Finite Group Databasebeta

← #13168223

Subgroups — #13168223

Order 1728.

1172 conjugacy classes of subgroups.

The subgroup lattice has 1070 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11723669C211yesmaximal, characteristic, complemented
2#11723462C211yesmaximal, characteristic, complemented
3#11723456C211yesmaximal, characteristic, complemented
4#11723420C211yesmaximal, characteristic, complemented
5C3×#63891C211yesmaximal, characteristic, complemented
6C3×#63887C211yesmaximal, characteristic, complemented
7C3×#63887C211yesmaximal, characteristic, complemented
8#11723028C211yesmaximal, characteristic, complemented
9#11723019C211yesmaximal, characteristic, complemented
10#11723013C211yesmaximal, characteristic, complemented
11#11722987C211yesmaximal, characteristic, complemented
12#11722987C211yesmaximal, characteristic, complemented
13#11722958C211yesmaximal, characteristic
14#11722924C211yesmaximal, characteristic, complemented
15D3×Dic3⋊Dic3C211yesmaximal, characteristic, complemented
16#10595378—31nomaximal
17#10594179—31nomaximal
18#10594129—31nomaximal
19C2×C4×C3⋊(C3⋊D3)C2211yescharacteristic
20C2×C32×Dic6C2211yescharacteristic
21C2×#6291C2211yescharacteristic
22C2×#6291C2211yescharacteristic
23C2×D3×C3⋊Dic3C2211yescharacteristic
24C2×C3×#625C2211yescharacteristic
25C2×C3×D3×Dic3C2211yescharacteristic
26C2×C3×D3×Dic3C2211yescharacteristic
27C2×C3×D3×Dic3C2211yescharacteristic
28C3×C4⋊(C3⋊Dic3)C2211yescharacteristic
29C3×#3750C2211yescharacteristic
30C3×#3750C2211yescharacteristic
31C32×(C2×D3)⋊C4C2211yescharacteristic
32C32×(C2×D3)⋊C4C2211yescharacteristic
33#88815C2211yescharacteristic
34#88815C2211yescharacteristic
35#88815C2211yescharacteristic
36#88813C2211yescharacteristic
37#88807C2211yescharacteristic
38#88807C2211yescharacteristic
39Dic3⋊(C3⋊Dic3)C2211yescharacteristic
40#88804C2211yescharacteristic
41#88804C2211yescharacteristic
42#88804C2211yescharacteristic
43#88804C2211yescharacteristic
44(C2×D3)⋊(C3⋊Dic3)C2211yescharacteristic
45Dic3×C3⋊Dic3C2211yescharacteristic
46C3×Dic3⋊Dic3C2211yescharacteristic
47C3×Dic3⋊Dic3C2211yescharacteristic
48C3×Dic3⋊Dic3C2211yescharacteristic
49C3×Dic3⋊Dic3C2211yescharacteristic
50C3×Dic3⋊Dic3C2211yescharacteristic
51C3×(C2×D3)⋊Dic3C2211yescharacteristic
52C3×(C2×D3)⋊Dic3C2211yescharacteristic
53C3×(C2×D3)⋊Dic3C2211yescharacteristic
54#64155—31no—
55#64092—31no—
56#64090—31no—
57C3×#946—31no—
58C3×#946—31no—
59C3×#886—31no—
60C3×#883—31no—
61C3×#878—31no—
62C3×#878—31no—
63#63978—31no—
64#67⋊Dic3—31no—
65Dic3×#67—31no—
66#63971—31no—
67#63966—31no—
68#63966—31no—
69C2×Dic3⋊Dic3—31no—
70#63956—31no—
71#63906—31no—
72#63891D311yescharacteristic, complemented
73#63890—31no—
74#63890—31no—
75D3×C4⋊Dic3—31no—
76#63887D311yescharacteristic, complemented
77#63887D311yescharacteristic, complemented
78#63881—31no—
79#63881—31no—
80#63881—61no—
81#63879—31no—
82D3×Dic3⋊C4—31no—
83#63872—31no—
84#63871—31no—
85#63871—31no—
86#63871—61no—
87#63862—31no—
88#63858—31no—
89#63853—31no—
90#63853—31no—
91#63853—61no—
92#63850—31no—
93#63850—31no—
94#63848—31no—
95#63848—31no—
96#63848—31no—
97#63847—31no—
98#63846—31no—
99#63846—31no—
100#63845—31no—
101#63845—31no—
102C22×C3⋊(C3⋊D3)C2311yescharacteristic
103C22×C32×D3C2311yescharacteristic
104C22×C32×D3C2311yescharacteristic
105C2×C33×C4C2311yescharacteristic
106C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
107C4×C3⋊(C3⋊D3)—41no—
108C2×C3×C3⋊Dic3C2311yescharacteristic
109C2×C3×C3⋊Dic3C2311yescharacteristic
110C2×C3×C3⋊Dic3C2311yescharacteristic
111C2×C3×C3⋊Dic3C2311yescharacteristic
112C2×C3×C3⋊Dic3C2311yescharacteristic
113C2×C3×C3⋊Dic3C2311yescharacteristic
114C2×C32×Dic3C2311yescharacteristic
115C2×C32×Dic3C2311yescharacteristic
116C2×C32×Dic3C2311yescharacteristic
117C2×C32×Dic3C2311yescharacteristic
118C32×Dic6—41no—
119#6291—22no—
120#6291—41no—
121D3×C3⋊Dic3—41no—
122C3×#625—22no—
123C3×D3×Dic3—22no—
124C3×D3×Dic3—41no—
125C3×D3×Dic3—41no—
126#5665—91no—
127#5645—91no—
128#5638—91no—
129C2×C32×Q8—31no—
130C2×#638—31no—
131C2×#638—31no—
132C22×C3⋊Dic3—31no—
133C2×C4×C3⋊D3—31no—
134C2×C4×C3⋊D3—31no—
135C2×C4×C3⋊D3—31no—
136C2×C4×C3⋊D3—61no—
137C2×C4×C3⋊D3—61no—
138C2×C4×C3⋊D3—61no—
139C2×C4×C3⋊D3—121no—
140C2×C3×#67—31no—
141C2×C3×#67—31no—
142C22×C3×Dic3—31no—
143C22×C3×Dic3—31no—
144C22×C3×Dic3—31no—
145C2×C3×C4×D3—31no—
146C2×C3×C4×D3—31no—
147C2×C3×C4×D3—31no—
148C2×C3×Dic6—21no—
149C2×C3×Dic6C2×D311yescharacteristic
150C2×C3×Dic6C2×D311yescharacteristic
151C2×#626—31no—
152C2×#626—31no—
153C2×#626—31no—
154C2×#626—31no—
155C2×#626—61no—
156C2×#626—61no—
157C2×#625C2×D311yescharacteristic
158C2×D3×Dic3—31no—
159C2×D3×Dic3—31no—
160C2×D3×Dic3—61no—
161C2×D3×Dic3C2×D311yescharacteristic
162C2×D3×Dic3C2×D311yescharacteristic
163C2×D3×Dic3C2×D311yescharacteristic
164C32×C22⋊C4—31no—
165C32×C22⋊C4—31no—
166#3757—31no—
167#3752—31no—
168#3752—31no—
169#3752—31no—
170#3752—31no—
171C4⋊(C3⋊Dic3)—31no—
172C4⋊(C3⋊Dic3)C2×D311yescharacteristic
173#3750—31no—
174#3750—31no—
175#3750C2×D311yescharacteristic
176#3750C2×D311yescharacteristic
177C4×C3⋊Dic3—31no—
178C3×#217—31no—
179C3×#217—31no—
180C3×#217—31no—
181C3×(C2×D3)⋊C4—21no—
182C3×(C2×D3)⋊C4—21no—
183C3×(C2×D3)⋊C4—31no—
184C3×(C2×D3)⋊C4—31no—
185C3×(C2×D3)⋊C4—31no—
186C3×(C2×D3)⋊C4C2×D311yescharacteristic
187C3×(C2×D3)⋊C4C2×D311yescharacteristic
188C3×(C2×D3)⋊C4C2×D311yescharacteristic
189C3×(C2×D3)⋊C4C2×D311yescharacteristic
190C3×C4⋊Dic3—31no—
191C3×C4⋊Dic3—31no—
192C3×C4⋊Dic3—31no—
193C3×C4⋊Dic3—31no—
194C3×C4⋊Dic3—31no—
195C3×C4⋊Dic3—31no—
196C3×C4⋊Dic3—31no—
197C3×C4⋊Dic3—61no—
198C3×Dic3⋊C4—31no—
199C3×Dic3⋊C4—31no—
200C3×Dic3⋊C4—31no—
201C3×Dic3⋊C4—31no—
202C3×Dic3⋊C4—31no—
203C3×Dic3⋊C4—31no—
204C3×Dic3⋊C4—31no—
205C3×Dic3⋊C4—31no—
206C3×Dic3⋊C4—31no—
207C3×Dic3⋊C4—61no—
208C3×Dic3⋊C4—61no—
209#3724—31no—
210#3724—31no—
211#3724—31no—
212Dic3⋊Dic3—31no—
213Dic3⋊Dic3—31no—
214Dic3⋊Dic3—31no—
215Dic3⋊Dic3—31no—
216Dic3⋊Dic3—31no—
217Dic3⋊Dic3—31no—
218Dic3⋊Dic3—31no—
219Dic3⋊Dic3—31no—
220Dic3⋊Dic3—31no—
221Dic3⋊Dic3—31no—
222Dic3⋊Dic3—31no—
223Dic3⋊Dic3—31no—
224Dic3⋊Dic3—61no—
225Dic3⋊Dic3—61no—
226Dic3⋊Dic3—61no—
227Dic3⋊Dic3C2×D311yescharacteristic
228Dic3⋊Dic3C2×D311yescharacteristic
229Dic3⋊Dic3C2×D311yescharacteristic
230Dic3⋊Dic3C2×D311yescharacteristic
231Dic3⋊Dic3C2×D311yescharacteristic
232#3722—31no—
233#3722—31no—
234#3722—31no—
235#3722—31no—
236#3722—31no—
237#3722—31no—
238#3722—31no—
239#3722—31no—
240#3722—61no—
241#3722—61no—
242#3722—61no—
243#3722—61no—
244(C2×D3)⋊Dic3—31no—
245(C2×D3)⋊Dic3—31no—
246(C2×D3)⋊Dic3—61no—
247(C2×D3)⋊Dic3C2×D311yescharacteristic
248(C2×D3)⋊Dic3C2×D311yescharacteristic
249(C2×D3)⋊Dic3C2×D311yescharacteristic
250Dic32—31no—
251Dic32—31no—
252Dic32—31no—
253Dic32—31no—
254Dic32—31no—
255Dic32—61no—
256C22×C33C2411yescharacteristic
257C2×C3⋊(C3⋊D3)—21no—
258C2×C3⋊(C3⋊D3)—21no—
259C2×C3⋊(C3⋊D3)—21no—
260C2×C32×D3—21no—
261C2×C32×D3—21no—
262C2×C32×D3—21no—
263C2×C32×D3—21no—
264C2×C32×D3—21no—
265C2×C32×D3#4112yes—
266C33×C4—21no—
267C3⋊(C3⋊Dic3)—21no—
268C3×C3⋊Dic3—21no—
269C3×C3⋊Dic3—21no—
270C3×C3⋊Dic3—21no—
271C3×C3⋊Dic3—21no—
272C3×C3⋊Dic3—21no—
273C3×C3⋊Dic3—21no—
274C32×Dic3—21no—
275C32×Dic3—21no—
276C32×Dic3—21no—
277C32×Dic3—21no—
278C3×#123—91no—
279C3×C22⋊Q8—91no—
280C3×C22⋊Q8—91no—
281#946—31no—
282#946—31no—
283#946—91no—
284#946—91no—
285#946—181no—
286#939—91no—
287D4×Dic3—91no—
288#930—91no—
289#929—91no—
290#929—91no—
291C4×#67—91no—
292C2×C4⋊Dic3—91no—
293C2×Dic3⋊C4—91no—
294#898—91no—
295#898—91no—
296#898—91no—
297#898—91no—
298#897—91no—
299#894—91no—
300#894—91no—
301#894—91no—
302#893—91no—
303D3×C4⋊C4—91no—
304#890—91no—
305#890—91no—
306#890—91no—
307#889—91no—
308#889—91no—
309#889—91no—
310#886—31no—
311#886—91no—
312#886—91no—
313#884—91no—
314#883—31no—
315#883—91no—
316#883—91no—
317#883—181no—
318#67⋊C4—91no—
319#67⋊C4—91no—
320#67⋊C4—91no—
321#67⋊C4—181no—
322#879—91no—
323#879—91no—
324#878—31no—
325#878—31no—
326C23×C32—31no—
327C23×C32—31no—
328C22×C3⋊D3—31no—
329C22×C3⋊D3—31no—
330C22×C3⋊D3—31no—
331C22×C3⋊D3—61no—
332C22×C3⋊D3—61no—
333C22×C3⋊D3—61no—
334C22×C3⋊D3—121no—
335C22×C3×D3—21no—
336C22×C3×D3—21no—
337C22×C3×D3C22×D311yescharacteristic
338C22×C3×D3C22×D311yescharacteristic
339C22×C3×D3C22×D311yescharacteristic
340C22×C3×D3C22×D311yescharacteristic
341C32×Q8—121no—
342C2×C32×C4—21no—
343C2×C32×C4—21no—
344C2×C32×C4—21no—
345C2×C32×C4—31no—
346C2×C32×C4—31no—
347C2×C32×C4—31no—
348C2×C32×C4—31no—
349C2×C32×C4—41no—
350C2×C32×C4C22×D311yescharacteristic
351C2×C32×C4C22×D311yescharacteristic
352C2×C32×C4C22×D311yescharacteristic
353#638—62no—
354#638—121no—
355C2×C3⋊Dic3—31no—
356C2×C3⋊Dic3—31no—
357C2×C3⋊Dic3—31no—
358C2×C3⋊Dic3—61no—
359C2×C3⋊Dic3—61no—
360C2×C3⋊Dic3—61no—
361C2×C3⋊Dic3—121no—
362C2×C3⋊Dic3—121no—
363C2×C3⋊Dic3C22×D311yescharacteristic
364C2×C3⋊Dic3C22×D311yescharacteristic
365C2×C3⋊Dic3C22×D311yescharacteristic
366C2×C3⋊Dic3C22×D311yescharacteristic
367C2×C3⋊Dic3C22×D311yescharacteristic
368C2×C3⋊Dic3C22×D311yescharacteristic
369C4×C3⋊D3—121no—
370C4×C3⋊D3—121no—
371C4×C3⋊D3—121no—
372C4×C3⋊D3—122no—
373C4×C3⋊D3—122no—
374C4×C3⋊D3—122no—
375C4×C3⋊D3—124no—
376C3×#67—62no—
377C3×#67—62no—
378C2×C3×Dic3—21no—
379C2×C3×Dic3—21no—
380C2×C3×Dic3—21no—
381C2×C3×Dic3—21no—
382C2×C3×Dic3—31no—
383C2×C3×Dic3—31no—
384C2×C3×Dic3—31no—
385C2×C3×Dic3—31no—
386C2×C3×Dic3—31no—
387C2×C3×Dic3—31no—
388C2×C3×Dic3—31no—
389C2×C3×Dic3—31no—
390C2×C3×Dic3—31no—
391C2×C3×Dic3—31no—
392C2×C3×Dic3—31no—
393C2×C3×Dic3—31no—
394C2×C3×Dic3—61no—
395C2×C3×Dic3—61no—
396C2×C3×Dic3—61no—
397C2×C3×Dic3—61no—
398C2×C3×Dic3—61no—
399C2×C3×Dic3—61no—
400C2×C3×Dic3—62no—
401C2×C3×Dic3—121no—
402C2×C3×Dic3—121no—
403C2×C3×Dic3C22×D311yescharacteristic
404C2×C3×Dic3C22×D311yescharacteristic
405C2×C3×Dic3C22×D311yescharacteristic
406C2×C3×Dic3C22×D311yescharacteristic
407C2×C3×Dic3C22×D311yescharacteristic
408C2×C3×Dic3C22×D311yescharacteristic
409C2×C3×Dic3C22×D311yescharacteristic
410C2×C3×Dic3C22×D311yescharacteristic
411C3×C4×D3—62no—
412C3×C4×D3—121no—
413C3×C4×D3—121no—
414C3×Dic6—41no—
415C3×Dic6—41no—
416C3×Dic6—42no—
417#626—64no—
418#626—62no—
419#626—62no—
420#626—121no—
421#626—121no—
422#626—122no—
423#625—22no—
424D3×Dic3—22no—
425D3×Dic3—41no—
426D3×Dic3—41no—
427D3×Dic3—121no—
428D3×Dic3—121no—
429D3×Dic3—122no—
430#539—271noSylow
431C2×C33C2×#4111yescharacteristic
432C2×C33H(5,𝔽2)11yescharacteristic
433C2×C332−1+411yescharacteristic
434C3⋊(C3⋊D3)—41no—
435C32×D3—22no—
436C32×D3—41no—
437C2×C3×Q8—31no—
438C2×C3×Q8—31no—
439C2×C3×Q8—61no—
440C2×C3×D4—91no—
441C22×C3×C4—91no—
442C22×C3×C4—91no—
443C22×C3×C4—91no—
444C2×#67—31no—
445C2×#67—31no—
446C2×#67—91no—
447C2×#67—91no—
448C2×#67—91no—
449C2×#67—91no—
450C2×#67—181no—
451C2×#67—181no—
452C22×Dic3—31no—
453C22×Dic3—31no—
454C22×Dic3—31no—
455C22×Dic3—91no—
456C22×Dic3—91no—
457C22×Dic3—181no—
458C2×D12—91no—
459C2×D12—91no—
460C2×C4×D3—31no—
461C2×C4×D3—31no—
462C2×C4×D3—31no—
463C2×C4×D3—91no—
464C2×C4×D3—91no—
465C2×C4×D3—91no—
466C2×C4×D3—91no—
467C2×C4×D3—181no—
468C2×C4×D3—181no—
469C2×C4×D3—181no—
470C2×C4×D3—361no—
471C2×Dic6D3211yescharacteristic
472C3×C4⋊C4—91no—
473C3×C4⋊C4—91no—
474C3×C4⋊C4—91no—
475C3×C4⋊C4—91no—
476C3×C4⋊C4—91no—
477C3×C4⋊C4—91no—
478C3×C4⋊C4—91no—
479C3×C4⋊C4—91no—
480C3×C22⋊C4—31no—
481C3×C22⋊C4—31no—
482C3×C22⋊C4—31no—
483C3×C22⋊C4—31no—
484C3×C22⋊C4—61no—
485C3×C22⋊C4—61no—
486C3×C22⋊C4—91no—
487C3×C22⋊C4—91no—
488C3×C22⋊C4—91no—
489#217—31no—
490#217—31no—
491#217—31no—
492#217—91no—
493#217—91no—
494#217—181no—
495(C2×D3)⋊C4—31no—
496(C2×D3)⋊C4—31no—
497(C2×D3)⋊C4—31no—
498(C2×D3)⋊C4—91no—
499(C2×D3)⋊C4—91no—
500(C2×D3)⋊C4—91no—
501(C2×D3)⋊C4—91no—
502(C2×D3)⋊C4—91no—
503(C2×D3)⋊C4—91no—
504(C2×D3)⋊C4—91no—
505(C2×D3)⋊C4—91no—
506(C2×D3)⋊C4—91no—
507(C2×D3)⋊C4—91no—
508(C2×D3)⋊C4—91no—
509(C2×D3)⋊C4—91no—
510(C2×D3)⋊C4—91no—
511(C2×D3)⋊C4—181no—
512(C2×D3)⋊C4—181no—
513(C2×D3)⋊C4—181no—
514(C2×D3)⋊C4—181no—
515(C2×D3)⋊C4D3211yescharacteristic
516(C2×D3)⋊C4D3211yescharacteristic
517C4⋊Dic3—31no—
518C4⋊Dic3—31no—
519C4⋊Dic3—31no—
520C4⋊Dic3—31no—
521C4⋊Dic3—31no—
522C4⋊Dic3—31no—
523C4⋊Dic3—31no—
524C4⋊Dic3—61no—
525C4⋊Dic3—91no—
526C4⋊Dic3—91no—
527C4⋊Dic3—91no—
528C4⋊Dic3—91no—
529C4⋊Dic3—91no—
530C4⋊Dic3—91no—
531C4⋊Dic3—91no—
532C4⋊Dic3—181no—
533Dic3⋊C4—31no—
534Dic3⋊C4—31no—
535Dic3⋊C4—31no—
536Dic3⋊C4—31no—
537Dic3⋊C4—31no—
538Dic3⋊C4—31no—
539Dic3⋊C4—31no—
540Dic3⋊C4—31no—
541Dic3⋊C4—31no—
542Dic3⋊C4—61no—
543Dic3⋊C4—61no—
544Dic3⋊C4—91no—
545Dic3⋊C4—91no—
546Dic3⋊C4—91no—
547Dic3⋊C4—91no—
548Dic3⋊C4—91no—
549Dic3⋊C4—91no—
550Dic3⋊C4—91no—
551Dic3⋊C4—91no—
552Dic3⋊C4—91no—
553Dic3⋊C4—91no—
554Dic3⋊C4—91no—
555Dic3⋊C4—181no—
556Dic3⋊C4—181no—
557C4×Dic3—91no—
558C4×Dic3—91no—
559C4×Dic3—91no—
560C4×Dic3—91no—
561C4×Dic3—91no—
562C4×Dic3—91no—
563C4×Dic3—181no—
564C22×C32—21no—
565C22×C32—21no—
566C22×C32—21no—
567C22×C32—32no—
568C22×C32—41no—
569C22×C32—61no—
570C22×C32—61no—
571C22×C32—61no—
572C22×C32—61no—
573C22×C32—61no—
574C22×C32C23×D311yescharacteristic
575C22×C32C23×D311yescharacteristic
576C22×C32C23×D311yescharacteristic
577C2×C3⋊D3—61no—
578C2×C3⋊D3—61no—
579C2×C3⋊D3—61no—
580C2×C3⋊D3—62no—
581C2×C3⋊D3—62no—
582C2×C3⋊D3—62no—
583C2×C3⋊D3—61no—
584C2×C3⋊D3—61no—
585C2×C3⋊D3—61no—
586C2×C3⋊D3—61no—
587C2×C3⋊D3—61no—
588C2×C3⋊D3—61no—
589C2×C3⋊D3—121no—
590C2×C3⋊D3—121no—
591C2×C3⋊D3—121no—
592C2×C3⋊D3—121no—
593C2×C3⋊D3—121no—
594C2×C3⋊D3—121no—
595C2×C3⋊D3—122no—
596C2×C3⋊D3—122no—
597C2×C3⋊D3—122no—
598C2×C3×D3—21no—
599C2×C3×D3—21no—
600C2×C3×D3—21no—
601C2×C3×D3—21no—
602C2×C3×D3—21no—
603C2×C3×D3—21no—
604C2×C3×D3—21no—
605C2×C3×D3—21no—
606C2×C3×D3—21no—
607C2×C3×D3—21no—
608C2×C3×D3—22no—
609C2×C3×D3—41no—
610C2×C3×D3—41no—
611C2×C3×D3—41no—
612C2×C3×D3—41no—
613C2×C3×D3—41no—
614C2×C3×D3#23712yes—
615C2×C3×D3#23912yes—
616C32×C4—21no—
617C32×C4—22no—
618C32×C4—21no—
619C32×C4—21no—
620C32×C4—41no—
621C32×C4—41no—
622C32×C4—42no—
623C32×C4—61no—
624C32×C4—61no—
625C32×C4—61no—
626C32×C4—61no—
627C3⋊Dic3—21no—
628C3⋊Dic3—21no—
629C3⋊Dic3—21no—
630C3⋊Dic3—21no—
631C3⋊Dic3—21no—
632C3⋊Dic3—21no—
633C3⋊Dic3—61no—
634C3⋊Dic3—62no—
635C3⋊Dic3—61no—
636C3⋊Dic3—61no—
637C3⋊Dic3—121no—
638C3⋊Dic3—121no—
639C3⋊Dic3—122no—
640C3×Dic3—21no—
641C3×Dic3—21no—
642C3×Dic3—21no—
643C3×Dic3—21no—
644C3×Dic3—21no—
645C3×Dic3—21no—
646C3×Dic3—21no—
647C3×Dic3—21no—
648C3×Dic3—41no—
649C3×Dic3—41no—
650C3×Dic3—41no—
651C3×Dic3—41no—
652C3×Dic3—62no—
653C3×Dic3—61no—
654C3×Dic3—61no—
655C3×Dic3—61no—
656C3×Dic3—61no—
657C3×Dic3—61no—
658C3×Dic3—61no—
659C3×Dic3—61no—
660C3×Dic3—61no—
661C3×Dic3—61no—
662C3×Dic3—61no—
663C3×Dic3—61no—
664C3×Dic3—61no—
665C3×Dic3—121no—
666C3×Dic3—121no—
667C3×Dic3—121no—
668C3×Dic3—121no—
669C3×Dic3—121no—
670#126—271no—
671#126—271no—
672#125—271no—
673#125—271no—
674#123—91no—
675#123—271no—
676#123—271no—
677#123—271no—
678C22⋊Q8—91no—
679C22⋊Q8—91no—
680C22⋊Q8—271no—
681#121—271no—
682C4×D4—271no—
683C4×D4—271no—
684C2×C4⋊C4—271no—
685C33#53911yescharacteristic, complemented, Sylow
686C23×C3—31no—
687C23×C3—31no—
688C23×C3—31no—
689C23×C3—31no—
690C23×C3—61no—
691C23×C3—61no—
692C22×D3—91no—
693C22×D3—91no—
694C22×D3—91no—
695C22×D3—181no—
696C22×D3—181no—
697C22×D3—181no—
698C22×D3—361no—
699C22×D3C2×D3211yescharacteristic
700C22×D3C2×D3211yescharacteristic
701C3×Q8—121no—
702C3×Q8—121no—
703C3×Q8—122no—
704C3×D4—182no—
705C2×C3×C4—21no—
706C2×C3×C4—21no—
707C2×C3×C4—21no—
708C2×C3×C4—31no—
709C2×C3×C4—31no—
710C2×C3×C4—31no—
711C2×C3×C4—31no—
712C2×C3×C4—31no—
713C2×C3×C4—31no—
714C2×C3×C4—31no—
715C2×C3×C4—31no—
716C2×C3×C4—41no—
717C2×C3×C4—61no—
718C2×C3×C4—61no—
719C2×C3×C4—61no—
720C2×C3×C4—61no—
721C2×C3×C4—91no—
722C2×C3×C4—91no—
723C2×C3×C4—91no—
724C2×C3×C4—91no—
725C2×C3×C4—91no—
726C2×C3×C4—91no—
727C2×C3×C4—182no—
728C2×C3×C4—361no—
729C2×C3×C4—361no—
730C2×C3×C4C2×D3211yescharacteristic
731C2×C3×C4C2×D3211yescharacteristic
732C2×C3×C4C2×D3211yescharacteristic
733#67—62no—
734#67—62no—
735#67—182no—
736#67—182no—
737#67—184no—
738#67—361no—
739#67—361no—
740#67—362no—
741C2×Dic3—31no—
742C2×Dic3—31no—
743C2×Dic3—31no—
744C2×Dic3—31no—
745C2×Dic3—31no—
746C2×Dic3—31no—
747C2×Dic3—31no—
748C2×Dic3—31no—
749C2×Dic3—31no—
750C2×Dic3—31no—
751C2×Dic3—31no—
752C2×Dic3—31no—
753C2×Dic3—61no—
754C2×Dic3—61no—
755C2×Dic3—61no—
756C2×Dic3—61no—
757C2×Dic3—61no—
758C2×Dic3—61no—
759C2×Dic3—62no—
760C2×Dic3—91no—
761C2×Dic3—91no—
762C2×Dic3—91no—
763C2×Dic3—121no—
764C2×Dic3—121no—
765C2×Dic3—181no—
766C2×Dic3—181no—
767C2×Dic3—181no—
768C2×Dic3—361no—
769C2×Dic3—361no—
770C2×Dic3—361no—
771C2×Dic3—362no—
772C2×Dic3C2×D3211yescharacteristic
773C2×Dic3C2×D3211yescharacteristic
774C2×Dic3C2×D3211yescharacteristic
775C2×Dic3C2×D3211yescharacteristic
776D12—182no—
777D12—361no—
778C4×D3—62no—
779C4×D3—121no—
780C4×D3—121no—
781C4×D3—361no—
782C4×D3—361no—
783C4×D3—361no—
784C4×D3—362no—
785C4×D3—361no—
786C4×D3—362no—
787C4×D3—362no—
788C4×D3—364no—
789Dic6—41no—
790C2×C32—21no—
791C2×C32—21no—
792C2×C32—21no—
793C2×C32—21no—
794C2×C32—21no—
795C2×C32—21no—
796C2×C32—21no—
797C2×C32—21no—
798C2×C32—21no—
799C2×C32—41no—
800C2×C32—41no—
801C2×C32—41no—
802C2×C32—62no—
803C2×C32—121no—
804C2×C32C2×#23711yescharacteristic
805C2×C32#100411yescharacteristic
806C2×C32#100411yescharacteristic
807C2×C32C2×#23911yescharacteristic
808C2×C32#100711yescharacteristic
809C2×C32D3×#4111yescharacteristic
810C2×C32#100911yescharacteristic
811C2×C32#101011yescharacteristic
812C2×C32#101011yescharacteristic
813C3⋊D3—122no—
814C3⋊D3—122no—
815C3⋊D3—122no—
816C3⋊D3—124no—
817C3⋊D3—121no—
818C3⋊D3—121no—
819C3⋊D3—121no—
820C3×D3—22no—
821C3×D3—22no—
822C3×D3—42no—
823C3×D3—41no—
824C3×D3—41no—
825C3×D3—81no—
826C2×Q8—31no—
827C2×D4—91no—
828C2×D4—271no—
829C2×D4—271no—
830C22×C4—91no—
831C22×C4—91no—
832C22×C4—91no—
833C22×C4—271no—
834C22×C4—271no—
835C4⋊C4—91no—
836C4⋊C4—91no—
837C4⋊C4—91no—
838C4⋊C4—91no—
839C4⋊C4—91no—
840C4⋊C4—91no—
841C4⋊C4—91no—
842C4⋊C4—91no—
843C4⋊C4—271no—
844C4⋊C4—271no—
845C4⋊C4—271no—
846C4⋊C4—271no—
847C4⋊C4—271no—
848C4⋊C4—271no—
849C22⋊C4—31no—
850C22⋊C4—31no—
851C22⋊C4—91no—
852C22⋊C4—91no—
853C22⋊C4—91no—
854C22⋊C4—271no—
855C22⋊C4—271no—
856C22⋊C4—271no—
857C22⋊C4—271no—
858C22⋊C4—271no—
859C42—271no—
860C42—271no—
861C22×C3—21no—
862C22×C3—21no—
863C22×C3—21no—
864C22×C3—32no—
865C22×C3—32no—
866C22×C3—41no—
867C22×C3—62no—
868C22×C3—61no—
869C22×C3—61no—
870C22×C3—61no—
871C22×C3—61no—
872C22×C3—61no—
873C22×C3—61no—
874C22×C3—61no—
875C22×C3—61no—
876C22×C3—61no—
877C22×C3—61no—
878C22×C3—121no—
879C22×C3—121no—
880C22×C3—121no—
881C22×C3—121no—
882C22×C3—121no—
883C22×C3C22×D3211yescharacteristic
884C22×C3C22×D3211yescharacteristic
885C22×C3C22×D3211yescharacteristic
886C2×D3—21no—
887C2×D3—21no—
888C2×D3—21no—
889C2×D3—21no—
890C2×D3—21no—
891C2×D3—182no—
892C2×D3—182no—
893C2×D3—182no—
894C2×D3—181no—
895C2×D3—181no—
896C2×D3—181no—
897C2×D3—181no—
898C2×D3—181no—
899C2×D3—181no—
900C2×D3—181no—
901C2×D3—181no—
902C2×D3—181no—
903C2×D3—361no—
904C2×D3—361no—
905C2×D3—361no—
906C2×D3—361no—
907C2×D3—361no—
908C2×D3—361no—
909C2×D3—362no—
910C2×D3—362no—
911C2×D3—362no—
912C2×D3#379612yes—
913C3×C4—22no—
914C3×C4—21no—
915C3×C4—21no—
916C3×C4—21no—
917C3×C4—41no—
918C3×C4—41no—
919C3×C4—42no—
920C3×C4—61no—
921C3×C4—61no—
922C3×C4—61no—
923C3×C4—61no—
924C3×C4—61no—
925C3×C4—61no—
926C3×C4—61no—
927C3×C4—61no—
928C3×C4—121no—
929C3×C4—121no—
930C3×C4—121no—
931C3×C4—121no—
932C3×C4—181no—
933C3×C4—181no—
934C3×C4—181no—
935C3×C4—181no—
936C3×C4—181no—
937C3×C4—181no—
938Dic3—21no—
939Dic3—21no—
940Dic3—21no—
941Dic3—21no—
942Dic3—62no—
943Dic3—61no—
944Dic3—61no—
945Dic3—61no—
946Dic3—61no—
947Dic3—61no—
948Dic3—61no—
949Dic3—61no—
950Dic3—61no—
951Dic3—61no—
952Dic3—61no—
953Dic3—61no—
954Dic3—61no—
955Dic3—121no—
956Dic3—121no—
957Dic3—121no—
958Dic3—121no—
959Dic3—121no—
960Dic3—182no—
961Dic3—181no—
962Dic3—181no—
963Dic3—181no—
964Dic3—361no—
965Dic3—361no—
966Dic3—362no—
967C32—21no—
968C32—21no—
969C32—21no—
970C32—41no—
971C32#563811yescharacteristic, complemented
972C32#564511yescharacteristic, complemented
973C32#566511yescharacteristic, complemented
974C23—31no—
975C23—31no—
976C23—271no—
977Q8—121no—
978D4—182no—
979D4—542no—
980D4—1081no—
981C2×C4—31no—
982C2×C4—31no—
983C2×C4—31no—
984C2×C4—31no—
985C2×C4—91no—
986C2×C4—91no—
987C2×C4—91no—
988C2×C4—91no—
989C2×C4—91no—
990C2×C4—91no—
991C2×C4—182no—
992C2×C4—271no—
993C2×C4—361no—
994C2×C4—361no—
995C2×C4—1081no—
996C2×C4—1081no—
997C2×C4D3311yescharacteristic
998C2×C3—21no—
999C2×C3—21no—
1000C2×C3—21no—
1001C2×C3—21no—
1002C2×C3—21no—
1003C2×C3—21no—
1004C2×C3—21no—
1005C2×C3—21no—
1006C2×C3—21no—
1007C2×C3—41no—
1008C2×C3—41no—
1009C2×C3—41no—
1010C2×C3—62no—
1011C2×C3—62no—
1012C2×C3—122no—
1013C2×C3—121no—
1014C2×C3—121no—
1015C2×C3—241no—
1016C2×C3C2×#379611yescharacteristic
1017C2×C3#6429711yescharacteristic
1018C2×C3#6430911yescharacteristic
1019C2×C3D3×#23711yescharacteristic
1020C2×C3#6431411yescharacteristic
1021C2×C3#6431411yescharacteristic
1022C2×C3#6431511yescharacteristic
1023C2×C3D3×#23911yescharacteristic
1024C2×C3#6433011yescharacteristic
1025D3—22no—
1026D3—41no—
1027D3—362no—
1028D3—362no—
1029D3—362no—
1030D3—364no—
1031D3—361no—
1032D3—361no—
1033D3—361no—
1034C22—32no—
1035C22—61no—
1036C22—61no—
1037C22—61no—
1038C22—61no—
1039C22—61no—
1040C22—541no—
1041C22—541no—
1042C22—541no—
1043C22C2×D3311yescharacteristic
1044C4—21no—
1045C4—61no—
1046C4—61no—
1047C4—61no—
1048C4—61no—
1049C4—181no—
1050C4—181no—
1051C4—181no—
1052C4—181no—
1053C4—181no—
1054C4—181no—
1055C4—541no—
1056C3—21no—
1057C3—21no—
1058C3—21no—
1059C3—41no—
1060C3#1059412911yescharacteristic, complemented
1061C3#1059417911yescharacteristic, complemented
1062C3#1059537811yescharacteristic, complemented
1063C2—62no—
1064C2—121no—
1065C2—1081no—
1066C2D3×#379611yescharacteristic
1067C2#1172439311yescharacteristic
1068C2#1172441911yescharacteristic
subgroupG/H
center, FrattiniC22C2×D33
commutator, socle, cosocleC22×C33C24
FittingC2×C33×C4C23
prime radical#11722958C2
hypercenterC2×C4D33
hypocenterC33#539
LCSG ▷ C22×C33 ▷ C33
UCSC1 ◁ C22 ◁ C2×C4

Complements

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

NH ≅ G/Ntype
1. #11723669C2semidirect
2. #11723462C2semidirect
3. #11723456C2semidirect
4. #11723420C2semidirect
5. C3×#63891C2semidirect
6. C3×#63887C2semidirect
7. C3×#63887C2semidirect
8. #11723028C2semidirect
9. #11723019C2semidirect
10. #11723013C2semidirect
11. #11722987C2semidirect
12. #11722987C2semidirect
14. #11722924C2semidirect
15. D3×Dic3⋊Dic3C2semidirect
72. #63891D3semidirect
76. #63887D3semidirect
77. #63887D3semidirect
685. C33#539semidirect
971. C32#5638semidirect
972. C32#5645semidirect
973. C32#5665semidirect
1060. C3#10594129semidirect
1061. C3#10594179semidirect
1062. C3#10595378semidirect

Maximal subgroups

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

subgroupindex
#117236692
#117234622
#117234562
#117234202
C3×#638912
C3×#638872
#117230282
#117230192
#117230132
#117229872
#117229582
#117229242
D3×Dic3⋊Dic32
#105953783
#105941793
#105941293