Finite Group Databasebeta

← C32×#2334 #11769383

Subgroups — C32×#2334 #11769383

Order 1152.

1428 conjugacy classes of subgroups.

The subgroup lattice has 540 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C32×#126C211yesmaximal, characteristic
2C32×#389C211yesmaximal, characteristic, complemented
3C32×#389C211yesmaximal, characteristic, complemented
4C32×#388C211yesmaximal, characteristic
5C32×#388C211yesmaximal, characteristic
6C32×#388C211yesmaximal, characteristic
7C32×#387C211yesmaximal, characteristic, complemented
8C32×#387C211yesmaximal, characteristic, complemented
9C32×#387C211yesmaximal, characteristic, complemented
10C32×#385C211yesmaximal, characteristic
11C32×#385C211yesmaximal, characteristic
12C32×#382C211yesmaximal, characteristic, complemented
13C32×C4×C4⋊C4C211yesmaximal, characteristic, complemented
14C32×C4×C4⋊C4C211yesmaximal, characteristic, complemented
15C32×C4×C22⋊C4C211yesmaximal, characteristic
16C3×#2334C314yesmaximal, direct product factor
17C23×C32×C4C2211yescharacteristic
18C32×#126C418yescomplemented
19C2×C32×C4⋊C4C2211yescharacteristic
20C2×C32×C4⋊C4C2211yescharacteristic
21C2×C32×C4⋊C4C2211yescharacteristic
22C2×C32×C4⋊C4C2211yescharacteristic
23C2×C32×C4⋊C4C2211yescharacteristic
24C2×C32×C4⋊C4C2211yescharacteristic
25C2×C32×C4⋊C4C2211yescharacteristic
26C2×C32×C4⋊C4C2211yescharacteristic
27C2×C32×C4⋊C4C2211yescharacteristic
28C2×C32×C4⋊C4C2211yescharacteristic
29C2×C32×C22⋊C4C2211yescharacteristic
30C2×C32×C22⋊C4C2211yescharacteristic
31C2×C32×C22⋊C4C2211yescharacteristic
32C2×C32×C22⋊C4C2211yescharacteristic
33C2×C32×C22⋊C4C2211yescharacteristic
34C2×C32×C22⋊C4C2211yescharacteristic
35C2×C32×C42C2211yescharacteristic
36C2×C32×C42C2211yescharacteristic
37C2×C32×C42C2211yescharacteristic
38C2×C32×C42C2211yescharacteristic
39C2×C32×C42C2211yescharacteristic
40C2×C32×C42C2211yescharacteristic
41C32×#95C2211yescharacteristic
42C32×#95C2211yescharacteristic
43C32×#95C2211yescharacteristic
44C32×#95C2211yescharacteristic
45C32×#95C2211yescharacteristic
46C32×#95C2211yescharacteristic
47C32×#95C2211yescharacteristic
48C32×#95C2211yescharacteristic
49C32×#95C2211yescharacteristic
50C32×#95C2211yescharacteristic
51C32×#95C2211yescharacteristic
52C32×#95C2211yescharacteristic
53C2×C3×#126C2×C314yes—
54C3×#389C2×C314yescomplemented
55C3×#389C2×C314yescomplemented
56C3×#388C2×C314yes—
57C3×#388C2×C314yes—
58C3×#388C2×C314yes—
59C3×#387C2×C314yescomplemented
60C3×#387C2×C314yescomplemented
61C3×#387C2×C314yescomplemented
62C3×#385C2×C314yes—
63C3×#385C2×C314yes—
64C3×#382C2×C314yescomplemented
65C3×C4×C4⋊C4C2×C314yescomplemented
66C3×C4×C4⋊C4C2×C314yescomplemented
67C3×C4×C22⋊C4C2×C314yes—
68C24×C32C2311yescharacteristic
69C22×C32×C4—22no—
70C22×C32×C4—41no—
71C22×C32×C4—41no—
72C22×C32×C4C2311yescharacteristic
73C22×C32×C4C2311yescharacteristic
74C22×C32×C4C2311yescharacteristic
75C22×C32×C4C2311yescharacteristic
76C22×C32×C4C2311yescharacteristic
77C22×C32×C4C2311yescharacteristic
78C22×C32×C4C2311yescharacteristic
79C22×C32×C4C2311yescharacteristic
80C22×C32×C4C2311yescharacteristic
81C22×C32×C4C2311yescharacteristic
82C22×C32×C4C2311yescharacteristic
83C22×C32×C4C2311yescharacteristic
84C22×C32×C4C2311yescharacteristic
85C22×C32×C4C2311yescharacteristic
86C32×C4⋊C4—22no—
87C32×C4⋊C4—22no—
88C32×C4⋊C4—22no—
89C32×C4⋊C4—41no—
90C32×C4⋊C4—41no—
91C32×C4⋊C4—41no—
92C32×C4⋊C4—41no—
93C32×C4⋊C4C2×C414yescomplemented
94C32×C4⋊C4C2×C414yescomplemented
95C32×C4⋊C4C2×C414yescomplemented
96C32×C22⋊C4—22no—
97C32×C22⋊C4—41no—
98C32×C22⋊C4—41no—
99C32×C22⋊C4C2×C414yes—
100C32×C22⋊C4C2×C414yes—
101C32×C22⋊C4C2×C414yes—
102C32×C42—22no—
103C32×C42—41no—
104C32×C42—41no—
105C32×C42—41no—
106C32×C42—41no—
107C32×C42C2×C414yescomplemented
108#2334C3211yescharacteristic, direct product factor, Sylow
109C23×C3×C4C22×C314yes—
110C3×#126C3×C4132yescomplemented
111C2×C3×C4⋊C4C22×C314yes—
112C2×C3×C4⋊C4C22×C314yes—
113C2×C3×C4⋊C4C22×C314yes—
114C2×C3×C4⋊C4C22×C314yes—
115C2×C3×C4⋊C4C22×C314yes—
116C2×C3×C4⋊C4C22×C314yes—
117C2×C3×C4⋊C4C22×C314yes—
118C2×C3×C4⋊C4C22×C314yes—
119C2×C3×C4⋊C4C22×C314yes—
120C2×C3×C4⋊C4C22×C314yes—
121C2×C3×C22⋊C4C22×C314yes—
122C2×C3×C22⋊C4C22×C314yes—
123C2×C3×C22⋊C4C22×C314yes—
124C2×C3×C22⋊C4C22×C314yes—
125C2×C3×C22⋊C4C22×C314yes—
126C2×C3×C22⋊C4C22×C314yes—
127C2×C3×C42C22×C314yes—
128C2×C3×C42C22×C314yes—
129C2×C3×C42C22×C314yes—
130C2×C3×C42C22×C314yes—
131C2×C3×C42C22×C314yes—
132C2×C3×C42C22×C314yes—
133C3×#95C22×C314yes—
134C3×#95C22×C314yes—
135C3×#95C22×C314yes—
136C3×#95C22×C314yes—
137C3×#95C22×C314yes—
138C3×#95C22×C314yes—
139C3×#95C22×C314yes—
140C3×#95C22×C314yes—
141C3×#95C22×C314yes—
142C3×#95C22×C314yes—
143C3×#95C22×C314yes—
144C3×#95C22×C314yes—
145C23×C32—21no—
146C23×C32—21no—
147C23×C32—21no—
148C23×C32—21no—
149C23×C32—21no—
150C23×C32—21no—
151C23×C32C22×C412yes—
152C23×C32C2411yescharacteristic
153C2×C32×C4—21no—
154C2×C32×C4—21no—
155C2×C32×C4—21no—
156C2×C32×C4—21no—
157C2×C32×C4—21no—
158C2×C32×C4—21no—
159C2×C32×C4—21no—
160C2×C32×C4—21no—
161C2×C32×C4—21no—
162C2×C32×C4—21no—
163C2×C32×C4—21no—
164C2×C32×C4—21no—
165C2×C32×C4—21no—
166C2×C32×C4—21no—
167C2×C32×C4—21no—
168C2×C32×C4—21no—
169C2×C32×C4—21no—
170C2×C32×C4—21no—
171C2×C32×C4—21no—
172C2×C32×C4—21no—
173C2×C32×C4—21no—
174C2×C32×C4—21no—
175C2×C32×C4—21no—
176C2×C32×C4—21no—
177C2×C32×C4—21no—
178C2×C32×C4—21no—
179C2×C32×C4—21no—
180C2×C32×C4—21no—
181C2×C32×C4—21no—
182C2×C32×C4—21no—
183C2×C32×C4—21no—
184C2×C32×C4—21no—
185C2×C32×C4—21no—
186C2×C32×C4—21no—
187C2×C32×C4—44no—
188C2×C32×C4C22×C412yes—
189C2×C32×C4C22×C412yes—
190C2×C32×C4C22×C412yes—
191C2×C32×C4C22×C412yes—
192C2×C32×C4C22×C412yes—
193C2×C32×C4C22×C412yes—
194C2×C32×C4#4112yes—
195C2×C32×C4#4112yes—
196C2×#126C2×C3211yescharacteristic
197#389C2×C3211yescharacteristic, complemented
198#389C2×C3211yescharacteristic, complemented
199#388C2×C3211yescharacteristic
200#388C2×C3211yescharacteristic
201#388C2×C3211yescharacteristic
202#387C2×C3211yescharacteristic, complemented
203#387C2×C3211yescharacteristic, complemented
204#387C2×C3211yescharacteristic, complemented
205#385C2×C3211yescharacteristic
206#385C2×C3211yescharacteristic
207#382C2×C3211yescharacteristic, complemented
208C4×C4⋊C4C2×C3211yescharacteristic, complemented
209C4×C4⋊C4C2×C3211yescharacteristic, complemented
210C4×C22⋊C4C2×C3211yescharacteristic
211C24×C3C23×C314yes—
212C22×C3×C4—28no—
213C22×C3×C4—44no—
214C22×C3×C4—44no—
215C22×C3×C4C23×C314yes—
216C22×C3×C4C23×C314yes—
217C22×C3×C4C23×C314yes—
218C22×C3×C4C23×C314yes—
219C22×C3×C4C23×C314yes—
220C22×C3×C4C23×C314yes—
221C22×C3×C4C23×C314yes—
222C22×C3×C4C23×C314yes—
223C22×C3×C4C23×C314yes—
224C22×C3×C4C23×C314yes—
225C22×C3×C4C23×C314yes—
226C22×C3×C4C23×C314yes—
227C22×C3×C4C23×C314yes—
228C22×C3×C4C23×C314yes—
229C3×C4⋊C4—28no—
230C3×C4⋊C4—28no—
231C3×C4⋊C4—28no—
232C3×C4⋊C4—44no—
233C3×C4⋊C4—44no—
234C3×C4⋊C4—44no—
235C3×C4⋊C4—44no—
236C3×C4⋊C4C2×C3×C4116yescomplemented
237C3×C4⋊C4C2×C3×C4116yescomplemented
238C3×C4⋊C4C2×C3×C4116yescomplemented
239C3×C22⋊C4—28no—
240C3×C22⋊C4—44no—
241C3×C22⋊C4—44no—
242C3×C22⋊C4C2×C3×C4116yes—
243C3×C22⋊C4C2×C3×C4116yes—
244C3×C22⋊C4C2×C3×C4116yes—
245C3×C42—28no—
246C3×C42—44no—
247C3×C42—44no—
248C3×C42—44no—
249C3×C42—44no—
250C3×C42C2×C3×C4116yescomplemented
251C22×C32—22no—
252C22×C32—22no—
253C22×C32—22no—
254C22×C32—41no—
255C22×C32—41no—
256C22×C32—41no—
257C22×C32—41no—
258C22×C32C23×C411yescharacteristic
259C22×C32C2×#4111yescharacteristic
260C22×C32C2×#4111yescharacteristic
261C22×C32H(5,𝔽2)11yescharacteristic
262C22×C32H(5,𝔽2)11yescharacteristic
263C22×C322−1+411yescharacteristic
264C22×C322−1+411yescharacteristic
265C32×C4—22no—
266C32×C4—22no—
267C32×C4—22no—
268C32×C4—22no—
269C32×C4—22no—
270C32×C4—22no—
271C32×C4—22no—
272C32×C4—22no—
273C32×C4—41no—
274C32×C4—41no—
275C32×C4—41no—
276C32×C4—41no—
277C32×C4—41no—
278C32×C4—41no—
279C23×C4C22×C3211yescharacteristic
280#126C32×C418yescomplemented
281C2×C4⋊C4C22×C3211yescharacteristic
282C2×C4⋊C4C22×C3211yescharacteristic
283C2×C4⋊C4C22×C3211yescharacteristic
284C2×C4⋊C4C22×C3211yescharacteristic
285C2×C4⋊C4C22×C3211yescharacteristic
286C2×C4⋊C4C22×C3211yescharacteristic
287C2×C4⋊C4C22×C3211yescharacteristic
288C2×C4⋊C4C22×C3211yescharacteristic
289C2×C4⋊C4C22×C3211yescharacteristic
290C2×C4⋊C4C22×C3211yescharacteristic
291C2×C22⋊C4C22×C3211yescharacteristic
292C2×C22⋊C4C22×C3211yescharacteristic
293C2×C22⋊C4C22×C3211yescharacteristic
294C2×C22⋊C4C22×C3211yescharacteristic
295C2×C22⋊C4C22×C3211yescharacteristic
296C2×C22⋊C4C22×C3211yescharacteristic
297C2×C42C22×C3211yescharacteristic
298C2×C42C22×C3211yescharacteristic
299C2×C42C22×C3211yescharacteristic
300C2×C42C22×C3211yescharacteristic
301C2×C42C22×C3211yescharacteristic
302C2×C42C22×C3211yescharacteristic
303#95C22×C3211yescharacteristic
304#95C22×C3211yescharacteristic
305#95C22×C3211yescharacteristic
306#95C22×C3211yescharacteristic
307#95C22×C3211yescharacteristic
308#95C22×C3211yescharacteristic
309#95C22×C3211yescharacteristic
310#95C22×C3211yescharacteristic
311#95C22×C3211yescharacteristic
312#95C22×C3211yescharacteristic
313#95C22×C3211yescharacteristic
314#95C22×C3211yescharacteristic
315C23×C3—24no—
316C23×C3—24no—
317C23×C3—24no—
318C23×C3—24no—
319C23×C3—24no—
320C23×C3—24no—
321C23×C3C22×C3×C418yes—
322C23×C3C24×C314yes—
323C2×C3×C4—24no—
324C2×C3×C4—24no—
325C2×C3×C4—24no—
326C2×C3×C4—24no—
327C2×C3×C4—24no—
328C2×C3×C4—24no—
329C2×C3×C4—24no—
330C2×C3×C4—24no—
331C2×C3×C4—24no—
332C2×C3×C4—24no—
333C2×C3×C4—24no—
334C2×C3×C4—24no—
335C2×C3×C4—24no—
336C2×C3×C4—24no—
337C2×C3×C4—24no—
338C2×C3×C4—24no—
339C2×C3×C4—24no—
340C2×C3×C4—24no—
341C2×C3×C4—24no—
342C2×C3×C4—24no—
343C2×C3×C4—24no—
344C2×C3×C4—24no—
345C2×C3×C4—24no—
346C2×C3×C4—24no—
347C2×C3×C4—24no—
348C2×C3×C4—24no—
349C2×C3×C4—24no—
350C2×C3×C4—24no—
351C2×C3×C4—24no—
352C2×C3×C4—24no—
353C2×C3×C4—24no—
354C2×C3×C4—24no—
355C2×C3×C4—24no—
356C2×C3×C4—24no—
357C2×C3×C4—416no—
358C2×C3×C4C22×C3×C418yes—
359C2×C3×C4C22×C3×C418yes—
360C2×C3×C4C22×C3×C418yes—
361C2×C3×C4C22×C3×C418yes—
362C2×C3×C4C22×C3×C418yes—
363C2×C3×C4C22×C3×C418yes—
364C2×C3×C4C3×#4118yes—
365C2×C3×C4C3×#4118yes—
366C2×C32—42no—
367C2×C32C4×#4111yescharacteristic
368C2×C32#52011yescharacteristic
369C2×C32#52011yescharacteristic
370C2×C32#53811yescharacteristic
371C2×C32#53911yescharacteristic
372C2×C32#54111yescharacteristic
373C2×C32#54211yescharacteristic
374C24C23×C3211yescharacteristic
375C22×C4—22no—
376C22×C4—41no—
377C22×C4—41no—
378C22×C4C23×C3211yescharacteristic
379C22×C4C23×C3211yescharacteristic
380C22×C4C23×C3211yescharacteristic
381C22×C4C23×C3211yescharacteristic
382C22×C4C23×C3211yescharacteristic
383C22×C4C23×C3211yescharacteristic
384C22×C4C23×C3211yescharacteristic
385C22×C4C23×C3211yescharacteristic
386C22×C4C23×C3211yescharacteristic
387C22×C4C23×C3211yescharacteristic
388C22×C4C23×C3211yescharacteristic
389C22×C4C23×C3211yescharacteristic
390C22×C4C23×C3211yescharacteristic
391C22×C4C23×C3211yescharacteristic
392C4⋊C4—22no—
393C4⋊C4—22no—
394C4⋊C4—22no—
395C4⋊C4—41no—
396C4⋊C4—41no—
397C4⋊C4—41no—
398C4⋊C4—41no—
399C4⋊C4C2×C32×C414yescomplemented
400C4⋊C4C2×C32×C414yescomplemented
401C4⋊C4C2×C32×C414yescomplemented
402C22⋊C4—22no—
403C22⋊C4—41no—
404C22⋊C4—41no—
405C22⋊C4C2×C32×C414yes—
406C22⋊C4C2×C32×C414yes—
407C22⋊C4C2×C32×C414yes—
408C42—22no—
409C42—41no—
410C42—41no—
411C42—41no—
412C42—41no—
413C42C2×C32×C414yescomplemented
414C22×C3—28no—
415C22×C3—28no—
416C22×C3—28no—
417C22×C3—44no—
418C22×C3—44no—
419C22×C3—44no—
420C22×C3—44no—
421C22×C3C23×C3×C414yes—
422C22×C3C2×C3×#4114yes—
423C22×C3C2×C3×#4114yes—
424C22×C3C3×H(5,𝔽2)14yes—
425C22×C3C3×H(5,𝔽2)14yes—
426C22×C3C3×2−1+414yes—
427C22×C3C3×2−1+414yes—
428C3×C4—28no—
429C3×C4—28no—
430C3×C4—28no—
431C3×C4—28no—
432C3×C4—28no—
433C3×C4—28no—
434C3×C4—28no—
435C3×C4—28no—
436C3×C4—44no—
437C3×C4—44no—
438C3×C4—44no—
439C3×C4—44no—
440C3×C4—44no—
441C3×C4—44no—
442C32#233411yescharacteristic, direct product factor, Sylow
443C23—21no—
444C23—21no—
445C23—21no—
446C23—21no—
447C23—21no—
448C23—21no—
449C23C22×C32×C412yes—
450C23C24×C3211yescharacteristic
451C2×C4—21no—
452C2×C4—21no—
453C2×C4—21no—
454C2×C4—21no—
455C2×C4—21no—
456C2×C4—21no—
457C2×C4—21no—
458C2×C4—21no—
459C2×C4—21no—
460C2×C4—21no—
461C2×C4—21no—
462C2×C4—21no—
463C2×C4—21no—
464C2×C4—21no—
465C2×C4—21no—
466C2×C4—21no—
467C2×C4—21no—
468C2×C4—21no—
469C2×C4—21no—
470C2×C4—21no—
471C2×C4—21no—
472C2×C4—21no—
473C2×C4—21no—
474C2×C4—21no—
475C2×C4—21no—
476C2×C4—21no—
477C2×C4—21no—
478C2×C4—21no—
479C2×C4—21no—
480C2×C4—21no—
481C2×C4—21no—
482C2×C4—21no—
483C2×C4—21no—
484C2×C4—21no—
485C2×C4—44no—
486C2×C4C22×C32×C412yes—
487C2×C4C22×C32×C412yes—
488C2×C4C22×C32×C412yes—
489C2×C4C22×C32×C412yes—
490C2×C4C22×C32×C412yes—
491C2×C4C22×C32×C412yes—
492C2×C4C32×#4112yes—
493C2×C4C32×#4112yes—
494C2×C3—48no—
495C2×C3C3×C4×#4114yes—
496C2×C3C3×#52014yes—
497C2×C3C3×#52014yes—
498C2×C3C3×#53814yes—
499C2×C3C3×#53914yes—
500C2×C3C3×#54114yes—
501C2×C3C3×#54214yes—
502C22—22no—
503C22—22no—
504C22—22no—
505C22—41no—
506C22—41no—
507C22—41no—
508C22—41no—
509C22C23×C32×C411yescharacteristic
510C22C2×C32×#4111yescharacteristic
511C22C2×C32×#4111yescharacteristic
512C22C32×H(5,𝔽2)11yescharacteristic
513C22C32×H(5,𝔽2)11yescharacteristic
514C22C32×2−1+411yescharacteristic
515C22C32×2−1+411yescharacteristic
516C4—22no—
517C4—22no—
518C4—22no—
519C4—22no—
520C4—22no—
521C4—22no—
522C4—22no—
523C4—22no—
524C4—41no—
525C4—41no—
526C4—41no—
527C4—41no—
528C4—41no—
529C4—41no—
530C3C3×#233414yesdirect product factor
531C2—42no—
532C2C32×C4×#4111yescharacteristic
533C2C32×#52011yescharacteristic
534C2C32×#52011yescharacteristic
535C2C32×#53811yescharacteristic
536C2C32×#53911yescharacteristic
537C2C32×#54111yescharacteristic
538C2C32×#54211yescharacteristic
subgroupG/H
center, socleC23×C32C24
commutatorC22C23×C32×C4
Frattini, cosocleC23C24×C32
prime radicalC24×C32C23
LCSG ▷ C22 ▷ C1
UCSC1 ◁ C23×C32 ◁ G

Complements

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

NH ≅ G/Ntype
2. C32×#389C2semidirect
3. C32×#389C2semidirect
7. C32×#387C2semidirect
8. C32×#387C2semidirect
9. C32×#387C2semidirect
12. C32×#382C2semidirect
13. C32×C4×C4⋊C4C2semidirect
14. C32×C4×C4⋊C4C2semidirect
16. C3×#2334C3direct (N × H)
18. C32×#126C4semidirect
54. C3×#389C2×C3semidirect
55. C3×#389C2×C3semidirect
59. C3×#387C2×C3semidirect
60. C3×#387C2×C3semidirect
61. C3×#387C2×C3semidirect
64. C3×#382C2×C3semidirect
65. C3×C4×C4⋊C4C2×C3semidirect
66. C3×C4×C4⋊C4C2×C3semidirect
93. C32×C4⋊C4C2×C4semidirect
94. C32×C4⋊C4C2×C4semidirect
95. C32×C4⋊C4C2×C4semidirect
107. C32×C42C2×C4semidirect
108. #2334C32direct (N × H)
110. C3×#126C3×C4semidirect
197. #389C2×C32semidirect
198. #389C2×C32semidirect
202. #387C2×C32semidirect
203. #387C2×C32semidirect
204. #387C2×C32semidirect
207. #382C2×C32semidirect
208. C4×C4⋊C4C2×C32semidirect
209. C4×C4⋊C4C2×C32semidirect
236. C3×C4⋊C4C2×C3×C4semidirect
237. C3×C4⋊C4C2×C3×C4semidirect
238. C3×C4⋊C4C2×C3×C4semidirect
250. C3×C42C2×C3×C4semidirect
280. #126C32×C4semidirect
399. C4⋊C4C2×C32×C4semidirect
400. C4⋊C4C2×C32×C4semidirect
401. C4⋊C4C2×C32×C4semidirect
413. C42C2×C32×C4semidirect
442. C32#2334direct (N × H)
530. C3C3×#2334direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C32×#1262
C32×#3892
C32×#3882
C32×#3872
C32×#3852
C32×#3822
C32×C4×C4⋊C42
C32×C4×C22⋊C42
C3×#23343