Finite Group Databasebeta

← #13178319

Subgroups — #13178319

Order 1728.

1122 conjugacy classes of subgroups.

The subgroup lattice has 1046 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#64105C211yesmaximal, characteristic, complemented
2C3×#64102C211yesmaximal, characteristic, complemented
3C3×#64098C211yesmaximal, characteristic, complemented
4#11723694C211yesmaximal, characteristic, complemented
5#11723694C211yesmaximal, characteristic, complemented
6C4×#6295C211yesmaximal, characteristic, complemented
7#11723690C211yesmaximal, characteristic, complemented
8#11723688C211yesmaximal, characteristic, complemented
9#11723687C211yesmaximal, characteristic
10#11723686C211yesmaximal, characteristic, complemented
11#11723682C211yesmaximal, characteristic, complemented
12#11723679C211yesmaximal, characteristic, complemented
13#11723676C211yesmaximal, characteristic, complemented
14#11723676C211yesmaximal, characteristic, complemented
15#11723674C211yesmaximal, characteristic, complemented
16#10594574—31nomaximal
17#10594407—31nomaximal
18#10594406—31nomaximal
19C2×C3×C4⋊(C3⋊D3)C2211yescharacteristic
20C2×C3×C4×C3⋊D3C2211yescharacteristic
21C2×C3×C4×C3⋊D3C2211yescharacteristic
22C2×C3×C4×C3⋊D3C2211yescharacteristic
23C2×C3×#634C2211yescharacteristic
24C2×#6295C2211yescharacteristic
25C2×#6295C2211yescharacteristic
26C2×#6294C2211yescharacteristic
27C2×#6294C2211yescharacteristic
28C33×C4⋊C4C2211yescharacteristic
29C3×#3752C2211yescharacteristic
30C3×#3752C2211yescharacteristic
31C3×#3752C2211yescharacteristic
32C3×#3752C2211yescharacteristic
33C3×C4⋊(C3⋊Dic3)C2211yescharacteristic
34C3×#3750C2211yescharacteristic
35C3×#3750C2211yescharacteristic
36C3×#3750C2211yescharacteristic
37C3×#3750C2211yescharacteristic
38C3×#3750C2211yescharacteristic
39C3×#3750C2211yescharacteristic
40C3×C4×C3⋊Dic3C2211yescharacteristic
41C3×C4×C3⋊Dic3C2211yescharacteristic
42#88815C2211yescharacteristic
43#88815C2211yescharacteristic
44#88815C2211yescharacteristic
45#88815C2211yescharacteristic
46#88815C2211yescharacteristic
47#88815C2211yescharacteristic
48#88814C2211yescharacteristic
49#88814C2211yescharacteristic
50#88814C2211yescharacteristic
51#88814C2211yescharacteristic
52#88814C2211yescharacteristic
53#88814C2211yescharacteristic
54#64105D311yescharacteristic, complemented
55#64102D311yescharacteristic, complemented
56#64098D311yescharacteristic, complemented
57C3×#896—31no—
58C3×#896—31no—
59C3×#896—61no—
60C3×#893—31no—
61C3×#893—31no—
62C3×#893—61no—
63C3×#889—31no—
64C3×#889—31no—
65C3×#889—61no—
66#63910—31no—
67#63905—31no—
68#63905—31no—
69C4×#626—31no—
70C4×#626—31no—
71C4×#625—31no—
72#63897—31no—
73#63896—31no—
74#63891—31no—
75#63890—31no—
76#63888—31no—
77#63887—31no—
78#63886—31no—
79#63885—31no—
80#63884—31no—
81#63884—31no—
82#63883—31no—
83D3×Dic3⋊C4—31no—
84D3×Dic3⋊C4—31no—
85#63871—31no—
86#63870—31no—
87#63868—31no—
88#63868—31no—
89#63867—31no—
90#63867—31no—
91#63862—31no—
92#63862—31no—
93#63859—31no—
94#63859—31no—
95#63857—31no—
96#63856—31no—
97#63854—31no—
98#63853—31no—
99#63853—31no—
100#63850—31no—
101#63850—31no—
102C22×C3×C3⋊D3C2311yescharacteristic
103C22×C3×C3⋊D3C2311yescharacteristic
104C22×C3×C3⋊D3C2311yescharacteristic
105C2×C33×C4C2311yescharacteristic
106C2×C33×C4C2311yescharacteristic
107C2×C33×C4C2311yescharacteristic
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×C3×C3⋊Dic3C2311yescharacteristic
115C2×C3×C3⋊Dic3C2311yescharacteristic
116C2×C3×C3⋊Dic3C2311yescharacteristic
117C3×C4⋊(C3⋊D3)—22no—
118C3×C4×C3⋊D3—41no—
119C3×C4×C3⋊D3—41no—
120C3×C4×C3⋊D3—41no—
121C3×#634—41no—
122#6295—22no—
123#6295—41no—
124#6294—22no—
125#6294—41no—
126#5692—91no—
127#5638—91no—
128#5564—91no—
129C2×C4⋊(C3⋊D3)C2×D311yescharacteristic
130C2×C4×C3⋊D3C2×D311yescharacteristic
131C2×C4×C3⋊D3C2×D311yescharacteristic
132C2×C4×C3⋊D3C2×D311yescharacteristic
133C2×#634C2×D311yescharacteristic
134C2×C3×D12—31no—
135C2×C3×D12—31no—
136C2×C3×D12—61no—
137C2×C3×C4×D3—31no—
138C2×C3×C4×D3—31no—
139C2×C3×C4×D3—31no—
140C2×C3×C4×D3—31no—
141C2×C3×C4×D3—31no—
142C2×C3×C4×D3—31no—
143C2×C3×C4×D3—61no—
144C2×C3×C4×D3—61no—
145C2×C3×C4×D3—61no—
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×#625—31no—
154C2×#625—31no—
155C2×#624—31no—
156C2×#624—31no—
157C2×D3×Dic3—31no—
158C2×D3×Dic3—31no—
159C2×D3×Dic3—31no—
160C2×D3×Dic3—31no—
161C32×C4⋊C4—21no—
162C32×C4⋊C4—21no—
163C32×C4⋊C4—21no—
164C32×C4⋊C4—41no—
165C32×C4⋊C4C2×D311yescharacteristic
166C32×C4⋊C4C2×D311yescharacteristic
167C32×C4⋊C4C2×D311yescharacteristic
168#3752C2×D311yescharacteristic
169#3752C2×D311yescharacteristic
170#3752C2×D311yescharacteristic
171#3752C2×D311yescharacteristic
172C4⋊(C3⋊Dic3)C2×D311yescharacteristic
173#3750C2×D311yescharacteristic
174#3750C2×D311yescharacteristic
175#3750C2×D311yescharacteristic
176#3750C2×D311yescharacteristic
177#3750C2×D311yescharacteristic
178#3750C2×D311yescharacteristic
179C4×C3⋊Dic3C2×D311yescharacteristic
180C4×C3⋊Dic3C2×D311yescharacteristic
181C3×(C2×D3)⋊C4—31no—
182C3×(C2×D3)⋊C4—31no—
183C3×(C2×D3)⋊C4—31no—
184C3×(C2×D3)⋊C4—31no—
185C3×(C2×D3)⋊C4—31no—
186C3×(C2×D3)⋊C4—31no—
187C3×(C2×D3)⋊C4—31no—
188C3×(C2×D3)⋊C4—31no—
189C3×(C2×D3)⋊C4—61no—
190C3×(C2×D3)⋊C4—61no—
191C3×(C2×D3)⋊C4—61no—
192C3×(C2×D3)⋊C4—61no—
193C3×C4⋊Dic3—31no—
194C3×C4⋊Dic3—31no—
195C3×C4⋊Dic3—61no—
196C3×Dic3⋊C4—31no—
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—31no—
207C3×Dic3⋊C4—31no—
208C3×Dic3⋊C4—61no—
209C3×Dic3⋊C4—61no—
210C3×Dic3⋊C4—61no—
211C3×Dic3⋊C4—61no—
212C3×Dic3⋊C4—61no—
213C3×Dic3⋊C4—61no—
214C3×C4×Dic3—31no—
215C3×C4×Dic3—31no—
216C3×C4×Dic3—31no—
217C3×C4×Dic3—31no—
218C3×C4×Dic3—61no—
219C3×C4×Dic3—61no—
220#3724—31no—
221#3724—31no—
222#3724—31no—
223#3724—31no—
224#3724—31no—
225#3724—31no—
226Dic3⋊Dic3—31no—
227Dic3⋊Dic3—31no—
228Dic3⋊Dic3—31no—
229Dic3⋊Dic3—31no—
230Dic3⋊Dic3—31no—
231Dic3⋊Dic3—31no—
232Dic3⋊Dic3—31no—
233Dic3⋊Dic3—31no—
234Dic3⋊Dic3—31no—
235Dic3⋊Dic3—31no—
236Dic3⋊Dic3—31no—
237Dic3⋊Dic3—31no—
238#3722—31no—
239#3722—31no—
240#3722—31no—
241#3722—31no—
242#3722—31no—
243#3722—31no—
244(C2×D3)⋊Dic3—31no—
245(C2×D3)⋊Dic3—31no—
246(C2×D3)⋊Dic3—31no—
247(C2×D3)⋊Dic3—31no—
248(C2×D3)⋊Dic3—31no—
249(C2×D3)⋊Dic3—31no—
250(C2×D3)⋊Dic3—31no—
251(C2×D3)⋊Dic3—31no—
252(C2×D3)⋊Dic3—31no—
253(C2×D3)⋊Dic3—31no—
254(C2×D3)⋊Dic3—31no—
255(C2×D3)⋊Dic3—31no—
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×C3×C3⋊D3—21no—
264C2×C3×C3⋊D3—21no—
265C2×C3×C3⋊D3#4112yes—
266C33×C4—21no—
267C33×C4—21no—
268C33×C4—21no—
269C3×C3⋊Dic3—21no—
270C3×C3⋊Dic3—21no—
271C3×C3⋊Dic3—21no—
272C3×C3⋊Dic3—21no—
273C3×C3⋊Dic3—21no—
274C3×C3⋊Dic3—21no—
275C3×C3⋊Dic3—21no—
276C3×C3⋊Dic3—21no—
277C3×C3⋊Dic3—21no—
278C3×#125—91no—
279C3×C22⋊Q8—91no—
280C3×C4×D4—91no—
281#946—91no—
282#946—91no—
283#939—91no—
284#935—91no—
285#929—91no—
286#929—91no—
287C4×#67—91no—
288C4×#67—91no—
289#924—91no—
290C2×Dic3⋊C4—91no—
291#898—91no—
292#898—91no—
293#897—91no—
294#896—31no—
295#896—31no—
296#896—61no—
297#896—91no—
298#895—91no—
299#894—91no—
300#894—91no—
301#894—91no—
302#894—91no—
303#894—91no—
304#893—31no—
305#893—31no—
306#893—61no—
307D3×C4⋊C4—91no—
308D3×C4⋊C4—91no—
309#889—31no—
310#889—31no—
311#889—61no—
312#889—91no—
313#889—91no—
314#886—91no—
315#884—91no—
316#883—91no—
317#883—91no—
318#883—91no—
319#879—91no—
320#879—91no—
321#878—91no—
322#876—91no—
323#876—91no—
324C4×D12—91no—
325#870—91no—
326C22×C3⋊D3C22×D311yescharacteristic
327C22×C3⋊D3C22×D311yescharacteristic
328C22×C3⋊D3C22×D311yescharacteristic
329C22×C3×D3—31no—
330C22×C3×D3—31no—
331C22×C3×D3—31no—
332C22×C3×D3—31no—
333C22×C3×D3—31no—
334C22×C3×D3—31no—
335C22×C3×D3—61no—
336C22×C3×D3—61no—
337C22×C3×D3—61no—
338C2×C32×C4—21no—
339C2×C32×C4—21no—
340C2×C32×C4—21no—
341C2×C32×C4—21no—
342C2×C32×C4—21no—
343C2×C32×C4—21no—
344C2×C32×C4—21no—
345C2×C32×C4—21no—
346C2×C32×C4—21no—
347C2×C32×C4—41no—
348C2×C32×C4—41no—
349C2×C32×C4—41no—
350C2×C32×C4C22×D311yescharacteristic
351C2×C32×C4C22×D311yescharacteristic
352C2×C32×C4C22×D311yescharacteristic
353C2×C32×C4C22×D311yescharacteristic
354C2×C32×C4C22×D311yescharacteristic
355C2×C32×C4C22×D311yescharacteristic
356C2×C32×C4C22×D311yescharacteristic
357C2×C32×C4C22×D311yescharacteristic
358C2×C32×C4C22×D311yescharacteristic
359C2×C3⋊Dic3C22×D311yescharacteristic
360C2×C3⋊Dic3C22×D311yescharacteristic
361C2×C3⋊Dic3C22×D311yescharacteristic
362C2×C3⋊Dic3C22×D311yescharacteristic
363C2×C3⋊Dic3C22×D311yescharacteristic
364C2×C3⋊Dic3C22×D311yescharacteristic
365C2×C3⋊Dic3C22×D311yescharacteristic
366C2×C3⋊Dic3C22×D311yescharacteristic
367C2×C3⋊Dic3C22×D311yescharacteristic
368C4⋊(C3⋊D3)—22no—
369C4×C3⋊D3—41no—
370C4×C3⋊D3—41no—
371C4×C3⋊D3—41no—
372#634—41no—
373C2×C3×Dic3—31no—
374C2×C3×Dic3—31no—
375C2×C3×Dic3—31no—
376C2×C3×Dic3—31no—
377C2×C3×Dic3—31no—
378C2×C3×Dic3—31no—
379C2×C3×Dic3—31no—
380C2×C3×Dic3—31no—
381C2×C3×Dic3—31no—
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—61no—
392C2×C3×Dic3—61no—
393C2×C3×Dic3—61no—
394C2×C3×Dic3—61no—
395C2×C3×Dic3—61no—
396C2×C3×Dic3—61no—
397C2×C3×Dic3—61no—
398C2×C3×Dic3—61no—
399C2×C3×Dic3—61no—
400C3×D12—62no—
401C3×D12—62no—
402C3×D12—64no—
403C3×C4×D3—121no—
404C3×C4×D3—121no—
405C3×C4×D3—121no—
406C3×C4×D3—121no—
407C3×C4×D3—121no—
408C3×C4×D3—121no—
409C3×C4×D3—122no—
410C3×C4×D3—122no—
411C3×C4×D3—122no—
412C3×Dic6—121no—
413C3×Dic6—121no—
414C3×Dic6—122no—
415#626—62no—
416#626—62no—
417#626—121no—
418#626—121no—
419#625—62no—
420#625—121no—
421#624—62no—
422#624—121no—
423D3×Dic3—62no—
424D3×Dic3—62no—
425D3×Dic3—121no—
426D3×Dic3—121no—
427#539—271noSylow
428C2×C33C2×#4111yescharacteristic
429C2×C33H(5,𝔽2)11yescharacteristic
430C2×C332−1+411yescharacteristic
431C3×C3⋊D3—22no—
432C3×C3⋊D3—41no—
433C3×C3⋊D3—41no—
434C2×C3×Q8—91no—
435C2×C3×D4—91no—
436C22×C3×C4—91no—
437C22×C3×C4—91no—
438C22×C3×C4—91no—
439C2×#67—91no—
440C2×#67—91no—
441C2×#67—91no—
442C2×#67—91no—
443C22×Dic3—91no—
444C22×Dic3—91no—
445C2×D12—31no—
446C2×D12—31no—
447C2×D12—61no—
448C2×D12—91no—
449C2×D12—91no—
450C2×C4×D3—31no—
451C2×C4×D3—31no—
452C2×C4×D3—31no—
453C2×C4×D3—31no—
454C2×C4×D3—31no—
455C2×C4×D3—31no—
456C2×C4×D3—61no—
457C2×C4×D3—61no—
458C2×C4×D3—61no—
459C2×C4×D3—91no—
460C2×C4×D3—91no—
461C2×C4×D3—91no—
462C2×C4×D3—91no—
463C2×Dic6—31no—
464C2×Dic6—31no—
465C2×Dic6—61no—
466C3×C4⋊C4—21no—
467C3×C4⋊C4—21no—
468C3×C4⋊C4—21no—
469C3×C4⋊C4—41no—
470C3×C4⋊C4—91no—
471C3×C4⋊C4—91no—
472C3×C4⋊C4—91no—
473C3×C4⋊C4—91no—
474C3×C4⋊C4—91no—
475C3×C4⋊C4—91no—
476C3×C4⋊C4—91no—
477C3×C4⋊C4D3211yescharacteristic
478C3×C4⋊C4D3211yescharacteristic
479C3×C4⋊C4D3211yescharacteristic
480C3×C22⋊C4—91no—
481C3×C22⋊C4—91no—
482C3×C22⋊C4—91no—
483C3×C22⋊C4—91no—
484C3×C42—91no—
485C3×C42—91no—
486#217—91no—
487#217—91no—
488#217—91no—
489#217—91no—
490#217—91no—
491#217—91no—
492(C2×D3)⋊C4—31no—
493(C2×D3)⋊C4—31no—
494(C2×D3)⋊C4—31no—
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—61no—
502(C2×D3)⋊C4—61no—
503(C2×D3)⋊C4—61no—
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—
516C4⋊Dic3—31no—
517C4⋊Dic3—31no—
518C4⋊Dic3—61no—
519C4⋊Dic3—91no—
520C4⋊Dic3—91no—
521C4⋊Dic3—91no—
522C4⋊Dic3—91no—
523C4⋊Dic3—91no—
524C4⋊Dic3—91no—
525Dic3⋊C4—31no—
526Dic3⋊C4—31no—
527Dic3⋊C4—31no—
528Dic3⋊C4—31no—
529Dic3⋊C4—31no—
530Dic3⋊C4—31no—
531Dic3⋊C4—31no—
532Dic3⋊C4—31no—
533Dic3⋊C4—31no—
534Dic3⋊C4—31no—
535Dic3⋊C4—31no—
536Dic3⋊C4—31no—
537Dic3⋊C4—61no—
538Dic3⋊C4—61no—
539Dic3⋊C4—61no—
540Dic3⋊C4—61no—
541Dic3⋊C4—61no—
542Dic3⋊C4—61no—
543Dic3⋊C4—91no—
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—
555C4×Dic3—31no—
556C4×Dic3—31no—
557C4×Dic3—31no—
558C4×Dic3—31no—
559C4×Dic3—61no—
560C4×Dic3—61no—
561C22×C32—21no—
562C22×C32—21no—
563C22×C32—21no—
564C22×C32—41no—
565C22×C32C23×D311yescharacteristic
566C22×C32C23×D311yescharacteristic
567C22×C32C23×D311yescharacteristic
568C2×C3⋊D3—21no—
569C2×C3⋊D3—21no—
570C2×C3⋊D3—21no—
571C2×C3⋊D3—21no—
572C2×C3⋊D3—21no—
573C2×C3⋊D3—21no—
574C2×C3⋊D3—21no—
575C2×C3⋊D3—21no—
576C2×C3⋊D3#23512yes—
577C2×C3×D3—32no—
578C2×C3×D3—32no—
579C2×C3×D3—62no—
580C2×C3×D3—61no—
581C2×C3×D3—61no—
582C2×C3×D3—61no—
583C2×C3×D3—61no—
584C2×C3×D3—62no—
585C2×C3×D3—62no—
586C2×C3×D3—61no—
587C2×C3×D3—61no—
588C2×C3×D3—61no—
589C2×C3×D3—61no—
590C2×C3×D3—61no—
591C2×C3×D3—61no—
592C2×C3×D3—61no—
593C2×C3×D3—61no—
594C2×C3×D3—61no—
595C2×C3×D3—61no—
596C2×C3×D3—61no—
597C2×C3×D3—61no—
598C2×C3×D3—121no—
599C2×C3×D3—121no—
600C2×C3×D3—121no—
601C2×C3×D3—121no—
602C2×C3×D3—121no—
603C2×C3×D3—121no—
604C32×C4—21no—
605C32×C4—22no—
606C32×C4—21no—
607C32×C4—21no—
608C32×C4—21no—
609C32×C4—21no—
610C32×C4—21no—
611C32×C4—21no—
612C32×C4—21no—
613C32×C4—21no—
614C32×C4—41no—
615C32×C4—41no—
616C32×C4—42no—
617C32×C4—41no—
618C32×C4—41no—
619C32×C4—41no—
620C32×C4—41no—
621C32×C4—41no—
622C32×C4—41no—
623C32×C4—81no—
624C32×C4—81no—
625C3⋊Dic3—21no—
626C3⋊Dic3—21no—
627C3⋊Dic3—21no—
628C3⋊Dic3—21no—
629C3⋊Dic3—21no—
630C3⋊Dic3—21no—
631C3⋊Dic3—21no—
632C3⋊Dic3—21no—
633C3⋊Dic3—21no—
634C3×Dic3—62no—
635C3×Dic3—62no—
636C3×Dic3—62no—
637C3×Dic3—61no—
638C3×Dic3—61no—
639C3×Dic3—61no—
640C3×Dic3—61no—
641C3×Dic3—61no—
642C3×Dic3—61no—
643C3×Dic3—61no—
644C3×Dic3—61no—
645C3×Dic3—61no—
646C3×Dic3—61no—
647C3×Dic3—61no—
648C3×Dic3—61no—
649C3×Dic3—61no—
650C3×Dic3—61no—
651C3×Dic3—61no—
652C3×Dic3—61no—
653C3×Dic3—61no—
654C3×Dic3—61no—
655C3×Dic3—121no—
656C3×Dic3—121no—
657C3×Dic3—121no—
658C3×Dic3—121no—
659C3×Dic3—121no—
660C3×Dic3—121no—
661#126—271no—
662#126—271no—
663#125—91no—
664#125—271no—
665#123—271no—
666#123—271no—
667#123—271no—
668#123—271no—
669C22⋊Q8—91no—
670C22⋊Q8—271no—
671C22⋊Q8—271no—
672#121—271no—
673C4×D4—91no—
674C4×D4—271no—
675C2×C4⋊C4—271no—
676C33#53911yescharacteristic, complemented, Sylow
677C23×C3—91no—
678C23×C3—91no—
679C23×C3—91no—
680C22×D3—31no—
681C22×D3—31no—
682C22×D3—31no—
683C22×D3—31no—
684C22×D3—31no—
685C22×D3—31no—
686C22×D3—61no—
687C22×D3—61no—
688C22×D3—61no—
689C3×Q8—361no—
690C3×D4—182no—
691C2×C3×C4—21no—
692C2×C3×C4—21no—
693C2×C3×C4—21no—
694C2×C3×C4—21no—
695C2×C3×C4—21no—
696C2×C3×C4—21no—
697C2×C3×C4—21no—
698C2×C3×C4—21no—
699C2×C3×C4—21no—
700C2×C3×C4—41no—
701C2×C3×C4—41no—
702C2×C3×C4—41no—
703C2×C3×C4—91no—
704C2×C3×C4—91no—
705C2×C3×C4—91no—
706C2×C3×C4—91no—
707C2×C3×C4—91no—
708C2×C3×C4—91no—
709C2×C3×C4—91no—
710C2×C3×C4—91no—
711C2×C3×C4—91no—
712C2×C3×C4—361no—
713C2×C3×C4—361no—
714C2×C3×C4—361no—
715C2×C3×C4C2×D3211yescharacteristic
716C2×C3×C4C2×D3211yescharacteristic
717C2×C3×C4C2×D3211yescharacteristic
718C2×C3×C4C2×D3211yescharacteristic
719C2×C3×C4C2×D3211yescharacteristic
720C2×C3×C4C2×D3211yescharacteristic
721C2×C3×C4C2×D3211yescharacteristic
722C2×C3×C4C2×D3211yescharacteristic
723C2×C3×C4C2×D3211yescharacteristic
724#67—182no—
725#67—182no—
726#67—361no—
727#67—361no—
728C2×Dic3—31no—
729C2×Dic3—31no—
730C2×Dic3—31no—
731C2×Dic3—31no—
732C2×Dic3—31no—
733C2×Dic3—31no—
734C2×Dic3—31no—
735C2×Dic3—31no—
736C2×Dic3—31no—
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—61no—
747C2×Dic3—61no—
748C2×Dic3—61no—
749C2×Dic3—61no—
750C2×Dic3—61no—
751C2×Dic3—61no—
752C2×Dic3—61no—
753C2×Dic3—61no—
754C2×Dic3—61no—
755C2×Dic3—182no—
756C2×Dic3—361no—
757D12—62no—
758D12—62no—
759D12—64no—
760D12—182no—
761D12—361no—
762C4×D3—121no—
763C4×D3—121no—
764C4×D3—121no—
765C4×D3—121no—
766C4×D3—121no—
767C4×D3—121no—
768C4×D3—122no—
769C4×D3—122no—
770C4×D3—122no—
771C4×D3—182no—
772C4×D3—182no—
773C4×D3—361no—
774C4×D3—361no—
775Dic6—121no—
776Dic6—121no—
777Dic6—122no—
778C2×C32—21no—
779C2×C32—21no—
780C2×C32—21no—
781C2×C32—21no—
782C2×C32—21no—
783C2×C32—21no—
784C2×C32—21no—
785C2×C32—21no—
786C2×C32—21no—
787C2×C32—41no—
788C2×C32—41no—
789C2×C32—41no—
790C2×C32C2×#23511yescharacteristic
791C2×C32#100411yescharacteristic
792C2×C32#100411yescharacteristic
793C2×C32#100711yescharacteristic
794C2×C32#100711yescharacteristic
795C2×C32D3×#4111yescharacteristic
796C2×C32D3×#4111yescharacteristic
797C2×C32#100911yescharacteristic
798C2×C32#101011yescharacteristic
799C3⋊D3—22no—
800C3⋊D3—41no—
801C3⋊D3—41no—
802C3×D3—62no—
803C3×D3—62no—
804C3×D3—122no—
805C3×D3—122no—
806C3×D3—122no—
807C3×D3—121no—
808C3×D3—121no—
809C3×D3—121no—
810C3×D3—121no—
811C2×Q8—91no—
812C2×D4—91no—
813C2×D4—271no—
814C2×D4—271no—
815C22×C4—91no—
816C22×C4—91no—
817C22×C4—91no—
818C22×C4—271no—
819C22×C4—271no—
820C4⋊C4—91no—
821C4⋊C4—91no—
822C4⋊C4—91no—
823C4⋊C4—91no—
824C4⋊C4—91no—
825C4⋊C4—91no—
826C4⋊C4—91no—
827C4⋊C4—271no—
828C4⋊C4—271no—
829C4⋊C4—271no—
830C4⋊C4—271no—
831C4⋊C4—271no—
832C4⋊C4—271no—
833C4⋊C4#111311yescharacteristic
834C22⋊C4—91no—
835C22⋊C4—91no—
836C22⋊C4—91no—
837C22⋊C4—91no—
838C22⋊C4—271no—
839C22⋊C4—271no—
840C22⋊C4—271no—
841C22⋊C4—271no—
842C22⋊C4—271no—
843C22⋊C4—271no—
844C42—91no—
845C42—91no—
846C22×C3—21no—
847C22×C3—21no—
848C22×C3—21no—
849C22×C3—41no—
850C22×C3—92no—
851C22×C3—181no—
852C22×C3—181no—
853C22×C3—181no—
854C22×C3—181no—
855C22×C3—181no—
856C22×C3—181no—
857C22×C3—181no—
858C22×C3—181no—
859C22×C3C22×D3211yescharacteristic
860C22×C3C22×D3211yescharacteristic
861C22×C3C22×D3211yescharacteristic
862C2×D3—32no—
863C2×D3—32no—
864C2×D3—62no—
865C2×D3—61no—
866C2×D3—61no—
867C2×D3—61no—
868C2×D3—61no—
869C2×D3—62no—
870C2×D3—62no—
871C2×D3—61no—
872C2×D3—61no—
873C2×D3—61no—
874C2×D3—61no—
875C2×D3—61no—
876C2×D3—61no—
877C2×D3—61no—
878C2×D3—61no—
879C2×D3—61no—
880C2×D3—61no—
881C2×D3—61no—
882C2×D3—61no—
883C2×D3—121no—
884C2×D3—121no—
885C2×D3—121no—
886C2×D3—121no—
887C2×D3—121no—
888C2×D3—121no—
889C3×C4—22no—
890C3×C4—21no—
891C3×C4—21no—
892C3×C4—21no—
893C3×C4—21no—
894C3×C4—21no—
895C3×C4—21no—
896C3×C4—21no—
897C3×C4—21no—
898C3×C4—21no—
899C3×C4—41no—
900C3×C4—41no—
901C3×C4—41no—
902C3×C4—41no—
903C3×C4—41no—
904C3×C4—41no—
905C3×C4—41no—
906C3×C4—41no—
907C3×C4—42no—
908C3×C4—81no—
909C3×C4—81no—
910C3×C4—181no—
911C3×C4—181no—
912C3×C4—181no—
913C3×C4—181no—
914C3×C4—181no—
915C3×C4—181no—
916C3×C4—181no—
917C3×C4—181no—
918C3×C4—181no—
919Dic3—62no—
920Dic3—62no—
921Dic3—62no—
922Dic3—61no—
923Dic3—61no—
924Dic3—61no—
925Dic3—61no—
926Dic3—61no—
927Dic3—61no—
928Dic3—61no—
929Dic3—61no—
930Dic3—61no—
931Dic3—61no—
932Dic3—61no—
933Dic3—61no—
934Dic3—61no—
935Dic3—61no—
936Dic3—61no—
937Dic3—61no—
938Dic3—61no—
939Dic3—61no—
940Dic3—121no—
941Dic3—121no—
942Dic3—121no—
943Dic3—121no—
944Dic3—121no—
945Dic3—121no—
946C32—21no—
947C32—21no—
948C32—21no—
949C32—41no—
950C32#556411yescharacteristic, complemented
951C32#563811yescharacteristic, complemented
952C32#569211yescharacteristic, complemented
953C23—91no—
954C23—91no—
955C23—91no—
956Q8—361no—
957D4—182no—
958D4—542no—
959D4—1081no—
960C2×C4—91no—
961C2×C4—91no—
962C2×C4—91no—
963C2×C4—91no—
964C2×C4—91no—
965C2×C4—91no—
966C2×C4—91no—
967C2×C4—91no—
968C2×C4—91no—
969C2×C4—361no—
970C2×C4—361no—
971C2×C4—361no—
972C2×C4—542no—
973C2×C4—1081no—
974C2×C4C2×#111311yescharacteristic
975C2×C4C2×#111311yescharacteristic
976C2×C4C2×#111311yescharacteristic
977C2×C3—21no—
978C2×C3—21no—
979C2×C3—21no—
980C2×C3—21no—
981C2×C3—21no—
982C2×C3—21no—
983C2×C3—21no—
984C2×C3—21no—
985C2×C3—21no—
986C2×C3—41no—
987C2×C3—41no—
988C2×C3—41no—
989C2×C3—182no—
990C2×C3—361no—
991C2×C3—361no—
992C2×C3D3×#23511yescharacteristic
993C2×C3D3×#23511yescharacteristic
994C2×C3#6430611yescharacteristic
995C2×C3#6431311yescharacteristic
996C2×C3#6431411yescharacteristic
997C2×C3#6431411yescharacteristic
998C2×C3#6431511yescharacteristic
999C2×C3#6431511yescharacteristic
1000C2×C3#6431611yescharacteristic
1001D3—62no—
1002D3—62no—
1003D3—122no—
1004D3—122no—
1005D3—122no—
1006D3—121no—
1007D3—121no—
1008D3—121no—
1009D3—121no—
1010C22—92no—
1011C22—181no—
1012C22—181no—
1013C22—181no—
1014C22—181no—
1015C22—181no—
1016C22—181no—
1017C22—181no—
1018C22—181no—
1019C22C22×#111311yescharacteristic
1020C4—21no—
1021C4—21no—
1022C4—21no—
1023C4—181no—
1024C4—181no—
1025C4—181no—
1026C4—181no—
1027C4—181no—
1028C4—181no—
1029C4—181no—
1030C4—181no—
1031C4—181no—
1032C3—21no—
1033C3—21no—
1034C3—21no—
1035C3—41no—
1036C3#1059440611yescharacteristic, complemented
1037C3#1059440711yescharacteristic, complemented
1038C3#1059457411yescharacteristic, complemented
1039C2—182no—
1040C2—361no—
1041C2—361no—
1042C2#1172461811yescharacteristic
1043C2#1172462311yescharacteristic
1044C2#1172462411yescharacteristic
subgroupG/H
center, FrattiniC22C22×#1113
commutator, socle, cosocleC22×C33C24
FittingC33×C4⋊C4C22
prime radical#11723687C2
hypercenterC4⋊C4#1113
hypocenterC33#539
LCSG ▷ C22×C33 ▷ C33
UCSC1 ◁ C22 ◁ C4⋊C4

Complements

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

NH ≅ G/Ntype
1. C3×#64105C2semidirect
2. C3×#64102C2semidirect
3. C3×#64098C2semidirect
4. #11723694C2semidirect
5. #11723694C2semidirect
6. C4×#6295C2semidirect
7. #11723690C2semidirect
8. #11723688C2semidirect
10. #11723686C2semidirect
11. #11723682C2semidirect
12. #11723679C2semidirect
13. #11723676C2semidirect
14. #11723676C2semidirect
15. #11723674C2semidirect
54. #64105D3semidirect
55. #64102D3semidirect
56. #64098D3semidirect
676. C33#539semidirect
950. C32#5564semidirect
951. C32#5638semidirect
952. C32#5692semidirect
1036. C3#10594406semidirect
1037. C3#10594407semidirect
1038. C3#10594574semidirect

Maximal subgroups

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

subgroupindex
C3×#641052
C3×#641022
C3×#640982
#117236942
C4×#62952
#117236902
#117236882
#117236872
#117236862
#117236822
#117236792
#117236762
#117236742
#105945743
#105944073
#105944063