Finite Group Databasebeta

← #34071928

Subgroups — #34071928

Order 19328.

1252 conjugacy classes of subgroups.

The subgroup lattice has 582 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×D4×D151C211yesmaximal, characteristic
2C2×C4×C22⋊D151C211yesmaximal, characteristic, complemented
3C2×(C22⋊D151)⋊C4C211yesmaximal, characteristic, complemented
4C22×(C2×D151)⋊C4C211yesmaximal, characteristic, complemented
5C2×C22⋊C4×D151C211yesmaximal, characteristic, complemented
6#23752112C211yesmaximal, characteristic, complemented
7#23752112C211yesmaximal, characteristic, complemented
8#23752092C211yesmaximal, characteristic, complemented
9#23752090C211yesmaximal, characteristic, complemented
10#23752090C211yesmaximal, characteristic, complemented
11#23752071C211yesmaximal, characteristic, complemented
12#23752067C211yesmaximal, characteristic, complemented
13#23752067C211yesmaximal, characteristic, complemented
14#23752059C211yesmaximal, characteristic, complemented
15#386×C151C211yesmaximal, characteristic, complemented
16C24×D151C2211yescharacteristic
17C24×D151C2211yescharacteristic
18C22×D604C2211yescharacteristic
19C22×C22⋊D151C2211yescharacteristic
20C22×C22⋊D151C2211yescharacteristic
21C2×D4×D151—24no—
22C2×D4×D151—24no—
23C2×D4×D151C418yescomplemented
24C23×Dic151C2211yescharacteristic, complemented
25C22×C4×D151C2211yescharacteristic
26C22×C4×D151C2211yescharacteristic, complemented
27C22×C4×D151C2211yescharacteristic, complemented
28C4×C22⋊D151—24no—
29(C22⋊D151)⋊C4—24no—
30C2×Dic151⋊C4C2211yescharacteristic, complemented
31C2×Dic151⋊C4C2211yescharacteristic, complemented
32C2×C22⋊Dic151C2211yescharacteristic, complemented
33C2×C22⋊Dic151C2211yescharacteristic, complemented
34C2×C22⋊Dic151C2211yescharacteristic, complemented
35C2×(C2×D151)⋊C4—24no—
36C2×(C2×D151)⋊C4C2211yescharacteristic
37C2×(C2×D151)⋊C4C2211yescharacteristic
38C2×(C2×D151)⋊C4C2211yescharacteristic
39C2×(C2×D151)⋊C4C2211yescharacteristic
40C2×(C2×D151)⋊C4C2211yescharacteristic, complemented
41C2×(C2×D151)⋊C4C2211yescharacteristic, complemented
42C2×(C2×D151)⋊C4C2211yescharacteristic, complemented
43C2×(C2×D151)⋊C4C2211yescharacteristic, complemented
44C2×(C2×D151)⋊C4C2211yescharacteristic, complemented
45C2×(C2×D151)⋊C4C2211yescharacteristic, complemented
46C22⋊C4×D151—24no—
47C2×C4×Dic151C2211yescharacteristic, complemented
48C2×C4×Dic151C2211yescharacteristic, complemented
49C151⋊#95C2211yescharacteristic, complemented
50C151⋊#95C2211yescharacteristic, complemented
51C22×D4×C151C2211yescharacteristic
52C23×C4×C151C2211yescharacteristic, complemented
53C2×C22⋊C4×C151C2211yescharacteristic, complemented
54C2×C22⋊C4×C151C2211yescharacteristic, complemented
55C2×C22⋊C4×C151C2211yescharacteristic, complemented
56#95×C151C2211yescharacteristic, complemented
57#95×C151C2211yescharacteristic, complemented
58C23×D151—22no—
59C23×D151—22no—
60C23×D151—22no—
61C23×D151—22no—
62C23×D151—22no—
63C23×D151—22no—
64C23×D151—22no—
65C23×D151—22no—
66C23×D151—41no—
67C23×D151—41no—
68C23×D151—41no—
69C23×D151—41no—
70C23×D151C2×C414yescomplemented
71C23×D151C2×C414yescomplemented
72C23×D151C2311yescharacteristic
73C23×D151C2311yescharacteristic
74C23×D151C2311yescharacteristic
75C2×D604—22no—
76C2×D604—22no—
77C2×D604C2×C414yescomplemented
78C2×C22⋊D151—22no—
79C2×C22⋊D151—22no—
80C2×C22⋊D151C2×C414yes—
81C2×C22⋊D151C2×C414yescomplemented
82C2×C22⋊D151D414yes—
83C2×C22⋊D151D414yes—
84D4×D151—232no—
85C22×Dic151—22no—
86C22×Dic151—22no—
87C22×Dic151—41no—
88C22×Dic151C2311yescharacteristic
89C22×Dic151C2311yescharacteristic
90C22×Dic151C2311yescharacteristic
91C22×Dic151C2311yescharacteristic
92C22×Dic151C2311yescharacteristic
93C2×C4×D151—22no—
94C2×C4×D151—22no—
95C2×C4×D151—22no—
96C2×C4×D151—22no—
97C2×C4×D151—22no—
98C2×C4×D151—22no—
99C2×C4×D151—41no—
100C2×C4×D151—41no—
101C2×C4×D151C2×C414yescomplemented
102Dic151⋊C4—22no—
103Dic151⋊C4—22no—
104C22⋊Dic151—22no—
105C22⋊Dic151—22no—
106C22⋊Dic151—41no—
107(C2×D151)⋊C4—22no—
108(C2×D151)⋊C4—22no—
109(C2×D151)⋊C4—22no—
110(C2×D151)⋊C4—22no—
111(C2×D151)⋊C4—22no—
112(C2×D151)⋊C4—22no—
113(C2×D151)⋊C4—22no—
114(C2×D151)⋊C4—41no—
115(C2×D151)⋊C4—41no—
116(C2×D151)⋊C4D414yescomplemented
117C4×Dic151—22no—
118C4×Dic151—22no—
119C24×C151C2311yescharacteristic
120C24×C151C2311yescharacteristic
121C2×D4×C151—22no—
122C2×D4×C151—22no—
123C2×D4×C151C2×C414yescomplemented
124C22×C4×C151—22no—
125C22×C4×C151—22no—
126C22×C4×C151—41no—
127C22×C4×C151C2311yescharacteristic
128C22×C4×C151C2311yescharacteristic
129C22×C4×C151C2311yescharacteristic
130C22×C4×C151C2311yescharacteristic
131C22×C4×C151C2311yescharacteristic
132C22⋊C4×C151—22no—
133C22⋊C4×C151—22no—
134C22⋊C4×C151—41no—
135C22×D151—21no—
136C22×D151—21no—
137C22×D151—21no—
138C22×D151—21no—
139C22×D151—21no—
140C22×D151—21no—
141C22×D151—21no—
142C22×D151—21no—
143C22×D151—28no—
144C22×D151—21no—
145C22×D151—21no—
146C22×D151—21no—
147C22×D151—21no—
148C22×D151—21no—
149C22×D151—21no—
150C22×D151—28no—
151C22×D151—28no—
152C22×D151—28no—
153C22×D151—44no—
154C22×D151—44no—
155C22×D151—44no—
156C22×D151—44no—
157C22×D151—44no—
158C22×D151—44no—
159C22×D151—44no—
160C22×D151—44no—
161C22×D151—44no—
162C22×D151—44no—
163C22×D151C22×C412yes—
164C22×D151C22×C412yes—
165C22×D151C22×C412yes—
166C22×D151C2×D412yes—
167C22×D151C2×D412yes—
168C22×D151C2×D412yes—
169C22×D151#4112yes—
170D604—28no—
171C22⋊D151—28no—
172C22⋊D151C22⋊C4116yescomplemented
173C2×Dic151—21no—
174C2×Dic151—21no—
175C2×Dic151—21no—
176C2×Dic151—21no—
177C2×Dic151—21no—
178C2×Dic151—21no—
179C2×Dic151—21no—
180C2×Dic151—21no—
181C2×Dic151—21no—
182C2×Dic151—21no—
183C2×Dic151—21no—
184C2×Dic151—44no—
185C2×Dic151C22×C412yes—
186C2×Dic151C2×D412yes—
187C2×Dic151C2×D412yes—
188C2×Dic151C2×D412yescomplemented
189C4×D151—28no—
190C4×D151—44no—
191C4×D151—44no—
192C23×C151—21no—
193C23×C151—21no—
194C23×C151—21no—
195C23×C151—21no—
196C23×C151—21no—
197C23×C151—21no—
198C23×C151—21no—
199C23×C151—21no—
200C23×C151—21no—
201C23×C151—21no—
202C23×C151C22×C412yes—
203C23×C151C22×C412yes—
204C23×C151C2×D412yes—
205C23×C151C2×D412yes—
206C23×C151C2411yescharacteristic
207D4×C151—28no—
208C2×C4×C151—21no—
209C2×C4×C151—21no—
210C2×C4×C151—21no—
211C2×C4×C151—21no—
212C2×C4×C151—21no—
213C2×C4×C151—21no—
214C2×C4×C151—21no—
215C2×C4×C151—21no—
216C2×C4×C151—21no—
217C2×C4×C151—21no—
218C2×C4×C151—21no—
219C2×C4×C151—21no—
220C2×C4×C151—21no—
221C2×C4×C151—44no—
222C2×C4×C151C22×C412yes—
223C2×C4×C151C2×D412yescomplemented
224C22×C151—22no—
225C22×C151—22no—
226C22×C151—22no—
227C22×C151—22no—
228C22×C151—22no—
229C22×C151—22no—
230C22×C151—22no—
231C22×C151—22no—
232C22×C151—22no—
233C22×C151—41no—
234C22×C151—41no—
235C22×C151—41no—
236C22×C151—41no—
237C22×C151C2×C22⋊C414yescomplemented
238C22×C151C23×C411yescharacteristic
239C22×C151C22×D411yescharacteristic
240C22×C151C22×D411yescharacteristic
241C22×C151C22×D411yescharacteristic
242C22×C151C2×#4111yescharacteristic
243C22×C151H(5,𝔽2)11yescharacteristic
244C22×C151H(5,𝔽2)11yescharacteristic
245C2×D151—22no—
246C2×D151—22no—
247C2×D151—22no—
248C2×D151—22no—
249C2×D151—22no—
250C2×D151—22no—
251C2×D151—22no—
252C2×D151—22no—
253C2×D151—22no—
254C2×D151—22no—
255C2×D151—22no—
256C2×D151—22no—
257C2×D151—22no—
258C2×D151—22no—
259C2×D151—22no—
260C2×D151—416no—
261C2×D151—416no—
262C2×D151—41no—
263C2×D151—41no—
264C2×D151—41no—
265C2×D151—41no—
266C2×D151C2×C22⋊C414yescomplemented
267C2×D151C4×D414yescomplemented
268C4×C151—22no—
269C4×C151—22no—
270C4×C151—41no—
271C4×C151—41no—
272C4×C151—41no—
273Dic151—22no—
274Dic151—41no—
275Dic151—41no—
276Dic151—41no—
277Dic151C2×C22⋊C414yescomplemented
278C2×C151—24no—
279C2×C151—42no—
280C2×C151C22×C22⋊C411yescharacteristic
281C2×C151C2×C4×D411yescharacteristic
282C2×C151#51811yescharacteristic
283C2×C151D4211yescharacteristic
284C2×C151D4211yescharacteristic
285C2×C151#54611yescharacteristic
286C2×C151#54611yescharacteristic
287D151—24no—
288D151—24no—
289D151—42no—
290C151D4×C22⋊C411yescharacteristic, complemented, Sylow
291D4×C22⋊C4—1511nomaximal, Sylow
292C23×D4—1511no—
293C2×C4×D4—1511no—
294C2×C4×D4—1511no—
295C22×C22⋊C4—1511no—
296C22×C22⋊C4—1511no—
297#390—1511no—
298#390—1511no—
299#386—1511no—
300#386—1511no—
301#386—1511no—
302#386D15111yescharacteristic, complemented
303#380—1511no—
304#379—1511no—
305#379—1511no—
306C4×C22⋊C4—1511no—
307C25—1511no—
308C25—1511no—
309C22×D4—3024no—
310C22×D4—3024no—
311C22×D4—1511no—
312C22×D4—1518no—
313C22×D4—1511no—
314C22×D4—1511no—
315C22×D4C2×D15111yescharacteristic
316C23×C4—1511no—
317C23×C4—1511no—
318C23×C4—1511no—
319C23×C4—1511no—
320C23×C4C2×D15111yescharacteristic, complemented
321C4×D4—3024no—
322C4×D4—3024no—
323C2×C4⋊C4—1511no—
324C2×C4⋊C4—1511no—
325C2×C22⋊C4—3024no—
326C2×C22⋊C4—3024no—
327C2×C22⋊C4—1511no—
328C2×C22⋊C4—1511no—
329C2×C22⋊C4—1511no—
330C2×C22⋊C4—1511no—
331C2×C22⋊C4—1511no—
332C2×C22⋊C4—1511no—
333C2×C22⋊C4—1511no—
334C2×C22⋊C4—1511no—
335C2×C22⋊C4—1511no—
336C2×C22⋊C4—1511no—
337C2×C22⋊C4—1511no—
338C2×C22⋊C4—1511no—
339C2×C22⋊C4—1511no—
340C2×C22⋊C4C2×D15111yescharacteristic, complemented
341C2×C22⋊C4C2×D15111yescharacteristic, complemented
342C2×C22⋊C4C2×D15111yescharacteristic, complemented
343C2×C42—1511no—
344C2×C42—1511no—
345#95—1511no—
346#95—1511no—
347#95C2×D15111yescharacteristic, complemented
348#95C2×D15111yescharacteristic, complemented
349C24—3022no—
350C24—3022no—
351C24—3022no—
352C24—3022no—
353C24—3022no—
354C24—3022no—
355C24—3022no—
356C24—3022no—
357C24—6041no—
358C24—6041no—
359C24—6041no—
360C24—6041no—
361C24—1511no—
362C24—1514no—
363C24—1514no—
364C24—1511no—
365C24—1511no—
366C24C22×D15111yescharacteristic
367C24C22×D15111yescharacteristic
368C2×D4—22no—
369C2×D4—22no—
370C2×D4—3022no—
371C2×D4—3022no—
372C2×D4—30232no—
373C2×D4—3022no—
374C2×D4—3022no—
375C2×D4—1514no—
376C2×D4—1514no—
377C2×D4—1514no—
378C2×D4—1514no—
379C2×D4—1514no—
380C2×D4C4×D15114yescomplemented
381C22×C4—22no—
382C22×C4—22no—
383C22×C4—41no—
384C22×C4—3022no—
385C22×C4—3022no—
386C22×C4—3022no—
387C22×C4—3022no—
388C22×C4—3022no—
389C22×C4—3022no—
390C22×C4—3022no—
391C22×C4—3022no—
392C22×C4—6041no—
393C22×C4—6041no—
394C22×C4—6041no—
395C22×C4—1511no—
396C22×C4—1511no—
397C22×C4—1511no—
398C22×C4—1511no—
399C22×C4—1514no—
400C22×C4—1511no—
401C22×C4C22×D15111yescharacteristic
402C22×C4C22×D15111yescharacteristic
403C22×C4C22×D15111yescharacteristic
404C22×C4C22×D15111yescharacteristic
405C22×C4C22×D15111yescharacteristic
406C4⋊C4—3022no—
407C4⋊C4—3022no—
408C22⋊C4—22no—
409C22⋊C4—22no—
410C22⋊C4—41no—
411C22⋊C4—3022no—
412C22⋊C4—3022no—
413C22⋊C4—3022no—
414C22⋊C4—3022no—
415C22⋊C4—3022no—
416C22⋊C4—3022no—
417C22⋊C4—3022no—
418C22⋊C4—3022no—
419C22⋊C4—3022no—
420C22⋊C4—6041no—
421C22⋊C4—6041no—
422C22⋊C4—6041no—
423C22⋊C4—1514no—
424C42—3022no—
425C42—3022no—
426C23—21no—
427C23—21no—
428C23—21no—
429C23—21no—
430C23—21no—
431C23—21no—
432C23—21no—
433C23—21no—
434C23—21no—
435C23—21no—
436C23—3028no—
437C23—3028no—
438C23—3028no—
439C23—3021no—
440C23—3021no—
441C23—3021no—
442C23—3021no—
443C23—3021no—
444C23—3021no—
445C23—3021no—
446C23—3021no—
447C23—3028no—
448C23—3021no—
449C23—3021no—
450C23—3021no—
451C23—3021no—
452C23—3021no—
453C23—3021no—
454C23—6044no—
455C23—6044no—
456C23—6044no—
457C23—6044no—
458C23—6044no—
459C23—6044no—
460C23—6044no—
461C23—6044no—
462C23—6044no—
463C23—6044no—
464C23—1512no—
465C23—1512no—
466C23—1512no—
467C23—1512no—
468C23—1512no—
469C23—1512no—
470C23—1512no—
471C23C2×C4×D15112yes—
472C23C2×C4×D15112yes—
473C23D4×D15112yes—
474C23D4×D15112yes—
475C23C23×D15111yescharacteristic
476D4—28no—
477D4—3028no—
478D4—3028no—
479D4—15116no—
480C2×C4—21no—
481C2×C4—21no—
482C2×C4—21no—
483C2×C4—21no—
484C2×C4—21no—
485C2×C4—21no—
486C2×C4—21no—
487C2×C4—21no—
488C2×C4—21no—
489C2×C4—21no—
490C2×C4—21no—
491C2×C4—21no—
492C2×C4—21no—
493C2×C4—44no—
494C2×C4—3028no—
495C2×C4—3021no—
496C2×C4—3021no—
497C2×C4—3021no—
498C2×C4—3021no—
499C2×C4—3021no—
500C2×C4—3021no—
501C2×C4—3021no—
502C2×C4—3021no—
503C2×C4—3021no—
504C2×C4—3021no—
505C2×C4—3021no—
506C2×C4—6044no—
507C2×C4—6044no—
508C2×C4—6044no—
509C2×C4—1512no—
510C2×C4—1512no—
511C2×C4—1512no—
512C2×C4—1512no—
513C2×C4C2×C4×D15112yes—
514C2×C4D4×D15112yescomplemented
515C22—22no—
516C22—22no—
517C22—22no—
518C22—22no—
519C22—22no—
520C22—22no—
521C22—22no—
522C22—22no—
523C22—22no—
524C22—41no—
525C22—41no—
526C22—41no—
527C22—41no—
528C22—3022no—
529C22—3022no—
530C22—3022no—
531C22—3022no—
532C22—3022no—
533C22—3022no—
534C22—3022no—
535C22—3022no—
536C22—3022no—
537C22—3022no—
538C22—3022no—
539C22—3022no—
540C22—3022no—
541C22—3022no—
542C22—3022no—
543C22—60416no—
544C22—60416no—
545C22—6041no—
546C22—6041no—
547C22—6041no—
548C22—6041no—
549C22—1514no—
550C22—1514no—
551C22C22⋊C4×D15114yescomplemented
552C22C22×C4×D15111yescharacteristic
553C22C2×D4×D15111yescharacteristic
554C22C2×D4×D15111yescharacteristic
555C22C2×D4×D15111yescharacteristic
556C22#41×D15111yescharacteristic
557C22#1801278411yescharacteristic
558C22#1801278511yescharacteristic
559C4—22no—
560C4—22no—
561C4—41no—
562C4—41no—
563C4—41no—
564C4—3022no—
565C4—6041no—
566C4—6041no—
567C4—6041no—
568C4—1514no—
569C2—24no—
570C2—42no—
571C2—3024no—
572C2—3024no—
573C2—6042no—
574C2C2×C22⋊C4×D15111yescharacteristic
575C2C4×D4×D15111yescharacteristic
576C2#2375268411yescharacteristic
577C2#2375284411yescharacteristic
578C2#2375284611yescharacteristic
579C2#2375285111yescharacteristic
580C2#2375285411yescharacteristic
subgroupG/H
center, FrattiniC23C23×D151
commutatorC22×C151C23×C4
Fitting#386×C151C2
socle, cosocleC23×C151C24
prime radicalC22×D4×D151C2
hypercenter#386D151
hypocenterC151D4×C22⋊C4
LCSG ▷ C22×C151 ▷ C151
UCSC1 ◁ C23 ◁ #386

Complements

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

NH ≅ G/Ntype
2. C2×C4×C22⋊D151C2semidirect
3. C2×(C22⋊D151)⋊C4C2semidirect
4. C22×(C2×D151)⋊C4C2semidirect
5. C2×C22⋊C4×D151C2semidirect
6. #23752112C2semidirect
7. #23752112C2semidirect
8. #23752092C2semidirect
9. #23752090C2semidirect
10. #23752090C2semidirect
11. #23752071C2semidirect
12. #23752067C2semidirect
13. #23752067C2semidirect
14. #23752059C2semidirect
15. #386×C151C2semidirect
23. C2×D4×D151C4semidirect
24. C23×Dic151C22semidirect
26. C22×C4×D151C22semidirect
27. C22×C4×D151C22semidirect
30. C2×Dic151⋊C4C22semidirect
31. C2×Dic151⋊C4C22semidirect
32. C2×C22⋊Dic151C22semidirect
33. C2×C22⋊Dic151C22semidirect
34. C2×C22⋊Dic151C22semidirect
40. C2×(C2×D151)⋊C4C22semidirect
41. C2×(C2×D151)⋊C4C22semidirect
42. C2×(C2×D151)⋊C4C22semidirect
43. C2×(C2×D151)⋊C4C22semidirect
44. C2×(C2×D151)⋊C4C22semidirect
45. C2×(C2×D151)⋊C4C22semidirect
47. C2×C4×Dic151C22semidirect
48. C2×C4×Dic151C22semidirect
49. C151⋊#95C22semidirect
50. C151⋊#95C22semidirect
52. C23×C4×C151C22semidirect
53. C2×C22⋊C4×C151C22semidirect
54. C2×C22⋊C4×C151C22semidirect
55. C2×C22⋊C4×C151C22semidirect
56. #95×C151C22semidirect
57. #95×C151C22semidirect
70. C23×D151C2×C4semidirect
71. C23×D151C2×C4semidirect
77. C2×D604C2×C4semidirect
81. C2×C22⋊D151C2×C4semidirect
101. C2×C4×D151C2×C4semidirect
116. (C2×D151)⋊C4D4semidirect
123. C2×D4×C151C2×C4semidirect
172. C22⋊D151C22⋊C4semidirect
188. C2×Dic151C2×D4semidirect
223. C2×C4×C151C2×D4semidirect
237. C22×C151C2×C22⋊C4semidirect
266. C2×D151C2×C22⋊C4semidirect
267. C2×D151C4×D4semidirect
277. Dic151C2×C22⋊C4semidirect
290. C151D4×C22⋊C4semidirect
302. #386D151semidirect
320. C23×C4C2×D151semidirect
340. C2×C22⋊C4C2×D151semidirect
341. C2×C22⋊C4C2×D151semidirect
342. C2×C22⋊C4C2×D151semidirect
347. #95C2×D151semidirect
348. #95C2×D151semidirect
380. C2×D4C4×D151semidirect
514. C2×C4D4×D151semidirect
551. C22C22⋊C4×D151semidirect

Maximal subgroups

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

subgroupindex
C22×D4×D1512
C2×C4×C22⋊D1512
C2×(C22⋊D151)⋊C42
C22×(C2×D151)⋊C42
C2×C22⋊C4×D1512
#237521122
#237520922
#237520902
#237520712
#237520672
#237520592
#386×C1512
D4×C22⋊C4151