Finite Group Databasebeta

← C149×#18399 #49197348

Subgroups — C149×#18399 #49197348

Order 38144.

894 conjugacy classes of subgroups.

The subgroup lattice has 478 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#3507×C149C211yesmaximal, characteristic
2#3230×C149C211yesmaximal, characteristic, complemented
3#3227×C149C211yesmaximal, characteristic
4#2568×C149C211yesmaximal, characteristic, complemented
5#1615×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#500×C149—21no—
24#498×C149—21no—
25#487×C149—21no—
26#486×C149—21no—
27#484×C149C2214yes—
28#481×C149C2214yes—
29#477×C149—22no—
30#476×C149—22no—
31#431×C149C2211yescharacteristic
32#431×C149C2211yescharacteristic
33#400×C149C2214yes—
34#391×C149—21no—
35#391×C149—22no—
36#382×C149—21no—
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×C149D411yescharacteristic
50C4⋊Q8×C149D411yescharacteristic
51C4⋊Q8×C149D411yescharacteristic
52#127×C149D411yescharacteristic
53#126×C149—24no—
54#126×C149—24no—
55#125×C149—22no—
56#125×C149—24no—
57#125×C149—21no—
58#124×C149—22no—
59#124×C149—22no—
60#124×C149—21no—
61#123×C149—24no—
62#123×C149—24no—
63C22⋊Q8×C149—22no—
64C22⋊Q8×C149—22no—
65C22⋊Q8×C149—24no—
66C22⋊Q8×C149—21no—
67C22⋊Q8×C149C2312yes—
68#121×C149—21no—
69#121×C149C2312yes—
70C4×Q8×C149—22no—
71C4×Q8×C149—22no—
72C4×Q8×C149—21no—
73C4×Q8×C149—21no—
74C4×Q8×C149—21no—
75C4×Q8×C149—21no—
76C4×Q8×C149—21no—
77C4×Q8×C149D412yes—
78C4×D4×C149—22no—
79C4×D4×C149—22no—
80C4×D4×C149—24no—
81C4×D4×C149—21no—
82C4×D4×C149D412yes—
83#117×C149—22no—
84#117×C149—24no—
85#117×C149—21no—
86C2×C4⋊C4×C149—22no—
87C2×C4⋊C4×C149—21no—
88C2×C4⋊C4×C149—21no—
89C2×C4⋊C4×C149D411yescharacteristic
90C2×C4⋊C4×C149C2312yes—
91C2×C4⋊C4×C149C2312yes—
92C2×C42×C149—21no—
93C2×C42×C149D412yes—
94C2×C42×C149C2311yescharacteristic
95#107×C149—24no—
96#106×C149—24no—
97C4⋊C8×C149—21no—
98C4⋊C8×C149—21no—
99#103×C149—24no—
100#102×C149—24no—
101C22⋊C8×C149C2312yes—
102C22⋊C8×C149C2312yes—
103C4×C8×C149—21no—
104C4×C8×C149—21no—
105#95×C149—24no—
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—44no—
117C2×Q8×C149—41no—
118C2×Q8×C149—41no—
119C2×Q8×C149C2×D412yes—
120C2×D4×C149—22no—
121C2×D4×C149—21no—
122C2×D4×C149—21no—
123C2×D4×C149C2×D412yes—
124C22×C4×C149—24no—
125C22×C4×C149—22no—
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
133C2×C8×C149—22no—
134C2×C8×C149—22no—
135C4⋊C4×C149—24no—
136C4⋊C4×C149—24no—
137C4⋊C4×C149—24no—
138C4⋊C4×C149—21no—
139C4⋊C4×C149—21no—
140C4⋊C4×C149—21no—
141C4⋊C4×C149—21no—
142C4⋊C4×C149—22no—
143C4⋊C4×C149—21no—
144C4⋊C4×C149—21no—
145C4⋊C4×C149—22no—
146C4⋊C4×C149—22no—
147C4⋊C4×C149—22no—
148C4⋊C4×C149—22no—
149C4⋊C4×C149—22no—
150C4⋊C4×C149—42no—
151C4⋊C4×C149—41no—
152C4⋊C4×C149—41no—
153C4⋊C4×C149C2×D412yes—
154C4⋊C4×C149C2×D412yes—
155C22⋊C4×C149—24no—
156C22⋊C4×C149—24no—
157C22⋊C4×C149—24no—
158C22⋊C4×C149—22no—
159C22⋊C4×C149—22no—
160C22⋊C4×C149—22no—
161C42×C149—24no—
162C42×C149—22no—
163C42×C149—22no—
164C42×C149—22no—
165C42×C149—42no—
166C42×C149C2×D411yescharacteristic
167C42×C149C2×D411yescharacteristic
168C42×C149C2×D411yescharacteristic
169C42×C149C2×D411yescharacteristic
170C23×C149—22no—
171C23×C149C22×D411yescharacteristic
172Q8×C149—42no—
173Q8×C149—42no—
174Q8×C149—42no—
175Q8×C149—42no—
176Q8×C149—42no—
177Q8×C149—82no—
178Q8×C149—82no—
179D4×C149—42no—
180D4×C149—42no—
181D4×C149—42no—
182D4×C149—42no—
183D4×C149—42no—
184C2×C4×C149—22no—
185C2×C4×C149—22no—
186C2×C4×C149—22no—
187C2×C4×C149—22no—
188C2×C4×C149—22no—
189C2×C4×C149—22no—
190C2×C4×C149—22no—
191C2×C4×C149—22no—
192C2×C4×C149—41no—
193C2×C4×C149—44no—
194C2×C4×C149—42no—
195C2×C4×C149—42no—
196C2×C4×C149—42no—
197C2×C4×C149—44no—
198C2×C4×C149—42no—
199C2×C4×C149—42no—
200C2×C4×C149—84no—
201C2×C4×C149#12011yescharacteristic
202C2×C4×C149#12011yescharacteristic
203C2×C4×C149#12011yescharacteristic
204C2×C4×C149#12011yescharacteristic
205C2×C4×C149#13512yes—
206C2×C4×C149#13712yes—
207C2×C4×C149C22×D411yescharacteristic
208C2×C4×C149C22×D411yescharacteristic
209C8×C149—42no—
210C8×C149—42no—
211C22×C149—21no—
212C22×C149—21no—
213C22×C149—42no—
214C22×C149—42no—
215C22×C149—42no—
216C22×C149C2×#12011yescharacteristic
217C22×C149C2×#13511yescharacteristic
218C22×C149C2×#13711yescharacteristic
219C4×C149—21no—
220C4×C149—21no—
221C4×C149—21no—
222C4×C149—42no—
223C4×C149—42no—
224C4×C149—42no—
225C4×C149—42no—
226C4×C149—42no—
227C4×C149—82no—
228C4×C149—82no—
229C4×C149#45212yes—
230C4×C149#45212yes—
231C4×C149#45412yes—
232C2×C149—21no—
233C2×C149—21no—
234C2×C149—82no—
235C2×C149C2×#45211yescharacteristic
236C2×C149C2×#45411yescharacteristic
237C2×C149#302811yescharacteristic
238#18399C14911yesmaximal, characteristic, direct product factor, Sylow
239C149#1839911yescharacteristic, direct product factor, Sylow
240#3507C2×C14911yescharacteristic
241#3230C2×C14911yescharacteristic, complemented
242#3227C2×C14911yescharacteristic
243#2568C2×C14911yescharacteristic, complemented
244#1615C2×C14918yescomplemented
245#1503C2×C14911yescharacteristic, complemented
246#1502C2×C14911yescharacteristic
247#1461C2×C14911yescharacteristic, complemented
248#559—21no—
249#557—21no—
250#556—21no—
251#556—22no—
252#554—21no—
253#552—22no—
254#539C22×C14914yes—
255#536—21no—
256#533C22×C14911yescharacteristic
257#532C22×C14911yescharacteristic
258C2×C4⋊Q8C22×C14911yescharacteristic
259#529—22no—
260#520—21no—
261C2×C4×Q8C22×C14911yescharacteristic
262#500—21no—
263#498—21no—
264#487—21no—
265#486—21no—
266#484C22×C14914yes—
267#481C22×C14914yes—
268#477—22no—
269#476—22no—
270#431C22×C14911yescharacteristic
271#431C22×C14911yescharacteristic
272#400C22×C14914yes—
273#391—21no—
274#391—22no—
275#382—21no—
276C4×C4⋊C4C22×C14911yescharacteristic
277#328C22×C14914yes—
278#327C22×C14914yes—
279#324C22×C14914yes—
280C2×#41—21no—
281C22×Q8—21no—
282C22×Q8D4×C14911yescharacteristic
283C4⋊Q8—22no—
284C4⋊Q8—21no—
285C4⋊Q8—21no—
286C4⋊Q8—21no—
287C4⋊Q8—21no—
288C4⋊Q8D4×C14911yescharacteristic
289C4⋊Q8D4×C14911yescharacteristic
290C4⋊Q8D4×C14911yescharacteristic
291#127D4×C14911yescharacteristic
292#126—24no—
293#126—24no—
294#125—22no—
295#125—24no—
296#125—21no—
297#124—22no—
298#124—22no—
299#124—21no—
300#123—24no—
301#123—24no—
302C22⋊Q8—22no—
303C22⋊Q8—22no—
304C22⋊Q8—24no—
305C22⋊Q8—21no—
306C22⋊Q8C23×C14912yes—
307#121—21no—
308#121C23×C14912yes—
309C4×Q8—22no—
310C4×Q8—22no—
311C4×Q8—21no—
312C4×Q8—21no—
313C4×Q8—21no—
314C4×Q8—21no—
315C4×Q8—21no—
316C4×Q8D4×C14912yes—
317C4×D4—22no—
318C4×D4—22no—
319C4×D4—24no—
320C4×D4—21no—
321C4×D4D4×C14912yes—
322#117—22no—
323#117—24no—
324#117—21no—
325C2×C4⋊C4—22no—
326C2×C4⋊C4—21no—
327C2×C4⋊C4—21no—
328C2×C4⋊C4D4×C14911yescharacteristic
329C2×C4⋊C4C23×C14912yes—
330C2×C4⋊C4C23×C14912yes—
331C2×C42—21no—
332C2×C42D4×C14912yes—
333C2×C42C23×C14911yescharacteristic
334#107—24no—
335#106—24no—
336C4⋊C8—21no—
337C4⋊C8—21no—
338#103—24no—
339#102—24no—
340C22⋊C8C23×C14912yes—
341C22⋊C8C23×C14912yes—
342C4×C8—21no—
343C4×C8—21no—
344#95—24no—
345#95—24no—
346#95C23×C14912yes—
347#41—42no—
348#41—42no—
349C2×Q8—21no—
350C2×Q8—21no—
351C2×Q8—21no—
352C2×Q8—21no—
353C2×Q8—22no—
354C2×Q8—22no—
355C2×Q8—44no—
356C2×Q8—41no—
357C2×Q8—41no—
358C2×Q8C2×D4×C14912yes—
359C2×D4—22no—
360C2×D4—21no—
361C2×D4—21no—
362C2×D4C2×D4×C14912yes—
363C22×C4—24no—
364C22×C4—22no—
365C22×C4—22no—
366C22×C4—22no—
367C22×C4C2×D4×C14912yes—
368C22×C4C2×D4×C14911yescharacteristic
369C22×C4C2×D4×C14912yes—
370C22×C4C2×D4×C14911yescharacteristic
371C22×C4C24×C14911yescharacteristic
372C2×C8—22no—
373C2×C8—22no—
374C4⋊C4—24no—
375C4⋊C4—24no—
376C4⋊C4—24no—
377C4⋊C4—21no—
378C4⋊C4—21no—
379C4⋊C4—21no—
380C4⋊C4—21no—
381C4⋊C4—22no—
382C4⋊C4—21no—
383C4⋊C4—21no—
384C4⋊C4—22no—
385C4⋊C4—22no—
386C4⋊C4—22no—
387C4⋊C4—22no—
388C4⋊C4—22no—
389C4⋊C4—42no—
390C4⋊C4—41no—
391C4⋊C4—41no—
392C4⋊C4C2×D4×C14912yes—
393C4⋊C4C2×D4×C14912yes—
394C22⋊C4—24no—
395C22⋊C4—24no—
396C22⋊C4—24no—
397C22⋊C4—22no—
398C22⋊C4—22no—
399C22⋊C4—22no—
400C42—24no—
401C42—22no—
402C42—22no—
403C42—22no—
404C42—42no—
405C42C2×D4×C14911yescharacteristic
406C42C2×D4×C14911yescharacteristic
407C42C2×D4×C14911yescharacteristic
408C42C2×D4×C14911yescharacteristic
409C23—22no—
410C23C22×D4×C14911yescharacteristic
411Q8—42no—
412Q8—42no—
413Q8—42no—
414Q8—42no—
415Q8—42no—
416Q8—82no—
417Q8—82no—
418D4—42no—
419D4—42no—
420D4—42no—
421D4—42no—
422D4—42no—
423C2×C4—22no—
424C2×C4—22no—
425C2×C4—22no—
426C2×C4—22no—
427C2×C4—22no—
428C2×C4—22no—
429C2×C4—22no—
430C2×C4—22no—
431C2×C4—41no—
432C2×C4—44no—
433C2×C4—42no—
434C2×C4—42no—
435C2×C4—42no—
436C2×C4—44no—
437C2×C4—42no—
438C2×C4—42no—
439C2×C4—84no—
440C2×C4#120×C14911yescharacteristic
441C2×C4#120×C14911yescharacteristic
442C2×C4#120×C14911yescharacteristic
443C2×C4#120×C14911yescharacteristic
444C2×C4#135×C14912yes—
445C2×C4#137×C14912yes—
446C2×C4C22×D4×C14911yescharacteristic
447C2×C4C22×D4×C14911yescharacteristic
448C8—42no—
449C8—42no—
450C22—21no—
451C22—21no—
452C22—42no—
453C22—42no—
454C22—42no—
455C22C2×#120×C14911yescharacteristic
456C22C2×#135×C14911yescharacteristic
457C22C2×#137×C14911yescharacteristic
458C4—21no—
459C4—21no—
460C4—21no—
461C4—42no—
462C4—42no—
463C4—42no—
464C4—42no—
465C4—42no—
466C4—82no—
467C4—82no—
468C4#452×C14912yes—
469C4#452×C14912yes—
470C4#454×C14912yes—
471C2—21no—
472C2—21no—
473C2—82no—
474C2C2×#452×C14911yescharacteristic
475C2C2×#454×C14911yescharacteristic
476C2#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. #3230×C149C2semidirect
4. #2568×C149C2semidirect
5. #1615×C149C2semidirect
6. #1503×C149C2semidirect
8. #1461×C149C2semidirect
238. #18399C149direct (N × H)
239. C149#18399direct (N × H)
241. #3230C2×C149semidirect
243. #2568C2×C149semidirect
244. #1615C2×C149semidirect
245. #1503C2×C149semidirect
247. #1461C2×C149semidirect

Maximal subgroups

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

subgroupindex
#3507×C1492
#3230×C1492
#3227×C1492
#2568×C1492
#1615×C1492
#1503×C1492
#1502×C1492
#1461×C1492
#18399149