Finite Group Databasebeta

← #11859134

Subgroups — #11859134

Order 1152.

839 conjugacy classes of subgroups.

The subgroup lattice has 648 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4×#3798C211yesmaximal, characteristic
2#10592534C211yesmaximal, characteristic, complemented
3C3×#4837C211yesmaximal, characteristic, complemented
4C3×#4833C211yesmaximal, characteristic, complemented
5#10590955C212yesmaximal
6#10590908C212yesmaximal, complemented
7#10590699C212yesmaximal, complemented
8#10590648C212yesmaximal, complemented
9D3×C4⋊(C3⋊C8)C211yesmaximal, characteristic, complemented
10#10590263C211yesmaximal, characteristic, complemented
11#10590256C211yesmaximal, characteristic, complemented
12#79285—31nomaximal
13#79040—31nomaximal
14C2×#3798C2211yescharacteristic
15C42×C3⋊D3C2211yescharacteristic
16C2×C3×ΓL(1,𝔽25)C2212yes—
17C3×C42×D3C2211yescharacteristic
18C3×C42×D3C2211yescharacteristic
19C4×#627C411yescharacteristic
20C4×#627C411yescharacteristic
21C4×#626C411yescharacteristic
22C4×#626C411yescharacteristic
23C4×#626C411yescharacteristic
24C4×#626C411yescharacteristic
25C4×#625C411yescharacteristic
26C4×#625C411yescharacteristic
27#63874C2211yescharacteristic
28#63855C2211yescharacteristic
29#63855C2211yescharacteristic
30C2×D3×C3⋊C8C2212yes—
31C32×C4⋊C8C2211yescharacteristic
32#63647C2212yes—
33#63642C2212yes—
34C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic
35C3×(C2×D3)⋊C8C2212yes—
36C3×Dic3⋊C8C2212yes—
37C3×C8×Dic3C2212yes—
38C3×C4⋊(C3⋊C8)C2211yescharacteristic
39C3×C4⋊(C3⋊C8)C2211yescharacteristic
40Dic3⋊(C3⋊C8)C2212yes—
41#63557C2212yes—
42(C2×D3)⋊(C3⋊C8)C2212yes—
43#63554C2212yes—
44#63553C2212yes—
45C4×#235—31no—
46C4×#235—31no—
47C3×#431—31no—
48C3×#423—31no—
49#5129—32no—
50#5122—32no—
51#4926—31no—
52C2×C4⋊(C3⋊C8)—31no—
53#4840—32no—
54#4840—32no—
55#4837D311yescharacteristic, complemented
56#4835—31no—
57#4835—31no—
58#4835—31no—
59#4835—61no—
60#4833—31no—
61#4833—31no—
62#4833D311yescharacteristic, complemented
63D3×C4⋊C8—31no—
64#4727—32no—
65#4720—32no—
66#4690—32no—
67#4689—32no—
68C2×C4×C3⋊D3C2×C411yescharacteristic
69C2×C4×C3⋊D3C2×C411yescharacteristic
70C2×C4×C3⋊D3C2311yescharacteristic
71C2×C3×C4×D3C2×C411yescharacteristic
72C2×C3×C4×D3C2×C411yescharacteristic
73C2×C3×C4×D3C2×C411yescharacteristic
74C2×C3×C4×D3C2×C411yescharacteristic
75C2×C3×C4×D3C2311yescharacteristic
76C2×C3×C4×D3C2311yescharacteristic
77C2×#627C2×C411yescharacteristic
78C2×#626C2×C411yescharacteristic
79C2×#626C2×C411yescharacteristic
80C2×#625C2×C411yescharacteristic
81#3798—22no—
82#3798—22no—
83C2×C32×C8C2312yes—
84C32×C42C2311yescharacteristic
85C4×C3⋊Dic3C2×C411yescharacteristic
86C4×C3⋊Dic3C2×C411yescharacteristic
87C4×C3⋊Dic3C2311yescharacteristic
88C2×C3⋊(C3⋊C8)C2312yes—
89C3×C4×Dic3C2×C411yescharacteristic
90C3×C4×Dic3C2×C411yescharacteristic
91C3×C4×Dic3C2×C411yescharacteristic
92C3×C4×Dic3C2×C411yescharacteristic
93C3×C4×Dic3C2311yescharacteristic
94C3×C4×Dic3C2311yescharacteristic
95C2×C3×C3⋊C8C2312yes—
96C2×C3×C3⋊C8C2312yes—
97C3×ΓL(1,𝔽25)—24no—
98#3724C2×C411yescharacteristic
99#3724C2×C411yescharacteristic
100Dic3⋊Dic3C2×C411yescharacteristic
101Dic3⋊Dic3C2×C411yescharacteristic
102Dic3⋊Dic3C2×C411yescharacteristic
103Dic3⋊Dic3C2×C411yescharacteristic
104#3722C2×C411yescharacteristic
105#3722C2×C411yescharacteristic
106(C2×D3)⋊Dic3C2×C411yescharacteristic
107(C2×D3)⋊Dic3C2×C411yescharacteristic
108(C2×D3)⋊Dic3C2×C411yescharacteristic
109(C2×D3)⋊Dic3C2×C411yescharacteristic
110D3×C3⋊C8—24no—
111#2925—91noSylow
112C2×#235—31no—
113C2×#235—31no—
114C2×C3×M16—32no—
115C2×C3×C42—31no—
116C2×C3×C42—31no—
117C4×#67—31no—
118C4×#67—31no—
119C4×#67—31no—
120C4×#67—31no—
121C4×#67—31no—
122C4×#67—31no—
123C4×#67—31no—
124C4×#67—31no—
125#926—31no—
126#926—31no—
127C22×C3⋊C8—32no—
128C2×ΓL(1,𝔽25)C2×D312yes—
129C2×D3×C8—32no—
130C4×D12—31no—
131C4×D12—31no—
132C4×D12—31no—
133C4×D12—31no—
134#872—31no—
135#872—31no—
136#872—31no—
137#872—31no—
138C42×D3—31no—
139C42×D3—31no—
140C42×D3—61no—
141C42×D3C2×D311yescharacteristic
142C42×D3C2×D311yescharacteristic
143C4×Dic6—31no—
144C4×Dic6—31no—
145C4×Dic6—31no—
146C4×Dic6—31no—
147C3×C4⋊C8—21no—
148C3×C4⋊C8—32no—
149C3×C4⋊C8—31no—
150C3×C4⋊C8—31no—
151C3×C4⋊C8C2×D311yescharacteristic
152C3×C4⋊C8C2×D311yescharacteristic
153C3×C22⋊C8—32no—
154C3×C4×C8—32no—
155#830—32no—
156(C2×D3)⋊C8—32no—
157(C2×D3)⋊C8—32no—
158(C2×D3)⋊C8—32no—
159(C2×D3)⋊C8—32no—
160(C2×D3)⋊C8—32no—
161(C2×D3)⋊C8—62no—
162(C2×D3)⋊C8C2×D312yes—
163#815—32no—
164#815—32no—
165#815—32no—
166#815—62no—
167Dic3⋊C8—32no—
168Dic3⋊C8C2×D312yes—
169C8×Dic3—32no—
170C8×Dic3—32no—
171C8×Dic3C2×D312yes—
172C4⋊(C3⋊C8)—31no—
173C4⋊(C3⋊C8)—31no—
174C4⋊(C3⋊C8)—32no—
175C4⋊(C3⋊C8)—61no—
176C4⋊(C3⋊C8)C2×D311yescharacteristic
177C4⋊(C3⋊C8)C2×D311yescharacteristic
178#803—32no—
179C22×C3⋊D3C22×C411yescharacteristic
180C22×C3×D3C22×C411yescharacteristic
181C22×C3×D3C22×C411yescharacteristic
182C2×C32×C4C22×C411yescharacteristic
183C2×C32×C4C22×C411yescharacteristic
184C2×C32×C4C2411yescharacteristic
185C2×C3⋊Dic3C22×C411yescharacteristic
186C2×C3⋊Dic3C22×C411yescharacteristic
187C2×C3⋊Dic3C22×C411yescharacteristic
188C4×C3⋊D3—22no—
189C4×C3⋊D3—21no—
190C4×C3⋊D3—21no—
191C4×C3⋊D3—41no—
192C2×C3×Dic3C22×C411yescharacteristic
193C2×C3×Dic3C22×C411yescharacteristic
194C2×C3×Dic3C22×C411yescharacteristic
195C2×C3×Dic3C22×C411yescharacteristic
196C2×C3×Dic3C22×C411yescharacteristic
197C2×C3×Dic3C22×C411yescharacteristic
198C3×C4×D3—22no—
199C3×C4×D3—22no—
200C3×C4×D3—21no—
201C3×C4×D3—21no—
202C3×C4×D3—41no—
203C3×C4×D3—41no—
204C3×C4×D3#4112yes—
205C3×C4×D3#4112yes—
206#627—22no—
207#626—22no—
208#626—22no—
209#625—22no—
210C32×C8—22no—
211C3⋊(C3⋊C8)—22no—
212C3×C3⋊C8—22no—
213C3×C3⋊C8—22no—
214C4×#41—91no—
215#433—92no—
216#433—92no—
217#432—91no—
218#432—91no—
219#431—31no—
220#431—91no—
221#423—31no—
222C2×C4⋊C8—91no—
223#408—92no—
224#405—92no—
225C22×C3×C4—31no—
226C22×C3×C4—31no—
227C22×C3×C4—31no—
228C22×C3×C4—31no—
229C22×C3×C4—31no—
230C22×C3×C4—31no—
231C2×#67—31no—
232C2×#67—31no—
233C2×#67—31no—
234C2×#67—31no—
235#235—62no—
236#235—62no—
237#235—62no—
238#235—62no—
239C2×D12—31no—
240C2×D12—31no—
241C2×C4×D3—31no—
242C2×C4×D3—31no—
243C2×C4×D3—31no—
244C2×C4×D3—31no—
245C2×C4×D3—31no—
246C2×C4×D3—31no—
247C2×C4×D3—61no—
248C2×C4×D3—61no—
249C2×C4×D3—61no—
250C2×C4×D3C4×D311yescharacteristic
251C2×C4×D3C4×D311yescharacteristic
252C2×C4×D3C4×D311yescharacteristic
253C2×C4×D3C4×D311yescharacteristic
254C2×C4×D3C22×D311yescharacteristic
255C2×C4×D3C22×D311yescharacteristic
256C2×Dic6—31no—
257C2×Dic6—31no—
258C3×M16—64no—
259C2×C3×C8—22no—
260C2×C3×C8—32no—
261C2×C3×C8—32no—
262C2×C3×C8C22×D312yes—
263C2×C3×C8C22×D312yes—
264C3×C42—21no—
265C3×C42—31no—
266C3×C42—31no—
267C3×C42—31no—
268C3×C42—31no—
269C3×C42—31no—
270C3×C42—31no—
271C3×C42C22×D311yescharacteristic
272C3×C42C22×D311yescharacteristic
273#217—31no—
274#217—31no—
275#217—31no—
276#217—31no—
277(C2×D3)⋊C4—31no—
278(C2×D3)⋊C4—31no—
279(C2×D3)⋊C4—31no—
280(C2×D3)⋊C4—31no—
281(C2×D3)⋊C4—31no—
282(C2×D3)⋊C4—31no—
283(C2×D3)⋊C4—31no—
284(C2×D3)⋊C4—31no—
285C4⋊Dic3—31no—
286C4⋊Dic3—31no—
287C4⋊Dic3—31no—
288C4⋊Dic3—31no—
289Dic3⋊C4—31no—
290Dic3⋊C4—31no—
291Dic3⋊C4—31no—
292Dic3⋊C4—31no—
293Dic3⋊C4—31no—
294Dic3⋊C4—31no—
295Dic3⋊C4—31no—
296Dic3⋊C4—31no—
297C4×Dic3—31no—
298C4×Dic3—31no—
299C4×Dic3—31no—
300C4×Dic3—31no—
301C4×Dic3—31no—
302C4×Dic3—31no—
303C4×Dic3—61no—
304C4×Dic3—61no—
305C4×Dic3—61no—
306C4×Dic3C4×D311yescharacteristic
307C4×Dic3C4×D311yescharacteristic
308C4×Dic3C4×D311yescharacteristic
309C4×Dic3C4×D311yescharacteristic
310C4×Dic3C22×D311yescharacteristic
311C4×Dic3C22×D311yescharacteristic
312C2×C3⋊C8—32no—
313C2×C3⋊C8—32no—
314C2×C3⋊C8—62no—
315C2×C3⋊C8—64no—
316C2×C3⋊C8C22×D312yes—
317C2×C3⋊C8C22×D312yes—
318ΓL(1,𝔽25)—24no—
319D3×C8—64no—
320C22×C32C23×C411yescharacteristic
321C2×C3⋊D3—21no—
322C2×C3⋊D3—21no—
323C2×C3⋊D3—21no—
324C2×C3×D3—21no—
325C2×C3×D3—21no—
326C2×C3×D3—21no—
327C2×C3×D3—21no—
328C2×C3×D3—21no—
329C2×C3×D3#11712yes—
330C32×C4—21no—
331C32×C4#13112yes—
332C32×C4C2×#4111yescharacteristic
333C32×C4C2×#4111yescharacteristic
334C3⋊Dic3—21no—
335C3⋊Dic3—21no—
336C3⋊Dic3—21no—
337C3×Dic3—21no—
338C3×Dic3—21no—
339C3×Dic3—21no—
340C3×Dic3—21no—
341C3×Dic3—21no—
342C3×Dic3#11712yes—
343C2×#41—91no—
344C2×M16—32no—
345C22×C8—92no—
346C4×Q8—91no—
347C4×Q8—91no—
348C4×D4—91no—
349C4×D4—91no—
350C4×D4—91no—
351C4×D4—91no—
352C4×D4—91no—
353C4×D4—91no—
354#117—91no—
355#117—91no—
356#117—91no—
357C2×C42—31no—
358C2×C42—31no—
359C2×C42—91no—
360C4⋊C8—32no—
361C4⋊C8—31no—
362C4⋊C8—31no—
363C4⋊C8—92no—
364C4⋊C8—91no—
365C4⋊C8D3211yescharacteristic
366C22⋊C8—32no—
367C22⋊C8—92no—
368C22⋊C8—92no—
369C22⋊C8—92no—
370#97—92no—
371#97—92no—
372C4×C8—32no—
373C4×C8—92no—
374C23×C3—31no—
375C23×C3—31no—
376C22×D3—31no—
377C22×D3—31no—
378C22×D3—61no—
379C22×D3C2×C4×D311yescharacteristic
380C22×D3C2×C4×D311yescharacteristic
381C2×C3×C4—21no—
382C2×C3×C4—21no—
383C2×C3×C4—21no—
384C2×C3×C4—31no—
385C2×C3×C4—32no—
386C2×C3×C4—32no—
387C2×C3×C4—31no—
388C2×C3×C4—31no—
389C2×C3×C4—31no—
390C2×C3×C4—31no—
391C2×C3×C4—31no—
392C2×C3×C4—62no—
393C2×C3×C4—62no—
394C2×C3×C4—61no—
395C2×C3×C4—61no—
396C2×C3×C4—121no—
397C2×C3×C4—121no—
398C2×C3×C4C2×C4×D311yescharacteristic
399C2×C3×C4C2×C4×D311yescharacteristic
400C2×C3×C4C2×C4×D311yescharacteristic
401C2×C3×C4C2×C4×D311yescharacteristic
402C2×C3×C4C23×D311yescharacteristic
403C2×C3×C4C23×D311yescharacteristic
404#67—62no—
405#67—62no—
406#67—62no—
407#67—62no—
408C2×Dic3—31no—
409C2×Dic3—31no—
410C2×Dic3—31no—
411C2×Dic3—31no—
412C2×Dic3—31no—
413C2×Dic3—31no—
414C2×Dic3—61no—
415C2×Dic3—61no—
416C2×Dic3—61no—
417C2×Dic3C2×C4×D311yescharacteristic
418C2×Dic3C2×C4×D311yescharacteristic
419C2×Dic3C2×C4×D311yescharacteristic
420C2×Dic3C2×C4×D311yescharacteristic
421C2×Dic3C2×C4×D311yescharacteristic
422C2×Dic3C2×C4×D311yescharacteristic
423D12—62no—
424D12—62no—
425C4×D3—22no—
426C4×D3—22no—
427C4×D3—21no—
428C4×D3—21no—
429C4×D3—41no—
430C4×D3—41no—
431C4×D3—62no—
432C4×D3—62no—
433C4×D3—61no—
434C4×D3—61no—
435C4×D3—61no—
436C4×D3—61no—
437C4×D3—121no—
438C4×D3—122no—
439C4×D3—121no—
440C4×D3—121no—
441C4×D3—121no—
442C4×D3—122no—
443C4×D3#23712yes—
444C4×D3#23912yes—
445Dic6—62no—
446Dic6—62no—
447C3×C8—22no—
448C3×C8—22no—
449C3×C8—42no—
450C3×C8—62no—
451C3×C8—62no—
452C3⋊C8—22no—
453C3⋊C8—22no—
454C3⋊C8—62no—
455C3⋊C8—62no—
456C3⋊C8—122no—
457C2×C32C2×#11711yescharacteristic
458C2×C32C2×#13111yescharacteristic
459C2×C32#56811yescharacteristic
460C3⋊D3—41no—
461C3×D3—22no—
462C3×D3—41no—
463#41—182no—
464#41—182no—
465C2×Q8—91no—
466C2×D4—91no—
467C2×D4—91no—
468C2×D4—91no—
469C22×C4—31no—
470C22×C4—31no—
471C22×C4—31no—
472C22×C4—31no—
473C22×C4—31no—
474C22×C4—31no—
475C22×C4—91no—
476C22×C4—91no—
477C22×C4—91no—
478M16—64no—
479C2×C8—32no—
480C2×C8—32no—
481C2×C8—92no—
482C2×C8—184no—
483C2×C8C2×D3212yes—
484C4⋊C4—91no—
485C4⋊C4—91no—
486C4⋊C4—91no—
487C4⋊C4—91no—
488C4⋊C4—91no—
489C4⋊C4—91no—
490C22⋊C4—91no—
491C22⋊C4—91no—
492C22⋊C4—91no—
493C22⋊C4—91no—
494C22⋊C4—91no—
495C22⋊C4—91no—
496C42—31no—
497C42—31no—
498C42—31no—
499C42—31no—
500C42—31no—
501C42—31no—
502C42—91no—
503C42—91no—
504C42—91no—
505C42C2×D3211yescharacteristic
506C22×C3—21no—
507C22×C3—32no—
508C22×C3—61no—
509C22×C3—61no—
510C22×C3—61no—
511C22×C3—61no—
512C22×C3—61no—
513C22×C3C22×C4×D311yescharacteristic
514C22×C3C22×C4×D311yescharacteristic
515C2×D3—21no—
516C2×D3—21no—
517C2×D3—21no—
518C2×D3—21no—
519C2×D3—21no—
520C2×D3—62no—
521C2×D3—61no—
522C2×D3—61no—
523C2×D3—61no—
524C2×D3—61no—
525C2×D3—61no—
526C2×D3—61no—
527C2×D3—121no—
528C2×D3—121no—
529C2×D3#89212yes—
530C3×C4—21no—
531C3×C4—21no—
532C3×C4—21no—
533C3×C4—22no—
534C3×C4—21no—
535C3×C4—32no—
536C3×C4—41no—
537C3×C4—61no—
538C3×C4—61no—
539C3×C4—61no—
540C3×C4—61no—
541C3×C4—61no—
542C3×C4#90112yes—
543C3×C4#90712yes—
544C3×C4C2×#23711yescharacteristic
545C3×C4C2×#23911yescharacteristic
546C3×C4D3×#4111yescharacteristic
547C3×C4D3×#4111yescharacteristic
548Dic3—21no—
549Dic3—21no—
550Dic3—21no—
551Dic3—21no—
552Dic3—21no—
553Dic3—61no—
554Dic3—61no—
555Dic3—61no—
556Dic3—61no—
557Dic3—61no—
558Dic3—61no—
559Dic3—121no—
560Dic3—121no—
561Dic3—121no—
562Dic3#89212yes—
563C32#292511yescharacteristic, complemented, Sylow
564C23—31no—
565C23—31no—
566C23—91no—
567Q8—182no—
568D4—182no—
569D4—182no—
570D4—182no—
571C2×C4—31no—
572C2×C4—32no—
573C2×C4—32no—
574C2×C4—31no—
575C2×C4—31no—
576C2×C4—31no—
577C2×C4—31no—
578C2×C4—31no—
579C2×C4—61no—
580C2×C4—62no—
581C2×C4—62no—
582C2×C4—61no—
583C2×C4—91no—
584C2×C4—91no—
585C2×C4—91no—
586C2×C4—121no—
587C2×C4—121no—
588C2×C4—181no—
589C2×C4—182no—
590C2×C4—181no—
591C2×C4—361no—
592C2×C4C4×D3211yescharacteristic
593C2×C4C4×D3211yescharacteristic
594C2×C4C22×D3211yescharacteristic
595C8—22no—
596C8—62no—
597C8—62no—
598C8—182no—
599C2×C3—21no—
600C2×C3—21no—
601C2×C3—21no—
602C2×C3—62no—
603C2×C3—121no—
604C2×C3C2×#89211yescharacteristic
605C2×C3D3×#11711yescharacteristic
606C2×C3C2×#90111yescharacteristic
607C2×C3C2×#90711yescharacteristic
608C2×C3#574511yescharacteristic
609C2×C3#574511yescharacteristic
610D3—22no—
611D3—41no—
612D3—122no—
613D3—121no—
614D3—121no—
615C22—32no—
616C22—61no—
617C22—61no—
618C22—61no—
619C22—61no—
620C22—61no—
621C22—181no—
622C22—181no—
623C22—181no—
624C22C2×C4×D3211yescharacteristic
625C4—21no—
626C4—32no—
627C4—61no—
628C4—61no—
629C4—61no—
630C4—61no—
631C4—61no—
632C4—181no—
633C4—181no—
634C4—181no—
635C4#6380412yes—
636C4D3×#23711yescharacteristic
637C4D3×#23911yescharacteristic
638C3—21no—
639C3#7904011yescharacteristic, complemented
640C3#7928511yescharacteristic, complemented
641C2—62no—
642C2—121no—
643C2—361no—
644C2D3×#89211yescharacteristic
645C2C2×#6380411yescharacteristic
646C2#1059472211yescharacteristic
subgroupG/H
center, FrattiniC2×C4C22×D32
commutator, socleC22×C32C23×C4
FittingC32×C4⋊C8C22
prime radicalC2×#3798C22
cosocleC2×C32×C4C24
hypercenterC4⋊C8D32
hypocenterC32#2925
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C2×C4 ◁ C4⋊C8

Complements

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

NH ≅ G/Ntype
2. #10592534C2semidirect
3. C3×#4837C2semidirect
4. C3×#4833C2semidirect
6. #10590908C2semidirect
7. #10590699C2semidirect
8. #10590648C2semidirect
9. D3×C4⋊(C3⋊C8)C2semidirect
10. #10590263C2semidirect
11. #10590256C2semidirect
55. #4837D3semidirect
62. #4833D3semidirect
563. C32#2925semidirect
639. C3#79040semidirect
640. C3#79285semidirect

Maximal subgroups

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

subgroupindex
C4×#37982
#105925342
C3×#48372
C3×#48332
#105909552
#105909082
#105906992
#105906482
D3×C4⋊(C3⋊C8)2
#105902632
#105902562
#792853
#790403