Finite Group Databasebeta

← #13168222

Subgroups — #13168222

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#11723688C211yesmaximal, characteristic, complemented
2#11723462C211yesmaximal, characteristic, complemented
3#11723449C211yesmaximal, characteristic, complemented
4#11723421C211yesmaximal, characteristic, complemented
5C3×#63896C211yesmaximal, characteristic, complemented
6C3×#63890C211yesmaximal, characteristic, complemented
7C3×#63846C211yesmaximal, characteristic, complemented
8#11723027C211yesmaximal, characteristic, complemented
9#11723021C211yesmaximal, characteristic, complemented
10#11723013C211yesmaximal, characteristic, complemented
11#11722999C211yesmaximal, characteristic, complemented
12#11722987C211yesmaximal, characteristic, complemented
13#11722959C211yesmaximal, characteristic
14#11722928C211yesmaximal, characteristic, complemented
15D3×Dic3⋊Dic3C211yesmaximal, characteristic, complemented
16#10594454—31nomaximal
17#10594443—31nomaximal
18#10594179—31nomaximal
19C2×C4×C3⋊(C3⋊D3)C2211yescharacteristic
20C2×C3×#634C2211yescharacteristic
21C2×#6294C2211yescharacteristic
22C2×#6292C2211yescharacteristic
23C2×#6291C2211yescharacteristic
24C2×D3×C3⋊Dic3C2211yescharacteristic
25C2×C3×#626C2211yescharacteristic
26C2×C3×D3×Dic3C2211yescharacteristic
27C2×C3×D3×Dic3C2211yescharacteristic
28C3×#3752C2211yescharacteristic
29C3×#3750C2211yescharacteristic
30C32×(C2×D3)⋊C4C2211yescharacteristic
31C32×C4⋊Dic3C2211yescharacteristic
32C32×Dic3⋊C4C2211yescharacteristic
33#88815C2211yescharacteristic
34#88815C2211yescharacteristic
35#88814C2211yescharacteristic
36#88807C2211yescharacteristic
37Dic3⋊(C3⋊Dic3)C2211yescharacteristic
38Dic3⋊(C3⋊Dic3)C2211yescharacteristic
39#88804C2211yescharacteristic
40#88804C2211yescharacteristic
41#88804C2211yescharacteristic
42#88804C2211yescharacteristic
43#88803C2211yescharacteristic
44Dic3×C3⋊Dic3C2211yescharacteristic
45C3×#3724C2211yescharacteristic
46C3×Dic3⋊Dic3C2211yescharacteristic
47C3×Dic3⋊Dic3C2211yescharacteristic
48C3×Dic3⋊Dic3C2211yescharacteristic
49C3×Dic3⋊Dic3C2211yescharacteristic
50C3×Dic3⋊Dic3C2211yescharacteristic
51C3×#3722C2211yescharacteristic
52C3×(C2×D3)⋊Dic3C2211yescharacteristic
53C3×Dic32C2211yescharacteristic
54#64106—31no—
55#64103—31no—
56#64090—31no—
57C3×#896—31no—
58C3×#894—31no—
59C3×#890—31no—
60C3×#889—31no—
61C3×#886—31no—
62C3×#878—31no—
63#63978—31no—
64#67⋊Dic3—31no—
65#63966—31no—
66C2×Dic3⋊Dic3—31no—
67#63909—31no—
68#63897—31no—
69#63896—31no—
70#63896D311yescharacteristic, complemented
71Dic3×D12—31no—
72#63890—31no—
73#63890—31no—
74#63890—31no—
75#63890D311yescharacteristic, complemented
76D3×C4⋊Dic3—31no—
77#63888—31no—
78#63887—31no—
79#63886—31no—
80#63881—31no—
81#63881—31no—
82#63881—61no—
83#63880—31no—
84D3×Dic3⋊C4—31no—
85#63872—31no—
86#63871—31no—
87#63871—31no—
88#63871—61no—
89#63868—31no—
90#63868—31no—
91#63862—31no—
92#63861—31no—
93#63853—31no—
94#63853—31no—
95#63853—61no—
96#63850—31no—
97#63848—31no—
98#63848—31no—
99#63846—31no—
100#63846D311yescharacteristic, complemented
101#63845—31no—
102C22×C3⋊(C3⋊D3)C2311yescharacteristic
103C22×C3×C3⋊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
113C3×#634—41no—
114C2×C32×Dic3C2311yescharacteristic
115C2×C32×Dic3C2311yescharacteristic
116C2×C32×Dic3C2311yescharacteristic
117C2×C32×Dic3C2311yescharacteristic
118C2×C32×Dic3C2311yescharacteristic
119#6294—41no—
120#6292—41no—
121#6291—22no—
122D3×C3⋊Dic3—41no—
123C3×#626—22no—
124C3×D3×Dic3—22no—
125C3×D3×Dic3—41no—
126#5692—91no—
127#5665—91no—
128#5645—91no—
129C2×#638—31no—
130C22×C3⋊Dic3—31no—
131C2×C4⋊(C3⋊D3)—31no—
132C2×C4×C3⋊D3—31no—
133C2×C4×C3⋊D3—31no—
134C2×C4×C3⋊D3—31no—
135C2×C4×C3⋊D3—61no—
136C2×C4×C3⋊D3—61no—
137C2×C4×C3⋊D3—61no—
138C2×C4×C3⋊D3—121no—
139C2×#634C2×D311yescharacteristic
140C2×C3×#67—31no—
141C22×C3×Dic3—31no—
142C22×C3×Dic3—31no—
143C2×C3×D12—31no—
144C2×C3×C4×D3—31no—
145C2×C3×C4×D3—31no—
146C2×C3×Dic6—31no—
147C2×C3×Dic6—31no—
148C2×C3×Dic6—61no—
149C2×#626—31no—
150C2×#626—31no—
151C2×#626—31no—
152C2×#626—31no—
153C2×#626—61no—
154C2×#626—61no—
155C2×#626C2×D311yescharacteristic
156C2×#624—31no—
157C2×D3×Dic3—31no—
158C2×D3×Dic3—31no—
159C2×D3×Dic3—31no—
160C2×D3×Dic3—31no—
161C2×D3×Dic3—61no—
162C2×D3×Dic3C2×D311yescharacteristic
163C2×D3×Dic3C2×D311yescharacteristic
164C32×C4⋊C4—31no—
165C32×C4⋊C4—31no—
166C32×C22⋊C4—31no—
167#3752—31no—
168#3752—31no—
169#3752—31no—
170#3752—31no—
171#3752—31no—
172#3752C2×D311yescharacteristic
173C4⋊(C3⋊Dic3)—31no—
174C4⋊(C3⋊Dic3)—31no—
175#3750—31no—
176#3750C2×D311yescharacteristic
177C4×C3⋊Dic3—31no—
178C3×#217—31no—
179C3×(C2×D3)⋊C4—21no—
180C3×(C2×D3)⋊C4—31no—
181C3×(C2×D3)⋊C4—31no—
182C3×(C2×D3)⋊C4—31no—
183C3×(C2×D3)⋊C4—31no—
184C3×(C2×D3)⋊C4—31no—
185C3×(C2×D3)⋊C4—61no—
186C3×(C2×D3)⋊C4C2×D311yescharacteristic
187C3×(C2×D3)⋊C4C2×D311yescharacteristic
188C3×C4⋊Dic3—21no—
189C3×C4⋊Dic3—31no—
190C3×C4⋊Dic3—31no—
191C3×C4⋊Dic3—31no—
192C3×C4⋊Dic3—31no—
193C3×C4⋊Dic3—31no—
194C3×C4⋊Dic3C2×D311yescharacteristic
195C3×C4⋊Dic3C2×D311yescharacteristic
196C3×Dic3⋊C4—21no—
197C3×Dic3⋊C4—31no—
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—61no—
207C3×Dic3⋊C4C2×D311yescharacteristic
208C3×Dic3⋊C4C2×D311yescharacteristic
209C3×C4×Dic3—31no—
210C3×C4×Dic3—31no—
211#3724—31no—
212#3724—31no—
213#3724C2×D311yescharacteristic
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—31no—
241#3722—61no—
242#3722—61no—
243#3722—61no—
244#3722—61no—
245#3722C2×D311yescharacteristic
246(C2×D3)⋊Dic3—31no—
247(C2×D3)⋊Dic3—31no—
248(C2×D3)⋊Dic3—31no—
249(C2×D3)⋊Dic3—31no—
250(C2×D3)⋊Dic3—61no—
251(C2×D3)⋊Dic3C2×D311yescharacteristic
252Dic32—31no—
253Dic32—31no—
254Dic32—61no—
255Dic32C2×D311yescharacteristic
256C22×C33C2411yescharacteristic
257C2×C3⋊(C3⋊D3)—21no—
258C2×C3⋊(C3⋊D3)—21no—
259C2×C3⋊(C3⋊D3)—21no—
260C2×C3×C3⋊D3—21no—
261C2×C3×C3⋊D3—21no—
262C2×C3×C3⋊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—
273C32×Dic3—21no—
274C32×Dic3—21no—
275C32×Dic3—21no—
276C32×Dic3—21no—
277C32×Dic3—21no—
278C3×#125—91no—
279C3×#123—91no—
280C3×C22⋊Q8—91no—
281#946—91no—
282#946—91no—
283#939—91no—
284D4×Dic3—91no—
285#930—91no—
286#929—91no—
287C2×C4⋊Dic3—91no—
288C2×Dic3⋊C4—91no—
289#898—91no—
290#898—91no—
291#898—91no—
292#898—91no—
293#897—91no—
294#897—91no—
295#897—181no—
296#896—31no—
297#896—91no—
298#895—91no—
299#894—31no—
300#894—91no—
301#894—91no—
302#894—91no—
303#894—91no—
304#894—91no—
305#894—181no—
306#893—91no—
307D3×C4⋊C4—91no—
308#890—31no—
309#890—91no—
310#890—91no—
311#889—31no—
312#889—91no—
313#886—31no—
314#886—91no—
315#886—91no—
316#883—91no—
317#67⋊C4—91no—
318#67⋊C4—91no—
319#67⋊C4—91no—
320#67⋊C4—181no—
321#879—91no—
322#878—31no—
323#878—91no—
324#876—91no—
325C4×D12—91no—
326C23×C32—31no—
327C22×C3⋊D3—31no—
328C22×C3⋊D3—31no—
329C22×C3⋊D3—31no—
330C22×C3⋊D3—61no—
331C22×C3⋊D3—61no—
332C22×C3⋊D3—61no—
333C22×C3⋊D3—121no—
334C22×C3⋊D3C22×D311yescharacteristic
335C22×C3×D3—21no—
336C22×C3×D3—31no—
337C22×C3×D3—31no—
338C22×C3×D3—61no—
339C22×C3×D3C22×D311yescharacteristic
340C22×C3×D3C22×D311yescharacteristic
341C2×C32×C4—21no—
342C2×C32×C4—21no—
343C2×C32×C4—21no—
344C2×C32×C4—31no—
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—
354C2×C3⋊Dic3—31no—
355C2×C3⋊Dic3—31no—
356C2×C3⋊Dic3—31no—
357C2×C3⋊Dic3—61no—
358C2×C3⋊Dic3—61no—
359C2×C3⋊Dic3—61no—
360C2×C3⋊Dic3—121no—
361C2×C3⋊Dic3—121no—
362C2×C3⋊Dic3C22×D311yescharacteristic
363C2×C3⋊Dic3C22×D311yescharacteristic
364C2×C3⋊Dic3C22×D311yescharacteristic
365C2×C3⋊Dic3C22×D311yescharacteristic
366C2×C3⋊Dic3C22×D311yescharacteristic
367C4⋊(C3⋊D3)—121no—
368C4×C3⋊D3—121no—
369C4×C3⋊D3—121no—
370C4×C3⋊D3—121no—
371C4×C3⋊D3—122no—
372C4×C3⋊D3—122no—
373C4×C3⋊D3—122no—
374C4×C3⋊D3—124no—
375#634—41no—
376C3×#67—62no—
377C2×C3×Dic3—21no—
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—61no—
393C2×C3×Dic3—61no—
394C2×C3×Dic3—61no—
395C2×C3×Dic3—61no—
396C2×C3×Dic3—61no—
397C2×C3×Dic3—62no—
398C2×C3×Dic3—121no—
399C2×C3×Dic3C22×D311yescharacteristic
400C2×C3×Dic3C22×D311yescharacteristic
401C2×C3×Dic3C22×D311yescharacteristic
402C2×C3×Dic3C22×D311yescharacteristic
403C2×C3×Dic3C22×D311yescharacteristic
404C2×C3×Dic3C22×D311yescharacteristic
405C2×C3×Dic3C22×D311yescharacteristic
406C2×C3×Dic3C22×D311yescharacteristic
407C2×C3×Dic3C22×D311yescharacteristic
408C2×C3×Dic3C22×D311yescharacteristic
409C3×D12—62no—
410C3×C4×D3—62no—
411C3×C4×D3—121no—
412C3×Dic6—121no—
413C3×Dic6—121no—
414C3×Dic6—122no—
415#626—22no—
416#626—64no—
417#626—62no—
418#626—62no—
419#626—121no—
420#626—121no—
421#626—122no—
422#624—121no—
423D3×Dic3—22no—
424D3×Dic3—41no—
425D3×Dic3—121no—
426D3×Dic3—121no—
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—
435C3×C3⋊D3—41no—
436C32×D3—22no—
437C2×C3×Q8—91no—
438C2×C3×D4—91no—
439C22×C3×C4—91no—
440C22×C3×C4—91no—
441C2×#67—31no—
442C2×#67—91no—
443C2×#67—91no—
444C2×#67—91no—
445C2×#67—181no—
446C22×Dic3—31no—
447C22×Dic3—31no—
448C22×Dic3—91no—
449C22×Dic3—91no—
450C22×Dic3—91no—
451C22×Dic3—181no—
452C2×D12—31no—
453C2×D12—91no—
454C2×D12—91no—
455C2×D12—91no—
456C2×D12—181no—
457C2×C4×D3—31no—
458C2×C4×D3—31no—
459C2×C4×D3—91no—
460C2×C4×D3—91no—
461C2×C4×D3—91no—
462C2×C4×D3—91no—
463C2×C4×D3—91no—
464C2×C4×D3—91no—
465C2×C4×D3—181no—
466C2×C4×D3—181no—
467C2×C4×D3—181no—
468C2×C4×D3—361no—
469C2×Dic6—31no—
470C2×Dic6—31no—
471C2×Dic6—61no—
472C3×C4⋊C4—31no—
473C3×C4⋊C4—31no—
474C3×C4⋊C4—31no—
475C3×C4⋊C4—31no—
476C3×C4⋊C4—61no—
477C3×C4⋊C4—61no—
478C3×C4⋊C4—91no—
479C3×C4⋊C4—91no—
480C3×C4⋊C4—91no—
481C3×C4⋊C4—91no—
482C3×C4⋊C4—91no—
483C3×C4⋊C4—91no—
484C3×C4⋊C4—91no—
485C3×C22⋊C4—31no—
486C3×C22⋊C4—31no—
487C3×C22⋊C4—61no—
488C3×C22⋊C4—91no—
489C3×C22⋊C4—91no—
490C3×C22⋊C4—91no—
491C3×C42—91no—
492#217—31no—
493#217—91no—
494#217—91no—
495(C2×D3)⋊C4—31no—
496(C2×D3)⋊C4—31no—
497(C2×D3)⋊C4—31no—
498(C2×D3)⋊C4—31no—
499(C2×D3)⋊C4—31no—
500(C2×D3)⋊C4—61no—
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—91no—
512(C2×D3)⋊C4—91no—
513(C2×D3)⋊C4—91no—
514(C2×D3)⋊C4—91no—
515(C2×D3)⋊C4—91no—
516(C2×D3)⋊C4—91no—
517(C2×D3)⋊C4—181no—
518(C2×D3)⋊C4—181no—
519(C2×D3)⋊C4—181no—
520(C2×D3)⋊C4—181no—
521(C2×D3)⋊C4—181no—
522(C2×D3)⋊C4D3211yescharacteristic
523C4⋊Dic3—31no—
524C4⋊Dic3—31no—
525C4⋊Dic3—31no—
526C4⋊Dic3—31no—
527C4⋊Dic3—31no—
528C4⋊Dic3—91no—
529C4⋊Dic3—91no—
530C4⋊Dic3—91no—
531C4⋊Dic3—91no—
532C4⋊Dic3—91no—
533C4⋊Dic3—91no—
534C4⋊Dic3—91no—
535C4⋊Dic3—181no—
536C4⋊Dic3—181no—
537C4⋊Dic3D3211yescharacteristic
538Dic3⋊C4—31no—
539Dic3⋊C4—31no—
540Dic3⋊C4—31no—
541Dic3⋊C4—31no—
542Dic3⋊C4—31no—
543Dic3⋊C4—31no—
544Dic3⋊C4—31no—
545Dic3⋊C4—31no—
546Dic3⋊C4—31no—
547Dic3⋊C4—61no—
548Dic3⋊C4—91no—
549Dic3⋊C4—91no—
550Dic3⋊C4—91no—
551Dic3⋊C4—91no—
552Dic3⋊C4—91no—
553Dic3⋊C4—91no—
554Dic3⋊C4—91no—
555Dic3⋊C4—91no—
556Dic3⋊C4—181no—
557Dic3⋊C4D3211yescharacteristic
558C4×Dic3—31no—
559C4×Dic3—31no—
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×C32C23×D311yescharacteristic
572C22×C32C23×D311yescharacteristic
573C22×C32C23×D311yescharacteristic
574C2×C3⋊D3—21no—
575C2×C3⋊D3—21no—
576C2×C3⋊D3—21no—
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—22no—
603C2×C3×D3—41no—
604C2×C3×D3—41no—
605C2×C3×D3—61no—
606C2×C3×D3—61no—
607C2×C3×D3—61no—
608C2×C3×D3—61no—
609C2×C3×D3—61no—
610C2×C3×D3—61no—
611C2×C3×D3—121no—
612C2×C3×D3—121no—
613C2×C3×D3—121no—
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—
627C32×C4—61no—
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—21no—
649C3×Dic3—21no—
650C3×Dic3—41no—
651C3×Dic3—41no—
652C3×Dic3—41no—
653C3×Dic3—41no—
654C3×Dic3—41no—
655C3×Dic3—62no—
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—61no—
666C3×Dic3—121no—
667C3×Dic3—121no—
668C3×Dic3—121no—
669C3×Dic3—121no—
670#126—271no—
671#126—271no—
672#125—91no—
673#125—271no—
674#123—91no—
675#123—271no—
676#123—271no—
677#123—271no—
678C22⋊Q8—91no—
679C22⋊Q8—271no—
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—61no—
689C23×C3—91no—
690C22×D3—31no—
691C22×D3—31no—
692C22×D3—61no—
693C22×D3—91no—
694C22×D3—91no—
695C22×D3—91no—
696C22×D3—181no—
697C22×D3—181no—
698C22×D3—181no—
699C22×D3—361no—
700C22×D3C2×D3211yescharacteristic
701C3×Q8—361no—
702C3×D4—182no—
703C2×C3×C4—21no—
704C2×C3×C4—21no—
705C2×C3×C4—21no—
706C2×C3×C4—31no—
707C2×C3×C4—31no—
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—61no—
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×C4C2×D3211yescharacteristic
730C2×C3×C4C2×D3211yescharacteristic
731C2×C3×C4C2×D3211yescharacteristic
732#67—62no—
733#67—182no—
734#67—182no—
735#67—184no—
736#67—361no—
737C2×Dic3—31no—
738C2×Dic3—31no—
739C2×Dic3—31no—
740C2×Dic3—31no—
741C2×Dic3—31no—
742C2×Dic3—31no—
743C2×Dic3—31no—
744C2×Dic3—31no—
745C2×Dic3—31no—
746C2×Dic3—31no—
747C2×Dic3—61no—
748C2×Dic3—61no—
749C2×Dic3—61no—
750C2×Dic3—61no—
751C2×Dic3—61no—
752C2×Dic3—62no—
753C2×Dic3—91no—
754C2×Dic3—91no—
755C2×Dic3—91no—
756C2×Dic3—121no—
757C2×Dic3—181no—
758C2×Dic3—181no—
759C2×Dic3—181no—
760C2×Dic3—361no—
761C2×Dic3—361no—
762C2×Dic3—361no—
763C2×Dic3—361no—
764C2×Dic3—362no—
765C2×Dic3C2×D3211yescharacteristic
766C2×Dic3C2×D3211yescharacteristic
767C2×Dic3C2×D3211yescharacteristic
768C2×Dic3C2×D3211yescharacteristic
769C2×Dic3C2×D3211yescharacteristic
770D12—62no—
771D12—182no—
772D12—361no—
773D12—361no—
774D12—362no—
775C4×D3—62no—
776C4×D3—121no—
777C4×D3—361no—
778C4×D3—361no—
779C4×D3—361no—
780C4×D3—361no—
781C4×D3—361no—
782C4×D3—362no—
783C4×D3—361no—
784C4×D3—362no—
785C4×D3—362no—
786C4×D3—364no—
787Dic6—121no—
788Dic6—121no—
789Dic6—122no—
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×C32C2×#23711yescharacteristic
804C2×C32#100411yescharacteristic
805C2×C32C2×#23911yescharacteristic
806C2×C32#100711yescharacteristic
807C2×C32D3×#4111yescharacteristic
808C2×C32#100911yescharacteristic
809C2×C32#100911yescharacteristic
810C2×C32#101011yescharacteristic
811C2×C32#101011yescharacteristic
812C3⋊D3—41no—
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—121no—
824C3×D3—121no—
825C3×D3—241no—
826C2×Q8—91no—
827C2×D4—91no—
828C2×D4—271no—
829C2×D4—271no—
830C22×C4—91no—
831C22×C4—91no—
832C22×C4—271no—
833C22×C4—271no—
834C22×C4—271no—
835C4⋊C4—31no—
836C4⋊C4—31no—
837C4⋊C4—91no—
838C4⋊C4—91no—
839C4⋊C4—91no—
840C4⋊C4—91no—
841C4⋊C4—91no—
842C4⋊C4—91no—
843C4⋊C4—91no—
844C4⋊C4—271no—
845C4⋊C4—271no—
846C4⋊C4—271no—
847C4⋊C4—271no—
848C4⋊C4—271no—
849C22⋊C4—31no—
850C22⋊C4—91no—
851C22⋊C4—91no—
852C22⋊C4—91no—
853C22⋊C4—271no—
854C22⋊C4—271no—
855C22⋊C4—271no—
856C22⋊C4—271no—
857C22⋊C4—271no—
858C22⋊C4—271no—
859C42—91no—
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—121no—
873C22×C3—121no—
874C22×C3—181no—
875C22×C3—181no—
876C22×C3—181no—
877C22×C3C22×D3211yescharacteristic
878C22×C3C22×D3211yescharacteristic
879C22×C3C22×D3211yescharacteristic
880C2×D3—21no—
881C2×D3—21no—
882C2×D3—61no—
883C2×D3—61no—
884C2×D3—61no—
885C2×D3—61no—
886C2×D3—61no—
887C2×D3—61no—
888C2×D3—121no—
889C2×D3—121no—
890C2×D3—121no—
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—61no—
929C3×C4—61no—
930C3×C4—121no—
931C3×C4—121no—
932C3×C4—121no—
933C3×C4—121no—
934C3×C4—121no—
935C3×C4—181no—
936C3×C4—181no—
937C3×C4—181no—
938C3×C4—181no—
939C3×C4—181no—
940Dic3—21no—
941Dic3—21no—
942Dic3—21no—
943Dic3—21no—
944Dic3—21no—
945Dic3—62no—
946Dic3—61no—
947Dic3—61no—
948Dic3—61no—
949Dic3—61no—
950Dic3—61no—
951Dic3—61no—
952Dic3—61no—
953Dic3—61no—
954Dic3—61no—
955Dic3—61no—
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#564511yescharacteristic, complemented
972C32#566511yescharacteristic, complemented
973C32#569211yescharacteristic, complemented
974C23—31no—
975C23—91no—
976C23—271no—
977Q8—361no—
978D4—182no—
979D4—542no—
980D4—1081no—
981C2×C4—31no—
982C2×C4—31no—
983C2×C4—31no—
984C2×C4—31no—
985C2×C4—31no—
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—1081no—
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—361no—
1014C2×C3C2×#379611yescharacteristic
1015C2×C3#6429711yescharacteristic
1016C2×C3#6430811yescharacteristic
1017C2×C3#6430911yescharacteristic
1018C2×C3D3×#23711yescharacteristic
1019C2×C3#6431411yescharacteristic
1020C2×C3#6431411yescharacteristic
1021C2×C3#6431511yescharacteristic
1022C2×C3D3×#23911yescharacteristic
1023D3—22no—
1024D3—121no—
1025D3—121no—
1026D3—241no—
1027D3—362no—
1028D3—362no—
1029D3—362no—
1030D3—364no—
1031D3—361no—
1032D3—361no—
1033D3—361no—
1034C22—32no—
1035C22—61no—
1036C22—61no—
1037C22—181no—
1038C22—181no—
1039C22—181no—
1040C22—541no—
1041C22—541no—
1042C22—541no—
1043C22C2×D3311yescharacteristic
1044C4—21no—
1045C4—61no—
1046C4—61no—
1047C4—61no—
1048C4—61no—
1049C4—61no—
1050C4—181no—
1051C4—181no—
1052C4—181no—
1053C4—181no—
1054C4—181no—
1055C4—541no—
1056C3—21no—
1057C3—21no—
1058C3—21no—
1059C3—41no—
1060C3#1059417911yescharacteristic, complemented
1061C3#1059444311yescharacteristic, complemented
1062C3#1059445411yescharacteristic, complemented
1063C2—62no—
1064C2—361no—
1065C2—1081no—
1066C2D3×#379611yescharacteristic
1067C2#1172439311yescharacteristic
1068C2#1172442011yescharacteristic
subgroupG/H
center, FrattiniC22C2×D33
commutator, socle, cosocleC22×C33C24
FittingC2×C33×C4C23
prime radical#11722959C2
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. #11723688C2semidirect
2. #11723462C2semidirect
3. #11723449C2semidirect
4. #11723421C2semidirect
5. C3×#63896C2semidirect
6. C3×#63890C2semidirect
7. C3×#63846C2semidirect
8. #11723027C2semidirect
9. #11723021C2semidirect
10. #11723013C2semidirect
11. #11722999C2semidirect
12. #11722987C2semidirect
14. #11722928C2semidirect
15. D3×Dic3⋊Dic3C2semidirect
70. #63896D3semidirect
75. #63890D3semidirect
100. #63846D3semidirect
685. C33#539semidirect
971. C32#5645semidirect
972. C32#5665semidirect
973. C32#5692semidirect
1060. C3#10594179semidirect
1061. C3#10594443semidirect
1062. C3#10594454semidirect

Maximal subgroups

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

subgroupindex
#117236882
#117234622
#117234492
#117234212
C3×#638962
C3×#638902
C3×#638462
#117230272
#117230212
#117230132
#117229992
#117229872
#117229592
#117229282
D3×Dic3⋊Dic32
#105944543
#105944433
#105941793