Finite Group Databasebeta

← C32×#5547 #13178927

Subgroups — C32×#5547 #13178927

Order 1728.

2356 conjugacy classes of subgroups.

The subgroup lattice has 810 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C32×#235C211yesmaximal, characteristic, complemented
2C22×C32×C4×D3C211yesmaximal, characteristic, complemented
3C33×C4×D4C211yesmaximal, characteristic, complemented
4C32×#939C211yesmaximal, characteristic, complemented
5C32×#937C211yesmaximal, characteristic, complemented
6C32×C4×#67C211yesmaximal, characteristic, complemented
7C32×C4×#67C211yesmaximal, characteristic, complemented
8C32×#896C211yesmaximal, characteristic, complemented
9C32×#894C211yesmaximal, characteristic, complemented
10C32×#884C211yesmaximal, characteristic, complemented
11C32×#883C211yesmaximal, characteristic, complemented
12C32×#882C211yesmaximal, characteristic, complemented
13C32×#878C211yesmaximal, characteristic, complemented
14C32×C4×D12C211yesmaximal, characteristic, complemented
15C32×#872C211yesmaximal, characteristic, complemented
16C32×#525—31nomaximal
17C3×#5547C314yesmaximal, direct product factor
18C23×C32×D3C2211yescharacteristic
19C2×C33×D4C2211yescharacteristic
20C22×C33×C4C2211yescharacteristic
21C22×C33×C4C2211yescharacteristic, complemented
22C2×C32×#67C2211yescharacteristic
23C2×C32×#67C2211yescharacteristic
24C2×C32×#67C2211yescharacteristic
25C2×C32×#67C2211yescharacteristic, complemented
26C22×C32×Dic3C2211yescharacteristic
27C32×#235—24no—
28C2×C32×D12C2211yescharacteristic
29C2×C32×D12C2211yescharacteristic
30C2×C32×C4×D3—24no—
31C2×C32×C4×D3C2211yescharacteristic
32C2×C32×C4×D3C2211yescharacteristic
33C2×C32×C4×D3C2211yescharacteristic
34C2×C32×C4×D3C2211yescharacteristic
35C2×C32×C4×D3C2211yescharacteristic, complemented
36C2×C32×Dic6C2211yescharacteristic, complemented
37C33×C4⋊C4C2211yescharacteristic, complemented
38C33×C22⋊C4C2211yescharacteristic
39C33×C22⋊C4C2211yescharacteristic, complemented
40C33×C42C2211yescharacteristic, complemented
41C32×#217C2211yescharacteristic
42C32×#217C2211yescharacteristic, complemented
43C32×(C2×D3)⋊C4C2211yescharacteristic
44C32×(C2×D3)⋊C4C2211yescharacteristic
45C32×(C2×D3)⋊C4C2211yescharacteristic
46C32×(C2×D3)⋊C4C2211yescharacteristic
47C32×(C2×D3)⋊C4C2211yescharacteristic, complemented
48C32×(C2×D3)⋊C4C2211yescharacteristic, complemented
49C32×C4⋊Dic3C2211yescharacteristic, complemented
50C32×Dic3⋊C4C2211yescharacteristic, complemented
51C32×Dic3⋊C4C2211yescharacteristic, complemented
52C32×Dic3⋊C4C2211yescharacteristic, complemented
53C32×Dic3⋊C4C2211yescharacteristic, complemented
54C32×C4×Dic3C2211yescharacteristic, complemented
55C2×C32×#41—31no—
56C23×C32×C4—31no—
57C2×C3×#235C2×C314yescomplemented
58C22×C3×C4×D3C2×C314yescomplemented
59C32×#123—31no—
60C32×#123—31no—
61C32×C22⋊Q8—31no—
62C32×C22⋊Q8—31no—
63C32×#121—31no—
64C32×#121—31no—
65C32×#120—31no—
66C32×#120—31no—
67C32×C4×D4—24no—
68C32×C4×D4—31no—
69C32×C4×D4—31no—
70C32×C4×D4—31no—
71C32×C4×D4D311yescharacteristic, complemented
72C32×C4×D4C2×C314yescomplemented
73C32×#117—31no—
74C3×#939C2×C314yescomplemented
75C3×#937C2×C314yescomplemented
76C3×C4×#67C2×C314yescomplemented
77C3×C4×#67C2×C314yescomplemented
78C3×#896C2×C314yescomplemented
79C3×#894C2×C314yescomplemented
80C3×#884C2×C314yescomplemented
81C3×#883C2×C314yescomplemented
82C3×#882C2×C314yescomplemented
83C3×#878C2×C314yescomplemented
84C3×C4×D12C2×C314yescomplemented
85C3×#872C2×C314yescomplemented
86C23×C33C2311yescharacteristic
87C23×C33C2311yescharacteristic
88C22×C32×D3—22no—
89C22×C32×D3—22no—
90C22×C32×D3—22no—
91C22×C32×D3C2311yescharacteristic
92C22×C32×D3C2311yescharacteristic
93C22×C32×D3C2311yescharacteristic
94C33×D4—22no—
95C2×C33×C4—22no—
96C2×C33×C4—22no—
97C2×C33×C4C2311yescharacteristic
98C2×C33×C4C2311yescharacteristic
99C2×C33×C4C2311yescharacteristic
100C2×C33×C4C2311yescharacteristic
101C2×C33×C4C2311yescharacteristic
102C32×#67—22no—
103C32×#67—22no—
104C32×#67—22no—
105C32×#67—22no—
106C2×C32×Dic3—22no—
107C2×C32×Dic3C2311yescharacteristic
108C2×C32×Dic3C2311yescharacteristic
109C2×C32×Dic3C2311yescharacteristic
110C2×C32×Dic3C2311yescharacteristic
111C2×C32×Dic3C2311yescharacteristic
112C32×D12—22no—
113C32×D12—22no—
114C32×C4×D3—22no—
115C32×C4×D3—22no—
116C32×C4×D3—22no—
117C32×C4×D3—22no—
118C32×C4×D3D414yescomplemented
119C32×Dic6—22no—
120C3×#525—34no—
121#5547C3211yescharacteristic, direct product factor
122C24×C32—31no—
123C23×C3×D3C22×C314yes—
124C32×#41—64no—
125C2×C32×Q8—31no—
126C2×C32×D4—24no—
127C2×C32×D4—31no—
128C2×C32×D4—31no—
129C2×C32×D4—31no—
130C2×C32×D4—31no—
131C2×C32×D4—31no—
132C2×C32×D4—31no—
133C2×C32×D4C2×D311yescharacteristic
134C2×C32×D4C22×C314yes—
135C22×C32×C4—24no—
136C22×C32×C4—24no—
137C22×C32×C4—31no—
138C22×C32×C4—31no—
139C22×C32×C4—31no—
140C22×C32×C4—31no—
141C22×C32×C4—31no—
142C22×C32×C4—31no—
143C22×C32×C4—64no—
144C22×C32×C4C2×D311yescharacteristic
145C22×C32×C4C2×D311yescharacteristic, complemented
146C22×C32×C4C22×C314yes—
147C22×C32×C4C22×C314yescomplemented
148C2×C3×#67C22×C314yes—
149C2×C3×#67C22×C314yes—
150C2×C3×#67C22×C314yes—
151C2×C3×#67C22×C314yescomplemented
152C22×C3×Dic3C22×C314yes—
153C3×#235—216no—
154C2×C3×D12C22×C314yes—
155C2×C3×D12C22×C314yes—
156C2×C3×C4×D3—216no—
157C2×C3×C4×D3C22×C314yes—
158C2×C3×C4×D3C22×C314yes—
159C2×C3×C4×D3C22×C314yes—
160C2×C3×C4×D3C22×C314yes—
161C2×C3×C4×D3C22×C314yescomplemented
162C2×C3×Dic6C22×C314yescomplemented
163C32×C4⋊C4—24no—
164C32×C4⋊C4—31no—
165C32×C4⋊C4—31no—
166C32×C4⋊C4—31no—
167C32×C4⋊C4—31no—
168C32×C4⋊C4—31no—
169C32×C4⋊C4C2×D311yescharacteristic, complemented
170C32×C4⋊C4C22×C314yescomplemented
171C32×C22⋊C4—24no—
172C32×C22⋊C4—24no—
173C32×C22⋊C4—31no—
174C32×C22⋊C4—31no—
175C32×C22⋊C4—31no—
176C32×C22⋊C4—31no—
177C32×C22⋊C4—31no—
178C32×C22⋊C4—31no—
179C32×C22⋊C4—31no—
180C32×C22⋊C4—31no—
181C32×C22⋊C4C2×D311yescharacteristic
182C32×C22⋊C4C2×D311yescharacteristic, complemented
183C32×C22⋊C4C22×C314yes—
184C32×C22⋊C4C22×C314yescomplemented
185C32×C42—24no—
186C32×C42—31no—
187C32×C42C2×D311yescharacteristic, complemented
188C32×C42C22×C314yescomplemented
189C3×#217C22×C314yes—
190C3×#217C22×C314yescomplemented
191C3×(C2×D3)⋊C4C22×C314yes—
192C3×(C2×D3)⋊C4C22×C314yes—
193C3×(C2×D3)⋊C4C22×C314yes—
194C3×(C2×D3)⋊C4C22×C314yes—
195C3×(C2×D3)⋊C4C22×C314yescomplemented
196C3×(C2×D3)⋊C4C22×C314yescomplemented
197C3×C4⋊Dic3C22×C314yescomplemented
198C3×Dic3⋊C4C22×C314yescomplemented
199C3×Dic3⋊C4C22×C314yescomplemented
200C3×Dic3⋊C4C22×C314yescomplemented
201C3×Dic3⋊C4C22×C314yescomplemented
202C3×C4×Dic3C22×C314yescomplemented
203C22×C33—21no—
204C22×C33—21no—
205C22×C33—21no—
206C22×C33—21no—
207C22×C33—21no—
208C22×C33#4112yescomplemented
209C22×C33C2411yescharacteristic
210C2×C32×D3—28no—
211C2×C32×D3—21no—
212C2×C32×D3—21no—
213C2×C32×D3—21no—
214C2×C32×D3—21no—
215C2×C32×D3—21no—
216C2×C32×D3—21no—
217C2×C32×D3—21no—
218C2×C32×D3C2×D412yes—
219C2×C32×D3#4112yescomplemented
220C33×C4—21no—
221C33×C4—21no—
222C33×C4—21no—
223C33×C4—21no—
224C33×C4C2×D412yes—
225C32×Dic3—21no—
226C32×Dic3—21no—
227C32×Dic3—21no—
228C32×Dic3—21no—
229C32×Dic3C2×D412yes—
230C2×C3×#41—34no—
231C23×C3×C4—34no—
232C2×#235C2×C3211yescharacteristic, complemented
233C22×C4×D3C2×C3211yescharacteristic, complemented
234C3×#123—34no—
235C3×#123—34no—
236C3×C22⋊Q8—34no—
237C3×C22⋊Q8—34no—
238C3×#121—34no—
239C3×#121—34no—
240C3×#120—34no—
241C3×#120—34no—
242C3×C4×D4—24no—
243C3×C4×D4—34no—
244C3×C4×D4—34no—
245C3×C4×D4—34no—
246C3×C4×D4C3×D314yescomplemented
247C3×C4×D4C2×C3211yescharacteristic, complemented
248C3×#117—34no—
249#939C2×C3211yescharacteristic, complemented
250#937C2×C3211yescharacteristic, complemented
251C4×#67C2×C3211yescharacteristic, complemented
252C4×#67C2×C3211yescharacteristic, complemented
253#896C2×C3211yescharacteristic, complemented
254#894C2×C3211yescharacteristic, complemented
255#884C2×C3211yescharacteristic, complemented
256#883C2×C3211yescharacteristic, complemented
257#882C2×C3211yescharacteristic, complemented
258#878C2×C3211yescharacteristic, complemented
259C4×D12C2×C3211yescharacteristic, complemented
260#872C2×C3211yescharacteristic, complemented
261C23×C32—24no—
262C23×C32—24no—
263C23×C32—31no—
264C23×C32—31no—
265C23×C32—31no—
266C23×C32—62no—
267C23×C32—62no—
268C23×C32—62no—
269C23×C32C22×D311yescharacteristic
270C23×C32C22×D311yescharacteristic
271C23×C32C23×C314yes—
272C23×C32C23×C314yes—
273C22×C3×D3—28no—
274C22×C3×D3—28no—
275C22×C3×D3—28no—
276C22×C3×D3C23×C314yes—
277C22×C3×D3C23×C314yes—
278C22×C3×D3C23×C314yes—
279C32×Q8—62no—
280C32×D4—216no—
281C32×D4—22no—
282C32×D4—28no—
283C32×D4—62no—
284C32×D4—62no—
285C32×D4—62no—
286C32×D4—62no—
287C32×D4—62no—
288C32×D4—62no—
289C2×C32×C4—22no—
290C2×C32×C4—22no—
291C2×C32×C4—24no—
292C2×C32×C4—24no—
293C2×C32×C4—24no—
294C2×C32×C4—24no—
295C2×C32×C4—24no—
296C2×C32×C4—28no—
297C2×C32×C4—28no—
298C2×C32×C4—31no—
299C2×C32×C4—34no—
300C2×C32×C4—31no—
301C2×C32×C4—31no—
302C2×C32×C4—31no—
303C2×C32×C4—31no—
304C2×C32×C4—48no—
305C2×C32×C4—48no—
306C2×C32×C4—62no—
307C2×C32×C4—62no—
308C2×C32×C4—62no—
309C2×C32×C4—62no—
310C2×C32×C4—62no—
311C2×C32×C4C22×D311yescharacteristic
312C2×C32×C4C22×D311yescharacteristic
313C2×C32×C4C22×D311yescharacteristic
314C2×C32×C4C22×D311yescharacteristic
315C2×C32×C4C22×D311yescharacteristic
316C2×C32×C4C23×C314yes—
317C2×C32×C4C23×C314yes—
318C2×C32×C4C23×C314yes—
319C2×C32×C4C23×C314yes—
320C2×C32×C4C23×C314yes—
321C3×#67—28no—
322C3×#67—28no—
323C3×#67—28no—
324C3×#67—28no—
325C2×C3×Dic3—28no—
326C2×C3×Dic3C23×C314yes—
327C2×C3×Dic3C23×C314yes—
328C2×C3×Dic3C23×C314yes—
329C2×C3×Dic3C23×C314yes—
330C2×C3×Dic3C23×C314yes—
331C3×D12—28no—
332C3×D12—28no—
333C3×C4×D3—28no—
334C3×C4×D3—28no—
335C3×C4×D3—28no—
336C3×C4×D3—28no—
337C3×C4×D3C3×D4116yescomplemented
338C3×Dic6—28no—
339#525—31noSylow
340C2×C33—22no—
341C2×C33—41no—
342C2×C33C22×D411yescharacteristic
343C2×C33C2×#4111yescharacteristic
344C2×C33C2×#4111yescharacteristic
345C32×D3—22no—
346C32×D3—22no—
347C32×D3—41no—
348C24×C3—34no—
349C23×D3C22×C3211yescharacteristic
350C3×#41—616no—
351C2×C3×Q8—34no—
352C2×C3×D4—24no—
353C2×C3×D4—34no—
354C2×C3×D4—34no—
355C2×C3×D4—34no—
356C2×C3×D4—34no—
357C2×C3×D4—34no—
358C2×C3×D4—34no—
359C2×C3×D4C2×C3×D314yes—
360C2×C3×D4C22×C3211yescharacteristic
361C22×C3×C4—24no—
362C22×C3×C4—24no—
363C22×C3×C4—34no—
364C22×C3×C4—34no—
365C22×C3×C4—34no—
366C22×C3×C4—34no—
367C22×C3×C4—34no—
368C22×C3×C4—34no—
369C22×C3×C4—616no—
370C22×C3×C4C2×C3×D314yes—
371C22×C3×C4C2×C3×D314yescomplemented
372C22×C3×C4C22×C3211yescharacteristic
373C22×C3×C4C22×C3211yescharacteristic, complemented
374C2×#67C22×C3211yescharacteristic
375C2×#67C22×C3211yescharacteristic
376C2×#67C22×C3211yescharacteristic
377C2×#67C22×C3211yescharacteristic, complemented
378C22×Dic3C22×C3211yescharacteristic
379#235—24no—
380C2×D12C22×C3211yescharacteristic
381C2×D12C22×C3211yescharacteristic
382C2×C4×D3—24no—
383C2×C4×D3C22×C3211yescharacteristic
384C2×C4×D3C22×C3211yescharacteristic
385C2×C4×D3C22×C3211yescharacteristic
386C2×C4×D3C22×C3211yescharacteristic
387C2×C4×D3C22×C3211yescharacteristic, complemented
388C2×Dic6C22×C3211yescharacteristic, complemented
389C3×C4⋊C4—24no—
390C3×C4⋊C4—34no—
391C3×C4⋊C4—34no—
392C3×C4⋊C4—34no—
393C3×C4⋊C4—34no—
394C3×C4⋊C4—34no—
395C3×C4⋊C4C2×C3×D314yescomplemented
396C3×C4⋊C4C22×C3211yescharacteristic, complemented
397C3×C22⋊C4—24no—
398C3×C22⋊C4—24no—
399C3×C22⋊C4—34no—
400C3×C22⋊C4—34no—
401C3×C22⋊C4—34no—
402C3×C22⋊C4—34no—
403C3×C22⋊C4—34no—
404C3×C22⋊C4—34no—
405C3×C22⋊C4—34no—
406C3×C22⋊C4—34no—
407C3×C22⋊C4C2×C3×D314yes—
408C3×C22⋊C4C2×C3×D314yescomplemented
409C3×C22⋊C4C22×C3211yescharacteristic
410C3×C22⋊C4C22×C3211yescharacteristic, complemented
411C3×C42—24no—
412C3×C42—34no—
413C3×C42C2×C3×D314yescomplemented
414C3×C42C22×C3211yescharacteristic, complemented
415#217C22×C3211yescharacteristic
416#217C22×C3211yescharacteristic, complemented
417(C2×D3)⋊C4C22×C3211yescharacteristic
418(C2×D3)⋊C4C22×C3211yescharacteristic
419(C2×D3)⋊C4C22×C3211yescharacteristic
420(C2×D3)⋊C4C22×C3211yescharacteristic
421(C2×D3)⋊C4C22×C3211yescharacteristic, complemented
422(C2×D3)⋊C4C22×C3211yescharacteristic, complemented
423C4⋊Dic3C22×C3211yescharacteristic, complemented
424Dic3⋊C4C22×C3211yescharacteristic, complemented
425Dic3⋊C4C22×C3211yescharacteristic, complemented
426Dic3⋊C4C22×C3211yescharacteristic, complemented
427Dic3⋊C4C22×C3211yescharacteristic, complemented
428C4×Dic3C22×C3211yescharacteristic, complemented
429C22×C32—21no—
430C22×C32—21no—
431C22×C32—28no—
432C22×C32—21no—
433C22×C32—21no—
434C22×C32—21no—
435C22×C32—24no—
436C22×C32—24no—
437C22×C32—28no—
438C22×C32—24no—
439C22×C32—24no—
440C22×C32—24no—
441C22×C32—24no—
442C22×C32—32no—
443C22×C32—32no—
444C22×C32—44no—
445C22×C32—44no—
446C22×C32—44no—
447C22×C32—44no—
448C22×C32—68no—
449C22×C32—61no—
450C22×C32—61no—
451C22×C32—61no—
452C22×C32—61no—
453C22×C32—61no—
454C22×C32—61no—
455C22×C32—61no—
456C22×C32#23512yescomplemented
457C22×C32C3×#4118yescomplemented
458C22×C32C23×D311yescharacteristic
459C22×C32C24×C314yes—
460C2×C3×D3—232no—
461C2×C3×D3—24no—
462C2×C3×D3—24no—
463C2×C3×D3—24no—
464C2×C3×D3—24no—
465C2×C3×D3—24no—
466C2×C3×D3—24no—
467C2×C3×D3—24no—
468C2×C3×D3C2×C3×D418yes—
469C2×C3×D3C3×#4118yescomplemented
470C32×C4—28no—
471C32×C4—21no—
472C32×C4—21no—
473C32×C4—21no—
474C32×C4—21no—
475C32×C4—24no—
476C32×C4—28no—
477C32×C4—24no—
478C32×C4—24no—
479C32×C4—24no—
480C32×C4—32no—
481C32×C4—44no—
482C32×C4—44no—
483C32×C4—44no—
484C32×C4—61no—
485C32×C4—61no—
486C32×C4—61no—
487C32×C4—61no—
488C32×C4D3×D412yes—
489C32×C4C2×C3×D418yes—
490C3×Dic3—24no—
491C3×Dic3—24no—
492C3×Dic3—24no—
493C3×Dic3—24no—
494C3×Dic3C2×C3×D418yes—
495C2×#41—31no—
496C23×C4—31no—
497#123—31no—
498#123—31no—
499C22⋊Q8—31no—
500C22⋊Q8—31no—
501#121—31no—
502#121—31no—
503#120—31no—
504#120—31no—
505C4×D4—31no—
506C4×D4—31no—
507C4×D4—31no—
508C4×D4C32×D311yescharacteristic, complemented
509#117—31no—
510C33#52511yescharacteristic, complemented, Sylow
511C23×C3—24no—
512C23×C3—24no—
513C23×C3—34no—
514C23×C3—34no—
515C23×C3—34no—
516C23×C3—68no—
517C23×C3—68no—
518C23×C3—68no—
519C23×C3C22×C3×D314yes—
520C23×C3C22×C3×D314yes—
521C23×C3C23×C3211yescharacteristic
522C23×C3C23×C3211yescharacteristic
523C22×D3—22no—
524C22×D3—22no—
525C22×D3—22no—
526C22×D3C23×C3211yescharacteristic
527C22×D3C23×C3211yescharacteristic
528C22×D3C23×C3211yescharacteristic
529C3×Q8—68no—
530C3×D4—216no—
531C3×D4—28no—
532C3×D4—22no—
533C3×D4—68no—
534C3×D4—68no—
535C3×D4—68no—
536C3×D4—68no—
537C3×D4—68no—
538C3×D4—68no—
539C2×C3×C4—28no—
540C2×C3×C4—28no—
541C2×C3×C4—22no—
542C2×C3×C4—22no—
543C2×C3×C4—24no—
544C2×C3×C4—24no—
545C2×C3×C4—24no—
546C2×C3×C4—24no—
547C2×C3×C4—24no—
548C2×C3×C4—34no—
549C2×C3×C4—316no—
550C2×C3×C4—34no—
551C2×C3×C4—34no—
552C2×C3×C4—34no—
553C2×C3×C4—34no—
554C2×C3×C4—48no—
555C2×C3×C4—48no—
556C2×C3×C4—68no—
557C2×C3×C4—68no—
558C2×C3×C4—68no—
559C2×C3×C4—68no—
560C2×C3×C4—68no—
561C2×C3×C4C22×C3×D314yes—
562C2×C3×C4C22×C3×D314yes—
563C2×C3×C4C22×C3×D314yes—
564C2×C3×C4C22×C3×D314yes—
565C2×C3×C4C22×C3×D314yes—
566C2×C3×C4C23×C3211yescharacteristic
567C2×C3×C4C23×C3211yescharacteristic
568C2×C3×C4C23×C3211yescharacteristic
569C2×C3×C4C23×C3211yescharacteristic
570C2×C3×C4C23×C3211yescharacteristic
571#67—22no—
572#67—22no—
573#67—22no—
574#67—22no—
575C2×Dic3—22no—
576C2×Dic3C23×C3211yescharacteristic
577C2×Dic3C23×C3211yescharacteristic
578C2×Dic3C23×C3211yescharacteristic
579C2×Dic3C23×C3211yescharacteristic
580C2×Dic3C23×C3211yescharacteristic
581D12—22no—
582D12—22no—
583C4×D3—22no—
584C4×D3—22no—
585C4×D3—22no—
586C4×D3—22no—
587C4×D3C32×D414yescomplemented
588Dic6—22no—
589C2×C32—22no—
590C2×C32—24no—
591C2×C32—24no—
592C2×C32—24no—
593C2×C32—28no—
594C2×C32—48no—
595C2×C32—48no—
596C2×C32—41no—
597C2×C32—44no—
598C2×C32—62no—
599C2×C32—62no—
600C2×C32—121no—
601C2×C32C2×#23511yescharacteristic
602C2×C32C2×D3×D411yescharacteristic
603C2×C32D3×#4111yescharacteristic
604C2×C32C22×C3×D414yes—
605C2×C32C2×C3×#4114yes—
606C2×C32C2×C3×#4114yes—
607C3×D3—28no—
608C3×D3—28no—
609C3×D3—44no—
610C24—31no—
611#41—64no—
612C2×Q8—31no—
613C2×D4—31no—
614C2×D4—31no—
615C2×D4—31no—
616C2×D4—31no—
617C2×D4—31no—
618C2×D4—31no—
619C2×D4C2×C32×D311yescharacteristic
620C22×C4—31no—
621C22×C4—31no—
622C22×C4—31no—
623C22×C4—31no—
624C22×C4—31no—
625C22×C4—31no—
626C22×C4—64no—
627C22×C4C2×C32×D311yescharacteristic
628C22×C4C2×C32×D311yescharacteristic, complemented
629C4⋊C4—31no—
630C4⋊C4—31no—
631C4⋊C4—31no—
632C4⋊C4—31no—
633C4⋊C4—31no—
634C4⋊C4C2×C32×D311yescharacteristic, complemented
635C22⋊C4—31no—
636C22⋊C4—31no—
637C22⋊C4—31no—
638C22⋊C4—31no—
639C22⋊C4—31no—
640C22⋊C4—31no—
641C22⋊C4—31no—
642C22⋊C4—31no—
643C22⋊C4C2×C32×D311yescharacteristic
644C22⋊C4C2×C32×D311yescharacteristic, complemented
645C42—31no—
646C42C2×C32×D311yescharacteristic, complemented
647C22×C3—24no—
648C22×C3—24no—
649C22×C3—21no—
650C22×C3—21no—
651C22×C3—28no—
652C22×C3—24no—
653C22×C3—24no—
654C22×C3—24no—
655C22×C3—21no—
656C22×C3—21no—
657C22×C3—21no—
658C22×C3—24no—
659C22×C3—28no—
660C22×C3—38no—
661C22×C3—38no—
662C22×C3—44no—
663C22×C3—44no—
664C22×C3—44no—
665C22×C3—44no—
666C22×C3—632no—
667C22×C3—64no—
668C22×C3—64no—
669C22×C3—64no—
670C22×C3—64no—
671C22×C3—64no—
672C22×C3—64no—
673C22×C3—64no—
674C22×C3C3×#23518yescomplemented
675C22×C3C32×#4112yescomplemented
676C22×C3C23×C3×D314yes—
677C22×C3C24×C3211yescharacteristic
678C2×D3—28no—
679C2×D3—21no—
680C2×D3—21no—
681C2×D3—21no—
682C2×D3—21no—
683C2×D3—21no—
684C2×D3—21no—
685C2×D3—21no—
686C2×D3C2×C32×D412yes—
687C2×D3C32×#4112yescomplemented
688C3×C4—28no—
689C3×C4—24no—
690C3×C4—24no—
691C3×C4—24no—
692C3×C4—24no—
693C3×C4—21no—
694C3×C4—21no—
695C3×C4—21no—
696C3×C4—21no—
697C3×C4—28no—
698C3×C4—38no—
699C3×C4—44no—
700C3×C4—44no—
701C3×C4—44no—
702C3×C4—64no—
703C3×C4—64no—
704C3×C4—64no—
705C3×C4—64no—
706C3×C4C3×D3×D418yes—
707C3×C4C2×C32×D412yes—
708Dic3—21no—
709Dic3—21no—
710Dic3—21no—
711Dic3—21no—
712Dic3C2×C32×D412yes—
713C32—24no—
714C32#554711yescharacteristic, direct product factor
715C32C3×#52514yescomplemented
716C23—31no—
717C23—31no—
718C23—31no—
719C23—62no—
720C23—62no—
721C23—62no—
722C23C22×C32×D311yescharacteristic
723C23C22×C32×D311yescharacteristic
724Q8—62no—
725D4—22no—
726D4—62no—
727D4—62no—
728D4—62no—
729D4—62no—
730D4—62no—
731D4—62no—
732C2×C4—22no—
733C2×C4—22no—
734C2×C4—31no—
735C2×C4—34no—
736C2×C4—31no—
737C2×C4—31no—
738C2×C4—31no—
739C2×C4—31no—
740C2×C4—62no—
741C2×C4—62no—
742C2×C4—62no—
743C2×C4—62no—
744C2×C4—62no—
745C2×C4C22×C32×D311yescharacteristic
746C2×C4C22×C32×D311yescharacteristic
747C2×C4C22×C32×D311yescharacteristic
748C2×C4C22×C32×D311yescharacteristic
749C2×C4C22×C32×D311yescharacteristic
750C2×C3—28no—
751C2×C3—22no—
752C2×C3—24no—
753C2×C3—24no—
754C2×C3—24no—
755C2×C3—48no—
756C2×C3—48no—
757C2×C3—44no—
758C2×C3—41no—
759C2×C3—68no—
760C2×C3—68no—
761C2×C3—124no—
762C2×C3C2×C3×#23514yes—
763C2×C3C2×C3×D3×D414yes—
764C2×C3C3×D3×#4114yes—
765C2×C3C22×C32×D411yescharacteristic
766C2×C3C2×C32×#4111yescharacteristic
767C2×C3C2×C32×#4111yescharacteristic
768D3—22no—
769D3—22no—
770D3—41no—
771C22—21no—
772C22—21no—
773C22—21no—
774C22—21no—
775C22—21no—
776C22—32no—
777C22—32no—
778C22—68no—
779C22—61no—
780C22—61no—
781C22—61no—
782C22—61no—
783C22—61no—
784C22—61no—
785C22—61no—
786C22C32×#23512yescomplemented
787C22C23×C32×D311yescharacteristic
788C4—21no—
789C4—21no—
790C4—21no—
791C4—21no—
792C4—32no—
793C4—61no—
794C4—61no—
795C4—61no—
796C4—61no—
797C4C32×D3×D412yes—
798C3—24no—
799C3C3×#554714yesdirect product factor
800C3C32×#52511yescharacteristic, complemented
801C2—22no—
802C2—41no—
803C2—62no—
804C2—62no—
805C2—121no—
806C2C2×C32×#23511yescharacteristic
807C2C2×C32×D3×D411yescharacteristic
808C2C32×D3×#4111yescharacteristic
subgroupG/H
centerC2×C32×C4C22×D3
commutator, cosocleC22×C3C24×C32
FrattiniC22C23×C32×D3
FittingC33×C4×D4C2
socleC22×C33C24
hypercenterC32×C4×D4D3
hypocenterC3C32×#525
LCSG ▷ C22×C3 ▷ C3
UCSC1 ◁ C2×C32×C4 ◁ C32×C4×D4

Complements

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

NH ≅ G/Ntype
1. C2×C32×#235C2semidirect
2. C22×C32×C4×D3C2semidirect
3. C33×C4×D4C2semidirect
4. C32×#939C2semidirect
5. C32×#937C2semidirect
6. C32×C4×#67C2semidirect
7. C32×C4×#67C2semidirect
8. C32×#896C2semidirect
9. C32×#894C2semidirect
10. C32×#884C2semidirect
11. C32×#883C2semidirect
12. C32×#882C2semidirect
13. C32×#878C2semidirect
14. C32×C4×D12C2semidirect
15. C32×#872C2semidirect
17. C3×#5547C3direct (N × H)
21. C22×C33×C4C22semidirect
25. C2×C32×#67C22semidirect
35. C2×C32×C4×D3C22semidirect
36. C2×C32×Dic6C22semidirect
37. C33×C4⋊C4C22semidirect
39. C33×C22⋊C4C22semidirect
40. C33×C42C22semidirect
42. C32×#217C22semidirect
47. C32×(C2×D3)⋊C4C22semidirect
48. C32×(C2×D3)⋊C4C22semidirect
49. C32×C4⋊Dic3C22semidirect
50. C32×Dic3⋊C4C22semidirect
51. C32×Dic3⋊C4C22semidirect
52. C32×Dic3⋊C4C22semidirect
53. C32×Dic3⋊C4C22semidirect
54. C32×C4×Dic3C22semidirect
57. C2×C3×#235C2×C3semidirect
58. C22×C3×C4×D3C2×C3semidirect
71. C32×C4×D4D3semidirect
72. C32×C4×D4C2×C3semidirect
74. C3×#939C2×C3semidirect
75. C3×#937C2×C3semidirect
76. C3×C4×#67C2×C3semidirect
77. C3×C4×#67C2×C3semidirect
78. C3×#896C2×C3semidirect
79. C3×#894C2×C3semidirect
80. C3×#884C2×C3semidirect
81. C3×#883C2×C3semidirect
82. C3×#882C2×C3semidirect
83. C3×#878C2×C3semidirect
84. C3×C4×D12C2×C3semidirect
85. C3×#872C2×C3semidirect
118. C32×C4×D3D4semidirect
121. #5547C32direct (N × H)
145. C22×C32×C4C2×D3semidirect
147. C22×C32×C4C22×C3semidirect
151. C2×C3×#67C22×C3semidirect
161. C2×C3×C4×D3C22×C3semidirect
162. C2×C3×Dic6C22×C3semidirect
169. C32×C4⋊C4C2×D3semidirect
170. C32×C4⋊C4C22×C3semidirect
182. C32×C22⋊C4C2×D3semidirect
184. C32×C22⋊C4C22×C3semidirect
187. C32×C42C2×D3semidirect
188. C32×C42C22×C3semidirect
190. C3×#217C22×C3semidirect
195. C3×(C2×D3)⋊C4C22×C3semidirect
196. C3×(C2×D3)⋊C4C22×C3semidirect
197. C3×C4⋊Dic3C22×C3semidirect
198. C3×Dic3⋊C4C22×C3semidirect
199. C3×Dic3⋊C4C22×C3semidirect
200. C3×Dic3⋊C4C22×C3semidirect
201. C3×Dic3⋊C4C22×C3semidirect
202. C3×C4×Dic3C22×C3semidirect
208. C22×C33#41semidirect
219. C2×C32×D3#41semidirect
232. C2×#235C2×C32semidirect
233. C22×C4×D3C2×C32semidirect
246. C3×C4×D4C3×D3semidirect
247. C3×C4×D4C2×C32semidirect
249. #939C2×C32semidirect
250. #937C2×C32semidirect
251. C4×#67C2×C32semidirect
252. C4×#67C2×C32semidirect
253. #896C2×C32semidirect
254. #894C2×C32semidirect
255. #884C2×C32semidirect
256. #883C2×C32semidirect
257. #882C2×C32semidirect
258. #878C2×C32semidirect
259. C4×D12C2×C32semidirect
260. #872C2×C32semidirect
337. C3×C4×D3C3×D4semidirect
371. C22×C3×C4C2×C3×D3semidirect
373. C22×C3×C4C22×C32semidirect
377. C2×#67C22×C32semidirect
387. C2×C4×D3C22×C32semidirect
388. C2×Dic6C22×C32semidirect
395. C3×C4⋊C4C2×C3×D3semidirect
396. C3×C4⋊C4C22×C32semidirect
408. C3×C22⋊C4C2×C3×D3semidirect
410. C3×C22⋊C4C22×C32semidirect
413. C3×C42C2×C3×D3semidirect
414. C3×C42C22×C32semidirect
416. #217C22×C32semidirect
421. (C2×D3)⋊C4C22×C32semidirect
422. (C2×D3)⋊C4C22×C32semidirect
423. C4⋊Dic3C22×C32semidirect
424. Dic3⋊C4C22×C32semidirect
425. Dic3⋊C4C22×C32semidirect
426. Dic3⋊C4C22×C32semidirect
427. Dic3⋊C4C22×C32semidirect
428. C4×Dic3C22×C32semidirect
456. C22×C32#235semidirect
457. C22×C32C3×#41semidirect
469. C2×C3×D3C3×#41semidirect
508. C4×D4C32×D3semidirect
510. C33#525semidirect
587. C4×D3C32×D4semidirect
628. C22×C4C2×C32×D3semidirect
634. C4⋊C4C2×C32×D3semidirect
644. C22⋊C4C2×C32×D3semidirect
646. C42C2×C32×D3semidirect
674. C22×C3C3×#235semidirect
675. C22×C3C32×#41semidirect
687. C2×D3C32×#41semidirect
714. C32#5547direct (N × H)
715. C32C3×#525semidirect
786. C22C32×#235semidirect
799. C3C3×#5547direct (N × H)
800. C3C32×#525semidirect

Maximal subgroups

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

subgroupindex
C2×C32×#2352
C22×C32×C4×D32
C33×C4×D42
C32×#9392
C32×#9372
C32×C4×#672
C32×#8962
C32×#8942
C32×#8842
C32×#8832
C32×#8822
C32×#8782
C32×C4×D122
C32×#8722
C32×#5253
C3×#55473