Finite Group Databasebeta

← C149×#9368 #49188317

Subgroups — C149×#9368 #49188317

Order 38144.

774 conjugacy classes of subgroups.

The subgroup lattice has 476 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#3006×C149C211yesmaximal, characteristic
2#2341×C149C211yesmaximal, characteristic, complemented
3#1964×C149C211yesmaximal, characteristic, complemented
4#1789×C149C211yesmaximal, characteristic, complemented
5#1507×C149C211yesmaximal, characteristic, complemented
6#1305×C149C211yesmaximal, characteristic, complemented
7#1297×C149C211yesmaximal, characteristic, complemented
8C22×#41×C149C2211yescharacteristic
9C2×AGL(1,ℤ/8)×C149C412yescomplemented
10C2×#121×C149C2211yescharacteristic
11C2×C4×Q8×C149—21no—
12#449×C149—22no—
13#448×C149—21no—
14#447×C149—21no—
15C2×#104×C149—22no—
16#417×C149C412yescomplemented
17C2×#99×C149—22no—
18#407×C149C2211yescharacteristic
19#407×C149C2211yescharacteristic
20#390×C149—21no—
21#390×C149—22no—
22#380×C149—21no—
23#380×C149C2211yescharacteristic
24C4×C22⋊C4×C149—21no—
25C4×C22⋊C4×C149C2211yescharacteristic
26C4×C22⋊C4×C149C2211yescharacteristic
27#327×C149—21no—
28#327×C149—21no—
29C2×#41×C149—21no—
30C2×#41×C149—21no—
31C2×#41×C149—44no—
32C2×#41×C149C2×C412yes—
33C2×#41×C149D412yes—
34C22×Q8×C149D411yescharacteristic
35C22×D4×C149—21no—
36C22×D4×C149—21no—
37C22×D4×C149C2×C411yescharacteristic
38C22×D4×C149D411yescharacteristic
39C23×C4×C149—21no—
40C23×C4×C149C2311yescharacteristic
41AGL(1,ℤ/8)×C149—44no—
42C2×SD16×C149—22no—
43C2×D8×C149—22no—
44C2×M16×C149—21no—
45C2×M16×C149C2×C412yes—
46#121×C149—21no—
47#121×C149—21no—
48#121×C149—21no—
49#121×C149—21no—
50C4×Q8×C149—44no—
51C2×C4⋊C4×C149—22no—
52C2×C4⋊C4×C149—21no—
53C2×C4⋊C4×C149C2×C411yescharacteristic
54C2×C22⋊C4×C149—21no—
55C2×C22⋊C4×C149—22no—
56C2×C22⋊C4×C149—21no—
57C2×C22⋊C4×C149—21no—
58C2×C22⋊C4×C149—22no—
59C2×C22⋊C4×C149D412yes—
60C2×C42×C149—22no—
61C2×C42×C149—21no—
62C2×C42×C149—21no—
63#104×C149—44no—
64#103×C149—22no—
65#102×C149—22no—
66#99×C149—44no—
67C22⋊C8×C149—21no—
68C22⋊C8×C149—21no—
69C22⋊C8×C149—21no—
70C22⋊C8×C149—21no—
71#95×C149—21no—
72#95×C149—21no—
73#95×C149D411yescharacteristic
74#95×C149D411yescharacteristic
75C24×C149—21no—
76C24×C149—21no—
77C24×C149C2×D411yescharacteristic
78#41×C149—24no—
79#41×C149—24no—
80#41×C149—42no—
81#41×C149—42no—
82#41×C149—44no—
83#41×C149—44no—
84C2×Q8×C149—24no—
85C2×Q8×C149—21no—
86C2×Q8×C149C22⋊C412yes—
87C2×D4×C149—22no—
88C2×D4×C149—22no—
89C2×D4×C149—21no—
90C2×D4×C149—21no—
91C2×D4×C149—21no—
92C2×D4×C149—42no—
93C2×D4×C149—44no—
94C2×D4×C149—42no—
95C2×D4×C149—42no—
96C2×D4×C149—42no—
97C2×D4×C149—41no—
98C2×D4×C149—41no—
99C2×D4×C149C22⋊C412yes—
100C22×C4×C149—21no—
101C22×C4×C149—21no—
102C22×C4×C149—22no—
103C22×C4×C149—22no—
104C22×C4×C149—21no—
105C22×C4×C149—22no—
106C22×C4×C149—21no—
107C22×C4×C149—42no—
108C22×C4×C149—44no—
109C22×C4×C149—41no—
110C22×C4×C149C22×C411yescharacteristic
111C22×C4×C149C2×D411yescharacteristic
112C22×C4×C149C2×D411yescharacteristic
113C22×C4×C149C2×D411yescharacteristic
114C22×C4×C149#4111yescharacteristic
115C22×C4×C149#4111yescharacteristic
116SD16×C149—44no—
117D8×C149—44no—
118M16×C149—42no—
119M16×C149—42no—
120C2×C8×C149—22no—
121C2×C8×C149—41no—
122C4⋊C4×C149—21no—
123C4⋊C4×C149—21no—
124C4⋊C4×C149—44no—
125C4⋊C4×C149—42no—
126C22⋊C4×C149—22no—
127C22⋊C4×C149—42no—
128C22⋊C4×C149—44no—
129C22⋊C4×C149—41no—
130C22⋊C4×C149—41no—
131C22⋊C4×C149—41no—
132C22⋊C4×C149—42no—
133C22⋊C4×C149—82no—
134C42×C149—44no—
135C42×C149—42no—
136C42×C149—42no—
137C23×C149—21no—
138C23×C149—21no—
139C23×C149—22no—
140C23×C149—41no—
141C23×C149—41no—
142C23×C149—42no—
143C23×C149—42no—
144C23×C149—42no—
145C23×C149—41no—
146C23×C149—41no—
147C23×C149—41no—
148C23×C149—81no—
149C23×C149—81no—
150C23×C149C4×D411yescharacteristic
151C23×C149#12011yescharacteristic
152C23×C149#12111yescharacteristic
153Q8×C149—24no—
154Q8×C149—22no—
155Q8×C149#9914yescomplemented
156D4×C149—22no—
157D4×C149—22no—
158D4×C149—44no—
159D4×C149—44no—
160D4×C149—42no—
161D4×C149—42no—
162D4×C149—81no—
163D4×C149—82no—
164D4×C149—81no—
165D4×C149—81no—
166C2×C4×C149—24no—
167C2×C4×C149—22no—
168C2×C4×C149—22no—
169C2×C4×C149—22no—
170C2×C4×C149—22no—
171C2×C4×C149—22no—
172C2×C4×C149—41no—
173C2×C4×C149—41no—
174C2×C4×C149—41no—
175C2×C4×C149—44no—
176C2×C4×C149—44no—
177C2×C4×C149—41no—
178C2×C4×C149—41no—
179C2×C4×C149—42no—
180C2×C4×C149—41no—
181C2×C4×C149—42no—
182C2×C4×C149—42no—
183C2×C4×C149—41no—
184C2×C4×C149—42no—
185C2×C4×C149—41no—
186C2×C4×C149—42no—
187C2×C4×C149—41no—
188C2×C4×C149—81no—
189C2×C4×C149—81no—
190C2×C4×C149C2×C22⋊C411yescharacteristic
191C2×C4×C149C4×D411yescharacteristic
192C2×C4×C149#12111yescharacteristic
193C2×C4×C149#12311yescharacteristic
194C8×C149—42no—
195C8×C149—81no—
196C22×C149—21no—
197C22×C149—21no—
198C22×C149—21no—
199C22×C149—21no—
200C22×C149—21no—
201C22×C149—21no—
202C22×C149—21no—
203C22×C149—21no—
204C22×C149—42no—
205C22×C149—42no—
206C22×C149—42no—
207C22×C149—81no—
208C22×C149—81no—
209C22×C149—82no—
210C22×C149—82no—
211C22×C149—81no—
212C22×C149—81no—
213C22×C149—81no—
214C22×C149—162no—
215C22×C149#38611yescharacteristic
216C22×C149#45311yescharacteristic
217C22×C149#45411yescharacteristic
218C4×C149—21no—
219C4×C149—24no—
220C4×C149—21no—
221C4×C149—21no—
222C4×C149—42no—
223C4×C149—82no—
224C4×C149—81no—
225C4×C149—82no—
226C4×C149—81no—
227C4×C149C2×#9912yes—
228C2×C149—21no—
229C2×C149—21no—
230C2×C149—41no—
231C2×C149—41no—
232C2×C149—82no—
233C2×C149—161no—
234C2×C149#188311yescharacteristic
235C2×C149#189811yescharacteristic
236C2×C149#190611yescharacteristic
237#9368C14911yesmaximal, characteristic, direct product factor, Sylow
238C149#936811yescharacteristic, direct product factor, Sylow
239#3006C2×C14911yescharacteristic
240#2341C2×C14911yescharacteristic, complemented
241#1964C2×C14911yescharacteristic, complemented
242#1789C2×C14911yescharacteristic, complemented
243#1507C2×C14911yescharacteristic, complemented
244#1305C2×C14911yescharacteristic, complemented
245#1297C2×C14911yescharacteristic, complemented
246C22×#41C22×C14911yescharacteristic
247C2×AGL(1,ℤ/8)C4×C14912yescomplemented
248C2×#121C22×C14911yescharacteristic
249C2×C4×Q8—21no—
250#449—22no—
251#448—21no—
252#447—21no—
253C2×#104—22no—
254#417C4×C14912yescomplemented
255C2×#99—22no—
256#407C22×C14911yescharacteristic
257#407C22×C14911yescharacteristic
258#390—21no—
259#390—22no—
260#380—21no—
261#380C22×C14911yescharacteristic
262C4×C22⋊C4—21no—
263C4×C22⋊C4C22×C14911yescharacteristic
264C4×C22⋊C4C22×C14911yescharacteristic
265#327—21no—
266#327—21no—
267C2×#41—21no—
268C2×#41—21no—
269C2×#41—44no—
270C2×#41C2×C4×C14912yes—
271C2×#41D4×C14912yes—
272C22×Q8D4×C14911yescharacteristic
273C22×D4—21no—
274C22×D4—21no—
275C22×D4C2×C4×C14911yescharacteristic
276C22×D4D4×C14911yescharacteristic
277C23×C4—21no—
278C23×C4C23×C14911yescharacteristic
279AGL(1,ℤ/8)—44no—
280C2×SD16—22no—
281C2×D8—22no—
282C2×M16—21no—
283C2×M16C2×C4×C14912yes—
284#121—21no—
285#121—21no—
286#121—21no—
287#121—21no—
288C4×Q8—44no—
289C2×C4⋊C4—22no—
290C2×C4⋊C4—21no—
291C2×C4⋊C4C2×C4×C14911yescharacteristic
292C2×C22⋊C4—21no—
293C2×C22⋊C4—22no—
294C2×C22⋊C4—21no—
295C2×C22⋊C4—21no—
296C2×C22⋊C4—22no—
297C2×C22⋊C4D4×C14912yes—
298C2×C42—22no—
299C2×C42—21no—
300C2×C42—21no—
301#104—44no—
302#103—22no—
303#102—22no—
304#99—44no—
305C22⋊C8—21no—
306C22⋊C8—21no—
307C22⋊C8—21no—
308C22⋊C8—21no—
309#95—21no—
310#95—21no—
311#95D4×C14911yescharacteristic
312#95D4×C14911yescharacteristic
313C24—21no—
314C24—21no—
315C24C2×D4×C14911yescharacteristic
316#41—24no—
317#41—24no—
318#41—42no—
319#41—42no—
320#41—44no—
321#41—44no—
322C2×Q8—24no—
323C2×Q8—21no—
324C2×Q8C22⋊C4×C14912yes—
325C2×D4—22no—
326C2×D4—22no—
327C2×D4—21no—
328C2×D4—21no—
329C2×D4—21no—
330C2×D4—42no—
331C2×D4—44no—
332C2×D4—42no—
333C2×D4—42no—
334C2×D4—42no—
335C2×D4—41no—
336C2×D4—41no—
337C2×D4C22⋊C4×C14912yes—
338C22×C4—21no—
339C22×C4—21no—
340C22×C4—22no—
341C22×C4—22no—
342C22×C4—21no—
343C22×C4—22no—
344C22×C4—21no—
345C22×C4—42no—
346C22×C4—44no—
347C22×C4—41no—
348C22×C4C22×C4×C14911yescharacteristic
349C22×C4C2×D4×C14911yescharacteristic
350C22×C4C2×D4×C14911yescharacteristic
351C22×C4C2×D4×C14911yescharacteristic
352C22×C4#41×C14911yescharacteristic
353C22×C4#41×C14911yescharacteristic
354SD16—44no—
355D8—44no—
356M16—42no—
357M16—42no—
358C2×C8—22no—
359C2×C8—41no—
360C4⋊C4—21no—
361C4⋊C4—21no—
362C4⋊C4—44no—
363C4⋊C4—42no—
364C22⋊C4—22no—
365C22⋊C4—42no—
366C22⋊C4—44no—
367C22⋊C4—41no—
368C22⋊C4—41no—
369C22⋊C4—41no—
370C22⋊C4—42no—
371C22⋊C4—82no—
372C42—44no—
373C42—42no—
374C42—42no—
375C23—21no—
376C23—21no—
377C23—22no—
378C23—41no—
379C23—41no—
380C23—42no—
381C23—42no—
382C23—42no—
383C23—41no—
384C23—41no—
385C23—41no—
386C23—81no—
387C23—81no—
388C23C4×D4×C14911yescharacteristic
389C23#120×C14911yescharacteristic
390C23#121×C14911yescharacteristic
391Q8—24no—
392Q8—22no—
393Q8#99×C14914yescomplemented
394D4—22no—
395D4—22no—
396D4—44no—
397D4—44no—
398D4—42no—
399D4—42no—
400D4—81no—
401D4—82no—
402D4—81no—
403D4—81no—
404C2×C4—24no—
405C2×C4—22no—
406C2×C4—22no—
407C2×C4—22no—
408C2×C4—22no—
409C2×C4—22no—
410C2×C4—41no—
411C2×C4—41no—
412C2×C4—41no—
413C2×C4—44no—
414C2×C4—44no—
415C2×C4—41no—
416C2×C4—41no—
417C2×C4—42no—
418C2×C4—41no—
419C2×C4—42no—
420C2×C4—42no—
421C2×C4—41no—
422C2×C4—42no—
423C2×C4—41no—
424C2×C4—42no—
425C2×C4—41no—
426C2×C4—81no—
427C2×C4—81no—
428C2×C4C2×C22⋊C4×C14911yescharacteristic
429C2×C4C4×D4×C14911yescharacteristic
430C2×C4#121×C14911yescharacteristic
431C2×C4#123×C14911yescharacteristic
432C8—42no—
433C8—81no—
434C22—21no—
435C22—21no—
436C22—21no—
437C22—21no—
438C22—21no—
439C22—21no—
440C22—21no—
441C22—21no—
442C22—42no—
443C22—42no—
444C22—42no—
445C22—81no—
446C22—81no—
447C22—82no—
448C22—82no—
449C22—81no—
450C22—81no—
451C22—81no—
452C22—162no—
453C22#386×C14911yescharacteristic
454C22#453×C14911yescharacteristic
455C22#454×C14911yescharacteristic
456C4—21no—
457C4—24no—
458C4—21no—
459C4—21no—
460C4—42no—
461C4—82no—
462C4—81no—
463C4—82no—
464C4—81no—
465C4C2×#99×C14912yes—
466C2—21no—
467C2—21no—
468C2—41no—
469C2—41no—
470C2—82no—
471C2—161no—
472C2#1883×C14911yescharacteristic
473C2#1898×C14911yescharacteristic
474C2#1906×C14911yescharacteristic
subgroupG/H
center, socleC22×C149#386
commutatorC22×C4C22×C4×C149
Frattini, cosocleC23×C4C23×C149
prime radical#3006×C149C2
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C149 ◁ C23×C4×C149 ◁ G

Complements

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

NH ≅ G/Ntype
2. #2341×C149C2semidirect
3. #1964×C149C2semidirect
4. #1789×C149C2semidirect
5. #1507×C149C2semidirect
6. #1305×C149C2semidirect
7. #1297×C149C2semidirect
9. C2×AGL(1,ℤ/8)×C149C4semidirect
16. #417×C149C4semidirect
155. Q8×C149#99semidirect
237. #9368C149direct (N × H)
238. C149#9368direct (N × H)
240. #2341C2×C149semidirect
241. #1964C2×C149semidirect
242. #1789C2×C149semidirect
243. #1507C2×C149semidirect
244. #1305C2×C149semidirect
245. #1297C2×C149semidirect
247. C2×AGL(1,ℤ/8)C4×C149semidirect
254. #417C4×C149semidirect
393. Q8#99×C149semidirect

Maximal subgroups

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

subgroupindex
#3006×C1492
#2341×C1492
#1964×C1492
#1789×C1492
#1507×C1492
#1305×C1492
#1297×C1492
#9368149