Finite Group Databasebeta

← C149×#18391 #49197340

Subgroups — C149×#18391 #49197340

Order 38144.

1022 conjugacy classes of subgroups.

The subgroup lattice has 518 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#3507×C149C211yesmaximal, characteristic, complemented
2#3208×C149C211yesmaximal, characteristic, complemented
3#3205×C149C211yesmaximal, characteristic
4#2548×C149C211yesmaximal, characteristic, complemented
5#1597×C149C218yesmaximal, complemented
6#1503×C149C211yesmaximal, characteristic, complemented
7#1502×C149C211yesmaximal, characteristic, complemented
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×#127×C149C2211yescharacteristic
20#529×C149—22no—
21C2×#124×C149—21no—
22#520×C149—21no—
23C2×C4×Q8×C149C2211yescharacteristic
24#493×C149—21no—
25#492×C149—21no—
26#486×C149—21no—
27#486×C149—21no—
28#460×C149—22no—
29#459×C149—22no—
30#450×C149C2214yes—
31#447×C149C2214yes—
32#431×C149C2211yescharacteristic
33#431×C149C2211yescharacteristic
34#394×C149C2214yes—
35#390×C149—21no—
36#390×C149—22no—
37C4×C4⋊C4×C149C2211yescharacteristic
38#328×C149C2214yes—
39#327×C149C2214yes—
40#324×C149C2214yes—
41C2×#41×C149—21no—
42C22×Q8×C149D411yescharacteristic
43C22×D4×C149—21no—
44C22×D4×C149—21no—
45C22×D4×C149C2312yes—
46C2×SD16×C149—24no—
47C2×D8×C149—24no—
48C4⋊Q8×C149—22no—
49C4⋊Q8×C149D411yescharacteristic
50C4⋊Q8×C149D411yescharacteristic
51C4⋊Q8×C149D411yescharacteristic
52#127×C149—21no—
53#127×C149—21no—
54#127×C149—21no—
55#127×C149—21no—
56#127×C149D411yescharacteristic
57#126×C149—24no—
58#126×C149—24no—
59#125×C149—22no—
60#125×C149—24no—
61#125×C149—21no—
62#124×C149—22no—
63#124×C149—22no—
64#124×C149—21no—
65#124×C149—44no—
66#123×C149—24no—
67#123×C149—24no—
68C22⋊Q8×C149—22no—
69C22⋊Q8×C149—22no—
70C22⋊Q8×C149—24no—
71C22⋊Q8×C149—21no—
72C22⋊Q8×C149C2312yes—
73#121×C149—21no—
74#121×C149C2312yes—
75C4×Q8×C149—22no—
76C4×Q8×C149—22no—
77C4×Q8×C149—21no—
78C4×Q8×C149—21no—
79C4×Q8×C149—21no—
80C4×Q8×C149—21no—
81C4×Q8×C149—21no—
82C4×Q8×C149D412yes—
83C4×D4×C149—22no—
84C4×D4×C149—22no—
85C4×D4×C149—24no—
86C4×D4×C149—21no—
87C4×D4×C149D412yes—
88#117×C149—22no—
89#117×C149—24no—
90#117×C149—21no—
91C2×C4⋊C4×C149—22no—
92C2×C4⋊C4×C149—21no—
93C2×C4⋊C4×C149D411yescharacteristic
94C2×C4⋊C4×C149C2312yes—
95C2×C22⋊C4×C149—24no—
96C2×C22⋊C4×C149—24no—
97C2×C42×C149—21no—
98C2×C42×C149D412yes—
99C2×C42×C149C2311yescharacteristic
100C4⋊C8×C149—21no—
101C4⋊C8×C149—21no—
102#102×C149—24no—
103#102×C149—24no—
104C22⋊C8×C149C2312yes—
105C22⋊C8×C149C2312yes—
106C4×C8×C149—21no—
107C4×C8×C149—21no—
108#95×C149C2312yes—
109C24×C149—22no—
110#41×C149—42no—
111#41×C149—42no—
112C2×Q8×C149—21no—
113C2×Q8×C149—21no—
114C2×Q8×C149—21no—
115C2×Q8×C149—21no—
116C2×Q8×C149—22no—
117C2×Q8×C149—22no—
118C2×Q8×C149C2×D412yes—
119C2×D4×C149—22no—
120C2×D4×C149—21no—
121C2×D4×C149—21no—
122C2×D4×C149—22no—
123C2×D4×C149—22no—
124C2×D4×C149—44no—
125C2×D4×C149—41no—
126C2×D4×C149—41no—
127C2×D4×C149—41no—
128C2×D4×C149—41no—
129C2×D4×C149—42no—
130C2×D4×C149—42no—
131C2×D4×C149—82no—
132C2×D4×C149C2×D412yes—
133C22×C4×C149—24no—
134C22×C4×C149—22no—
135C22×C4×C149—22no—
136C22×C4×C149C2×D412yes—
137C22×C4×C149C2×D411yescharacteristic
138C22×C4×C149C2×D412yes—
139C22×C4×C149C2×D411yescharacteristic
140C22×C4×C149C2411yescharacteristic
141SD16×C149—84no—
142D8×C149—84no—
143C2×C8×C149—22no—
144C2×C8×C149—22no—
145C4⋊C4×C149—24no—
146C4⋊C4×C149—24no—
147C4⋊C4×C149—24no—
148C4⋊C4×C149—21no—
149C4⋊C4×C149—21no—
150C4⋊C4×C149—21no—
151C4⋊C4×C149—21no—
152C4⋊C4×C149—22no—
153C4⋊C4×C149—21no—
154C4⋊C4×C149—21no—
155C4⋊C4×C149—22no—
156C4⋊C4×C149—22no—
157C4⋊C4×C149—22no—
158C4⋊C4×C149—42no—
159C4⋊C4×C149C2×D412yes—
160C4⋊C4×C149C2×D412yes—
161C22⋊C4×C149—24no—
162C22⋊C4×C149—24no—
163C22⋊C4×C149—24no—
164C22⋊C4×C149—22no—
165C22⋊C4×C149—22no—
166C22⋊C4×C149—22no—
167C22⋊C4×C149—48no—
168C22⋊C4×C149—84no—
169C42×C149—24no—
170C42×C149—22no—
171C42×C149—22no—
172C42×C149—22no—
173C42×C149—42no—
174C42×C149C2×D411yescharacteristic
175C42×C149C2×D411yescharacteristic
176C42×C149C2×D411yescharacteristic
177C42×C149C2×D411yescharacteristic
178C23×C149—22no—
179C23×C149—44no—
180C23×C149—44no—
181C23×C149—42no—
182C23×C149—42no—
183C23×C149—42no—
184C23×C149C22×D411yescharacteristic
185Q8×C149—42no—
186Q8×C149—42no—
187Q8×C149—42no—
188Q8×C149—42no—
189Q8×C149—42no—
190D4×C149—42no—
191D4×C149—44no—
192D4×C149—44no—
193D4×C149—42no—
194D4×C149—42no—
195D4×C149—42no—
196D4×C149—42no—
197D4×C149—82no—
198D4×C149—82no—
199D4×C149—82no—
200D4×C149—82no—
201C2×C4×C149—22no—
202C2×C4×C149—22no—
203C2×C4×C149—22no—
204C2×C4×C149—22no—
205C2×C4×C149—22no—
206C2×C4×C149—22no—
207C2×C4×C149—22no—
208C2×C4×C149—22no—
209C2×C4×C149—41no—
210C2×C4×C149—44no—
211C2×C4×C149—42no—
212C2×C4×C149—42no—
213C2×C4×C149—42no—
214C2×C4×C149—42no—
215C2×C4×C149—84no—
216C2×C4×C149#12011yescharacteristic
217C2×C4×C149#12011yescharacteristic
218C2×C4×C149#12011yescharacteristic
219C2×C4×C149#12011yescharacteristic
220C2×C4×C149#13512yes—
221C2×C4×C149AGL(1,ℤ/8)12yes—
222C2×C4×C149C22×D411yescharacteristic
223C2×C4×C149C22×D411yescharacteristic
224C8×C149—42no—
225C8×C149—42no—
226C22×C149—21no—
227C22×C149—21no—
228C22×C149—42no—
229C22×C149—42no—
230C22×C149—42no—
231C22×C149—84no—
232C22×C149—84no—
233C22×C149—82no—
234C22×C149—82no—
235C22×C149—82no—
236C22×C149C2×#12011yescharacteristic
237C22×C149C2×#13511yescharacteristic
238C22×C149C2×AGL(1,ℤ/8)11yescharacteristic
239C4×C149—21no—
240C4×C149—21no—
241C4×C149—21no—
242C4×C149—42no—
243C4×C149—42no—
244C4×C149—42no—
245C4×C149—42no—
246C4×C149—42no—
247C4×C149—82no—
248C4×C149#44912yes—
249C4×C149#44912yes—
250C4×C149#45412yes—
251C2×C149—21no—
252C2×C149—21no—
253C2×C149—82no—
254C2×C149—162no—
255C2×C149C2×#44911yescharacteristic
256C2×C149C2×#45411yescharacteristic
257C2×C149#302711yescharacteristic
258#18391C14911yesmaximal, characteristic, direct product factor, Sylow
259C149#1839111yescharacteristic, direct product factor, Sylow
260#3507C2×C14911yescharacteristic, complemented
261#3208C2×C14911yescharacteristic, complemented
262#3205C2×C14911yescharacteristic
263#2548C2×C14911yescharacteristic, complemented
264#1597C2×C14918yescomplemented
265#1503C2×C14911yescharacteristic, complemented
266#1502C2×C14911yescharacteristic, complemented
267#1461C2×C14911yescharacteristic, complemented
268#559—21no—
269#557—21no—
270#556—21no—
271#556—22no—
272#554—21no—
273#552—22no—
274#539C22×C14914yes—
275#536—21no—
276#533C22×C14911yescharacteristic
277#532C22×C14911yescharacteristic
278C2×#127C22×C14911yescharacteristic
279#529—22no—
280C2×#124—21no—
281#520—21no—
282C2×C4×Q8C22×C14911yescharacteristic
283#493—21no—
284#492—21no—
285#486—21no—
286#486—21no—
287#460—22no—
288#459—22no—
289#450C22×C14914yes—
290#447C22×C14914yes—
291#431C22×C14911yescharacteristic
292#431C22×C14911yescharacteristic
293#394C22×C14914yes—
294#390—21no—
295#390—22no—
296C4×C4⋊C4C22×C14911yescharacteristic
297#328C22×C14914yes—
298#327C22×C14914yes—
299#324C22×C14914yes—
300C2×#41—21no—
301C22×Q8D4×C14911yescharacteristic
302C22×D4—21no—
303C22×D4—21no—
304C22×D4C23×C14912yes—
305C2×SD16—24no—
306C2×D8—24no—
307C4⋊Q8—22no—
308C4⋊Q8D4×C14911yescharacteristic
309C4⋊Q8D4×C14911yescharacteristic
310C4⋊Q8D4×C14911yescharacteristic
311#127—21no—
312#127—21no—
313#127—21no—
314#127—21no—
315#127D4×C14911yescharacteristic
316#126—24no—
317#126—24no—
318#125—22no—
319#125—24no—
320#125—21no—
321#124—22no—
322#124—22no—
323#124—21no—
324#124—44no—
325#123—24no—
326#123—24no—
327C22⋊Q8—22no—
328C22⋊Q8—22no—
329C22⋊Q8—24no—
330C22⋊Q8—21no—
331C22⋊Q8C23×C14912yes—
332#121—21no—
333#121C23×C14912yes—
334C4×Q8—22no—
335C4×Q8—22no—
336C4×Q8—21no—
337C4×Q8—21no—
338C4×Q8—21no—
339C4×Q8—21no—
340C4×Q8—21no—
341C4×Q8D4×C14912yes—
342C4×D4—22no—
343C4×D4—22no—
344C4×D4—24no—
345C4×D4—21no—
346C4×D4D4×C14912yes—
347#117—22no—
348#117—24no—
349#117—21no—
350C2×C4⋊C4—22no—
351C2×C4⋊C4—21no—
352C2×C4⋊C4D4×C14911yescharacteristic
353C2×C4⋊C4C23×C14912yes—
354C2×C22⋊C4—24no—
355C2×C22⋊C4—24no—
356C2×C42—21no—
357C2×C42D4×C14912yes—
358C2×C42C23×C14911yescharacteristic
359C4⋊C8—21no—
360C4⋊C8—21no—
361#102—24no—
362#102—24no—
363C22⋊C8C23×C14912yes—
364C22⋊C8C23×C14912yes—
365C4×C8—21no—
366C4×C8—21no—
367#95C23×C14912yes—
368C24—22no—
369#41—42no—
370#41—42no—
371C2×Q8—21no—
372C2×Q8—21no—
373C2×Q8—21no—
374C2×Q8—21no—
375C2×Q8—22no—
376C2×Q8—22no—
377C2×Q8C2×D4×C14912yes—
378C2×D4—22no—
379C2×D4—21no—
380C2×D4—21no—
381C2×D4—22no—
382C2×D4—22no—
383C2×D4—44no—
384C2×D4—41no—
385C2×D4—41no—
386C2×D4—41no—
387C2×D4—41no—
388C2×D4—42no—
389C2×D4—42no—
390C2×D4—82no—
391C2×D4C2×D4×C14912yes—
392C22×C4—24no—
393C22×C4—22no—
394C22×C4—22no—
395C22×C4C2×D4×C14912yes—
396C22×C4C2×D4×C14911yescharacteristic
397C22×C4C2×D4×C14912yes—
398C22×C4C2×D4×C14911yescharacteristic
399C22×C4C24×C14911yescharacteristic
400SD16—84no—
401D8—84no—
402C2×C8—22no—
403C2×C8—22no—
404C4⋊C4—24no—
405C4⋊C4—24no—
406C4⋊C4—24no—
407C4⋊C4—21no—
408C4⋊C4—21no—
409C4⋊C4—21no—
410C4⋊C4—21no—
411C4⋊C4—22no—
412C4⋊C4—21no—
413C4⋊C4—21no—
414C4⋊C4—22no—
415C4⋊C4—22no—
416C4⋊C4—22no—
417C4⋊C4—42no—
418C4⋊C4C2×D4×C14912yes—
419C4⋊C4C2×D4×C14912yes—
420C22⋊C4—24no—
421C22⋊C4—24no—
422C22⋊C4—24no—
423C22⋊C4—22no—
424C22⋊C4—22no—
425C22⋊C4—22no—
426C22⋊C4—48no—
427C22⋊C4—84no—
428C42—24no—
429C42—22no—
430C42—22no—
431C42—22no—
432C42—42no—
433C42C2×D4×C14911yescharacteristic
434C42C2×D4×C14911yescharacteristic
435C42C2×D4×C14911yescharacteristic
436C42C2×D4×C14911yescharacteristic
437C23—22no—
438C23—44no—
439C23—44no—
440C23—42no—
441C23—42no—
442C23—42no—
443C23C22×D4×C14911yescharacteristic
444Q8—42no—
445Q8—42no—
446Q8—42no—
447Q8—42no—
448Q8—42no—
449D4—42no—
450D4—44no—
451D4—44no—
452D4—42no—
453D4—42no—
454D4—42no—
455D4—42no—
456D4—82no—
457D4—82no—
458D4—82no—
459D4—82no—
460C2×C4—22no—
461C2×C4—22no—
462C2×C4—22no—
463C2×C4—22no—
464C2×C4—22no—
465C2×C4—22no—
466C2×C4—22no—
467C2×C4—22no—
468C2×C4—41no—
469C2×C4—44no—
470C2×C4—42no—
471C2×C4—42no—
472C2×C4—42no—
473C2×C4—42no—
474C2×C4—84no—
475C2×C4#120×C14911yescharacteristic
476C2×C4#120×C14911yescharacteristic
477C2×C4#120×C14911yescharacteristic
478C2×C4#120×C14911yescharacteristic
479C2×C4#135×C14912yes—
480C2×C4AGL(1,ℤ/8)×C14912yes—
481C2×C4C22×D4×C14911yescharacteristic
482C2×C4C22×D4×C14911yescharacteristic
483C8—42no—
484C8—42no—
485C22—21no—
486C22—21no—
487C22—42no—
488C22—42no—
489C22—42no—
490C22—84no—
491C22—84no—
492C22—82no—
493C22—82no—
494C22—82no—
495C22C2×#120×C14911yescharacteristic
496C22C2×#135×C14911yescharacteristic
497C22C2×AGL(1,ℤ/8)×C14911yescharacteristic
498C4—21no—
499C4—21no—
500C4—21no—
501C4—42no—
502C4—42no—
503C4—42no—
504C4—42no—
505C4—42no—
506C4—82no—
507C4#449×C14912yes—
508C4#449×C14912yes—
509C4#454×C14912yes—
510C2—21no—
511C2—21no—
512C2—82no—
513C2—162no—
514C2C2×#449×C14911yescharacteristic
515C2C2×#454×C14911yescharacteristic
516C2#3027×C14911yescharacteristic
subgroupG/H
center, socleC22×C149C2×#120
commutator, Frattini, cosocleC22×C4C24×C149
prime radical#3205×C149C2
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
1. #3507×C149C2semidirect
2. #3208×C149C2semidirect
4. #2548×C149C2semidirect
5. #1597×C149C2semidirect
6. #1503×C149C2semidirect
7. #1502×C149C2semidirect
8. #1461×C149C2semidirect
258. #18391C149direct (N × H)
259. C149#18391direct (N × H)
260. #3507C2×C149semidirect
261. #3208C2×C149semidirect
263. #2548C2×C149semidirect
264. #1597C2×C149semidirect
265. #1503C2×C149semidirect
266. #1502C2×C149semidirect
267. #1461C2×C149semidirect

Maximal subgroups

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

subgroupindex
#3507×C1492
#3208×C1492
#3205×C1492
#2548×C1492
#1597×C1492
#1503×C1492
#1502×C1492
#1461×C1492
#18391149