Finite Group Databasebeta

← #29598341

Subgroups — #29598341

Order 15616.

490 conjugacy classes of subgroups; only the 91 normal subgroups are shown.

normal subgroups only

This group has 490 conjugacy classes of subgroups — too many to draw. Only its 91 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#21450798C211yesmaximal, characteristic
2C2×#16839560C211yesmaximal, characteristic, complemented
3C2×#16839560C211yesmaximal, characteristic, complemented
4C2×#16839559C211yesmaximal, characteristic
5#21445813C211yesmaximal, characteristic, complemented
6#101×Dic61C211yesmaximal, characteristic, complemented
7C2×C61×#355C211yesmaximal, characteristic
8C2×#14519775C2211yescharacteristic
9C2×#14519764C411yescharacteristic
10C2×Q8×Dic61C2211yescharacteristic
11#16839785—21no—
12C2×#14519696C2211yescharacteristic
13C2×#14519696C2211yescharacteristic
14M16×Dic61—21no—
15#16839685—21no—
16#16839685—21no—
17#16839668C411yescharacteristic
18#16839665C411yescharacteristic
19#16839656—21no—
20#16839656—21no—
21C4×#11758196C411yescharacteristic
22#16839560—22no—
23#16839560—22no—
24#16839559—22no—
25#16839530—21no—
26#16839530—21no—
27C2×#124×C61C2211yescharacteristic
28C2×#101×C61C2211yescharacteristic
29C2×#101×C61C2211yescharacteristic
30C61×#355—22no—
31C22×Dic122C2×C411yescharacteristic
32C2×#11758194—21no—
33C2×#11758194—21no—
34#14519775—21no—
35#14519775—21no—
36#14519775—21no—
37#14519775—21no—
38#14519764—41no—
39#14519764—41no—
40Q8×Dic61—41no—
41Q8×Dic61—41no—
42C2×C4⋊Dic61C2×C411yescharacteristic
43C2×C4⋊Dic61D411yescharacteristic
44C2×C4⋊Dic61D411yescharacteristic
45C2×#11758196—21no—
46C2×#11758196—21no—
47C2×#11758196—21no—
48C2×C22⋊Dic61—21no—
49C2×C22⋊Dic61—21no—
50C2×C22⋊Dic61—21no—
51C2×C22⋊Dic61—21no—
52C2×C4×Dic61C2×C411yescharacteristic
53C2×C4×Dic61C2×C411yescharacteristic
54C2×C4×Dic61D411yescharacteristic
55C2×C4×Dic61D411yescharacteristic
56#14519706—41no—
57#14519706—41no—
58#14519696—21no—
59#14519696—21no—
60#14519696—21no—
61#14519696D412yes—
62#14519687—41no—
63C8×Dic61—41no—
64#14519684—21no—
65#14519684—21no—
66#14519684—21no—
67C22×Q8×C61C2311yescharacteristic
68C22×D4×C61C2×C411yescharacteristic
69C2×M16×C61—21no—
70C2×M16×C61—21no—
71#124×C61—21no—
72#124×C61—21no—
73#124×C61—21no—
74#124×C61—21no—
75C2×C22⋊C4×C61—21no—
76C2×C22⋊C4×C61—21no—
77C2×C42×C61C2×C411yescharacteristic
78#101×C61—21no—
79#101×C61—21no—
80#101×C61—21no—
81#101×C61D412yes—
82C24×C61—21no—
83C2×Q8×C61—41no—
84C2×Q8×C61—41no—
85C2×Q8×C61C2×D411yescharacteristic
86C2×Q8×C61C2×D411yescharacteristic
87C2×Q8×C61#4111yescharacteristic
88C2×Q8×C61#4111yescharacteristic
89C2×D4×C61—21no—
90C2×D4×C61—21no—
91C2×D4×C61—41no—
92C2×D4×C61—41no—
93C22×C4×C61—21no—
94C22×C4×C61C22×C411yescharacteristic
95C22×C4×C61C2×D411yescharacteristic
96C22×C4×C61C2×D411yescharacteristic
97C22×Dic61—21no—
98C22×Dic61—21no—
99C22×Dic61C22⋊C411yescharacteristic
100C22×Dic61C22⋊C411yescharacteristic
101C22×Dic61C22⋊C411yescharacteristic
102C22×Dic61C22⋊C411yescharacteristic
103C2×Dic122—21no—
104C2×Dic122—21no—
105C2×Dic122—41no—
106C2×Dic122—41no—
107M16×C61—22no—
108M16×C61—41no—
109M16×C61—41no—
110M16×C61—41no—
111C2×C8×C61—41no—
112C2×C8×C61—41no—
113C22⋊C4×C61—41no—
114C22⋊C4×C61—41no—
115C22⋊C4×C61—41no—
116C22⋊C4×C61—41no—
117C42×C61—21no—
118C42×C61—21no—
119C22⋊Dic61—42no—
120C22⋊Dic61—42no—
121C22⋊Dic61—42no—
122C22⋊Dic61—41no—
123C22⋊Dic61—41no—
124C4⋊Dic61—41no—
125C4⋊Dic61—41no—
126C4⋊Dic61—41no—
127#11758196—42no—
128#11758196—41no—
129#11758196—41no—
130#11758196—41no—
131#11758196—41no—
132C4×Dic61—21no—
133C4×Dic61—21no—
134C4×Dic61—21no—
135C4×Dic61—21no—
136C4×Dic61—21no—
137C4×Dic61—21no—
138C4×Dic61—21no—
139C4×Dic61—21no—
140#11758194—22no—
141#11758194—41no—
142#11758194—41no—
143#11758194—41no—
144C2×#92418—41no—
145C2×#92418—41no—
146C23×C61—41no—
147C23×C61—41no—
148C23×C61—41no—
149C23×C61—41no—
150C23×C61—41no—
151C23×C61—41no—
152C23×C61—41no—
153C23×C61C2×C22⋊C411yescharacteristic
154Q8×C61—41no—
155Q8×C61—41no—
156Q8×C61—41no—
157Q8×C61—41no—
158D4×C61—81no—
159D4×C61—81no—
160C2×C4×C61—21no—
161C2×C4×C61—21no—
162C2×C4×C61—21no—
163C2×C4×C61—21no—
164C2×C4×C61—21no—
165C2×C4×C61—21no—
166C2×C4×C61—41no—
167C2×C4×C61—41no—
168C2×C4×C61—41no—
169C2×C4×C61C4×D411yescharacteristic
170C2×C4×C61C4×D411yescharacteristic
171C2×C4×C61#12111yescharacteristic
172C2×C4×C61#12111yescharacteristic
173C2×C4×C61#12411yescharacteristic
174C2×C4×C61#12711yescharacteristic
175C2×Dic61—22no—
176C2×Dic61—21no—
177C2×Dic61—21no—
178C2×Dic61—21no—
179C2×Dic61—41no—
180C2×Dic61—41no—
181C2×Dic61—41no—
182C2×Dic61—41no—
183C2×Dic61—41no—
184C2×Dic61—41no—
185C2×Dic61—41no—
186C2×Dic61—41no—
187C2×Dic61—41no—
188C2×Dic61#9911yescharacteristic
189C2×Dic61#9911yescharacteristic
190Dic122—81no—
191Dic122—81no—
192C8×C61—42no—
193C8×C61—81no—
194#92418—42no—
195#92418—81no—
196#13228—611nomaximal, Sylow
197C22×C61—21no—
198C22×C61—21no—
199C22×C61—81no—
200C22×C61—81no—
201C22×C61—81no—
202C22×C61—81no—
203C22×C61—81no—
204C22×C61—81no—
205C22×C61—81no—
206C22×C61#39011yescharacteristic
207C22×C61C2×#9911yescharacteristic
208C22×C61#41011yescharacteristic
209C4×C61—21no—
210C4×C61—21no—
211C4×C61—21no—
212C4×C61—21no—
213C4×C61—21no—
214C4×C61—21no—
215C4×C61—81no—
216Dic61—21no—
217Dic61—21no—
218Dic61—42no—
219Dic61—41no—
220Dic61—41no—
221Dic61—41no—
222Dic61—81no—
223#2545—611no—
224C2×#356—611no—
225C2×#356—611no—
226C2×#355—611no—
227C2×#355D6111yescharacteristic
228#1801—611no—
229C4×#101—611no—
230C2×C61—21no—
231C2×C61—21no—
232C2×C61—161no—
233C2×C61#196411yescharacteristic
234C2×C61#213211yescharacteristic
235C2×C61#213311yescharacteristic
236C2×C4⋊Q8—611no—
237C2×#124—611no—
238C2×#124C2×D6111yescharacteristic
239C2×C4×Q8—611no—
240#423—1221no—
241C2×#101—611no—
242C2×#101—611no—
243C2×#101C2×D6111yescharacteristic
244C2×#101C2×D6111yescharacteristic
245C4×M16—1221no—
246#396—1221no—
247#396—1221no—
248#391—611no—
249#390—611no—
250#388—1221no—
251#388—1221no—
252C4×C4⋊C4—611no—
253#356—1222no—
254#356—1222no—
255#355—22no—
256#355—1222no—
257#343—1221no—
258#343—1221no—
259C61#1322811yescharacteristic, complemented, Sylow
260C22×Q8—611no—
261C22×Q8C22×D6111yescharacteristic
262C22×D4C4×D6111yescharacteristic
263C2×M16—21no—
264C2×M16—21no—
265C2×M16—1221no—
266C2×M16—1221no—
267C4⋊Q8—1221no—
268C4⋊Q8—1221no—
269C4⋊Q8—1221no—
270C4⋊Q8—1221no—
271#124—21no—
272#124—21no—
273#124—21no—
274#124—21no—
275#124—2441no—
276#124—2441no—
277C4×Q8—2441no—
278C4×Q8—2441no—
279C2×C4⋊C4—611no—
280C2×C4⋊C4—611no—
281C2×C4⋊C4—611no—
282C2×C4⋊C4—1221no—
283C2×C4⋊C4—1221no—
284C2×C4⋊C4—1221no—
285C2×C22⋊C4—21no—
286C2×C22⋊C4—21no—
287C2×C22⋊C4—1221no—
288C2×C22⋊C4—1221no—
289C2×C22⋊C4—1221no—
290C2×C22⋊C4—1221no—
291C2×C42—611no—
292C2×C42—611no—
293C2×C42—611no—
294C2×C42—611no—
295C2×C42C4×D6111yescharacteristic
296C4⋊C8—2441no—
297C4⋊C8—2441no—
298#101—21no—
299#101—21no—
300#101—21no—
301#101—612no—
302#101—1221no—
303#101—1221no—
304#101—1221no—
305#101C22⋊D6112yes—
306#97—2441no—
307C4×C8—2441no—
308#95—1221no—
309#95—1221no—
310#95—1221no—
311C24—21no—
312C2×Q8—41no—
313C2×Q8—41no—
314C2×Q8—1221no—
315C2×Q8—1221no—
316C2×Q8—2441no—
317C2×Q8—2441no—
318C2×Q8#1175822211yescharacteristic
319C2×Q8D4×D6111yescharacteristic
320C2×Q8#1175822411yescharacteristic
321C2×Q8C2×C22⋊D6111yescharacteristic
322C2×D4—21no—
323C2×D4—21no—
324C2×D4—41no—
325C2×D4—41no—
326C22×C4—21no—
327C22×C4—611no—
328C22×C4—611no—
329C22×C4—611no—
330C22×C4—611no—
331C22×C4—1221no—
332C22×C4—1221no—
333C22×C4C2×C4×D6111yescharacteristic
334C22×C4D4×D6111yescharacteristic
335C22×C4D4×D6111yescharacteristic
336M16—22no—
337M16—41no—
338M16—41no—
339M16—41no—
340M16—1222no—
341M16—2441no—
342M16—2441no—
343M16—2441no—
344C2×C8—41no—
345C2×C8—41no—
346C2×C8—2441no—
347C2×C8—2441no—
348C4⋊C4—2441no—
349C4⋊C4—2441no—
350C4⋊C4—2441no—
351C4⋊C4—2442no—
352C4⋊C4—2441no—
353C4⋊C4—2441no—
354C4⋊C4—2441no—
355C4⋊C4—2441no—
356C22⋊C4—41no—
357C22⋊C4—41no—
358C22⋊C4—41no—
359C22⋊C4—41no—
360C22⋊C4—2441no—
361C22⋊C4—2441no—
362C22⋊C4—2442no—
363C22⋊C4—2442no—
364C22⋊C4—2442no—
365C42—21no—
366C42—21no—
367C42—1221no—
368C42—1221no—
369C42—1221no—
370C42—1221no—
371C42—1221no—
372C42—1221no—
373C42—1221no—
374C42—1221no—
375C23—41no—
376C23—41no—
377C23—41no—
378C23—41no—
379C23—41no—
380C23—41no—
381C23—41no—
382C23C22⋊C4×D6111yescharacteristic
383Q8—41no—
384Q8—41no—
385Q8—41no—
386Q8—41no—
387Q8—4881no—
388Q8—4881no—
389D4—81no—
390D4—81no—
391C2×C4—21no—
392C2×C4—21no—
393C2×C4—21no—
394C2×C4—21no—
395C2×C4—21no—
396C2×C4—21no—
397C2×C4—41no—
398C2×C4—41no—
399C2×C4—41no—
400C2×C4—611no—
401C2×C4—611no—
402C2×C4—1222no—
403C2×C4—1221no—
404C2×C4—1221no—
405C2×C4—1221no—
406C2×C4—2441no—
407C2×C4—2441no—
408C2×C4—2441no—
409C2×C4—2441no—
410C2×C4—2441no—
411C2×C4—2441no—
412C2×C4—2441no—
413C2×C4—2441no—
414C2×C4—2441no—
415C2×C4#1451973711yescharacteristic
416C2×C4C4×C22⋊D6111yescharacteristic
417C2×C4#1451974911yescharacteristic
418C2×C4#1451975011yescharacteristic
419C2×C4#1451976311yescharacteristic
420C2×C4#1451977311yescharacteristic
421C8—42no—
422C8—81no—
423C8—4881no—
424C8—2442no—
425C22—21no—
426C22—21no—
427C22—81no—
428C22—81no—
429C22—81no—
430C22—81no—
431C22—81no—
432C22—81no—
433C22—81no—
434C22#1683966211yescharacteristic
435C22#99×D6111yescharacteristic
436C22#1683973411yescharacteristic
437C4—21no—
438C4—21no—
439C4—21no—
440C4—21no—
441C4—21no—
442C4—21no—
443C4—81no—
444C4—1221no—
445C4—1221no—
446C4—4881no—
447C4—2442no—
448C4—2441no—
449C4—2441no—
450C4—2441no—
451C2—21no—
452C2—21no—
453C2—161no—
454C2#2144665311yescharacteristic
455C2#2144750111yescharacteristic
456C2#2144750511yescharacteristic
subgroupG/H
centerC22#99×D61
commutatorC22×C4×C61C22×C4
FrattiniC22×Q8C22×D61
FittingC2×C61×#355C2
socleC22×C61C2×#99
prime radicalC22×D4×C61C2×C4
cosocleC22×Q8×C61C23
hypercenterC2×#355D61
hypocenterC61#13228
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23 ◁ C22×Q8 ◁ C2×#355

Complements

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

NH ≅ G/Ntype
2. C2×#16839560C2semidirect
3. C2×#16839560C2semidirect
5. #21445813C2semidirect
6. #101×Dic61C2semidirect
259. C61#13228semidirect

Maximal subgroups

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

subgroupindex
#214507982
C2×#168395602
C2×#168395592
#214458132
#101×Dic612
C2×C61×#3552
#1322861