Finite Group Databasebeta

← C149×#12959 #49191908

Subgroups — C149×#12959 #49191908

Order 38144.

524 conjugacy classes of subgroups.

The subgroup lattice has 454 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#2374×C149C211yesmaximal, characteristic
2C2×#352×C149C211yesmaximal, characteristic
3#1890×C149C211yesmaximal, characteristic
4#1867×C149C211yesmaximal, characteristic
5#1856×C149C211yesmaximal, characteristic
6#1393×C149C211yesmaximal, characteristic
7#1390×C149C211yesmaximal, characteristic
8C2×#123×C149C2211yescharacteristic
9#518×C149C2211yescharacteristic
10#428×C149—21no—
11C2×#100×C149C2211yescharacteristic
12C2×#99×C149C2211yescharacteristic
13C2×#99×C149C2211yescharacteristic
14#390×C149C2211yescharacteristic
15#388×C149—21no—
16#388×C149—21no—
17#387×C149—21no—
18#386×C149C2211yescharacteristic
19#385×C149—21no—
20#381×C149—21no—
21C4×C4⋊C4×C149—21no—
22C4×C22⋊C4×C149—21no—
23C4×C22⋊C4×C149—21no—
24#352×C149C414yescomplemented
25#342×C149—21no—
26#342×C149—21no—
27#339×C149—21no—
28C22×D4×C149C2311yescharacteristic
29C23×C4×C149D411yescharacteristic
30C23×C4×C149D411yescharacteristic
31C2×M16×C149—21no—
32#123×C149—21no—
33#123×C149—21no—
34#123×C149C2×C412yes—
35#123×C149Q812yes—
36C4×D4×C149—41no—
37C4×D4×C149—41no—
38#117×C149—21no—
39C2×C4⋊C4×C149—21no—
40C2×C4⋊C4×C149—21no—
41C2×C4⋊C4×C149—41no—
42C2×C4⋊C4×C149D411yescharacteristic
43C2×C22⋊C4×C149—21no—
44C2×C22⋊C4×C149—21no—
45C2×C22⋊C4×C149—21no—
46C2×C22⋊C4×C149—21no—
47C2×C22⋊C4×C149—21no—
48C2×C22⋊C4×C149—21no—
49C2×C22⋊C4×C149—21no—
50C2×C22⋊C4×C149—21no—
51C2×C22⋊C4×C149D411yescharacteristic
52C2×C22⋊C4×C149D411yescharacteristic
53C2×C42×C149—21no—
54C2×C42×C149—21no—
55C2×C42×C149—21no—
56C2×C42×C149D411yescharacteristic
57#107×C149—41no—
58#106×C149—41no—
59#100×C149—21no—
60#100×C149C2×C412yes—
61#99×C149—21no—
62#99×C149—21no—
63#99×C149—21no—
64#99×C149C2×C412yes—
65#95×C149—21no—
66#95×C149—21no—
67#95×C149—21no—
68#95×C149—21no—
69#95×C149—21no—
70#95×C149—41no—
71#95×C149—41no—
72#95×C149—41no—
73C24×C149C2×D411yescharacteristic
74C24×C149C2×D411yescharacteristic
75C2×D4×C149—41no—
76C2×D4×C149—41no—
77C2×D4×C149C22×C411yescharacteristic
78C2×D4×C149C2×Q811yescharacteristic
79C2×D4×C149#4111yescharacteristic
80C2×D4×C149#4111yescharacteristic
81C22×C4×C149—21no—
82C22×C4×C149—21no—
83C22×C4×C149—21no—
84C22×C4×C149—21no—
85C22×C4×C149—21no—
86C22×C4×C149—21no—
87C22×C4×C149—21no—
88C22×C4×C149—21no—
89C22×C4×C149—21no—
90C22×C4×C149—21no—
91C22×C4×C149—21no—
92C22×C4×C149—42no—
93C22×C4×C149—41no—
94C22×C4×C149—41no—
95C22×C4×C149—41no—
96C22×C4×C149—41no—
97C22×C4×C149—41no—
98C22×C4×C149C4⋊C412yescomplemented
99C22×C4×C149C2×D411yescharacteristic
100M16×C149—22no—
101M16×C149—41no—
102C2×C8×C149—41no—
103C4⋊C4×C149—22no—
104C4⋊C4×C149—22no—
105C4⋊C4×C149—21no—
106C4⋊C4×C149—21no—
107C4⋊C4×C149—42no—
108C4⋊C4×C149—41no—
109C4⋊C4×C149—82no—
110C22⋊C4×C149—22no—
111C22⋊C4×C149—22no—
112C22⋊C4×C149—21no—
113C22⋊C4×C149—22no—
114C22⋊C4×C149—42no—
115C22⋊C4×C149—42no—
116C22⋊C4×C149—42no—
117C22⋊C4×C149—41no—
118C22⋊C4×C149—41no—
119C22⋊C4×C149—41no—
120C22⋊C4×C149—41no—
121C22⋊C4×C149—41no—
122C22⋊C4×C149—41no—
123C22⋊C4×C149—41no—
124C22⋊C4×C149C4⋊C412yescomplemented
125C42×C149—42no—
126C42×C149—41no—
127C42×C149—41no—
128C42×C149—81no—
129C42×C149—81no—
130C23×C149—21no—
131C23×C149—21no—
132C23×C149—21no—
133C23×C149—21no—
134C23×C149—41no—
135C23×C149—41no—
136C23×C149—41no—
137C23×C149—41no—
138C23×C149C2×C4⋊C411yescharacteristic
139C23×C149C4×D411yescharacteristic
140C23×C149#12011yescharacteristic
141C23×C149C22⋊Q811yescharacteristic
142C23×C149#12311yescharacteristic
143D4×C149—41no—
144D4×C149—41no—
145D4×C149—41no—
146D4×C149—41no—
147C2×C4×C149—21no—
148C2×C4×C149—21no—
149C2×C4×C149—22no—
150C2×C4×C149—22no—
151C2×C4×C149—22no—
152C2×C4×C149—22no—
153C2×C4×C149—41no—
154C2×C4×C149—41no—
155C2×C4×C149—41no—
156C2×C4×C149—41no—
157C2×C4×C149—41no—
158C2×C4×C149—41no—
159C2×C4×C149—41no—
160C2×C4×C149—41no—
161C2×C4×C149—42no—
162C2×C4×C149—42no—
163C2×C4×C149—42no—
164C2×C4×C149—41no—
165C2×C4×C149—41no—
166C2×C4×C149—41no—
167C2×C4×C149—41no—
168C2×C4×C149—41no—
169C2×C4×C149—41no—
170C2×C4×C149—41no—
171C2×C4×C149—41no—
172C2×C4×C149—81no—
173C2×C4×C149—81no—
174C2×C4×C149—81no—
175C2×C4×C149—81no—
176C2×C4×C149—81no—
177C2×C4×C149—81no—
178C2×C4×C149—81no—
179C2×C4×C149—81no—
180C2×C4×C149—81no—
181C2×C4×C149—81no—
182C2×C4×C149—81no—
183C2×C4×C149C4×D411yescharacteristic
184C2×C4×C149C22⋊Q811yescharacteristic
185C8×C149—42no—
186C22×C149—21no—
187C22×C149—21no—
188C22×C149—21no—
189C22×C149—21no—
190C22×C149—21no—
191C22×C149—21no—
192C22×C149—41no—
193C22×C149—41no—
194C22×C149—41no—
195C22×C149—41no—
196C22×C149—41no—
197C22×C149—41no—
198C22×C149—41no—
199C22×C149—41no—
200C22×C149—81no—
201C22×C149—81no—
202C22×C149#38511yescharacteristic
203C22×C149B(4,𝔽2)11yescharacteristic
204C22×C149#45811yescharacteristic
205C4×C149—21no—
206C4×C149—21no—
207C4×C149—42no—
208C4×C149—42no—
209C4×C149—42no—
210C4×C149—42no—
211C4×C149—81no—
212C4×C149—82no—
213C4×C149—81no—
214C4×C149—81no—
215C4×C149—81no—
216C4×C149—161no—
217C2×C149—21no—
218C2×C149—21no—
219C2×C149—41no—
220C2×C149—41no—
221C2×C149—41no—
222C2×C149—41no—
223C2×C149#186711yescharacteristic
224C2×C149#219711yescharacteristic
225C2×C149#219811yescharacteristic
226#12959C14911yesmaximal, characteristic, direct product factor, Sylow
227C149#1295911yescharacteristic, direct product factor, Sylow
228#2374C2×C14911yescharacteristic
229C2×#352C2×C14911yescharacteristic
230#1890C2×C14911yescharacteristic
231#1867C2×C14911yescharacteristic
232#1856C2×C14911yescharacteristic
233#1393C2×C14911yescharacteristic
234#1390C2×C14911yescharacteristic
235C2×#123C22×C14911yescharacteristic
236#518C22×C14911yescharacteristic
237#428—21no—
238C2×#100C22×C14911yescharacteristic
239C2×#99C22×C14911yescharacteristic
240C2×#99C22×C14911yescharacteristic
241#390C22×C14911yescharacteristic
242#388—21no—
243#388—21no—
244#387—21no—
245#386C22×C14911yescharacteristic
246#385—21no—
247#381—21no—
248C4×C4⋊C4—21no—
249C4×C22⋊C4—21no—
250C4×C22⋊C4—21no—
251#352C4×C14914yescomplemented
252#342—21no—
253#342—21no—
254#339—21no—
255C22×D4C23×C14911yescharacteristic
256C23×C4D4×C14911yescharacteristic
257C23×C4D4×C14911yescharacteristic
258C2×M16—21no—
259#123—21no—
260#123—21no—
261#123C2×C4×C14912yes—
262#123Q8×C14912yes—
263C4×D4—41no—
264C4×D4—41no—
265#117—21no—
266C2×C4⋊C4—21no—
267C2×C4⋊C4—21no—
268C2×C4⋊C4—41no—
269C2×C4⋊C4D4×C14911yescharacteristic
270C2×C22⋊C4—21no—
271C2×C22⋊C4—21no—
272C2×C22⋊C4—21no—
273C2×C22⋊C4—21no—
274C2×C22⋊C4—21no—
275C2×C22⋊C4—21no—
276C2×C22⋊C4—21no—
277C2×C22⋊C4—21no—
278C2×C22⋊C4D4×C14911yescharacteristic
279C2×C22⋊C4D4×C14911yescharacteristic
280C2×C42—21no—
281C2×C42—21no—
282C2×C42—21no—
283C2×C42D4×C14911yescharacteristic
284#107—41no—
285#106—41no—
286#100—21no—
287#100C2×C4×C14912yes—
288#99—21no—
289#99—21no—
290#99—21no—
291#99C2×C4×C14912yes—
292#95—21no—
293#95—21no—
294#95—21no—
295#95—21no—
296#95—21no—
297#95—41no—
298#95—41no—
299#95—41no—
300C24C2×D4×C14911yescharacteristic
301C24C2×D4×C14911yescharacteristic
302C2×D4—41no—
303C2×D4—41no—
304C2×D4C22×C4×C14911yescharacteristic
305C2×D4C2×Q8×C14911yescharacteristic
306C2×D4#41×C14911yescharacteristic
307C2×D4#41×C14911yescharacteristic
308C22×C4—21no—
309C22×C4—21no—
310C22×C4—21no—
311C22×C4—21no—
312C22×C4—21no—
313C22×C4—21no—
314C22×C4—21no—
315C22×C4—21no—
316C22×C4—21no—
317C22×C4—21no—
318C22×C4—21no—
319C22×C4—42no—
320C22×C4—41no—
321C22×C4—41no—
322C22×C4—41no—
323C22×C4—41no—
324C22×C4—41no—
325C22×C4C4⋊C4×C14912yescomplemented
326C22×C4C2×D4×C14911yescharacteristic
327M16—22no—
328M16—41no—
329C2×C8—41no—
330C4⋊C4—22no—
331C4⋊C4—22no—
332C4⋊C4—21no—
333C4⋊C4—21no—
334C4⋊C4—41no—
335C4⋊C4—42no—
336C4⋊C4—82no—
337C22⋊C4—22no—
338C22⋊C4—22no—
339C22⋊C4—21no—
340C22⋊C4—22no—
341C22⋊C4—42no—
342C22⋊C4—42no—
343C22⋊C4—42no—
344C22⋊C4—41no—
345C22⋊C4—41no—
346C22⋊C4—41no—
347C22⋊C4—41no—
348C22⋊C4—41no—
349C22⋊C4—41no—
350C22⋊C4—41no—
351C22⋊C4C4⋊C4×C14912yescomplemented
352C42—41no—
353C42—42no—
354C42—41no—
355C42—81no—
356C42—81no—
357C23—21no—
358C23—21no—
359C23—21no—
360C23—21no—
361C23—41no—
362C23—41no—
363C23—41no—
364C23—41no—
365C23C2×C4⋊C4×C14911yescharacteristic
366C23C4×D4×C14911yescharacteristic
367C23#120×C14911yescharacteristic
368C23C22⋊Q8×C14911yescharacteristic
369C23#123×C14911yescharacteristic
370D4—41no—
371D4—41no—
372D4—41no—
373D4—41no—
374C2×C4—21no—
375C2×C4—21no—
376C2×C4—22no—
377C2×C4—22no—
378C2×C4—22no—
379C2×C4—22no—
380C2×C4—41no—
381C2×C4—41no—
382C2×C4—41no—
383C2×C4—41no—
384C2×C4—41no—
385C2×C4—41no—
386C2×C4—41no—
387C2×C4—41no—
388C2×C4—42no—
389C2×C4—42no—
390C2×C4—42no—
391C2×C4—41no—
392C2×C4—41no—
393C2×C4—41no—
394C2×C4—41no—
395C2×C4—41no—
396C2×C4—41no—
397C2×C4—41no—
398C2×C4—41no—
399C2×C4—81no—
400C2×C4—81no—
401C2×C4—81no—
402C2×C4—81no—
403C2×C4—81no—
404C2×C4—81no—
405C2×C4—81no—
406C2×C4—81no—
407C2×C4—81no—
408C2×C4—81no—
409C2×C4—81no—
410C2×C4C4×D4×C14911yescharacteristic
411C2×C4C22⋊Q8×C14911yescharacteristic
412C8—42no—
413C22—21no—
414C22—21no—
415C22—21no—
416C22—21no—
417C22—21no—
418C22—21no—
419C22—41no—
420C22—41no—
421C22—41no—
422C22—41no—
423C22—41no—
424C22—41no—
425C22—41no—
426C22—41no—
427C22—81no—
428C22—81no—
429C22#385×C14911yescharacteristic
430C22B(4,𝔽2)×C14911yescharacteristic
431C22#458×C14911yescharacteristic
432C4—21no—
433C4—21no—
434C4—42no—
435C4—42no—
436C4—42no—
437C4—42no—
438C4—81no—
439C4—82no—
440C4—81no—
441C4—81no—
442C4—81no—
443C4—161no—
444C2—21no—
445C2—21no—
446C2—41no—
447C2—41no—
448C2—41no—
449C2—41no—
450C2#1867×C14911yescharacteristic
451C2#2197×C14911yescharacteristic
452C2#2198×C14911yescharacteristic
subgroupG/H
center, socleC22×C149B(4,𝔽2)
commutatorC2×D4C22×C4×C149
Frattini, cosocleC22×D4C23×C149
prime radicalC22×D4×C149C23
LCSG ▷ C2×D4 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C22×C149 ◁ C23×C149 ◁ C22×D4×C149 ◁ G

Complements

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

NH ≅ G/Ntype
24. #352×C149C4semidirect
98. C22×C4×C149C4⋊C4semidirect
124. C22⋊C4×C149C4⋊C4semidirect
226. #12959C149direct (N × H)
227. C149#12959direct (N × H)
251. #352C4×C149semidirect
325. C22×C4C4⋊C4×C149semidirect
351. C22⋊C4C4⋊C4×C149semidirect

Maximal subgroups

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

subgroupindex
#2374×C1492
C2×#352×C1492
#1890×C1492
#1867×C1492
#1856×C1492
#1393×C1492
#1390×C1492
#12959149