Finite Group Databasebeta

← #13177530

Subgroups — #13177530

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×#89028C211yesmaximal, characteristic, complemented
3#11723978C211yesmaximal, characteristic, complemented
4C3×#64148C211yesmaximal, characteristic, complemented
5C32×#938C211yesmaximal, characteristic, complemented
6#11723643C211yesmaximal, characteristic, complemented
7#11723627C211yesmaximal, characteristic, complemented
8#11723623C211yesmaximal, characteristic, complemented
9#11723622C211yesmaximal, characteristic, complemented
10#11723614C211yesmaximal, characteristic, complemented
11#11723591C211yesmaximal, characteristic, complemented
12D3×#3752C211yesmaximal, characteristic, complemented
13#11723510C211yesmaximal, characteristic, complemented
14#11723504C211yesmaximal, characteristic, complemented
15#11723495C211yesmaximal, characteristic, complemented
16#10596081—31nomaximal
17#10595296—34nomaximal
18C23×C3⋊(C3⋊D3)C2211yescharacteristic
19C22×D3×C3⋊D3C2211yescharacteristic
20C2×C33×D4C2211yescharacteristic, complemented
21C2×#6312C2211yescharacteristic
22C2×#6312C2211yescharacteristic, complemented
23C2×C3×#638C2211yescharacteristic
24C2×C3×#638C2211yescharacteristic, complemented
25C22×C3×C3⋊Dic3C2211yescharacteristic, complemented
26C2×C32×#67C2211yescharacteristic
27C2×C32×#67C2211yescharacteristic, complemented
28C2×C32×C4×D3C2211yescharacteristic, complemented
29#89039—24no—
30C2×#6293C2211yescharacteristic, complemented
31C2×#6292C2211yescharacteristic
32C2×#6291C2211yescharacteristic
33C2×#6289C2211yescharacteristic
34C2×#6289C2211yescharacteristic, complemented
35C2×#6289C2211yescharacteristic, complemented
36#89028—24no—
37C2×D3×C3⋊Dic3C2211yescharacteristic, complemented
38#88864C2211yescharacteristic, complemented
39#88859C2211yescharacteristic
40#88859C2211yescharacteristic, complemented
41C3×#3757C2211yescharacteristic, complemented
42C3×#3752C2211yescharacteristic, complemented
43C3×#3750C2211yescharacteristic, complemented
44C32×#217C2211yescharacteristic, complemented
45C32×#217C2211yescharacteristic, complemented
46C32×C4⋊Dic3C2211yescharacteristic, complemented
47#88807C2211yescharacteristic, complemented
48#88806C2211yescharacteristic, complemented
49#88804C2211yescharacteristic
50#88804C2211yescharacteristic
51#88803C2211yescharacteristic, complemented
52#88803C2211yescharacteristic, complemented
53(C2×D3)⋊(C3⋊Dic3)C2211yescharacteristic, complemented
54Dic3×C3⋊Dic3C2211yescharacteristic, complemented
55C2×#3830—31no—
56C2×D4×C3⋊D3—31no—
57C2×#3811—34no—
58C2×#3804—34no—
59C32×#121—31no—
60#64148D311yescharacteristic, complemented
61#64146—31no—
62#64146—31no—
63#64146—34no—
64#64146—64no—
65#64144—31no—
66C4×#638—31no—
67C2×#3752—31no—
68#64105—31no—
69#64103—31no—
70#64094—31no—
71#64093—31no—
72#64090—31no—
73C22⋊C4×C3⋊D3—31no—
74C3×#939—34no—
75C3×#938D314yescomplemented
76#63983—34no—
77#63974—34no—
78#63969—34no—
79#63959—34no—
80#63958—34no—
81#63952—34no—
82D3×(C2×D3)⋊C4—34no—
83#63904—34no—
84#63895—34no—
85#63854—34no—
86C23×C33C2311yescharacteristic
87C23×C33C2311yescharacteristic
88C22×C3⋊(C3⋊D3)—22no—
89C22×C3⋊(C3⋊D3)—22no—
90C22×C3⋊(C3⋊D3)—41no—
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—
98C33×D4—41no—
99C2×C33×C4C2311yescharacteristic
100#6312—22no—
101#6312—22no—
102C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
103C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
104C3×#638—22no—
105C3×#638—41no—
106C2×C3×C3⋊Dic3—22no—
107C2×C3×C3⋊Dic3C2311yescharacteristic
108C2×C3×C3⋊Dic3C2311yescharacteristic
109C2×C3×C3⋊Dic3C2311yescharacteristic
110C32×#67—22no—
111C32×#67—22no—
112C2×C32×Dic3C2311yescharacteristic
113C2×C32×Dic3C2311yescharacteristic
114C2×C32×Dic3C2311yescharacteristic
115C32×C4×D3—41no—
116#6293—22no—
117#6292—22no—
118#6291D414yescomplemented
119#6289—22no—
120#6289—22no—
121#6289—41no—
122D3×C3⋊Dic3—22no—
123#5612—91no—
124#5610—94no—
125C23×C3⋊D3—31no—
126C23×C3⋊D3—34no—
127C23×C3⋊D3—31no—
128C23×C3⋊D3—64no—
129C22×D32—34no—
130C2×C32×D4—24no—
131C2×C32×D4—31no—
132C2×C32×D4—31no—
133C2×C32×D4C2×D314yescomplemented
134C2×C32×D4C2×D311yescharacteristic, complemented
135C22×C32×C4—31no—
136C2×#638—31no—
137C2×#638—31no—
138C2×#638—34no—
139C2×#638—34no—
140C2×#638—31no—
141C2×#638—64no—
142C2×#638—64no—
143C2×#638C2×D311yescharacteristic
144C2×#638C2×D311yescharacteristic, complemented
145C22×C3⋊Dic3—31no—
146C22×C3⋊Dic3C2×D311yescharacteristic, complemented
147#3830—64no—
148D4×C3⋊D3—64no—
149C2×C4⋊(C3⋊D3)—31no—
150C2×C4×C3⋊D3—31no—
151C2×C4×C3⋊D3—31no—
152C2×C4×C3⋊D3—31no—
153C2×#634—31no—
154C2×C3×#67—34no—
155C2×C3×#67—34no—
156C2×C3×#67C2×D314yes—
157C2×C3×#67C2×D314yescomplemented
158C22×C3×Dic3—34no—
159C2×C3×C4×D3C2×D314yescomplemented
160#3811—616no—
161C2×#627—34no—
162C2×#626—34no—
163C2×#626—34no—
164C2×#624—34no—
165C2×#624—34no—
166C2×#624—34no—
167#3804—616no—
168C2×D3×Dic3—34no—
169C32×C4⋊C4—31no—
170C32×C22⋊C4—31no—
171C32×C22⋊C4—31no—
172#3757—31no—
173#3757—34no—
174#3757—31no—
175#3757—64no—
176#3757C2×D311yescharacteristic, complemented
177#3752—31no—
178#3752—31no—
179#3752—31no—
180#3752—31no—
181#3752—34no—
182#3752—34no—
183#3752—31no—
184#3752—31no—
185#3752—64no—
186#3752—64no—
187#3752C2×D311yescharacteristic, complemented
188#3750—31no—
189#3750—31no—
190#3750C2×D311yescharacteristic, complemented
191C4×C3⋊Dic3—31no—
192C3×#217—34no—
193C3×#217C2×D314yescomplemented
194C3×#217C2×D314yescomplemented
195C3×(C2×D3)⋊C4—34no—
196C3×C4⋊Dic3C2×D314yescomplemented
197C3×Dic3⋊C4—34no—
198#3724—34no—
199Dic3⋊Dic3—34no—
200#3722—34no—
201#3722—34no—
202(C2×D3)⋊Dic3—34no—
203(C2×D3)⋊Dic3—34no—
204(C2×D3)⋊Dic3—34no—
205Dic32—34no—
206C22×C33—21no—
207C22×C33—21no—
208C22×C33—21no—
209C22×C33—21no—
210C22×C33—21no—
211C22×C33—21no—
212C22×C33C2411yescharacteristic
213C2×C3⋊(C3⋊D3)—21no—
214C2×C3⋊(C3⋊D3)—21no—
215C2×C3⋊(C3⋊D3)—21no—
216C2×C3⋊(C3⋊D3)—21no—
217C2×C3⋊(C3⋊D3)—44no—
218C2×C3⋊(C3⋊D3)C2×D412yes—
219C2×C3⋊(C3⋊D3)#4112yescomplemented
220C2×C3×C3⋊D3—21no—
221C2×C3×C3⋊D3—21no—
222C2×C3×C3⋊D3—21no—
223C2×C32×D3—21no—
224C2×C32×D3—21no—
225C2×C32×D3C2×D412yes—
226D3×C3⋊D3—44no—
227C33×C4—21no—
228C3⋊(C3⋊Dic3)—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—94no—
237C2×D3×D4—94no—
238C2×D3×D4—91no—
239C2×#235—91no—
240C3×#121—34no—
241C3×#121—91no—
242#939—34no—
243#938—91no—
244#938C3⋊D311yescharacteristic, complemented
245#937—94no—
246#937—94no—
247#937—91no—
248#937—91no—
249#937—184no—
250#936—91no—
251#935—94no—
252C4×#67—94no—
253C4×#67—91no—
254C2×(C2×D3)⋊C4—94no—
255#897—91no—
256#896—94no—
257#894—94no—
258#893—91no—
259#885—94no—
260#884—94no—
261#883—91no—
262#883—91no—
263#67⋊C4—94no—
264D3×C22⋊C4—94no—
265D3×C22⋊C4—91no—
266D3×C22⋊C4—91no—
267C23×C32—24no—
268C23×C32—24no—
269C23×C32—31no—
270C23×C32C22×D314yes—
271C23×C32C22×D314yes—
272C23×C32C22×D311yescharacteristic
273C23×C32C22×D311yescharacteristic
274C22×C3⋊D3—31no—
275C22×C3⋊D3—31no—
276C22×C3⋊D3—34no—
277C22×C3⋊D3—34no—
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—41no—
299C32×D4—44no—
300C32×D4—48no—
301C32×D4—62no—
302C32×D4—62no—
303C2×C32×C4—24no—
304C2×C32×C4—31no—
305C2×C32×C4—31no—
306C2×C32×C4—31no—
307C2×C32×C4—121no—
308C2×C32×C4C22×D314yes—
309C2×C32×C4C22×D311yescharacteristic
310#638—22no—
311#638—34no—
312#638—41no—
313#638—62no—
314#638—62no—
315#638—68no—
316#638—68no—
317#638—128no—
318#638—128no—
319C2×C3⋊Dic3—22no—
320C2×C3⋊Dic3—31no—
321C2×C3⋊Dic3—31no—
322C2×C3⋊Dic3—34no—
323C2×C3⋊Dic3—34no—
324C2×C3⋊Dic3—64no—
325C2×C3⋊Dic3—64no—
326C2×C3⋊Dic3—62no—
327C2×C3⋊Dic3C22×D311yescharacteristic
328C2×C3⋊Dic3C22×D311yescharacteristic
329C2×C3⋊Dic3C22×D311yescharacteristic
330C4⋊(C3⋊D3)—62no—
331C4×C3⋊D3—62no—
332C4×C3⋊D3—62no—
333C4×C3⋊D3—121no—
334#634—62no—
335C3×#67—28no—
336C3×#67—28no—
337C3×#67—68no—
338C3×#67—124no—
339C2×C3×Dic3—34no—
340C2×C3×Dic3—34no—
341C2×C3×Dic3—34no—
342C2×C3×Dic3—68no—
343C2×C3×Dic3C22×D314yes—
344C2×C3×Dic3C22×D314yes—
345C2×C3×Dic3C22×D314yes—
346C3×C4×D3—44no—
347#627—68no—
348#626—316no—
349#626—68no—
350#624—68no—
351#624—68no—
352#624—124no—
353D3×Dic3—68no—
354#546—271noSylow
355C2×C33—41no—
356C2×C33—41no—
357C2×C33C22×D411yescharacteristic
358C2×C33C2×#4111yescharacteristic
359C2×C33H(5,𝔽2)11yescharacteristic
360C3⋊(C3⋊D3)—22no—
361C3⋊(C3⋊D3)—22no—
362C3×C3⋊D3—41no—
363C32×D3—22no—
364C23×D3—94no—
365C23×D3—94no—
366C23×D3—91no—
367C23×D3—91no—
368C23×D3—184no—
369C2×C3×D4—24no—
370C2×C3×D4—34no—
371C2×C3×D4—34no—
372C2×C3×D4—91no—
373C2×C3×D4—91no—
374C2×C3×D4D3214yescomplemented
375C2×C3×D4C2×C3⋊D311yescharacteristic, complemented
376C22×C3×C4—34no—
377C22×C3×C4—91no—
378C2×#67—34no—
379C2×#67—34no—
380C2×#67—94no—
381C2×#67—94no—
382C2×#67—94no—
383C2×#67—91no—
384C2×#67—91no—
385C2×#67—91no—
386C2×#67—184no—
387C2×#67—184no—
388C2×#67C2×C3⋊D311yescharacteristic
389C2×#67C2×C3⋊D311yescharacteristic, complemented
390C22×Dic3—34no—
391C22×Dic3—94no—
392#237—1816no—
393D3×D4—184no—
394D3×D4—1816no—
395#235—184no—
396C2×D12—91no—
397C2×D12—94no—
398C2×C4×D3—94no—
399C2×C4×D3—94no—
400C2×C4×D3—91no—
401C2×C4×D3—91no—
402C2×C4×D3—91no—
403C2×C4×D3—94no—
404C2×C4×D3—91no—
405C2×C4×D3C2×C3⋊D311yescharacteristic, complemented
406C2×Dic6—94no—
407C2×Dic6—91no—
408C3×C4⋊C4—34no—
409C3×C4⋊C4—91no—
410C3×C22⋊C4—34no—
411C3×C22⋊C4—34no—
412C3×C22⋊C4—91no—
413C3×C22⋊C4—91no—
414#217—34no—
415#217—94no—
416#217—94no—
417#217—91no—
418#217—91no—
419#217—91no—
420#217—184no—
421#217C2×C3⋊D311yescharacteristic, complemented
422#217C2×C3⋊D311yescharacteristic, complemented
423(C2×D3)⋊C4—34no—
424(C2×D3)⋊C4—94no—
425(C2×D3)⋊C4—94no—
426(C2×D3)⋊C4—94no—
427(C2×D3)⋊C4—94no—
428(C2×D3)⋊C4—91no—
429(C2×D3)⋊C4—94no—
430(C2×D3)⋊C4—94no—
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—
437C4⋊Dic3—91no—
438C4⋊Dic3C2×C3⋊D311yescharacteristic, complemented
439Dic3⋊C4—34no—
440Dic3⋊C4—94no—
441Dic3⋊C4—94no—
442Dic3⋊C4—91no—
443C4×Dic3—94no—
444C4×Dic3—91no—
445C22×C32—28no—
446C22×C32—21no—
447C22×C32—21no—
448C22×C32—21no—
449C22×C32—24no—
450C22×C32—21no—
451C22×C32—21no—
452C22×C32—21no—
453C22×C32—24no—
454C22×C32—24no—
455C22×C32—24no—
456C22×C32—24no—
457C22×C32—24no—
458C22×C32—24no—
459C22×C32—32no—
460C22×C32—44no—
461C22×C32—44no—
462C22×C32—44no—
463C22×C32—44no—
464C22×C32—44no—
465C22×C32—61no—
466C22×C32—61no—
467C22×C32C23×D314yes—
468C22×C32C23×D311yescharacteristic
469C2×C3⋊D3—21no—
470C2×C3⋊D3—21no—
471C2×C3⋊D3—21no—
472C2×C3⋊D3—32no—
473C2×C3⋊D3—32no—
474C2×C3⋊D3—38no—
475C2×C3⋊D3—38no—
476C2×C3⋊D3—68no—
477C2×C3⋊D3—68no—
478C2×C3⋊D3—61no—
479C2×C3⋊D3—61no—
480C2×C3⋊D3—61no—
481C2×C3⋊D3—61no—
482C2×C3⋊D3—64no—
483C2×C3⋊D3—64no—
484C2×C3⋊D3—64no—
485C2×C3⋊D3—64no—
486C2×C3⋊D3—124no—
487C2×C3⋊D3—124no—
488C2×C3⋊D3—124no—
489C2×C3⋊D3—124no—
490C2×C3⋊D3—124no—
491C2×C3⋊D3—124no—
492C2×C3⋊D3—1216no—
493C2×C3⋊D3—1232no—
494C2×C3×D3—24no—
495C2×C3×D3—24no—
496C2×C3×D3—64no—
497C2×C3×D3—64no—
498C2×C3×D3—64no—
499C2×C3×D3D3×D418yes—
500D32—1216no—
501C32×C4—21no—
502C32×C4—24no—
503C32×C4—44no—
504C32×C4—61no—
505C32×C4—61no—
506C32×C4—61no—
507C3⋊Dic3—21no—
508C3⋊Dic3—21no—
509C3⋊Dic3—61no—
510C3⋊Dic3—61no—
511C3⋊Dic3—64no—
512C3⋊Dic3—64no—
513C3⋊Dic3—124no—
514C3⋊Dic3—124no—
515C3⋊Dic3D3×D412yes—
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—271no—
526#123—271no—
527C22⋊Q8—271no—
528#121—31no—
529#121—91no—
530#121—271no—
531#120—271no—
532#120—271no—
533C4×D4—271no—
534C4×D4—271no—
535C2×C22⋊C4—271no—
536C2×C22⋊C4—271no—
537C33#54611yescharacteristic, complemented, Sylow
538C23×C3—24no—
539C23×C3—24no—
540C23×C3—34no—
541C23×C3—91no—
542C23×C3C2×D3214yes—
543C23×C3C2×D3214yes—
544C23×C3C22×C3⋊D311yescharacteristic
545C23×C3C22×C3⋊D311yescharacteristic
546C22×D3—34no—
547C22×D3—94no—
548C22×D3—94no—
549C22×D3—91no—
550C22×D3—91no—
551C22×D3—184no—
552C22×D3—184no—
553C22×D3—182no—
554C22×D3—188no—
555C22×D3—188no—
556C22×D3—182no—
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—44no—
570C3×D4—41no—
571C3×D4—48no—
572C3×D4—68no—
573C3×D4—68no—
574C3×D4—182no—
575C3×D4—361no—
576C2×C3×C4—24no—
577C2×C3×C4—34no—
578C2×C3×C4—34no—
579C2×C3×C4—34no—
580C2×C3×C4—91no—
581C2×C3×C4—91no—
582C2×C3×C4—91no—
583C2×C3×C4—124no—
584C2×C3×C4—182no—
585C2×C3×C4C2×D3214yes—
586C2×C3×C4C22×C3⋊D311yescharacteristic
587#67—22no—
588#67—22no—
589#67—68no—
590#67—916no—
591#67—124no—
592#67—182no—
593#67—182no—
594#67—182no—
595#67—188no—
596#67—188no—
597#67—368no—
598#67—368no—
599C2×Dic3—34no—
600C2×Dic3—34no—
601C2×Dic3—34no—
602C2×Dic3—68no—
603C2×Dic3—94no—
604C2×Dic3—94no—
605C2×Dic3—91no—
606C2×Dic3—91no—
607C2×Dic3—184no—
608C2×Dic3—184no—
609C2×Dic3—188no—
610C2×Dic3C22×C3⋊D311yescharacteristic
611C2×Dic3C22×C3⋊D311yescharacteristic
612C2×Dic3C22×C3⋊D311yescharacteristic
613D12—94no—
614D12—188no—
615C4×D3—41no—
616C4×D3—182no—
617C4×D3—182no—
618C4×D3—188no—
619C4×D3—188no—
620C4×D3—182no—
621C4×D3—361no—
622C4×D3—364no—
623Dic6—182no—
624Dic6—188no—
625C2×C32—24no—
626C2×C32—24no—
627C2×C32—24no—
628C2×C32—48no—
629C2×C32—44no—
630C2×C32—41no—
631C2×C32—41no—
632C2×C32—44no—
633C2×C32—62no—
634C2×C32—84no—
635C2×C32C2×D3×D414yes—
636C2×C32C2×D3×D411yescharacteristic
637C2×C32#100414yes—
638C2×C32#100411yescharacteristic
639C2×C32D3×#4114yes—
640C2×C32D3×#4111yescharacteristic
641C3⋊D3—41no—
642C3⋊D3—62no—
643C3⋊D3—62no—
644C3⋊D3—68no—
645C3⋊D3—68no—
646C3⋊D3—128no—
647C3⋊D3—128no—
648C3×D3—28no—
649C3×D3—124no—
650C24—271no—
651C24—271no—
652#41—544no—
653C2×Q8—271no—
654C2×D4—31no—
655C2×D4—31no—
656C2×D4—91no—
657C2×D4—91no—
658C2×D4—271no—
659C2×D4—271no—
660C2×D4—271no—
661C2×D4—271no—
662C2×D4—544no—
663C2×D4D3×C3⋊D311yescharacteristic, complemented
664C22×C4—31no—
665C22×C4—91no—
666C22×C4—271no—
667C22×C4—271no—
668C22×C4—271no—
669C22×C4—271no—
670C4⋊C4—31no—
671C4⋊C4—91no—
672C4⋊C4—271no—
673C4⋊C4—271no—
674C22⋊C4—31no—
675C22⋊C4—31no—
676C22⋊C4—91no—
677C22⋊C4—91no—
678C22⋊C4—271no—
679C22⋊C4—271no—
680C22⋊C4—271no—
681C22⋊C4—271no—
682C22⋊C4—271no—
683C22⋊C4—271no—
684C22⋊C4—271no—
685C22⋊C4—271no—
686C42—271no—
687C22×C3—28no—
688C22×C3—24no—
689C22×C3—24no—
690C22×C3—24no—
691C22×C3—24no—
692C22×C3—24no—
693C22×C3—24no—
694C22×C3—21no—
695C22×C3—21no—
696C22×C3—21no—
697C22×C3—21no—
698C22×C3—21no—
699C22×C3—21no—
700C22×C3—24no—
701C22×C3—38no—
702C22×C3—44no—
703C22×C3—44no—
704C22×C3—44no—
705C22×C3—44no—
706C22×C3—44no—
707C22×C3—64no—
708C22×C3—64no—
709C22×C3—181no—
710C22×C3—181no—
711C22×C3—181no—
712C22×C3C22×D3214yes—
713C22×C3C23×C3⋊D311yescharacteristic
714C2×D3—21no—
715C2×D3—21no—
716C2×D3—64no—
717C2×D3—64no—
718C2×D3—64no—
719C2×D3—98no—
720C2×D3—98no—
721C2×D3—92no—
722C2×D3—92no—
723C2×D3—188no—
724C2×D3—188no—
725C2×D3—184no—
726C2×D3—184no—
727C2×D3—184no—
728C2×D3—184no—
729C2×D3—181no—
730C2×D3—181no—
731C2×D3—181no—
732C2×D3—181no—
733C2×D3—364no—
734C2×D3—364no—
735C2×D3—364no—
736C2×D3—364no—
737C2×D3—364no—
738C2×D3—3616no—
739C2×D3—3616no—
740C2×D3—364no—
741C2×D3—3632no—
742C2×D3D4×C3⋊D312yes—
743C3×C4—24no—
744C3×C4—21no—
745C3×C4—44no—
746C3×C4—64no—
747C3×C4—64no—
748C3×C4—64no—
749C3×C4—92no—
750C3×C4—181no—
751C3×C4—181no—
752Dic3—21no—
753Dic3—21no—
754Dic3—21no—
755Dic3—38no—
756Dic3—64no—
757Dic3—64no—
758Dic3—184no—
759Dic3—184no—
760Dic3—181no—
761Dic3—181no—
762Dic3—364no—
763Dic3—364no—
764C32—24no—
765C32#561014yescomplemented
766C32#561211yescharacteristic, complemented
767C23—31no—
768C23—91no—
769C23—271no—
770C23—271no—
771C23—542no—
772C23—542no—
773C23—542no—
774C23—542no—
775C23—1081no—
776C23—1081no—
777C23C2×D3×C3⋊D311yescharacteristic
778C23C2×D3×C3⋊D311yescharacteristic
779Q8—542no—
780D4—41no—
781D4—62no—
782D4—62no—
783D4—182no—
784D4—274no—
785D4—361no—
786D4—542no—
787D4—542no—
788D4—542no—
789C2×C4—31no—
790C2×C4—31no—
791C2×C4—31no—
792C2×C4—91no—
793C2×C4—91no—
794C2×C4—91no—
795C2×C4—121no—
796C2×C4—182no—
797C2×C4—271no—
798C2×C4—271no—
799C2×C4—542no—
800C2×C4—542no—
801C2×C4—542no—
802C2×C4—1081no—
803C2×C4C2×D3×C3⋊D311yescharacteristic
804C2×C3—24no—
805C2×C3—24no—
806C2×C3—24no—
807C2×C3—48no—
808C2×C3—44no—
809C2×C3—44no—
810C2×C3—41no—
811C2×C3—41no—
812C2×C3—68no—
813C2×C3—84no—
814C2×C3—361no—
815C2×C3D32×D414yes—
816C2×C3#6431214yes—
817C2×C3#6433014yes—
818C2×C3C2×D4×C3⋊D311yescharacteristic
819C2×C3#6436111yescharacteristic
820C2×C3#41×C3⋊D311yescharacteristic
821D3—22no—
822D3—124no—
823D3—188no—
824D3—188no—
825D3—182no—
826D3—182no—
827D3—368no—
828D3—368no—
829C22—21no—
830C22—21no—
831C22—21no—
832C22—21no—
833C22—21no—
834C22—21no—
835C22—32no—
836C22—61no—
837C22—61no—
838C22—181no—
839C22—181no—
840C22—181no—
841C22—272no—
842C22—272no—
843C22—541no—
844C22—541no—
845C22—541no—
846C22—541no—
847C22—1084no—
848C22—1084no—
849C22C22×D3×C3⋊D311yescharacteristic
850C4—21no—
851C4—61no—
852C4—61no—
853C4—61no—
854C4—92no—
855C4—181no—
856C4—181no—
857C4—541no—
858C4—541no—
859C3—24no—
860C3#1059529614yescomplemented
861C3#1059608111yescharacteristic, complemented
862C2—41no—
863C2—41no—
864C2—62no—
865C2—361no—
866C2—542no—
867C2—542no—
868C2D3×D4×C3⋊D311yescharacteristic
869C2#1172458611yescharacteristic
870C2#1172461111yescharacteristic
subgroupG/H
center, FrattiniC22C22×D3×C3⋊D3
commutator, socle, cosocleC22×C33C24
FittingC2×C33×D4C22
hypercenterC2×D4D3×C3⋊D3
hypocenterC33#546
LCSG ▷ C22×C33 ▷ C33
UCSC1 ◁ C22 ◁ C2×D4

Complements

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

NH ≅ G/Ntype
1. C2×#89039C2semidirect
2. C2×#89028C2semidirect
3. #11723978C2semidirect
4. C3×#64148C2semidirect
5. C32×#938C2semidirect
6. #11723643C2semidirect
7. #11723627C2semidirect
8. #11723623C2semidirect
9. #11723622C2semidirect
10. #11723614C2semidirect
11. #11723591C2semidirect
12. D3×#3752C2semidirect
13. #11723510C2semidirect
14. #11723504C2semidirect
15. #11723495C2semidirect
20. C2×C33×D4C22semidirect
22. C2×#6312C22semidirect
24. C2×C3×#638C22semidirect
25. C22×C3×C3⋊Dic3C22semidirect
27. C2×C32×#67C22semidirect
28. C2×C32×C4×D3C22semidirect
30. C2×#6293C22semidirect
34. C2×#6289C22semidirect
35. C2×#6289C22semidirect
37. C2×D3×C3⋊Dic3C22semidirect
38. #88864C22semidirect
40. #88859C22semidirect
41. C3×#3757C22semidirect
42. C3×#3752C22semidirect
43. C3×#3750C22semidirect
44. C32×#217C22semidirect
45. C32×#217C22semidirect
46. C32×C4⋊Dic3C22semidirect
47. #88807C22semidirect
48. #88806C22semidirect
51. #88803C22semidirect
52. #88803C22semidirect
53. (C2×D3)⋊(C3⋊Dic3)C22semidirect
54. Dic3×C3⋊Dic3C22semidirect
60. #64148D3semidirect
75. C3×#938D3semidirect
118. #6291D4semidirect
133. C2×C32×D4C2×D3semidirect
134. C2×C32×D4C2×D3semidirect
144. C2×#638C2×D3semidirect
146. C22×C3⋊Dic3C2×D3semidirect
157. C2×C3×#67C2×D3semidirect
159. C2×C3×C4×D3C2×D3semidirect
176. #3757C2×D3semidirect
187. #3752C2×D3semidirect
190. #3750C2×D3semidirect
193. C3×#217C2×D3semidirect
194. C3×#217C2×D3semidirect
196. C3×C4⋊Dic3C2×D3semidirect
219. C2×C3⋊(C3⋊D3)#41semidirect
244. #938C3⋊D3semidirect
374. C2×C3×D4D32semidirect
375. C2×C3×D4C2×C3⋊D3semidirect
389. C2×#67C2×C3⋊D3semidirect
405. C2×C4×D3C2×C3⋊D3semidirect
421. #217C2×C3⋊D3semidirect
422. #217C2×C3⋊D3semidirect
438. C4⋊Dic3C2×C3⋊D3semidirect
537. C33#546semidirect
663. C2×D4D3×C3⋊D3semidirect
765. C32#5610semidirect
766. C32#5612semidirect
860. C3#10595296semidirect
861. C3#10596081semidirect

Maximal subgroups

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

subgroupindex
C2×#890392
C2×#890282
#117239782
C3×#641482
C32×#9382
#117236432
#117236272
#117236232
#117236222
#117236142
#117235912
D3×#37522
#117235102
#117235042
#117234952
#105960813
#105952963