Finite Group Databasebeta

← #13175933

Subgroups — #13175933

Order 1728.

2524 conjugacy classes of subgroups.

The subgroup lattice has 872 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#89039C211yesmaximal, characteristic, complemented
2C2×#89031C211yesmaximal, characteristic, complemented
3#11723923C211yesmaximal, characteristic, complemented
4C3×#64090C211yesmaximal, characteristic, complemented
5C32×#886C211yesmaximal, characteristic, complemented
6#11723635C211yesmaximal, characteristic, complemented
7C2×#88804C211yesmaximal, characteristic, complemented
8#11723542C211yesmaximal, characteristic, complemented
9C3⋊D3×(C2×D3)⋊C4C211yesmaximal, characteristic, complemented
10#11723526C211yesmaximal, characteristic, complemented
11#11723525C211yesmaximal, characteristic, complemented
12#11723495C211yesmaximal, characteristic, complemented
13#11723494C211yesmaximal, characteristic, complemented
14#11723493C211yesmaximal, characteristic, complemented
15#11723419C211yesmaximal, characteristic, complemented
16#10596125—31nomaximal
17#10594293—34nomaximal
18C23×C3⋊(C3⋊D3)C2211yescharacteristic
19C22×D3×C3⋊D3C2211yescharacteristic
20C2×#6312C2211yescharacteristic, complemented
21C2×C4⋊(C3⋊(C3⋊D3))C2211yescharacteristic
22C2×C4⋊(C3⋊(C3⋊D3))C2211yescharacteristic, complemented
23C2×C3×#638C2211yescharacteristic
24C22×C3×C3⋊Dic3C2211yescharacteristic, complemented
25C2×C3×C4×C3⋊D3C2211yescharacteristic, complemented
26C2×C32×#67C2211yescharacteristic
27C22×C32×Dic3C2211yescharacteristic, complemented
28#89039—24no—
29C2×#6293C2211yescharacteristic, complemented
30C2×#6292C2211yescharacteristic
31C2×#6292C2211yescharacteristic, complemented
32C2×#6291C2211yescharacteristic
33C2×#6291C2211yescharacteristic, complemented
34C2×#6289C2211yescharacteristic
35C2×#6289C2211yescharacteristic, complemented
36#89031—24no—
37C2×Dic3×C3⋊D3C2211yescharacteristic, complemented
38C33×C22⋊C4C2211yescharacteristic, complemented
39#88859C2211yescharacteristic
40#88859C2211yescharacteristic, complemented
41C3×#3752C2211yescharacteristic, complemented
42C3×#3750C2211yescharacteristic, complemented
43C3×C4×C3⋊Dic3C2211yescharacteristic, complemented
44C32×(C2×D3)⋊C4C2211yescharacteristic, complemented
45C32×(C2×D3)⋊C4C2211yescharacteristic, complemented
46C32×C4⋊Dic3C2211yescharacteristic, complemented
47C32×C4⋊Dic3C2211yescharacteristic, complemented
48#88807C2211yescharacteristic, complemented
49#88804C2211yescharacteristic
50#88804C2211yescharacteristic
51#88804C2211yescharacteristic, complemented
52#88804C2211yescharacteristic, complemented
53#88804C2211yescharacteristic, complemented
54(C2×D3)⋊(C3⋊Dic3)C2211yescharacteristic, complemented
55C2×D4×C3⋊D3—31no—
56C2×#3828—31no—
57C2×#3811—34no—
58C2×#3804—34no—
59C32×#123—31no—
60#64148—31no—
61C2×#3752—31no—
62#64105—31no—
63#64104—31no—
64#64103—31no—
65#64102—31no—
66#64094—31no—
67#64093—31no—
68#64091—31no—
69#64091—31no—
70#64091—34no—
71#64091—64no—
72#64090D311yescharacteristic, complemented
73C22⋊C4×C3⋊D3—31no—
74C3×#886D314yescomplemented
75C3×#67⋊C4—34no—
76#63978—34no—
77C2×#3722—34no—
78#63923—34no—
79D3×(C2×D3)⋊C4—34no—
80#63910—34no—
81#63909—34no—
82#63895—34no—
83#63894—34no—
84#63890—34no—
85#63852—34no—
86C23×C33C2311yescharacteristic
87C22×C3⋊(C3⋊D3)—22no—
88C22×C3⋊(C3⋊D3)—22no—
89C22×C3⋊(C3⋊D3)—41no—
90C22×C3⋊(C3⋊D3)C2311yescharacteristic
91C22×C3⋊(C3⋊D3)C2311yescharacteristic
92C22×C3⋊(C3⋊D3)C2311yescharacteristic
93C22×C3×C3⋊D3C2311yescharacteristic
94C22×C32×D3C2311yescharacteristic
95C2×D3×C3⋊D3—22no—
96C2×D3×C3⋊D3—22no—
97C2×D3×C3⋊D3—41no—
98C2×C33×C4C2311yescharacteristic
99C2×C33×C4C2311yescharacteristic
100#6312—22no—
101C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
102C4⋊(C3⋊(C3⋊D3))—22no—
103C4⋊(C3⋊(C3⋊D3))—41no—
104C3×#638D414yescomplemented
105C2×C3×C3⋊Dic3—41no—
106C2×C3×C3⋊Dic3C2311yescharacteristic
107C2×C3×C3⋊Dic3C2311yescharacteristic
108C2×C3×C3⋊Dic3C2311yescharacteristic
109C3×C4×C3⋊D3—41no—
110C32×#67—22no—
111C2×C32×Dic3—22no—
112C2×C32×Dic3C2311yescharacteristic
113C2×C32×Dic3C2311yescharacteristic
114C2×C32×Dic3C2311yescharacteristic
115#6293—22no—
116#6292—22no—
117#6292—22no—
118#6291—22no—
119#6291—41no—
120#6289—22no—
121#6289—22no—
122Dic3×C3⋊D3—22no—
123#5654—94no—
124#5554—91no—
125C23×C3⋊D3—31no—
126C23×C3⋊D3—34no—
127C23×C3⋊D3—31no—
128C23×C3⋊D3—64no—
129C22×D32—34no—
130C2×C32×D4—31no—
131C22×C32×C4—31no—
132C2×#638—31no—
133C2×#638—34no—
134C2×#638—31no—
135C2×#638—31no—
136C2×#638—64no—
137C2×#638C2×D311yescharacteristic
138C22×C3⋊Dic3C2×D311yescharacteristic, complemented
139D4×C3⋊D3—64no—
140#3828—64no—
141C2×C4⋊(C3⋊D3)—31no—
142C2×C4⋊(C3⋊D3)—31no—
143C2×C4⋊(C3⋊D3)—31no—
144C2×C4⋊(C3⋊D3)—34no—
145C2×C4⋊(C3⋊D3)—31no—
146C2×C4⋊(C3⋊D3)—34no—
147C2×C4⋊(C3⋊D3)—64no—
148C2×C4⋊(C3⋊D3)—64no—
149C2×C4×C3⋊D3—31no—
150C2×C4×C3⋊D3—31no—
151C2×C4×C3⋊D3—31no—
152C2×C4×C3⋊D3C2×D311yescharacteristic, complemented
153C2×#634—31no—
154C2×C3×#67—34no—
155C2×C3×#67C2×D314yes—
156C22×C3×Dic3—34no—
157C22×C3×Dic3C2×D314yescomplemented
158C2×C3×C4×D3—34no—
159#3811—616no—
160C2×#627—34no—
161C2×#626—34no—
162C2×#626—34no—
163C2×#626—34no—
164C2×#626—34no—
165C2×#624—34no—
166C2×#624—34no—
167#3804—616no—
168C2×D3×Dic3—34no—
169C32×C4⋊C4—31no—
170C32×C4⋊C4—31no—
171C32×C22⋊C4—24no—
172C32×C22⋊C4—31no—
173C32×C22⋊C4—31no—
174C32×C22⋊C4C2×D314yescomplemented
175C32×C22⋊C4C2×D311yescharacteristic, complemented
176#3757—31no—
177#3752—31no—
178#3752—31no—
179#3752—34no—
180#3752—34no—
181#3752—31no—
182#3752—31no—
183#3752—31no—
184#3752—31no—
185#3752—31no—
186#3752—64no—
187#3752—64no—
188#3752C2×D311yescharacteristic, complemented
189#3750—31no—
190#3750C2×D311yescharacteristic, complemented
191C4×C3⋊Dic3C2×D311yescharacteristic, complemented
192C3×(C2×D3)⋊C4—34no—
193C3×(C2×D3)⋊C4C2×D314yescomplemented
194C3×(C2×D3)⋊C4C2×D314yescomplemented
195C3×C4⋊Dic3C2×D314yescomplemented
196C3×C4⋊Dic3C2×D314yescomplemented
197C3×Dic3⋊C4—34no—
198C3×C4×Dic3—34no—
199Dic3⋊Dic3—34no—
200#3722—34no—
201#3722—34no—
202#3722—34no—
203#3722—34no—
204#3722—34no—
205(C2×D3)⋊Dic3—34no—
206C22×C33—21no—
207C22×C33—21no—
208C22×C33C2×D412yes—
209C22×C33C2411yescharacteristic
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⋊D3)—21no—
216C2×C3⋊(C3⋊D3)—21no—
217C2×C3⋊(C3⋊D3)—21no—
218C2×C3⋊(C3⋊D3)—44no—
219C2×C3⋊(C3⋊D3)#4112yescomplemented
220C2×C3×C3⋊D3—21no—
221C2×C3×C3⋊D3—21no—
222C2×C3×C3⋊D3C2×D412yes—
223C2×C32×D3—21no—
224C2×C32×D3—21no—
225C2×C32×D3—21no—
226D3×C3⋊D3—44no—
227C33×C4—21no—
228C33×C4—21no—
229C3⋊(C3⋊Dic3)—21no—
230C3×C3⋊Dic3—21no—
231C3×C3⋊Dic3—21no—
232C3×C3⋊Dic3C2×D412yes—
233C32×Dic3—21no—
234C32×Dic3—21no—
235C32×Dic3—21no—
236C2×#237—91no—
237C2×D3×D4—94no—
238C2×D3×D4—91no—
239C2×#235—94no—
240C3×#123—34no—
241C3×C4×D4—91no—
242#939—94no—
243#930—91no—
244#930—91no—
245C2×(C2×D3)⋊C4—94no—
246C2×(C2×D3)⋊C4—91no—
247C2×(C2×D3)⋊C4—91no—
248#897—91no—
249#896—94no—
250#895—94no—
251#895—91no—
252#894—94no—
253#893—94no—
254#886—91no—
255#886C3⋊D311yescharacteristic, complemented
256#885—94no—
257#884—94no—
258#882—94no—
259#882—94no—
260#882—91no—
261#882—91no—
262#882—184no—
263#67⋊C4—34no—
264D3×C22⋊C4—94no—
265#875—91no—
266C4×D12—91no—
267C23×C32—24no—
268C23×C32—31no—
269C23×C32C22×D314yes—
270C23×C32C22×D311yescharacteristic
271C22×C3⋊D3—31no—
272C22×C3⋊D3—31no—
273C22×C3⋊D3—31no—
274C22×C3⋊D3—34no—
275C22×C3⋊D3—34no—
276C22×C3⋊D3—34no—
277C22×C3⋊D3—64no—
278C22×C3⋊D3—64no—
279C22×C3⋊D3—64no—
280C22×C3⋊D3—62no—
281C22×C3⋊D3—62no—
282C22×C3⋊D3—62no—
283C22×C3⋊D3—62no—
284C22×C3⋊D3—68no—
285C22×C3⋊D3—68no—
286C22×C3⋊D3—128no—
287C22×C3⋊D3—128no—
288C22×C3⋊D3—121no—
289C22×C3⋊D3—121no—
290C22×C3⋊D3—124no—
291C22×C3⋊D3—128no—
292C22×C3⋊D3C22×D311yescharacteristic
293C22×C3×D3—34no—
294C22×C3×D3C22×D314yes—
295C2×D32—68no—
296C2×D32—68no—
297C2×D32—124no—
298C32×D4—62no—
299C2×C32×C4—24no—
300C2×C32×C4—24no—
301C2×C32×C4—31no—
302C2×C32×C4—31no—
303C2×C32×C4—31no—
304C2×C32×C4—62no—
305C2×C32×C4C22×D314yes—
306C2×C32×C4C22×D314yes—
307C2×C32×C4C22×D311yescharacteristic
308C2×C32×C4C22×D311yescharacteristic
309#638—62no—
310#638—62no—
311#638—68no—
312#638—128no—
313#638—121no—
314#638D1214yescomplemented
315C2×C3⋊Dic3—31no—
316C2×C3⋊Dic3—34no—
317C2×C3⋊Dic3—41no—
318C2×C3⋊Dic3—64no—
319C2×C3⋊Dic3C22×D311yescharacteristic
320C2×C3⋊Dic3C22×D311yescharacteristic
321C2×C3⋊Dic3C22×D311yescharacteristic
322C4⋊(C3⋊D3)—62no—
323C4⋊(C3⋊D3)—62no—
324C4⋊(C3⋊D3)—62no—
325C4⋊(C3⋊D3)—68no—
326C4⋊(C3⋊D3)—128no—
327C4⋊(C3⋊D3)—121no—
328C4⋊(C3⋊D3)—124no—
329C4⋊(C3⋊D3)—128no—
330C4×C3⋊D3—41no—
331C4×C3⋊D3—62no—
332C4×C3⋊D3—62no—
333C4×C3⋊D3—62no—
334#634—62no—
335C3×#67—28no—
336C3×#67—316no—
337C2×C3×Dic3—28no—
338C2×C3×Dic3—34no—
339C2×C3×Dic3—34no—
340C2×C3×Dic3—34no—
341C2×C3×Dic3—124no—
342C2×C3×Dic3C22×D314yes—
343C2×C3×Dic3C22×D314yes—
344C2×C3×Dic3C22×D314yes—
345C3×C4×D3—124no—
346#627—68no—
347#626—68no—
348#626—68no—
349#626—68no—
350#626—124no—
351#624—68no—
352#624—68no—
353D3×Dic3—68no—
354#546—271noSylow
355C2×C33—22no—
356C2×C33C22×D411yescharacteristic
357C2×C33C2×#4111yescharacteristic
358C2×C33H(5,𝔽2)11yescharacteristic
359C3⋊(C3⋊D3)—22no—
360C3⋊(C3⋊D3)—41no—
361C3⋊(C3⋊D3)—41no—
362C3×C3⋊D3—22no—
363C32×D3—41no—
364C23×D3—94no—
365C23×D3—94no—
366C23×D3—91no—
367C23×D3—91no—
368C23×D3—184no—
369C2×C3×D4—34no—
370C2×C3×D4—91no—
371C22×C3×C4—34no—
372C22×C3×C4—91no—
373C22×C3×C4—91no—
374C2×#67—34no—
375C2×#67—94no—
376C2×#67—94no—
377C2×#67—94no—
378C2×#67—91no—
379C2×#67—91no—
380C2×#67—91no—
381C2×#67—184no—
382C2×#67C2×C3⋊D311yescharacteristic
383C22×Dic3—34no—
384C22×Dic3—91no—
385C22×Dic3C2×C3⋊D311yescharacteristic, complemented
386#237—184no—
387D3×D4—184no—
388D3×D4—1816no—
389#235—1816no—
390C2×D12—94no—
391C2×D12—94no—
392C2×D12—91no—
393C2×D12—94no—
394C2×D12—91no—
395C2×D12—91no—
396C2×D12—94no—
397C2×D12—91no—
398C2×D12—184no—
399C2×D12—184no—
400C2×C4×D3—34no—
401C2×C4×D3—94no—
402C2×C4×D3—94no—
403C2×C4×D3—94no—
404C2×C4×D3—91no—
405C2×C4×D3—91no—
406C2×Dic6—94no—
407C2×Dic6—91no—
408C3×C4⋊C4—34no—
409C3×C4⋊C4—34no—
410C3×C4⋊C4—91no—
411C3×C22⋊C4—24no—
412C3×C22⋊C4—34no—
413C3×C22⋊C4—34no—
414C3×C22⋊C4—91no—
415C3×C22⋊C4D3214yescomplemented
416C3×C22⋊C4C2×C3⋊D311yescharacteristic, complemented
417C3×C42—91no—
418#217—94no—
419(C2×D3)⋊C4—34no—
420(C2×D3)⋊C4—94no—
421(C2×D3)⋊C4—94no—
422(C2×D3)⋊C4—94no—
423(C2×D3)⋊C4—94no—
424(C2×D3)⋊C4—94no—
425(C2×D3)⋊C4—91no—
426(C2×D3)⋊C4—94no—
427(C2×D3)⋊C4—94no—
428(C2×D3)⋊C4—91no—
429(C2×D3)⋊C4—91no—
430(C2×D3)⋊C4—91no—
431(C2×D3)⋊C4—91no—
432(C2×D3)⋊C4—91no—
433(C2×D3)⋊C4—91no—
434(C2×D3)⋊C4—91no—
435(C2×D3)⋊C4—184no—
436(C2×D3)⋊C4—184no—
437(C2×D3)⋊C4C2×C3⋊D311yescharacteristic, complemented
438(C2×D3)⋊C4C2×C3⋊D311yescharacteristic, complemented
439C4⋊Dic3—91no—
440C4⋊Dic3C2×C3⋊D311yescharacteristic, complemented
441C4⋊Dic3C2×C3⋊D311yescharacteristic, complemented
442Dic3⋊C4—34no—
443Dic3⋊C4—94no—
444C4×Dic3—34no—
445C22×C32—21no—
446C22×C32—21no—
447C22×C32—24no—
448C22×C32—28no—
449C22×C32—24no—
450C22×C32—24no—
451C22×C32—44no—
452C22×C32—44no—
453C22×C32—61no—
454C22×C32—61no—
455C22×C32—61no—
456C22×C32C2×D1212yes—
457C22×C32D3×D418yes—
458C22×C32C23×D314yes—
459C22×C32C23×D311yescharacteristic
460C2×C3⋊D3—21no—
461C2×C3⋊D3—21no—
462C2×C3⋊D3—32no—
463C2×C3⋊D3—38no—
464C2×C3⋊D3—68no—
465C2×C3⋊D3—61no—
466C2×C3⋊D3—61no—
467C2×C3⋊D3—68no—
468C2×C3⋊D3—61no—
469C2×C3⋊D3—61no—
470C2×C3⋊D3—61no—
471C2×C3⋊D3—61no—
472C2×C3⋊D3—61no—
473C2×C3⋊D3—61no—
474C2×C3⋊D3—64no—
475C2×C3⋊D3—64no—
476C2×C3⋊D3—64no—
477C2×C3⋊D3—64no—
478C2×C3⋊D3—64no—
479C2×C3⋊D3—64no—
480C2×C3⋊D3—64no—
481C2×C3⋊D3—64no—
482C2×C3⋊D3—124no—
483C2×C3⋊D3—124no—
484C2×C3⋊D3—124no—
485C2×C3⋊D3—124no—
486C2×C3⋊D3—124no—
487C2×C3⋊D3—124no—
488C2×C3⋊D3—124no—
489C2×C3⋊D3—124no—
490C2×C3⋊D3—124no—
491C2×C3⋊D3—1216no—
492C2×C3⋊D3—1232no—
493C2×C3⋊D3C2×D1212yes—
494C2×C3×D3—24no—
495C2×C3×D3—24no—
496C2×C3×D3—24no—
497C2×C3×D3—38no—
498C2×C3×D3—64no—
499C2×C3×D3—64no—
500D32—1216no—
501C32×C4—21no—
502C32×C4—21no—
503C32×C4—24no—
504C32×C4—24no—
505C32×C4—44no—
506C32×C4—44no—
507C32×C4—61no—
508C32×C4—61no—
509C32×C4—61no—
510C3⋊Dic3—21no—
511C3⋊Dic3—21no—
512C3⋊Dic3—61no—
513C3⋊Dic3—64no—
514C3⋊Dic3—124no—
515C3⋊Dic3C2×D1212yes—
516C3×Dic3—24no—
517C3×Dic3—24no—
518C3×Dic3—24no—
519C3×Dic3—38no—
520C3×Dic3—64no—
521C3×Dic3—64no—
522C2×#41—271no—
523C22×D4—271no—
524#124—271no—
525#123—31no—
526#123—271no—
527C22⋊Q8—271no—
528#121—271no—
529#121—271no—
530#121—271no—
531#120—271no—
532#120—271no—
533C4×D4—91no—
534C4×D4—271no—
535C2×C22⋊C4—271no—
536C2×C22⋊C4—271no—
537C33#54611yescharacteristic, complemented, Sylow
538C23×C3—24no—
539C23×C3—34no—
540C23×C3—91no—
541C23×C3C2×D3214yes—
542C23×C3C22×C3⋊D311yescharacteristic
543C22×D3—34no—
544C22×D3—94no—
545C22×D3—91no—
546C22×D3—94no—
547C22×D3—94no—
548C22×D3—91no—
549C22×D3—91no—
550C22×D3—184no—
551C22×D3—184no—
552C22×D3—184no—
553C22×D3—182no—
554C22×D3—182no—
555C22×D3—188no—
556C22×D3—188no—
557C22×D3—182no—
558C22×D3—188no—
559C22×D3—188no—
560C22×D3—182no—
561C22×D3—368no—
562C22×D3—368no—
563C22×D3—361no—
564C22×D3—364no—
565C22×D3—364no—
566C22×D3—361no—
567C22×D3—368no—
568C22×D3C22×C3⋊D311yescharacteristic
569C3×D4—68no—
570C3×D4—94no—
571C2×C3×C4—24no—
572C2×C3×C4—24no—
573C2×C3×C4—34no—
574C2×C3×C4—34no—
575C2×C3×C4—34no—
576C2×C3×C4—68no—
577C2×C3×C4—91no—
578C2×C3×C4—91no—
579C2×C3×C4—91no—
580C2×C3×C4—361no—
581C2×C3×C4—361no—
582C2×C3×C4C2×D3214yes—
583C2×C3×C4C2×D3214yes—
584C2×C3×C4C22×C3⋊D311yescharacteristic
585C2×C3×C4C22×C3⋊D311yescharacteristic
586#67—22no—
587#67—316no—
588#67—182no—
589#67—182no—
590#67—188no—
591#67—188no—
592#67—182no—
593#67—368no—
594#67—364no—
595C2×Dic3—22no—
596C2×Dic3—34no—
597C2×Dic3—34no—
598C2×Dic3—34no—
599C2×Dic3—94no—
600C2×Dic3—91no—
601C2×Dic3—124no—
602C2×Dic3—184no—
603C2×Dic3—182no—
604C2×Dic3C22×C3⋊D311yescharacteristic
605C2×Dic3C22×C3⋊D311yescharacteristic
606C2×Dic3C22×C3⋊D311yescharacteristic
607D12—182no—
608D12—188no—
609D12—188no—
610D12—188no—
611D12—182no—
612D12—368no—
613D12—364no—
614D12—361no—
615D12—368no—
616D12—361no—
617C4×D3—124no—
618C4×D3—182no—
619C4×D3—182no—
620C4×D3—188no—
621C4×D3—188no—
622C4×D3—188no—
623Dic6—182no—
624Dic6—188no—
625C2×C32—22no—
626C2×C32—24no—
627C2×C32—24no—
628C2×C32—24no—
629C2×C32—28no—
630C2×C32—48no—
631C2×C32—121no—
632C2×C32C22×D1211yescharacteristic
633C2×C32C2×D3×D414yes—
634C2×C32#100411yescharacteristic
635C2×C32D3×#4114yes—
636C2×C32D3×#4111yescharacteristic
637C2×C32#100914yes—
638C3⋊D3—22no—
639C3⋊D3—62no—
640C3⋊D3—68no—
641C3⋊D3—128no—
642C3⋊D3—128no—
643C3⋊D3—124no—
644C3⋊D3—121no—
645C3⋊D3—121no—
646C3⋊D3—124no—
647C3⋊D3—244no—
648C3×D3—44no—
649C3×D3—68no—
650C24—271no—
651C24—271no—
652#41—544no—
653C2×Q8—271no—
654C2×D4—31no—
655C2×D4—91no—
656C2×D4—271no—
657C2×D4—271no—
658C2×D4—271no—
659C2×D4—271no—
660C2×D4—271no—
661C2×D4—271no—
662C2×D4—271no—
663C2×D4—544no—
664C22×C4—31no—
665C22×C4—91no—
666C22×C4—91no—
667C22×C4—271no—
668C22×C4—271no—
669C22×C4—271no—
670C4⋊C4—31no—
671C4⋊C4—31no—
672C4⋊C4—91no—
673C4⋊C4—271no—
674C22⋊C4—31no—
675C22⋊C4—31no—
676C22⋊C4—91no—
677C22⋊C4—271no—
678C22⋊C4—271no—
679C22⋊C4—271no—
680C22⋊C4—271no—
681C22⋊C4—271no—
682C22⋊C4—271no—
683C22⋊C4—271no—
684C22⋊C4—271no—
685C22⋊C4D3×C3⋊D311yescharacteristic, complemented
686C42—91no—
687C22×C3—24no—
688C22×C3—24no—
689C22×C3—21no—
690C22×C3—21no—
691C22×C3—24no—
692C22×C3—28no—
693C22×C3—44no—
694C22×C3—44no—
695C22×C3—64no—
696C22×C3—64no—
697C22×C3—64no—
698C22×C3—92no—
699C22×C3—181no—
700C22×C3—181no—
701C22×C3D3×D1218yes—
702C22×C3D4×C3⋊D312yes—
703C22×C3C22×D3214yes—
704C22×C3C23×C3⋊D311yescharacteristic
705C2×D3—21no—
706C2×D3—21no—
707C2×D3—21no—
708C2×D3—38no—
709C2×D3—64no—
710C2×D3—64no—
711C2×D3—98no—
712C2×D3—92no—
713C2×D3—188no—
714C2×D3—184no—
715C2×D3—184no—
716C2×D3—181no—
717C2×D3—181no—
718C2×D3—188no—
719C2×D3—184no—
720C2×D3—184no—
721C2×D3—184no—
722C2×D3—184no—
723C2×D3—184no—
724C2×D3—184no—
725C2×D3—181no—
726C2×D3—181no—
727C2×D3—181no—
728C2×D3—181no—
729C2×D3—181no—
730C2×D3—181no—
731C2×D3—364no—
732C2×D3—364no—
733C2×D3—364no—
734C2×D3—364no—
735C2×D3—364no—
736C2×D3—364no—
737C2×D3—364no—
738C2×D3—364no—
739C2×D3—3616no—
740C2×D3—364no—
741C2×D3—3616no—
742C2×D3—3632no—
743C3×C4—24no—
744C3×C4—24no—
745C3×C4—21no—
746C3×C4—21no—
747C3×C4—44no—
748C3×C4—44no—
749C3×C4—64no—
750C3×C4—64no—
751C3×C4—64no—
752C3×C4—92no—
753C3×C4—181no—
754C3×C4—181no—
755Dic3—21no—
756Dic3—21no—
757Dic3—21no—
758Dic3—38no—
759Dic3—64no—
760Dic3—64no—
761Dic3—184no—
762Dic3—181no—
763Dic3—364no—
764C32—24no—
765C32#555411yescharacteristic, complemented
766C32#565414yescomplemented
767C23—31no—
768C23—91no—
769C23—271no—
770C23—271no—
771C23—271no—
772C23—542no—
773C23—542no—
774C23—542no—
775C23—542no—
776C23—1081no—
777C23—1081no—
778C23C2×D3×C3⋊D311yescharacteristic
779Q8—542no—
780D4—62no—
781D4—94no—
782D4—542no—
783D4—542no—
784D4—542no—
785D4—542no—
786D4—542no—
787D4—1081no—
788D4—1081no—
789C2×C4—31no—
790C2×C4—31no—
791C2×C4—31no—
792C2×C4—62no—
793C2×C4—91no—
794C2×C4—91no—
795C2×C4—91no—
796C2×C4—271no—
797C2×C4—361no—
798C2×C4—361no—
799C2×C4—542no—
800C2×C4—542no—
801C2×C4—542no—
802C2×C4C2×D3×C3⋊D311yescharacteristic
803C2×C4C2×D3×C3⋊D311yescharacteristic
804C2×C3—22no—
805C2×C3—28no—
806C2×C3—24no—
807C2×C3—24no—
808C2×C3—24no—
809C2×C3—48no—
810C2×C3—124no—
811C2×C3—182no—
812C2×C3C2×D3×D1214yes—
813C2×C3#6431214yes—
814C2×C3#6431414yes—
815C2×C3C2×D4×C3⋊D311yescharacteristic
816C2×C3#41×C3⋊D311yescharacteristic
817C2×C3#6436611yescharacteristic
818D3—41no—
819D3—68no—
820D3—182no—
821D3—188no—
822D3—368no—
823D3—368no—
824D3—361no—
825D3—361no—
826D3—364no—
827D3—364no—
828D3—724no—
829C22—21no—
830C22—21no—
831C22—61no—
832C22—61no—
833C22—61no—
834C22—92no—
835C22—181no—
836C22—181no—
837C22—272no—
838C22—541no—
839C22—541no—
840C22—541no—
841C22—541no—
842C22—541no—
843C22—541no—
844C22—541no—
845C22—541no—
846C22—1084no—
847C22—1084no—
848C22C3⋊D3×D1212yes—
849C22C22×D3×C3⋊D311yescharacteristic
850C4—21no—
851C4—21no—
852C4—61no—
853C4—61no—
854C4—61no—
855C4—92no—
856C4—181no—
857C4—181no—
858C4—541no—
859C3—24no—
860C3#1059429314yescomplemented
861C3#1059612511yescharacteristic, complemented
862C2—22no—
863C2—121no—
864C2—182no—
865C2—542no—
866C2—1081no—
867C2—1081no—
868C2C2×C3⋊D3×D1211yescharacteristic
869C2#1172458611yescharacteristic
870C2#1172458911yescharacteristic
subgroupG/H
center, FrattiniC22C22×D3×C3⋊D3
commutator, socle, cosocleC22×C33C24
FittingC33×C22⋊C4C22
hypercenterC22⋊C4D3×C3⋊D3
hypocenterC33#546
LCSG ▷ C22×C33 ▷ C33
UCSC1 ◁ C22 ◁ C22⋊C4

Complements

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

NH ≅ G/Ntype
1. C2×#89039C2semidirect
2. C2×#89031C2semidirect
3. #11723923C2semidirect
4. C3×#64090C2semidirect
5. C32×#886C2semidirect
6. #11723635C2semidirect
7. C2×#88804C2semidirect
8. #11723542C2semidirect
9. C3⋊D3×(C2×D3)⋊C4C2semidirect
10. #11723526C2semidirect
11. #11723525C2semidirect
12. #11723495C2semidirect
13. #11723494C2semidirect
14. #11723493C2semidirect
15. #11723419C2semidirect
20. C2×#6312C22semidirect
22. C2×C4⋊(C3⋊(C3⋊D3))C22semidirect
24. C22×C3×C3⋊Dic3C22semidirect
25. C2×C3×C4×C3⋊D3C22semidirect
27. C22×C32×Dic3C22semidirect
29. C2×#6293C22semidirect
31. C2×#6292C22semidirect
33. C2×#6291C22semidirect
35. C2×#6289C22semidirect
37. C2×Dic3×C3⋊D3C22semidirect
38. C33×C22⋊C4C22semidirect
40. #88859C22semidirect
41. C3×#3752C22semidirect
42. C3×#3750C22semidirect
43. C3×C4×C3⋊Dic3C22semidirect
44. C32×(C2×D3)⋊C4C22semidirect
45. C32×(C2×D3)⋊C4C22semidirect
46. C32×C4⋊Dic3C22semidirect
47. C32×C4⋊Dic3C22semidirect
48. #88807C22semidirect
51. #88804C22semidirect
52. #88804C22semidirect
53. #88804C22semidirect
54. (C2×D3)⋊(C3⋊Dic3)C22semidirect
72. #64090D3semidirect
74. C3×#886D3semidirect
104. C3×#638D4semidirect
138. C22×C3⋊Dic3C2×D3semidirect
152. C2×C4×C3⋊D3C2×D3semidirect
157. C22×C3×Dic3C2×D3semidirect
174. C32×C22⋊C4C2×D3semidirect
175. C32×C22⋊C4C2×D3semidirect
188. #3752C2×D3semidirect
190. #3750C2×D3semidirect
191. C4×C3⋊Dic3C2×D3semidirect
193. C3×(C2×D3)⋊C4C2×D3semidirect
194. C3×(C2×D3)⋊C4C2×D3semidirect
195. C3×C4⋊Dic3C2×D3semidirect
196. C3×C4⋊Dic3C2×D3semidirect
219. C2×C3⋊(C3⋊D3)#41semidirect
255. #886C3⋊D3semidirect
314. #638D12semidirect
385. C22×Dic3C2×C3⋊D3semidirect
415. C3×C22⋊C4D32semidirect
416. C3×C22⋊C4C2×C3⋊D3semidirect
437. (C2×D3)⋊C4C2×C3⋊D3semidirect
438. (C2×D3)⋊C4C2×C3⋊D3semidirect
440. C4⋊Dic3C2×C3⋊D3semidirect
441. C4⋊Dic3C2×C3⋊D3semidirect
537. C33#546semidirect
685. C22⋊C4D3×C3⋊D3semidirect
765. C32#5554semidirect
766. C32#5654semidirect
860. C3#10594293semidirect
861. C3#10596125semidirect

Maximal subgroups

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

subgroupindex
C2×#890392
C2×#890312
#117239232
C3×#640902
C32×#8862
#117236352
C2×#888042
#117235422
C3⋊D3×(C2×D3)⋊C42
#117235262
#117235252
#117234952
#117234942
#117234932
#117234192
#105961253
#105942933