Finite Group Databasebeta

← C2×#1899×C151 #50325907

Subgroups — C2×#1899×C151 #50325907

Order 38656.

2066 conjugacy classes of subgroups.

The subgroup lattice has 576 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#123×C151C211yesmaximal, characteristic
2C22×#117×C151C211yesmaximal, characteristic, complemented
3C22×#99×C151C212yesmaximal
4C2×#381×C151C211yesmaximal, characteristic, complemented
5#1899×C151C218yesmaximal, direct product factor
6C2×#342×C151C212yesmaximal, complemented
7C23×D4×C151C2211yescharacteristic
8C24×C4×C151C2211yescharacteristic
9C2×#123×C151—22no—
10C2×#123×C151—22no—
11C2×#123×C151—21no—
12C2×#123×C151—21no—
13C2×#123×C151—22no—
14C2×#123×C151C414yescomplemented
15C2×#123×C151C2214yes—
16C2×#117×C151—22no—
17C2×#117×C151—28no—
18C2×#117×C151C2214yescomplemented
19C22×C4⋊C4×C151—21no—
20C22×C4⋊C4×C151C412yescomplemented
21C22×C22⋊C4×C151C412yescomplemented
22C22×C22⋊C4×C151C2212yes—
23C22×C22⋊C4×C151C2211yescharacteristic
24C22×C22⋊C4×C151C2212yes—
25C22×C42×C151—21no—
26C2×#99×C151—28no—
27C2×#99×C151C2218yes—
28#381×C151—22no—
29#381×C151C2214yescomplemented
30C2×#95×C151—22no—
31#342×C151C2218yescomplemented
32C25×C151C2×C411yescharacteristic
33C25×C151C2311yescharacteristic
34C22×D4×C151—24no—
35C22×D4×C151—21no—
36C22×D4×C151—21no—
37C22×D4×C151—21no—
38C22×D4×C151—21no—
39C22×D4×C151—24no—
40C22×D4×C151C2×C412yes—
41C22×D4×C151C2312yes—
42C23×C4×C151—24no—
43C23×C4×C151—22no—
44C23×C4×C151—22no—
45C23×C4×C151—24no—
46C23×C4×C151C2×C411yescharacteristic
47C23×C4×C151C2×C412yes—
48C23×C4×C151C2×C412yes—
49C23×C4×C151C2×C412yes—
50C23×C4×C151D412yes—
51C23×C4×C151D412yes—
52C23×C4×C151D411yescharacteristic
53C23×C4×C151D411yescharacteristic
54C23×C4×C151D412yes—
55C23×C4×C151C2312yes—
56#123×C151—28no—
57#123×C151—24no—
58#123×C151—24no—
59#123×C151—28no—
60#123×C151—24no—
61#123×C151—24no—
62#117×C151—216no—
63#117×C151—216no—
64C2×C4⋊C4×C151—28no—
65C2×C4⋊C4×C151—24no—
66C2×C4⋊C4×C151—22no—
67C2×C4⋊C4×C151—22no—
68C2×C4⋊C4×C151—24no—
69C2×C4⋊C4×C151C2×C418yescomplemented
70C2×C22⋊C4×C151—24no—
71C2×C22⋊C4×C151—22no—
72C2×C22⋊C4×C151—22no—
73C2×C22⋊C4×C151—22no—
74C2×C22⋊C4×C151—24no—
75C2×C22⋊C4×C151—21no—
76C2×C22⋊C4×C151—21no—
77C2×C22⋊C4×C151—21no—
78C2×C22⋊C4×C151—21no—
79C2×C22⋊C4×C151—24no—
80C2×C22⋊C4×C151—22no—
81C2×C22⋊C4×C151—24no—
82C2×C22⋊C4×C151C2×C412yes—
83C2×C22⋊C4×C151C2×C418yescomplemented
84C2×C22⋊C4×C151D418yes—
85C2×C22⋊C4×C151C2314yes—
86C2×C22⋊C4×C151C2312yes—
87C2×C22⋊C4×C151C2314yes—
88C2×C42×C151—28no—
89C2×C42×C151—24no—
90#99×C151—216no—
91#95×C151—28no—
92C24×C151—21no—
93C24×C151—21no—
94C24×C151—24no—
95C24×C151—44no—
96C24×C151—44no—
97C24×C151C22×C411yescharacteristic
98C24×C151C22×C412yes—
99C24×C151C22×C411yescharacteristic
100C24×C151C2×D411yescharacteristic
101C24×C151C2×D411yescharacteristic
102C24×C151C2×D411yescharacteristic
103C24×C151C2×D411yescharacteristic
104C24×C151C2×D414yes—
105C24×C151#4114yes—
106C24×C151C2411yescharacteristic
107C2×D4×C151—22no—
108C2×D4×C151—22no—
109C2×D4×C151—28no—
110C2×D4×C151—24no—
111C2×D4×C151—22no—
112C2×D4×C151—22no—
113C2×D4×C151—24no—
114C2×D4×C151—42no—
115C2×D4×C151—42no—
116C2×D4×C151—44no—
117C2×D4×C151—44no—
118C2×D4×C151—42no—
119C2×D4×C151—42no—
120C22×C4×C151—28no—
121C22×C4×C151—28no—
122C22×C4×C151—22no—
123C22×C4×C151—22no—
124C22×C4×C151—24no—
125C22×C4×C151—28no—
126C22×C4×C151—28no—
127C22×C4×C151—22no—
128C22×C4×C151—22no—
129C22×C4×C151—24no—
130C22×C4×C151—24no—
131C22×C4×C151—24no—
132C22×C4×C151—22no—
133C22×C4×C151—21no—
134C22×C4×C151—22no—
135C22×C4×C151—21no—
136C22×C4×C151—24no—
137C22×C4×C151—28no—
138C22×C4×C151—24no—
139C22×C4×C151—24no—
140C22×C4×C151—48no—
141C22×C4×C151—44no—
142C22×C4×C151—48no—
143C22×C4×C151—44no—
144C22×C4×C151C22⋊C414yes—
145C22×C4×C151C22⋊C414yes—
146C22×C4×C151C22⋊C412yes—
147C22×C4×C151C22⋊C412yes—
148C22×C4×C151C22⋊C412yes—
149C22×C4×C151C22⋊C412yes—
150C22×C4×C151C22×C412yes—
151C22×C4×C151C22×C414yes—
152C22×C4×C151C22×C414yes—
153C22×C4×C151C2×D414yes—
154C22×C4×C151C2×D412yes—
155C22×C4×C151C2×D412yes—
156C4⋊C4×C151—216no—
157C4⋊C4×C151—28no—
158C4⋊C4×C151—28no—
159C22⋊C4×C151—22no—
160C22⋊C4×C151—22no—
161C22⋊C4×C151—28no—
162C22⋊C4×C151—24no—
163C22⋊C4×C151—22no—
164C22⋊C4×C151—22no—
165C22⋊C4×C151—28no—
166C22⋊C4×C151—28no—
167C22⋊C4×C151—24no—
168C22⋊C4×C151—24no—
169C22⋊C4×C151—44no—
170C22⋊C4×C151C2×D418yes—
171C42×C151—216no—
172C23×C151—24no—
173C23×C151—24no—
174C23×C151—24no—
175C23×C151—22no—
176C23×C151—24no—
177C23×C151—42no—
178C23×C151—42no—
179C23×C151—42no—
180C23×C151—48no—
181C23×C151—48no—
182C23×C151—42no—
183C23×C151—44no—
184C23×C151—44no—
185C23×C151—42no—
186C23×C151—42no—
187C23×C151—44no—
188C23×C151—88no—
189C23×C151C2×C22⋊C411yescharacteristic
190C23×C151C2×C22⋊C411yescharacteristic
191C23×C151C2×C22⋊C411yescharacteristic
192C23×C151C2×C22⋊C411yescharacteristic
193C23×C151C4×D414yes—
194C23×C151C4×D414yes—
195C23×C151#12012yes—
196C23×C151#12012yes—
197C23×C151#12114yes—
198C23×C151#12114yes—
199C23×C151#12312yes—
200C23×C151#12312yes—
201C23×C151C23×C411yescharacteristic
202C23×C151C22×D411yescharacteristic
203C23×C151C22×D411yescharacteristic
204C23×C151C22×D412yes—
205C23×C151C2×#4112yes—
206D4×C151—42no—
207D4×C151—44no—
208D4×C151—42no—
209D4×C151—44no—
210D4×C151—44no—
211C2×C4×C151—28no—
212C2×C4×C151—22no—
213C2×C4×C151—22no—
214C2×C4×C151—28no—
215C2×C4×C151—22no—
216C2×C4×C151—22no—
217C2×C4×C151—28no—
218C2×C4×C151—24no—
219C2×C4×C151—24no—
220C2×C4×C151—28no—
221C2×C4×C151—24no—
222C2×C4×C151—24no—
223C2×C4×C151—24no—
224C2×C4×C151—22no—
225C2×C4×C151—24no—
226C2×C4×C151—28no—
227C2×C4×C151—48no—
228C2×C4×C151—416no—
229C2×C4×C151—44no—
230C2×C4×C151—42no—
231C2×C4×C151—42no—
232C2×C4×C151—44no—
233C2×C4×C151—44no—
234C2×C4×C151—48no—
235C2×C4×C151—44no—
236C2×C4×C151—88no—
237C2×C4×C151C2×C22⋊C414yes—
238C2×C4×C151C2×C22⋊C414yes—
239C22×C151—22no—
240C22×C151—22no—
241C22×C151—22no—
242C22×C151—22no—
243C22×C151—22no—
244C22×C151—22no—
245C22×C151—24no—
246C22×C151—28no—
247C22×C151—28no—
248C22×C151—24no—
249C22×C151—44no—
250C22×C151—42no—
251C22×C151—44no—
252C22×C151—42no—
253C22×C151—42no—
254C22×C151—42no—
255C22×C151—44no—
256C22×C151—42no—
257C22×C151—84no—
258C22×C151—84no—
259C22×C151—84no—
260C22×C151#38612yes—
261C22×C151#38612yes—
262C22×C151#38612yes—
263C22×C151#38612yes—
264C22×C151#41014yes—
265C22×C151C22×C22⋊C411yescharacteristic
266C22×C151C2×C4×D412yes—
267C22×C151C2×#12011yescharacteristic
268C22×C151C2×#12112yes—
269C22×C151C2×#12311yescharacteristic
270C4×C151—24no—
271C4×C151—24no—
272C4×C151—48no—
273C4×C151—44no—
274C4×C151—42no—
275C4×C151—84no—
276C2×C151—21no—
277C2×C151—22no—
278C2×C151—22no—
279C2×C151—22no—
280C2×C151—21no—
281C2×C151—22no—
282C2×C151—22no—
283C2×C151—82no—
284C2×C151#189914yesdirect product factor
285C2×C151C2×#38611yescharacteristic
286C2×C151C2×#41012yes—
287C2×#1899C15111yesmaximal, characteristic, direct product factor, Sylow
288C151C2×#189911yescharacteristic, direct product factor, Sylow
289C22×#123C2×C15111yescharacteristic
290C22×#117C2×C15111yescharacteristic, complemented
291C22×#99C2×C15112yes—
292C2×#381C2×C15111yescharacteristic, complemented
293#1899C2×C15118yesdirect product factor
294C2×#342C2×C15112yescomplemented
295C23×D4C22×C15111yescharacteristic
296C24×C4C22×C15111yescharacteristic
297C2×#123—21no—
298C2×#123—22no—
299C2×#123—22no—
300C2×#123—22no—
301C2×#123—21no—
302C2×#123C4×C15114yescomplemented
303C2×#123C22×C15114yes—
304C2×#117—22no—
305C2×#117—28no—
306C2×#117C22×C15114yescomplemented
307C22×C4⋊C4—21no—
308C22×C4⋊C4C4×C15112yescomplemented
309C22×C22⋊C4C4×C15112yescomplemented
310C22×C22⋊C4C22×C15112yes—
311C22×C22⋊C4C22×C15111yescharacteristic
312C22×C22⋊C4C22×C15112yes—
313C22×C42—21no—
314C2×#99—28no—
315C2×#99C22×C15118yes—
316#381—22no—
317#381C22×C15114yescomplemented
318C2×#95—22no—
319#342C22×C15118yescomplemented
320C25C2×C4×C15111yescharacteristic
321C25C23×C15111yescharacteristic
322C22×D4—24no—
323C22×D4—21no—
324C22×D4—21no—
325C22×D4—21no—
326C22×D4—21no—
327C22×D4—24no—
328C22×D4C2×C4×C15112yes—
329C22×D4C23×C15112yes—
330C23×C4—24no—
331C23×C4—24no—
332C23×C4—22no—
333C23×C4—22no—
334C23×C4C2×C4×C15111yescharacteristic
335C23×C4C2×C4×C15112yes—
336C23×C4C2×C4×C15112yes—
337C23×C4C2×C4×C15112yes—
338C23×C4D4×C15111yescharacteristic
339C23×C4D4×C15112yes—
340C23×C4D4×C15112yes—
341C23×C4D4×C15112yes—
342C23×C4D4×C15111yescharacteristic
343C23×C4C23×C15112yes—
344#123—24no—
345#123—28no—
346#123—24no—
347#123—28no—
348#123—24no—
349#123—24no—
350#117—216no—
351#117—216no—
352C2×C4⋊C4—28no—
353C2×C4⋊C4—24no—
354C2×C4⋊C4—22no—
355C2×C4⋊C4—22no—
356C2×C4⋊C4—24no—
357C2×C4⋊C4C2×C4×C15118yescomplemented
358C2×C22⋊C4—22no—
359C2×C22⋊C4—24no—
360C2×C22⋊C4—21no—
361C2×C22⋊C4—21no—
362C2×C22⋊C4—21no—
363C2×C22⋊C4—21no—
364C2×C22⋊C4—24no—
365C2×C22⋊C4—22no—
366C2×C22⋊C4—22no—
367C2×C22⋊C4—24no—
368C2×C22⋊C4—24no—
369C2×C22⋊C4—22no—
370C2×C22⋊C4C2×C4×C15112yes—
371C2×C22⋊C4C2×C4×C15118yescomplemented
372C2×C22⋊C4D4×C15118yes—
373C2×C22⋊C4C23×C15114yes—
374C2×C22⋊C4C23×C15112yes—
375C2×C22⋊C4C23×C15114yes—
376C2×C42—28no—
377C2×C42—24no—
378#99—216no—
379#95—28no—
380C24—21no—
381C24—21no—
382C24—24no—
383C24—44no—
384C24—44no—
385C24C22×C4×C15111yescharacteristic
386C24C22×C4×C15112yes—
387C24C22×C4×C15111yescharacteristic
388C24C2×D4×C15111yescharacteristic
389C24C2×D4×C15111yescharacteristic
390C24C2×D4×C15111yescharacteristic
391C24C2×D4×C15111yescharacteristic
392C24C2×D4×C15114yes—
393C24#41×C15114yes—
394C24C24×C15111yescharacteristic
395C2×D4—22no—
396C2×D4—22no—
397C2×D4—28no—
398C2×D4—24no—
399C2×D4—22no—
400C2×D4—22no—
401C2×D4—24no—
402C2×D4—42no—
403C2×D4—42no—
404C2×D4—44no—
405C2×D4—44no—
406C2×D4—42no—
407C2×D4—42no—
408C22×C4—28no—
409C22×C4—28no—
410C22×C4—22no—
411C22×C4—22no—
412C22×C4—24no—
413C22×C4—28no—
414C22×C4—28no—
415C22×C4—22no—
416C22×C4—22no—
417C22×C4—24no—
418C22×C4—24no—
419C22×C4—24no—
420C22×C4—22no—
421C22×C4—22no—
422C22×C4—21no—
423C22×C4—21no—
424C22×C4—24no—
425C22×C4—28no—
426C22×C4—24no—
427C22×C4—24no—
428C22×C4—48no—
429C22×C4—44no—
430C22×C4—48no—
431C22×C4—44no—
432C22×C4C22⋊C4×C15114yes—
433C22×C4C22⋊C4×C15112yes—
434C22×C4C22⋊C4×C15112yes—
435C22×C4C22⋊C4×C15112yes—
436C22×C4C22⋊C4×C15114yes—
437C22×C4C22⋊C4×C15112yes—
438C22×C4C22×C4×C15112yes—
439C22×C4C22×C4×C15114yes—
440C22×C4C22×C4×C15114yes—
441C22×C4C2×D4×C15114yes—
442C22×C4C2×D4×C15112yes—
443C22×C4C2×D4×C15112yes—
444C4⋊C4—216no—
445C4⋊C4—28no—
446C4⋊C4—28no—
447C22⋊C4—22no—
448C22⋊C4—22no—
449C22⋊C4—28no—
450C22⋊C4—24no—
451C22⋊C4—22no—
452C22⋊C4—22no—
453C22⋊C4—28no—
454C22⋊C4—28no—
455C22⋊C4—24no—
456C22⋊C4—24no—
457C22⋊C4—44no—
458C22⋊C4C2×D4×C15118yes—
459C42—216no—
460C23—24no—
461C23—24no—
462C23—24no—
463C23—22no—
464C23—24no—
465C23—48no—
466C23—42no—
467C23—42no—
468C23—42no—
469C23—42no—
470C23—48no—
471C23—44no—
472C23—44no—
473C23—42no—
474C23—42no—
475C23—44no—
476C23—88no—
477C23C2×C22⋊C4×C15111yescharacteristic
478C23C2×C22⋊C4×C15111yescharacteristic
479C23C2×C22⋊C4×C15111yescharacteristic
480C23C2×C22⋊C4×C15111yescharacteristic
481C23C4×D4×C15114yes—
482C23C4×D4×C15114yes—
483C23#120×C15112yes—
484C23#120×C15112yes—
485C23#121×C15114yes—
486C23#121×C15114yes—
487C23#123×C15112yes—
488C23#123×C15112yes—
489C23C23×C4×C15111yescharacteristic
490C23C22×D4×C15111yescharacteristic
491C23C22×D4×C15111yescharacteristic
492C23C22×D4×C15112yes—
493C23C2×#41×C15112yes—
494D4—44no—
495D4—44no—
496D4—42no—
497D4—44no—
498D4—42no—
499C2×C4—28no—
500C2×C4—24no—
501C2×C4—24no—
502C2×C4—28no—
503C2×C4—24no—
504C2×C4—24no—
505C2×C4—28no—
506C2×C4—22no—
507C2×C4—22no—
508C2×C4—28no—
509C2×C4—22no—
510C2×C4—22no—
511C2×C4—24no—
512C2×C4—22no—
513C2×C4—24no—
514C2×C4—28no—
515C2×C4—48no—
516C2×C4—416no—
517C2×C4—44no—
518C2×C4—42no—
519C2×C4—42no—
520C2×C4—44no—
521C2×C4—44no—
522C2×C4—48no—
523C2×C4—44no—
524C2×C4—88no—
525C2×C4C2×C22⋊C4×C15114yes—
526C2×C4C2×C22⋊C4×C15114yes—
527C22—22no—
528C22—22no—
529C22—22no—
530C22—22no—
531C22—22no—
532C22—22no—
533C22—24no—
534C22—28no—
535C22—28no—
536C22—24no—
537C22—44no—
538C22—42no—
539C22—44no—
540C22—42no—
541C22—42no—
542C22—42no—
543C22—44no—
544C22—42no—
545C22—84no—
546C22—84no—
547C22—84no—
548C22#386×C15112yes—
549C22#386×C15112yes—
550C22#386×C15112yes—
551C22#386×C15112yes—
552C22#410×C15114yes—
553C22C22×C22⋊C4×C15111yescharacteristic
554C22C2×C4×D4×C15112yes—
555C22C2×#120×C15111yescharacteristic
556C22C2×#121×C15112yes—
557C22C2×#123×C15111yescharacteristic
558C4—24no—
559C4—24no—
560C4—48no—
561C4—44no—
562C4—42no—
563C4—84no—
564C2—21no—
565C2—22no—
566C2—22no—
567C2—22no—
568C2—22no—
569C2—22no—
570C2—21no—
571C2—82no—
572C2#1899×C15114yesdirect product factor
573C2C2×#386×C15111yescharacteristic
574C2C2×#410×C15112yes—
subgroupG/H
center, socleC23×C151C2×C22⋊C4
commutatorC23C23×C4×C151
Frattini, cosocleC24C24×C151
prime radicalC23×D4×C151C22
LCSG ▷ C23 ▷ C2 ▷ C1
UCSC1 ◁ C23×C151 ◁ C24×C4×C151 ◁ G

Complements

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

NH ≅ G/Ntype
2. C22×#117×C151C2semidirect
4. C2×#381×C151C2semidirect
5. #1899×C151C2direct (N × H)
6. C2×#342×C151C2semidirect
14. C2×#123×C151C4semidirect
18. C2×#117×C151C22semidirect
20. C22×C4⋊C4×C151C4semidirect
21. C22×C22⋊C4×C151C4semidirect
29. #381×C151C22semidirect
31. #342×C151C22semidirect
69. C2×C4⋊C4×C151C2×C4semidirect
83. C2×C22⋊C4×C151C2×C4semidirect
284. C2×C151#1899direct (N × H)
287. C2×#1899C151direct (N × H)
288. C151C2×#1899direct (N × H)
290. C22×#117C2×C151semidirect
292. C2×#381C2×C151semidirect
293. #1899C2×C151direct (N × H)
294. C2×#342C2×C151semidirect
302. C2×#123C4×C151semidirect
306. C2×#117C22×C151semidirect
308. C22×C4⋊C4C4×C151semidirect
309. C22×C22⋊C4C4×C151semidirect
317. #381C22×C151semidirect
319. #342C22×C151semidirect
357. C2×C4⋊C4C2×C4×C151semidirect
371. C2×C22⋊C4C2×C4×C151semidirect
572. C2#1899×C151direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#123×C1512
C22×#117×C1512
C22×#99×C1512
C2×#381×C1512
#1899×C1512
C2×#342×C1512
C2×#1899151