Finite Group Databasebeta

← #13178259

Subgroups — #13178259

Order 1728.

1326 conjugacy classes of subgroups.

The subgroup lattice has 1246 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#64093C211yesmaximal, characteristic, complemented
2C3×#64091C211yesmaximal, characteristic, complemented
3C3×#64088C211yesmaximal, characteristic, complemented
4#11723727C211yesmaximal, characteristic, complemented
5#11723727C211yesmaximal, characteristic, complemented
6#11723725C211yesmaximal, characteristic, complemented
7#11723725C211yesmaximal, characteristic, complemented
8#11723697C211yesmaximal, characteristic, complemented
9#11723696C211yesmaximal, characteristic, complemented
10#11723694C211yesmaximal, characteristic, complemented
11#11723690C211yesmaximal, characteristic, complemented
12#11723687C211yesmaximal, characteristic, complemented
13#11723687C211yesmaximal, characteristic, complemented
14#11723686C211yesmaximal, characteristic, complemented
15#11723676C211yesmaximal, characteristic, complemented
16#10594242—31nomaximal
17#10594236—31nomaximal
18#10594234—31nomaximal
19C23×C3×C3⋊D3C2211yescharacteristic
20C2×C3×#638C2211yescharacteristic
21C2×C3×#638C2211yescharacteristic
22C2×C3×#638C2211yescharacteristic
23C2×C3×C4⋊(C3⋊D3)C2211yescharacteristic
24C2×C3×C4⋊(C3⋊D3)C2211yescharacteristic
25C2×C3×C4⋊(C3⋊D3)C2211yescharacteristic, complemented
26C2×C3×C4×C3⋊D3C2211yescharacteristic, complemented
27C2×#6295C2211yescharacteristic
28C2×#6295C2211yescharacteristic
29C2×#6295C2211yescharacteristic
30C2×#6295C2211yescharacteristic
31C2×#6295C2211yescharacteristic, complemented
32C2×#6295C2211yescharacteristic, complemented
33C2×#6294C2211yescharacteristic, complemented
34C2×#6294C2211yescharacteristic, complemented
35C33×C22⋊C4C2211yescharacteristic
36C3×#3757C2211yescharacteristic
37C3×#3757C2211yescharacteristic
38C3×#3752C2211yescharacteristic
39C3×#3752C2211yescharacteristic
40C3×#3752C2211yescharacteristic, complemented
41C3×C4⋊(C3⋊Dic3)C2211yescharacteristic, complemented
42C3×#3750C2211yescharacteristic, complemented
43C3×#3750C2211yescharacteristic, complemented
44C3×#3750C2211yescharacteristic, complemented
45C3×C4×C3⋊Dic3C2211yescharacteristic, complemented
46#88815C2211yescharacteristic, complemented
47#88815C2211yescharacteristic, complemented
48#88814C2211yescharacteristic
49#88814C2211yescharacteristic
50#88814C2211yescharacteristic
51#88814C2211yescharacteristic
52#88814C2211yescharacteristic, complemented
53#88814C2211yescharacteristic, complemented
54#64093D311yescharacteristic, complemented
55#64091D311yescharacteristic, complemented
56#64088D311yescharacteristic, complemented
57C3×#884—31no—
58C3×#884—31no—
59C3×#884—61no—
60C3×#882—31no—
61C3×#882—31no—
62C3×#882—61no—
63C3×#879—31no—
64C3×#879—31no—
65C3×#879—61no—
66#63981—31no—
67#63981—31no—
68#63977—31no—
69#63977—31no—
70#63976—31no—
71#63976—31no—
72#63971—31no—
73#63971—31no—
74#63970—31no—
75#63970—31no—
76#63958—31no—
77#63958—31no—
78#63916—31no—
79#63914—31no—
80#63911—31no—
81#63911—31no—
82#63910—31no—
83#63910—31no—
84#63909—31no—
85#63908—31no—
86#63905—31no—
87#63897—31no—
88#63891—31no—
89#63890—31no—
90#63886—31no—
91#63886—31no—
92#63885—31no—
93#63885—31no—
94#63884—31no—
95#63884—31no—
96#63868—31no—
97#63862—31no—
98#63859—31no—
99#63854—31no—
100#63853—31no—
101#63850—31no—
102C23×C33C2311yescharacteristic
103C22×C3×C3⋊D3—41no—
104C22×C3×C3⋊D3—41no—
105C22×C3×C3⋊D3—41no—
106C22×C3×C3⋊D3C2311yescharacteristic
107C22×C3×C3⋊D3C2311yescharacteristic
108C22×C3×C3⋊D3C2311yescharacteristic
109C22×C3×C3⋊D3C2311yescharacteristic
110C22×C3×C3⋊D3C2311yescharacteristic
111C2×C33×C4C2311yescharacteristic
112C2×C33×C4C2311yescharacteristic
113C3×#638—41no—
114C3×#638—41no—
115C3×#638—41no—
116C2×C3×C3⋊Dic3C2311yescharacteristic
117C2×C3×C3⋊Dic3C2311yescharacteristic
118C2×C3×C3⋊Dic3C2311yescharacteristic
119C2×C3×C3⋊Dic3C2311yescharacteristic
120C2×C3×C3⋊Dic3C2311yescharacteristic
121C2×C3×C3⋊Dic3C2311yescharacteristic
122C2×C3×C3⋊Dic3C2311yescharacteristic
123C3×C4⋊(C3⋊D3)—41no—
124C3×C4⋊(C3⋊D3)—41no—
125C3×C4⋊(C3⋊D3)—41no—
126C3×C4×C3⋊D3—41no—
127#6295—41no—
128#6295—41no—
129#6295—41no—
130#6295—41no—
131#6295—41no—
132#6295—41no—
133#6294—41no—
134#6294—41no—
135#5711—91no—
136#5620—91no—
137#5595—91no—
138C23×C3⋊D3C2×D311yescharacteristic
139C23×C3×D3—31no—
140C23×C3×D3—31no—
141C23×C3×D3—61no—
142C2×#638C2×D311yescharacteristic
143C2×#638C2×D311yescharacteristic
144C2×#638C2×D311yescharacteristic
145C2×C4⋊(C3⋊D3)C2×D311yescharacteristic
146C2×C4⋊(C3⋊D3)C2×D311yescharacteristic
147C2×C4⋊(C3⋊D3)C2×D311yescharacteristic, complemented
148C2×C4×C3⋊D3C2×D311yescharacteristic, complemented
149C2×C3×#67—31no—
150C2×C3×#67—31no—
151C2×C3×#67—31no—
152C2×C3×#67—31no—
153C2×C3×#67—31no—
154C2×C3×#67—31no—
155C2×C3×#67—61no—
156C2×C3×#67—61no—
157C2×C3×#67—61no—
158C2×C3×D12—31no—
159C2×C3×D12—31no—
160C2×C3×D12—31no—
161C2×C3×D12—31no—
162C2×C3×D12—31no—
163C2×C3×D12—31no—
164C2×C3×D12—61no—
165C2×C3×D12—61no—
166C2×C3×D12—61no—
167C2×C3×C4×D3—31no—
168C2×C3×C4×D3—31no—
169C2×C3×C4×D3—61no—
170C2×#626—31no—
171C2×#626—31no—
172C2×#626—31no—
173C2×#626—31no—
174C2×#626—31no—
175C2×#626—31no—
176C2×#626—31no—
177C2×#626—31no—
178C2×#626—31no—
179C2×#626—31no—
180C2×#626—31no—
181C2×#626—31no—
182C2×#625—31no—
183C2×#625—31no—
184C2×#625—31no—
185C2×#625—31no—
186C2×#625—31no—
187C2×#625—31no—
188C2×#624—31no—
189C2×#624—31no—
190C2×D3×Dic3—31no—
191C2×D3×Dic3—31no—
192C2×D3×Dic3—31no—
193C2×D3×Dic3—31no—
194C32×C22⋊C4—21no—
195C32×C22⋊C4—21no—
196C32×C22⋊C4—21no—
197C32×C22⋊C4—41no—
198C32×C22⋊C4C2×D311yescharacteristic
199C32×C22⋊C4C2×D311yescharacteristic
200C32×C22⋊C4C2×D311yescharacteristic
201#3757C2×D311yescharacteristic
202#3757C2×D311yescharacteristic
203#3752C2×D311yescharacteristic
204#3752C2×D311yescharacteristic
205#3752C2×D311yescharacteristic, complemented
206C4⋊(C3⋊Dic3)C2×D311yescharacteristic, complemented
207#3750C2×D311yescharacteristic, complemented
208#3750C2×D311yescharacteristic, complemented
209#3750C2×D311yescharacteristic, complemented
210C4×C3⋊Dic3C2×D311yescharacteristic, complemented
211C3×#217—31no—
212C3×#217—31no—
213C3×#217—31no—
214C3×#217—31no—
215C3×#217—61no—
216C3×#217—61no—
217C3×(C2×D3)⋊C4—31no—
218C3×(C2×D3)⋊C4—31no—
219C3×(C2×D3)⋊C4—31no—
220C3×(C2×D3)⋊C4—31no—
221C3×(C2×D3)⋊C4—31no—
222C3×(C2×D3)⋊C4—31no—
223C3×(C2×D3)⋊C4—61no—
224C3×(C2×D3)⋊C4—61no—
225C3×(C2×D3)⋊C4—61no—
226C3×C4⋊Dic3—31no—
227C3×C4⋊Dic3—31no—
228C3×C4⋊Dic3—61no—
229C3×Dic3⋊C4—31no—
230C3×Dic3⋊C4—31no—
231C3×Dic3⋊C4—31no—
232C3×Dic3⋊C4—31no—
233C3×Dic3⋊C4—31no—
234C3×Dic3⋊C4—31no—
235C3×Dic3⋊C4—61no—
236C3×Dic3⋊C4—61no—
237C3×Dic3⋊C4—61no—
238C3×C4×Dic3—31no—
239C3×C4×Dic3—31no—
240C3×C4×Dic3—61no—
241#3724—31no—
242#3724—31no—
243Dic3⋊Dic3—31no—
244Dic3⋊Dic3—31no—
245Dic3⋊Dic3—31no—
246Dic3⋊Dic3—31no—
247#3722—31no—
248#3722—31no—
249#3722—31no—
250#3722—31no—
251#3722—31no—
252#3722—31no—
253(C2×D3)⋊Dic3—31no—
254(C2×D3)⋊Dic3—31no—
255(C2×D3)⋊Dic3—31no—
256(C2×D3)⋊Dic3—31no—
257(C2×D3)⋊Dic3—31no—
258(C2×D3)⋊Dic3—31no—
259(C2×D3)⋊Dic3—31no—
260(C2×D3)⋊Dic3—31no—
261(C2×D3)⋊Dic3—31no—
262(C2×D3)⋊Dic3—31no—
263(C2×D3)⋊Dic3—31no—
264(C2×D3)⋊Dic3—31no—
265C22×C33—21no—
266C22×C33—21no—
267C22×C33—21no—
268C22×C33C2411yescharacteristic
269C2×C3×C3⋊D3—21no—
270C2×C3×C3⋊D3—21no—
271C2×C3×C3⋊D3—21no—
272C2×C3×C3⋊D3—21no—
273C2×C3×C3⋊D3—21no—
274C2×C3×C3⋊D3—21no—
275C2×C3×C3⋊D3—21no—
276C2×C3×C3⋊D3—21no—
277C2×C3×C3⋊D3—21no—
278C2×C3×C3⋊D3—21no—
279C2×C3×C3⋊D3—21no—
280C2×C3×C3⋊D3—21no—
281C2×C3×C3⋊D3—21no—
282C2×C3×C3⋊D3—21no—
283C2×C3×C3⋊D3—21no—
284C2×C3×C3⋊D3—44no—
285C33×C4—21no—
286C33×C4—21no—
287C3×C3⋊Dic3—21no—
288C3×C3⋊Dic3—21no—
289C3×C3⋊Dic3—21no—
290C3×C3⋊Dic3—21no—
291C3×C3⋊Dic3—21no—
292C3×C3⋊Dic3—21no—
293C3×C3⋊Dic3—21no—
294C3×#126—91no—
295C3×#121—91no—
296C3×#120—91no—
297#953—91no—
298#953—91no—
299#940—91no—
300#940—91no—
301#939—91no—
302#939—91no—
303#939—91no—
304#939—91no—
305#938—91no—
306#938—91no—
307#938—91no—
308#937—91no—
309#937—91no—
310#935—91no—
311#930—91no—
312#929—91no—
313#898—91no—
314#895—91no—
315#895—91no—
316#895—91no—
317#894—91no—
318#894—91no—
319#894—91no—
320#894—91no—
321#886—91no—
322#884—31no—
323#884—31no—
324#884—61no—
325#884—91no—
326#884—91no—
327#884—91no—
328#884—91no—
329#883—91no—
330#883—91no—
331#882—31no—
332#882—31no—
333#882—61no—
334#882—91no—
335#882—91no—
336#879—31no—
337#879—31no—
338#879—61no—
339#879—91no—
340#876—91no—
341#874—91no—
342C23×C32—21no—
343C23×C32—21no—
344C23×C32—21no—
345C23×C32—41no—
346C23×C32C22×D311yescharacteristic
347C23×C32C22×D311yescharacteristic
348C23×C32C22×D311yescharacteristic
349C22×C3⋊D3—41no—
350C22×C3⋊D3—41no—
351C22×C3⋊D3—41no—
352C22×C3⋊D3C22×D311yescharacteristic
353C22×C3⋊D3C22×D311yescharacteristic
354C22×C3⋊D3C22×D311yescharacteristic
355C22×C3⋊D3C22×D311yescharacteristic
356C22×C3⋊D3C22×D311yescharacteristic
357C22×C3×D3—31no—
358C22×C3×D3—31no—
359C22×C3×D3—31no—
360C22×C3×D3—31no—
361C22×C3×D3—31no—
362C22×C3×D3—31no—
363C22×C3×D3—31no—
364C22×C3×D3—31no—
365C22×C3×D3—31no—
366C22×C3×D3—31no—
367C22×C3×D3—61no—
368C22×C3×D3—61no—
369C22×C3×D3—61no—
370C22×C3×D3—61no—
371C22×C3×D3—61no—
372C22×C3×D3—121no—
373C22×C3×D3—121no—
374C22×C3×D3—121no—
375C22×C3×D3—121no—
376C22×C3×D3—121no—
377C22×C3×D3—121no—
378C22×C3×D3—122no—
379C22×C3×D3—122no—
380C22×C3×D3—122no—
381C2×C32×C4—21no—
382C2×C32×C4—21no—
383C2×C32×C4—21no—
384C2×C32×C4—21no—
385C2×C32×C4—21no—
386C2×C32×C4—21no—
387C2×C32×C4—41no—
388C2×C32×C4—41no—
389C2×C32×C4C22×D311yescharacteristic
390C2×C32×C4C22×D311yescharacteristic
391C2×C32×C4C22×D311yescharacteristic
392C2×C32×C4C22×D311yescharacteristic
393C2×C32×C4C22×D311yescharacteristic
394C2×C32×C4C22×D311yescharacteristic
395#638—41no—
396#638—41no—
397#638—41no—
398C2×C3⋊Dic3C22×D311yescharacteristic
399C2×C3⋊Dic3C22×D311yescharacteristic
400C2×C3⋊Dic3C22×D311yescharacteristic
401C2×C3⋊Dic3C22×D311yescharacteristic
402C2×C3⋊Dic3C22×D311yescharacteristic
403C2×C3⋊Dic3C22×D311yescharacteristic
404C2×C3⋊Dic3C22×D311yescharacteristic
405C4⋊(C3⋊D3)—41no—
406C4⋊(C3⋊D3)—41no—
407C4⋊(C3⋊D3)—41no—
408C4×C3⋊D3—41no—
409C3×#67—121no—
410C3×#67—121no—
411C3×#67—121no—
412C3×#67—121no—
413C3×#67—121no—
414C3×#67—121no—
415C3×#67—122no—
416C3×#67—122no—
417C3×#67—122no—
418C2×C3×Dic3—31no—
419C2×C3×Dic3—31no—
420C2×C3×Dic3—31no—
421C2×C3×Dic3—31no—
422C2×C3×Dic3—31no—
423C2×C3×Dic3—31no—
424C2×C3×Dic3—31no—
425C2×C3×Dic3—31no—
426C2×C3×Dic3—31no—
427C2×C3×Dic3—31no—
428C2×C3×Dic3—31no—
429C2×C3×Dic3—31no—
430C2×C3×Dic3—31no—
431C2×C3×Dic3—31no—
432C2×C3×Dic3—61no—
433C2×C3×Dic3—61no—
434C2×C3×Dic3—61no—
435C2×C3×Dic3—61no—
436C2×C3×Dic3—61no—
437C2×C3×Dic3—61no—
438C2×C3×Dic3—61no—
439C3×D12—121no—
440C3×D12—121no—
441C3×D12—121no—
442C3×D12—121no—
443C3×D12—121no—
444C3×D12—121no—
445C3×D12—122no—
446C3×D12—122no—
447C3×D12—122no—
448C3×C4×D3—121no—
449C3×C4×D3—121no—
450C3×C4×D3—122no—
451#626—121no—
452#626—121no—
453#626—121no—
454#626—121no—
455#626—121no—
456#626—121no—
457#626—121no—
458#626—121no—
459#626—121no—
460#626—121no—
461#626—121no—
462#626—121no—
463#625—121no—
464#625—121no—
465#625—121no—
466#625—121no—
467#625—121no—
468#625—121no—
469#624—121no—
470#624—121no—
471D3×Dic3—121no—
472D3×Dic3—121no—
473D3×Dic3—121no—
474D3×Dic3—121no—
475#560—271noSylow
476C2×C33—41no—
477C2×C33H(5,𝔽2)11yescharacteristic
478C2×C33H(5,𝔽2)11yescharacteristic
479C2×C33H(5,𝔽2)11yescharacteristic
480C3×C3⋊D3—41no—
481C3×C3⋊D3—41no—
482C3×C3⋊D3—41no—
483C3×C3⋊D3—41no—
484C3×C3⋊D3—41no—
485C24×C3—91no—
486C23×D3—31no—
487C23×D3—31no—
488C23×D3—61no—
489C2×C3×D4—91no—
490C2×C3×D4—91no—
491C2×C3×D4—91no—
492C2×C3×D4—91no—
493C2×C3×D4—91no—
494C2×C3×D4—91no—
495C22×C3×C4—91no—
496C2×#67—31no—
497C2×#67—31no—
498C2×#67—31no—
499C2×#67—31no—
500C2×#67—31no—
501C2×#67—31no—
502C2×#67—61no—
503C2×#67—61no—
504C2×#67—61no—
505C2×#67—91no—
506C2×#67—91no—
507C2×#67—91no—
508C2×#67—91no—
509C2×#67—91no—
510C2×#67—91no—
511C2×#67—91no—
512C2×#67—91no—
513C2×#67—91no—
514C2×#67—91no—
515C2×#67—91no—
516C2×#67—91no—
517C22×Dic3—91no—
518C22×Dic3—91no—
519C2×D12—31no—
520C2×D12—31no—
521C2×D12—31no—
522C2×D12—31no—
523C2×D12—31no—
524C2×D12—31no—
525C2×D12—61no—
526C2×D12—61no—
527C2×D12—61no—
528C2×D12—91no—
529C2×D12—91no—
530C2×D12—91no—
531C2×D12—91no—
532C2×D12—91no—
533C2×D12—91no—
534C2×C4×D3—31no—
535C2×C4×D3—31no—
536C2×C4×D3—61no—
537C2×C4×D3—91no—
538C2×C4×D3—91no—
539C2×C4×D3—91no—
540C2×C4×D3—91no—
541C3×C4⋊C4—91no—
542C3×C4⋊C4—91no—
543C3×C4⋊C4—91no—
544C3×C4⋊C4—91no—
545C3×C22⋊C4—21no—
546C3×C22⋊C4—21no—
547C3×C22⋊C4—21no—
548C3×C22⋊C4—41no—
549C3×C22⋊C4—91no—
550C3×C22⋊C4—91no—
551C3×C22⋊C4—91no—
552C3×C22⋊C4—91no—
553C3×C22⋊C4—91no—
554C3×C22⋊C4D3211yescharacteristic
555C3×C22⋊C4D3211yescharacteristic
556C3×C22⋊C4D3211yescharacteristic
557C3×C42—91no—
558#217—31no—
559#217—31no—
560#217—31no—
561#217—31no—
562#217—61no—
563#217—61no—
564#217—91no—
565#217—91no—
566#217—91no—
567#217—91no—
568#217—91no—
569#217—91no—
570(C2×D3)⋊C4—31no—
571(C2×D3)⋊C4—31no—
572(C2×D3)⋊C4—31no—
573(C2×D3)⋊C4—31no—
574(C2×D3)⋊C4—31no—
575(C2×D3)⋊C4—31no—
576(C2×D3)⋊C4—61no—
577(C2×D3)⋊C4—61no—
578(C2×D3)⋊C4—61no—
579(C2×D3)⋊C4—91no—
580(C2×D3)⋊C4—91no—
581(C2×D3)⋊C4—91no—
582(C2×D3)⋊C4—91no—
583(C2×D3)⋊C4—91no—
584(C2×D3)⋊C4—91no—
585(C2×D3)⋊C4—91no—
586(C2×D3)⋊C4—91no—
587(C2×D3)⋊C4—91no—
588(C2×D3)⋊C4—91no—
589(C2×D3)⋊C4—91no—
590(C2×D3)⋊C4—91no—
591C4⋊Dic3—31no—
592C4⋊Dic3—31no—
593C4⋊Dic3—61no—
594C4⋊Dic3—91no—
595C4⋊Dic3—91no—
596Dic3⋊C4—31no—
597Dic3⋊C4—31no—
598Dic3⋊C4—31no—
599Dic3⋊C4—31no—
600Dic3⋊C4—31no—
601Dic3⋊C4—31no—
602Dic3⋊C4—61no—
603Dic3⋊C4—61no—
604Dic3⋊C4—61no—
605Dic3⋊C4—91no—
606Dic3⋊C4—91no—
607Dic3⋊C4—91no—
608Dic3⋊C4—91no—
609C4×Dic3—31no—
610C4×Dic3—31no—
611C4×Dic3—61no—
612C22×C32—21no—
613C22×C32—22no—
614C22×C32—21no—
615C22×C32—21no—
616C22×C32—21no—
617C22×C32—21no—
618C22×C32—21no—
619C22×C32—21no—
620C22×C32—21no—
621C22×C32—21no—
622C22×C32—21no—
623C22×C32—21no—
624C22×C32—21no—
625C22×C32—41no—
626C22×C32—41no—
627C22×C32—41no—
628C22×C32—42no—
629C22×C32—41no—
630C22×C32—41no—
631C22×C32—41no—
632C22×C32—41no—
633C22×C32—41no—
634C22×C32—41no—
635C22×C32—81no—
636C22×C32—81no—
637C22×C32C23×D311yescharacteristic
638C22×C32C23×D311yescharacteristic
639C22×C32C23×D311yescharacteristic
640C2×C3⋊D3—21no—
641C2×C3⋊D3—21no—
642C2×C3⋊D3—21no—
643C2×C3⋊D3—21no—
644C2×C3⋊D3—21no—
645C2×C3⋊D3—21no—
646C2×C3⋊D3—21no—
647C2×C3⋊D3—21no—
648C2×C3⋊D3—21no—
649C2×C3⋊D3—21no—
650C2×C3⋊D3—21no—
651C2×C3⋊D3—21no—
652C2×C3⋊D3—21no—
653C2×C3⋊D3—21no—
654C2×C3⋊D3—21no—
655C2×C3⋊D3—44no—
656C2×C3×D3—62no—
657C2×C3×D3—62no—
658C2×C3×D3—62no—
659C2×C3×D3—61no—
660C2×C3×D3—61no—
661C2×C3×D3—61no—
662C2×C3×D3—61no—
663C2×C3×D3—61no—
664C2×C3×D3—61no—
665C2×C3×D3—61no—
666C2×C3×D3—61no—
667C2×C3×D3—61no—
668C2×C3×D3—61no—
669C2×C3×D3—61no—
670C2×C3×D3—61no—
671C2×C3×D3—61no—
672C2×C3×D3—61no—
673C2×C3×D3—61no—
674C2×C3×D3—61no—
675C2×C3×D3—61no—
676C2×C3×D3—61no—
677C2×C3×D3—61no—
678C2×C3×D3—61no—
679C2×C3×D3—61no—
680C2×C3×D3—61no—
681C2×C3×D3—61no—
682C2×C3×D3—61no—
683C2×C3×D3—61no—
684C2×C3×D3—61no—
685C2×C3×D3—61no—
686C2×C3×D3—61no—
687C2×C3×D3—61no—
688C2×C3×D3—61no—
689C2×C3×D3—121no—
690C2×C3×D3—121no—
691C2×C3×D3—121no—
692C2×C3×D3—121no—
693C2×C3×D3—121no—
694C2×C3×D3—121no—
695C2×C3×D3—121no—
696C2×C3×D3—121no—
697C2×C3×D3—121no—
698C2×C3×D3—121no—
699C2×C3×D3—121no—
700C2×C3×D3—121no—
701C2×C3×D3—128no—
702C2×C3×D3—124no—
703C2×C3×D3—124no—
704C32×C4—21no—
705C32×C4—21no—
706C32×C4—21no—
707C32×C4—21no—
708C32×C4—21no—
709C32×C4—21no—
710C32×C4—41no—
711C32×C4—41no—
712C32×C4—41no—
713C32×C4—41no—
714C32×C4—41no—
715C32×C4—41no—
716C32×C4—81no—
717C32×C4—81no—
718C3⋊Dic3—21no—
719C3⋊Dic3—21no—
720C3⋊Dic3—21no—
721C3⋊Dic3—21no—
722C3⋊Dic3—21no—
723C3⋊Dic3—21no—
724C3⋊Dic3—21no—
725C3×Dic3—62no—
726C3×Dic3—61no—
727C3×Dic3—61no—
728C3×Dic3—61no—
729C3×Dic3—61no—
730C3×Dic3—61no—
731C3×Dic3—61no—
732C3×Dic3—61no—
733C3×Dic3—61no—
734C3×Dic3—61no—
735C3×Dic3—61no—
736C3×Dic3—61no—
737C3×Dic3—61no—
738C3×Dic3—61no—
739C3×Dic3—61no—
740C3×Dic3—121no—
741C3×Dic3—121no—
742C3×Dic3—121no—
743C3×Dic3—121no—
744C3×Dic3—121no—
745C3×Dic3—121no—
746#127—271no—
747#126—91no—
748#126—271no—
749#123—271no—
750#123—271no—
751#123—271no—
752#121—91no—
753#121—271no—
754#121—271no—
755#121—271no—
756#121—271no—
757#121—271no—
758#120—91no—
759#120—271no—
760#120—271no—
761C33#56011yescharacteristic, complemented, Sylow
762C23×C3—21no—
763C23×C3—21no—
764C23×C3—21no—
765C23×C3—41no—
766C23×C3—91no—
767C23×C3—91no—
768C23×C3—91no—
769C23×C3—91no—
770C23×C3—91no—
771C23×C3—361no—
772C23×C3—361no—
773C23×C3—361no—
774C23×C3C2×D3211yescharacteristic
775C23×C3C2×D3211yescharacteristic
776C23×C3C2×D3211yescharacteristic
777C22×D3—31no—
778C22×D3—31no—
779C22×D3—31no—
780C22×D3—31no—
781C22×D3—31no—
782C22×D3—31no—
783C22×D3—31no—
784C22×D3—31no—
785C22×D3—31no—
786C22×D3—31no—
787C22×D3—61no—
788C22×D3—61no—
789C22×D3—61no—
790C22×D3—61no—
791C22×D3—61no—
792C22×D3—121no—
793C22×D3—121no—
794C22×D3—121no—
795C22×D3—121no—
796C22×D3—121no—
797C22×D3—121no—
798C22×D3—122no—
799C22×D3—122no—
800C22×D3—122no—
801C3×D4—361no—
802C3×D4—361no—
803C3×D4—361no—
804C3×D4—361no—
805C3×D4—361no—
806C3×D4—361no—
807C2×C3×C4—21no—
808C2×C3×C4—21no—
809C2×C3×C4—21no—
810C2×C3×C4—21no—
811C2×C3×C4—21no—
812C2×C3×C4—21no—
813C2×C3×C4—41no—
814C2×C3×C4—41no—
815C2×C3×C4—91no—
816C2×C3×C4—91no—
817C2×C3×C4—91no—
818C2×C3×C4—91no—
819C2×C3×C4—91no—
820C2×C3×C4—91no—
821C2×C3×C4—91no—
822C2×C3×C4—361no—
823C2×C3×C4C2×D3211yescharacteristic
824C2×C3×C4C2×D3211yescharacteristic
825C2×C3×C4C2×D3211yescharacteristic
826C2×C3×C4C2×D3211yescharacteristic
827C2×C3×C4C2×D3211yescharacteristic
828C2×C3×C4C2×D3211yescharacteristic
829#67—121no—
830#67—121no—
831#67—121no—
832#67—121no—
833#67—121no—
834#67—121no—
835#67—122no—
836#67—122no—
837#67—122no—
838#67—361no—
839#67—361no—
840#67—361no—
841#67—361no—
842#67—361no—
843#67—361no—
844#67—361no—
845#67—361no—
846#67—361no—
847#67—361no—
848#67—361no—
849#67—361no—
850C2×Dic3—31no—
851C2×Dic3—31no—
852C2×Dic3—31no—
853C2×Dic3—31no—
854C2×Dic3—31no—
855C2×Dic3—31no—
856C2×Dic3—31no—
857C2×Dic3—31no—
858C2×Dic3—31no—
859C2×Dic3—31no—
860C2×Dic3—31no—
861C2×Dic3—31no—
862C2×Dic3—31no—
863C2×Dic3—31no—
864C2×Dic3—61no—
865C2×Dic3—61no—
866C2×Dic3—61no—
867C2×Dic3—61no—
868C2×Dic3—61no—
869C2×Dic3—61no—
870C2×Dic3—61no—
871C2×Dic3—361no—
872C2×Dic3—361no—
873D12—121no—
874D12—121no—
875D12—121no—
876D12—121no—
877D12—121no—
878D12—121no—
879D12—122no—
880D12—122no—
881D12—122no—
882D12—361no—
883D12—361no—
884D12—361no—
885D12—361no—
886D12—361no—
887D12—361no—
888C4×D3—121no—
889C4×D3—121no—
890C4×D3—122no—
891C4×D3—361no—
892C4×D3—361no—
893C4×D3—361no—
894C4×D3—361no—
895C2×C32—21no—
896C2×C32—21no—
897C2×C32—21no—
898C2×C32—21no—
899C2×C32—21no—
900C2×C32—21no—
901C2×C32—21no—
902C2×C32—21no—
903C2×C32—21no—
904C2×C32—41no—
905C2×C32—41no—
906C2×C32—41no—
907C2×C32—41no—
908C2×C32—42no—
909C2×C32—41no—
910C2×C32—41no—
911C2×C32—81no—
912C2×C32—81no—
913C2×C32—82no—
914C2×C32#100411yescharacteristic
915C2×C32#100411yescharacteristic
916C2×C32#100411yescharacteristic
917C2×C32#100411yescharacteristic
918C2×C32#100411yescharacteristic
919C2×C32#100911yescharacteristic
920C2×C32#100911yescharacteristic
921C2×C32#100911yescharacteristic
922C2×C32#100911yescharacteristic
923C3⋊D3—41no—
924C3⋊D3—41no—
925C3⋊D3—41no—
926C3⋊D3—41no—
927C3⋊D3—41no—
928C3×D3—122no—
929C3×D3—122no—
930C3×D3—122no—
931C3×D3—121no—
932C3×D3—121no—
933C3×D3—121no—
934C3×D3—121no—
935C3×D3—121no—
936C3×D3—121no—
937C3×D3—121no—
938C3×D3—121no—
939C3×D3—121no—
940C3×D3—121no—
941C3×D3—241no—
942C3×D3—241no—
943C24—91no—
944C2×D4—91no—
945C2×D4—91no—
946C2×D4—91no—
947C2×D4—91no—
948C2×D4—91no—
949C2×D4—91no—
950C2×D4—271no—
951C2×D4—271no—
952C2×D4—271no—
953C2×D4—271no—
954C2×D4—271no—
955C2×D4—271no—
956C22×C4—91no—
957C22×C4—271no—
958C22×C4—271no—
959C4⋊C4—91no—
960C4⋊C4—91no—
961C4⋊C4—91no—
962C4⋊C4—91no—
963C4⋊C4—271no—
964C4⋊C4—271no—
965C22⋊C4—91no—
966C22⋊C4—91no—
967C22⋊C4—91no—
968C22⋊C4—91no—
969C22⋊C4—91no—
970C22⋊C4—271no—
971C22⋊C4—271no—
972C22⋊C4—271no—
973C22⋊C4—271no—
974C22⋊C4—271no—
975C22⋊C4—271no—
976C22⋊C4#111311yescharacteristic
977C42—91no—
978C22×C3—22no—
979C22×C3—21no—
980C22×C3—21no—
981C22×C3—21no—
982C22×C3—21no—
983C22×C3—21no—
984C22×C3—21no—
985C22×C3—21no—
986C22×C3—21no—
987C22×C3—21no—
988C22×C3—21no—
989C22×C3—21no—
990C22×C3—21no—
991C22×C3—41no—
992C22×C3—41no—
993C22×C3—41no—
994C22×C3—41no—
995C22×C3—41no—
996C22×C3—41no—
997C22×C3—41no—
998C22×C3—41no—
999C22×C3—42no—
1000C22×C3—41no—
1001C22×C3—81no—
1002C22×C3—81no—
1003C22×C3—181no—
1004C22×C3—181no—
1005C22×C3—181no—
1006C22×C3—181no—
1007C22×C3—181no—
1008C22×C3—181no—
1009C22×C3—181no—
1010C22×C3—181no—
1011C22×C3—181no—
1012C22×C3—181no—
1013C22×C3—181no—
1014C22×C3—181no—
1015C22×C3—181no—
1016C22×C3—181no—
1017C22×C3—181no—
1018C22×C3—364no—
1019C22×C3C22×D3211yescharacteristic
1020C22×C3C22×D3211yescharacteristic
1021C22×C3C22×D3211yescharacteristic
1022C2×D3—62no—
1023C2×D3—62no—
1024C2×D3—62no—
1025C2×D3—61no—
1026C2×D3—61no—
1027C2×D3—61no—
1028C2×D3—61no—
1029C2×D3—61no—
1030C2×D3—61no—
1031C2×D3—61no—
1032C2×D3—61no—
1033C2×D3—61no—
1034C2×D3—61no—
1035C2×D3—61no—
1036C2×D3—61no—
1037C2×D3—61no—
1038C2×D3—61no—
1039C2×D3—61no—
1040C2×D3—61no—
1041C2×D3—61no—
1042C2×D3—61no—
1043C2×D3—61no—
1044C2×D3—61no—
1045C2×D3—61no—
1046C2×D3—61no—
1047C2×D3—61no—
1048C2×D3—61no—
1049C2×D3—61no—
1050C2×D3—61no—
1051C2×D3—61no—
1052C2×D3—61no—
1053C2×D3—61no—
1054C2×D3—61no—
1055C2×D3—121no—
1056C2×D3—121no—
1057C2×D3—121no—
1058C2×D3—121no—
1059C2×D3—121no—
1060C2×D3—121no—
1061C2×D3—121no—
1062C2×D3—121no—
1063C2×D3—121no—
1064C2×D3—121no—
1065C2×D3—121no—
1066C2×D3—121no—
1067C2×D3—128no—
1068C2×D3—124no—
1069C2×D3—124no—
1070C3×C4—21no—
1071C3×C4—21no—
1072C3×C4—21no—
1073C3×C4—21no—
1074C3×C4—21no—
1075C3×C4—21no—
1076C3×C4—41no—
1077C3×C4—41no—
1078C3×C4—41no—
1079C3×C4—41no—
1080C3×C4—41no—
1081C3×C4—41no—
1082C3×C4—81no—
1083C3×C4—81no—
1084C3×C4—181no—
1085C3×C4—181no—
1086C3×C4—181no—
1087C3×C4—181no—
1088C3×C4—181no—
1089C3×C4—181no—
1090C3×C4—181no—
1091Dic3—62no—
1092Dic3—61no—
1093Dic3—61no—
1094Dic3—61no—
1095Dic3—61no—
1096Dic3—61no—
1097Dic3—61no—
1098Dic3—61no—
1099Dic3—61no—
1100Dic3—61no—
1101Dic3—61no—
1102Dic3—61no—
1103Dic3—61no—
1104Dic3—61no—
1105Dic3—61no—
1106Dic3—121no—
1107Dic3—121no—
1108Dic3—121no—
1109Dic3—121no—
1110Dic3—121no—
1111Dic3—121no—
1112C32—21no—
1113C32—21no—
1114C32—21no—
1115C32—41no—
1116C32#559511yescharacteristic, complemented
1117C32#562011yescharacteristic, complemented
1118C32#571111yescharacteristic, complemented
1119C23—91no—
1120C23—91no—
1121C23—91no—
1122C23—91no—
1123C23—91no—
1124C23—361no—
1125C23—361no—
1126C23—361no—
1127C23C2×#111311yescharacteristic
1128D4—361no—
1129D4—361no—
1130D4—361no—
1131D4—361no—
1132D4—361no—
1133D4—361no—
1134D4—1081no—
1135D4—1081no—
1136D4—1081no—
1137D4—1081no—
1138D4—1081no—
1139D4—1081no—
1140C2×C4—91no—
1141C2×C4—91no—
1142C2×C4—91no—
1143C2×C4—91no—
1144C2×C4—91no—
1145C2×C4—91no—
1146C2×C4—91no—
1147C2×C4—361no—
1148C2×C4—1081no—
1149C2×C4—1081no—
1150C2×C4C2×#111311yescharacteristic
1151C2×C4C2×#111311yescharacteristic
1152C2×C3—21no—
1153C2×C3—21no—
1154C2×C3—21no—
1155C2×C3—21no—
1156C2×C3—21no—
1157C2×C3—21no—
1158C2×C3—21no—
1159C2×C3—21no—
1160C2×C3—21no—
1161C2×C3—42no—
1162C2×C3—41no—
1163C2×C3—41no—
1164C2×C3—41no—
1165C2×C3—41no—
1166C2×C3—41no—
1167C2×C3—41no—
1168C2×C3—81no—
1169C2×C3—81no—
1170C2×C3—82no—
1171C2×C3—361no—
1172C2×C3—361no—
1173C2×C3—361no—
1174C2×C3—361no—
1175C2×C3—361no—
1176C2×C3#6430711yescharacteristic
1177C2×C3#6430711yescharacteristic
1178C2×C3#6430811yescharacteristic
1179C2×C3#6431311yescharacteristic
1180C2×C3#6431311yescharacteristic
1181C2×C3#6431411yescharacteristic
1182C2×C3#6431411yescharacteristic
1183C2×C3#6431411yescharacteristic
1184C2×C3#6431411yescharacteristic
1185D3—122no—
1186D3—122no—
1187D3—122no—
1188D3—121no—
1189D3—121no—
1190D3—121no—
1191D3—121no—
1192D3—121no—
1193D3—121no—
1194D3—121no—
1195D3—121no—
1196D3—121no—
1197D3—121no—
1198D3—241no—
1199D3—241no—
1200C22—21no—
1201C22—21no—
1202C22—21no—
1203C22—181no—
1204C22—181no—
1205C22—181no—
1206C22—181no—
1207C22—181no—
1208C22—181no—
1209C22—181no—
1210C22—181no—
1211C22—181no—
1212C22—181no—
1213C22—181no—
1214C22—181no—
1215C22—181no—
1216C22—181no—
1217C22—181no—
1218C22—364no—
1219C22C22×#111311yescharacteristic
1220C4—21no—
1221C4—21no—
1222C4—181no—
1223C4—181no—
1224C4—181no—
1225C4—181no—
1226C4—181no—
1227C4—181no—
1228C4—181no—
1229C3—21no—
1230C3—21no—
1231C3—21no—
1232C3—41no—
1233C3#1059423411yescharacteristic, complemented
1234C3#1059423611yescharacteristic, complemented
1235C3#1059424211yescharacteristic, complemented
1236C2—41no—
1237C2—361no—
1238C2—361no—
1239C2—361no—
1240C2—361no—
1241C2—361no—
1242C2#1172461911yescharacteristic
1243C2#1172462311yescharacteristic
1244C2#1172462311yescharacteristic
subgroupG/H
center, FrattiniC22C22×#1113
commutator, socle, cosocleC22×C33C24
FittingC33×C22⋊C4C22
hypercenterC22⋊C4#1113
hypocenterC33#560
LCSG ▷ C22×C33 ▷ C33
UCSC1 ◁ C22 ◁ C22⋊C4

Complements

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

NH ≅ G/Ntype
1. C3×#64093C2semidirect
2. C3×#64091C2semidirect
3. C3×#64088C2semidirect
4. #11723727C2semidirect
5. #11723727C2semidirect
6. #11723725C2semidirect
7. #11723725C2semidirect
8. #11723697C2semidirect
9. #11723696C2semidirect
10. #11723694C2semidirect
11. #11723690C2semidirect
12. #11723687C2semidirect
13. #11723687C2semidirect
14. #11723686C2semidirect
15. #11723676C2semidirect
25. C2×C3×C4⋊(C3⋊D3)C22semidirect
26. C2×C3×C4×C3⋊D3C22semidirect
31. C2×#6295C22semidirect
32. C2×#6295C22semidirect
33. C2×#6294C22semidirect
34. C2×#6294C22semidirect
40. C3×#3752C22semidirect
41. C3×C4⋊(C3⋊Dic3)C22semidirect
42. C3×#3750C22semidirect
43. C3×#3750C22semidirect
44. C3×#3750C22semidirect
45. C3×C4×C3⋊Dic3C22semidirect
46. #88815C22semidirect
47. #88815C22semidirect
52. #88814C22semidirect
53. #88814C22semidirect
54. #64093D3semidirect
55. #64091D3semidirect
56. #64088D3semidirect
147. C2×C4⋊(C3⋊D3)C2×D3semidirect
148. C2×C4×C3⋊D3C2×D3semidirect
205. #3752C2×D3semidirect
206. C4⋊(C3⋊Dic3)C2×D3semidirect
207. #3750C2×D3semidirect
208. #3750C2×D3semidirect
209. #3750C2×D3semidirect
210. C4×C3⋊Dic3C2×D3semidirect
761. C33#560semidirect
1116. C32#5595semidirect
1117. C32#5620semidirect
1118. C32#5711semidirect
1233. C3#10594234semidirect
1234. C3#10594236semidirect
1235. C3#10594242semidirect

Maximal subgroups

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

subgroupindex
C3×#640932
C3×#640912
C3×#640882
#117237272
#117237252
#117236972
#117236962
#117236942
#117236902
#117236872
#117236862
#117236762
#105942423
#105942363
#105942343