Finite Group Databasebeta

← #10596098⋊C3 #13152952

Subgroups — #10596098⋊C3 #13152952

Order 1728.

1229 conjugacy classes of subgroups.

The subgroup lattice has 696 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#88722C211yesmaximal, characteristic, complemented
2C22×C4×(C3⋊D3)⋊C3C211yesmaximal, characteristic, complemented
3H(3,𝔽3)×C22⋊Q8C211yesmaximal, characteristic, complemented
4#64155⋊C3C211yesmaximal, characteristic, complemented
5#64139⋊C3C211yesmaximal, characteristic, complemented
6#64104⋊C3C211yesmaximal, characteristic, complemented
7#64103⋊C3C212yesmaximal, complemented
8#64102⋊C3C212yesmaximal, complemented
9#64101⋊C3C211yesmaximal, characteristic, complemented
10#64091⋊C3C212yesmaximal, complemented
11#64090⋊C3C212yesmaximal, complemented
12#10596098C311yesmaximal, characteristic, complemented
13C3×#5627—31nomaximal
14C23×(C3⋊D3)⋊C3C2211yescharacteristic
15C2×Q8×H(3,𝔽3)C2211yescharacteristic, complemented
16C22×C4×H(3,𝔽3)C2211yescharacteristic
17C2×#638⋊C3C2212yes—
18C22×(C3⋊Dic3)⋊C3C2211yescharacteristic
19#88722—24no—
20C2×C4⋊((C3⋊D3)⋊C3)C2212yes—
21C2×C4⋊((C3⋊D3)⋊C3)C2212yes—
22C2×C4⋊((C3⋊D3)⋊C3)C2211yescharacteristic, complemented
23C2×C4×(C3⋊D3)⋊C3—24no—
24C2×C4×(C3⋊D3)⋊C3C2211yescharacteristic
25C2×C4×(C3⋊D3)⋊C3C2211yescharacteristic
26C2×C4×(C3⋊D3)⋊C3C2211yescharacteristic
27C2×C4×(C3⋊D3)⋊C3C2211yescharacteristic
28C2×C4×(C3⋊D3)⋊C3C2212yescomplemented
29C4⋊C4×H(3,𝔽3)C2211yescharacteristic, complemented
30C4⋊C4×H(3,𝔽3)C2212yescomplemented
31C22⋊C4×H(3,𝔽3)C2212yes—
32#3752⋊C3C2212yes—
33#3752⋊C3C2212yes—
34#3752⋊C3C2212yescomplemented
35#3752⋊C3C2212yescomplemented
36C4⋊((C3⋊Dic3)⋊C3)C2211yescharacteristic, complemented
37#3750⋊C3C2212yescomplemented
38C4×(C3⋊Dic3)⋊C3C2212yescomplemented
39C2×#3832C2×C311yescharacteristic, complemented
40C22×C4×C3⋊D3C2×C311yescharacteristic, complemented
41C2×C3×#239—31no—
42C22×C3×C4×D3—31no—
43C32×C22⋊Q8—21no—
44C32×C22⋊Q8D311yescharacteristic, complemented
45C32×C22⋊Q8C2×C311yescharacteristic, complemented
46#64155C2×C311yescharacteristic, complemented
47#64139C2×C311yescharacteristic, complemented
48#64104C2×C311yescharacteristic, complemented
49#64103C2×C312yescomplemented
50#64102C2×C312yescomplemented
51#64101C2×C311yescharacteristic, complemented
52#64091C2×C312yescomplemented
53#64090C2×C312yescomplemented
54C3×#946—31no—
55C3×#930—31no—
56C3×#895—31no—
57C3×#894—32no—
58C3×#893—32no—
59C3×#892—31no—
60C3×#882—32no—
61C3×#67⋊C4—32no—
62C23×H(3,𝔽3)C2311yescharacteristic
63C22×(C3⋊D3)⋊C3—22no—
64C22×(C3⋊D3)⋊C3—22no—
65C22×(C3⋊D3)⋊C3—22no—
66C22×(C3⋊D3)⋊C3C2312yes—
67C22×(C3⋊D3)⋊C3C2311yescharacteristic
68C22×(C3⋊D3)⋊C3C2311yescharacteristic
69Q8×H(3,𝔽3)—22no—
70C2×C4×H(3,𝔽3)—22no—
71C2×C4×H(3,𝔽3)C2311yescharacteristic
72C2×C4×H(3,𝔽3)C2312yes—
73C2×C4×H(3,𝔽3)C2312yes—
74C2×C4×H(3,𝔽3)C2311yescharacteristic
75#638⋊C3—24no—
76C2×(C3⋊Dic3)⋊C3—22no—
77C2×(C3⋊Dic3)⋊C3C2311yescharacteristic
78C2×(C3⋊Dic3)⋊C3C2312yes—
79C2×(C3⋊Dic3)⋊C3C2311yescharacteristic
80C4⋊((C3⋊D3)⋊C3)—24no—
81C4⋊((C3⋊D3)⋊C3)—24no—
82C4⋊((C3⋊D3)⋊C3)—22no—
83C4×(C3⋊D3)⋊C3—22no—
84C4×(C3⋊D3)⋊C3—22no—
85C4×(C3⋊D3)⋊C3—22no—
86C4×(C3⋊D3)⋊C3—24no—
87C4×(C3⋊D3)⋊C3D414yescomplemented
88C3×#525—91no—
89#5627—31no—
90#5627—91no—
91C23×C3⋊D3C22×C311yescharacteristic
92C23×C3×D3—31no—
93C2×C32×Q8—21no—
94C2×C32×Q8C2×D311yescharacteristic, complemented
95C2×C32×Q8C22×C311yescharacteristic, complemented
96C22×C32×C4—21no—
97C22×C32×C4C2×D311yescharacteristic
98C22×C32×C4C22×C311yescharacteristic
99C2×#638C22×C312yes—
100C22×C3⋊Dic3C22×C311yescharacteristic
101#3832—24no—
102C2×C4⋊(C3⋊D3)C22×C312yes—
103C2×C4⋊(C3⋊D3)C22×C312yes—
104C2×C4⋊(C3⋊D3)C22×C311yescharacteristic, complemented
105C2×C4×C3⋊D3—24no—
106C2×C4×C3⋊D3C22×C311yescharacteristic
107C2×C4×C3⋊D3C22×C311yescharacteristic
108C2×C4×C3⋊D3C22×C311yescharacteristic
109C2×C4×C3⋊D3C22×C311yescharacteristic
110C2×C4×C3⋊D3C22×C312yescomplemented
111C2×C3×#67—32no—
112C22×C3×Dic3—31no—
113C3×#239—64no—
114C2×C3×D12—32no—
115C2×C3×D12—32no—
116C2×C3×D12—31no—
117C2×C3×C4×D3—31no—
118C2×C3×C4×D3—32no—
119C2×C3×C4×D3—31no—
120C2×C3×C4×D3—31no—
121C2×C3×C4×D3—31no—
122C2×C3×C4×D3—64no—
123C32×C4⋊C4—21no—
124C32×C4⋊C4—22no—
125C32×C4⋊C4C2×D311yescharacteristic, complemented
126C32×C4⋊C4C2×D312yescomplemented
127C32×C4⋊C4C22×C311yescharacteristic, complemented
128C32×C4⋊C4C22×C312yescomplemented
129C32×C22⋊C4—22no—
130C32×C22⋊C4C2×D312yes—
131C32×C22⋊C4C22×C312yes—
132#3752C22×C312yes—
133#3752C22×C312yes—
134#3752C22×C312yescomplemented
135#3752C22×C312yescomplemented
136C4⋊(C3⋊Dic3)C22×C311yescharacteristic, complemented
137#3750C22×C312yescomplemented
138C4×C3⋊Dic3C22×C312yescomplemented
139C3×(C2×D3)⋊C4—32no—
140C3×(C2×D3)⋊C4—32no—
141C3×(C2×D3)⋊C4—32no—
142C3×(C2×D3)⋊C4—32no—
143C3×C4⋊Dic3—31no—
144C3×Dic3⋊C4—32no—
145C3×C4×Dic3—32no—
146C22×H(3,𝔽3)—21no—
147C22×H(3,𝔽3)—21no—
148C22×H(3,𝔽3)#4112yescomplemented
149C22×H(3,𝔽3)C2411yescharacteristic
150C2×(C3⋊D3)⋊C3—28no—
151C2×(C3⋊D3)⋊C3—21no—
152C2×(C3⋊D3)⋊C3—21no—
153C2×(C3⋊D3)⋊C3—21no—
154C2×(C3⋊D3)⋊C3—21no—
155C2×(C3⋊D3)⋊C3—22no—
156C2×(C3⋊D3)⋊C3—22no—
157C2×(C3⋊D3)⋊C3—22no—
158C2×(C3⋊D3)⋊C3C2×D412yes—
159C2×(C3⋊D3)⋊C3#4112yescomplemented
160C4×H(3,𝔽3)—21no—
161C4×H(3,𝔽3)—22no—
162C4×H(3,𝔽3)—22no—
163C4×H(3,𝔽3)C2×D412yes—
164(C3⋊Dic3)⋊C3—21no—
165(C3⋊Dic3)⋊C3—22no—
166(C3⋊Dic3)⋊C3C2×D412yes—
167C2×C3×#41—91no—
168C23×C3×C4—91no—
169C2×#239—31no—
170C2×#239—91no—
171C22×C4×D3—31no—
172C22×C4×D3—91no—
173C3×#123—92no—
174C3×C22⋊Q8—31no—
175C3×C22⋊Q8—31no—
176C3×C22⋊Q8—61no—
177C3×C22⋊Q8—91no—
178C3×C22⋊Q8C3×D311yescharacteristic
179C3×#121—91no—
180C3×#121—91no—
181C3×#120—92no—
182C3×C4×D4—92no—
183C3×C4×D4—92no—
184C3×#117—91no—
185#946—31no—
186#946—91no—
187#930—31no—
188#930—91no—
189#895—31no—
190#895—91no—
191#894—32no—
192#894—92no—
193#893—32no—
194#893—92no—
195#892—31no—
196#892—91no—
197#882—32no—
198#882—92no—
199#67⋊C4—32no—
200#67⋊C4—92no—
201C23×C32—21no—
202C23×C32C22×D311yescharacteristic
203C23×C32C23×C311yescharacteristic
204C22×C3⋊D3—22no—
205C22×C3⋊D3—22no—
206C22×C3⋊D3—22no—
207C22×C3⋊D3C23×C312yes—
208C22×C3⋊D3C23×C311yescharacteristic
209C22×C3⋊D3C23×C311yescharacteristic
210C22×C3×D3—31no—
211C22×C3×D3—31no—
212C22×C3×D3—32no—
213C22×C3×D3—62no—
214C22×C3×D3—62no—
215C22×C3×D3—62no—
216C32×Q8—22no—
217C32×Q8—22no—
218C32×Q8—42no—
219C2×C32×C4—22no—
220C2×C32×C4—22no—
221C2×C32×C4—21no—
222C2×C32×C4—22no—
223C2×C32×C4—22no—
224C2×C32×C4—21no—
225C2×C32×C4—42no—
226C2×C32×C4C22×D312yes—
227C2×C32×C4C22×D312yes—
228C2×C32×C4C22×D311yescharacteristic
229C2×C32×C4C22×D311yescharacteristic
230C2×C32×C4C23×C312yes—
231C2×C32×C4C23×C312yes—
232C2×C32×C4C23×C311yescharacteristic
233C2×C32×C4C23×C311yescharacteristic
234#638—24no—
235C2×C3⋊Dic3—22no—
236C2×C3⋊Dic3C23×C312yes—
237C2×C3⋊Dic3C23×C311yescharacteristic
238C2×C3⋊Dic3C23×C311yescharacteristic
239C4⋊(C3⋊D3)—24no—
240C4⋊(C3⋊D3)—24no—
241C4⋊(C3⋊D3)—22no—
242C4×C3⋊D3—22no—
243C4×C3⋊D3—22no—
244C4×C3⋊D3—22no—
245C4×C3⋊D3—24no—
246C4×C3⋊D3C3×D414yescomplemented
247C3×#67—64no—
248C2×C3×Dic3—31no—
249C2×C3×Dic3—32no—
250C2×C3×Dic3—31no—
251C2×C3×Dic3—62no—
252C3×D12—64no—
253C3×D12—64no—
254C3×D12—62no—
255C3×C4×D3—34no—
256C3×C4×D3—62no—
257C3×C4×D3—64no—
258C3×C4×D3—62no—
259C3×C4×D3—62no—
260#525—91noSylow
261C2×H(3,𝔽3)—22no—
262C2×H(3,𝔽3)C22×D411yescharacteristic
263C2×H(3,𝔽3)C2×#4111yescharacteristic
264C2×H(3,𝔽3)C2×#4111yescharacteristic
265(C3⋊D3)⋊C3—22no—
266(C3⋊D3)⋊C3—22no—
267(C3⋊D3)⋊C3—42no—
268C24×C3—91no—
269C23×D3—31no—
270C23×D3—91no—
271C3×#41—184no—
272C2×C3×Q8—31no—
273C2×C3×Q8—31no—
274C2×C3×Q8—61no—
275C2×C3×Q8C2×C3×D311yescharacteristic
276C2×C3×D4—92no—
277C2×C3×D4—92no—
278C2×C3×D4—91no—
279C2×C3×D4—92no—
280C22×C3×C4—31no—
281C22×C3×C4—31no—
282C22×C3×C4—61no—
283C22×C3×C4—91no—
284C22×C3×C4—91no—
285C22×C3×C4—92no—
286C22×C3×C4—91no—
287C22×C3×C4—91no—
288C22×C3×C4—91no—
289C22×C3×C4—184no—
290C22×C3×C4C2×C3×D311yescharacteristic
291C2×#67—32no—
292C2×#67—92no—
293C22×Dic3—31no—
294C22×Dic3—91no—
295#239—64no—
296#239—184no—
297C2×D12—32no—
298C2×D12—32no—
299C2×D12—31no—
300C2×D12—92no—
301C2×D12—92no—
302C2×D12—91no—
303C2×C4×D3—31no—
304C2×C4×D3—32no—
305C2×C4×D3—31no—
306C2×C4×D3—31no—
307C2×C4×D3—31no—
308C2×C4×D3—64no—
309C2×C4×D3—91no—
310C2×C4×D3—92no—
311C2×C4×D3—91no—
312C2×C4×D3—91no—
313C2×C4×D3—91no—
314C2×C4×D3—184no—
315C3×C4⋊C4—31no—
316C3×C4⋊C4—32no—
317C3×C4⋊C4—31no—
318C3×C4⋊C4—32no—
319C3×C4⋊C4—61no—
320C3×C4⋊C4—62no—
321C3×C4⋊C4—92no—
322C3×C4⋊C4—91no—
323C3×C4⋊C4C2×C3×D311yescharacteristic
324C3×C4⋊C4C2×C3×D312yes—
325C3×C22⋊C4—32no—
326C3×C22⋊C4—32no—
327C3×C22⋊C4—62no—
328C3×C22⋊C4—92no—
329C3×C22⋊C4—92no—
330C3×C22⋊C4—92no—
331C3×C22⋊C4—92no—
332C3×C22⋊C4C2×C3×D312yes—
333C3×C42—92no—
334(C2×D3)⋊C4—32no—
335(C2×D3)⋊C4—32no—
336(C2×D3)⋊C4—32no—
337(C2×D3)⋊C4—32no—
338(C2×D3)⋊C4—92no—
339(C2×D3)⋊C4—92no—
340(C2×D3)⋊C4—92no—
341(C2×D3)⋊C4—92no—
342C4⋊Dic3—31no—
343C4⋊Dic3—91no—
344Dic3⋊C4—32no—
345Dic3⋊C4—92no—
346C4×Dic3—32no—
347C4×Dic3—92no—
348C22×C32—21no—
349C22×C32—21no—
350C22×C32—21no—
351C22×C32—21no—
352C22×C32—21no—
353C22×C32—22no—
354C22×C32—41no—
355C22×C32—41no—
356C22×C32#23912yescomplemented
357C22×C32C3×#4112yescomplemented
358C22×C32C23×D311yescharacteristic
359C22×C32C24×C311yescharacteristic
360C2×C3⋊D3—28no—
361C2×C3⋊D3—21no—
362C2×C3⋊D3—21no—
363C2×C3⋊D3—21no—
364C2×C3⋊D3—21no—
365C2×C3⋊D3—22no—
366C2×C3⋊D3—22no—
367C2×C3⋊D3—22no—
368C2×C3⋊D3C2×C3×D412yes—
369C2×C3⋊D3C3×#4112yescomplemented
370C2×C3×D3—32no—
371C2×C3×D3—32no—
372C2×C3×D3—68no—
373C2×C3×D3—61no—
374C2×C3×D3—61no—
375C2×C3×D3—61no—
376C2×C3×D3—61no—
377C2×C3×D3—62no—
378C2×C3×D3—62no—
379C2×C3×D3—62no—
380C32×C4—21no—
381C32×C4—22no—
382C32×C4—22no—
383C32×C4—21no—
384C32×C4—22no—
385C32×C4—22no—
386C32×C4—22no—
387C32×C4—42no—
388C32×C4—41no—
389C32×C4—42no—
390C32×C4D3×D412yes—
391C32×C4C2×C3×D412yes—
392C3⋊Dic3—21no—
393C3⋊Dic3—22no—
394C3⋊Dic3C2×C3×D412yes—
395C3×Dic3—32no—
396C3×Dic3—61no—
397C3×Dic3—62no—
398C2×#41—91no—
399C23×C4—91no—
400#123—92no—
401C22⋊Q8—91no—
402C22⋊Q8(C3⋊D3)⋊C311yescharacteristic, complemented
403#121—91no—
404#121—91no—
405#120—92no—
406C4×D4—92no—
407C4×D4—92no—
408#117—91no—
409H(3,𝔽3)#52511yescharacteristic, complemented, Sylow
410C23×C3—31no—
411C23×C3—31no—
412C23×C3—61no—
413C23×C3—91no—
414C23×C3—91no—
415C23×C3—92no—
416C23×C3—182no—
417C23×C3—182no—
418C23×C3—182no—
419C23×C3C22×C3×D311yescharacteristic
420C22×D3—31no—
421C22×D3—31no—
422C22×D3—32no—
423C22×D3—62no—
424C22×D3—62no—
425C22×D3—62no—
426C22×D3—91no—
427C22×D3—91no—
428C22×D3—92no—
429C22×D3—182no—
430C22×D3—182no—
431C22×D3—182no—
432C3×Q8—22no—
433C3×Q8—62no—
434C3×Q8—62no—
435C3×Q8—122no—
436C3×D4—182no—
437C3×D4—184no—
438C3×D4—184no—
439C3×D4—184no—
440C2×C3×C4—22no—
441C2×C3×C4—31no—
442C2×C3×C4—31no—
443C2×C3×C4—32no—
444C2×C3×C4—32no—
445C2×C3×C4—31no—
446C2×C3×C4—32no—
447C2×C3×C4—32no—
448C2×C3×C4—31no—
449C2×C3×C4—62no—
450C2×C3×C4—62no—
451C2×C3×C4—61no—
452C2×C3×C4—62no—
453C2×C3×C4—62no—
454C2×C3×C4—61no—
455C2×C3×C4—94no—
456C2×C3×C4—91no—
457C2×C3×C4—92no—
458C2×C3×C4—91no—
459C2×C3×C4—122no—
460C2×C3×C4—182no—
461C2×C3×C4—182no—
462C2×C3×C4—184no—
463C2×C3×C4—182no—
464C2×C3×C4—182no—
465C2×C3×C4C22×C3×D312yes—
466C2×C3×C4C22×C3×D312yes—
467C2×C3×C4C22×C3×D311yescharacteristic
468C2×C3×C4C22×C3×D311yescharacteristic
469#67—64no—
470#67—184no—
471C2×Dic3—31no—
472C2×Dic3—32no—
473C2×Dic3—31no—
474C2×Dic3—62no—
475C2×Dic3—91no—
476C2×Dic3—92no—
477C2×Dic3—91no—
478C2×Dic3—182no—
479D12—64no—
480D12—64no—
481D12—62no—
482D12—182no—
483D12—184no—
484D12—184no—
485C4×D3—34no—
486C4×D3—62no—
487C4×D3—64no—
488C4×D3—62no—
489C4×D3—62no—
490C4×D3—94no—
491C4×D3—182no—
492C4×D3—184no—
493C4×D3—182no—
494C4×D3—182no—
495C2×C32—22no—
496C2×C32—22no—
497C2×C32—21no—
498C2×C32—21no—
499C2×C32—21no—
500C2×C32—42no—
501C2×C32C2×D3×D411yescharacteristic
502C2×C32C2×#23911yescharacteristic
503C2×C32D3×#4111yescharacteristic
504C2×C32C22×C3×D411yescharacteristic
505C2×C32C2×C3×#4111yescharacteristic
506C2×C32C2×C3×#4111yescharacteristic
507C3⋊D3—22no—
508C3⋊D3—22no—
509C3⋊D3—42no—
510C3×D3—62no—
511C3×D3—62no—
512C3×D3—122no—
513C24—91no—
514#41—184no—
515C2×Q8C2×(C3⋊D3)⋊C311yescharacteristic, complemented
516C2×D4—92no—
517C2×D4—92no—
518C2×D4—92no—
519C2×D4—91no—
520C22×C4—91no—
521C22×C4—91no—
522C22×C4—91no—
523C22×C4—92no—
524C22×C4—91no—
525C22×C4—91no—
526C22×C4—184no—
527C22×C4C2×(C3⋊D3)⋊C311yescharacteristic
528C4⋊C4—91no—
529C4⋊C4—92no—
530C4⋊C4C2×(C3⋊D3)⋊C311yescharacteristic, complemented
531C4⋊C4C2×(C3⋊D3)⋊C312yescomplemented
532C22⋊C4—92no—
533C22⋊C4—92no—
534C22⋊C4—92no—
535C22⋊C4—92no—
536C22⋊C4C2×(C3⋊D3)⋊C312yes—
537C42—92no—
538C22×C3—21no—
539C22×C3—21no—
540C22×C3—31no—
541C22×C3—31no—
542C22×C3—32no—
543C22×C3—32no—
544C22×C3—61no—
545C22×C3—61no—
546C22×C3—61no—
547C22×C3—61no—
548C22×C3—61no—
549C22×C3—62no—
550C22×C3—92no—
551C22×C3—92no—
552C22×C3—121no—
553C22×C3—121no—
554C22×C3—181no—
555C22×C3—181no—
556C22×C3—181no—
557C22×C3—181no—
558C22×C3—182no—
559C22×C3—182no—
560C22×C3—182no—
561C22×C3—188no—
562C22×C3C3×#23912yes—
563C22×C3C23×C3×D311yescharacteristic
564C2×D3—32no—
565C2×D3—32no—
566C2×D3—68no—
567C2×D3—61no—
568C2×D3—61no—
569C2×D3—61no—
570C2×D3—61no—
571C2×D3—62no—
572C2×D3—62no—
573C2×D3—62no—
574C2×D3—92no—
575C2×D3—92no—
576C2×D3—181no—
577C2×D3—181no—
578C2×D3—181no—
579C2×D3—181no—
580C2×D3—188no—
581C2×D3—182no—
582C2×D3—182no—
583C2×D3—182no—
584C3×C4—21no—
585C3×C4—22no—
586C3×C4—22no—
587C3×C4—32no—
588C3×C4—32no—
589C3×C4—61no—
590C3×C4—62no—
591C3×C4—62no—
592C3×C4—61no—
593C3×C4—62no—
594C3×C4—62no—
595C3×C4—62no—
596C3×C4—92no—
597C3×C4—121no—
598C3×C4—122no—
599C3×C4—122no—
600C3×C4—181no—
601C3×C4—182no—
602C3×C4C3×D3×D412yes—
603Dic3—32no—
604Dic3—61no—
605Dic3—62no—
606Dic3—92no—
607Dic3—181no—
608Dic3—182no—
609C32—21no—
610C32#562711yescharacteristic, complemented
611C32C3×#52511yescharacteristic, complemented
612C23—91no—
613C23—91no—
614C23—92no—
615C23—182no—
616C23—182no—
617C23—182no—
618C23C22×(C3⋊D3)⋊C311yescharacteristic
619Q8—22no—
620D4—184no—
621D4—184no—
622D4—184no—
623D4—182no—
624C2×C4—22no—
625C2×C4—91no—
626C2×C4—94no—
627C2×C4—92no—
628C2×C4—91no—
629C2×C4—182no—
630C2×C4—184no—
631C2×C4—182no—
632C2×C4—182no—
633C2×C4—182no—
634C2×C4C22×(C3⋊D3)⋊C312yes—
635C2×C4C22×(C3⋊D3)⋊C311yescharacteristic
636C2×C4C22×(C3⋊D3)⋊C312yes—
637C2×C4C22×(C3⋊D3)⋊C311yescharacteristic
638C2×C3—22no—
639C2×C3—31no—
640C2×C3—31no—
641C2×C3—31no—
642C2×C3—31no—
643C2×C3—31no—
644C2×C3—31no—
645C2×C3—62no—
646C2×C3—62no—
647C2×C3—61no—
648C2×C3—61no—
649C2×C3—61no—
650C2×C3—122no—
651C2×C3—182no—
652C2×C3—182no—
653C2×C3—362no—
654C2×C3C2×C3×D3×D411yescharacteristic
655C2×C3C2×C3×#23911yescharacteristic
656C2×C3C3×D3×#4111yescharacteristic
657D3—62no—
658D3—62no—
659D3—122no—
660D3—182no—
661D3—182no—
662D3—362no—
663C22—21no—
664C22—21no—
665C22—92no—
666C22—92no—
667C22—188no—
668C22—181no—
669C22—181no—
670C22—181no—
671C22—181no—
672C22—182no—
673C22—182no—
674C22—182no—
675C22#8872212yescomplemented
676C22C23×(C3⋊D3)⋊C311yescharacteristic
677C4—21no—
678C4—22no—
679C4—22no—
680C4—92no—
681C4—181no—
682C4—182no—
683C4D4×(C3⋊D3)⋊C312yes—
684C3—31no—
685C3—31no—
686C3—61no—
687C3C3×#562711yescharacteristic
688C2—22no—
689C2—182no—
690C2—182no—
691C2—362no—
692C2C2×D4×(C3⋊D3)⋊C311yescharacteristic
693C2C2×#8872211yescharacteristic
694C2#41×(C3⋊D3)⋊C311yescharacteristic
subgroupG/H
centerC22C23×(C3⋊D3)⋊C3
commutator, cosocleC22×C32C24×C3
Frattini, socleC22×C3C23×C3×D3
FittingH(3,𝔽3)×C22⋊Q8C2
hypercenterC22⋊Q8(C3⋊D3)⋊C3
hypocenterC32C3×#525
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22⋊Q8

Complements

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

NH ≅ G/Ntype
1. C2×#88722C2semidirect
2. C22×C4×(C3⋊D3)⋊C3C2semidirect
3. H(3,𝔽3)×C22⋊Q8C2semidirect
4. #64155⋊C3C2semidirect
5. #64139⋊C3C2semidirect
6. #64104⋊C3C2semidirect
7. #64103⋊C3C2semidirect
8. #64102⋊C3C2semidirect
9. #64101⋊C3C2semidirect
10. #64091⋊C3C2semidirect
11. #64090⋊C3C2semidirect
12. #10596098C3semidirect
15. C2×Q8×H(3,𝔽3)C22semidirect
22. C2×C4⋊((C3⋊D3)⋊C3)C22semidirect
28. C2×C4×(C3⋊D3)⋊C3C22semidirect
29. C4⋊C4×H(3,𝔽3)C22semidirect
30. C4⋊C4×H(3,𝔽3)C22semidirect
34. #3752⋊C3C22semidirect
35. #3752⋊C3C22semidirect
36. C4⋊((C3⋊Dic3)⋊C3)C22semidirect
37. #3750⋊C3C22semidirect
38. C4×(C3⋊Dic3)⋊C3C22semidirect
39. C2×#3832C2×C3semidirect
40. C22×C4×C3⋊D3C2×C3semidirect
44. C32×C22⋊Q8D3semidirect
45. C32×C22⋊Q8C2×C3semidirect
46. #64155C2×C3semidirect
47. #64139C2×C3semidirect
48. #64104C2×C3semidirect
49. #64103C2×C3semidirect
50. #64102C2×C3semidirect
51. #64101C2×C3semidirect
52. #64091C2×C3semidirect
53. #64090C2×C3semidirect
87. C4×(C3⋊D3)⋊C3D4semidirect
94. C2×C32×Q8C2×D3semidirect
95. C2×C32×Q8C22×C3semidirect
104. C2×C4⋊(C3⋊D3)C22×C3semidirect
110. C2×C4×C3⋊D3C22×C3semidirect
125. C32×C4⋊C4C2×D3semidirect
126. C32×C4⋊C4C2×D3semidirect
127. C32×C4⋊C4C22×C3semidirect
128. C32×C4⋊C4C22×C3semidirect
134. #3752C22×C3semidirect
135. #3752C22×C3semidirect
136. C4⋊(C3⋊Dic3)C22×C3semidirect
137. #3750C22×C3semidirect
138. C4×C3⋊Dic3C22×C3semidirect
148. C22×H(3,𝔽3)#41semidirect
159. C2×(C3⋊D3)⋊C3#41semidirect
246. C4×C3⋊D3C3×D4semidirect
356. C22×C32#239semidirect
357. C22×C32C3×#41semidirect
369. C2×C3⋊D3C3×#41semidirect
402. C22⋊Q8(C3⋊D3)⋊C3semidirect
409. H(3,𝔽3)#525semidirect
515. C2×Q8C2×(C3⋊D3)⋊C3semidirect
530. C4⋊C4C2×(C3⋊D3)⋊C3semidirect
531. C4⋊C4C2×(C3⋊D3)⋊C3semidirect
610. C32#5627semidirect
611. C32C3×#525semidirect
675. C22#88722semidirect

Maximal subgroups

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

subgroupindex
C2×#887222
C22×C4×(C3⋊D3)⋊C32
H(3,𝔽3)×C22⋊Q82
#64155⋊C32
#64139⋊C32
#64104⋊C32
#64103⋊C32
#64102⋊C32
#64101⋊C32
#64091⋊C32
#64090⋊C32
#105960983
C3×#56273