Finite Group Databasebeta

← C149×#18398 #49197347

Subgroups — C149×#18398 #49197347

Order 38144.

930 conjugacy classes of subgroups.

The subgroup lattice has 486 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#3507×C149C211yesmaximal, characteristic
2#3229×C149C211yesmaximal, characteristic, complemented
3#3226×C149C211yesmaximal, characteristic
4#2546×C149C211yesmaximal, characteristic, complemented
5#1609×C149C218yesmaximal, complemented
6#1503×C149C211yesmaximal, characteristic, complemented
7#1502×C149C211yesmaximal, characteristic
8#1461×C149C211yesmaximal, characteristic, complemented
9#559×C149—21no—
10#557×C149—21no—
11#556×C149—21no—
12#556×C149—22no—
13#554×C149—21no—
14#552×C149—22no—
15#539×C149C2214yes—
16#536×C149—21no—
17#533×C149C2211yescharacteristic
18#532×C149C2211yescharacteristic
19C2×C4⋊Q8×C149—21no—
20C2×C4⋊Q8×C149C2211yescharacteristic
21#529×C149—22no—
22#520×C149—21no—
23C2×C4×Q8×C149C2211yescharacteristic
24#500×C149—21no—
25#498×C149—21no—
26#487×C149—21no—
27#486×C149—21no—
28#483×C149C2214yes—
29#480×C149C2214yes—
30#475×C149—22no—
31#474×C149—22no—
32#431×C149C2211yescharacteristic
33#431×C149C2211yescharacteristic
34#398×C149C2214yes—
35#391×C149—21no—
36#389×C149—22no—
37C4×C4⋊C4×C149C2211yescharacteristic
38#328×C149C2214yes—
39#327×C149C2214yes—
40#324×C149C2214yes—
41C2×#41×C149—21no—
42C22×Q8×C149—21no—
43C22×Q8×C149D411yescharacteristic
44C4⋊Q8×C149—22no—
45C4⋊Q8×C149—21no—
46C4⋊Q8×C149—21no—
47C4⋊Q8×C149—21no—
48C4⋊Q8×C149—21no—
49C4⋊Q8×C149—44no—
50C4⋊Q8×C149D411yescharacteristic
51C4⋊Q8×C149D411yescharacteristic
52C4⋊Q8×C149D411yescharacteristic
53#127×C149D411yescharacteristic
54#126×C149—24no—
55#126×C149—24no—
56#125×C149—22no—
57#125×C149—24no—
58#125×C149—21no—
59#124×C149—22no—
60#124×C149—22no—
61#124×C149—21no—
62#123×C149—24no—
63#123×C149—24no—
64C22⋊Q8×C149—22no—
65C22⋊Q8×C149—22no—
66C22⋊Q8×C149—24no—
67C22⋊Q8×C149—21no—
68C22⋊Q8×C149C2312yes—
69#121×C149—21no—
70#121×C149C2312yes—
71C4×Q8×C149—22no—
72C4×Q8×C149—22no—
73C4×Q8×C149—21no—
74C4×Q8×C149—21no—
75C4×Q8×C149—21no—
76C4×Q8×C149—21no—
77C4×Q8×C149—21no—
78C4×Q8×C149D412yes—
79C4×D4×C149—22no—
80C4×D4×C149—22no—
81C4×D4×C149—24no—
82C4×D4×C149—21no—
83C4×D4×C149D412yes—
84#117×C149—22no—
85#117×C149—24no—
86#117×C149—21no—
87C2×C4⋊C4×C149—22no—
88C2×C4⋊C4×C149—21no—
89C2×C4⋊C4×C149—21no—
90C2×C4⋊C4×C149—24no—
91C2×C4⋊C4×C149D411yescharacteristic
92C2×C4⋊C4×C149C2312yes—
93C2×C4⋊C4×C149C2312yes—
94C2×C42×C149—21no—
95C2×C42×C149D412yes—
96C2×C42×C149C2311yescharacteristic
97#107×C149—24no—
98#106×C149—24no—
99C4⋊C8×C149—21no—
100C4⋊C8×C149—21no—
101#103×C149—24no—
102#102×C149—24no—
103C22⋊C8×C149C2312yes—
104C22⋊C8×C149C2312yes—
105C4×C8×C149—21no—
106C4×C8×C149—21no—
107#95×C149—24no—
108#95×C149C2312yes—
109#41×C149—42no—
110#41×C149—42no—
111C2×Q8×C149—21no—
112C2×Q8×C149—21no—
113C2×Q8×C149—21no—
114C2×Q8×C149—21no—
115C2×Q8×C149—22no—
116C2×Q8×C149—22no—
117C2×Q8×C149—41no—
118C2×Q8×C149—41no—
119C2×Q8×C149—42no—
120C2×Q8×C149—42no—
121C2×Q8×C149C2×D412yes—
122C2×D4×C149—22no—
123C2×D4×C149—21no—
124C2×D4×C149—21no—
125C2×D4×C149C2×D412yes—
126C22×C4×C149—22no—
127C22×C4×C149—24no—
128C22×C4×C149—22no—
129C22×C4×C149—22no—
130C22×C4×C149C2×D412yes—
131C22×C4×C149C2×D411yescharacteristic
132C22×C4×C149C2×D412yes—
133C22×C4×C149C2×D411yescharacteristic
134C22×C4×C149C2411yescharacteristic
135C2×C8×C149—22no—
136C2×C8×C149—22no—
137C4⋊C4×C149—24no—
138C4⋊C4×C149—24no—
139C4⋊C4×C149—24no—
140C4⋊C4×C149—24no—
141C4⋊C4×C149—21no—
142C4⋊C4×C149—21no—
143C4⋊C4×C149—21no—
144C4⋊C4×C149—21no—
145C4⋊C4×C149—22no—
146C4⋊C4×C149—21no—
147C4⋊C4×C149—21no—
148C4⋊C4×C149—22no—
149C4⋊C4×C149—22no—
150C4⋊C4×C149—22no—
151C4⋊C4×C149—22no—
152C4⋊C4×C149—22no—
153C4⋊C4×C149—48no—
154C4⋊C4×C149—41no—
155C4⋊C4×C149—41no—
156C4⋊C4×C149C2×D412yes—
157C4⋊C4×C149C2×D412yes—
158C22⋊C4×C149—24no—
159C22⋊C4×C149—24no—
160C22⋊C4×C149—24no—
161C22⋊C4×C149—22no—
162C22⋊C4×C149—22no—
163C22⋊C4×C149—22no—
164C42×C149—24no—
165C42×C149—22no—
166C42×C149—22no—
167C42×C149—22no—
168C42×C149—42no—
169C42×C149C2×D411yescharacteristic
170C42×C149C2×D411yescharacteristic
171C42×C149C2×D411yescharacteristic
172C42×C149C2×D411yescharacteristic
173C23×C149—22no—
174C23×C149C22×D411yescharacteristic
175Q8×C149—42no—
176Q8×C149—42no—
177Q8×C149—42no—
178Q8×C149—42no—
179Q8×C149—42no—
180Q8×C149—82no—
181Q8×C149—82no—
182D4×C149—42no—
183D4×C149—42no—
184D4×C149—42no—
185D4×C149—42no—
186D4×C149—42no—
187C2×C4×C149—22no—
188C2×C4×C149—24no—
189C2×C4×C149—22no—
190C2×C4×C149—22no—
191C2×C4×C149—22no—
192C2×C4×C149—22no—
193C2×C4×C149—22no—
194C2×C4×C149—22no—
195C2×C4×C149—22no—
196C2×C4×C149—41no—
197C2×C4×C149—42no—
198C2×C4×C149—42no—
199C2×C4×C149—44no—
200C2×C4×C149—42no—
201C2×C4×C149—42no—
202C2×C4×C149—42no—
203C2×C4×C149—42no—
204C2×C4×C149—84no—
205C2×C4×C149#12011yescharacteristic
206C2×C4×C149#12011yescharacteristic
207C2×C4×C149#12011yescharacteristic
208C2×C4×C149#12011yescharacteristic
209C2×C4×C149#13512yes—
210C2×C4×C149AGL(1,ℤ/8)12yes—
211C2×C4×C149C22×D411yescharacteristic
212C2×C4×C149C22×D411yescharacteristic
213C8×C149—42no—
214C8×C149—42no—
215C22×C149—21no—
216C22×C149—21no—
217C22×C149—42no—
218C22×C149—42no—
219C22×C149—42no—
220C22×C149C2×#12011yescharacteristic
221C22×C149C2×#13511yescharacteristic
222C22×C149C2×AGL(1,ℤ/8)11yescharacteristic
223C4×C149—21no—
224C4×C149—21no—
225C4×C149—21no—
226C4×C149—44no—
227C4×C149—42no—
228C4×C149—42no—
229C4×C149—42no—
230C4×C149—42no—
231C4×C149—42no—
232C4×C149—82no—
233C4×C149#44912yes—
234C4×C149#44912yes—
235C4×C149#45612yes—
236C2×C149—21no—
237C2×C149—21no—
238C2×C149—82no—
239C2×C149C2×#44911yescharacteristic
240C2×C149C2×#45611yescharacteristic
241C2×C149#302811yescharacteristic
242#18398C14911yesmaximal, characteristic, direct product factor, Sylow
243C149#1839811yescharacteristic, direct product factor, Sylow
244#3507C2×C14911yescharacteristic
245#3229C2×C14911yescharacteristic, complemented
246#3226C2×C14911yescharacteristic
247#2546C2×C14911yescharacteristic, complemented
248#1609C2×C14918yescomplemented
249#1503C2×C14911yescharacteristic, complemented
250#1502C2×C14911yescharacteristic
251#1461C2×C14911yescharacteristic, complemented
252#559—21no—
253#557—21no—
254#556—21no—
255#556—22no—
256#554—21no—
257#552—22no—
258#539C22×C14914yes—
259#536—21no—
260#533C22×C14911yescharacteristic
261#532C22×C14911yescharacteristic
262C2×C4⋊Q8—21no—
263C2×C4⋊Q8C22×C14911yescharacteristic
264#529—22no—
265#520—21no—
266C2×C4×Q8C22×C14911yescharacteristic
267#500—21no—
268#498—21no—
269#487—21no—
270#486—21no—
271#483C22×C14914yes—
272#480C22×C14914yes—
273#475—22no—
274#474—22no—
275#431C22×C14911yescharacteristic
276#431C22×C14911yescharacteristic
277#398C22×C14914yes—
278#391—21no—
279#389—22no—
280C4×C4⋊C4C22×C14911yescharacteristic
281#328C22×C14914yes—
282#327C22×C14914yes—
283#324C22×C14914yes—
284C2×#41—21no—
285C22×Q8—21no—
286C22×Q8D4×C14911yescharacteristic
287C4⋊Q8—22no—
288C4⋊Q8—21no—
289C4⋊Q8—21no—
290C4⋊Q8—21no—
291C4⋊Q8—21no—
292C4⋊Q8—44no—
293C4⋊Q8D4×C14911yescharacteristic
294C4⋊Q8D4×C14911yescharacteristic
295C4⋊Q8D4×C14911yescharacteristic
296#127D4×C14911yescharacteristic
297#126—24no—
298#126—24no—
299#125—22no—
300#125—24no—
301#125—21no—
302#124—22no—
303#124—22no—
304#124—21no—
305#123—24no—
306#123—24no—
307C22⋊Q8—22no—
308C22⋊Q8—22no—
309C22⋊Q8—24no—
310C22⋊Q8—21no—
311C22⋊Q8C23×C14912yes—
312#121—21no—
313#121C23×C14912yes—
314C4×Q8—22no—
315C4×Q8—22no—
316C4×Q8—21no—
317C4×Q8—21no—
318C4×Q8—21no—
319C4×Q8—21no—
320C4×Q8—21no—
321C4×Q8D4×C14912yes—
322C4×D4—22no—
323C4×D4—22no—
324C4×D4—24no—
325C4×D4—21no—
326C4×D4D4×C14912yes—
327#117—22no—
328#117—24no—
329#117—21no—
330C2×C4⋊C4—22no—
331C2×C4⋊C4—21no—
332C2×C4⋊C4—24no—
333C2×C4⋊C4—21no—
334C2×C4⋊C4D4×C14911yescharacteristic
335C2×C4⋊C4C23×C14912yes—
336C2×C4⋊C4C23×C14912yes—
337C2×C42—21no—
338C2×C42D4×C14912yes—
339C2×C42C23×C14911yescharacteristic
340#107—24no—
341#106—24no—
342C4⋊C8—21no—
343C4⋊C8—21no—
344#103—24no—
345#102—24no—
346C22⋊C8C23×C14912yes—
347C22⋊C8C23×C14912yes—
348C4×C8—21no—
349C4×C8—21no—
350#95—24no—
351#95C23×C14912yes—
352#41—42no—
353#41—42no—
354C2×Q8—21no—
355C2×Q8—21no—
356C2×Q8—21no—
357C2×Q8—21no—
358C2×Q8—22no—
359C2×Q8—22no—
360C2×Q8—41no—
361C2×Q8—41no—
362C2×Q8—42no—
363C2×Q8—42no—
364C2×Q8C2×D4×C14912yes—
365C2×D4—22no—
366C2×D4—21no—
367C2×D4—21no—
368C2×D4C2×D4×C14912yes—
369C22×C4—22no—
370C22×C4—24no—
371C22×C4—22no—
372C22×C4—22no—
373C22×C4C2×D4×C14912yes—
374C22×C4C2×D4×C14911yescharacteristic
375C22×C4C2×D4×C14912yes—
376C22×C4C2×D4×C14911yescharacteristic
377C22×C4C24×C14911yescharacteristic
378C2×C8—22no—
379C2×C8—22no—
380C4⋊C4—24no—
381C4⋊C4—24no—
382C4⋊C4—24no—
383C4⋊C4—24no—
384C4⋊C4—21no—
385C4⋊C4—21no—
386C4⋊C4—21no—
387C4⋊C4—21no—
388C4⋊C4—22no—
389C4⋊C4—21no—
390C4⋊C4—21no—
391C4⋊C4—22no—
392C4⋊C4—22no—
393C4⋊C4—22no—
394C4⋊C4—22no—
395C4⋊C4—22no—
396C4⋊C4—48no—
397C4⋊C4—41no—
398C4⋊C4—41no—
399C4⋊C4C2×D4×C14912yes—
400C4⋊C4C2×D4×C14912yes—
401C22⋊C4—24no—
402C22⋊C4—24no—
403C22⋊C4—24no—
404C22⋊C4—22no—
405C22⋊C4—22no—
406C22⋊C4—22no—
407C42—24no—
408C42—22no—
409C42—22no—
410C42—22no—
411C42—42no—
412C42C2×D4×C14911yescharacteristic
413C42C2×D4×C14911yescharacteristic
414C42C2×D4×C14911yescharacteristic
415C42C2×D4×C14911yescharacteristic
416C23—22no—
417C23C22×D4×C14911yescharacteristic
418Q8—42no—
419Q8—42no—
420Q8—42no—
421Q8—42no—
422Q8—42no—
423Q8—82no—
424Q8—82no—
425D4—42no—
426D4—42no—
427D4—42no—
428D4—42no—
429D4—42no—
430C2×C4—22no—
431C2×C4—24no—
432C2×C4—22no—
433C2×C4—22no—
434C2×C4—22no—
435C2×C4—22no—
436C2×C4—22no—
437C2×C4—22no—
438C2×C4—22no—
439C2×C4—41no—
440C2×C4—42no—
441C2×C4—42no—
442C2×C4—44no—
443C2×C4—42no—
444C2×C4—42no—
445C2×C4—42no—
446C2×C4—42no—
447C2×C4—84no—
448C2×C4#120×C14911yescharacteristic
449C2×C4#120×C14911yescharacteristic
450C2×C4#120×C14911yescharacteristic
451C2×C4#120×C14911yescharacteristic
452C2×C4#135×C14912yes—
453C2×C4AGL(1,ℤ/8)×C14912yes—
454C2×C4C22×D4×C14911yescharacteristic
455C2×C4C22×D4×C14911yescharacteristic
456C8—42no—
457C8—42no—
458C22—21no—
459C22—21no—
460C22—42no—
461C22—42no—
462C22—42no—
463C22C2×#120×C14911yescharacteristic
464C22C2×#135×C14911yescharacteristic
465C22C2×AGL(1,ℤ/8)×C14911yescharacteristic
466C4—21no—
467C4—21no—
468C4—21no—
469C4—44no—
470C4—42no—
471C4—42no—
472C4—42no—
473C4—42no—
474C4—42no—
475C4—82no—
476C4#449×C14912yes—
477C4#449×C14912yes—
478C4#456×C14912yes—
479C2—21no—
480C2—21no—
481C2—82no—
482C2C2×#449×C14911yescharacteristic
483C2C2×#456×C14911yescharacteristic
484C2#3028×C14911yescharacteristic
subgroupG/H
center, socleC22×C149C2×#120
commutator, Frattini, cosocleC22×C4C24×C149
prime radical#532×C149C22
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C149 ◁ C2×C42×C149 ◁ G

Complements

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

NH ≅ G/Ntype
2. #3229×C149C2semidirect
4. #2546×C149C2semidirect
5. #1609×C149C2semidirect
6. #1503×C149C2semidirect
8. #1461×C149C2semidirect
242. #18398C149direct (N × H)
243. C149#18398direct (N × H)
245. #3229C2×C149semidirect
247. #2546C2×C149semidirect
248. #1609C2×C149semidirect
249. #1503C2×C149semidirect
251. #1461C2×C149semidirect

Maximal subgroups

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

subgroupindex
#3507×C1492
#3229×C1492
#3226×C1492
#2546×C1492
#1609×C1492
#1503×C1492
#1502×C1492
#1461×C1492
#18398149