Finite Group Databasebeta

← #29587011

Subgroups — #29587011

Order 15616.

970 conjugacy classes of subgroups.

The subgroup lattice has 586 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16839768C211yesmaximal, characteristic
2C2×#16839766C211yesmaximal, characteristic
3C22×#14519693C211yesmaximal, characteristic
4C2×#16839534C211yesmaximal, characteristic, complemented
5#21445528C211yesmaximal, characteristic, complemented
6C2×#16839520C211yesmaximal, characteristic, complemented
7C61×#2905C211yesmaximal, characteristic, complemented
8C23×D244C2211yescharacteristic
9C22×#11758194C2211yescharacteristic
10C22×#11758194C2211yescharacteristic
11C2×#14519736C2211yescharacteristic
12#16839768—22no—
13#16839768—22no—
14#16839766—22no—
15#16839766—22no—
16C2×#14519699—22no—
17C2×#14519697C414yescomplemented
18C2×#14519693—22no—
19C2×#14519693—22no—
20C2×#14519693—22no—
21#16839534—22no—
22#16839521—22no—
23#16839520—22no—
24C22×M16×C61C2211yescharacteristic
25C22×M16×C61C2211yescharacteristic
26C2×#117×C61C2211yescharacteristic
27C61×#424—22no—
28C61×#424—22no—
29C61×#423—22no—
30C24×D61—21no—
31C22×D244—21no—
32C22×D244—21no—
33C22×D244—21no—
34C22×D244—21no—
35C22×D244—21no—
36C22×D244—21no—
37C22×D244—21no—
38C22×D244—21no—
39C22×D244—21no—
40C22×D244—21no—
41C22×D244—21no—
42C22×D244C2×C412yes—
43C22×D244D412yes—
44C22×D244Q812yes—
45C2×#11758194—21no—
46C2×#11758194—21no—
47C2×#11758194—21no—
48C2×#11758194—21no—
49C2×#11758194—21no—
50C2×#11758194—21no—
51C2×#11758194—21no—
52C2×#11758194—21no—
53C2×#11758194—21no—
54C2×#11758194—21no—
55C2×#11758194—21no—
56C2×#11758194D412yes—
57C22×#92418—21no—
58C22×#92418C2×C412yes—
59#14519736—21no—
60#14519736—21no—
61#14519736—21no—
62#14519736D412yes—
63C2×C4⋊Dic61—21no—
64C2×C22⋊Dic61—21no—
65C2×C4×Dic61—21no—
66#14519699—28no—
67#14519697—28no—
68#14519693—28no—
69C23×C4×C61C2311yescharacteristic
70C2×M16×C61—21no—
71C2×M16×C61—21no—
72C2×M16×C61—21no—
73C2×M16×C61—21no—
74C2×M16×C61—21no—
75C2×M16×C61—21no—
76C2×M16×C61—21no—
77C2×M16×C61—21no—
78C2×M16×C61—21no—
79C2×M16×C61—21no—
80C2×M16×C61—21no—
81C2×M16×C61D412yes—
82C22×C8×C61—21no—
83C22×C8×C61D412yes—
84#117×C61—21no—
85#117×C61—21no—
86#117×C61D412yes—
87#117×C61D412yes—
88C2×C4⋊C4×C61C2×C412yes—
89C2×C22⋊C4×C61—21no—
90C2×C42×C61—21no—
91C4⋊C8×C61—28no—
92C24×C61#4111yescharacteristic
93C23×D61—22no—
94C23×D61—22no—
95C23×D61—22no—
96C23×D61—41no—
97C23×D61—41no—
98C23×D61—41no—
99C23×D61—41no—
100C23×D61—84no—
101C22×C4×C61—22no—
102C22×C4×C61C22×C411yescharacteristic
103C22×C4×C61C2×D411yescharacteristic
104C22×C4×C61C2×D411yescharacteristic
105C22×C4×C61C2×D411yescharacteristic
106C22×C4×C61C2×D411yescharacteristic
107C22×C4×C61C2×D411yescharacteristic
108C22×C4×C61C2×D411yescharacteristic
109C22×C4×C61C2×D411yescharacteristic
110C22×C4×C61C2×Q811yescharacteristic
111C22×C4×C61#4111yescharacteristic
112C22×C4×C61#4111yescharacteristic
113C22×C4×C61#4111yescharacteristic
114C22×C4×C61#4111yescharacteristic
115C22×C4×C61#4111yescharacteristic
116C22×Dic61—41no—
117C2×D244—22no—
118C2×D244—22no—
119C2×D244—22no—
120C2×D244—22no—
121C2×D244—22no—
122C2×D244—22no—
123C2×D244—22no—
124C2×D244—22no—
125C2×D244—22no—
126C2×D244—22no—
127C2×D244—22no—
128C2×D244—22no—
129C2×D244—22no—
130C2×D244—22no—
131C2×D244—22no—
132C2×D244—41no—
133C2×D244—41no—
134C2×D244—41no—
135C2×D244—41no—
136C2×D244—41no—
137C2×D244—41no—
138C2×D244—41no—
139C2×D244—41no—
140C2×D244—41no—
141C2×D244—41no—
142C2×D244—41no—
143C2×D244—41no—
144C2×D244C4⋊C414yes—
145M16×C61—22no—
146M16×C61—22no—
147M16×C61—41no—
148M16×C61—41no—
149M16×C61—41no—
150M16×C61—41no—
151M16×C61—41no—
152M16×C61—41no—
153C2×C8×C61—22no—
154C2×C8×C61—22no—
155C2×C8×C61—22no—
156C2×C8×C61—22no—
157C2×C8×C61—41no—
158C2×C8×C61—41no—
159C4⋊C4×C61—22no—
160C4⋊C4×C61C22⋊C414yes—
161C22⋊C4×C61—22no—
162C22⋊C4×C61—22no—
163C42×C61—22no—
164C42×C61—22no—
165C22⋊Dic61—22no—
166C22⋊Dic61—41no—
167C4⋊Dic61—22no—
168C4⋊Dic61—41no—
169C4×Dic61—22no—
170C4×Dic61—41no—
171#11758194—22no—
172#11758194—22no—
173#11758194—41no—
174#11758194—41no—
175#11758194—41no—
176#11758194—41no—
177#11758194—41no—
178#11758194—41no—
179C2×#92418—22no—
180C2×#92418—22no—
181C2×#92418—22no—
182C2×#92418—22no—
183C2×#92418—41no—
184C2×#92418—41no—
185C23×C61—42no—
186C23×C61C4×D411yescharacteristic
187C23×C61#12111yescharacteristic
188C23×C61C22⋊Q811yescharacteristic
189C23×C61#12311yescharacteristic
190C23×C61#12311yescharacteristic
191C23×C61#12311yescharacteristic
192C23×C61#12611yescharacteristic
193C22×D61—24no—
194C22×D61—42no—
195C22×D61—42no—
196C22×D61—42no—
197C22×D61—42no—
198C22×D61—42no—
199C22×D61—42no—
200C22×D61—84no—
201C22×D61—84no—
202C22×D61—84no—
203C22×D61—84no—
204C22×D61—84no—
205C22×D61—84no—
206C22×D61—84no—
207C2×C4×C61—24no—
208C2×C4×C61—82no—
209C2×C4×C61C2×C22⋊C411yescharacteristic
210C2×C4×C61C2×C4⋊C411yescharacteristic
211C2×C4×C61#11711yescharacteristic
212C2×C4×C61C4×D411yescharacteristic
213C2×C4×C61C4×D411yescharacteristic
214C2×C4×C61C4×D411yescharacteristic
215C2×C4×C61#12011yescharacteristic
216C2×C4×C61#12011yescharacteristic
217C2×C4×C61#12011yescharacteristic
218C2×C4×C61#12111yescharacteristic
219C2×C4×C61#12111yescharacteristic
220C2×C4×C61#12111yescharacteristic
221C2×C4×C61#12111yescharacteristic
222C2×C4×C61#12111yescharacteristic
223C2×C4×C61#12111yescharacteristic
224C2×C4×C61#12111yescharacteristic
225C2×C4×C61C22⋊Q811yescharacteristic
226C2×C4×C61C22⋊Q811yescharacteristic
227C2×C4×C61C22⋊Q811yescharacteristic
228C2×C4×C61C22⋊Q811yescharacteristic
229C2×C4×C61C22⋊Q811yescharacteristic
230C2×C4×C61#12311yescharacteristic
231C2×C4×C61#12311yescharacteristic
232C2×C4×C61#12411yescharacteristic
233C2×C4×C61#12411yescharacteristic
234C2×C4×C61#12411yescharacteristic
235C2×C4×C61#12611yescharacteristic
236C2×C4×C61#12711yescharacteristic
237C2×Dic61—42no—
238C2×Dic61—82no—
239D244—24no—
240D244—24no—
241D244—42no—
242D244—42no—
243D244—42no—
244D244—42no—
245D244—42no—
246D244—42no—
247C8×C61—42no—
248C8×C61—42no—
249#92418—42no—
250#92418—42no—
251#11058—611nomaximal, Sylow
252C22×C61—22no—
253C22×C61—22no—
254C22×C61—22no—
255C22×C61—41no—
256C22×C61—41no—
257C22×C61—41no—
258C22×C61—41no—
259C22×C61#38511yescharacteristic
260C22×C61#38611yescharacteristic
261C22×C61#38811yescharacteristic
262C22×C61#39411yescharacteristic
263C22×C61#39611yescharacteristic
264C22×C61#39711yescharacteristic
265C22×C61#39911yescharacteristic
266C2×D61—44no—
267C2×D61—84no—
268C2×D61—84no—
269C2×D61—84no—
270C2×D61—84no—
271C2×D61—84no—
272C2×D61—84no—
273C2×D61—84no—
274C4×C61—44no—
275C4×C61#38011yescharacteristic
276C4×C61#38511yescharacteristic
277C4×C61#38811yescharacteristic
278C4×C61#39011yescharacteristic
279C4×C61#39211yescharacteristic
280C4×C61#39311yescharacteristic
281C4×C61#39411yescharacteristic
282C4×C61#39611yescharacteristic
283Dic61—82no—
284#2905D6111yescharacteristic, complemented
285C2×#418—611no—
286C2×#418—611no—
287C22×#100—611no—
288C2×#344—611no—
289#1733—611no—
290C2×#338—611no—
291C2×C61—21no—
292C2×C61—21no—
293C2×C61—21no—
294C2×C61—21no—
295C2×C61—21no—
296C2×C61—21no—
297C2×C61#143911yescharacteristic
298C2×C61#190312yes—
299D61—84no—
300C23×D4—611no—
301C22×M16—611no—
302C22×M16—611no—
303C22×M16C2×D6111yescharacteristic
304C22×M16C2×D6111yescharacteristic
305C2×#117—611no—
306C2×#117C2×D6111yescharacteristic
307#424—22no—
308#424—22no—
309#423—22no—
310#418—1222no—
311#418—1222no—
312#418—1222no—
313#418—1222no—
314C2×#102—614no—
315C2×#102—1222no—
316C2×#100—1222no—
317C2×#100—1222no—
318C2×#100—1222no—
319#344—1222no—
320#339—1222no—
321#338—1222no—
322C61#1105811yescharacteristic, complemented, Sylow
323C25—1221no—
324C22×D4—612no—
325C22×D4—612no—
326C22×D4—612no—
327C22×D4—1221no—
328C22×D4—1221no—
329C22×D4—1221no—
330C22×D4—1221no—
331C22×D4—1221no—
332C22×D4—1221no—
333C22×D4—1221no—
334C22×D4—1221no—
335C22×D4—1221no—
336C22×D4—1221no—
337C22×D4—1221no—
338C23×C4C22×D6111yescharacteristic
339C2×M16—21no—
340C2×M16—21no—
341C2×M16—21no—
342C2×M16—21no—
343C2×M16—21no—
344C2×M16—21no—
345C2×M16—21no—
346C2×M16—21no—
347C2×M16—21no—
348C2×M16—21no—
349C2×M16—21no—
350C2×M16—612no—
351C2×M16—1221no—
352C2×M16—1221no—
353C2×M16—1221no—
354C2×M16—1221no—
355C2×M16—1221no—
356C2×M16—1221no—
357C2×M16—1221no—
358C2×M16—1221no—
359C2×M16—1221no—
360C2×M16—1221no—
361C2×M16—1221no—
362C2×M16C22⋊D6112yes—
363C22×C8—21no—
364C22×C8—612no—
365C22×C8—1221no—
366C22×C8C22⋊D6112yes—
367#117—21no—
368#117—21no—
369#117—612no—
370#117—1221no—
371#117—1221no—
372#117—1221no—
373#117D24412yes—
374#117C22⋊D6112yes—
375C2×C4⋊C4—1221no—
376C2×C4⋊C4C4×D6112yes—
377C2×C22⋊C4—21no—
378C2×C22⋊C4—1221no—
379C2×C42—21no—
380C2×C42—1221no—
381C4⋊C8—28no—
382#102—1228no—
383#102—1228no—
384#100—1228no—
385C24—1222no—
386C24—1222no—
387C24—1222no—
388C24—4884no—
389C24—2441no—
390C24—2441no—
391C24—2441no—
392C24—2441no—
393C24#1175822211yescharacteristic
394C2×D4—614no—
395C2×D4—1222no—
396C2×D4—1222no—
397C2×D4—1222no—
398C2×D4—1222no—
399C2×D4—1222no—
400C2×D4—1222no—
401C2×D4—1222no—
402C2×D4—1222no—
403C2×D4—1222no—
404C2×D4—1222no—
405C2×D4—1222no—
406C2×D4—1222no—
407C2×D4—1222no—
408C2×D4—1222no—
409C2×D4—1222no—
410C2×D4—2441no—
411C2×D4—2441no—
412C2×D4—2441no—
413C2×D4—2441no—
414C2×D4—2441no—
415C2×D4—2441no—
416C2×D4—2441no—
417C2×D4—2441no—
418C2×D4—2441no—
419C2×D4—2441no—
420C2×D4—2441no—
421C2×D4—2441no—
422C22×C4—22no—
423C22×C4—2441no—
424C22×C4C2×C4×D6111yescharacteristic
425C22×C4C2×D24411yescharacteristic
426C22×C4#1175822211yescharacteristic
427C22×C4D4×D6111yescharacteristic
428C22×C4D4×D6111yescharacteristic
429C22×C4D4×D6111yescharacteristic
430C22×C4#1175822411yescharacteristic
431C22×C4Q8×D6111yescharacteristic
432C22×C4#1175822611yescharacteristic
433C22×C4#1175822611yescharacteristic
434C22×C4#1175822611yescharacteristic
435C22×C4C2×C22⋊D6111yescharacteristic
436C22×C4C2×C22⋊D6111yescharacteristic
437C22×C4C2×C22⋊D6111yescharacteristic
438M16—22no—
439M16—22no—
440M16—41no—
441M16—41no—
442M16—41no—
443M16—41no—
444M16—41no—
445M16—41no—
446M16—1222no—
447M16—1222no—
448M16—2441no—
449M16—2441no—
450M16—2441no—
451M16—2441no—
452M16—2441no—
453M16—2441no—
454C2×C8—22no—
455C2×C8—22no—
456C2×C8—22no—
457C2×C8—22no—
458C2×C8—41no—
459C2×C8—41no—
460C2×C8—1222no—
461C2×C8—1222no—
462C2×C8—1222no—
463C2×C8—1222no—
464C2×C8—2441no—
465C2×C8—2441no—
466C4⋊C4—22no—
467C4⋊C4—1222no—
468C4⋊C4—2441no—
469C4⋊C4#1175819814yes—
470C22⋊C4—22no—
471C22⋊C4—22no—
472C22⋊C4—1222no—
473C22⋊C4—2441no—
474C42—22no—
475C42—22no—
476C42—1222no—
477C42—2441no—
478C23—42no—
479C23—1224no—
480C23—4884no—
481C23—4884no—
482C23—4884no—
483C23—4884no—
484C23—4884no—
485C23—4884no—
486C23—4884no—
487C23—2442no—
488C23—2442no—
489C23—2442no—
490C23—2442no—
491C23—2442no—
492C23—2442no—
493C23C4×C22⋊D6111yescharacteristic
494C23#1451975111yescharacteristic
495C23#1451975511yescharacteristic
496C23#1451976011yescharacteristic
497C23#1451976211yescharacteristic
498C23#1451976211yescharacteristic
499C23#1451977211yescharacteristic
500D4—1224no—
501D4—1224no—
502D4—2442no—
503D4—2442no—
504D4—2442no—
505D4—2442no—
506D4—2442no—
507D4—2442no—
508C2×C4—24no—
509C2×C4—82no—
510C2×C4—4882no—
511C2×C4—2442no—
512C2×C4C2×#1175819811yescharacteristic
513C2×C4C4⋊C4×D6111yescharacteristic
514C2×C4#1451973511yescharacteristic
515C2×C4C4×C22⋊D6111yescharacteristic
516C2×C4#1451973911yescharacteristic
517C2×C4#1451973911yescharacteristic
518C2×C4#1451974511yescharacteristic
519C2×C4#1451974511yescharacteristic
520C2×C4#1451974611yescharacteristic
521C2×C4#1451974811yescharacteristic
522C2×C4#1451974911yescharacteristic
523C2×C4#1451974911yescharacteristic
524C2×C4#1451975111yescharacteristic
525C2×C4#1451975211yescharacteristic
526C2×C4#1451975211yescharacteristic
527C2×C4#1451975211yescharacteristic
528C2×C4#1451975311yescharacteristic
529C2×C4#1451975311yescharacteristic
530C2×C4#1451975311yescharacteristic
531C2×C4#1451975511yescharacteristic
532C2×C4#1451975711yescharacteristic
533C2×C4#1451976211yescharacteristic
534C2×C4#1451976211yescharacteristic
535C2×C4#1451976611yescharacteristic
536C2×C4#1451976611yescharacteristic
537C2×C4#1451976611yescharacteristic
538C2×C4#1451977211yescharacteristic
539C2×C4#1451977311yescharacteristic
540C8—42no—
541C8—42no—
542C8—2442no—
543C8—2442no—
544C22—22no—
545C22—22no—
546C22—22no—
547C22—41no—
548C22—41no—
549C22—41no—
550C22—41no—
551C22—4884no—
552C22—4884no—
553C22—4884no—
554C22—4884no—
555C22—4884no—
556C22—4884no—
557C22—4884no—
558C22—2444no—
559C22#1683963311yescharacteristic
560C22#1683964111yescharacteristic
561C22#1683965211yescharacteristic
562C22#1683967911yescharacteristic
563C22#1683968411yescharacteristic
564C22#1683968811yescharacteristic
565C22#1683969711yescharacteristic
566C4—44no—
567C4—4882no—
568C4#1683961911yescharacteristic
569C4#1683963311yescharacteristic
570C4#1683965211yescharacteristic
571C4#1683966311yescharacteristic
572C4#1683967011yescharacteristic
573C4#1683967311yescharacteristic
574C4#1683967911yescharacteristic
575C4#1683968411yescharacteristic
576C2—21no—
577C2—21no—
578C2—21no—
579C2—21no—
580C2—21no—
581C2—21no—
582C2—4884no—
583C2#2144406111yescharacteristic
584C2#2144629912yes—
subgroupG/H
centerC22#16839641
commutatorC22×C4×C61C22×C4
FrattiniC23×C4C22×D61
FittingC61×#2905C2
socleC22×C61#386
prime radicalC23×D244C22
cosocleC23×C4×C61C23
hypercenter#2905D61
hypocenterC61#11058
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23×C4 ◁ #2905

Complements

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

NH ≅ G/Ntype
4. C2×#16839534C2semidirect
5. #21445528C2semidirect
6. C2×#16839520C2semidirect
7. C61×#2905C2semidirect
17. C2×#14519697C4semidirect
284. #2905D61semidirect
322. C61#11058semidirect

Maximal subgroups

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

subgroupindex
C2×#168397682
C2×#168397662
C22×#145196932
C2×#168395342
#214455282
C2×#168395202
C61×#29052
#1105861