Finite Group Databasebeta

← #15770434

Subgroups — #15770434

Order 3328.

950 conjugacy classes of subgroups.

The subgroup lattice has 578 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11718786C211yesmaximal, characteristic, complemented
2C22×#88063C211yesmaximal, characteristic
3C22×#88063C211yesmaximal, characteristic
4C22×#88063C211yesmaximal, characteristic
5#13114562C211yesmaximal, characteristic, complemented
6C2×#11718152C211yesmaximal, characteristic, complemented
7C13×#1738C211yesmaximal, characteristic, complemented
8C23×D52C2211yescharacteristic
9C22×C13×M16C2211yescharacteristic
10C22×C13×M16C2211yescharacteristic
11C22×C13×M16C2211yescharacteristic
12C22×#6099C2211yescharacteristic
13C22×#6099C2211yescharacteristic
14C22×#6099C2211yescharacteristic
15C2×#88063—22no—
16C2×#88063—22no—
17C2×#88063—22no—
18C2×#88063—22no—
19C2×#88063—22no—
20C2×#88063—22no—
21C2×#88063—22no—
22C2×#88063—22no—
23C2×#88063C414yes—
24#11718786—22no—
25#11718786—22no—
26C2×#88059—22no—
27C13×#341—22no—
28#11718152—22no—
29#11718150—22no—
30C24×D13Q812yes—
31C23×C4×C13C2311yescharacteristic
32C22×D52—21no—
33C22×D52—21no—
34C22×D52—21no—
35C22×D52—21no—
36C22×D52—21no—
37C22×D52—21no—
38C22×D52—21no—
39C22×D52—21no—
40C22×D52—21no—
41C22×D52—21no—
42C22×D52—21no—
43C22×D52—21no—
44C22×D52C2×C412yes—
45C22×D52D412yes—
46C2×C13×M16—21no—
47C2×C13×M16—21no—
48C2×C13×M16—21no—
49C2×C13×M16—21no—
50C2×C13×M16—21no—
51C2×C13×M16—21no—
52C2×C13×M16—21no—
53C2×C13×M16—21no—
54C2×C13×M16—21no—
55C2×C13×M16—21no—
56C2×C13×M16—21no—
57C2×C13×M16—21no—
58C2×C13×M16—21no—
59C2×C13×M16C2×C412yes—
60C2×C13×M16D412yes—
61C2×C13×M16D412yes—
62C2×C13×M16D412yes—
63C2×C13×M16D412yes—
64C22×C8×C13—21no—
65C22×C8×C13—21no—
66C22×C8×C13—21no—
67C2×#6099—21no—
68C2×#6099—21no—
69C2×#6099—21no—
70C2×#6099—21no—
71C2×#6099—21no—
72C2×#6099—21no—
73C2×#6099—21no—
74C2×#6099—21no—
75C2×#6099—21no—
76C2×#6099—21no—
77C2×#6099—21no—
78C2×#6099—21no—
79C2×#6099—21no—
80C2×#6099—21no—
81C2×#6099—21no—
82C2×#6099C2×C412yes—
83C2×#6099D412yes—
84C2×#6099D412yes—
85C22×#1055—21no—
86C22×#1055—21no—
87C22×#1055—21no—
88#88063—28no—
89#88063—28no—
90#88063—28no—
91#88059—28no—
92#11139—131nomaximal, Sylow
93C24×C13C2×Q811yescharacteristic
94C23×D13—22no—
95C23×D13—22no—
96C23×D13—22no—
97C23×D13—22no—
98C23×D13—22no—
99C23×D13—22no—
100C23×D13—84no—
101C23×D13C4⋊C414yes—
102C22×C4×C13C22×C411yescharacteristic
103C22×C4×C13C2×D411yescharacteristic
104C22×C4×C13C2×D411yescharacteristic
105C22×C4×C13C2×D411yescharacteristic
106C22×C4×C13C2×D411yescharacteristic
107C22×C4×C13C2×D411yescharacteristic
108C22×C4×C13C2×D411yescharacteristic
109C22×C4×C13C2×D411yescharacteristic
110C22×C4×C13#4111yescharacteristic
111C22×C4×C13#4111yescharacteristic
112C22×C4×C13#4111yescharacteristic
113C22×C4×C13#4111yescharacteristic
114C22×C4×C13#4111yescharacteristic
115C22×C4×C13#4111yescharacteristic
116C2×D52—22no—
117C2×D52—22no—
118C2×D52—22no—
119C2×D52—22no—
120C2×D52—22no—
121C2×D52—22no—
122C2×D52—22no—
123C2×D52—22no—
124C2×D52—22no—
125C2×D52—22no—
126C2×D52—22no—
127C2×D52—22no—
128C2×D52—41no—
129C2×D52—41no—
130C2×D52—41no—
131C2×D52—41no—
132C2×D52—41no—
133C2×D52—41no—
134C2×D52—41no—
135C2×D52—41no—
136C2×D52—41no—
137C2×D52—41no—
138C2×D52—41no—
139C2×D52—41no—
140C2×D52—41no—
141C2×D52—41no—
142C2×D52—41no—
143C2×D52—41no—
144C13×M16—22no—
145C13×M16—22no—
146C13×M16—22no—
147C13×M16—22no—
148C13×M16—22no—
149C13×M16—22no—
150C13×M16—22no—
151C13×M16—41no—
152C13×M16—41no—
153C13×M16—41no—
154C13×M16—41no—
155C13×M16C22⋊C414yes—
156C2×C8×C13—22no—
157C2×C8×C13—22no—
158C2×C8×C13—22no—
159C2×C8×C13—22no—
160C2×C8×C13—22no—
161C2×C8×C13—41no—
162C2×C8×C13—41no—
163C2×C8×C13—41no—
164C2×C8×C13—41no—
165#6099—22no—
166#6099—22no—
167#6099—22no—
168#6099—22no—
169#6099—22no—
170#6099—22no—
171#6099—41no—
172#6099—41no—
173#6099—41no—
174#6099—41no—
175#6099—41no—
176#6099—41no—
177C2×#1055—22no—
178C2×#1055—22no—
179C2×#1055—22no—
180C2×#1055—41no—
181C2×#1055—41no—
182C2×#1055—41no—
183C2×#1055—41no—
184C2×#1055—41no—
185C2×#1055—41no—
186C2×#430—131no—
187C22×#100—131no—
188C22×#100—131no—
189C22×#100—131no—
190#1738—131no—
191#1738D1311yescharacteristic, complemented
192C2×#338—131no—
193C23×C13—42no—
194C23×C13C2×C4⋊C411yescharacteristic
195C23×C13C22⋊Q811yescharacteristic
196C23×C13C22⋊Q811yescharacteristic
197C23×C13C22⋊Q811yescharacteristic
198C23×C13C22⋊Q811yescharacteristic
199C23×C13C22⋊Q811yescharacteristic
200C23×C13C22⋊Q811yescharacteristic
201C22×D13—24no—
202C22×D13—24no—
203C22×D13—24no—
204C22×D13—42no—
205C22×D13—42no—
206C22×D13—42no—
207C22×D13—42no—
208C22×D13—84no—
209C22×D13—84no—
210C22×D13—84no—
211C22×D13—84no—
212C22×D13—84no—
213C22×D13—84no—
214C22×D13—84no—
215C2×C4×C13C2×C22⋊C411yescharacteristic
216C2×C4×C13#11711yescharacteristic
217C2×C4×C13C4×D411yescharacteristic
218C2×C4×C13C4×D411yescharacteristic
219C2×C4×C13C4×D411yescharacteristic
220C2×C4×C13C4×D411yescharacteristic
221C2×C4×C13#12011yescharacteristic
222C2×C4×C13#12011yescharacteristic
223C2×C4×C13#12011yescharacteristic
224C2×C4×C13#12111yescharacteristic
225C2×C4×C13#12111yescharacteristic
226C2×C4×C13#12111yescharacteristic
227C2×C4×C13#12111yescharacteristic
228C2×C4×C13#12111yescharacteristic
229C2×C4×C13#12111yescharacteristic
230C2×C4×C13#12111yescharacteristic
231C2×C4×C13#12111yescharacteristic
232C2×C4×C13#12311yescharacteristic
233C2×C4×C13#12311yescharacteristic
234C2×C4×C13#12311yescharacteristic
235C2×C4×C13#12311yescharacteristic
236C2×C4×C13#12311yescharacteristic
237C2×C4×C13#12411yescharacteristic
238C2×C4×C13#12411yescharacteristic
239C2×C4×C13#12411yescharacteristic
240C2×C4×C13#12611yescharacteristic
241C2×C4×C13#12611yescharacteristic
242C2×C4×C13#12711yescharacteristic
243D52—42no—
244D52—42no—
245D52—42no—
246D52—42no—
247D52—42no—
248D52—42no—
249D52—42no—
250D52—42no—
251C8×C13—24no—
252C8×C13—42no—
253C8×C13—42no—
254#1055—42no—
255#1055—42no—
256#1055—42no—
257C23×D4—131no—
258C22×M16—131no—
259C22×M16—131no—
260C22×M16—131no—
261C22×M16C2×D1311yescharacteristic
262C22×M16C2×D1311yescharacteristic
263C22×M16C2×D1311yescharacteristic
264#430—262no—
265#430—262no—
266C2×#108—262no—
267C2×#100—134no—
268C2×#100—262no—
269C2×#100—262no—
270C2×#100—262no—
271C2×#100—262no—
272C2×#100—262no—
273C2×#100—262no—
274C2×#100—262no—
275C2×#100—262no—
276#341—22no—
277#341—262no—
278#338—262no—
279C22×C13—22no—
280C22×C13—22no—
281C22×C13—22no—
282C22×C13—41no—
283C22×C13—41no—
284C22×C13—41no—
285C22×C13—41no—
286C22×C13#38011yescharacteristic
287C22×C13#38511yescharacteristic
288C22×C13#38511yescharacteristic
289C22×C13#39311yescharacteristic
290C22×C13#39611yescharacteristic
291C22×C13#39611yescharacteristic
292C22×C13#39911yescharacteristic
293C2×D13—44no—
294C2×D13—84no—
295C2×D13—84no—
296C2×D13—84no—
297C2×D13—84no—
298C2×D13—84no—
299C2×D13—84no—
300C2×D13—84no—
301C4×C13#38611yescharacteristic
302C4×C13#38811yescharacteristic
303C4×C13#38811yescharacteristic
304C4×C13#39011yescharacteristic
305C4×C13#39211yescharacteristic
306C4×C13#39411yescharacteristic
307C4×C13#39411yescharacteristic
308C4×C13#39711yescharacteristic
309C25—132no—
310C22×D4—132no—
311C22×D4—132no—
312C22×D4—261no—
313C22×D4—261no—
314C22×D4—261no—
315C22×D4—261no—
316C22×D4—261no—
317C22×D4—261no—
318C22×D4—261no—
319C22×D4—261no—
320C22×D4—261no—
321C22×D4—261no—
322C22×D4—261no—
323C22×D4—261no—
324C23×C4C22×D1311yescharacteristic
325C2×M16—21no—
326C2×M16—21no—
327C2×M16—21no—
328C2×M16—21no—
329C2×M16—21no—
330C2×M16—21no—
331C2×M16—21no—
332C2×M16—21no—
333C2×M16—21no—
334C2×M16—21no—
335C2×M16—21no—
336C2×M16—21no—
337C2×M16—21no—
338C2×M16—132no—
339C2×M16—132no—
340C2×M16—132no—
341C2×M16—261no—
342C2×M16—261no—
343C2×M16—261no—
344C2×M16—261no—
345C2×M16—261no—
346C2×M16—261no—
347C2×M16—261no—
348C2×M16—261no—
349C2×M16—261no—
350C2×M16—261no—
351C2×M16—261no—
352C2×M16—261no—
353C2×M16—261no—
354C2×M16—261no—
355C2×M16—261no—
356C2×M16C4×D1312yes—
357C2×M16D5212yes—
358C2×M16D5212yes—
359C2×M16D5212yes—
360C2×M16C22⋊D1312yes—
361C22×C8—21no—
362C22×C8—21no—
363C22×C8—21no—
364C22×C8—261no—
365C22×C8—261no—
366C22×C8—261no—
367#108—268no—
368#100—268no—
369#100—268no—
370#100—268no—
371C2×C13—21no—
372C2×C13—21no—
373C2×C13—21no—
374C2×C13—21no—
375C2×C13—21no—
376C2×C13—21no—
377C2×C13#143911yescharacteristic
378C2×C13#206912yes—
379D13—84no—
380C24—134no—
381C24—262no—
382C24—262no—
383C24—262no—
384C24—262no—
385C24—262no—
386C24—262no—
387C24—1044no—
388C24Q8×D1311yescharacteristic
389C2×D4—262no—
390C2×D4—262no—
391C2×D4—262no—
392C2×D4—262no—
393C2×D4—262no—
394C2×D4—262no—
395C2×D4—262no—
396C2×D4—262no—
397C2×D4—262no—
398C2×D4—262no—
399C2×D4—262no—
400C2×D4—262no—
401C2×D4—521no—
402C2×D4—521no—
403C2×D4—521no—
404C2×D4—521no—
405C2×D4—521no—
406C2×D4—521no—
407C2×D4—521no—
408C2×D4—521no—
409C2×D4—521no—
410C2×D4—521no—
411C2×D4—521no—
412C2×D4—521no—
413C2×D4—521no—
414C2×D4—521no—
415C2×D4—521no—
416C2×D4—521no—
417C22×C4C2×C4×D1311yescharacteristic
418C22×C4C2×D5211yescharacteristic
419C22×C4C2×D5211yescharacteristic
420C22×C4C2×D5211yescharacteristic
421C22×C4#612711yescharacteristic
422C22×C4#612711yescharacteristic
423C22×C4D4×D1311yescharacteristic
424C22×C4D4×D1311yescharacteristic
425C22×C4D4×D1311yescharacteristic
426C22×C4#612911yescharacteristic
427C22×C4#612911yescharacteristic
428C22×C4#612911yescharacteristic
429C22×C4#613111yescharacteristic
430C22×C4C2×C22⋊D1311yescharacteristic
431M16—22no—
432M16—22no—
433M16—22no—
434M16—22no—
435M16—22no—
436M16—22no—
437M16—22no—
438M16—41no—
439M16—41no—
440M16—41no—
441M16—41no—
442M16—262no—
443M16—262no—
444M16—262no—
445M16—262no—
446M16—262no—
447M16—262no—
448M16—521no—
449M16—521no—
450M16—521no—
451M16—521no—
452M16—521no—
453M16—521no—
454M16#610314yes—
455C2×C8—22no—
456C2×C8—22no—
457C2×C8—22no—
458C2×C8—22no—
459C2×C8—22no—
460C2×C8—41no—
461C2×C8—41no—
462C2×C8—41no—
463C2×C8—41no—
464C2×C8—262no—
465C2×C8—262no—
466C2×C8—262no—
467C2×C8—521no—
468C2×C8—521no—
469C2×C8—521no—
470C2×C8—521no—
471C2×C8—521no—
472C2×C8—521no—
473C13#1113911yescharacteristic, complemented, Sylow
474C23—42no—
475C23—264no—
476C23—264no—
477C23—264no—
478C23—522no—
479C23—522no—
480C23—522no—
481C23—522no—
482C23—1044no—
483C23—1044no—
484C23—1044no—
485C23—1044no—
486C23—1044no—
487C23—1044no—
488C23—1044no—
489C23C4⋊C4×D1311yescharacteristic
490C23#8815011yescharacteristic
491C23#8815011yescharacteristic
492C23#8815111yescharacteristic
493C23#8815111yescharacteristic
494C23#8815111yescharacteristic
495C23#8820011yescharacteristic
496D4—522no—
497D4—522no—
498D4—522no—
499D4—522no—
500D4—522no—
501D4—522no—
502D4—522no—
503D4—522no—
504C2×C4C4×D5211yescharacteristic
505C2×C4C4×D5211yescharacteristic
506C2×C4#8812811yescharacteristic
507C2×C4#8812911yescharacteristic
508C2×C4#8813511yescharacteristic
509C2×C4#8813511yescharacteristic
510C2×C4#8813611yescharacteristic
511C2×C4#8813611yescharacteristic
512C2×C4#8813611yescharacteristic
513C2×C4#8813711yescharacteristic
514C2×C4#8813711yescharacteristic
515C2×C4#8813911yescharacteristic
516C2×C4#8813911yescharacteristic
517C2×C4#8814011yescharacteristic
518C2×C4#8814011yescharacteristic
519C2×C4#8814011yescharacteristic
520C2×C4#8814611yescharacteristic
521C2×C4#8814911yescharacteristic
522C2×C4#8814911yescharacteristic
523C2×C4#8814911yescharacteristic
524C2×C4#8815211yescharacteristic
525C2×C4#8815211yescharacteristic
526C2×C4C2×#610311yescharacteristic
527C2×C4#8818411yescharacteristic
528C2×C4#8818411yescharacteristic
529C2×C4#8819211yescharacteristic
530C2×C4#8819311yescharacteristic
531C2×C4#8819311yescharacteristic
532C8—24no—
533C8—42no—
534C8—42no—
535C8—522no—
536C8—522no—
537C8—522no—
538C22—22no—
539C22—22no—
540C22—22no—
541C22—41no—
542C22—41no—
543C22—41no—
544C22—41no—
545C22—524no—
546C22—1044no—
547C22—1044no—
548C22—1044no—
549C22—1044no—
550C22—1044no—
551C22—1044no—
552C22—1044no—
553C22#1171832911yescharacteristic
554C22#1171832911yescharacteristic
555C22#1171833411yescharacteristic
556C22#1171833811yescharacteristic
557C22#1171864811yescharacteristic
558C22#1171865511yescharacteristic
559C22#1171865511yescharacteristic
560C4#1171833111yescharacteristic
561C4#1171833111yescharacteristic
562C4#1171833211yescharacteristic
563C4#1171833511yescharacteristic
564C4#1171860011yescharacteristic
565C4#1171861911yescharacteristic
566C4#1171862211yescharacteristic
567C4#1171862211yescharacteristic
568C2—21no—
569C2—21no—
570C2—21no—
571C2—21no—
572C2—21no—
573C2—21no—
574C2—1044no—
575C2#1311308211yescharacteristic
576C2#1311623312yes—
subgroupG/H
centerC22#11718655
commutatorC22×C4×C13C22×C4
FrattiniC23×C4C22×D13
FittingC13×#1738C2
socleC22×C13#396
prime radicalC23×D52C22
cosocleC23×C4×C13C23
hypercenter#1738D13
hypocenterC13#11139
LCSG ▷ C22×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1738

Complements

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

NH ≅ G/Ntype
1. C2×#11718786C2semidirect
5. #13114562C2semidirect
6. C2×#11718152C2semidirect
7. C13×#1738C2semidirect
191. #1738D13semidirect
473. C13#11139semidirect

Maximal subgroups

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

subgroupindex
C2×#117187862
C22×#880632
#131145622
C2×#117181522
C13×#17382
#1113913