Finite Group Databasebeta

← #10596100⋊C3 #13152954

Subgroups — #10596100⋊C3 #13152954

Order 1728.

1103 conjugacy classes of subgroups.

The subgroup lattice has 682 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#88722C211yesmaximal, characteristic, complemented
2C2×#3828⋊C3C211yesmaximal, characteristic, complemented
3H(3,𝔽3)×C22⋊Q8C211yesmaximal, characteristic, complemented
4#64155⋊C3C211yesmaximal, characteristic, complemented
5#64139⋊C3C211yesmaximal, characteristic, complemented
6#64105⋊C3C212yesmaximal, complemented
7#64104⋊C3C211yesmaximal, characteristic, complemented
8#64104⋊C3C212yesmaximal, complemented
9C4⋊C4×(C3⋊D3)⋊C3C211yesmaximal, characteristic, complemented
10#64093⋊C3C212yesmaximal, complemented
11#64093⋊C3C212yesmaximal, complemented
12#10596100C311yesmaximal, characteristic, complemented
13C3×#5629—31nomaximal
14C2×Q8×H(3,𝔽3)C2211yescharacteristic
15C22×C4×H(3,𝔽3)C2211yescharacteristic
16C2×#638⋊C3C2211yescharacteristic
17C2×#638⋊C3C2211yescharacteristic
18C2×#638⋊C3C2212yes—
19#88722—24no—
20#3828⋊C3—24no—
21C2×C4⋊((C3⋊D3)⋊C3)C2211yescharacteristic
22C2×C4⋊((C3⋊D3)⋊C3)C2211yescharacteristic
23C2×C4⋊((C3⋊D3)⋊C3)C2212yes—
24C2×C4⋊((C3⋊D3)⋊C3)C2212yes—
25C2×C4×(C3⋊D3)⋊C3C2211yescharacteristic
26C2×C4×(C3⋊D3)⋊C3C2212yes—
27C2×C4×(C3⋊D3)⋊C3C2212yes—
28C2×C4×(C3⋊D3)⋊C3C2211yescharacteristic
29C2×#634⋊C3C2211yescharacteristic
30C4⋊C4×H(3,𝔽3)C2211yescharacteristic
31C4⋊C4×H(3,𝔽3)C2212yes—
32C22⋊C4×H(3,𝔽3)C2212yes—
33#3752⋊C3C2212yes—
34#3752⋊C3C2212yes—
35#3752⋊C3C2212yes—
36C4⋊((C3⋊Dic3)⋊C3)C2211yescharacteristic
37#3750⋊C3C2212yes—
38#3750⋊C3C2212yes—
39C2×#3832C2×C311yescharacteristic, complemented
40C2×#3828C2×C311yescharacteristic, complemented
41C2×C3×#239—31no—
42C2×C3×#235—31no—
43C32×C22⋊Q8—21no—
44C32×C22⋊Q8D311yescharacteristic, complemented
45C32×C22⋊Q8C2×C311yescharacteristic, complemented
46#64155C2×C311yescharacteristic, complemented
47#64139C2×C311yescharacteristic, complemented
48#64105C2×C312yescomplemented
49#64104C2×C311yescharacteristic, complemented
50#64104C2×C312yescomplemented
51C4⋊C4×C3⋊D3C2×C311yescharacteristic, complemented
52#64093C2×C312yescomplemented
53#64093C2×C312yescomplemented
54C3×#946—31no—
55C3×#930—31no—
56C3×#896—32no—
57C3×#895—31no—
58C3×#895—32no—
59C3×D3×C4⋊C4—31no—
60C3×#884—32no—
61C3×#884—32no—
62C23×H(3,𝔽3)C2311yescharacteristic
63C22×(C3⋊D3)⋊C3C2312yes—
64C22×(C3⋊D3)⋊C3C2311yescharacteristic
65C22×(C3⋊D3)⋊C3C2311yescharacteristic
66Q8×H(3,𝔽3)—22no—
67C2×C4×H(3,𝔽3)—22no—
68C2×C4×H(3,𝔽3)C2311yescharacteristic
69C2×C4×H(3,𝔽3)C2312yes—
70C2×C4×H(3,𝔽3)C2312yes—
71C2×C4×H(3,𝔽3)C2311yescharacteristic
72#638⋊C3—22no—
73#638⋊C3—22no—
74#638⋊C3—42no—
75C2×(C3⋊Dic3)⋊C3C2311yescharacteristic
76C2×(C3⋊Dic3)⋊C3C2312yes—
77C2×(C3⋊Dic3)⋊C3C2311yescharacteristic
78C4⋊((C3⋊D3)⋊C3)—22no—
79C4⋊((C3⋊D3)⋊C3)—24no—
80C4⋊((C3⋊D3)⋊C3)—22no—
81C4⋊((C3⋊D3)⋊C3)—42no—
82C4×(C3⋊D3)⋊C3—22no—
83C4×(C3⋊D3)⋊C3—24no—
84C4×(C3⋊D3)⋊C3—42no—
85C4×(C3⋊D3)⋊C3D414yescomplemented
86#634⋊C3—22no—
87C3×#537—91no—
88#5629—31no—
89#5629—91no—
90C2×C32×Q8—21no—
91C2×C32×Q8C2×D311yescharacteristic
92C2×C32×Q8C22×C311yescharacteristic
93C22×C32×C4—21no—
94C22×C32×C4C2×D311yescharacteristic
95C22×C32×C4C22×C311yescharacteristic
96C2×#638C22×C311yescharacteristic
97C2×#638C22×C311yescharacteristic
98C2×#638C22×C312yes—
99#3832—24no—
100#3828—24no—
101C2×C4⋊(C3⋊D3)C22×C312yes—
102C2×C4⋊(C3⋊D3)C22×C311yescharacteristic
103C2×C4⋊(C3⋊D3)C22×C311yescharacteristic
104C2×C4⋊(C3⋊D3)C22×C312yes—
105C2×C4×C3⋊D3C22×C312yes—
106C2×C4×C3⋊D3C22×C311yescharacteristic
107C2×C4×C3⋊D3C22×C312yes—
108C2×C4×C3⋊D3C22×C311yescharacteristic
109C2×#634C22×C311yescharacteristic
110C2×C3×#67—31no—
111C2×C3×#67—31no—
112C2×C3×#67—32no—
113C3×#239—64no—
114C3×#235—64no—
115C2×C3×D12—32no—
116C2×C3×D12—31no—
117C2×C3×D12—31no—
118C2×C3×D12—32no—
119C2×C3×C4×D3—31no—
120C2×C3×C4×D3—32no—
121C2×C3×C4×D3—31no—
122C2×C3×C4×D3—32no—
123C2×C3×Dic6—31no—
124C32×C4⋊C4—21no—
125C32×C4⋊C4—22no—
126C32×C4⋊C4C2×D311yescharacteristic
127C32×C4⋊C4C2×D312yes—
128C32×C4⋊C4C22×C311yescharacteristic
129C32×C4⋊C4C22×C312yes—
130C32×C22⋊C4—22no—
131C32×C22⋊C4C2×D312yes—
132C32×C22⋊C4C22×C312yes—
133#3752C22×C312yes—
134#3752C22×C312yes—
135#3752C22×C312yes—
136C4⋊(C3⋊Dic3)C22×C311yescharacteristic
137#3750C22×C312yes—
138#3750C22×C312yes—
139C3×(C2×D3)⋊C4—32no—
140C3×(C2×D3)⋊C4—32no—
141C3×(C2×D3)⋊C4—32no—
142C3×C4⋊Dic3—31no—
143C3×Dic3⋊C4—32no—
144C3×Dic3⋊C4—32no—
145C22×H(3,𝔽3)—21no—
146C22×H(3,𝔽3)—21no—
147C22×H(3,𝔽3)—21no—
148C22×H(3,𝔽3)C2411yescharacteristic
149C2×(C3⋊D3)⋊C3—21no—
150C2×(C3⋊D3)⋊C3—21no—
151C2×(C3⋊D3)⋊C3—22no—
152C2×(C3⋊D3)⋊C3—21no—
153C2×(C3⋊D3)⋊C3—21no—
154C2×(C3⋊D3)⋊C3—22no—
155C2×(C3⋊D3)⋊C3—22no—
156C2×(C3⋊D3)⋊C3—21no—
157C2×(C3⋊D3)⋊C3C2×D412yes—
158C4×H(3,𝔽3)—21no—
159C4×H(3,𝔽3)—22no—
160C4×H(3,𝔽3)—22no—
161C4×H(3,𝔽3)C2×D412yes—
162(C3⋊Dic3)⋊C3—21no—
163(C3⋊Dic3)⋊C3—22no—
164(C3⋊Dic3)⋊C3C2×D412yes—
165C2×C3×#41—91no—
166C2×C3×#41—91no—
167C2×#239—31no—
168C2×#239—91no—
169C2×#235—31no—
170C2×#235—91no—
171C3×C22⋊Q8—31no—
172C3×C22⋊Q8—31no—
173C3×C22⋊Q8—61no—
174C3×C22⋊Q8—92no—
175C3×C22⋊Q8—91no—
176C3×C22⋊Q8C3×D311yescharacteristic
177C3×#121—92no—
178C3×#121—92no—
179C3×#121—91no—
180C3×#121—92no—
181C3×#121—91no—
182C2×C3×C4⋊C4—91no—
183#946—31no—
184#946—91no—
185#930—31no—
186#930—91no—
187#896—32no—
188#896—92no—
189#895—31no—
190#895—32no—
191#895—91no—
192#895—92no—
193D3×C4⋊C4—31no—
194D3×C4⋊C4—91no—
195#884—32no—
196#884—32no—
197#884—92no—
198#884—92no—
199C23×C32—21no—
200C23×C32C22×D311yescharacteristic
201C23×C32C23×C311yescharacteristic
202C22×C3⋊D3C23×C312yes—
203C22×C3⋊D3C23×C311yescharacteristic
204C22×C3⋊D3C23×C311yescharacteristic
205C22×C3×D3—31no—
206C22×C3×D3—32no—
207C22×C3×D3—31no—
208C32×Q8—22no—
209C32×Q8—22no—
210C32×Q8—42no—
211C2×C32×C4—22no—
212C2×C32×C4—22no—
213C2×C32×C4—21no—
214C2×C32×C4—22no—
215C2×C32×C4—22no—
216C2×C32×C4—21no—
217C2×C32×C4—42no—
218C2×C32×C4C22×D312yes—
219C2×C32×C4C22×D312yes—
220C2×C32×C4C22×D311yescharacteristic
221C2×C32×C4C22×D311yescharacteristic
222C2×C32×C4C23×C312yes—
223C2×C32×C4C23×C312yes—
224C2×C32×C4C23×C311yescharacteristic
225C2×C32×C4C23×C311yescharacteristic
226#638—22no—
227#638—22no—
228#638—42no—
229C2×C3⋊Dic3C23×C312yes—
230C2×C3⋊Dic3C23×C311yescharacteristic
231C2×C3⋊Dic3C23×C311yescharacteristic
232C4⋊(C3⋊D3)—22no—
233C4⋊(C3⋊D3)—24no—
234C4⋊(C3⋊D3)—22no—
235C4⋊(C3⋊D3)—42no—
236C4×C3⋊D3—22no—
237C4×C3⋊D3—24no—
238C4×C3⋊D3—42no—
239C4×C3⋊D3C3×D414yescomplemented
240#634—22no—
241C3×#67—62no—
242C3×#67—62no—
243C3×#67—122no—
244C2×C3×Dic3—31no—
245C2×C3×Dic3—32no—
246C2×C3×Dic3—31no—
247C3×D12—62no—
248C3×D12—64no—
249C3×D12—62no—
250C3×D12—122no—
251C3×C4×D3—34no—
252C3×C4×D3—64no—
253C3×C4×D3—62no—
254C3×C4×D3—122no—
255C3×Dic6—62no—
256#537—91noSylow
257C2×H(3,𝔽3)—41no—
258C2×H(3,𝔽3)C22×D411yescharacteristic
259C2×H(3,𝔽3)H(5,𝔽2)11yescharacteristic
260C2×H(3,𝔽3)2−1+411yescharacteristic
261(C3⋊D3)⋊C3—22no—
262(C3⋊D3)⋊C3—42no—
263(C3⋊D3)⋊C3—41no—
264C3×#41—184no—
265C3×#41—184no—
266C2×C3×Q8—31no—
267C2×C3×Q8—31no—
268C2×C3×Q8—61no—
269C2×C3×Q8—91no—
270C2×C3×Q8C2×C3×D311yescharacteristic
271C2×C3×D4—91no—
272C2×C3×D4—92no—
273C2×C3×D4—91no—
274C2×C3×D4—92no—
275C2×C3×D4—91no—
276C2×C3×D4—91no—
277C2×C3×D4—92no—
278C22×C3×C4—31no—
279C22×C3×C4—31no—
280C22×C3×C4—61no—
281C22×C3×C4—91no—
282C22×C3×C4—91no—
283C22×C3×C4—92no—
284C22×C3×C4—92no—
285C22×C3×C4C2×C3×D311yescharacteristic
286C2×#67—31no—
287C2×#67—31no—
288C2×#67—32no—
289C2×#67—91no—
290C2×#67—91no—
291C2×#67—92no—
292#239—64no—
293#239—184no—
294#235—64no—
295#235—184no—
296C2×D12—32no—
297C2×D12—31no—
298C2×D12—31no—
299C2×D12—32no—
300C2×D12—92no—
301C2×D12—91no—
302C2×D12—91no—
303C2×D12—92no—
304C2×C4×D3—31no—
305C2×C4×D3—32no—
306C2×C4×D3—31no—
307C2×C4×D3—32no—
308C2×C4×D3—91no—
309C2×C4×D3—92no—
310C2×C4×D3—91no—
311C2×C4×D3—92no—
312C2×Dic6—31no—
313C2×Dic6—91no—
314C3×C4⋊C4—31no—
315C3×C4⋊C4—32no—
316C3×C4⋊C4—31no—
317C3×C4⋊C4—32no—
318C3×C4⋊C4—61no—
319C3×C4⋊C4—62no—
320C3×C4⋊C4—92no—
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⋊C4C2×C3×D312yes—
332(C2×D3)⋊C4—32no—
333(C2×D3)⋊C4—32no—
334(C2×D3)⋊C4—32no—
335(C2×D3)⋊C4—92no—
336(C2×D3)⋊C4—92no—
337(C2×D3)⋊C4—92no—
338C4⋊Dic3—31no—
339C4⋊Dic3—91no—
340Dic3⋊C4—32no—
341Dic3⋊C4—32no—
342Dic3⋊C4—92no—
343Dic3⋊C4—92no—
344C22×C32—22no—
345C22×C32—21no—
346C22×C32—21no—
347C22×C32—21no—
348C22×C32—21no—
349C22×C32—21no—
350C22×C32—21no—
351C22×C32—21no—
352C22×C32—41no—
353C22×C32—41no—
354C22×C32C23×D311yescharacteristic
355C22×C32C24×C311yescharacteristic
356C2×C3⋊D3—21no—
357C2×C3⋊D3—21no—
358C2×C3⋊D3—22no—
359C2×C3⋊D3—21no—
360C2×C3⋊D3—21no—
361C2×C3⋊D3—22no—
362C2×C3⋊D3—22no—
363C2×C3⋊D3—21no—
364C2×C3⋊D3C2×C3×D412yes—
365C2×C3×D3—32no—
366C2×C3×D3—61no—
367C2×C3×D3—61no—
368C2×C3×D3—62no—
369C2×C3×D3—61no—
370C2×C3×D3—62no—
371C2×C3×D3—61no—
372C2×C3×D3—61no—
373C2×C3×D3—62no—
374C32×C4—21no—
375C32×C4—22no—
376C32×C4—22no—
377C32×C4—21no—
378C32×C4—22no—
379C32×C4—22no—
380C32×C4—22no—
381C32×C4—42no—
382C32×C4—41no—
383C32×C4—42no—
384C32×C4D3×D412yes—
385C32×C4C2×C3×D412yes—
386C3⋊Dic3—21no—
387C3⋊Dic3—22no—
388C3⋊Dic3C2×C3×D412yes—
389C3×Dic3—32no—
390C3×Dic3—61no—
391C3×Dic3—62no—
392C2×#41—91no—
393C2×#41—91no—
394C22⋊Q8—91no—
395C22⋊Q8—92no—
396C22⋊Q8(C3⋊D3)⋊C311yescharacteristic, complemented
397#121—91no—
398#121—91no—
399#121—92no—
400#121—92no—
401#121—92no—
402C2×C4⋊C4—91no—
403H(3,𝔽3)#53711yescharacteristic, complemented, Sylow
404C23×C3—31no—
405C23×C3—31no—
406C23×C3—61no—
407C23×C3—91no—
408C23×C3—92no—
409C23×C3—91no—
410C23×C3C22×C3×D311yescharacteristic
411C22×D3—31no—
412C22×D3—32no—
413C22×D3—31no—
414C22×D3—91no—
415C22×D3—92no—
416C22×D3—91no—
417C3×Q8—22no—
418C3×Q8—62no—
419C3×Q8—62no—
420C3×Q8—122no—
421C3×Q8—182no—
422C3×D4—182no—
423C3×D4—182no—
424C3×D4—184no—
425C3×D4—182no—
426C3×D4—182no—
427C3×D4—362no—
428C3×D4—362no—
429C2×C3×C4—22no—
430C2×C3×C4—31no—
431C2×C3×C4—31no—
432C2×C3×C4—32no—
433C2×C3×C4—32no—
434C2×C3×C4—31no—
435C2×C3×C4—32no—
436C2×C3×C4—32no—
437C2×C3×C4—31no—
438C2×C3×C4—62no—
439C2×C3×C4—62no—
440C2×C3×C4—61no—
441C2×C3×C4—62no—
442C2×C3×C4—62no—
443C2×C3×C4—61no—
444C2×C3×C4—94no—
445C2×C3×C4—91no—
446C2×C3×C4—92no—
447C2×C3×C4—91no—
448C2×C3×C4—122no—
449C2×C3×C4—182no—
450C2×C3×C4—184no—
451C2×C3×C4—362no—
452C2×C3×C4C22×C3×D312yes—
453C2×C3×C4C22×C3×D312yes—
454C2×C3×C4C22×C3×D311yescharacteristic
455C2×C3×C4C22×C3×D311yescharacteristic
456#67—62no—
457#67—62no—
458#67—122no—
459#67—182no—
460#67—182no—
461#67—362no—
462C2×Dic3—31no—
463C2×Dic3—32no—
464C2×Dic3—31no—
465C2×Dic3—91no—
466C2×Dic3—92no—
467C2×Dic3—91no—
468D12—62no—
469D12—64no—
470D12—62no—
471D12—122no—
472D12—182no—
473D12—182no—
474D12—184no—
475D12—362no—
476C4×D3—34no—
477C4×D3—64no—
478C4×D3—62no—
479C4×D3—94no—
480C4×D3—122no—
481C4×D3—184no—
482C4×D3—182no—
483C4×D3—362no—
484Dic6—62no—
485Dic6—182no—
486C2×C32—21no—
487C2×C32—21no—
488C2×C32—21no—
489C2×C32—42no—
490C2×C32—41no—
491C2×C32—41no—
492C2×C32C2×D3×D411yescharacteristic
493C2×C32#100711yescharacteristic
494C2×C32#100911yescharacteristic
495C2×C32C22×C3×D411yescharacteristic
496C2×C32C3×H(5,𝔽2)11yescharacteristic
497C2×C32C3×2−1+411yescharacteristic
498C3⋊D3—22no—
499C3⋊D3—42no—
500C3⋊D3—41no—
501C3×D3—62no—
502C3×D3—122no—
503C3×D3—121no—
504#41—184no—
505#41—184no—
506C2×Q8—91no—
507C2×Q8C2×(C3⋊D3)⋊C311yescharacteristic
508C2×D4—91no—
509C2×D4—91no—
510C2×D4—92no—
511C2×D4—91no—
512C2×D4—92no—
513C2×D4—91no—
514C2×D4—92no—
515C22×C4—91no—
516C22×C4—92no—
517C22×C4—91no—
518C22×C4—92no—
519C22×C4C2×(C3⋊D3)⋊C311yescharacteristic
520C4⋊C4—92no—
521C4⋊C4—91no—
522C4⋊C4—92no—
523C4⋊C4C2×(C3⋊D3)⋊C311yescharacteristic
524C4⋊C4C2×(C3⋊D3)⋊C312yes—
525C22⋊C4—92no—
526C22⋊C4—92no—
527C22⋊C4—92no—
528C22⋊C4C2×(C3⋊D3)⋊C312yes—
529C22×C3—21no—
530C22×C3—21no—
531C22×C3—21no—
532C22×C3—31no—
533C22×C3—31no—
534C22×C3—61no—
535C22×C3—61no—
536C22×C3—61no—
537C22×C3—61no—
538C22×C3—61no—
539C22×C3—61no—
540C22×C3—62no—
541C22×C3—61no—
542C22×C3—92no—
543C22×C3—121no—
544C22×C3—121no—
545C22×C3—181no—
546C22×C3—181no—
547C22×C3—181no—
548C22×C3—182no—
549C22×C3—181no—
550C22×C3—182no—
551C22×C3—182no—
552C22×C3—181no—
553C22×C3C23×C3×D311yescharacteristic
554C2×D3—32no—
555C2×D3—61no—
556C2×D3—61no—
557C2×D3—62no—
558C2×D3—61no—
559C2×D3—62no—
560C2×D3—61no—
561C2×D3—61no—
562C2×D3—62no—
563C2×D3—92no—
564C2×D3—181no—
565C2×D3—181no—
566C2×D3—182no—
567C2×D3—181no—
568C2×D3—181no—
569C2×D3—182no—
570C2×D3—182no—
571C2×D3—181no—
572C3×C4—21no—
573C3×C4—22no—
574C3×C4—22no—
575C3×C4—32no—
576C3×C4—32no—
577C3×C4—61no—
578C3×C4—62no—
579C3×C4—62no—
580C3×C4—61no—
581C3×C4—62no—
582C3×C4—62no—
583C3×C4—62no—
584C3×C4—92no—
585C3×C4—121no—
586C3×C4—122no—
587C3×C4—122no—
588C3×C4—181no—
589C3×C4—182no—
590C3×C4C3×D3×D412yes—
591Dic3—32no—
592Dic3—61no—
593Dic3—62no—
594Dic3—92no—
595Dic3—181no—
596Dic3—182no—
597C32—21no—
598C32#562911yescharacteristic, complemented
599C32C3×#53711yescharacteristic, complemented
600C23—91no—
601C23—91no—
602C23—92no—
603C23C22×(C3⋊D3)⋊C311yescharacteristic
604Q8—22no—
605Q8—182no—
606D4—182no—
607D4—184no—
608D4—182no—
609D4—182no—
610D4—182no—
611D4—362no—
612D4—362no—
613C2×C4—22no—
614C2×C4—91no—
615C2×C4—94no—
616C2×C4—92no—
617C2×C4—91no—
618C2×C4—184no—
619C2×C4—182no—
620C2×C4—362no—
621C2×C4C22×(C3⋊D3)⋊C311yescharacteristic
622C2×C4C22×(C3⋊D3)⋊C312yes—
623C2×C4C22×(C3⋊D3)⋊C312yes—
624C2×C4C22×(C3⋊D3)⋊C311yescharacteristic
625C2×C3—31no—
626C2×C3—31no—
627C2×C3—31no—
628C2×C3—31no—
629C2×C3—31no—
630C2×C3—31no—
631C2×C3—41no—
632C2×C3—61no—
633C2×C3—61no—
634C2×C3—61no—
635C2×C3—121no—
636C2×C3—121no—
637C2×C3—122no—
638C2×C3—182no—
639C2×C3—361no—
640C2×C3—362no—
641C2×C3C2×C3×D3×D411yescharacteristic
642C2×C3C3×#100711yescharacteristic
643C2×C3C3×#100911yescharacteristic
644D3—62no—
645D3—122no—
646D3—121no—
647D3—182no—
648D3—362no—
649D3—361no—
650C22—21no—
651C22—21no—
652C22—21no—
653C22—92no—
654C22—181no—
655C22—181no—
656C22—182no—
657C22—181no—
658C22—181no—
659C22—182no—
660C22—181no—
661C22—182no—
662C22C23×(C3⋊D3)⋊C311yescharacteristic
663C4—21no—
664C4—22no—
665C4—22no—
666C4—92no—
667C4—181no—
668C4—182no—
669C4D4×(C3⋊D3)⋊C312yes—
670C3—31no—
671C3—31no—
672C3—61no—
673C3C3×#562911yescharacteristic
674C2—41no—
675C2—182no—
676C2—362no—
677C2—361no—
678C2C2×D4×(C3⋊D3)⋊C311yescharacteristic
679C2#1172262711yescharacteristic
680C2#1172263811yescharacteristic
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×#537
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. C2×#3828⋊C3C2semidirect
3. H(3,𝔽3)×C22⋊Q8C2semidirect
4. #64155⋊C3C2semidirect
5. #64139⋊C3C2semidirect
6. #64105⋊C3C2semidirect
7. #64104⋊C3C2semidirect
8. #64104⋊C3C2semidirect
9. C4⋊C4×(C3⋊D3)⋊C3C2semidirect
10. #64093⋊C3C2semidirect
11. #64093⋊C3C2semidirect
12. #10596100C3semidirect
39. C2×#3832C2×C3semidirect
40. C2×#3828C2×C3semidirect
44. C32×C22⋊Q8D3semidirect
45. C32×C22⋊Q8C2×C3semidirect
46. #64155C2×C3semidirect
47. #64139C2×C3semidirect
48. #64105C2×C3semidirect
49. #64104C2×C3semidirect
50. #64104C2×C3semidirect
51. C4⋊C4×C3⋊D3C2×C3semidirect
52. #64093C2×C3semidirect
53. #64093C2×C3semidirect
85. C4×(C3⋊D3)⋊C3D4semidirect
239. C4×C3⋊D3C3×D4semidirect
396. C22⋊Q8(C3⋊D3)⋊C3semidirect
403. H(3,𝔽3)#537semidirect
598. C32#5629semidirect
599. C32C3×#537semidirect

Maximal subgroups

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

subgroupindex
C2×#887222
C2×#3828⋊C32
H(3,𝔽3)×C22⋊Q82
#64155⋊C32
#64139⋊C32
#64105⋊C32
#64104⋊C32
C4⋊C4×(C3⋊D3)⋊C32
#64093⋊C32
#105961003
C3×#56293