Finite Group Databasebeta

← C149×#11070 #49190019

Subgroups — C149×#11070 #49190019

Order 38144.

1202 conjugacy classes of subgroups.

The subgroup lattice has 476 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#2315×C149C211yesmaximal, characteristic
2C2×#381×C149C212yesmaximal
3C2×#381×C149C211yesmaximal, characteristic
4C2×#342×C149C212yesmaximal
5C2×#342×C149C211yesmaximal, characteristic
6C24×C4×C149C2211yescharacteristic
7C22×C22⋊C4×C149C2212yes—
8C22×C22⋊C4×C149C2211yescharacteristic
9C22×C22⋊C4×C149C2212yes—
10C22×C22⋊C4×C149C2211yescharacteristic
11#385×C149—24no—
12#381×C149—24no—
13#381×C149—24no—
14#381×C149—22no—
15#381×C149C414yescomplemented
16#380×C149—22no—
17C2×#95×C149—24no—
18C2×#95×C149—22no—
19#342×C149—22no—
20#342×C149—24no—
21C25×C149C2311yescharacteristic
22C23×C4×C149—21no—
23C23×C4×C149—22no—
24C23×C4×C149—21no—
25C23×C4×C149—22no—
26C23×C4×C149—21no—
27C23×C4×C149—21no—
28C23×C4×C149—22no—
29C23×C4×C149—22no—
30C23×C4×C149—21no—
31C23×C4×C149—22no—
32C23×C4×C149C2×C412yes—
33C23×C4×C149D412yes—
34C23×C4×C149D414yes—
35C23×C4×C149D412yes—
36C23×C4×C149Q812yes—
37C2×C4⋊C4×C149—24no—
38C2×C22⋊C4×C149—22no—
39C2×C22⋊C4×C149—22no—
40C2×C22⋊C4×C149—22no—
41C2×C22⋊C4×C149—22no—
42C2×C22⋊C4×C149—22no—
43C2×C22⋊C4×C149—22no—
44C2×C22⋊C4×C149—22no—
45C2×C22⋊C4×C149—22no—
46C2×C22⋊C4×C149—22no—
47C2×C22⋊C4×C149—22no—
48C2×C22⋊C4×C149—21no—
49C2×C22⋊C4×C149—22no—
50C2×C22⋊C4×C149—22no—
51C2×C22⋊C4×C149—22no—
52C2×C22⋊C4×C149—22no—
53C2×C22⋊C4×C149—22no—
54C2×C22⋊C4×C149C2×C412yes—
55C2×C22⋊C4×C149C2×C412yes—
56C2×C22⋊C4×C149D414yes—
57C2×C22⋊C4×C149D412yes—
58#95×C149—216no—
59#95×C149—24no—
60#95×C149—28no—
61C24×C149—44no—
62C24×C149C22×C411yescharacteristic
63C24×C149C2×D411yescharacteristic
64C24×C149C2×D412yes—
65C24×C149C2×D411yescharacteristic
66C24×C149C2×D411yescharacteristic
67C24×C149C2×D412yes—
68C24×C149C2×Q811yescharacteristic
69C24×C149#4111yescharacteristic
70C24×C149#4111yescharacteristic
71C24×C149#4112yes—
72C24×C149#4112yes—
73C22×C4×C149—22no—
74C22×C4×C149—22no—
75C22×C4×C149—24no—
76C22×C4×C149—24no—
77C22×C4×C149—24no—
78C22×C4×C149—22no—
79C22×C4×C149—22no—
80C22×C4×C149—22no—
81C22×C4×C149—22no—
82C22×C4×C149—22no—
83C22×C4×C149—24no—
84C22×C4×C149—24no—
85C22×C4×C149—24no—
86C22×C4×C149—22no—
87C22×C4×C149—22no—
88C22×C4×C149—24no—
89C22×C4×C149—24no—
90C22×C4×C149—24no—
91C22×C4×C149—24no—
92C22×C4×C149—41no—
93C22×C4×C149—42no—
94C22×C4×C149—42no—
95C22×C4×C149—42no—
96C22×C4×C149—41no—
97C22×C4×C149—42no—
98C22×C4×C149—42no—
99C22×C4×C149—41no—
100C22×C4×C149—42no—
101C22×C4×C149—41no—
102C22×C4×C149—44no—
103C22×C4×C149—48no—
104C22×C4×C149—44no—
105C22×C4×C149—48no—
106C22×C4×C149—42no—
107C22×C4×C149—41no—
108C22×C4×C149—42no—
109C22×C4×C149—41no—
110C22×C4×C149C22⋊C414yes—
111C22×C4×C149C4⋊C414yescomplemented
112C4⋊C4×C149—84no—
113C22⋊C4×C149—24no—
114C22⋊C4×C149—24no—
115C22⋊C4×C149—24no—
116C22⋊C4×C149—24no—
117C22⋊C4×C149—24no—
118C22⋊C4×C149—42no—
119C22⋊C4×C149—42no—
120C22⋊C4×C149—42no—
121C22⋊C4×C149—42no—
122C22⋊C4×C149—42no—
123C22⋊C4×C149—42no—
124C22⋊C4×C149—42no—
125C23×C149—24no—
126C23×C149—28no—
127C23×C149—42no—
128C23×C149—42no—
129C23×C149—42no—
130C23×C149—44no—
131C23×C149—42no—
132C23×C149—44no—
133C23×C149—42no—
134C23×C149—42no—
135C23×C149—44no—
136C23×C149C2×C22⋊C411yescharacteristic
137C23×C149C2×C4⋊C411yescharacteristic
138C23×C149#11711yescharacteristic
139C23×C149C4×D412yes—
140C23×C149C4×D412yes—
141C23×C149#12012yes—
142C23×C149#12011yescharacteristic
143C23×C149#12111yescharacteristic
144C23×C149#12112yes—
145C23×C149#12112yes—
146C23×C149#12111yescharacteristic
147C23×C149#12112yes—
148C23×C149C22⋊Q811yescharacteristic
149C23×C149C22⋊Q812yes—
150C23×C149C22⋊Q811yescharacteristic
151C23×C149C22⋊Q812yes—
152C23×C149#12311yescharacteristic
153C23×C149#12312yes—
154C23×C149#12312yes—
155C23×C149#12412yes—
156C23×C149#12411yescharacteristic
157C23×C149#12612yes—
158C23×C149#12711yescharacteristic
159C2×C4×C149—24no—
160C2×C4×C149—28no—
161C2×C4×C149—24no—
162C2×C4×C149—42no—
163C2×C4×C149—44no—
164C2×C4×C149—42no—
165C2×C4×C149—42no—
166C2×C4×C149—42no—
167C2×C4×C149—44no—
168C2×C4×C149—44no—
169C2×C4×C149—42no—
170C2×C4×C149—42no—
171C2×C4×C149—44no—
172C2×C4×C149—44no—
173C2×C4×C149—44no—
174C2×C4×C149—48no—
175C2×C4×C149—48no—
176C2×C4×C149—42no—
177C2×C4×C149—44no—
178C2×C4×C149—44no—
179C2×C4×C149—48no—
180C2×C4×C149—82no—
181C2×C4×C149—84no—
182C2×C4×C149—82no—
183C2×C4×C149—82no—
184C2×C4×C149—84no—
185C2×C4×C149—84no—
186C22×C149—22no—
187C22×C149—24no—
188C22×C149—22no—
189C22×C149—24no—
190C22×C149—24no—
191C22×C149—24no—
192C22×C149—22no—
193C22×C149—22no—
194C22×C149—22no—
195C22×C149—24no—
196C22×C149—22no—
197C22×C149—24no—
198C22×C149—41no—
199C22×C149—41no—
200C22×C149—42no—
201C22×C149—42no—
202C22×C149—41no—
203C22×C149—41no—
204C22×C149—42no—
205C22×C149—42no—
206C22×C149—42no—
207C22×C149—42no—
208C22×C149#38011yescharacteristic
209C22×C149#38512yes—
210C22×C149#38611yescharacteristic
211C22×C149#38812yes—
212C22×C149#39011yescharacteristic
213C22×C149#39211yescharacteristic
214C22×C149#39311yescharacteristic
215C22×C149#39412yes—
216C22×C149#39612yes—
217C22×C149#39711yescharacteristic
218C22×C149#39911yescharacteristic
219C22×C149#45814yes—
220C4×C149—44no—
221C4×C149—44no—
222C4×C149—82no—
223C4×C149—84no—
224C4×C149—84no—
225C2×C149—21no—
226C2×C149—22no—
227C2×C149—21no—
228C2×C149—22no—
229C2×C149—22no—
230C2×C149—22no—
231C2×C149—21no—
232C2×C149—21no—
233C2×C149#143911yescharacteristic
234C2×C149#189012yes—
235C2×C149#202212yes—
236C2×C149#203012yes—
237#11070C14911yesmaximal, characteristic, direct product factor, Sylow
238C149#1107011yescharacteristic, direct product factor, Sylow
239#2315C2×C14911yescharacteristic
240C2×#381C2×C14912yes—
241C2×#381C2×C14911yescharacteristic
242C2×#342C2×C14912yes—
243C2×#342C2×C14911yescharacteristic
244C24×C4C22×C14911yescharacteristic
245C22×C22⋊C4C22×C14912yes—
246C22×C22⋊C4C22×C14911yescharacteristic
247C22×C22⋊C4C22×C14912yes—
248C22×C22⋊C4C22×C14911yescharacteristic
249#385—24no—
250#381—24no—
251#381—24no—
252#381—22no—
253#381C4×C14914yescomplemented
254#380—22no—
255C2×#95—24no—
256C2×#95—22no—
257#342—22no—
258#342—24no—
259C25C23×C14911yescharacteristic
260C23×C4—21no—
261C23×C4—22no—
262C23×C4—21no—
263C23×C4—22no—
264C23×C4—21no—
265C23×C4—21no—
266C23×C4—22no—
267C23×C4—22no—
268C23×C4—21no—
269C23×C4—22no—
270C23×C4C2×C4×C14912yes—
271C23×C4D4×C14912yes—
272C23×C4D4×C14914yes—
273C23×C4D4×C14912yes—
274C23×C4Q8×C14912yes—
275C2×C4⋊C4—24no—
276C2×C22⋊C4—22no—
277C2×C22⋊C4—22no—
278C2×C22⋊C4—22no—
279C2×C22⋊C4—22no—
280C2×C22⋊C4—22no—
281C2×C22⋊C4—22no—
282C2×C22⋊C4—22no—
283C2×C22⋊C4—22no—
284C2×C22⋊C4—22no—
285C2×C22⋊C4—22no—
286C2×C22⋊C4—22no—
287C2×C22⋊C4—21no—
288C2×C22⋊C4—22no—
289C2×C22⋊C4—22no—
290C2×C22⋊C4—22no—
291C2×C22⋊C4—22no—
292C2×C22⋊C4C2×C4×C14912yes—
293C2×C22⋊C4C2×C4×C14912yes—
294C2×C22⋊C4D4×C14914yes—
295C2×C22⋊C4D4×C14912yes—
296#95—216no—
297#95—24no—
298#95—28no—
299C24—44no—
300C24C22×C4×C14911yescharacteristic
301C24C2×D4×C14911yescharacteristic
302C24C2×D4×C14912yes—
303C24C2×D4×C14911yescharacteristic
304C24C2×D4×C14911yescharacteristic
305C24C2×D4×C14912yes—
306C24C2×Q8×C14911yescharacteristic
307C24#41×C14911yescharacteristic
308C24#41×C14911yescharacteristic
309C24#41×C14912yes—
310C24#41×C14912yes—
311C22×C4—22no—
312C22×C4—22no—
313C22×C4—24no—
314C22×C4—24no—
315C22×C4—24no—
316C22×C4—22no—
317C22×C4—22no—
318C22×C4—22no—
319C22×C4—22no—
320C22×C4—22no—
321C22×C4—24no—
322C22×C4—24no—
323C22×C4—24no—
324C22×C4—22no—
325C22×C4—22no—
326C22×C4—24no—
327C22×C4—24no—
328C22×C4—24no—
329C22×C4—24no—
330C22×C4—41no—
331C22×C4—42no—
332C22×C4—42no—
333C22×C4—42no—
334C22×C4—41no—
335C22×C4—42no—
336C22×C4—42no—
337C22×C4—41no—
338C22×C4—42no—
339C22×C4—41no—
340C22×C4—44no—
341C22×C4—48no—
342C22×C4—48no—
343C22×C4—44no—
344C22×C4—42no—
345C22×C4—41no—
346C22×C4—42no—
347C22×C4—41no—
348C22×C4C22⋊C4×C14914yes—
349C22×C4C4⋊C4×C14914yescomplemented
350C4⋊C4—84no—
351C22⋊C4—24no—
352C22⋊C4—24no—
353C22⋊C4—24no—
354C22⋊C4—24no—
355C22⋊C4—24no—
356C22⋊C4—42no—
357C22⋊C4—42no—
358C22⋊C4—42no—
359C22⋊C4—42no—
360C22⋊C4—42no—
361C22⋊C4—42no—
362C22⋊C4—42no—
363C23—28no—
364C23—24no—
365C23—42no—
366C23—42no—
367C23—44no—
368C23—42no—
369C23—42no—
370C23—42no—
371C23—42no—
372C23—44no—
373C23—44no—
374C23C2×C22⋊C4×C14911yescharacteristic
375C23C2×C4⋊C4×C14911yescharacteristic
376C23#117×C14911yescharacteristic
377C23C4×D4×C14912yes—
378C23C4×D4×C14912yes—
379C23#120×C14912yes—
380C23#120×C14911yescharacteristic
381C23#121×C14911yescharacteristic
382C23#121×C14912yes—
383C23#121×C14912yes—
384C23#121×C14911yescharacteristic
385C23#121×C14912yes—
386C23C22⋊Q8×C14911yescharacteristic
387C23C22⋊Q8×C14912yes—
388C23C22⋊Q8×C14911yescharacteristic
389C23C22⋊Q8×C14912yes—
390C23#123×C14911yescharacteristic
391C23#123×C14912yes—
392C23#123×C14912yes—
393C23#124×C14912yes—
394C23#124×C14911yescharacteristic
395C23#126×C14912yes—
396C23#127×C14911yescharacteristic
397C2×C4—24no—
398C2×C4—28no—
399C2×C4—24no—
400C2×C4—42no—
401C2×C4—44no—
402C2×C4—42no—
403C2×C4—42no—
404C2×C4—42no—
405C2×C4—44no—
406C2×C4—44no—
407C2×C4—42no—
408C2×C4—42no—
409C2×C4—44no—
410C2×C4—44no—
411C2×C4—48no—
412C2×C4—44no—
413C2×C4—48no—
414C2×C4—42no—
415C2×C4—44no—
416C2×C4—44no—
417C2×C4—48no—
418C2×C4—82no—
419C2×C4—82no—
420C2×C4—82no—
421C2×C4—84no—
422C2×C4—84no—
423C2×C4—84no—
424C22—24no—
425C22—24no—
426C22—22no—
427C22—22no—
428C22—22no—
429C22—24no—
430C22—22no—
431C22—24no—
432C22—22no—
433C22—24no—
434C22—22no—
435C22—24no—
436C22—41no—
437C22—41no—
438C22—42no—
439C22—42no—
440C22—41no—
441C22—41no—
442C22—42no—
443C22—42no—
444C22—42no—
445C22—42no—
446C22#380×C14911yescharacteristic
447C22#385×C14912yes—
448C22#386×C14911yescharacteristic
449C22#388×C14912yes—
450C22#390×C14911yescharacteristic
451C22#392×C14911yescharacteristic
452C22#393×C14911yescharacteristic
453C22#394×C14912yes—
454C22#396×C14912yes—
455C22#397×C14911yescharacteristic
456C22#399×C14911yescharacteristic
457C22#458×C14914yes—
458C4—44no—
459C4—44no—
460C4—82no—
461C4—84no—
462C4—84no—
463C2—21no—
464C2—22no—
465C2—21no—
466C2—22no—
467C2—22no—
468C2—22no—
469C2—21no—
470C2—21no—
471C2#1439×C14911yescharacteristic
472C2#1890×C14912yes—
473C2#2022×C14912yes—
474C2#2030×C14912yes—
subgroupG/H
center, socleC23×C149#120
commutatorC24C22×C4×C149
Frattini, cosocleC25C23×C149
prime radicalC25×C149C23
LCSG ▷ C24 ▷ C2 ▷ C1
UCSC1 ◁ C23×C149 ◁ C25×C149 ◁ G

Complements

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

NH ≅ G/Ntype
15. #381×C149C4semidirect
111. C22×C4×C149C4⋊C4semidirect
237. #11070C149direct (N × H)
238. C149#11070direct (N × H)
253. #381C4×C149semidirect
349. C22×C4C4⋊C4×C149semidirect

Maximal subgroups

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

subgroupindex
#2315×C1492
C2×#381×C1492
C2×#342×C1492
#11070149