Finite Group Databasebeta

← C22⋊Q8×(C3⋊D3)⋊C3 #13152951

Subgroups — C22⋊Q8×(C3⋊D3)⋊C3 #13152951

Order 1728.

1201 conjugacy classes of subgroups.

The subgroup lattice has 668 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×Q8×(C3⋊D3)⋊C3C211yesmaximal, characteristic, complemented
2C22×C4×(C3⋊D3)⋊C3C211yesmaximal, characteristic
3H(3,𝔽3)×C22⋊Q8C211yesmaximal, characteristic, complemented
4#64155⋊C3C211yesmaximal, characteristic, complemented
5#64133⋊C3C211yesmaximal, characteristic, complemented
6#64106⋊C3C211yesmaximal, characteristic, complemented
7#64105⋊C3C212yesmaximal, complemented
8C4⋊C4×(C3⋊D3)⋊C3C212yesmaximal, complemented
9C4⋊C4×(C3⋊D3)⋊C3C211yesmaximal, characteristic, complemented
10C22⋊C4×(C3⋊D3)⋊C3C212yesmaximal
11#64087⋊C3C212yesmaximal, complemented
12C3⋊D3×C22⋊Q8C311yesmaximal, characteristic, complemented
13C3×D3×C22⋊Q8—31nomaximal
14C23×(C3⋊D3)⋊C3C2211yescharacteristic
15C2×Q8×H(3,𝔽3)C2211yescharacteristic, complemented
16C22×C4×H(3,𝔽3)C2211yescharacteristic
17C22×(C3⋊Dic3)⋊C3C2211yescharacteristic
18Q8×(C3⋊D3)⋊C3—24no—
19C2×C4×(C3⋊D3)⋊C3—24no—
20C2×C4×(C3⋊D3)⋊C3C2211yescharacteristic
21C2×C4×(C3⋊D3)⋊C3C2211yescharacteristic
22C2×C4×(C3⋊D3)⋊C3C2211yescharacteristic
23C2×C4×(C3⋊D3)⋊C3C2212yes—
24C2×C4×(C3⋊D3)⋊C3C2212yes—
25C2×C4×(C3⋊D3)⋊C3C2211yescharacteristic
26C2×#634⋊C3C2211yescharacteristic, complemented
27C2×#634⋊C3C2212yescomplemented
28C4⋊C4×H(3,𝔽3)C2212yescomplemented
29C4⋊C4×H(3,𝔽3)C2211yescharacteristic, complemented
30C22⋊C4×H(3,𝔽3)C2212yes—
31#3757⋊C3C2212yes—
32#3752⋊C3C2212yes—
33#3752⋊C3C2212yes—
34C4⋊((C3⋊Dic3)⋊C3)C2211yescharacteristic, complemented
35C4⋊((C3⋊Dic3)⋊C3)C2212yescomplemented
36#3750⋊C3C2212yescomplemented
37#3750⋊C3C2212yescomplemented
38#3750⋊C3C2212yescomplemented
39C2×Q8×C3⋊D3C2×C311yescharacteristic, complemented
40C22×C4×C3⋊D3C2×C311yescharacteristic
41C2×C3×D3×Q8—31no—
42C22×C3×C4×D3—31no—
43C32×C22⋊Q8—21no—
44C32×C22⋊Q8D311yescharacteristic, complemented
45C32×C22⋊Q8C2×C311yescharacteristic, complemented
46#64155C2×C311yescharacteristic, complemented
47#64133C2×C311yescharacteristic, complemented
48#64106C2×C311yescharacteristic, complemented
49#64105C2×C312yescomplemented
50C4⋊C4×C3⋊D3C2×C311yescharacteristic, complemented
51C4⋊C4×C3⋊D3C2×C312yescomplemented
52C22⋊C4×C3⋊D3C2×C312yes—
53#64087C2×C312yescomplemented
54C3×#946—31no—
55C3×#924—31no—
56C3×#897—31no—
57C3×#896—32no—
58C3×D3×C4⋊C4—31no—
59C3×D3×C4⋊C4—32no—
60C3×D3×C22⋊C4—32no—
61C3×#878—32no—
62C23×H(3,𝔽3)C2311yescharacteristic
63C22×(C3⋊D3)⋊C3—22no—
64C22×(C3⋊D3)⋊C3—22no—
65C22×(C3⋊D3)⋊C3Q814yescomplemented
66C22×(C3⋊D3)⋊C3C2311yescharacteristic
67C22×(C3⋊D3)⋊C3C2311yescharacteristic
68Q8×H(3,𝔽3)—22no—
69C2×C4×H(3,𝔽3)—22no—
70C2×C4×H(3,𝔽3)C2312yes—
71C2×C4×H(3,𝔽3)C2311yescharacteristic
72C2×C4×H(3,𝔽3)C2312yes—
73C2×C4×H(3,𝔽3)C2311yescharacteristic
74C2×(C3⋊Dic3)⋊C3—22no—
75C2×(C3⋊Dic3)⋊C3C2312yes—
76C2×(C3⋊Dic3)⋊C3C2311yescharacteristic
77C2×(C3⋊Dic3)⋊C3C2312yes—
78C2×(C3⋊Dic3)⋊C3C2311yescharacteristic
79C4×(C3⋊D3)⋊C3—22no—
80C4×(C3⋊D3)⋊C3—24no—
81C4×(C3⋊D3)⋊C3—24no—
82C4×(C3⋊D3)⋊C3—22no—
83C4×(C3⋊D3)⋊C3—22no—
84C4×(C3⋊D3)⋊C3D414yes—
85#634⋊C3—22no—
86#634⋊C3—24no—
87C2×C3×C22⋊Q8—91no—
88D3×C22⋊Q8—31no—
89D3×C22⋊Q8—91no—
90C23×C3⋊D3C22×C311yescharacteristic
91C23×C3×D3—31no—
92C2×C32×Q8—21no—
93C2×C32×Q8C2×D311yescharacteristic, complemented
94C2×C32×Q8C22×C311yescharacteristic, complemented
95C22×C32×C4—21no—
96C22×C32×C4C2×D311yescharacteristic
97C22×C32×C4C22×C311yescharacteristic
98C22×C3⋊Dic3C22×C311yescharacteristic
99Q8×C3⋊D3—24no—
100C2×C4×C3⋊D3—24no—
101C2×C4×C3⋊D3C22×C312yes—
102C2×C4×C3⋊D3C22×C312yes—
103C2×C4×C3⋊D3C22×C311yescharacteristic
104C2×C4×C3⋊D3C22×C311yescharacteristic
105C2×C4×C3⋊D3C22×C311yescharacteristic
106C2×C4×C3⋊D3C22×C311yescharacteristic
107C2×#634C22×C312yescomplemented
108C2×#634C22×C311yescharacteristic, complemented
109C22×C3×Dic3—31no—
110C3×D3×Q8—64no—
111C2×C3×C4×D3—31no—
112C2×C3×C4×D3—32no—
113C2×C3×C4×D3—32no—
114C2×C3×C4×D3—31no—
115C2×C3×C4×D3—31no—
116C2×C3×C4×D3—31no—
117C2×C3×C4×D3—64no—
118C2×C3×Dic6—32no—
119C2×C3×Dic6—31no—
120C32×C4⋊C4—21no—
121C32×C4⋊C4—22no—
122C32×C4⋊C4C2×D312yescomplemented
123C32×C4⋊C4C2×D311yescharacteristic, complemented
124C32×C4⋊C4C22×C312yescomplemented
125C32×C4⋊C4C22×C311yescharacteristic, complemented
126C32×C22⋊C4—22no—
127C32×C22⋊C4C2×D312yes—
128C32×C22⋊C4C22×C312yes—
129#3757C22×C312yes—
130#3752C22×C312yes—
131#3752C22×C312yes—
132C4⋊(C3⋊Dic3)C22×C312yescomplemented
133C4⋊(C3⋊Dic3)C22×C311yescharacteristic, complemented
134#3750C22×C312yescomplemented
135#3750C22×C312yescomplemented
136#3750C22×C312yescomplemented
137C3×#217—32no—
138C3×(C2×D3)⋊C4—32no—
139C3×(C2×D3)⋊C4—32no—
140C3×C4⋊Dic3—32no—
141C3×C4⋊Dic3—31no—
142C3×Dic3⋊C4—32no—
143C3×Dic3⋊C4—32no—
144C3×Dic3⋊C4—32no—
145C22×H(3,𝔽3)—21no—
146C22×H(3,𝔽3)—21no—
147C22×H(3,𝔽3)C2×Q812yescomplemented
148C22×H(3,𝔽3)C2411yescharacteristic
149C2×(C3⋊D3)⋊C3—21no—
150C2×(C3⋊D3)⋊C3—21no—
151C2×(C3⋊D3)⋊C3—28no—
152C2×(C3⋊D3)⋊C3C2×D412yes—
153C2×(C3⋊D3)⋊C3C2×Q812yes—
154C2×(C3⋊D3)⋊C3C2×Q812yescomplemented
155C2×(C3⋊D3)⋊C3#4112yes—
156C4×H(3,𝔽3)—22no—
157C4×H(3,𝔽3)—21no—
158C4×H(3,𝔽3)—22no—
159C4×H(3,𝔽3)C2×D412yes—
160(C3⋊Dic3)⋊C3—22no—
161(C3⋊Dic3)⋊C3—21no—
162(C3⋊Dic3)⋊C3—22no—
163(C3⋊Dic3)⋊C3C2×D412yes—
164C22×C3×Q8—91no—
165C23×C3×C4—91no—
166C2×D3×Q8—31no—
167C2×D3×Q8—91no—
168C22×C4×D3—31no—
169C22×C4×D3—91no—
170C3×C22⋊Q8—31no—
171C3×C22⋊Q8—31no—
172C3×C22⋊Q8—61no—
173C3×C22⋊Q8—92no—
174C3×C22⋊Q8—92no—
175C3×C22⋊Q8—91no—
176C3×C22⋊Q8—91no—
177C3×C22⋊Q8—91no—
178C3×C22⋊Q8C3×D311yescharacteristic
179C2×C3×C4⋊C4—91no—
180C2×C3×C4⋊C4—92no—
181C2×C3×C22⋊C4—92no—
182#946—31no—
183#946—91no—
184#924—31no—
185#924—91no—
186#897—31no—
187#897—91no—
188#896—32no—
189#896—92no—
190D3×C4⋊C4—31no—
191D3×C4⋊C4—32no—
192D3×C4⋊C4—91no—
193D3×C4⋊C4—92no—
194D3×C22⋊C4—32no—
195D3×C22⋊C4—92no—
196#878—32no—
197#878—92no—
198C23×C32—21no—
199C23×C32C22×D311yescharacteristic
200C23×C32C23×C311yescharacteristic
201C22×C3⋊D3—22no—
202C22×C3⋊D3—22no—
203C22×C3⋊D3C3×Q814yescomplemented
204C22×C3⋊D3C23×C311yescharacteristic
205C22×C3⋊D3C23×C311yescharacteristic
206C22×C3×D3—31no—
207C22×C3×D3—34no—
208C22×C3×D3—31no—
209C22×C3×D3—62no—
210C22×C3×D3—62no—
211C32×Q8—22no—
212C32×Q8—22no—
213C32×Q8—42no—
214C2×C32×C4—22no—
215C2×C32×C4—22no—
216C2×C32×C4—21no—
217C2×C32×C4—22no—
218C2×C32×C4—22no—
219C2×C32×C4—21no—
220C2×C32×C4—42no—
221C2×C32×C4C22×D311yescharacteristic
222C2×C32×C4C22×D312yes—
223C2×C32×C4C22×D312yes—
224C2×C32×C4C22×D311yescharacteristic
225C2×C32×C4C23×C311yescharacteristic
226C2×C32×C4C23×C312yes—
227C2×C32×C4C23×C312yes—
228C2×C32×C4C23×C311yescharacteristic
229C2×C3⋊Dic3—22no—
230C2×C3⋊Dic3C23×C312yes—
231C2×C3⋊Dic3C23×C311yescharacteristic
232C2×C3⋊Dic3C23×C312yes—
233C2×C3⋊Dic3C23×C311yescharacteristic
234C4×C3⋊D3—22no—
235C4×C3⋊D3—24no—
236C4×C3⋊D3—24no—
237C4×C3⋊D3—22no—
238C4×C3⋊D3—22no—
239C4×C3⋊D3C3×D414yes—
240#634—22no—
241#634—24no—
242C2×C3×Dic3—31no—
243C2×C3×Dic3—32no—
244C2×C3×Dic3—31no—
245C2×C3×Dic3—32no—
246C2×C3×Dic3—62no—
247C3×C4×D3—34no—
248C3×C4×D3—62no—
249C3×C4×D3—64no—
250C3×C4×D3—62no—
251C3×C4×D3—64no—
252C3×C4×D3—62no—
253C3×Dic6—64no—
254C3×Dic6—62no—
255C2×C22⋊Q8—91noSylow
256C2×H(3,𝔽3)—22no—
257C2×H(3,𝔽3)C22×D411yescharacteristic
258C2×H(3,𝔽3)C22×Q811yescharacteristic
259C2×H(3,𝔽3)C2×#4111yescharacteristic
260(C3⋊D3)⋊C3—22no—
261(C3⋊D3)⋊C3C22⋊Q814yesdirect product factor
262C24×C3—91no—
263C23×D3—31no—
264C23×D3—91no—
265C2×C3×Q8—31no—
266C2×C3×Q8—31no—
267C2×C3×Q8—61no—
268C2×C3×Q8—91no—
269C2×C3×Q8—92no—
270C2×C3×Q8—184no—
271C2×C3×Q8C2×C3×D311yescharacteristic
272C22×C3×C4—31no—
273C22×C3×C4—31no—
274C22×C3×C4—61no—
275C22×C3×C4—91no—
276C22×C3×C4—92no—
277C22×C3×C4—92no—
278C22×C3×C4—91no—
279C22×C3×C4—91no—
280C22×C3×C4—91no—
281C22×C3×C4—91no—
282C22×C3×C4—184no—
283C22×C3×C4C2×C3×D311yescharacteristic
284C22×Dic3—31no—
285C22×Dic3—91no—
286D3×Q8—64no—
287D3×Q8—184no—
288C2×C4×D3—31no—
289C2×C4×D3—32no—
290C2×C4×D3—32no—
291C2×C4×D3—31no—
292C2×C4×D3—31no—
293C2×C4×D3—31no—
294C2×C4×D3—64no—
295C2×C4×D3—91no—
296C2×C4×D3—92no—
297C2×C4×D3—92no—
298C2×C4×D3—91no—
299C2×C4×D3—91no—
300C2×C4×D3—91no—
301C2×C4×D3—184no—
302C2×Dic6—32no—
303C2×Dic6—31no—
304C2×Dic6—92no—
305C2×Dic6—91no—
306C3×C4⋊C4—32no—
307C3×C4⋊C4—31no—
308C3×C4⋊C4—31no—
309C3×C4⋊C4—32no—
310C3×C4⋊C4—61no—
311C3×C4⋊C4—62no—
312C3×C4⋊C4—92no—
313C3×C4⋊C4—92no—
314C3×C4⋊C4—92no—
315C3×C4⋊C4—91no—
316C3×C4⋊C4—92no—
317C3×C4⋊C4C2×C3×D312yes—
318C3×C4⋊C4C2×C3×D311yescharacteristic
319C3×C22⋊C4—32no—
320C3×C22⋊C4—32no—
321C3×C22⋊C4—62no—
322C3×C22⋊C4—92no—
323C3×C22⋊C4—92no—
324C3×C22⋊C4—92no—
325C3×C22⋊C4C2×C3×D312yes—
326#217—32no—
327#217—92no—
328(C2×D3)⋊C4—32no—
329(C2×D3)⋊C4—32no—
330(C2×D3)⋊C4—92no—
331(C2×D3)⋊C4—92no—
332C4⋊Dic3—32no—
333C4⋊Dic3—31no—
334C4⋊Dic3—92no—
335C4⋊Dic3—91no—
336Dic3⋊C4—32no—
337Dic3⋊C4—32no—
338Dic3⋊C4—32no—
339Dic3⋊C4—92no—
340Dic3⋊C4—92no—
341Dic3⋊C4—92no—
342C22×C32—21no—
343C22×C32—21no—
344C22×C32—21no—
345C22×C32—21no—
346C22×C32—21no—
347C22×C32—22no—
348C22×C32—41no—
349C22×C32—41no—
350C22×C32D3×Q812yescomplemented
351C22×C32C2×C3×Q812yescomplemented
352C22×C32C23×D311yescharacteristic
353C22×C32C24×C311yescharacteristic
354C2×C3⋊D3—21no—
355C2×C3⋊D3—21no—
356C2×C3⋊D3—28no—
357C2×C3⋊D3C2×C3×D412yes—
358C2×C3⋊D3C2×C3×Q812yes—
359C2×C3⋊D3C2×C3×Q812yescomplemented
360C2×C3⋊D3C3×#4112yes—
361C2×C3×D3—32no—
362C2×C3×D3—32no—
363C2×C3×D3—32no—
364C2×C3×D3—32no—
365C2×C3×D3—68no—
366C2×C3×D3—61no—
367C2×C3×D3—61no—
368C32×C4—22no—
369C32×C4—21no—
370C32×C4—22no—
371C32×C4—22no—
372C32×C4—21no—
373C32×C4—22no—
374C32×C4—22no—
375C32×C4—42no—
376C32×C4—41no—
377C32×C4—42no—
378C32×C4D3×D412yes—
379C32×C4C2×C3×D412yes—
380C3⋊Dic3—22no—
381C3⋊Dic3—21no—
382C3⋊Dic3—22no—
383C3⋊Dic3C2×C3×D412yes—
384C3×Dic3—32no—
385C3×Dic3—62no—
386C3×Dic3—61no—
387C3×Dic3—62no—
388C22×Q8—91no—
389C23×C4—91no—
390C22⋊Q8—91no—
391C22⋊Q8—91no—
392C22⋊Q8—92no—
393C22⋊Q8—91no—
394C22⋊Q8—92no—
395C22⋊Q8(C3⋊D3)⋊C311yescharacteristic, direct product factor
396C2×C4⋊C4—91no—
397C2×C4⋊C4—92no—
398C2×C22⋊C4—92no—
399H(3,𝔽3)C2×C22⋊Q811yescharacteristic, complemented, Sylow
400C23×C3—31no—
401C23×C3—31no—
402C23×C3—61no—
403C23×C3—91no—
404C23×C3—91no—
405C23×C3—94no—
406C23×C3—182no—
407C23×C3—182no—
408C23×C3C22×C3×D311yescharacteristic
409C22×D3—31no—
410C22×D3—31no—
411C22×D3—34no—
412C22×D3—62no—
413C22×D3—62no—
414C22×D3—91no—
415C22×D3—94no—
416C22×D3—91no—
417C22×D3—182no—
418C22×D3—182no—
419C3×Q8—22no—
420C3×Q8—62no—
421C3×Q8—62no—
422C3×Q8—122no—
423C3×Q8—182no—
424C3×Q8—184no—
425C2×C3×C4—22no—
426C2×C3×C4—31no—
427C2×C3×C4—31no—
428C2×C3×C4—32no—
429C2×C3×C4—32no—
430C2×C3×C4—31no—
431C2×C3×C4—31no—
432C2×C3×C4—32no—
433C2×C3×C4—32no—
434C2×C3×C4—62no—
435C2×C3×C4—62no—
436C2×C3×C4—61no—
437C2×C3×C4—62no—
438C2×C3×C4—62no—
439C2×C3×C4—61no—
440C2×C3×C4—94no—
441C2×C3×C4—91no—
442C2×C3×C4—92no—
443C2×C3×C4—92no—
444C2×C3×C4—91no—
445C2×C3×C4—122no—
446C2×C3×C4—182no—
447C2×C3×C4—182no—
448C2×C3×C4—184no—
449C2×C3×C4—182no—
450C2×C3×C4—184no—
451C2×C3×C4—182no—
452C2×C3×C4C22×C3×D311yescharacteristic
453C2×C3×C4C22×C3×D312yes—
454C2×C3×C4C22×C3×D312yes—
455C2×C3×C4C22×C3×D311yescharacteristic
456C2×Dic3—31no—
457C2×Dic3—32no—
458C2×Dic3—31no—
459C2×Dic3—32no—
460C2×Dic3—62no—
461C2×Dic3—91no—
462C2×Dic3—92no—
463C2×Dic3—91no—
464C2×Dic3—92no—
465C2×Dic3—182no—
466C4×D3—34no—
467C4×D3—62no—
468C4×D3—64no—
469C4×D3—62no—
470C4×D3—64no—
471C4×D3—62no—
472C4×D3—94no—
473C4×D3—182no—
474C4×D3—182no—
475C4×D3—184no—
476C4×D3—182no—
477C4×D3—184no—
478Dic6—64no—
479Dic6—62no—
480Dic6—184no—
481Dic6—182no—
482C2×C32—22no—
483C2×C32—22no—
484C2×C32—21no—
485C2×C32—21no—
486C2×C32—21no—
487C2×C32—42no—
488C2×C32C2×D3×D411yescharacteristic
489C2×C32C2×D3×Q811yescharacteristic
490C2×C32D3×#4111yescharacteristic
491C2×C32C22×C3×D411yescharacteristic
492C2×C32C22×C3×Q811yescharacteristic
493C2×C32C2×C3×#4111yescharacteristic
494C3⋊D3—22no—
495C3⋊D3C3×C22⋊Q814yescomplemented
496C3×D3—34no—
497C3×D3—62no—
498C24—91no—
499C2×Q8—92no—
500C2×Q8—91no—
501C2×Q8—184no—
502C2×Q8C2×(C3⋊D3)⋊C311yescharacteristic, complemented
503C22×C4—91no—
504C22×C4—91no—
505C22×C4—92no—
506C22×C4—92no—
507C22×C4—91no—
508C22×C4—91no—
509C22×C4—91no—
510C22×C4—184no—
511C22×C4C2×(C3⋊D3)⋊C311yescharacteristic
512C4⋊C4—92no—
513C4⋊C4—92no—
514C4⋊C4—92no—
515C4⋊C4—91no—
516C4⋊C4—92no—
517C4⋊C4C2×(C3⋊D3)⋊C311yescharacteristic, complemented
518C4⋊C4C2×(C3⋊D3)⋊C312yescomplemented
519C22⋊C4—92no—
520C22⋊C4—92no—
521C22⋊C4—92no—
522C22⋊C4C2×(C3⋊D3)⋊C312yes—
523C22×C3—21no—
524C22×C3—21no—
525C22×C3—31no—
526C22×C3—31no—
527C22×C3—32no—
528C22×C3—32no—
529C22×C3—61no—
530C22×C3—61no—
531C22×C3—61no—
532C22×C3—61no—
533C22×C3—61no—
534C22×C3—62no—
535C22×C3—92no—
536C22×C3—92no—
537C22×C3—92no—
538C22×C3—92no—
539C22×C3—121no—
540C22×C3—121no—
541C22×C3—181no—
542C22×C3—181no—
543C22×C3—188no—
544C22×C3C3×D3×Q812yes—
545C22×C3C23×C3×D311yescharacteristic
546C2×D3—32no—
547C2×D3—32no—
548C2×D3—32no—
549C2×D3—32no—
550C2×D3—68no—
551C2×D3—61no—
552C2×D3—61no—
553C2×D3—92no—
554C2×D3—92no—
555C2×D3—92no—
556C2×D3—92no—
557C2×D3—188no—
558C2×D3—181no—
559C2×D3—181no—
560C3×C4—22no—
561C3×C4—21no—
562C3×C4—22no—
563C3×C4—32no—
564C3×C4—32no—
565C3×C4—62no—
566C3×C4—61no—
567C3×C4—62no—
568C3×C4—61no—
569C3×C4—62no—
570C3×C4—62no—
571C3×C4—62no—
572C3×C4—92no—
573C3×C4—121no—
574C3×C4—122no—
575C3×C4—122no—
576C3×C4—181no—
577C3×C4—182no—
578C3×C4—182no—
579C3×C4C3×D3×D412yes—
580Dic3—32no—
581Dic3—62no—
582Dic3—61no—
583Dic3—62no—
584Dic3—92no—
585Dic3—182no—
586Dic3—181no—
587Dic3—182no—
588C32—21no—
589C32D3×C22⋊Q811yescharacteristic, complemented
590C32C2×C3×C22⋊Q811yescharacteristic, complemented
591C23—91no—
592C23—91no—
593C23—94no—
594C23—182no—
595C23—182no—
596C23C22×(C3⋊D3)⋊C311yescharacteristic
597Q8—22no—
598Q8—184no—
599Q8—182no—
600C2×C4—22no—
601C2×C4—91no—
602C2×C4—94no—
603C2×C4—92no—
604C2×C4—92no—
605C2×C4—91no—
606C2×C4—182no—
607C2×C4—182no—
608C2×C4—184no—
609C2×C4—184no—
610C2×C4—182no—
611C2×C4—182no—
612C2×C4C22×(C3⋊D3)⋊C312yes—
613C2×C4C22×(C3⋊D3)⋊C312yes—
614C2×C4C22×(C3⋊D3)⋊C311yescharacteristic
615C2×C4C22×(C3⋊D3)⋊C311yescharacteristic
616C2×C3—22no—
617C2×C3—31no—
618C2×C3—31no—
619C2×C3—31no—
620C2×C3—31no—
621C2×C3—31no—
622C2×C3—31no—
623C2×C3—62no—
624C2×C3—62no—
625C2×C3—61no—
626C2×C3—61no—
627C2×C3—61no—
628C2×C3—94no—
629C2×C3—122no—
630C2×C3—182no—
631C2×C3C2×C3×D3×D411yescharacteristic
632C2×C3C2×C3×D3×Q811yescharacteristic
633C2×C3C3×D3×#4111yescharacteristic
634D3—34no—
635D3—62no—
636D3—94no—
637D3—182no—
638C22—21no—
639C22—21no—
640C22—92no—
641C22—92no—
642C22—92no—
643C22—92no—
644C22—188no—
645C22—181no—
646C22—181no—
647C22Q8×(C3⋊D3)⋊C312yescomplemented
648C22C23×(C3⋊D3)⋊C311yescharacteristic
649C4—21no—
650C4—22no—
651C4—22no—
652C4—92no—
653C4—181no—
654C4—182no—
655C4—182no—
656C4D4×(C3⋊D3)⋊C312yes—
657C3—31no—
658C3—31no—
659C3—61no—
660C3C3×D3×C22⋊Q811yescharacteristic
661C2—22no—
662C2—94no—
663C2—182no—
664C2C2×D4×(C3⋊D3)⋊C311yescharacteristic
665C2C2×Q8×(C3⋊D3)⋊C311yescharacteristic
666C2#41×(C3⋊D3)⋊C311yescharacteristic
subgroupG/H
centerC22C23×(C3⋊D3)⋊C3
commutator, cosocleC22×C32C24×C3
Frattini, socleC22×C3C23×C3×D3
FittingH(3,𝔽3)×C22⋊Q8C2
prime radicalC23×(C3⋊D3)⋊C3C22
hypercenterC22⋊Q8(C3⋊D3)⋊C3
hypocenterC32C2×C3×C22⋊Q8
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22⋊Q8

Complements

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

NH ≅ G/Ntype
1. C2×Q8×(C3⋊D3)⋊C3C2semidirect
3. H(3,𝔽3)×C22⋊Q8C2semidirect
4. #64155⋊C3C2semidirect
5. #64133⋊C3C2semidirect
6. #64106⋊C3C2semidirect
7. #64105⋊C3C2semidirect
8. C4⋊C4×(C3⋊D3)⋊C3C2semidirect
9. C4⋊C4×(C3⋊D3)⋊C3C2semidirect
11. #64087⋊C3C2semidirect
12. C3⋊D3×C22⋊Q8C3semidirect
15. C2×Q8×H(3,𝔽3)C22semidirect
26. C2×#634⋊C3C22semidirect
27. C2×#634⋊C3C22semidirect
28. C4⋊C4×H(3,𝔽3)C22semidirect
29. C4⋊C4×H(3,𝔽3)C22semidirect
34. C4⋊((C3⋊Dic3)⋊C3)C22semidirect
35. C4⋊((C3⋊Dic3)⋊C3)C22semidirect
36. #3750⋊C3C22semidirect
37. #3750⋊C3C22semidirect
38. #3750⋊C3C22semidirect
39. C2×Q8×C3⋊D3C2×C3semidirect
44. C32×C22⋊Q8D3semidirect
45. C32×C22⋊Q8C2×C3semidirect
46. #64155C2×C3semidirect
47. #64133C2×C3semidirect
48. #64106C2×C3semidirect
49. #64105C2×C3semidirect
50. C4⋊C4×C3⋊D3C2×C3semidirect
51. C4⋊C4×C3⋊D3C2×C3semidirect
53. #64087C2×C3semidirect
65. C22×(C3⋊D3)⋊C3Q8semidirect
93. C2×C32×Q8C2×D3semidirect
94. C2×C32×Q8C22×C3semidirect
107. C2×#634C22×C3semidirect
108. C2×#634C22×C3semidirect
122. C32×C4⋊C4C2×D3semidirect
123. C32×C4⋊C4C2×D3semidirect
124. C32×C4⋊C4C22×C3semidirect
125. C32×C4⋊C4C22×C3semidirect
132. C4⋊(C3⋊Dic3)C22×C3semidirect
133. C4⋊(C3⋊Dic3)C22×C3semidirect
134. #3750C22×C3semidirect
135. #3750C22×C3semidirect
136. #3750C22×C3semidirect
147. C22×H(3,𝔽3)C2×Q8semidirect
154. C2×(C3⋊D3)⋊C3C2×Q8semidirect
203. C22×C3⋊D3C3×Q8semidirect
261. (C3⋊D3)⋊C3C22⋊Q8direct (N × H)
350. C22×C32D3×Q8semidirect
351. C22×C32C2×C3×Q8semidirect
359. C2×C3⋊D3C2×C3×Q8semidirect
395. C22⋊Q8(C3⋊D3)⋊C3direct (N × H)
399. H(3,𝔽3)C2×C22⋊Q8semidirect
495. C3⋊D3C3×C22⋊Q8semidirect
502. C2×Q8C2×(C3⋊D3)⋊C3semidirect
517. C4⋊C4C2×(C3⋊D3)⋊C3semidirect
518. C4⋊C4C2×(C3⋊D3)⋊C3semidirect
589. C32D3×C22⋊Q8semidirect
590. C32C2×C3×C22⋊Q8semidirect
647. C22Q8×(C3⋊D3)⋊C3semidirect

Maximal subgroups

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

subgroupindex
C2×Q8×(C3⋊D3)⋊C32
C22×C4×(C3⋊D3)⋊C32
H(3,𝔽3)×C22⋊Q82
#64155⋊C32
#64133⋊C32
#64106⋊C32
#64105⋊C32
C4⋊C4×(C3⋊D3)⋊C32
C22⋊C4×(C3⋊D3)⋊C32
#64087⋊C32
C3⋊D3×C22⋊Q83
C3×D3×C22⋊Q83