Finite Group Databasebeta

← C151×#9984 #50314909

Subgroups — C151×#9984 #50314909

Order 38656.

544 conjugacy classes of subgroups; only the 98 normal subgroups are shown.

normal subgroups only

This group has 544 conjugacy classes of subgroups — too many to draw. Only its 98 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#3095×C151C211yesmaximal, characteristic, complemented
2#3094×C151C211yesmaximal, characteristic
3#2816×C151C211yesmaximal, characteristic
4#1820×C151C211yesmaximal, characteristic, complemented
5#1511×C151C211yesmaximal, characteristic, complemented
6#1510×C151C211yesmaximal, characteristic
7#1306×C151C211yesmaximal, characteristic, complemented
8C2×C22⋊Q8×C151C2211yescharacteristic
9C2×#121×C151C2211yescharacteristic
10C2×#117×C151C2211yescharacteristic
11#485×C151—22no—
12#484×C151—21no—
13#483×C151—21no—
14#482×C151—22no—
15#481×C151—21no—
16#480×C151—21no—
17#428×C151—21no—
18#428×C151—21no—
19#419×C151—21no—
20#418×C151—21no—
21#407×C151C2211yescharacteristic
22#407×C151C2211yescharacteristic
23#399×C151—21no—
24#398×C151—21no—
25#394×C151—21no—
26#394×C151—22no—
27#393×C151—21no—
28#381×C151C2211yescharacteristic
29#381×C151C2211yescharacteristic
30#342×C151—22no—
31#328×C151—22no—
32#327×C151—22no—
33C22×Q8×C151D411yescharacteristic
34C22×D4×C151—21no—
35C22×D4×C151D411yescharacteristic
36C23×C4×C151C2311yescharacteristic
37C2×M16×C151—21no—
38C2×M16×C151—21no—
39C22⋊Q8×C151—21no—
40C22⋊Q8×C151—21no—
41C22⋊Q8×C151—21no—
42C22⋊Q8×C151—21no—
43#121×C151—21no—
44#121×C151—21no—
45#121×C151—21no—
46#121×C151—21no—
47#117×C151—21no—
48#117×C151—21no—
49#117×C151—21no—
50#117×C151—21no—
51C2×C4⋊C4×C151—21no—
52C2×C4⋊C4×C151—22no—
53C2×C4⋊C4×C151D411yescharacteristic
54C2×C4⋊C4×C151D411yescharacteristic
55C2×C4⋊C4×C151D411yescharacteristic
56C2×C4⋊C4×C151D411yescharacteristic
57C2×C22⋊C4×C151—21no—
58C2×C22⋊C4×C151—22no—
59C2×C22⋊C4×C151—22no—
60C2×C22⋊C4×C151—21no—
61C2×C22⋊C4×C151—21no—
62C2×C22⋊C4×C151—21no—
63C2×C22⋊C4×C151D412yes—
64C2×C42×C151—21no—
65#107×C151—22no—
66#107×C151—22no—
67#106×C151—22no—
68#106×C151—22no—
69#103×C151—22no—
70#103×C151—22no—
71#102×C151—22no—
72#102×C151—22no—
73C22⋊C8×C151—21no—
74C22⋊C8×C151—21no—
75C22⋊C8×C151D412yes—
76C22⋊C8×C151D412yes—
77#95×C151—22no—
78#95×C151—21no—
79#95×C151—21no—
80#95×C151—21no—
81#95×C151—21no—
82C24×C151—21no—
83C24×C151C2×D411yescharacteristic
84C2×Q8×C151—21no—
85C2×Q8×C151—21no—
86C2×Q8×C151—42no—
87C2×D4×C151—21no—
88C2×D4×C151—21no—
89C2×D4×C151—42no—
90C2×D4×C151—41no—
91C2×D4×C151—41no—
92C2×D4×C151—82no—
93C22×C4×C151—22no—
94C22×C4×C151—21no—
95C22×C4×C151—21no—
96C22×C4×C151—21no—
97C22×C4×C151—21no—
98C22×C4×C151—21no—
99C22×C4×C151—42no—
100C22×C4×C151—41no—
101C22×C4×C151C2×D411yescharacteristic
102C22×C4×C151C2×D411yescharacteristic
103C22×C4×C151C2×D411yescharacteristic
104C22×C4×C151C2×D411yescharacteristic
105C22×C4×C151C2×D411yescharacteristic
106C22×C4×C151#4111yescharacteristic
107M16×C151—42no—
108M16×C151—42no—
109C2×C8×C151—22no—
110C2×C8×C151—22no—
111C4⋊C4×C151—21no—
112C4⋊C4×C151—21no—
113C4⋊C4×C151—21no—
114C4⋊C4×C151—21no—
115C4⋊C4×C151—21no—
116C4⋊C4×C151—21no—
117C4⋊C4×C151—21no—
118C4⋊C4×C151—21no—
119C4⋊C4×C151—41no—
120C4⋊C4×C151—41no—
121C4⋊C4×C151—82no—
122C22⋊C4×C151—41no—
123C22⋊C4×C151—41no—
124C22⋊C4×C151—41no—
125C22⋊C4×C151—41no—
126C22⋊C4×C151—41no—
127C22⋊C4×C151—41no—
128C22⋊C4×C151—42no—
129C22⋊C4×C151—42no—
130C22⋊C4×C151—82no—
131C22⋊C4×C151—82no—
132C42×C151—41no—
133C42×C151—41no—
134C23×C151—22no—
135C23×C151—41no—
136C23×C151—41no—
137C23×C151—42no—
138C23×C151—42no—
139C23×C151—41no—
140C23×C151—42no—
141C23×C151#12011yescharacteristic
142C23×C151#12111yescharacteristic
143C23×C151#12711yescharacteristic
144Q8×C151—42no—
145Q8×C151—81no—
146D4×C151—42no—
147D4×C151—81no—
148D4×C151—82no—
149D4×C151—82no—
150C2×C4×C151—22no—
151C2×C4×C151—22no—
152C2×C4×C151—41no—
153C2×C4×C151—41no—
154C2×C4×C151—41no—
155C2×C4×C151—41no—
156C2×C4×C151—41no—
157C2×C4×C151—42no—
158C2×C4×C151—41no—
159C2×C4×C151—42no—
160C2×C4×C151—42no—
161C2×C4×C151—41no—
162C2×C4×C151—41no—
163C2×C4×C151—41no—
164C2×C4×C151—41no—
165C2×C4×C151—41no—
166C2×C4×C151—42no—
167C2×C4×C151—42no—
168C2×C4×C151—81no—
169C2×C4×C151—81no—
170C2×C4×C151—81no—
171C2×C4×C151—81no—
172C2×C4×C151—81no—
173C2×C4×C151#12011yescharacteristic
174C2×C4×C151#12011yescharacteristic
175C2×C4×C151#12111yescharacteristic
176C2×C4×C151#12111yescharacteristic
177C8×C151—42no—
178C8×C151—42no—
179C22×C151—21no—
180C22×C151—21no—
181C22×C151—21no—
182C22×C151—21no—
183C22×C151—21no—
184C22×C151—21no—
185C22×C151—21no—
186C22×C151—21no—
187C22×C151—82no—
188C22×C151—84no—
189C22×C151—81no—
190C22×C151—81no—
191C22×C151—81no—
192C22×C151#39211yescharacteristic
193C22×C151#45812yes—
194C4×C151—21no—
195C4×C151—21no—
196C4×C151—21no—
197C4×C151—21no—
198C4×C151—82no—
199C4×C151—81no—
200C4×C151—81no—
201C4×C151—81no—
202C4×C151—81no—
203C4×C151—81no—
204C4×C151—161no—
205C2×C151—22no—
206C2×C151—41no—
207C2×C151—41no—
208C2×C151—161no—
209C2×C151#200811yescharacteristic
210C2×C151#200911yescharacteristic
211C2×C151#202211yescharacteristic
212#9984C15111yesmaximal, characteristic, direct product factor, Sylow
213C151#998411yescharacteristic, direct product factor, Sylow
214#3095C2×C15111yescharacteristic, complemented
215#3094C2×C15111yescharacteristic
216#2816C2×C15111yescharacteristic
217#1820C2×C15111yescharacteristic, complemented
218#1511C2×C15111yescharacteristic, complemented
219#1510C2×C15111yescharacteristic
220#1306C2×C15111yescharacteristic, complemented
221C2×C22⋊Q8C22×C15111yescharacteristic
222C2×#121C22×C15111yescharacteristic
223C2×#117C22×C15111yescharacteristic
224#485—22no—
225#484—21no—
226#483—21no—
227#482—22no—
228#481—21no—
229#480—21no—
230#428—21no—
231#428—21no—
232#419—21no—
233#418—21no—
234#407C22×C15111yescharacteristic
235#407C22×C15111yescharacteristic
236#399—21no—
237#398—21no—
238#394—21no—
239#394—22no—
240#393—21no—
241#381C22×C15111yescharacteristic
242#381C22×C15111yescharacteristic
243#342—22no—
244#328—22no—
245#327—22no—
246C22×Q8D4×C15111yescharacteristic
247C22×D4—21no—
248C22×D4D4×C15111yescharacteristic
249C23×C4C23×C15111yescharacteristic
250C2×M16—21no—
251C2×M16—21no—
252C22⋊Q8—21no—
253C22⋊Q8—21no—
254C22⋊Q8—21no—
255C22⋊Q8—21no—
256#121—21no—
257#121—21no—
258#121—21no—
259#121—21no—
260#117—21no—
261#117—21no—
262#117—21no—
263#117—21no—
264C2×C4⋊C4—21no—
265C2×C4⋊C4—22no—
266C2×C4⋊C4D4×C15111yescharacteristic
267C2×C4⋊C4D4×C15111yescharacteristic
268C2×C4⋊C4D4×C15111yescharacteristic
269C2×C4⋊C4D4×C15111yescharacteristic
270C2×C22⋊C4—21no—
271C2×C22⋊C4—21no—
272C2×C22⋊C4—21no—
273C2×C22⋊C4—21no—
274C2×C22⋊C4—22no—
275C2×C22⋊C4—22no—
276C2×C22⋊C4D4×C15112yes—
277C2×C42—21no—
278#107—22no—
279#107—22no—
280#106—22no—
281#106—22no—
282#103—22no—
283#103—22no—
284#102—22no—
285#102—22no—
286C22⋊C8—21no—
287C22⋊C8—21no—
288C22⋊C8D4×C15112yes—
289C22⋊C8D4×C15112yes—
290#95—22no—
291#95—21no—
292#95—21no—
293#95—21no—
294#95—21no—
295C24—21no—
296C24C2×D4×C15111yescharacteristic
297C2×Q8—21no—
298C2×Q8—21no—
299C2×Q8—42no—
300C2×D4—21no—
301C2×D4—21no—
302C2×D4—42no—
303C2×D4—41no—
304C2×D4—41no—
305C2×D4—82no—
306C22×C4—22no—
307C22×C4—21no—
308C22×C4—21no—
309C22×C4—21no—
310C22×C4—21no—
311C22×C4—21no—
312C22×C4—42no—
313C22×C4—41no—
314C22×C4C2×D4×C15111yescharacteristic
315C22×C4C2×D4×C15111yescharacteristic
316C22×C4C2×D4×C15111yescharacteristic
317C22×C4C2×D4×C15111yescharacteristic
318C22×C4C2×D4×C15111yescharacteristic
319C22×C4#41×C15111yescharacteristic
320M16—42no—
321M16—42no—
322C2×C8—22no—
323C2×C8—22no—
324C4⋊C4—21no—
325C4⋊C4—21no—
326C4⋊C4—21no—
327C4⋊C4—21no—
328C4⋊C4—21no—
329C4⋊C4—21no—
330C4⋊C4—21no—
331C4⋊C4—21no—
332C4⋊C4—41no—
333C4⋊C4—41no—
334C4⋊C4—82no—
335C22⋊C4—41no—
336C22⋊C4—41no—
337C22⋊C4—41no—
338C22⋊C4—41no—
339C22⋊C4—41no—
340C22⋊C4—41no—
341C22⋊C4—42no—
342C22⋊C4—42no—
343C22⋊C4—82no—
344C22⋊C4—82no—
345C42—41no—
346C42—41no—
347C23—22no—
348C23—41no—
349C23—41no—
350C23—42no—
351C23—42no—
352C23—41no—
353C23—42no—
354C23#120×C15111yescharacteristic
355C23#121×C15111yescharacteristic
356C23#127×C15111yescharacteristic
357Q8—42no—
358Q8—81no—
359D4—42no—
360D4—81no—
361D4—82no—
362D4—82no—
363C2×C4—22no—
364C2×C4—22no—
365C2×C4—41no—
366C2×C4—41no—
367C2×C4—41no—
368C2×C4—41no—
369C2×C4—41no—
370C2×C4—42no—
371C2×C4—41no—
372C2×C4—42no—
373C2×C4—42no—
374C2×C4—41no—
375C2×C4—41no—
376C2×C4—41no—
377C2×C4—41no—
378C2×C4—41no—
379C2×C4—42no—
380C2×C4—42no—
381C2×C4—81no—
382C2×C4—81no—
383C2×C4—81no—
384C2×C4—81no—
385C2×C4—81no—
386C2×C4#120×C15111yescharacteristic
387C2×C4#120×C15111yescharacteristic
388C2×C4#121×C15111yescharacteristic
389C2×C4#121×C15111yescharacteristic
390C8—42no—
391C8—42no—
392C22—21no—
393C22—21no—
394C22—21no—
395C22—21no—
396C22—21no—
397C22—21no—
398C22—21no—
399C22—21no—
400C22—82no—
401C22—84no—
402C22—81no—
403C22—81no—
404C22—81no—
405C22#392×C15111yescharacteristic
406C22#458×C15112yes—
407C4—21no—
408C4—21no—
409C4—21no—
410C4—21no—
411C4—82no—
412C4—81no—
413C4—81no—
414C4—81no—
415C4—81no—
416C4—81no—
417C4—161no—
418C2—22no—
419C2—41no—
420C2—41no—
421C2—161no—
422C2#2008×C15111yescharacteristic
423C2#2009×C15111yescharacteristic
424C2#2022×C15111yescharacteristic
subgroupG/H
center, socleC22×C151#392
commutator, Frattini, cosocleC23×C4C23×C151
prime radicalC2×#121×C151C22
LCSG ▷ C23×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C151 ◁ C23×C4×C151 ◁ G

Complements

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

NH ≅ G/Ntype
1. #3095×C151C2semidirect
4. #1820×C151C2semidirect
5. #1511×C151C2semidirect
7. #1306×C151C2semidirect
212. #9984C151direct (N × H)
213. C151#9984direct (N × H)
214. #3095C2×C151semidirect
217. #1820C2×C151semidirect
218. #1511C2×C151semidirect
220. #1306C2×C151semidirect

Maximal subgroups

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

subgroupindex
#3095×C1512
#3094×C1512
#2816×C1512
#1820×C1512
#1511×C1512
#1510×C1512
#1306×C1512
#9984151