊Q8×C149—21no—
51C4×Q8×C149—21no—
52C4×Q8×C149—21no—
53C4×D4×C149—21no—
54C4×D4×C149—21no—
55C4×D4×C149—21no—
56C4×D4×C149—21no—
57#117×C149—21no—
58C2×C4⋊C4×C149D411yescharacteristic
59C2×C22⋊C4×C149—21no—
60C2×C42×C149C2311yescharacteristic
61#107×C149—22no—
62#106×C149—22no—
63C4⋊C8×C149—21no—
64C4⋊C8×C149—21no—
65C4⋊C8×C149—21no—
66C4⋊C8×C149—21no—
67C4⋊C8×C149D412yes—
68C4⋊C8×C149D412yes—
69#102×C149—24no—
70#102×C149—22no—
71#102×C149—22no—
72#102×C149—24no—
73C22⋊C8×C149—21no—
74C22⋊C8×C149D412yes—
75C4×C8×C149—21no—
76C4×C8×C149—21no—
77C24×C149—21no—
78C24×C149—41no—
79C2×Q8×C149—21no—
80C2×Q8×C149—21no—
81C2×D4×C149—21no—
82C2×D4×C149—21no—
83C2×D4×C149—22no—
84C2×D4×C149—22no—
85C2×D4×C149—22no—
86C2×D4×C149—21no—
87C2×D4×C149—21no—
88C2×D4×C149—21no—
89C2×D4×C149—41no—
90C2×D4×C149—41no—
91C2×D4×C149—41no—
92C2×D4×C149—41no—
93C2×D4×C149—41no—
94C2×D4×C149—41no—
95C2×D4×C149—41no—
96C2×D4×C149—82no—
97C2×D4×C149—82no—
98C2×D4×C149SD1612yescomplemented
99C22×C4×C149—21no—
100C22×C4×C149—41no—
101C22×C4×C149—41no—
102C22×C4×C149—82no—
103C22×C4×C149C2×D411yescharacteristic
104C22×C4×C149C2×D411yescharacteristic
105C22×C4×C149#4111yescharacteristic
106SD16×C149—84no—
107D8×C149—48no—
108M16×C149—41no—
109M16×C149—41no—
110C2×C8×C149—22no—
111C2×C8×C149—22no—
112C2×C8×C149—22no—
113C2×C8×C149—41no—
114C2×C8×C149—41no—
115C2×C8×C149—41no—
116C4⋊C4×C149—21no—
117C4⋊C4×C149—21no—
118C4⋊C4×C149—21no—
119C4⋊C4×C149—21no—
120C4⋊C4×C149—21no—
121C4⋊C4×C149—21no—
122C4⋊C4×C149—41no—
123C4⋊C4×C149—41no—
124C22⋊C4×C149—41no—
125C22⋊C4×C149—41no—
126C22⋊C4×C149—41no—
127C42×C149—41no—
128C42×C149C2×D411yescharacteristic
129C42×C149C2×D411yescharacteristic
130C42×C149C2×D411yescharacteristic
131C42×C149C2×D411yescharacteristic
132C23×C149—22no—
133C23×C149—41no—
134C23×C149—41no—
135C23×C149—42no—
136C23×C149—81no—
137C23×C149—81no—
138C23×C149—82no—
139C23×C149—82no—
140C23×C149—81no—
141C23×C149—81no—
142C23×C149#12111yescharacteristic
143Q8×C149—42no—
144Q8×C149—42no—
145D4×C149—22no—
146D4×C149—22no—
147D4×C149—44no—
148D4×C149—41no—
149D4×C149—42no—
150D4×C149—41no—
151D4×C149—42no—
152D4×C149—82no—
153D4×C149—82no—
154D4×C149—81no—
155D4×C149—81no—
156D4×C149—82no—
157C2×C4×C149—22no—
158C2×C4×C149—41no—
159C2×C4×C149—41no—
160C2×C4×C149—41no—
161C2×C4×C149—41no—
162C2×C4×C149—82no—
163C2×C4×C149—82no—
164C2×C4×C149—81no—
165C2×C4×C149#12011yescharacteristic
166C2×C4×C149#12011yescharacteristic
167C2×C4×C149#12011yescharacteristic
168C2×C4×C149#12111yescharacteristic
169C2×C4×C149#12111yescharacteristic
170C2×C4×C149#12711yescharacteristic
171C2×C4×C149C2×SD1611yescharacteristic
172C2×C4×C149#13511yescharacteristic
173C2×C4×C149AGL(1,ℤ/8)11yescharacteristic
174C2×C4×C149#13711yescharacteristic
175C8×C149—42no—
176C8×C149—42no—
177C8×C149—42no—
178C8×C149—81no—
179C22×C149—21no—
180C22×C149—21no—
181C22×C149—42no—
182C22×C149—82no—
183C22×C149—82no—
184C22×C149—81no—
185C22×C149—81no—
186C22×C149—82no—
187C22×C149—82no—
188C22×C149—82no—
189C22×C149—162no—
190C22×C149—162no—
191C22×C149#39211yescharacteristic
192C22×C149#46511yescharacteristic
193C22×C149#46811yescharacteristic
194C4×C149—21no—
195C4×C149—21no—
196C4×C149—21no—
197C4×C149—81no—
198C4×C149—81no—
199C4×C149—81no—
200C4×C149#44811yescharacteristic
201C4×C149#44911yescharacteristic
202C4×C149#45011yescharacteristic
203C4×C149#45211yescharacteristic
204C4×C149#47212yes—
205C2×C149—21no—
206C2×C149—21no—
207C2×C149—82no—
208C2×C149—162no—
209C2×C149#200011yescharacteristic
210C2×C149#200811yescharacteristic
211C2×C149#201811yescharacteristic
212#10178C14911yesmaximal, characteristic, direct product factor, Sylow
213C149#1017811yescharacteristic, direct product factor, Sylow
214#3208C2×C14911yescharacteristic, complemented
215#3077C2×C14911yescharacteristic, complemented
216C2×#459C2×C14911yescharacteristic
217#1545C2×C14911yescharacteristic, complemented
218#1481C2×C14911yescharacteristic, complemented
219#1460C2×C14911yescharacteristic, complemented
220#1301C2×C14911yescharacteristic, complemented
221C22×D8—21no—
222#533C22×C14911yescharacteristic
223C2×#127C22×C14911yescharacteristic
224C2×C4×D4C22×C14911yescharacteristic
225#492—21no—
226#486—21no—
227#478—22no—
228#476—21no—
229#474—21no—
230#460—22no—
231#459—22no—
232#459—22no—
233#450—22no—
234#431C22×C14911yescharacteristic
235#431C22×C14911yescharacteristic
236#428—21no—
237#423C22×C14911yescharacteristic
238C2×C4⋊C8C22×C14911yescharacteristic
239#418—21no—
240C2×#102—21no—
241#331—22no—
242Q8⋊C8—22no—
243#323—22no—
244C22×D4—21no—
245C22×D4—21no—
246C22×D4—21no—
247C22×D4D4×C14911yescharacteristic
248C23×C4—21no—
249C2×SD16—24no—
250C2×D8—24no—
251C2×D8—42no—
252C2×D8—42no—
253C2×M16—21no—
254C22×C8—21no—
255C4⋊Q8D4×C14911yescharacteristic
256C4⋊Q8D4×C14911yescharacteristic
257#127—21no—
258#127—21no—
259#127—21no—
260#127D4×C14912yes—
261#125—21no—
262C22⋊Q8—21no—
263C22⋊Q8—21no—
264C4×Q8—21no—
265C4×Q8—21no—
266C4×D4—21no—
267C4×D4—21no—
268C4×D4—21no—
269C4×D4—21no—
270#117—21no—
271C2×C4⋊C4D4×C14911yescharacteristic
272C2×C22⋊C4—21no—
273C2×C42C23×C14911yescharacteristic
274#107—22no—
275#106—22no—
276C4⋊C8—21no—
277C4⋊C8—21no—
278C4⋊C8—21no—
279C4⋊C8—21no—
280C4⋊C8D4×C14912yes—
281C4⋊C8D4×C14912yes—
282#102—24no—
283#102—22no—
284#102—22no—
285#102—24no—
286C22⋊C8—21no—
287C22⋊C8D4×C14912yes—
288C4×C8—21no—
289C4×C8—21no—
290C24—21no—
291C24—41no—
292C2×Q8—21no—
293C2×Q8—21no—
294C2×D4—21no—
295C2×D4—21no—
296C2×D4—22no—
297C2×D4—22no—
298C2×D4—22no—
299C2×D4—21no—
300C2×D4—21no—
301C2×D4—21no—
302C2×D4—41no—
303C2×D4—41no—
304C2×D4—41no—
305C2×D4—41no—
306C2×D4—41no—
307C2×D4—41no—
308C2×D4—41no—
309C2×D4—82no—
310C2×D4—82no—
311C2×D4SD16×C14912yescomplemented
312C22×C4—21no—
313C22×C4—41no—
314C22×C4—41no—
315C22×C4—82no—
316C22×C4C2×D4×C14911yescharacteristic
317C22×C4C2×D4×C14911yescharacteristic
318C22×C4#41×C14911yescharacteristic
319SD16—84no—
320D8—48no—
321M16—41no—
322M16—41no—
323C2×C8—22no—
324C2×C8—22no—
325C2×C8—22no—
326C2×C8—41no—
327C2×C8—41no—
328C2×C8—41no—
329C4⋊C4—21no—
330C4⋊C4—21no—
331C4⋊C4—21no—
332C4⋊C4—21no—
333C4⋊C4—21no—
334C4⋊C4—21no—
335C4⋊C4—41no—
336C4⋊C4—41no—
337C22⋊C4—41no—
338C22⋊C4—41no—
339C22⋊C4—41no—
340C42—41no—
341C42C2×D4×C14911yescharacteristic
342C42C2×D4×C14911yescharacteristic
343C42C2×D4×C14911yescharacteristic
344C42C2×D4×C14911yescharacteristic
345C23—22no—
346C23—41no—
347C23—41no—
348C23—42no—
349C23—81no—
350C23—81no—
351C23—82no—
352C23—82no—
353C23—81no—
354C23—81no—
355C23#121×C14911yescharacteristic
356Q8—42no—
357Q8—42no—
358D4—22no—
359D4—22no—
360D4—44no—
361D4—41no—
362D4—42no—
363D4—41no—
364D4—42no—
365D4—82no—
366D4—82no—
367D4—81no—
368D4—81no—
369D4—82no—
370C2×C4—22no—
371C2×C4—41no—
372C2×C4—41no—
373C2×C4—41no—
374C2×C4—41no—
375C2×C4—82no—
376C2×C4—82no—
377C2×C4—81no—
378C2×C4#120×C14911yescharacteristic
379C2×C4#120×C14911yescharacteristic
380C2×C4#120×C14911yescharacteristic
381C2×C4#121×C14911yescharacteristic
382C2×C4#121×C14911yescharacteristic
383C2×C4#127×C14911yescharacteristic
384C2×C4C2×SD16×C14911yescharacteristic
385C2×C4#135×C14911yescharacteristic
386C2×C4AGL(1,ℤ/8)×C14911yescharacteristic
387C2×C4#137×C14911yescharacteristic
388C8—42no—
389C8—42no—
390C8—42no—
391C8—81no—
392C22—21no—
393C22—21no—
394C22—42no—
395C22—82no—
396C22—82no—
397C22—81no—
398C22—81no—
399C22—82no—
400C22—82no—
401C22—82no—
402C22—162no—
403C22—162no—
404C22#392×C14911yescharacteristic
405C22#465×C14911yescharacteristic
406C22#468×C14911yescharacteristic
407C4—21no—
408C4—21no—
409C4—21no—
410C4—81no—
411C4—81no—
412C4—81no—
413C4#448×C14911yescharacteristic
414C4#449×C14911yescharacteristic
415C4#450×C14911yescharacteristic
416C4#452×C14911yescharacteristic
417C4#472×C14912yes—
418C2—21no—
419C2—21no—
420C2—82no—
421C2—162no—
422C2#2000×C14911yescharacteristic
423C2#2008×C14911yescharacteristic
424C2#2018×C14911yescharacteristic
subgroupG/H
center, socleC22×C149#392
commutator, Frattini, cosocleC2×C42C23×C149
prime radicalC2×#459×C149C2
LCSG ▷ C2×C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C149 ◁ C2×C42×C149 ◁ G

Complements

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

NH ≅ G/Ntype
1. #3208×C149C2semidirect
2. #3077×C149C2semidirect
4. #1545×C149C2semidirect
5. #1481×C149C2semidirect
6. #1460×C149C2semidirect
7. #1301×C149C2semidirect
98. C2×D4×C149SD16semidirect
212. #10178C149direct (N × H)
213. C149#10178direct (N × H)
214. #3208C2×C149semidirect
215. #3077C2×C149semidirect
217. #1545C2×C149semidirect
218. #1481C2×C149semidirect
219. #1460C2×C149semidirect
220. #1301C2×C149semidirect
311. C2×D4SD16×C149semidirect

Maximal subgroups

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

subgroupindex
#3208×C1492
#3077×C1492
C2×#459×C1492
#1545×C1492
#1481×C1492
#1460×C1492
#1301×C1492
#10178149