Finite Group Databasebeta

← #29598333

Subgroups — #29598333

Order 15616.

540 conjugacy classes of subgroups; only the 93 normal subgroups are shown.

normal subgroups only

This group has 540 conjugacy classes of subgroups — too many to draw. Only its 93 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#21450819C211yesmaximal, characteristic
2C2×#16839559C211yesmaximal, characteristic, complemented
3C2×#16839558C211yesmaximal, characteristic, complemented
4C2×#16839558C211yesmaximal, characteristic, complemented
5#21445813C211yesmaximal, characteristic, complemented
6#101×Dic61C211yesmaximal, characteristic, complemented
7C2×C61×#355C211yesmaximal, characteristic, complemented
8C2×#14519773C411yescharacteristic
9C2×#14519766C2211yescharacteristic
10C2×Q8×Dic61C2211yescharacteristic
11#16839785—21no—
12C2×#14519696C2211yescharacteristic
13C2×#14519696C2211yescharacteristic
14M16×Dic61—21no—
15#16839678—21no—
16#16839678—21no—
17#16839665C411yescharacteristic
18#16839664C411yescharacteristic
19#16839662—21no—
20#16839662—21no—
21C4×#11758196C411yescharacteristic
22#16839559—22no—
23#16839558—22no—
24#16839558—22no—
25#16839530—21no—
26#16839530—21no—
27C2×#124×C61C2211yescharacteristic
28C2×#101×C61C2211yescharacteristic
29C2×#101×C61C2211yescharacteristic
30C61×#355—22no—
31C22×D244C2×C411yescharacteristic
32C22×C22⋊D61—21no—
33C22×C22⋊D61—21no—
34C2×#11758194—21no—
35C2×#11758194—21no—
36#14519773—41no—
37#14519773—41no—
38#14519766—21no—
39#14519766—21no—
40#14519766—21no—
41#14519766—21no—
42Q8×Dic61—41no—
43Q8×Dic61—41no—
44C2×C4⋊Dic61C2×C411yescharacteristic
45C2×C4⋊Dic61D411yescharacteristic
46C2×C4⋊Dic61D411yescharacteristic
47C2×#11758196—21no—
48C2×C22⋊Dic61—21no—
49C2×C22⋊Dic61—21no—
50C2×#11758198—21no—
51C2×#11758198—21no—
52C2×#11758198—21no—
53C2×#11758198—21no—
54C2×C4×Dic61C2×C411yescharacteristic
55C2×C4×Dic61C2×C411yescharacteristic
56C2×C4×Dic61D411yescharacteristic
57C2×C4×Dic61D411yescharacteristic
58#14519706—41no—
59#14519706—41no—
60#14519696—21no—
61#14519696—21no—
62#14519696—21no—
63#14519696D412yescomplemented
64#14519687—41no—
65C8×Dic61—41no—
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×C61D412yescomplemented
82C24×C61—21no—
83C23×D61—21no—
84C2×Q8×C61—41no—
85C2×Q8×C61—41no—
86C2×Q8×C61C2×D411yescharacteristic
87C2×Q8×C61C2×D411yescharacteristic
88C2×Q8×C61#4111yescharacteristic
89C2×Q8×C61#4111yescharacteristic
90C2×D4×C61—21no—
91C2×D4×C61—21no—
92C2×D4×C61—41no—
93C2×D4×C61—41no—
94C22×C4×C61—21no—
95C22×C4×C61C22×C411yescharacteristic
96C22×C4×C61C2×D411yescharacteristic
97C22×C4×C61C2×D411yescharacteristic
98C2×C22⋊D61—42no—
99C2×C22⋊D61—42no—
100C2×C22⋊D61—42no—
101C2×C22⋊D61—41no—
102C2×C22⋊D61—41no—
103C2×C22⋊D61—81no—
104C2×C22⋊D61—81no—
105C22×Dic61—21no—
106C22×Dic61C22⋊C411yescharacteristic
107C22×Dic61C22⋊C411yescharacteristic
108C22×Dic61C22⋊C411yescharacteristic
109C22×Dic61C22⋊C411yescharacteristic
110C2×D244—21no—
111C2×D244—21no—
112C2×D244—41no—
113C2×D244—41no—
114M16×C61—22no—
115M16×C61—41no—
116M16×C61—41no—
117M16×C61—41no—
118C2×C8×C61—41no—
119C2×C8×C61—41no—
120C22⋊C4×C61—41no—
121C22⋊C4×C61—41no—
122C22⋊C4×C61—41no—
123C22⋊C4×C61—41no—
124C42×C61—21no—
125C42×C61—21no—
126C22⋊Dic61—81no—
127C22⋊Dic61—81no—
128#11758198—41no—
129#11758198—41no—
130#11758198—41no—
131#11758198—41no—
132#11758198—81no—
133#11758198—81no—
134C4⋊Dic61—41no—
135C4⋊Dic61—41no—
136C4⋊Dic61—41no—
137#11758196—42no—
138C4×Dic61—21no—
139C4×Dic61—21no—
140C4×Dic61—21no—
141C4×Dic61—21no—
142C4×Dic61—21no—
143C4×Dic61—21no—
144C4×Dic61—21no—
145C4×Dic61—21no—
146#11758194—22no—
147#11758194—41no—
148#11758194—41no—
149#11758194—41no—
150C2×#92418—41no—
151C2×#92418—41no—
152C23×C61—41no—
153C23×C61—41no—
154C23×C61—41no—
155C23×C61—41no—
156C23×C61—41no—
157C23×C61—41no—
158C23×C61—41no—
159C23×C61C2×C22⋊C411yescharacteristic
160C22×D61—41no—
161C22×D61—41no—
162C22×D61—41no—
163C22×D61—41no—
164C22×D61—41no—
165C22×D61—41no—
166C22×D61—41no—
167Q8×C61—41no—
168Q8×C61—41no—
169Q8×C61—41no—
170Q8×C61—41no—
171D4×C61—81no—
172D4×C61—81no—
173C2×C4×C61—21no—
174C2×C4×C61—21no—
175C2×C4×C61—21no—
176C2×C4×C61—21no—
177C2×C4×C61—21no—
178C2×C4×C61—21no—
179C2×C4×C61—41no—
180C2×C4×C61—41no—
181C2×C4×C61—41no—
182C2×C4×C61C4×D411yescharacteristic
183C2×C4×C61C4×D411yescharacteristic
184C2×C4×C61#12111yescharacteristic
185C2×C4×C61#12111yescharacteristic
186C2×C4×C61#12411yescharacteristic
187C2×C4×C61#12711yescharacteristic
188C22⋊D61—82no—
189C22⋊D61—84no—
190C22⋊D61—82no—
191C2×Dic61—22no—
192C2×Dic61—21no—
193C2×Dic61—21no—
194C2×Dic61—21no—
195C2×Dic61—41no—
196C2×Dic61—41no—
197C2×Dic61—41no—
198C2×Dic61—41no—
199C2×Dic61—41no—
200C2×Dic61—41no—
201C2×Dic61#9911yescharacteristic
202C2×Dic61#9911yescharacteristic
203D244—81no—
204D244—81no—
205C8×C61—42no—
206C8×C61—81no—
207#92418—42no—
208#92418—81no—
209#13226—611nomaximal, Sylow
210C22×C61—21no—
211C22×C61—21no—
212C22×C61—81no—
213C22×C61—81no—
214C22×C61—81no—
215C22×C61—81no—
216C22×C61—81no—
217C22×C61—81no—
218C22×C61—81no—
219C22×C61#39011yescharacteristic
220C22×C61C2×#9911yescharacteristic
221C22×C61#41011yescharacteristic
222C2×D61—81no—
223C2×D61—81no—
224C2×D61—81no—
225C2×D61—81no—
226C2×D61—81no—
227C2×D61—81no—
228C2×D61—81no—
229C4×C61—21no—
230C4×C61—21no—
231C4×C61—21no—
232C4×C61—21no—
233C4×C61—21no—
234C4×C61—21no—
235C4×C61—81no—
236Dic61—21no—
237Dic61—41no—
238Dic61—41no—
239Dic61—41no—
240Dic61—81no—
241Dic61#35512yescomplemented
242#2548—611no—
243C2×#355—611no—
244C2×#355—611no—
245C2×#355—611no—
246C2×#355D6111yescharacteristic, complemented
247#1801—611no—
248C4×#101—611no—
249C2×C61—21no—
250C2×C61—21no—
251C2×C61—161no—
252C2×C61#196411yescharacteristic
253C2×C61C2×#35511yescharacteristic
254C2×C61#213411yescharacteristic
255D61—161no—
256C2×#127—611no—
257C2×#124—611no—
258C2×#124C2×D6111yescharacteristic
259C2×C4×Q8—611no—
260#423—1221no—
261C2×#101—611no—
262C2×#101—611no—
263C2×#101C2×D6111yescharacteristic
264C2×#101C2×D6111yescharacteristic
265C4×M16—1221no—
266#394—1221no—
267#394—1221no—
268#390—611no—
269#390—611no—
270#390—1221no—
271#390—1221no—
272C4×C4⋊C4—611no—
273#355—22no—
274#355—1222no—
275#355—1222no—
276#355—1222no—
277#343—1221no—
278#343—1221no—
279C61#1322611yescharacteristic, complemented, Sylow
280C22×Q8C22×D6111yescharacteristic
281C22×D4—611no—
282C22×D4—1221no—
283C22×D4—1221no—
284C22×D4C4×D6111yescharacteristic
285C2×M16—21no—
286C2×M16—21no—
287C2×M16—1221no—
288C2×M16—1221no—
289#127—2441no—
290#127—2441no—
291#124—21no—
292#124—21no—
293#124—21no—
294#124—21no—
295#124—1221no—
296#124—1221no—
297#124—1221no—
298#124—1221no—
299C4×Q8—2441no—
300C4×Q8—2441no—
301C2×C4⋊C4—611no—
302C2×C4⋊C4—611no—
303C2×C4⋊C4—611no—
304C2×C4⋊C4—1221no—
305C2×C22⋊C4—21no—
306C2×C22⋊C4—21no—
307C2×C22⋊C4—1221no—
308C2×C22⋊C4—1221no—
309C2×C22⋊C4—1221no—
310C2×C22⋊C4—1221no—
311C2×C22⋊C4—1221no—
312C2×C22⋊C4—1221no—
313C2×C42—611no—
314C2×C42—611no—
315C2×C42—611no—
316C2×C42—611no—
317C2×C42C4×D6111yescharacteristic
318C4⋊C8—2441no—
319C4⋊C8—2441no—
320#101—21no—
321#101—21no—
322#101—21no—
323#101—612no—
324#101—1221no—
325#101—1221no—
326#101—1221no—
327#101C22⋊D6112yescomplemented
328#97—2441no—
329C4×C8—2441no—
330#95—1221no—
331C24—21no—
332C24—1221no—
333C2×Q8—41no—
334C2×Q8—41no—
335C2×Q8#1175822211yescharacteristic
336C2×Q8D4×D6111yescharacteristic
337C2×Q8#1175822411yescharacteristic
338C2×Q8C2×C22⋊D6111yescharacteristic
339C2×D4—21no—
340C2×D4—21no—
341C2×D4—41no—
342C2×D4—41no—
343C2×D4—1221no—
344C2×D4—1221no—
345C2×D4—4881no—
346C2×D4—4881no—
347C2×D4—2441no—
348C2×D4—2441no—
349C2×D4—2441no—
350C2×D4—2441no—
351C2×D4—2442no—
352C2×D4—2442no—
353C2×D4—2442no—
354C22×C4—21no—
355C22×C4—611no—
356C22×C4—611no—
357C22×C4—611no—
358C22×C4—611no—
359C22×C4—1221no—
360C22×C4C2×C4×D6111yescharacteristic
361C22×C4D4×D6111yescharacteristic
362C22×C4D4×D6111yescharacteristic
363M16—22no—
364M16—41no—
365M16—41no—
366M16—41no—
367M16—1222no—
368M16—2441no—
369M16—2441no—
370M16—2441no—
371C2×C8—41no—
372C2×C8—41no—
373C2×C8—2441no—
374C2×C8—2441no—
375C4⋊C4—2441no—
376C4⋊C4—2441no—
377C4⋊C4—2441no—
378C4⋊C4—2442no—
379C22⋊C4—41no—
380C22⋊C4—41no—
381C22⋊C4—41no—
382C22⋊C4—41no—
383C22⋊C4—4881no—
384C22⋊C4—4881no—
385C22⋊C4—4881no—
386C22⋊C4—4881no—
387C22⋊C4—2441no—
388C22⋊C4—2441no—
389C22⋊C4—2441no—
390C22⋊C4—2441no—
391C42—21no—
392C42—21no—
393C42—1221no—
394C42—1221no—
395C42—1221no—
396C42—1221no—
397C42—1221no—
398C42—1221no—
399C42—1221no—
400C42—1221no—
401C23—41no—
402C23—41no—
403C23—41no—
404C23—41no—
405C23—41no—
406C23—41no—
407C23—41no—
408C23—2441no—
409C23—2441no—
410C23—2441no—
411C23—2441no—
412C23—2441no—
413C23—2441no—
414C23—2441no—
415C23C22⋊C4×D6111yescharacteristic
416Q8—41no—
417Q8—41no—
418Q8—41no—
419Q8—41no—
420D4—81no—
421D4—81no—
422D4—4881no—
423D4—4881no—
424D4—4882no—
425D4—4882no—
426D4—4884no—
427C2×C4—21no—
428C2×C4—21no—
429C2×C4—21no—
430C2×C4—21no—
431C2×C4—21no—
432C2×C4—21no—
433C2×C4—41no—
434C2×C4—41no—
435C2×C4—41no—
436C2×C4—611no—
437C2×C4—611no—
438C2×C4—1222no—
439C2×C4—1221no—
440C2×C4—1221no—
441C2×C4—1221no—
442C2×C4—2441no—
443C2×C4—2441no—
444C2×C4—2441no—
445C2×C4—2441no—
446C2×C4—2441no—
447C2×C4—2441no—
448C2×C4#1451973711yescharacteristic
449C2×C4C4×C22⋊D6111yescharacteristic
450C2×C4#1451974911yescharacteristic
451C2×C4#1451975011yescharacteristic
452C2×C4#1451976311yescharacteristic
453C2×C4#1451977311yescharacteristic
454C8—42no—
455C8—81no—
456C8—4881no—
457C8—2442no—
458C22—21no—
459C22—21no—
460C22—81no—
461C22—81no—
462C22—81no—
463C22—81no—
464C22—81no—
465C22—81no—
466C22—81no—
467C22—4881no—
468C22—4881no—
469C22—4881no—
470C22—4881no—
471C22—4881no—
472C22—4881no—
473C22—4881no—
474C22#1683966211yescharacteristic
475C22#99×D6111yescharacteristic
476C22#1683973411yescharacteristic
477C4—21no—
478C4—21no—
479C4—21no—
480C4—21no—
481C4—21no—
482C4—21no—
483C4—81no—
484C4—612no—
485C4—1221no—
486C4—4881no—
487C4—2441no—
488C4—2441no—
489C4—2441no—
490C2—21no—
491C2—21no—
492C2—161no—
493C2—9761no—
494C2#2144665311yescharacteristic
495C2#355×D6111yescharacteristic
496C2#2144750911yescharacteristic
subgroupG/H
centerC22#99×D61
commutatorC22×C4×C61C22×C4
FrattiniC22×Q8C22×D61
FittingC2×C61×#355C2
socleC22×C61C2×#99
prime radicalC2×#14519773C4
cosocleC22×Q8×C61C23
hypercenterC2×#355D61
hypocenterC61#13226
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×#16839559C2semidirect
3. C2×#16839558C2semidirect
4. C2×#16839558C2semidirect
5. #21445813C2semidirect
6. #101×Dic61C2semidirect
7. C2×C61×#355C2semidirect
63. #14519696D4semidirect
81. #101×C61D4semidirect
241. Dic61#355semidirect
246. C2×#355D61semidirect
279. C61#13226semidirect
327. #101C22⋊D61semidirect

Maximal subgroups

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

subgroupindex
#214508192
C2×#168395592
C2×#168395582
#214458132
#101×Dic612
C2×C61×#3552
#1322661