Finite Group Databasebeta

← #13175996

Subgroups — #13175996

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×C4×D3×C3⋊D3C211yesmaximal, characteristic, complemented
2C2×#89017C211yesmaximal, characteristic, complemented
3#11723934C211yesmaximal, characteristic, complemented
4C3×#64103C211yesmaximal, characteristic, complemented
5C32×#896C211yesmaximal, characteristic, complemented
6#11723542C211yesmaximal, characteristic, complemented
7#11723541C211yesmaximal, characteristic, complemented
8#11723514C211yesmaximal, characteristic, complemented
9#11723508C211yesmaximal, characteristic, complemented
10#11723486C211yesmaximal, characteristic, complemented
11#11723477C211yesmaximal, characteristic, complemented
12#11723472C211yesmaximal, characteristic, complemented
13#11723466C211yesmaximal, characteristic, complemented
14#11723462C211yesmaximal, characteristic, complemented
15#11723417C211yesmaximal, characteristic, complemented
16#10596098—31nomaximal
17#10594615—34nomaximal
18C22×D3×C3⋊D3C2211yescharacteristic
19C2×C4⋊(C3⋊(C3⋊D3))C2211yescharacteristic
20C2×C4×C3⋊(C3⋊D3)C2211yescharacteristic
21C2×C4×C3⋊(C3⋊D3)C2211yescharacteristic, complemented
22C2×C3×C4⋊(C3⋊D3)C2211yescharacteristic
23C2×C3×C4×C3⋊D3C2211yescharacteristic
24C2×C32×C4×D3C2211yescharacteristic
25C2×C32×Dic6C2211yescharacteristic, complemented
26C2×#6292C2211yescharacteristic
27C2×#6292C2211yescharacteristic
28C2×#6292C2211yescharacteristic, complemented
29C2×#6291C2211yescharacteristic
30C2×#6290C2211yescharacteristic
31C2×#6289C2211yescharacteristic
32C2×Dic3×C3⋊D3C2211yescharacteristic
33C2×Dic3×C3⋊D3C2211yescharacteristic, complemented
34C2×D3×C3⋊Dic3C2211yescharacteristic
35C4×D3×C3⋊D3—24no—
36#89017—24no—
37C33×C4⋊C4C2211yescharacteristic, complemented
38#88859C2211yescharacteristic
39#88859C2211yescharacteristic, complemented
40C4×C3⋊(C3⋊Dic3)C2211yescharacteristic, complemented
41C3×#3752C2211yescharacteristic
42C3×#3752C2211yescharacteristic, complemented
43C3×#3752C2211yescharacteristic, complemented
44C3×#3750C2211yescharacteristic, complemented
45C32×(C2×D3)⋊C4C2211yescharacteristic
46C32×(C2×D3)⋊C4C2211yescharacteristic
47C32×Dic3⋊C4C2211yescharacteristic, complemented
48C32×Dic3⋊C4C2211yescharacteristic, complemented
49#88806C2211yescharacteristic, complemented
50Dic3⋊(C3⋊Dic3)C2211yescharacteristic, complemented
51#88804C2211yescharacteristic
52#88804C2211yescharacteristic, complemented
53#88803C2211yescharacteristic
54Dic3×C3⋊Dic3C2211yescharacteristic, complemented
55C2×#3832—31no—
56C22×C4×C3⋊D3—31no—
57C2×C4×D32—34no—
58C2×#3796—34no—
59C32×C22⋊Q8—31no—
60#64155—31no—
61#64139—31no—
62#64104—31no—
63#64103—31no—
64#64103D311yescharacteristic, complemented
65#64102—31no—
66#64102—31no—
67#64102—34no—
68#64102—64no—
69#64101—31no—
70#64091—31no—
71#64091—31no—
72#64090—31no—
73#64090—31no—
74C3×#896D314yescomplemented
75C3×#894—34no—
76#63923—34no—
77#63922—34no—
78#63910—34no—
79#63906—34no—
80#63902—34no—
81#63888—34no—
82#63881—34no—
83#63881—34no—
84#63878—34no—
85#63850—34no—
86C22×C3⋊(C3⋊D3)C2311yescharacteristic
87C22×C3⋊(C3⋊D3)C2311yescharacteristic
88C22×C3×C3⋊D3C2311yescharacteristic
89C22×C3×C3⋊D3C2311yescharacteristic
90C22×C32×D3C2311yescharacteristic
91C2×D3×C3⋊D3—22no—
92C2×D3×C3⋊D3—22no—
93C2×D3×C3⋊D3—22no—
94C2×C33×C4C2311yescharacteristic
95C2×C33×C4C2311yescharacteristic
96C2×C33×C4C2311yescharacteristic
97C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
98C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
99C4⋊(C3⋊(C3⋊D3))—22no—
100C4×C3⋊(C3⋊D3)—22no—
101C4×C3⋊(C3⋊D3)—22no—
102C2×C3×C3⋊Dic3C2311yescharacteristic
103C2×C3×C3⋊Dic3C2311yescharacteristic
104C3×C4⋊(C3⋊D3)—22no—
105C3×C4×C3⋊D3—22no—
106C2×C32×Dic3C2311yescharacteristic
107C2×C32×Dic3C2311yescharacteristic
108C2×C32×Dic3C2311yescharacteristic
109C32×C4×D3—22no—
110C32×Dic6—22no—
111#6292—22no—
112#6292—22no—
113#6292—22no—
114#6291—22no—
115#6290—22no—
116#6289—22no—
117Dic3×C3⋊D3—22no—
118Dic3×C3⋊D3D414yescomplemented
119D3×C3⋊Dic3—22no—
120#5656—91no—
121#5627—94no—
122C23×C3⋊D3—31no—
123C22×D32—34no—
124C2×C32×Q8—31no—
125C22×C32×C4—31no—
126C2×#638—31no—
127C2×#638—31no—
128C22×C3⋊Dic3—31no—
129#3832—64no—
130C2×C4⋊(C3⋊D3)—31no—
131C2×C4⋊(C3⋊D3)—31no—
132C2×C4⋊(C3⋊D3)—31no—
133C2×C4⋊(C3⋊D3)—31no—
134C2×C4⋊(C3⋊D3)—34no—
135C2×C4⋊(C3⋊D3)—64no—
136C2×C4⋊(C3⋊D3)C2×D311yescharacteristic
137C2×C4×C3⋊D3—31no—
138C2×C4×C3⋊D3—31no—
139C2×C4×C3⋊D3—31no—
140C2×C4×C3⋊D3—31no—
141C2×C4×C3⋊D3—34no—
142C2×C4×C3⋊D3—34no—
143C2×C4×C3⋊D3—31no—
144C2×C4×C3⋊D3—64no—
145C2×C4×C3⋊D3—64no—
146C2×C4×C3⋊D3—64no—
147C2×C4×C3⋊D3C2×D311yescharacteristic
148C2×C3×D12—34no—
149C2×C3×C4×D3—34no—
150C2×C3×C4×D3C2×D314yes—
151C2×C3×Dic6C2×D314yescomplemented
152C2×#626—34no—
153C2×#626—34no—
154C2×#626—34no—
155C2×#626—34no—
156C2×#625—34no—
157C2×#624—34no—
158C2×D3×Dic3—34no—
159C2×D3×Dic3—34no—
160C2×D3×Dic3—34no—
161C4×D32—616no—
162#3796—616no—
163C32×C4⋊C4—24no—
164C32×C4⋊C4—31no—
165C32×C4⋊C4—31no—
166C32×C4⋊C4C2×D314yescomplemented
167C32×C4⋊C4C2×D311yescharacteristic, complemented
168C32×C22⋊C4—31no—
169C32×C22⋊C4—31no—
170#3752—31no—
171#3752—31no—
172#3752—31no—
173#3752—34no—
174#3752—34no—
175#3752—31no—
176#3752—31no—
177#3752—64no—
178#3752—64no—
179#3752C2×D311yescharacteristic
180#3752C2×D311yescharacteristic, complemented
181#3752C2×D311yescharacteristic, complemented
182C4⋊(C3⋊Dic3)—31no—
183#3750—31no—
184#3750C2×D311yescharacteristic, complemented
185C4×C3⋊Dic3—31no—
186C4×C3⋊Dic3—34no—
187C4×C3⋊Dic3—31no—
188C4×C3⋊Dic3—64no—
189C3×(C2×D3)⋊C4—34no—
190C3×(C2×D3)⋊C4—34no—
191C3×(C2×D3)⋊C4—34no—
192C3×(C2×D3)⋊C4C2×D314yes—
193C3×(C2×D3)⋊C4C2×D314yes—
194C3×Dic3⋊C4—34no—
195C3×Dic3⋊C4C2×D314yescomplemented
196C3×Dic3⋊C4C2×D314yescomplemented
197#3724—34no—
198Dic3⋊Dic3—34no—
199#3722—34no—
200#3722—34no—
201(C2×D3)⋊Dic3—34no—
202Dic32—34no—
203C22×C33C2411yescharacteristic
204C2×C3⋊(C3⋊D3)—21no—
205C2×C3⋊(C3⋊D3)—21no—
206C2×C3⋊(C3⋊D3)—21no—
207C2×C3⋊(C3⋊D3)—21no—
208C2×C3⋊(C3⋊D3)—21no—
209C2×C3⋊(C3⋊D3)#4112yescomplemented
210C2×C3×C3⋊D3—21no—
211C2×C3×C3⋊D3—21no—
212C2×C3×C3⋊D3—21no—
213C2×C3×C3⋊D3—21no—
214C2×C3×C3⋊D3—21no—
215C2×C3×C3⋊D3C2×D412yes—
216C2×C32×D3—21no—
217C2×C32×D3—21no—
218C2×C32×D3#4112yescomplemented
219D3×C3⋊D3—28no—
220C33×C4—21no—
221C33×C4—21no—
222C33×C4—21no—
223C3⋊(C3⋊Dic3)—21no—
224C3⋊(C3⋊Dic3)C2×D412yes—
225C3×C3⋊Dic3—21no—
226C3×C3⋊Dic3—21no—
227C32×Dic3—21no—
228C32×Dic3—21no—
229C32×Dic3C2×D412yes—
230C2×#239—94no—
231C2×#237—91no—
232C22×C4×D3—94no—
233C22×C4×D3—91no—
234C3×#123—91no—
235C3×C22⋊Q8—34no—
236#946—94no—
237#937—91no—
238#930—94no—
239#929—91no—
240#896—91no—
241#896C3⋊D311yescharacteristic, complemented
242#895—94no—
243#894—34no—
244#894—94no—
245#893—94no—
246#893—94no—
247#893—91no—
248#893—91no—
249#893—184no—
250#892—94no—
251#884—91no—
252#884—91no—
253#882—94no—
254#882—94no—
255#882—91no—
256#67⋊C4—94no—
257#67⋊C4—94no—
258#67⋊C4—91no—
259#67⋊C4—91no—
260#877—91no—
261C23×C32—31no—
262C22×C3⋊D3—31no—
263C22×C3⋊D3—31no—
264C22×C3⋊D3—34no—
265C22×C3⋊D3—34no—
266C22×C3⋊D3—64no—
267C22×C3⋊D3—64no—
268C22×C3⋊D3—62no—
269C22×C3⋊D3—62no—
270C22×C3⋊D3—62no—
271C22×C3⋊D3C22×D311yescharacteristic
272C22×C3⋊D3C22×D311yescharacteristic
273C22×C3×D3—34no—
274C22×C3×D3—34no—
275C22×C3×D3C22×D314yes—
276C2×D32—68no—
277C2×D32—68no—
278C2×D32—68no—
279C32×Q8—62no—
280C2×C32×C4—24no—
281C2×C32×C4—24no—
282C2×C32×C4—24no—
283C2×C32×C4—31no—
284C2×C32×C4—31no—
285C2×C32×C4—31no—
286C2×C32×C4—62no—
287C2×C32×C4C22×D314yes—
288C2×C32×C4C22×D314yes—
289C2×C32×C4C22×D314yes—
290C2×C32×C4C22×D311yescharacteristic
291C2×C32×C4C22×D311yescharacteristic
292C2×C32×C4C22×D311yescharacteristic
293#638—62no—
294#638—62no—
295C2×C3⋊Dic3—31no—
296C2×C3⋊Dic3—31no—
297C2×C3⋊Dic3—34no—
298C2×C3⋊Dic3—34no—
299C2×C3⋊Dic3—64no—
300C2×C3⋊Dic3—64no—
301C2×C3⋊Dic3—62no—
302C2×C3⋊Dic3C22×D311yescharacteristic
303C2×C3⋊Dic3C22×D311yescharacteristic
304C4⋊(C3⋊D3)—22no—
305C4⋊(C3⋊D3)—62no—
306C4⋊(C3⋊D3)—68no—
307C4⋊(C3⋊D3)—616no—
308C4⋊(C3⋊D3)—62no—
309C4⋊(C3⋊D3)—62no—
310C4⋊(C3⋊D3)—62no—
311C4×C3⋊D3—22no—
312C4×C3⋊D3—34no—
313C4×C3⋊D3—62no—
314C4×C3⋊D3—62no—
315C4×C3⋊D3—62no—
316C4×C3⋊D3—62no—
317C4×C3⋊D3—68no—
318C4×C3⋊D3—68no—
319C4×C3⋊D3—128no—
320C4×C3⋊D3—128no—
321C2×C3×Dic3—34no—
322C2×C3×Dic3—34no—
323C2×C3×Dic3C22×D314yes—
324C2×C3×Dic3C22×D314yes—
325C2×C3×Dic3C22×D314yes—
326C3×D12—68no—
327C3×C4×D3—28no—
328C3×C4×D3—68no—
329C3×Dic6—28no—
330#626—68no—
331#626—68no—
332#626—68no—
333#626—68no—
334#625—68no—
335#624—68no—
336D3×Dic3—316no—
337D3×Dic3—68no—
338D3×Dic3—68no—
339#525—271noSylow
340C2×C33C22×D411yescharacteristic
341C2×C33C2×#4111yescharacteristic
342C2×C33C2×#4111yescharacteristic
343C3⋊(C3⋊D3)—22no—
344C3⋊(C3⋊D3)—41no—
345C3×C3⋊D3—22no—
346C3×C3⋊D3—41no—
347C32×D3—22no—
348C23×D3—94no—
349C23×D3—91no—
350C2×C3×Q8—34no—
351C2×C3×D4—91no—
352C22×C3×C4—34no—
353C22×C3×C4—91no—
354C2×#67—94no—
355C2×#67—94no—
356C2×#67—91no—
357C2×#67—91no—
358C2×#67—91no—
359C2×#67—91no—
360C22×Dic3—94no—
361C22×Dic3—91no—
362C22×Dic3—91no—
363#239—1816no—
364#237—184no—
365C2×D12—34no—
366C2×D12—94no—
367C2×D12—94no—
368C2×D12—94no—
369C2×D12—91no—
370C2×D12—94no—
371C2×D12—91no—
372C2×D12—184no—
373C2×C4×D3—34no—
374C2×C4×D3—94no—
375C2×C4×D3—94no—
376C2×C4×D3—94no—
377C2×C4×D3—91no—
378C2×C4×D3—94no—
379C2×C4×D3—94no—
380C2×C4×D3—91no—
381C2×C4×D3—91no—
382C2×C4×D3—91no—
383C2×C4×D3—184no—
384C2×C4×D3—184no—
385C2×C4×D3—184no—
386C2×C4×D3—1816no—
387C2×C4×D3C2×C3⋊D311yescharacteristic
388C2×Dic6C2×C3⋊D311yescharacteristic, complemented
389C3×C4⋊C4—24no—
390C3×C4⋊C4—34no—
391C3×C4⋊C4—34no—
392C3×C4⋊C4—91no—
393C3×C4⋊C4D3214yescomplemented
394C3×C4⋊C4C2×C3⋊D311yescharacteristic, complemented
395C3×C22⋊C4—34no—
396C3×C22⋊C4—34no—
397C3×C22⋊C4—91no—
398C3×C22⋊C4—91no—
399C3×C22⋊C4—91no—
400#217—91no—
401(C2×D3)⋊C4—34no—
402(C2×D3)⋊C4—34no—
403(C2×D3)⋊C4—34no—
404(C2×D3)⋊C4—94no—
405(C2×D3)⋊C4—94no—
406(C2×D3)⋊C4—94no—
407(C2×D3)⋊C4—94no—
408(C2×D3)⋊C4—94no—
409(C2×D3)⋊C4—91no—
410(C2×D3)⋊C4—91no—
411(C2×D3)⋊C4—91no—
412(C2×D3)⋊C4—91no—
413(C2×D3)⋊C4—184no—
414(C2×D3)⋊C4—184no—
415(C2×D3)⋊C4C2×C3⋊D311yescharacteristic
416(C2×D3)⋊C4C2×C3⋊D311yescharacteristic
417C4⋊Dic3—94no—
418Dic3⋊C4—34no—
419Dic3⋊C4—94no—
420Dic3⋊C4—91no—
421Dic3⋊C4—91no—
422Dic3⋊C4C2×C3⋊D311yescharacteristic, complemented
423Dic3⋊C4C2×C3⋊D311yescharacteristic, complemented
424C4×Dic3—94no—
425C4×Dic3—94no—
426C4×Dic3—91no—
427C4×Dic3—91no—
428C4×Dic3—184no—
429C22×C32—24no—
430C22×C32—32no—
431C22×C32—61no—
432C22×C32—61no—
433C22×C32C23×D314yes—
434C22×C32C23×D311yescharacteristic
435C2×C3⋊D3—21no—
436C2×C3⋊D3—21no—
437C2×C3⋊D3—21no—
438C2×C3⋊D3—21no—
439C2×C3⋊D3—21no—
440C2×C3⋊D3—32no—
441C2×C3⋊D3—38no—
442C2×C3⋊D3—68no—
443C2×C3⋊D3—68no—
444C2×C3⋊D3—61no—
445C2×C3⋊D3—61no—
446C2×C3⋊D3—68no—
447C2×C3⋊D3—61no—
448C2×C3⋊D3—64no—
449C2×C3⋊D3—61no—
450C2×C3⋊D3—61no—
451C2×C3⋊D3—64no—
452C2×C3⋊D3—64no—
453C2×C3⋊D3—64no—
454C2×C3⋊D3—64no—
455C2×C3⋊D3—124no—
456C2×C3⋊D3—124no—
457C2×C3⋊D3—124no—
458C2×C3⋊D3—124no—
459C2×C3⋊D3D3×D412yes—
460C2×C3×D3—24no—
461C2×C3×D3—24no—
462C2×C3×D3—38no—
463C2×C3×D3—64no—
464C2×C3×D3—64no—
465C2×C3×D3—64no—
466C2×C3×D3—64no—
467C2×C3×D3—64no—
468C2×C3×D3#23918yescomplemented
469D32—632no—
470C32×C4—28no—
471C32×C4—21no—
472C32×C4—21no—
473C32×C4—24no—
474C32×C4—21no—
475C32×C4—24no—
476C32×C4—24no—
477C32×C4—32no—
478C32×C4—44no—
479C32×C4—44no—
480C32×C4—61no—
481C32×C4—61no—
482C3⋊Dic3—21no—
483C3⋊Dic3—21no—
484C3⋊Dic3—32no—
485C3⋊Dic3—38no—
486C3⋊Dic3—68no—
487C3⋊Dic3—61no—
488C3⋊Dic3—64no—
489C3⋊Dic3—124no—
490C3×Dic3—24no—
491C3×Dic3—24no—
492C3×Dic3—64no—
493C3×Dic3—64no—
494C3×Dic3D3×D418yes—
495C2×#41—271no—
496C23×C4—271no—
497#123—91no—
498#123—271no—
499C22⋊Q8—31no—
500C22⋊Q8—271no—
501#121—271no—
502#121—271no—
503#120—271no—
504#120—271no—
505C4×D4—271no—
506C4×D4—271no—
507C4×D4—271no—
508C4×D4—271no—
509#117—271no—
510C33#52511yescharacteristic, complemented, Sylow
511C23×C3—34no—
512C23×C3—91no—
513C23×C3—91no—
514C22×D3—34no—
515C22×D3—34no—
516C22×D3—94no—
517C22×D3—91no—
518C22×D3—94no—
519C22×D3—91no—
520C22×D3—184no—
521C22×D3—184no—
522C22×D3—182no—
523C22×D3—182no—
524C22×D3—188no—
525C22×D3—188no—
526C22×D3—188no—
527C22×D3—182no—
528C22×D3C22×C3⋊D311yescharacteristic
529C3×Q8—68no—
530C3×D4—182no—
531C2×C3×C4—24no—
532C2×C3×C4—24no—
533C2×C3×C4—24no—
534C2×C3×C4—34no—
535C2×C3×C4—34no—
536C2×C3×C4—34no—
537C2×C3×C4—68no—
538C2×C3×C4—91no—
539C2×C3×C4—91no—
540C2×C3×C4—182no—
541C2×C3×C4C2×D3214yes—
542C2×C3×C4C2×D3214yes—
543C2×C3×C4C2×D3214yes—
544C2×C3×C4C22×C3⋊D311yescharacteristic
545C2×C3×C4C22×C3⋊D311yescharacteristic
546C2×C3×C4C22×C3⋊D311yescharacteristic
547#67—182no—
548#67—182no—
549#67—188no—
550#67—188no—
551#67—182no—
552#67—182no—
553C2×Dic3—34no—
554C2×Dic3—34no—
555C2×Dic3—94no—
556C2×Dic3—91no—
557C2×Dic3—94no—
558C2×Dic3—94no—
559C2×Dic3—91no—
560C2×Dic3—184no—
561C2×Dic3—184no—
562C2×Dic3—182no—
563C2×Dic3—188no—
564C2×Dic3C22×C3⋊D311yescharacteristic
565C2×Dic3C22×C3⋊D311yescharacteristic
566C2×Dic3C22×C3⋊D311yescharacteristic
567D12—68no—
568D12—188no—
569D12—182no—
570D12—1816no—
571D12—188no—
572D12—188no—
573D12—188no—
574D12—182no—
575C4×D3—22no—
576C4×D3—68no—
577C4×D3—916no—
578C4×D3—188no—
579C4×D3—182no—
580C4×D3—182no—
581C4×D3—188no—
582C4×D3—188no—
583C4×D3—188no—
584C4×D3—182no—
585C4×D3—182no—
586C4×D3—368no—
587C4×D3—368no—
588Dic6—22no—
589C2×C32—24no—
590C2×C32—24no—
591C2×C32—24no—
592C2×C32—62no—
593C2×C32C2×D3×D414yes—
594C2×C32C2×D3×D411yescharacteristic
595C2×C32C2×#23914yes—
596C2×C32D3×#4114yes—
597C2×C32D3×#4111yescharacteristic
598C2×C32D3×#4111yescharacteristic
599C3⋊D3—22no—
600C3⋊D3—41no—
601C3⋊D3—62no—
602C3⋊D3—68no—
603C3⋊D3—128no—
604C3⋊D3—128no—
605C3⋊D3—121no—
606C3⋊D3—124no—
607C3×D3—28no—
608C3×D3—68no—
609C3×D3—124no—
610C24—271no—
611#41—544no—
612C2×Q8—31no—
613C2×D4—91no—
614C2×D4—271no—
615C2×D4—271no—
616C2×D4—271no—
617C2×D4—271no—
618C2×D4—271no—
619C2×D4—271no—
620C22×C4—31no—
621C22×C4—91no—
622C22×C4—271no—
623C22×C4—271no—
624C22×C4—271no—
625C22×C4—271no—
626C22×C4—271no—
627C22×C4—271no—
628C22×C4—544no—
629C4⋊C4—31no—
630C4⋊C4—31no—
631C4⋊C4—91no—
632C4⋊C4—271no—
633C4⋊C4—271no—
634C4⋊C4D3×C3⋊D311yescharacteristic, complemented
635C22⋊C4—31no—
636C22⋊C4—31no—
637C22⋊C4—91no—
638C22⋊C4—91no—
639C22⋊C4—91no—
640C22⋊C4—271no—
641C22⋊C4—271no—
642C22⋊C4—271no—
643C22⋊C4—271no—
644C22⋊C4—271no—
645C42—271no—
646C42—271no—
647C22×C3—24no—
648C22×C3—38no—
649C22×C3—64no—
650C22×C3—64no—
651C22×C3—92no—
652C22×C3—181no—
653C22×C3—181no—
654C22×C3—181no—
655C22×C3—181no—
656C22×C3—181no—
657C22×C3C22×D3214yes—
658C22×C3C23×C3⋊D311yescharacteristic
659C2×D3—21no—
660C2×D3—21no—
661C2×D3—38no—
662C2×D3—64no—
663C2×D3—64no—
664C2×D3—64no—
665C2×D3—64no—
666C2×D3—64no—
667C2×D3—98no—
668C2×D3—92no—
669C2×D3—188no—
670C2×D3—188no—
671C2×D3—1832no—
672C2×D3—184no—
673C2×D3—184no—
674C2×D3—181no—
675C2×D3—181no—
676C2×D3—188no—
677C2×D3—184no—
678C2×D3—184no—
679C2×D3—184no—
680C2×D3—181no—
681C2×D3—181no—
682C2×D3—181no—
683C2×D3—364no—
684C2×D3—364no—
685C2×D3—364no—
686C2×D3—364no—
687C2×D3#383212yescomplemented
688C3×C4—28no—
689C3×C4—24no—
690C3×C4—24no—
691C3×C4—24no—
692C3×C4—21no—
693C3×C4—21no—
694C3×C4—21no—
695C3×C4—38no—
696C3×C4—44no—
697C3×C4—44no—
698C3×C4—64no—
699C3×C4—64no—
700C3×C4—181no—
701C3×C4—181no—
702Dic3—21no—
703Dic3—21no—
704Dic3—64no—
705Dic3—64no—
706Dic3—98no—
707Dic3—92no—
708Dic3—188no—
709Dic3—184no—
710Dic3—181no—
711Dic3—364no—
712Dic3D4×C3⋊D312yes—
713C32—24no—
714C32#562714yescomplemented
715C32#565611yescharacteristic, complemented
716C23—31no—
717C23—91no—
718C23—91no—
719C23—271no—
720C23—271no—
721C23—542no—
722C23—542no—
723C23—542no—
724Q8—62no—
725D4—182no—
726D4—542no—
727D4—542no—
728D4—542no—
729D4—542no—
730D4—542no—
731D4—542no—
732C2×C4—31no—
733C2×C4—31no—
734C2×C4—31no—
735C2×C4—62no—
736C2×C4—91no—
737C2×C4—91no—
738C2×C4—182no—
739C2×C4—274no—
740C2×C4—271no—
741C2×C4—271no—
742C2×C4—542no—
743C2×C4—542no—
744C2×C4—542no—
745C2×C4—542no—
746C2×C4—542no—
747C2×C4C2×D3×C3⋊D311yescharacteristic
748C2×C4C2×D3×C3⋊D311yescharacteristic
749C2×C4C2×D3×C3⋊D311yescharacteristic
750C2×C3—24no—
751C2×C3—24no—
752C2×C3—24no—
753C2×C3—68no—
754C2×C3—182no—
755C2×C3—361no—
756C2×C3#6430614yes—
757C2×C3D32×D414yes—
758C2×C3D3×#23914yes—
759C2×C3C2×D4×C3⋊D311yescharacteristic
760C2×C3C2×#383211yescharacteristic
761C2×C3#41×C3⋊D311yescharacteristic
762D3—22no—
763D3—68no—
764D3—124no—
765D3—182no—
766D3—188no—
767D3—368no—
768D3—368no—
769D3—361no—
770D3—364no—
771C22—32no—
772C22—61no—
773C22—61no—
774C22—92no—
775C22—181no—
776C22—181no—
777C22—181no—
778C22—181no—
779C22—181no—
780C22—272no—
781C22—548no—
782C22—541no—
783C22—541no—
784C22—541no—
785C22—541no—
786C22—541no—
787C22C22×D3×C3⋊D311yescharacteristic
788C4—21no—
789C4—21no—
790C4—21no—
791C4—32no—
792C4—61no—
793C4—61no—
794C4—181no—
795C4—181no—
796C4—272no—
797C4—541no—
798C3—24no—
799C3#1059461514yescomplemented
800C3#1059609811yescharacteristic, complemented
801C2—62no—
802C2—182no—
803C2—361no—
804C2—542no—
805C2—1081no—
806C2#1172457811yescharacteristic
807C2D3×D4×C3⋊D311yescharacteristic
808C2D3×#383211yescharacteristic
subgroupG/H
center, FrattiniC22C22×D3×C3⋊D3
commutator, socle, cosocleC22×C33C24
FittingC33×C4⋊C4C22
hypercenterC4⋊C4D3×C3⋊D3
hypocenterC33#525
LCSG ▷ C22×C33 ▷ C33
UCSC1 ◁ C22 ◁ C4⋊C4

Complements

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

NH ≅ G/Ntype
1. C2×C4×D3×C3⋊D3C2semidirect
2. C2×#89017C2semidirect
3. #11723934C2semidirect
4. C3×#64103C2semidirect
5. C32×#896C2semidirect
6. #11723542C2semidirect
7. #11723541C2semidirect
8. #11723514C2semidirect
9. #11723508C2semidirect
10. #11723486C2semidirect
11. #11723477C2semidirect
12. #11723472C2semidirect
13. #11723466C2semidirect
14. #11723462C2semidirect
15. #11723417C2semidirect
21. C2×C4×C3⋊(C3⋊D3)C22semidirect
25. C2×C32×Dic6C22semidirect
28. C2×#6292C22semidirect
33. C2×Dic3×C3⋊D3C22semidirect
37. C33×C4⋊C4C22semidirect
39. #88859C22semidirect
40. C4×C3⋊(C3⋊Dic3)C22semidirect
42. C3×#3752C22semidirect
43. C3×#3752C22semidirect
44. C3×#3750C22semidirect
47. C32×Dic3⋊C4C22semidirect
48. C32×Dic3⋊C4C22semidirect
49. #88806C22semidirect
50. Dic3⋊(C3⋊Dic3)C22semidirect
52. #88804C22semidirect
54. Dic3×C3⋊Dic3C22semidirect
64. #64103D3semidirect
74. C3×#896D3semidirect
118. Dic3×C3⋊D3D4semidirect
151. C2×C3×Dic6C2×D3semidirect
166. C32×C4⋊C4C2×D3semidirect
167. C32×C4⋊C4C2×D3semidirect
180. #3752C2×D3semidirect
181. #3752C2×D3semidirect
184. #3750C2×D3semidirect
195. C3×Dic3⋊C4C2×D3semidirect
196. C3×Dic3⋊C4C2×D3semidirect
209. C2×C3⋊(C3⋊D3)#41semidirect
218. C2×C32×D3#41semidirect
241. #896C3⋊D3semidirect
388. C2×Dic6C2×C3⋊D3semidirect
393. C3×C4⋊C4D32semidirect
394. C3×C4⋊C4C2×C3⋊D3semidirect
422. Dic3⋊C4C2×C3⋊D3semidirect
423. Dic3⋊C4C2×C3⋊D3semidirect
468. C2×C3×D3#239semidirect
510. C33#525semidirect
634. C4⋊C4D3×C3⋊D3semidirect
687. C2×D3#3832semidirect
714. C32#5627semidirect
715. C32#5656semidirect
799. C3#10594615semidirect
800. C3#10596098semidirect

Maximal subgroups

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

subgroupindex
C2×C4×D3×C3⋊D32
C2×#890172
#117239342
C3×#641032
C32×#8962
#117235422
#117235412
#117235142
#117235082
#117234862
#117234772
#117234722
#117234662
#117234622
#117234172
#105960983
#105946153