Finite Group Databasebeta

← C32×#5655 #13179036

Subgroups — C32×#5655 #13179036

Order 1728.

2064 conjugacy classes of subgroups.

The subgroup lattice has 766 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C32×#237C211yesmaximal, characteristic, complemented
2C2×C32×#235C211yesmaximal, characteristic, complemented
3C33×#123C211yesmaximal, characteristic, complemented
4C32×#939C211yesmaximal, characteristic, complemented
5C2×C32×Dic3⋊C4C211yesmaximal, characteristic, complemented
6C32×#896C211yesmaximal, characteristic, complemented
7C32×#894C211yesmaximal, characteristic, complemented
8C32×D3×C4⋊C4C211yesmaximal, characteristic, complemented
9C32×#888C211yesmaximal, characteristic, complemented
10C32×#886C211yesmaximal, characteristic, complemented
11C32×#884C211yesmaximal, characteristic, complemented
12C32×#883C211yesmaximal, characteristic, complemented
13C32×#67⋊C4C211yesmaximal, characteristic, complemented
14C32×#67⋊C4C211yesmaximal, characteristic, complemented
15C32×#878C211yesmaximal, characteristic, complemented
16C32×#547—31nomaximal
17C3×#5655C314yesmaximal, direct product factor
18C2×C33×D4C2211yescharacteristic
19C22×C33×C4C2211yescharacteristic
20C2×C32×#67C2211yescharacteristic
21C2×C32×#67C2211yescharacteristic
22C2×C32×#67C2211yescharacteristic
23C2×C32×#67C2211yescharacteristic
24C22×C32×Dic3C2211yescharacteristic
25C22×C32×Dic3C2211yescharacteristic
26C22×C32×Dic3C2211yescharacteristic
27C32×#237—24no—
28C32×#235—24no—
29C2×C32×D12C2211yescharacteristic
30C2×C32×C4×D3C2211yescharacteristic
31C2×C32×C4×D3C2211yescharacteristic
32C2×C32×C4×D3C2211yescharacteristic
33C2×C32×C4×D3C2211yescharacteristic
34C2×C32×Dic6C2211yescharacteristic
35C2×C32×Dic6C2211yescharacteristic
36C33×C4⋊C4C2211yescharacteristic
37C33×C4⋊C4C2211yescharacteristic
38C33×C22⋊C4C2211yescharacteristic
39C33×C22⋊C4C2211yescharacteristic
40C33×C22⋊C4C2211yescharacteristic
41C32×#217C2211yescharacteristic
42C32×(C2×D3)⋊C4C2211yescharacteristic
43C32×(C2×D3)⋊C4C2211yescharacteristic
44C32×(C2×D3)⋊C4C2211yescharacteristic
45C32×(C2×D3)⋊C4C2211yescharacteristic
46C32×C4⋊Dic3C2211yescharacteristic
47C32×C4⋊Dic3C2211yescharacteristic
48C32×Dic3⋊C4C2211yescharacteristic
49C32×Dic3⋊C4C2211yescharacteristic
50C32×Dic3⋊C4C2211yescharacteristic
51C32×Dic3⋊C4C2211yescharacteristic
52C32×Dic3⋊C4C2211yescharacteristic
53C32×Dic3⋊C4C2211yescharacteristic
54C32×C4×Dic3C2211yescharacteristic
55C2×C32×#41—31no—
56C2×C32×#41—31no—
57C2×C3×#237C2×C314yescomplemented
58C2×C3×#235C2×C314yescomplemented
59C32×C4⋊Q8—31no—
60C32×#123—24no—
61C32×#123—31no—
62C32×#123—31no—
63C32×#123—31no—
64C32×#123D311yescharacteristic, complemented
65C32×#123C2×C314yescomplemented
66C32×C22⋊Q8—31no—
67C32×C22⋊Q8—31no—
68C32×#121—31no—
69C32×#121—31no—
70C32×C4×D4—31no—
71C32×C4×D4—31no—
72C2×C32×C4⋊C4—31no—
73C2×C32×C4⋊C4—31no—
74C3×#939C2×C314yescomplemented
75C2×C3×Dic3⋊C4C2×C314yescomplemented
76C3×#896C2×C314yescomplemented
77C3×#894C2×C314yescomplemented
78C3×D3×C4⋊C4C2×C314yescomplemented
79C3×#888C2×C314yescomplemented
80C3×#886C2×C314yescomplemented
81C3×#884C2×C314yescomplemented
82C3×#883C2×C314yescomplemented
83C3×#67⋊C4C2×C314yescomplemented
84C3×#67⋊C4C2×C314yescomplemented
85C3×#878C2×C314yescomplemented
86C23×C33C2311yescharacteristic
87C23×C33C2311yescharacteristic
88C22×C32×D3C2311yescharacteristic
89C22×C32×D3C2311yescharacteristic
90C33×D4—22no—
91C2×C33×C4—22no—
92C2×C33×C4C2311yescharacteristic
93C2×C33×C4C2311yescharacteristic
94C2×C33×C4C2311yescharacteristic
95C2×C33×C4C2311yescharacteristic
96C2×C33×C4C2311yescharacteristic
97C32×#67—22no—
98C32×#67—22no—
99C32×#67—22no—
100C32×#67D414yescomplemented
101C2×C32×Dic3—22no—
102C2×C32×Dic3—22no—
103C2×C32×Dic3—22no—
104C2×C32×Dic3C2311yescharacteristic
105C2×C32×Dic3C2311yescharacteristic
106C2×C32×Dic3C2311yescharacteristic
107C2×C32×Dic3C2311yescharacteristic
108C2×C32×Dic3C2311yescharacteristic
109C2×C32×Dic3C2311yescharacteristic
110C32×D12—22no—
111C32×C4×D3—22no—
112C32×C4×D3—22no—
113C32×C4×D3—22no—
114C32×C4×D3—22no—
115C32×Dic6—22no—
116C32×Dic6—22no—
117C3×#547—34no—
118#5655C3211yescharacteristic, direct product factor
119C32×#41—64no—
120C32×#41—64no—
121C2×C32×Q8—31no—
122C2×C32×Q8—31no—
123C2×C32×D4—24no—
124C2×C32×D4—31no—
125C2×C32×D4—31no—
126C2×C32×D4—31no—
127C2×C32×D4—31no—
128C2×C32×D4—31no—
129C2×C32×D4C2×D311yescharacteristic
130C2×C32×D4C22×C314yes—
131C22×C32×C4—24no—
132C22×C32×C4—31no—
133C22×C32×C4—31no—
134C22×C32×C4—31no—
135C22×C32×C4—31no—
136C22×C32×C4—31no—
137C22×C32×C4—31no—
138C22×C32×C4—31no—
139C22×C32×C4C2×D311yescharacteristic
140C22×C32×C4C22×C314yes—
141C2×C3×#67C22×C314yes—
142C2×C3×#67C22×C314yes—
143C2×C3×#67C22×C314yes—
144C2×C3×#67C22×C314yes—
145C22×C3×Dic3C22×C314yes—
146C22×C3×Dic3C22×C314yes—
147C22×C3×Dic3C22×C314yes—
148C3×#237—216no—
149C3×#235—216no—
150C2×C3×D12C22×C314yes—
151C2×C3×C4×D3C22×C314yes—
152C2×C3×C4×D3C22×C314yes—
153C2×C3×C4×D3C22×C314yes—
154C2×C3×C4×D3C22×C314yes—
155C2×C3×Dic6C22×C314yes—
156C2×C3×Dic6C22×C314yes—
157C32×C4⋊C4—24no—
158C32×C4⋊C4—24no—
159C32×C4⋊C4—31no—
160C32×C4⋊C4—31no—
161C32×C4⋊C4—31no—
162C32×C4⋊C4—31no—
163C32×C4⋊C4—31no—
164C32×C4⋊C4—31no—
165C32×C4⋊C4—31no—
166C32×C4⋊C4—31no—
167C32×C4⋊C4C2×D311yescharacteristic
168C32×C4⋊C4C2×D311yescharacteristic
169C32×C4⋊C4C22×C314yes—
170C32×C4⋊C4C22×C314yes—
171C32×C22⋊C4—24no—
172C32×C22⋊C4—24no—
173C32×C22⋊C4—24no—
174C32×C22⋊C4—31no—
175C32×C22⋊C4—31no—
176C32×C22⋊C4—31no—
177C32×C22⋊C4—31no—
178C32×C22⋊C4—31no—
179C32×C22⋊C4C2×D311yescharacteristic
180C32×C22⋊C4C2×D311yescharacteristic
181C32×C22⋊C4C2×D311yescharacteristic
182C32×C22⋊C4C22×C314yes—
183C32×C22⋊C4C22×C314yes—
184C32×C22⋊C4C22×C314yes—
185C32×C42—31no—
186C3×#217C22×C314yes—
187C3×(C2×D3)⋊C4C22×C314yes—
188C3×(C2×D3)⋊C4C22×C314yes—
189C3×(C2×D3)⋊C4C22×C314yes—
190C3×(C2×D3)⋊C4C22×C314yes—
191C3×C4⋊Dic3C22×C314yes—
192C3×C4⋊Dic3C22×C314yes—
193C3×Dic3⋊C4C22×C314yes—
194C3×Dic3⋊C4C22×C314yes—
195C3×Dic3⋊C4C22×C314yes—
196C3×Dic3⋊C4C22×C314yes—
197C3×Dic3⋊C4C22×C314yes—
198C3×Dic3⋊C4C22×C314yes—
199C3×C4×Dic3C22×C314yes—
200C22×C33—21no—
201C22×C33—21no—
202C22×C33—21no—
203C22×C33—21no—
204C22×C33—21no—
205C22×C33C2×D412yes—
206C22×C33C2411yescharacteristic
207C2×C32×D3—21no—
208C2×C32×D3—21no—
209C2×C32×D3—21no—
210C2×C32×D3—21no—
211C2×C32×D3—21no—
212C2×C32×D3C2×D412yes—
213C33×C4—21no—
214C33×C4—21no—
215C33×C4—21no—
216C33×C4—21no—
217C33×C4—21no—
218C32×Dic3—21no—
219C32×Dic3—21no—
220C32×Dic3—21no—
221C32×Dic3—21no—
222C32×Dic3C2×D412yes—
223C32×Dic3#4112yescomplemented
224C2×C3×#41—34no—
225C2×C3×#41—34no—
226C2×#237C2×C3211yescharacteristic, complemented
227C2×#235C2×C3211yescharacteristic, complemented
228C3×C4⋊Q8—34no—
229C3×#123—24no—
230C3×#123—34no—
231C3×#123—34no—
232C3×#123—34no—
233C3×#123C3×D314yescomplemented
234C3×#123C2×C3211yescharacteristic, complemented
235C3×C22⋊Q8—34no—
236C3×C22⋊Q8—34no—
237C3×#121—34no—
238C3×#121—34no—
239C3×C4×D4—34no—
240C3×C4×D4—34no—
241C2×C3×C4⋊C4—34no—
242C2×C3×C4⋊C4—34no—
243#939C2×C3211yescharacteristic, complemented
244C2×Dic3⋊C4C2×C3211yescharacteristic, complemented
245#896C2×C3211yescharacteristic, complemented
246#894C2×C3211yescharacteristic, complemented
247D3×C4⋊C4C2×C3211yescharacteristic, complemented
248#888C2×C3211yescharacteristic, complemented
249#886C2×C3211yescharacteristic, complemented
250#884C2×C3211yescharacteristic, complemented
251#883C2×C3211yescharacteristic, complemented
252#67⋊C4C2×C3211yescharacteristic, complemented
253#67⋊C4C2×C3211yescharacteristic, complemented
254#878C2×C3211yescharacteristic, complemented
255C23×C32—24no—
256C23×C32—24no—
257C23×C32—31no—
258C23×C32—31no—
259C23×C32C22×D311yescharacteristic
260C23×C32C22×D311yescharacteristic
261C23×C32C23×C314yes—
262C23×C32C23×C314yes—
263C22×C3×D3C23×C314yes—
264C22×C3×D3C23×C314yes—
265C32×Q8—62no—
266C32×Q8—62no—
267C32×D4—22no—
268C32×D4—28no—
269C32×D4—34no—
270C32×D4—48no—
271C32×D4—62no—
272C32×D4—62no—
273C32×D4—62no—
274C32×D4—62no—
275C2×C32×C4—22no—
276C2×C32×C4—24no—
277C2×C32×C4—24no—
278C2×C32×C4—24no—
279C2×C32×C4—24no—
280C2×C32×C4—24no—
281C2×C32×C4—28no—
282C2×C32×C4—31no—
283C2×C32×C4—31no—
284C2×C32×C4—31no—
285C2×C32×C4—31no—
286C2×C32×C4—31no—
287C2×C32×C4—31no—
288C2×C32×C4—48no—
289C2×C32×C4—62no—
290C2×C32×C4—62no—
291C2×C32×C4—62no—
292C2×C32×C4—62no—
293C2×C32×C4—62no—
294C2×C32×C4—62no—
295C2×C32×C4—62no—
296C2×C32×C4C22×D311yescharacteristic
297C2×C32×C4C22×D311yescharacteristic
298C2×C32×C4C22×D311yescharacteristic
299C2×C32×C4C22×D311yescharacteristic
300C2×C32×C4C22×D311yescharacteristic
301C2×C32×C4C23×C314yes—
302C2×C32×C4C23×C314yes—
303C2×C32×C4C23×C314yes—
304C2×C32×C4C23×C314yes—
305C2×C32×C4C23×C314yes—
306C3×#67—28no—
307C3×#67—28no—
308C3×#67—28no—
309C3×#67C3×D4116yescomplemented
310C2×C3×Dic3—28no—
311C2×C3×Dic3—28no—
312C2×C3×Dic3—28no—
313C2×C3×Dic3C23×C314yes—
314C2×C3×Dic3C23×C314yes—
315C2×C3×Dic3C23×C314yes—
316C2×C3×Dic3C23×C314yes—
317C2×C3×Dic3C23×C314yes—
318C2×C3×Dic3C23×C314yes—
319C3×D12—28no—
320C3×C4×D3—28no—
321C3×C4×D3—28no—
322C3×C4×D3—28no—
323C3×C4×D3—28no—
324C3×Dic6—28no—
325C3×Dic6—28no—
326#547—31noSylow
327C2×C33—22no—
328C2×C33—41no—
329C2×C33C22×D411yescharacteristic
330C2×C33C2×#4111yescharacteristic
331C2×C332−1+411yescharacteristic
332C32×D3—22no—
333C32×D3—41no—
334C3×#41—616no—
335C3×#41—616no—
336C2×C3×Q8—34no—
337C2×C3×Q8—34no—
338C2×C3×D4—24no—
339C2×C3×D4—34no—
340C2×C3×D4—34no—
341C2×C3×D4—34no—
342C2×C3×D4—34no—
343C2×C3×D4—34no—
344C2×C3×D4C2×C3×D314yes—
345C2×C3×D4C22×C3211yescharacteristic
346C22×C3×C4—24no—
347C22×C3×C4—34no—
348C22×C3×C4—34no—
349C22×C3×C4—34no—
350C22×C3×C4—34no—
351C22×C3×C4—34no—
352C22×C3×C4—34no—
353C22×C3×C4—34no—
354C22×C3×C4C2×C3×D314yes—
355C22×C3×C4C22×C3211yescharacteristic
356C2×#67C22×C3211yescharacteristic
357C2×#67C22×C3211yescharacteristic
358C2×#67C22×C3211yescharacteristic
359C2×#67C22×C3211yescharacteristic
360C22×Dic3C22×C3211yescharacteristic
361C22×Dic3C22×C3211yescharacteristic
362C22×Dic3C22×C3211yescharacteristic
363#237—24no—
364#235—24no—
365C2×D12C22×C3211yescharacteristic
366C2×C4×D3C22×C3211yescharacteristic
367C2×C4×D3C22×C3211yescharacteristic
368C2×C4×D3C22×C3211yescharacteristic
369C2×C4×D3C22×C3211yescharacteristic
370C2×Dic6C22×C3211yescharacteristic
371C2×Dic6C22×C3211yescharacteristic
372C3×C4⋊C4—24no—
373C3×C4⋊C4—24no—
374C3×C4⋊C4—34no—
375C3×C4⋊C4—34no—
376C3×C4⋊C4—34no—
377C3×C4⋊C4—34no—
378C3×C4⋊C4—34no—
379C3×C4⋊C4—34no—
380C3×C4⋊C4—34no—
381C3×C4⋊C4—34no—
382C3×C4⋊C4C2×C3×D314yes—
383C3×C4⋊C4C2×C3×D314yes—
384C3×C4⋊C4C22×C3211yescharacteristic
385C3×C4⋊C4C22×C3211yescharacteristic
386C3×C22⋊C4—24no—
387C3×C22⋊C4—24no—
388C3×C22⋊C4—24no—
389C3×C22⋊C4—34no—
390C3×C22⋊C4—34no—
391C3×C22⋊C4—34no—
392C3×C22⋊C4—34no—
393C3×C22⋊C4—34no—
394C3×C22⋊C4C2×C3×D314yes—
395C3×C22⋊C4C2×C3×D314yes—
396C3×C22⋊C4C2×C3×D314yes—
397C3×C22⋊C4C22×C3211yescharacteristic
398C3×C22⋊C4C22×C3211yescharacteristic
399C3×C22⋊C4C22×C3211yescharacteristic
400C3×C42—34no—
401#217C22×C3211yescharacteristic
402(C2×D3)⋊C4C22×C3211yescharacteristic
403(C2×D3)⋊C4C22×C3211yescharacteristic
404(C2×D3)⋊C4C22×C3211yescharacteristic
405(C2×D3)⋊C4C22×C3211yescharacteristic
406C4⋊Dic3C22×C3211yescharacteristic
407C4⋊Dic3C22×C3211yescharacteristic
408Dic3⋊C4C22×C3211yescharacteristic
409Dic3⋊C4C22×C3211yescharacteristic
410Dic3⋊C4C22×C3211yescharacteristic
411Dic3⋊C4C22×C3211yescharacteristic
412Dic3⋊C4C22×C3211yescharacteristic
413Dic3⋊C4C22×C3211yescharacteristic
414C4×Dic3C22×C3211yescharacteristic
415C22×C32—21no—
416C22×C32—21no—
417C22×C32—21no—
418C22×C32—21no—
419C22×C32—21no—
420C22×C32—24no—
421C22×C32—28no—
422C22×C32—24no—
423C22×C32—24no—
424C22×C32—24no—
425C22×C32—24no—
426C22×C32—24no—
427C22×C32—32no—
428C22×C32—44no—
429C22×C32—44no—
430C22×C32—44no—
431C22×C32—44no—
432C22×C32—44no—
433C22×C32—61no—
434C22×C32—61no—
435C22×C32—61no—
436C22×C32—61no—
437C22×C32—61no—
438C22×C32D3×D412yes—
439C22×C32C2×C3×D418yes—
440C22×C32C23×D311yescharacteristic
441C22×C32C24×C314yes—
442C2×C3×D3—24no—
443C2×C3×D3—24no—
444C2×C3×D3—24no—
445C2×C3×D3—24no—
446C2×C3×D3—24no—
447C2×C3×D3C2×C3×D418yes—
448C32×C4—21no—
449C32×C4—21no—
450C32×C4—21no—
451C32×C4—21no—
452C32×C4—21no—
453C32×C4—24no—
454C32×C4—24no—
455C32×C4—24no—
456C32×C4—24no—
457C32×C4—24no—
458C32×C4—32no—
459C32×C4—32no—
460C32×C4—44no—
461C32×C4—44no—
462C32×C4—44no—
463C32×C4—44no—
464C32×C4—44no—
465C32×C4—61no—
466C32×C4—61no—
467C32×C4—61no—
468C32×C4—61no—
469C3×Dic3—24no—
470C3×Dic3—24no—
471C3×Dic3—24no—
472C3×Dic3—24no—
473C3×Dic3C2×C3×D418yes—
474C3×Dic3C3×#4118yescomplemented
475C2×#41—31no—
476C2×#41—31no—
477C4⋊Q8—31no—
478#123—31no—
479#123—31no—
480#123—31no—
481#123C32×D311yescharacteristic, complemented
482C22⋊Q8—31no—
483C22⋊Q8—31no—
484#121—31no—
485#121—31no—
486C4×D4—31no—
487C4×D4—31no—
488C2×C4⋊C4—31no—
489C2×C4⋊C4—31no—
490C33#54711yescharacteristic, complemented, Sylow
491C23×C3—24no—
492C23×C3—24no—
493C23×C3—34no—
494C23×C3—34no—
495C23×C3C22×C3×D314yes—
496C23×C3C22×C3×D314yes—
497C23×C3C23×C3211yescharacteristic
498C23×C3C23×C3211yescharacteristic
499C22×D3C23×C3211yescharacteristic
500C22×D3C23×C3211yescharacteristic
501C3×Q8—68no—
502C3×Q8—68no—
503C3×D4—28no—
504C3×D4—22no—
505C3×D4—316no—
506C3×D4—48no—
507C3×D4—68no—
508C3×D4—68no—
509C3×D4—68no—
510C3×D4—68no—
511C2×C3×C4—28no—
512C2×C3×C4—22no—
513C2×C3×C4—24no—
514C2×C3×C4—24no—
515C2×C3×C4—24no—
516C2×C3×C4—24no—
517C2×C3×C4—24no—
518C2×C3×C4—34no—
519C2×C3×C4—34no—
520C2×C3×C4—34no—
521C2×C3×C4—34no—
522C2×C3×C4—34no—
523C2×C3×C4—34no—
524C2×C3×C4—48no—
525C2×C3×C4—68no—
526C2×C3×C4—68no—
527C2×C3×C4—68no—
528C2×C3×C4—68no—
529C2×C3×C4—68no—
530C2×C3×C4—68no—
531C2×C3×C4—68no—
532C2×C3×C4C22×C3×D314yes—
533C2×C3×C4C22×C3×D314yes—
534C2×C3×C4C22×C3×D314yes—
535C2×C3×C4C22×C3×D314yes—
536C2×C3×C4C22×C3×D314yes—
537C2×C3×C4C23×C3211yescharacteristic
538C2×C3×C4C23×C3211yescharacteristic
539C2×C3×C4C23×C3211yescharacteristic
540C2×C3×C4C23×C3211yescharacteristic
541C2×C3×C4C23×C3211yescharacteristic
542#67—22no—
543#67—22no—
544#67—22no—
545#67C32×D414yescomplemented
546C2×Dic3—22no—
547C2×Dic3—22no—
548C2×Dic3—22no—
549C2×Dic3C23×C3211yescharacteristic
550C2×Dic3C23×C3211yescharacteristic
551C2×Dic3C23×C3211yescharacteristic
552C2×Dic3C23×C3211yescharacteristic
553C2×Dic3C23×C3211yescharacteristic
554C2×Dic3C23×C3211yescharacteristic
555D12—22no—
556C4×D3—22no—
557C4×D3—22no—
558C4×D3—22no—
559C4×D3—22no—
560Dic6—22no—
561Dic6—22no—
562C2×C32—22no—
563C2×C32—24no—
564C2×C32—24no—
565C2×C32—24no—
566C2×C32—28no—
567C2×C32—48no—
568C2×C32—41no—
569C2×C32—44no—
570C2×C32—62no—
571C2×C32—84no—
572C2×C32—121no—
573C2×C32C2×D3×D411yescharacteristic
574C2×C32D3×#4111yescharacteristic
575C2×C32#101011yescharacteristic
576C2×C32C22×C3×D414yes—
577C2×C32C2×C3×#4114yes—
578C2×C32C3×2−1+414yes—
579C3×D3—28no—
580C3×D3—44no—
581#41—64no—
582#41—64no—
583C2×Q8—31no—
584C2×Q8—31no—
585C2×D4—31no—
586C2×D4—31no—
587C2×D4—31no—
588C2×D4—31no—
589C2×D4—31no—
590C2×D4C2×C32×D311yescharacteristic
591C22×C4—31no—
592C22×C4—31no—
593C22×C4—31no—
594C22×C4—31no—
595C22×C4—31no—
596C22×C4—31no—
597C22×C4—31no—
598C22×C4C2×C32×D311yescharacteristic
599C4⋊C4—31no—
600C4⋊C4—31no—
601C4⋊C4—31no—
602C4⋊C4—31no—
603C4⋊C4—31no—
604C4⋊C4—31no—
605C4⋊C4—31no—
606C4⋊C4—31no—
607C4⋊C4C2×C32×D311yescharacteristic
608C4⋊C4C2×C32×D311yescharacteristic
609C22⋊C4—31no—
610C22⋊C4—31no—
611C22⋊C4—31no—
612C22⋊C4—31no—
613C22⋊C4—31no—
614C22⋊C4C2×C32×D311yescharacteristic
615C22⋊C4C2×C32×D311yescharacteristic
616C22⋊C4C2×C32×D311yescharacteristic
617C42—31no—
618C22×C3—24no—
619C22×C3—24no—
620C22×C3—21no—
621C22×C3—21no—
622C22×C3—24no—
623C22×C3—24no—
624C22×C3—24no—
625C22×C3—21no—
626C22×C3—21no—
627C22×C3—21no—
628C22×C3—24no—
629C22×C3—28no—
630C22×C3—38no—
631C22×C3—44no—
632C22×C3—44no—
633C22×C3—44no—
634C22×C3—44no—
635C22×C3—44no—
636C22×C3—64no—
637C22×C3—64no—
638C22×C3—64no—
639C22×C3—64no—
640C22×C3—64no—
641C22×C3C3×D3×D418yes—
642C22×C3C2×C32×D412yes—
643C22×C3C23×C3×D314yes—
644C22×C3C24×C3211yescharacteristic
645C2×D3—21no—
646C2×D3—21no—
647C2×D3—21no—
648C2×D3—21no—
649C2×D3—21no—
650C2×D3C2×C32×D412yes—
651C3×C4—24no—
652C3×C4—24no—
653C3×C4—24no—
654C3×C4—24no—
655C3×C4—24no—
656C3×C4—21no—
657C3×C4—21no—
658C3×C4—21no—
659C3×C4—21no—
660C3×C4—21no—
661C3×C4—38no—
662C3×C4—38no—
663C3×C4—44no—
664C3×C4—44no—
665C3×C4—44no—
666C3×C4—44no—
667C3×C4—44no—
668C3×C4—64no—
669C3×C4—64no—
670C3×C4—64no—
671C3×C4—64no—
672Dic3—21no—
673Dic3—21no—
674Dic3—21no—
675Dic3—21no—
676Dic3C2×C32×D412yes—
677Dic3C32×#4112yescomplemented
678C32—24no—
679C32#565511yescharacteristic, direct product factor
680C32C3×#54714yescomplemented
681C23—31no—
682C23—31no—
683C23C22×C32×D311yescharacteristic
684C23C22×C32×D311yescharacteristic
685Q8—62no—
686Q8—62no—
687D4—22no—
688D4—34no—
689D4—62no—
690D4—62no—
691D4—62no—
692D4—62no—
693C2×C4—22no—
694C2×C4—31no—
695C2×C4—31no—
696C2×C4—31no—
697C2×C4—31no—
698C2×C4—31no—
699C2×C4—31no—
700C2×C4—62no—
701C2×C4—62no—
702C2×C4—62no—
703C2×C4—62no—
704C2×C4—62no—
705C2×C4—62no—
706C2×C4—62no—
707C2×C4C22×C32×D311yescharacteristic
708C2×C4C22×C32×D311yescharacteristic
709C2×C4C22×C32×D311yescharacteristic
710C2×C4C22×C32×D311yescharacteristic
711C2×C4C22×C32×D311yescharacteristic
712C2×C3—28no—
713C2×C3—22no—
714C2×C3—24no—
715C2×C3—24no—
716C2×C3—24no—
717C2×C3—48no—
718C2×C3—44no—
719C2×C3—41no—
720C2×C3—68no—
721C2×C3—84no—
722C2×C3—124no—
723C2×C3C2×C3×D3×D414yes—
724C2×C3C3×D3×#4114yes—
725C2×C3C3×#101014yes—
726C2×C3C22×C32×D411yescharacteristic
727C2×C3C2×C32×#4111yescharacteristic
728C2×C3C32×2−1+411yescharacteristic
729D3—22no—
730D3—41no—
731C22—21no—
732C22—21no—
733C22—21no—
734C22—21no—
735C22—21no—
736C22—32no—
737C22—61no—
738C22—61no—
739C22—61no—
740C22—61no—
741C22—61no—
742C22C32×D3×D412yes—
743C22C23×C32×D311yescharacteristic
744C4—21no—
745C4—21no—
746C4—21no—
747C4—21no—
748C4—21no—
749C4—32no—
750C4—32no—
751C4—61no—
752C4—61no—
753C4—61no—
754C4—61no—
755C3—24no—
756C3C3×#565514yesdirect product factor
757C3C32×#54711yescharacteristic, complemented
758C2—22no—
759C2—41no—
760C2—62no—
761C2—121no—
762C2C2×C32×D3×D411yescharacteristic
763C2C32×D3×#4111yescharacteristic
764C2C32×#101011yescharacteristic
subgroupG/H
centerC22×C32C23×D3
commutator, cosocleC22×C3C24×C32
FrattiniC22C23×C32×D3
FittingC33×#123C2
socleC22×C33C24
hypercenterC32×#123D3
hypocenterC3C32×#547
LCSG ▷ C22×C3 ▷ C3
UCSC1 ◁ C22×C32 ◁ C32×#123

Complements

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

NH ≅ G/Ntype
1. C2×C32×#237C2semidirect
2. C2×C32×#235C2semidirect
3. C33×#123C2semidirect
4. C32×#939C2semidirect
5. C2×C32×Dic3⋊C4C2semidirect
6. C32×#896C2semidirect
7. C32×#894C2semidirect
8. C32×D3×C4⋊C4C2semidirect
9. C32×#888C2semidirect
10. C32×#886C2semidirect
11. C32×#884C2semidirect
12. C32×#883C2semidirect
13. C32×#67⋊C4C2semidirect
14. C32×#67⋊C4C2semidirect
15. C32×#878C2semidirect
17. C3×#5655C3direct (N × H)
57. C2×C3×#237C2×C3semidirect
58. C2×C3×#235C2×C3semidirect
64. C32×#123D3semidirect
65. C32×#123C2×C3semidirect
74. C3×#939C2×C3semidirect
75. C2×C3×Dic3⋊C4C2×C3semidirect
76. C3×#896C2×C3semidirect
77. C3×#894C2×C3semidirect
78. C3×D3×C4⋊C4C2×C3semidirect
79. C3×#888C2×C3semidirect
80. C3×#886C2×C3semidirect
81. C3×#884C2×C3semidirect
82. C3×#883C2×C3semidirect
83. C3×#67⋊C4C2×C3semidirect
84. C3×#67⋊C4C2×C3semidirect
85. C3×#878C2×C3semidirect
100. C32×#67D4semidirect
118. #5655C32direct (N × H)
223. C32×Dic3#41semidirect
226. C2×#237C2×C32semidirect
227. C2×#235C2×C32semidirect
233. C3×#123C3×D3semidirect
234. C3×#123C2×C32semidirect
243. #939C2×C32semidirect
244. C2×Dic3⋊C4C2×C32semidirect
245. #896C2×C32semidirect
246. #894C2×C32semidirect
247. D3×C4⋊C4C2×C32semidirect
248. #888C2×C32semidirect
249. #886C2×C32semidirect
250. #884C2×C32semidirect
251. #883C2×C32semidirect
252. #67⋊C4C2×C32semidirect
253. #67⋊C4C2×C32semidirect
254. #878C2×C32semidirect
309. C3×#67C3×D4semidirect
474. C3×Dic3C3×#41semidirect
481. #123C32×D3semidirect
490. C33#547semidirect
545. #67C32×D4semidirect
677. Dic3C32×#41semidirect
679. C32#5655direct (N × H)
680. C32C3×#547semidirect
756. C3C3×#5655direct (N × H)
757. C3C32×#547semidirect

Maximal subgroups

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

subgroupindex
C2×C32×#2372
C2×C32×#2352
C33×#1232
C32×#9392
C2×C32×Dic3⋊C42
C32×#8962
C32×#8942
C32×D3×C4⋊C42
C32×#8882
C32×#8862
C32×#8842
C32×#8832
C32×#67⋊C42
C32×#8782
C32×#5473
C3×#56553