Finite Group Databasebeta

← #11786400

Subgroups — #11786400

Order 1152.

797 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
1C22×#3743C211yesmaximal, characteristic
2C2×C3×Dic3⋊C8C211yesmaximal, characteristic, complemented
3C4×#3722C211yesmaximal, characteristic
4C2×Dic3⋊(C3⋊C8)C211yesmaximal, characteristic, complemented
5C2×#63557C211yesmaximal, characteristic
6C3×#4550C211yesmaximal, characteristic, complemented
7#10589155C211yesmaximal, characteristic, complemented
8#70478—31nomaximal
9#68667—31nomaximal
10C22×C4×C3⋊D3C2211yescharacteristic
11C22×C32×C8C2211yescharacteristic
12C22×C3⋊(C3⋊C8)C2211yescharacteristic
13C2×#3743—22no—
14C2×#3743—22no—
15C2×#3743—22no—
16C2×C3×C4×Dic3C2211yescharacteristic
17C2×C3×C4×Dic3C2211yescharacteristic
18C22×C3×C3⋊C8C2211yescharacteristic
19C22×C3×C3⋊C8C2211yescharacteristic
20C2×#3722C411yescharacteristic
21C2×#3722C411yescharacteristic
22C3×Dic3⋊C8—22no—
23#63579C411yescharacteristic
24#63579C411yescharacteristic
25Dic3⋊(C3⋊C8)—22no—
26#63557—22no—
27C22×ΓL(1,𝔽25)—31no—
28C22×ΓL(1,𝔽25)—31no—
29C22×ΓL(1,𝔽25)—61no—
30C2×C3×C4⋊C8—31no—
31C2×(C2×D3)⋊C8—31no—
32C2×(C2×D3)⋊C8—31no—
33C2×Dic3⋊C8—31no—
34C2×Dic3⋊C8D311yescharacteristic, complemented
35C4×(C2×D3)⋊C4—31no—
36C4×(C2×D3)⋊C4—31no—
37C2×C4⋊(C3⋊C8)—31no—
38C3×#336—31no—
39#4550—31no—
40#4550D311yescharacteristic, complemented
41#4524—31no—
42C23×C3⋊D3C2×C411yescharacteristic
43C22×C32×C4C2311yescharacteristic
44C22×C3⋊Dic3C2×C411yescharacteristic
45C2×C4×C3⋊D3—21no—
46C2×C4×C3⋊D3—21no—
47C2×C4×C3⋊D3—21no—
48C2×C4×C3⋊D3—21no—
49C2×C4×C3⋊D3D412yes—
50C2×C4×C3⋊D3Q812yes—
51C22×C3×Dic3C2×C411yescharacteristic
52C22×C3×Dic3C2×C411yescharacteristic
53C22×C3×Dic3C2×C411yescharacteristic
54C22×C3×Dic3C2×C411yescharacteristic
55C2×C32×C8—21no—
56C2×C32×C8—21no—
57C2×C32×C8D412yes—
58C2×C3⋊(C3⋊C8)—21no—
59C2×C3⋊(C3⋊C8)—21no—
60C2×C3⋊(C3⋊C8)D412yes—
61#3743—28no—
62C3×C4×Dic3—21no—
63C3×C4×Dic3—21no—
64C3×C4×Dic3—21no—
65C3×C4×Dic3—21no—
66C2×C3×C3⋊C8—21no—
67C2×C3×C3⋊C8—21no—
68C2×C3×C3⋊C8—21no—
69C2×C3×C3⋊C8—21no—
70C2×C3×C3⋊C8—21no—
71C2×C3×C3⋊C8—21no—
72#3722—22no—
73#3722—22no—
74#1851—91noSylow
75C22×C4×D3—31no—
76C22×C4×D3—31no—
77C22×C4×D3—61no—
78C22×C3×C8—21no—
79C22×C3×C8—31no—
80C22×C3×C8—31no—
81C22×C3×C8C2×D311yescharacteristic
82C22×C3×C8C2×D311yescharacteristic
83C2×C3×C42—31no—
84C2×C3×C42—31no—
85C2×(C2×D3)⋊C4—31no—
86C2×(C2×D3)⋊C4—31no—
87C2×(C2×D3)⋊C4—31no—
88C2×(C2×D3)⋊C4—31no—
89C2×C4×Dic3C2×D311yescharacteristic
90C2×C4×Dic3C2×D311yescharacteristic
91C22×C3⋊C8—31no—
92C22×C3⋊C8—31no—
93C22×C3⋊C8—61no—
94C22×C3⋊C8C2×D311yescharacteristic
95C22×C3⋊C8C2×D311yescharacteristic
96C2×ΓL(1,𝔽25)—62no—
97C2×ΓL(1,𝔽25)—62no—
98C2×ΓL(1,𝔽25)—62no—
99C2×ΓL(1,𝔽25)—62no—
100C2×ΓL(1,𝔽25)—64no—
101C2×ΓL(1,𝔽25)—64no—
102C2×ΓL(1,𝔽25)—64no—
103C2×ΓL(1,𝔽25)—62no—
104C2×ΓL(1,𝔽25)—62no—
105C3×C4⋊C8—62no—
106C3⋊#95—31no—
107C3⋊#95—31no—
108C3⋊#95—31no—
109C3⋊#95—31no—
110(C2×D3)⋊C8—62no—
111(C2×D3)⋊C8—62no—
112Dic3⋊C8—22no—
113Dic3⋊C8—62no—
114C4⋊(C3⋊C8)—62no—
115C23×C32C22×C411yescharacteristic
116C22×C3⋊D3—21no—
117C22×C3⋊D3—21no—
118C22×C3⋊D3—21no—
119C22×C3⋊D3—21no—
120C22×C3⋊D3—21no—
121C22×C3⋊D3—21no—
122C22×C3⋊D3C4⋊C412yes—
123C2×C32×C4C2×D411yescharacteristic
124C2×C32×C4C2×D411yescharacteristic
125C2×C32×C4C2×D411yescharacteristic
126C2×C32×C4C2×Q811yescharacteristic
127C2×C32×C4#4111yescharacteristic
128C2×C32×C4#4111yescharacteristic
129C2×C3⋊Dic3—21no—
130C2×C3⋊Dic3—21no—
131C2×C3⋊Dic3C4⋊C412yes—
132C4×C3⋊D3—22no—
133C4×C3⋊D3—22no—
134C4×C3⋊D3—22no—
135C4×C3⋊D3—22no—
136C2×C3×Dic3—21no—
137C2×C3×Dic3—21no—
138C2×C3×Dic3—21no—
139C2×C3×Dic3—21no—
140C2×C3×Dic3—21no—
141C2×C3×Dic3—21no—
142C2×C3×Dic3—21no—
143C2×C3×Dic3—21no—
144C2×C3×Dic3—21no—
145C2×C3×Dic3—21no—
146C2×C3×Dic3M1612yescomplemented
147C2×C3×Dic3M1612yescomplemented
148C32×C8—22no—
149C3⋊(C3⋊C8)—22no—
150C3×C3⋊C8—41no—
151C3×C3⋊C8—41no—
152C22×M16—91no—
153C2×C4⋊C8—31no—
154C2×C4⋊C8—91no—
155C2×C22⋊C8—91no—
156C4×C22⋊C4—91no—
157#336—31no—
158#336—91no—
159C23×D3—31no—
160C23×D3—31no—
161C23×D3—61no—
162C22×C3×C4—21no—
163C22×C3×C4—31no—
164C22×C3×C4—31no—
165C22×C3×C4—31no—
166C22×C3×C4—31no—
167C22×C3×C4C22×D311yescharacteristic
168C22×C3×C4C22×D311yescharacteristic
169C22×Dic3—31no—
170C22×Dic3—31no—
171C22×Dic3—61no—
172C22×Dic3C4×D311yescharacteristic
173C22×Dic3C4×D311yescharacteristic
174C22×Dic3C4×D311yescharacteristic
175C22×Dic3C4×D311yescharacteristic
176C2×C4×D3—32no—
177C2×C4×D3—32no—
178C2×C4×D3—32no—
179C2×C4×D3—32no—
180C2×C4×D3—62no—
181C2×C4×D3—62no—
182C2×C4×D3—62no—
183C2×C4×D3—62no—
184C2×C4×D3—62no—
185C2×C4×D3—62no—
186C2×C4×D3—61no—
187C2×C4×D3—61no—
188C2×C4×D3—61no—
189C2×C4×D3—61no—
190C2×C4×D3—61no—
191C2×C4×D3—61no—
192C2×C4×D3—61no—
193C2×C4×D3—61no—
194C2×C3×C8—22no—
195C2×C3×C8—22no—
196C2×C3×C8—21no—
197C2×C3×C8—21no—
198C2×C3×C8—21no—
199C2×C3×C8—21no—
200C2×C3×C8—22no—
201C2×C3×C8—61no—
202C2×C3×C8—61no—
203C2×C3×C8—61no—
204C2×C3×C8—61no—
205C2×C3×C8—61no—
206C2×C3×C8—61no—
207C2×C3×C8D1212yes—
208C2×C3×C8#6712yes—
209C3×C42—61no—
210C3×C42—61no—
211C3×C42—61no—
212C3×C42—61no—
213(C2×D3)⋊C4—62no—
214(C2×D3)⋊C4—62no—
215(C2×D3)⋊C4—62no—
216(C2×D3)⋊C4—62no—
217C4×Dic3—21no—
218C4×Dic3—21no—
219C4×Dic3—21no—
220C4×Dic3—21no—
221C2×C3⋊C8—21no—
222C2×C3⋊C8—21no—
223C2×C3⋊C8—21no—
224C2×C3⋊C8—21no—
225C2×C3⋊C8—21no—
226C2×C3⋊C8—21no—
227C2×C3⋊C8—32no—
228C2×C3⋊C8—32no—
229C2×C3⋊C8—62no—
230C2×C3⋊C8—62no—
231C2×C3⋊C8—62no—
232C2×C3⋊C8—61no—
233C2×C3⋊C8—61no—
234C2×C3⋊C8—61no—
235C2×C3⋊C8—61no—
236ΓL(1,𝔽25)—616no—
237ΓL(1,𝔽25)—68no—
238ΓL(1,𝔽25)—68no—
239C22×C32C2×C4⋊C411yescharacteristic
240C22×C32C4×D411yescharacteristic
241C22×C32C4×D411yescharacteristic
242C22×C32C2×M1611yescharacteristic
243C22×C32C2×M1611yescharacteristic
244C22×C32#13111yescharacteristic
245C22×C32#13111yescharacteristic
246C2×C3⋊D3—22no—
247C2×C3⋊D3—22no—
248C2×C3⋊D3—22no—
249C2×C3⋊D3—41no—
250C2×C3⋊D3—41no—
251C2×C3⋊D3—41no—
252C2×C3⋊D3—41no—
253C32×C4#12011yescharacteristic
254C32×C4C22⋊Q811yescharacteristic
255C32×C4C22⋊Q811yescharacteristic
256C32×C4#12311yescharacteristic
257C3⋊Dic3—22no—
258C3×Dic3—22no—
259C3×Dic3—22no—
260C3×Dic3—41no—
261C3×Dic3—41no—
262C23×C4—91no—
263C2×M16—182no—
264C2×M16—182no—
265C2×M16—182no—
266C22×C8—31no—
267C22×C8—31no—
268C22×C8—91no—
269C22×C8D3211yescharacteristic
270C2×C22⋊C4—91no—
271C2×C22⋊C4—91no—
272C2×C42—31no—
273C2×C42—31no—
274C4⋊C8—62no—
275C4⋊C8—182no—
276C22⋊C8—182no—
277#95—91no—
278#95—91no—
279C23×C3—21no—
280C23×C3C2×C4×D311yescharacteristic
281C23×C3C2×C4×D311yescharacteristic
282C22×D3—32no—
283C22×D3—32no—
284C22×D3—62no—
285C22×D3—62no—
286C22×D3—62no—
287C22×D3—61no—
288C22×D3—61no—
289C22×D3—61no—
290C22×D3—61no—
291C22×D3—61no—
292C22×D3—61no—
293C22×D3—61no—
294C22×D3—61no—
295C22×D3—61no—
296C22×D3—61no—
297C22×D3—61no—
298C22×D3—61no—
299C22×D3—121no—
300C22×D3—121no—
301C22×D3—121no—
302C22×D3—121no—
303C2×C3×C4—21no—
304C2×C3×C4—21no—
305C2×C3×C4—21no—
306C2×C3×C4—21no—
307C2×C3×C4—21no—
308C2×C3×C4—21no—
309C2×C3×C4—32no—
310C2×C3×C4—32no—
311C2×C3×C4—61no—
312C2×C3×C4—61no—
313C2×C3×C4—61no—
314C2×C3×C4—61no—
315C2×C3×C4—61no—
316C2×C3×C4—61no—
317C2×C3×C4—61no—
318C2×C3×C4—61no—
319C2×C3×C4—61no—
320C2×C3×C4—61no—
321C2×C3×C4C2×D1211yescharacteristic
322C2×C3×C4#23511yescharacteristic
323C2×C3×C4#23511yescharacteristic
324C2×C3×C4D3×D411yescharacteristic
325C2×C3×C4D3×D411yescharacteristic
326C2×C3×C4D3×D411yescharacteristic
327C2×C3×C4D3×D411yescharacteristic
328C2×C3×C4#23711yescharacteristic
329C2×C3×C4D3×Q811yescharacteristic
330C2×C3×C4D3×Q811yescharacteristic
331C2×C3×C4#23911yescharacteristic
332C2×C3×C4C2×#6711yescharacteristic
333C2×Dic3—21no—
334C2×Dic3—21no—
335C2×Dic3—21no—
336C2×Dic3—21no—
337C2×Dic3—21no—
338C2×Dic3—21no—
339C2×Dic3—21no—
340C2×Dic3—21no—
341C2×Dic3—21no—
342C2×Dic3—21no—
343C2×Dic3—32no—
344C2×Dic3—32no—
345C2×Dic3—62no—
346C2×Dic3—62no—
347C2×Dic3—62no—
348C2×Dic3—61no—
349C2×Dic3—61no—
350C2×Dic3—61no—
351C2×Dic3—61no—
352C2×Dic3ΓL(1,𝔽25)12yescomplemented
353C2×Dic3ΓL(1,𝔽25)12yescomplemented
354C4×D3—64no—
355C4×D3—64no—
356C4×D3—64no—
357C4×D3—64no—
358C4×D3—62no—
359C4×D3—62no—
360C4×D3—62no—
361C4×D3—62no—
362C4×D3—62no—
363C4×D3—62no—
364C4×D3—62no—
365C4×D3—62no—
366C3×C8—24no—
367C3×C8—22no—
368C3×C8—22no—
369C3×C8—121no—
370C3×C8—121no—
371C3⋊C8—41no—
372C3⋊C8—41no—
373C3⋊C8—64no—
374C3⋊C8—62no—
375C3⋊C8—62no—
376C2×C32#38511yescharacteristic
377C2×C32#42311yescharacteristic
378C2×C32#42411yescharacteristic
379C2×C32#43511yescharacteristic
380C2×C32#43511yescharacteristic
381C2×C32#43611yescharacteristic
382C2×C32#43611yescharacteristic
383C3⋊D3—42no—
384C24—91no—
385C22×C4—31no—
386C22×C4—31no—
387C22×C4—31no—
388C22×C4—31no—
389C22×C4—91no—
390C22×C4—92no—
391C22×C4—92no—
392C22×C4—181no—
393C22×C4—181no—
394C22×C4—181no—
395C22×C4—181no—
396C22×C4C2×D3211yescharacteristic
397M16—188no—
398C2×C8—21no—
399C2×C8—21no—
400C2×C8—61no—
401C2×C8—61no—
402C2×C8—61no—
403C2×C8—61no—
404C2×C8—61no—
405C2×C8—61no—
406C2×C8—92no—
407C2×C8—181no—
408C2×C8—181no—
409C2×C8#62612yes—
410C22⋊C4—182no—
411C22⋊C4—182no—
412C42—61no—
413C42—61no—
414C42—61no—
415C42—61no—
416C22×C3—21no—
417C22×C3—21no—
418C22×C3—21no—
419C22×C3—21no—
420C22×C3—21no—
421C22×C3—21no—
422C22×C3—21no—
423C22×C3C4×D1211yescharacteristic
424C22×C3#67⋊C411yescharacteristic
425C22×C3D3×C4⋊C411yescharacteristic
426C22×C3D3×C4⋊C411yescharacteristic
427C22×C3#89311yescharacteristic
428C22×C3C2×ΓL(1,𝔽25)11yescharacteristic
429C22×C3C2×ΓL(1,𝔽25)11yescharacteristic
430C22×C3#90111yescharacteristic
431C22×C3#90111yescharacteristic
432C22×C3D3×M1611yescharacteristic
433C22×C3D3×M1611yescharacteristic
434C22×C3#90711yescharacteristic
435C22×C3#90711yescharacteristic
436C22×C3C4×#6711yescharacteristic
437C2×D3—64no—
438C2×D3—62no—
439C2×D3—62no—
440C2×D3—62no—
441C2×D3—62no—
442C2×D3—62no—
443C2×D3—62no—
444C2×D3—122no—
445C2×D3—122no—
446C2×D3—122no—
447C2×D3—122no—
448C2×D3—122no—
449C2×D3—122no—
450C2×D3—121no—
451C2×D3—121no—
452C2×D3—121no—
453C2×D3—121no—
454C2×D3—121no—
455C2×D3—121no—
456C2×D3—121no—
457C2×D3—121no—
458C3×C4—21no—
459C3×C4—21no—
460C3×C4—21no—
461C3×C4—21no—
462C3×C4—62no—
463C3×C4—62no—
464C3×C4—121no—
465C3×C4—121no—
466C3×C4#88211yescharacteristic
467C3×C4#88311yescharacteristic
468C3×C4#89411yescharacteristic
469C3×C4#89611yescharacteristic
470C3×C4#89611yescharacteristic
471C3×C4#89711yescharacteristic
472C3×C4#93711yescharacteristic
473C3×C4#94611yescharacteristic
474Dic3—22no—
475Dic3—22no—
476Dic3—41no—
477Dic3—41no—
478Dic3—64no—
479Dic3—62no—
480Dic3—62no—
481C32#185111yescharacteristic, complemented, Sylow
482C23—92no—
483C23—181no—
484C23—181no—
485C23—181no—
486C23—181no—
487C23—181no—
488C23—181no—
489C23C4×D3211yescharacteristic
490C2×C4—32no—
491C2×C4—32no—
492C2×C4—61no—
493C2×C4—61no—
494C2×C4—61no—
495C2×C4—61no—
496C2×C4—61no—
497C2×C4—61no—
498C2×C4—61no—
499C2×C4—61no—
500C2×C4—61no—
501C2×C4—61no—
502C2×C4—92no—
503C2×C4—181no—
504C2×C4—181no—
505C2×C4—182no—
506C2×C4—182no—
507C2×C4—182no—
508C2×C4—182no—
509C2×C4#379611yescharacteristic
510C2×C4#379711yescharacteristic
511C2×C4#379811yescharacteristic
512C2×C4C2×#62611yescharacteristic
513C2×C4#381111yescharacteristic
514C2×C4#381111yescharacteristic
515C8—22no—
516C8—121no—
517C8—121no—
518C8—182no—
519C2×C3—21no—
520C2×C3—21no—
521C2×C3—21no—
522C2×C3—21no—
523C2×C3—21no—
524C2×C3—21no—
525C2×C3—21no—
526C2×C3#466811yescharacteristic
527C2×C3#468811yescharacteristic
528C2×C3#470611yescharacteristic
529C2×C3#472911yescharacteristic
530C2×C3#473011yescharacteristic
531C2×C3#483611yescharacteristic
532C2×C3#483711yescharacteristic
533C2×C3#483711yescharacteristic
534C2×C3#483811yescharacteristic
535C2×C3#483911yescharacteristic
536C2×C3#483911yescharacteristic
537C2×C3#498911yescharacteristic
538C2×C3#511111yescharacteristic
539C2×C3#512811yescharacteristic
540D3—124no—
541D3—122no—
542D3—122no—
543C22—182no—
544C22—182no—
545C22—182no—
546C22—361no—
547C22—361no—
548C22—361no—
549C22—361no—
550C22D3×ΓL(1,𝔽25)11yescharacteristic
551C22D3×ΓL(1,𝔽25)11yescharacteristic
552C22#6380411yescharacteristic
553C22#6380411yescharacteristic
554C22#6388111yescharacteristic
555C22#6388311yescharacteristic
556C22C4×#62611yescharacteristic
557C4—62no—
558C4—62no—
559C4—121no—
560C4—121no—
561C4—182no—
562C4#6385311yescharacteristic
563C4#6386511yescharacteristic
564C4#6387111yescharacteristic
565C4#6398111yescharacteristic
566C3—21no—
567C3#6866711yescharacteristic, complemented
568C3#7047811yescharacteristic, complemented
569C2—362no—
570C2#1059066611yescharacteristic
571C2#1059070211yescharacteristic
572C2#1059072611yescharacteristic
573C2#1059072911yescharacteristic
574C2#1059073211yescharacteristic
575C2#1059090711yescharacteristic
576C2#1059129011yescharacteristic
subgroupG/H
center, FrattiniC22×C4C2×D32
commutator, socleC23×C32C22×C4
FittingC22×C32×C8C22
prime radicalC23×C3⋊D3C2×C4
cosocleC22×C32×C4C23
hypercenterC22×C8D32
hypocenterC32#1851
LCSG ▷ C23×C32 ▷ C32
UCSC1 ◁ C22×C4 ◁ C22×C8

Complements

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

NH ≅ G/Ntype
2. C2×C3×Dic3⋊C8C2semidirect
4. C2×Dic3⋊(C3⋊C8)C2semidirect
6. C3×#4550C2semidirect
7. #10589155C2semidirect
34. C2×Dic3⋊C8D3semidirect
40. #4550D3semidirect
146. C2×C3×Dic3M16semidirect
147. C2×C3×Dic3M16semidirect
352. C2×Dic3ΓL(1,𝔽25)semidirect
353. C2×Dic3ΓL(1,𝔽25)semidirect
481. C32#1851semidirect
567. C3#68667semidirect
568. C3#70478semidirect

Maximal subgroups

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

subgroupindex
C22×#37432
C2×C3×Dic3⋊C82
C4×#37222
C2×Dic3⋊(C3⋊C8)2
C2×#635572
C3×#45502
#105891552
#704783
#686673