Finite Group Databasebeta

← C149×#10403 #49189352

Subgroups — C149×#10403 #49189352

Order 38144.

716 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#2656×C149C211yesmaximal, characteristic
2#1874×C149C212yesmaximal, complemented
3C2×#327×C149C212yesmaximal, complemented
4#1442×C149C211yesmaximal, characteristic, complemented
5#1280×C149C211yesmaximal, characteristic, complemented
6C2×#121×C149—21no—
7C2×#121×C149—21no—
8C2×#121×C149C2212yes—
9C22×C4⋊C4×C149C2211yescharacteristic
10C2×#102×C149—22no—
11C2×C22⋊C8×C149C2212yes—
12#399×C149—22no—
13#392×C149—22no—
14C2×#95×C149—21no—
15C2×#95×C149—21no—
16C2×#95×C149C2211yescharacteristic
17C2×#95×C149C2211yescharacteristic
18#340×C149—22no—
19#327×C149—24no—
20C22×D4×C149—22no—
21C22×D4×C149—21no—
22C22×D4×C149—21no—
23C22×D4×C149D412yes—
24C23×C4×C149—21no—
25C23×C4×C149—21no—
26C23×C4×C149D411yescharacteristic
27C23×C4×C149D411yescharacteristic
28C23×C4×C149C2311yescharacteristic
29C22×C8×C149—22no—
30#121×C149—22no—
31#121×C149—22no—
32#121×C149—22no—
33#121×C149—22no—
34#121×C149—42no—
35#121×C149—42no—
36#121×C149—42no—
37#121×C149—42no—
38C2×C4⋊C4×C149—22no—
39C2×C4⋊C4×C149—21no—
40C2×C4⋊C4×C149—21no—
41C2×C4⋊C4×C149—42no—
42C2×C4⋊C4×C149D412yes—
43C2×C22⋊C4×C149—22no—
44C2×C22⋊C4×C149—22no—
45C2×C22⋊C4×C149—22no—
46#102×C149—44no—
47C22⋊C8×C149—22no—
48C22⋊C8×C149—22no—
49#95×C149—22no—
50#95×C149—21no—
51#95×C149—42no—
52#95×C149—42no—
53#95×C149D412yescomplemented
54C24×C149—22no—
55C24×C149C2×D411yescharacteristic
56C2×D4×C149—22no—
57C2×D4×C149—22no—
58C2×D4×C149—42no—
59C2×D4×C149—42no—
60C2×D4×C149—42no—
61C2×D4×C149—42no—
62C2×D4×C149—42no—
63C2×D4×C149—42no—
64C2×D4×C149—42no—
65C2×D4×C149—42no—
66C2×D4×C149—42no—
67C2×D4×C149—42no—
68C2×D4×C149—81no—
69C2×D4×C149—81no—
70C2×D4×C149—81no—
71C2×D4×C149—81no—
72C22×C4×C149—21no—
73C22×C4×C149—21no—
74C22×C4×C149—21no—
75C22×C4×C149—21no—
76C22×C4×C149—22no—
77C22×C4×C149—22no—
78C22×C4×C149—22no—
79C22×C4×C149—41no—
80C22×C4×C149—41no—
81C22×C4×C149—41no—
82C22×C4×C149—41no—
83C22×C4×C149—41no—
84C22×C4×C149—41no—
85C22×C4×C149—41no—
86C22×C4×C149—41no—
87C22×C4×C149—41no—
88C22×C4×C149—41no—
89C22×C4×C149—41no—
90C22×C4×C149—41no—
91C22×C4×C149—41no—
92C22×C4×C149—41no—
93C22×C4×C149—41no—
94C22×C4×C149—41no—
95C22×C4×C149—41no—
96C22×C4×C149—41no—
97C22×C4×C149D812yes—
98C22×C4×C149SD1612yes—
99C22×C4×C149C2×D412yes—
100C22×C4×C149C2×D411yescharacteristic
101C22×C4×C149#4112yes—
102C22×C4×C149#4111yescharacteristic
103C2×C8×C149—42no—
104C2×C8×C149—42no—
105C2×C8×C149—42no—
106C4⋊C4×C149—24no—
107C4⋊C4×C149—22no—
108C4⋊C4×C149—22no—
109C4⋊C4×C149—42no—
110C4⋊C4×C149—42no—
111C4⋊C4×C149—42no—
112C22⋊C4×C149—44no—
113C22⋊C4×C149—44no—
114C22⋊C4×C149—42no—
115C22⋊C4×C149—42no—
116C23×C149—21no—
117C23×C149—21no—
118C23×C149—21no—
119C23×C149—21no—
120C23×C149—42no—
121C23×C149—42no—
122C23×C149—42no—
123C23×C149—42no—
124C23×C149—42no—
125C23×C149—42no—
126C23×C149—42no—
127C23×C149#12011yescharacteristic
128C23×C149#12111yescharacteristic
129C23×C149#12411yescharacteristic
130C23×C149C2×D811yescharacteristic
131C23×C149C2×SD1611yescharacteristic
132C23×C149AGL(1,ℤ/8)11yescharacteristic
133C23×C149AGL(1,ℤ/8)11yescharacteristic
134D4×C149—44no—
135D4×C149—82no—
136D4×C149—84no—
137D4×C149—84no—
138D4×C149—82no—
139D4×C149—82no—
140D4×C149—82no—
141D4×C149—82no—
142C2×C4×C149—22no—
143C2×C4×C149—22no—
144C2×C4×C149—22no—
145C2×C4×C149—22no—
146C2×C4×C149—41no—
147C2×C4×C149—42no—
148C2×C4×C149—41no—
149C2×C4×C149—41no—
150C2×C4×C149—41no—
151C2×C4×C149—41no—
152C2×C4×C149—41no—
153C2×C4×C149—42no—
154C2×C4×C149—42no—
155C2×C4×C149—42no—
156C2×C4×C149—42no—
157C2×C4×C149—42no—
158C2×C4×C149—42no—
159C2×C4×C149—42no—
160C2×C4×C149—42no—
161C2×C4×C149—42no—
162C2×C4×C149—42no—
163C2×C4×C149—42no—
164C2×C4×C149—81no—
165C2×C4×C149—81no—
166C2×C4×C149—81no—
167C2×C4×C149—81no—
168C2×C4×C149—81no—
169C2×C4×C149—81no—
170C2×C4×C149—81no—
171C2×C4×C149—81no—
172C2×C4×C149—81no—
173C2×C4×C149—81no—
174C2×C4×C149#12112yes—
175C2×C4×C149#12312yes—
176C8×C149—82no—
177C22×C149—21no—
178C22×C149—21no—
179C22×C149—21no—
180C22×C149—21no—
181C22×C149—21no—
182C22×C149—21no—
183C22×C149—21no—
184C22×C149—21no—
185C22×C149—21no—
186C22×C149—21no—
187C22×C149—21no—
188C22×C149—21no—
189C22×C149—82no—
190C22×C149—82no—
191C22×C149—82no—
192C22×C149—82no—
193C22×C149—82no—
194C22×C149—82no—
195C22×C149—82no—
196C22×C149#39411yescharacteristic
197C22×C149#44711yescharacteristic
198C22×C149#45011yescharacteristic
199C22×C149#45411yescharacteristic
200C22×C149#45511yescharacteristic
201C22×C149B(4,𝔽2)11yescharacteristic
202C22×C149#45811yescharacteristic
203C22×C149#45911yescharacteristic
204C22×C149#46011yescharacteristic
205C22×C149#48611yescharacteristic
206C22×C149#49011yescharacteristic
207C4×C149—22no—
208C4×C149—22no—
209C4×C149—42no—
210C4×C149—42no—
211C4×C149—82no—
212C4×C149—82no—
213C4×C149—82no—
214C2×C149—21no—
215C2×C149—21no—
216C2×C149—21no—
217C2×C149—21no—
218C2×C149—162no—
219C2×C149#159811yescharacteristic
220C2×C149#160111yescharacteristic
221C2×C149#160711yescharacteristic
222C2×C149#161611yescharacteristic
223C2×C149#204011yescharacteristic
224C2×C149#204111yescharacteristic
225C2×C149#204411yescharacteristic
226#10403C14911yesmaximal, characteristic, direct product factor, Sylow
227C149#1040311yescharacteristic, direct product factor, Sylow
228#2656C2×C14911yescharacteristic
229#1874C2×C14912yescomplemented
230C2×#327C2×C14912yescomplemented
231#1442C2×C14911yescharacteristic, complemented
232#1280C2×C14911yescharacteristic, complemented
233C2×#121—21no—
234C2×#121—21no—
235C2×#121C22×C14912yes—
236C22×C4⋊C4C22×C14911yescharacteristic
237C2×#102—22no—
238C2×C22⋊C8C22×C14912yes—
239#399—22no—
240#392—22no—
241C2×#95—21no—
242C2×#95—21no—
243C2×#95C22×C14911yescharacteristic
244C2×#95C22×C14911yescharacteristic
245#340—22no—
246#327—24no—
247C22×D4—22no—
248C22×D4—21no—
249C22×D4—21no—
250C22×D4D4×C14912yes—
251C23×C4—21no—
252C23×C4—21no—
253C23×C4D4×C14911yescharacteristic
254C23×C4D4×C14911yescharacteristic
255C23×C4C23×C14911yescharacteristic
256C22×C8—22no—
257#121—22no—
258#121—22no—
259#121—22no—
260#121—22no—
261#121—42no—
262#121—42no—
263#121—42no—
264#121—42no—
265C2×C4⋊C4—22no—
266C2×C4⋊C4—21no—
267C2×C4⋊C4—21no—
268C2×C4⋊C4—42no—
269C2×C4⋊C4D4×C14912yes—
270C2×C22⋊C4—22no—
271C2×C22⋊C4—22no—
272C2×C22⋊C4—22no—
273#102—44no—
274C22⋊C8—22no—
275C22⋊C8—22no—
276#95—22no—
277#95—21no—
278#95—42no—
279#95—42no—
280#95D4×C14912yescomplemented
281C24—22no—
282C24C2×D4×C14911yescharacteristic
283C2×D4—22no—
284C2×D4—22no—
285C2×D4—42no—
286C2×D4—42no—
287C2×D4—42no—
288C2×D4—42no—
289C2×D4—42no—
290C2×D4—42no—
291C2×D4—42no—
292C2×D4—42no—
293C2×D4—42no—
294C2×D4—42no—
295C2×D4—81no—
296C2×D4—81no—
297C2×D4—81no—
298C2×D4—81no—
299C22×C4—21no—
300C22×C4—21no—
301C22×C4—21no—
302C22×C4—21no—
303C22×C4—22no—
304C22×C4—22no—
305C22×C4—22no—
306C22×C4—41no—
307C22×C4—41no—
308C22×C4—41no—
309C22×C4—41no—
310C22×C4—41no—
311C22×C4—41no—
312C22×C4—41no—
313C22×C4—41no—
314C22×C4—41no—
315C22×C4—41no—
316C22×C4—41no—
317C22×C4—41no—
318C22×C4—41no—
319C22×C4—41no—
320C22×C4—41no—
321C22×C4—41no—
322C22×C4—41no—
323C22×C4—41no—
324C22×C4D8×C14912yes—
325C22×C4SD16×C14912yes—
326C22×C4C2×D4×C14912yes—
327C22×C4C2×D4×C14911yescharacteristic
328C22×C4#41×C14912yes—
329C22×C4#41×C14911yescharacteristic
330C2×C8—42no—
331C2×C8—42no—
332C2×C8—42no—
333C4⋊C4—24no—
334C4⋊C4—22no—
335C4⋊C4—22no—
336C4⋊C4—42no—
337C4⋊C4—42no—
338C4⋊C4—42no—
339C22⋊C4—44no—
340C22⋊C4—44no—
341C22⋊C4—42no—
342C22⋊C4—42no—
343C23—21no—
344C23—21no—
345C23—21no—
346C23—21no—
347C23—42no—
348C23—42no—
349C23—42no—
350C23—42no—
351C23—42no—
352C23—42no—
353C23—42no—
354C23#120×C14911yescharacteristic
355C23#121×C14911yescharacteristic
356C23#124×C14911yescharacteristic
357C23C2×D8×C14911yescharacteristic
358C23C2×SD16×C14911yescharacteristic
359C23AGL(1,ℤ/8)×C14911yescharacteristic
360C23AGL(1,ℤ/8)×C14911yescharacteristic
361D4—44no—
362D4—82no—
363D4—84no—
364D4—84no—
365D4—82no—
366D4—82no—
367D4—82no—
368D4—82no—
369C2×C4—22no—
370C2×C4—22no—
371C2×C4—22no—
372C2×C4—22no—
373C2×C4—41no—
374C2×C4—42no—
375C2×C4—41no—
376C2×C4—41no—
377C2×C4—41no—
378C2×C4—41no—
379C2×C4—41no—
380C2×C4—42no—
381C2×C4—42no—
382C2×C4—42no—
383C2×C4—42no—
384C2×C4—42no—
385C2×C4—42no—
386C2×C4—42no—
387C2×C4—42no—
388C2×C4—42no—
389C2×C4—42no—
390C2×C4—42no—
391C2×C4—81no—
392C2×C4—81no—
393C2×C4—81no—
394C2×C4—81no—
395C2×C4—81no—
396C2×C4—81no—
397C2×C4—81no—
398C2×C4—81no—
399C2×C4—81no—
400C2×C4—81no—
401C2×C4#121×C14912yes—
402C2×C4#123×C14912yes—
403C8—82no—
404C22—21no—
405C22—21no—
406C22—21no—
407C22—21no—
408C22—21no—
409C22—21no—
410C22—21no—
411C22—21no—
412C22—21no—
413C22—21no—
414C22—21no—
415C22—21no—
416C22—82no—
417C22—82no—
418C22—82no—
419C22—82no—
420C22—82no—
421C22—82no—
422C22—82no—
423C22#394×C14911yescharacteristic
424C22#447×C14911yescharacteristic
425C22#450×C14911yescharacteristic
426C22#454×C14911yescharacteristic
427C22#455×C14911yescharacteristic
428C22B(4,𝔽2)×C14911yescharacteristic
429C22#458×C14911yescharacteristic
430C22#459×C14911yescharacteristic
431C22#460×C14911yescharacteristic
432C22#486×C14911yescharacteristic
433C22#490×C14911yescharacteristic
434C4—22no—
435C4—22no—
436C4—42no—
437C4—42no—
438C4—82no—
439C4—82no—
440C4—82no—
441C2—21no—
442C2—21no—
443C2—21no—
444C2—21no—
445C2—162no—
446C2#1598×C14911yescharacteristic
447C2#1601×C14911yescharacteristic
448C2#1607×C14911yescharacteristic
449C2#1616×C14911yescharacteristic
450C2#2040×C14911yescharacteristic
451C2#2041×C14911yescharacteristic
452C2#2044×C14911yescharacteristic
subgroupG/H
center, socleC23×C149#120
commutator, Frattini, cosocleC23×C4C23×C149
prime radical#2656×C149C2
LCSG ▷ C23×C4 ▷ C22 ▷ C1
UCSC1 ◁ C23×C149 ◁ C23×C4×C149 ◁ G

Complements

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

NH ≅ G/Ntype
2. #1874×C149C2semidirect
3. C2×#327×C149C2semidirect
4. #1442×C149C2semidirect
5. #1280×C149C2semidirect
53. #95×C149D4semidirect
226. #10403C149direct (N × H)
227. C149#10403direct (N × H)
229. #1874C2×C149semidirect
230. C2×#327C2×C149semidirect
231. #1442C2×C149semidirect
232. #1280C2×C149semidirect
280. #95D4×C149semidirect

Maximal subgroups

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

subgroupindex
#2656×C1492
#1874×C1492
C2×#327×C1492
#1442×C1492
#1280×C1492
#10403149