Finite Group Databasebeta

← C149×#13229 #49192178

Subgroups — C149×#13229 #49192178

Order 38144.

452 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#3057×C149C211yesmaximal, characteristic
2#2129×C149C211yesmaximal, characteristic, complemented
3#2128×C149C211yesmaximal, characteristic
4#2123×C149C211yesmaximal, characteristic, complemented
5#2122×C149C211yesmaximal, characteristic
6#1812×C149C211yesmaximal, characteristic, complemented
7#1757×C149C211yesmaximal, characteristic, complemented
8C22×SD16×C149C411yescharacteristic, complemented
9C2×#131×C149C2211yescharacteristic
10#536×C149C2211yescharacteristic
11#535×C149C2211yescharacteristic
12#468×C149—21no—
13#468×C149—21no—
14#465×C149—21no—
15#465×C149—21no—
16#427×C149—21no—
17#427×C149C411yescharacteristic, complemented
18#419×C149C411yescharacteristic, complemented
19#418×C149C411yescharacteristic, complemented
20#413×C149C2211yescharacteristic
21#410×C149C2211yescharacteristic
22#410×C149C2211yescharacteristic
23#410×C149C2211yescharacteristic
24#405×C149—21no—
25#354×C149—22no—
26#353×C149—22no—
27#352×C149—22no—
28AΣL(1,𝔽16)×C149—22no—
29#344×C149—21no—
30H(3,ℤ/4)×C149—21no—
31C2×#41×C149C2311yescharacteristic
32C22×Q8×C149C2×C411yescharacteristic
33C22×D4×C149C2×C411yescharacteristic
34C2×SD16×C149—21no—
35C2×SD16×C149—21no—
36C2×SD16×C149—41no—
37C2×SD16×C149—41no—
38#131×C149—41no—
39#131×C149—41no—
40C2×M16×C149—21no—
41C2×M16×C149C2×C411yescharacteristic
42C2×M16×C149D411yescharacteristic
43C2×M16×C149D411yescharacteristic
44C22×C8×C149C2×C411yescharacteristic
45C22×C8×C149D411yescharacteristic
46C22×C8×C149D411yescharacteristic
47C4⋊Q8×C149—21no—
48#127×C149—21no—
49#124×C149—21no—
50#124×C149—21no—
51#123×C149—21no—
52#123×C149—21no—
53C22⋊Q8×C149—21no—
54C22⋊Q8×C149—21no—
55#121×C149—21no—
56#121×C149—21no—
57#120×C149—21no—
58#120×C149—21no—
59#117×C149—21no—
60#117×C149—21no—
61#117×C149—21no—
62#117×C149C2×C411yescharacteristic
63#117×C149C2×C411yescharacteristic
64#107×C149—21no—
65#107×C149—41no—
66#106×C149—21no—
67#106×C149—41no—
68#103×C149—21no—
69#103×C149—21no—
70#102×C149—21no—
71#102×C149—21no—
72#101×C149—21no—
73#100×C149D412yes—
74#99×C149—21no—
75#99×C149—21no—
76#99×C149—21no—
77#99×C149—21no—
78#99×C149—21no—
79#99×C149D412yes—
80#97×C149—41no—
81C4×C8×C149—41no—
82C24×C149—21no—
83#41×C149—41no—
84#41×C149—41no—
85C2×Q8×C149—21no—
86C2×Q8×C149—21no—
87C2×Q8×C149—41no—
88C2×Q8×C149—41no—
89C2×Q8×C149#4111yescharacteristic
90C2×D4×C149—21no—
91C2×D4×C149—21no—
92C2×D4×C149—41no—
93C2×D4×C149—41no—
94C2×D4×C149—41no—
95C2×D4×C149—41no—
96C2×D4×C149C2×D411yescharacteristic
97C2×D4×C149C2×D411yescharacteristic
98C2×D4×C149#4111yescharacteristic
99C22×C4×C149—21no—
100C22×C4×C149C22×C411yescharacteristic
101C22×C4×C149C2×D411yescharacteristic
102C22×C4×C149C2×D411yescharacteristic
103SD16×C149—42no—
104SD16×C149—41no—
105SD16×C149—41no—
106M16×C149—22no—
107M16×C149—41no—
108M16×C149—41no—
109M16×C149—41no—
110M16×C149—41no—
111C2×C8×C149—21no—
112C2×C8×C149—21no—
113C2×C8×C149—21no—
114C2×C8×C149—21no—
115C2×C8×C149—21no—
116C2×C8×C149—21no—
117C2×C8×C149—41no—
118C2×C8×C149C22⋊C411yescharacteristic
119C2×C8×C149C22⋊C411yescharacteristic
120C2×C8×C149C22⋊C411yescharacteristic
121C2×C8×C149C22⋊C411yescharacteristic
122C4⋊C4×C149—21no—
123C4⋊C4×C149—21no—
124C4⋊C4×C149—41no—
125C4⋊C4×C149—41no—
126C4⋊C4×C149—41no—
127C4⋊C4×C149—41no—
128C4⋊C4×C149—41no—
129C22⋊C4×C149—21no—
130C22⋊C4×C149—21no—
131C22⋊C4×C149—22no—
132C22⋊C4×C149—41no—
133C22⋊C4×C149—41no—
134C22⋊C4×C149—41no—
135C22⋊C4×C149—41no—
136C22⋊C4×C149—41no—
137C22⋊C4×C149—41no—
138C42×C149—21no—
139C42×C149—21no—
140C42×C149—41no—
141C42×C149—41no—
142C42×C149—41no—
143C23×C149—41no—
144C23×C149—81no—
145C23×C149—161no—
146C23×C149C4×D411yescharacteristic
147C23×C149#12111yescharacteristic
148C23×C149#12711yescharacteristic
149Q8×C149—41no—
150Q8×C149—41no—
151Q8×C149—41no—
152Q8×C149—81no—
153D4×C149—41no—
154D4×C149—41no—
155D4×C149—41no—
156D4×C149—41no—
157D4×C149—41no—
158D4×C149—81no—
159D4×C149—161no—
160D4×C149—161no—
161C2×C4×C149—21no—
162C2×C4×C149—21no—
163C2×C4×C149—21no—
164C2×C4×C149—21no—
165C2×C4×C149—21no—
166C2×C4×C149—21no—
167C2×C4×C149—42no—
168C2×C4×C149—41no—
169C2×C4×C149—41no—
170C2×C4×C149—41no—
171C2×C4×C149—81no—
172C2×C4×C149—81no—
173C2×C4×C149—81no—
174C2×C4×C149C2×C22⋊C411yescharacteristic
175C2×C4×C149C4×D411yescharacteristic
176C2×C4×C149#12111yescharacteristic
177C2×C4×C149#12411yescharacteristic
178C8×C149—21no—
179C8×C149—21no—
180C8×C149—21no—
181C8×C149—42no—
182C8×C149#9911yescharacteristic
183C8×C149#9911yescharacteristic
184C22×C149—21no—
185C22×C149—21no—
186C22×C149—21no—
187C22×C149—41no—
188C22×C149—41no—
189C22×C149—41no—
190C22×C149—81no—
191C22×C149—81no—
192C22×C149—81no—
193C22×C149—162no—
194C22×C149#39011yescharacteristic
195C4×C149—21no—
196C4×C149—21no—
197C4×C149—21no—
198C4×C149—81no—
199C4×C149—81no—
200C4×C149—82no—
201C4×C149—81no—
202C4×C149—161no—
203C4×C149—161no—
204C4×C149C2×#9911yescharacteristic
205C4×C149#41011yescharacteristic
206C2×C149—21no—
207C2×C149—41no—
208C2×C149—41no—
209C2×C149—41no—
210C2×C149—161no—
211C2×C149#196411yescharacteristic
212#13229C14911yesmaximal, characteristic, direct product factor, Sylow
213C149#1322911yescharacteristic, direct product factor, Sylow
214#3057C2×C14911yescharacteristic
215#2129C2×C14911yescharacteristic, complemented
216#2128C2×C14911yescharacteristic
217#2123C2×C14911yescharacteristic, complemented
218#2122C2×C14911yescharacteristic
219#1812C2×C14911yescharacteristic, complemented
220#1757C2×C14911yescharacteristic, complemented
221C22×SD16C4×C14911yescharacteristic, complemented
222C2×#131C22×C14911yescharacteristic
223#536C22×C14911yescharacteristic
224#535C22×C14911yescharacteristic
225#468—21no—
226#468—21no—
227#465—21no—
228#465—21no—
229#427—21no—
230#427C4×C14911yescharacteristic, complemented
231#419C4×C14911yescharacteristic, complemented
232#418C4×C14911yescharacteristic, complemented
233#413C22×C14911yescharacteristic
234#410C22×C14911yescharacteristic
235#410C22×C14911yescharacteristic
236#410C22×C14911yescharacteristic
237#405—21no—
238#354—22no—
239#353—22no—
240#352—22no—
241AΣL(1,𝔽16)—22no—
242#344—21no—
243H(3,ℤ/4)—21no—
244C2×#41C23×C14911yescharacteristic
245C22×Q8C2×C4×C14911yescharacteristic
246C22×D4C2×C4×C14911yescharacteristic
247C2×SD16—21no—
248C2×SD16—21no—
249C2×SD16—41no—
250C2×SD16—41no—
251#131—41no—
252#131—41no—
253C2×M16—21no—
254C2×M16C2×C4×C14911yescharacteristic
255C2×M16D4×C14911yescharacteristic
256C2×M16D4×C14911yescharacteristic
257C22×C8C2×C4×C14911yescharacteristic
258C22×C8D4×C14911yescharacteristic
259C22×C8D4×C14911yescharacteristic
260C4⋊Q8—21no—
261#127—21no—
262#124—21no—
263#124—21no—
264#123—21no—
265#123—21no—
266C22⋊Q8—21no—
267C22⋊Q8—21no—
268#121—21no—
269#121—21no—
270#120—21no—
271#120—21no—
272#117—21no—
273#117—21no—
274#117—21no—
275#117C2×C4×C14911yescharacteristic
276#117C2×C4×C14911yescharacteristic
277#107—21no—
278#107—41no—
279#106—21no—
280#106—41no—
281#103—21no—
282#103—21no—
283#102—21no—
284#102—21no—
285#101—21no—
286#100D4×C14912yes—
287#99—21no—
288#99—21no—
289#99—21no—
290#99—21no—
291#99—21no—
292#99D4×C14912yes—
293#97—41no—
294C4×C8—41no—
295C24—21no—
296#41—41no—
297#41—41no—
298C2×Q8—21no—
299C2×Q8—21no—
300C2×Q8—41no—
301C2×Q8—41no—
302C2×Q8#41×C14911yescharacteristic
303C2×D4—21no—
304C2×D4—21no—
305C2×D4—41no—
306C2×D4—41no—
307C2×D4—41no—
308C2×D4—41no—
309C2×D4C2×D4×C14911yescharacteristic
310C2×D4C2×D4×C14911yescharacteristic
311C2×D4#41×C14911yescharacteristic
312C22×C4—21no—
313C22×C4C22×C4×C14911yescharacteristic
314C22×C4C2×D4×C14911yescharacteristic
315C22×C4C2×D4×C14911yescharacteristic
316SD16—42no—
317SD16—41no—
318SD16—41no—
319M16—22no—
320M16—41no—
321M16—41no—
322M16—41no—
323M16—41no—
324C2×C8—21no—
325C2×C8—21no—
326C2×C8—21no—
327C2×C8—21no—
328C2×C8—21no—
329C2×C8—21no—
330C2×C8—41no—
331C2×C8C22⋊C4×C14911yescharacteristic
332C2×C8C22⋊C4×C14911yescharacteristic
333C2×C8C22⋊C4×C14911yescharacteristic
334C2×C8C22⋊C4×C14911yescharacteristic
335C4⋊C4—21no—
336C4⋊C4—21no—
337C4⋊C4—41no—
338C4⋊C4—41no—
339C4⋊C4—41no—
340C4⋊C4—41no—
341C4⋊C4—41no—
342C22⋊C4—21no—
343C22⋊C4—21no—
344C22⋊C4—22no—
345C22⋊C4—41no—
346C22⋊C4—41no—
347C22⋊C4—41no—
348C22⋊C4—41no—
349C22⋊C4—41no—
350C22⋊C4—41no—
351C42—21no—
352C42—21no—
353C42—41no—
354C42—41no—
355C42—41no—
356C23—41no—
357C23—81no—
358C23—161no—
359C23C4×D4×C14911yescharacteristic
360C23#121×C14911yescharacteristic
361C23#127×C14911yescharacteristic
362Q8—41no—
363Q8—41no—
364Q8—41no—
365Q8—81no—
366D4—41no—
367D4—41no—
368D4—41no—
369D4—41no—
370D4—41no—
371D4—81no—
372D4—161no—
373D4—161no—
374C2×C4—21no—
375C2×C4—21no—
376C2×C4—21no—
377C2×C4—21no—
378C2×C4—21no—
379C2×C4—21no—
380C2×C4—42no—
381C2×C4—41no—
382C2×C4—41no—
383C2×C4—41no—
384C2×C4—81no—
385C2×C4—81no—
386C2×C4—81no—
387C2×C4C2×C22⋊C4×C14911yescharacteristic
388C2×C4C4×D4×C14911yescharacteristic
389C2×C4#121×C14911yescharacteristic
390C2×C4#124×C14911yescharacteristic
391C8—21no—
392C8—21no—
393C8—21no—
394C8—42no—
395C8#99×C14911yescharacteristic
396C8#99×C14911yescharacteristic
397C22—21no—
398C22—21no—
399C22—21no—
400C22—41no—
401C22—41no—
402C22—41no—
403C22—81no—
404C22—81no—
405C22—81no—
406C22—162no—
407C22#390×C14911yescharacteristic
408C4—21no—
409C4—21no—
410C4—21no—
411C4—81no—
412C4—81no—
413C4—82no—
414C4—81no—
415C4—161no—
416C4—161no—
417C4C2×#99×C14911yescharacteristic
418C4#410×C14911yescharacteristic
419C2—21no—
420C2—41no—
421C2—41no—
422C2—41no—
423C2—161no—
424C2#1964×C14911yescharacteristic
subgroupG/H
center, socleC2×C149#1964
commutatorC22×C4C22×C4×C149
Frattini, cosocleC2×#41C23×C149
prime radical#535×C149C22
LCSG ▷ C22×C4 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C2×C149 ◁ C2×C4×C149 ◁ C2×#131×C149 ◁ G

Complements

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

NH ≅ G/Ntype
2. #2129×C149C2semidirect
4. #2123×C149C2semidirect
6. #1812×C149C2semidirect
7. #1757×C149C2semidirect
8. C22×SD16×C149C4semidirect
17. #427×C149C4semidirect
18. #419×C149C4semidirect
19. #418×C149C4semidirect
212. #13229C149direct (N × H)
213. C149#13229direct (N × H)
215. #2129C2×C149semidirect
217. #2123C2×C149semidirect
219. #1812C2×C149semidirect
220. #1757C2×C149semidirect
221. C22×SD16C4×C149semidirect
230. #427C4×C149semidirect
231. #419C4×C149semidirect
232. #418C4×C149semidirect

Maximal subgroups

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

subgroupindex
#3057×C1492
#2129×C1492
#2128×C1492
#2123×C1492
#2122×C1492
#1812×C1492
#1757×C1492
#13229149