Finite Group Databasebeta

← C149×#18392 #49197341

Subgroups — C149×#18392 #49197341

Order 38144.

934 conjugacy classes of subgroups.

The subgroup lattice has 484 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#3507×C149C211yesmaximal, characteristic
2#3209×C149C211yesmaximal, characteristic, complemented
3#3206×C149C211yesmaximal, characteristic
4#2567×C149C211yesmaximal, characteristic, complemented
5#1603×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×C149C2211yescharacteristic
20#529×C149—22no—
21#520×C149—21no—
22C2×C4×Q8×C149C2211yescharacteristic
23#494×C149—21no—
24#492×C149—21no—
25#487×C149—21no—
26#487×C149—21no—
27#462×C149—22no—
28#461×C149—22no—
29#451×C149C2214yes—
30#448×C149C2214yes—
31#431×C149C2211yescharacteristic
32#431×C149C2211yescharacteristic
33#395×C149C2214yes—
34#391×C149—21no—
35#389×C149—22no—
36#384×C149—21no—
37C4×C4⋊C4×C149C2211yescharacteristic
38#328×C149C2214yes—
39#327×C149C2214yes—
40#324×C149C2214yes—
41C2×#41×C149—21no—
42C22×Q8×C149D411yescharacteristic
43C22×Q8×C149C2312yes—
44C2×Q16×C149—24no—
45C2×SD16×C149—24no—
46C4⋊Q8×C149—22no—
47C4⋊Q8×C149—21no—
48C4⋊Q8×C149—21no—
49C4⋊Q8×C149—21no—
50C4⋊Q8×C149—21no—
51C4⋊Q8×C149D411yescharacteristic
52C4⋊Q8×C149D411yescharacteristic
53C4⋊Q8×C149D411yescharacteristic
54#127×C149D411yescharacteristic
55#126×C149—24no—
56#126×C149—24no—
57#125×C149—22no—
58#125×C149—24no—
59#125×C149—21no—
60#124×C149—22no—
61#124×C149—22no—
62#124×C149—21no—
63#123×C149—24no—
64#123×C149—24no—
65C22⋊Q8×C149—22no—
66C22⋊Q8×C149—22no—
67C22⋊Q8×C149—24no—
68C22⋊Q8×C149—21no—
69C22⋊Q8×C149C2312yes—
70#121×C149—21no—
71#121×C149C2312yes—
72C4×Q8×C149—22no—
73C4×Q8×C149—22no—
74C4×Q8×C149—21no—
75C4×Q8×C149—21no—
76C4×Q8×C149—21no—
77C4×Q8×C149—21no—
78C4×Q8×C149—21no—
79C4×Q8×C149D412yes—
80C4×D4×C149—22no—
81C4×D4×C149—22no—
82C4×D4×C149—24no—
83C4×D4×C149—21no—
84C4×D4×C149D412yes—
85#117×C149—22no—
86#117×C149—24no—
87#117×C149—21no—
88C2×C4⋊C4×C149—22no—
89C2×C4⋊C4×C149—21no—
90C2×C4⋊C4×C149—21no—
91C2×C4⋊C4×C149—21no—
92C2×C4⋊C4×C149—24no—
93C2×C4⋊C4×C149D411yescharacteristic
94C2×C4⋊C4×C149C2312yes—
95C2×C42×C149—21no—
96C2×C42×C149D412yes—
97C2×C42×C149C2311yescharacteristic
98C4⋊C8×C149—21no—
99C4⋊C8×C149—21no—
100#103×C149—24no—
101#103×C149—24no—
102C22⋊C8×C149C2312yes—
103C22⋊C8×C149C2312yes—
104C4×C8×C149—21no—
105C4×C8×C149—21no—
106#95×C149—24no—
107#95×C149C2312yes—
108#41×C149—42no—
109#41×C149—42no—
110C2×Q8×C149—21no—
111C2×Q8×C149—21no—
112C2×Q8×C149—21no—
113C2×Q8×C149—21no—
114C2×Q8×C149—22no—
115C2×Q8×C149—22no—
116C2×Q8×C149—22no—
117C2×Q8×C149—22no—
118C2×Q8×C149—82no—
119C2×Q8×C149C2×D412yes—
120C2×D4×C149—22no—
121C2×D4×C149—21no—
122C2×D4×C149—21no—
123C2×D4×C149C2×D412yes—
124C22×C4×C149—22no—
125C22×C4×C149—24no—
126C22×C4×C149—22no—
127C22×C4×C149—22no—
128C22×C4×C149C2×D412yes—
129C22×C4×C149C2×D411yescharacteristic
130C22×C4×C149C2×D412yes—
131C22×C4×C149C2×D411yescharacteristic
132C22×C4×C149C2411yescharacteristic
133Q16×C149—84no—
134SD16×C149—84no—
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—41no—
152C4⋊C4×C149—41no—
153C4⋊C4×C149—41no—
154C4⋊C4×C149—41no—
155C4⋊C4×C149—84no—
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—44no—
177Q8×C149—44no—
178Q8×C149—42no—
179Q8×C149—42no—
180Q8×C149—42no—
181Q8×C149—42no—
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—44no—
202C2×C4×C149—42no—
203C2×C4×C149—84no—
204C2×C4×C149#12011yescharacteristic
205C2×C4×C149#12011yescharacteristic
206C2×C4×C149#12011yescharacteristic
207C2×C4×C149#12011yescharacteristic
208C2×C4×C149#13512yes—
209C2×C4×C149#13712yes—
210C2×C4×C149C22×D411yescharacteristic
211C2×C4×C149C22×D411yescharacteristic
212C8×C149—42no—
213C8×C149—42no—
214C22×C149—21no—
215C22×C149—21no—
216C22×C149—42no—
217C22×C149—42no—
218C22×C149—42no—
219C22×C149C2×#12011yescharacteristic
220C22×C149C2×#13511yescharacteristic
221C22×C149C2×#13711yescharacteristic
222C4×C149—21no—
223C4×C149—21no—
224C4×C149—21no—
225C4×C149—44no—
226C4×C149—42no—
227C4×C149—42no—
228C4×C149—42no—
229C4×C149—42no—
230C4×C149—42no—
231C4×C149—82no—
232C4×C149#45212yes—
233C4×C149#45212yes—
234C4×C149#45612yes—
235C2×C149—21no—
236C2×C149—21no—
237C2×C149—82no—
238C2×C149C2×#45211yescharacteristic
239C2×C149C2×#45611yescharacteristic
240C2×C149#302711yescharacteristic
241#18392C14911yesmaximal, characteristic, direct product factor, Sylow
242C149#1839211yescharacteristic, direct product factor, Sylow
243#3507C2×C14911yescharacteristic
244#3209C2×C14911yescharacteristic, complemented
245#3206C2×C14911yescharacteristic
246#2567C2×C14911yescharacteristic, complemented
247#1603C2×C14918yescomplemented
248#1503C2×C14911yescharacteristic, complemented
249#1502C2×C14911yescharacteristic
250#1461C2×C14911yescharacteristic, complemented
251#559—21no—
252#557—21no—
253#556—21no—
254#556—22no—
255#554—21no—
256#552—22no—
257#539C22×C14914yes—
258#536—21no—
259#533C22×C14911yescharacteristic
260#532C22×C14911yescharacteristic
261C2×C4⋊Q8C22×C14911yescharacteristic
262#529—22no—
263#520—21no—
264C2×C4×Q8C22×C14911yescharacteristic
265#494—21no—
266#492—21no—
267#487—21no—
268#487—21no—
269#462—22no—
270#461—22no—
271#451C22×C14914yes—
272#448C22×C14914yes—
273#431C22×C14911yescharacteristic
274#431C22×C14911yescharacteristic
275#395C22×C14914yes—
276#391—21no—
277#389—22no—
278#384—21no—
279C4×C4⋊C4C22×C14911yescharacteristic
280#328C22×C14914yes—
281#327C22×C14914yes—
282#324C22×C14914yes—
283C2×#41—21no—
284C22×Q8D4×C14911yescharacteristic
285C22×Q8C23×C14912yes—
286C2×Q16—24no—
287C2×SD16—24no—
288C4⋊Q8—22no—
289C4⋊Q8—21no—
290C4⋊Q8—21no—
291C4⋊Q8—21no—
292C4⋊Q8—21no—
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—21no—
333C2×C4⋊C4—21no—
334C2×C4⋊C4—24no—
335C2×C4⋊C4D4×C14911yescharacteristic
336C2×C4⋊C4C23×C14912yes—
337C2×C42—21no—
338C2×C42D4×C14912yes—
339C2×C42C23×C14911yescharacteristic
340C4⋊C8—21no—
341C4⋊C8—21no—
342#103—24no—
343#103—24no—
344C22⋊C8C23×C14912yes—
345C22⋊C8C23×C14912yes—
346C4×C8—21no—
347C4×C8—21no—
348#95—24no—
349#95C23×C14912yes—
350#41—42no—
351#41—42no—
352C2×Q8—21no—
353C2×Q8—21no—
354C2×Q8—21no—
355C2×Q8—21no—
356C2×Q8—22no—
357C2×Q8—22no—
358C2×Q8—22no—
359C2×Q8—22no—
360C2×Q8—82no—
361C2×Q8C2×D4×C14912yes—
362C2×D4—22no—
363C2×D4—21no—
364C2×D4—21no—
365C2×D4C2×D4×C14912yes—
366C22×C4—22no—
367C22×C4—24no—
368C22×C4—22no—
369C22×C4—22no—
370C22×C4C2×D4×C14912yes—
371C22×C4C2×D4×C14911yescharacteristic
372C22×C4C2×D4×C14912yes—
373C22×C4C2×D4×C14911yescharacteristic
374C22×C4C24×C14911yescharacteristic
375Q16—84no—
376SD16—84no—
377C2×C8—22no—
378C2×C8—22no—
379C4⋊C4—24no—
380C4⋊C4—24no—
381C4⋊C4—24no—
382C4⋊C4—24no—
383C4⋊C4—21no—
384C4⋊C4—21no—
385C4⋊C4—21no—
386C4⋊C4—21no—
387C4⋊C4—22no—
388C4⋊C4—21no—
389C4⋊C4—21no—
390C4⋊C4—22no—
391C4⋊C4—22no—
392C4⋊C4—22no—
393C4⋊C4—41no—
394C4⋊C4—41no—
395C4⋊C4—41no—
396C4⋊C4—41no—
397C4⋊C4—84no—
398C4⋊C4C2×D4×C14912yes—
399C4⋊C4C2×D4×C14912yes—
400C22⋊C4—24no—
401C22⋊C4—24no—
402C22⋊C4—24no—
403C22⋊C4—22no—
404C22⋊C4—22no—
405C22⋊C4—22no—
406C42—24no—
407C42—22no—
408C42—22no—
409C42—22no—
410C42—42no—
411C42C2×D4×C14911yescharacteristic
412C42C2×D4×C14911yescharacteristic
413C42C2×D4×C14911yescharacteristic
414C42C2×D4×C14911yescharacteristic
415C23—22no—
416C23C22×D4×C14911yescharacteristic
417Q8—42no—
418Q8—44no—
419Q8—44no—
420Q8—42no—
421Q8—42no—
422Q8—42no—
423Q8—42no—
424D4—42no—
425D4—42no—
426D4—42no—
427D4—42no—
428D4—42no—
429C2×C4—22no—
430C2×C4—24no—
431C2×C4—22no—
432C2×C4—22no—
433C2×C4—22no—
434C2×C4—22no—
435C2×C4—22no—
436C2×C4—22no—
437C2×C4—22no—
438C2×C4—41no—
439C2×C4—42no—
440C2×C4—42no—
441C2×C4—44no—
442C2×C4—42no—
443C2×C4—44no—
444C2×C4—42no—
445C2×C4—84no—
446C2×C4#120×C14911yescharacteristic
447C2×C4#120×C14911yescharacteristic
448C2×C4#120×C14911yescharacteristic
449C2×C4#120×C14911yescharacteristic
450C2×C4#135×C14912yes—
451C2×C4#137×C14912yes—
452C2×C4C22×D4×C14911yescharacteristic
453C2×C4C22×D4×C14911yescharacteristic
454C8—42no—
455C8—42no—
456C22—21no—
457C22—21no—
458C22—42no—
459C22—42no—
460C22—42no—
461C22C2×#120×C14911yescharacteristic
462C22C2×#135×C14911yescharacteristic
463C22C2×#137×C14911yescharacteristic
464C4—21no—
465C4—21no—
466C4—21no—
467C4—44no—
468C4—42no—
469C4—42no—
470C4—42no—
471C4—42no—
472C4—42no—
473C4—82no—
474C4#452×C14912yes—
475C4#452×C14912yes—
476C4#456×C14912yes—
477C2—21no—
478C2—21no—
479C2—82no—
480C2C2×#452×C14911yescharacteristic
481C2C2×#456×C14911yescharacteristic
482C2#3027×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. #3209×C149C2semidirect
4. #2567×C149C2semidirect
5. #1603×C149C2semidirect
6. #1503×C149C2semidirect
8. #1461×C149C2semidirect
241. #18392C149direct (N × H)
242. C149#18392direct (N × H)
244. #3209C2×C149semidirect
246. #2567C2×C149semidirect
247. #1603C2×C149semidirect
248. #1503C2×C149semidirect
250. #1461C2×C149semidirect

Maximal subgroups

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

subgroupindex
#3507×C1492
#3209×C1492
#3206×C1492
#2567×C1492
#1603×C1492
#1503×C1492
#1502×C1492
#1461×C1492
#18392149