Finite Group Databasebeta

← #13172108

Subgroups — #13172108

Order 1728.

1320 conjugacy classes of subgroups.

The subgroup lattice has 1190 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11723729C211yesmaximal, characteristic, complemented
2#11723637C211yesmaximal, characteristic, complemented
3#11723626C211yesmaximal, characteristic, complemented
4#11723609C211yesmaximal, characteristic, complemented
5C3×#63971C211yesmaximal, characteristic, complemented
6C3×#63958C211yesmaximal, characteristic, complemented
7C3×#63953C211yesmaximal, characteristic, complemented
8#11723027C211yesmaximal, characteristic, complemented
9#11723024C211yesmaximal, characteristic, complemented
10#11723001C211yesmaximal, characteristic, complemented
11#11722988C211yesmaximal, characteristic, complemented
12#11722970C211yesmaximal, characteristic, complemented
13#11722951C211yesmaximal, characteristic, complemented
14Dic3×#626C211yesmaximal, characteristic, complemented
15#11722905C211yesmaximal, characteristic, complemented
16#10595310—31nomaximal
17#10594306—31nomaximal
18#10594301—31nomaximal
19C22×#1113C2211yescharacteristic
20C22×C3⋊(C3⋊Dic3)C2211yescharacteristic, complemented
21C2×C3×#638C2211yescharacteristic
22C2×C3×#638C2211yescharacteristic
23C2×C3×#638C2211yescharacteristic
24C2×C32×#67C2211yescharacteristic, complemented
25C2×#6290C2211yescharacteristic
26C2×Dic3×C3⋊D3C2211yescharacteristic
27C2×C3×#627C2211yescharacteristic, complemented
28C2×C3×#626C2211yescharacteristic
29C2×C3×#626C2211yescharacteristic
30C2×C3×#624C2211yescharacteristic
31C2×C3×D3×Dic3C2211yescharacteristic, complemented
32C32×#217C2211yescharacteristic, complemented
33C32×#217C2211yescharacteristic, complemented
34#88814C2211yescharacteristic
35#88814C2211yescharacteristic
36#88814C2211yescharacteristic
37#88807C2211yescharacteristic, complemented
38#88806C2211yescharacteristic, complemented
39Dic3⋊(C3⋊Dic3)C2211yescharacteristic, complemented
40Dic3⋊(C3⋊Dic3)C2211yescharacteristic, complemented
41#88803C2211yescharacteristic
42#88803C2211yescharacteristic
43#88803C2211yescharacteristic
44#88803C2211yescharacteristic
45(C2×D3)⋊(C3⋊Dic3)C2211yescharacteristic, complemented
46Dic3×C3⋊Dic3C2211yescharacteristic, complemented
47C3×#3724C2211yescharacteristic, complemented
48C3×Dic3⋊Dic3C2211yescharacteristic, complemented
49C3×#3722C2211yescharacteristic
50C3×#3722C2211yescharacteristic
51C3×#3722C2211yescharacteristic
52C3×(C2×D3)⋊Dic3C2211yescharacteristic, complemented
53C3×Dic32C2211yescharacteristic, complemented
54#64148—31no—
55#64095—31no—
56#64090—31no—
57C3×#939—31no—
58C3×#938—31no—
59C3×#885—31no—
60C3×#885—31no—
61C3×#884—31no—
62C3×#884—31no—
63#63983—31no—
64#63983—31no—
65#63983—31no—
66#63983—31no—
67#63980—31no—
68#63980—31no—
69#63980—61no—
70#67⋊Dic3—31no—
71#67⋊Dic3—31no—
72#67⋊Dic3—61no—
73Dic3×#67—31no—
74#63971D311yescharacteristic, complemented
75#63966—31no—
76#63962—31no—
77#63962—31no—
78#63962—61no—
79#63959—31no—
80#63958D311yescharacteristic, complemented
81#63953D311yescharacteristic, complemented
82#63922—31no—
83#63922—31no—
84#63921—31no—
85D3×(C2×D3)⋊C4—31no—
86D3×(C2×D3)⋊C4—31no—
87#63907—31no—
88#63905—31no—
89C4×#626—31no—
90Dic3×D12—31no—
91#63891—31no—
92#63888—31no—
93#63868—31no—
94#63863—31no—
95#63862—31no—
96#63861—31no—
97#63859—31no—
98#63858—31no—
99#63856—31no—
100#63851—31no—
101#63848—31no—
102C23×C33C2311yescharacteristic
103C22×C3×C3⋊D3C2311yescharacteristic
104C22×C3×C3⋊D3C2311yescharacteristic
105C22×C3×C3⋊D3C2311yescharacteristic
106C22×C32×D3C2311yescharacteristic
107C2×#1113—22no—
108C2×#1113—41no—
109C2×#1113—41no—
110C2×C3⋊(C3⋊Dic3)—41no—
111C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
112C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
113C3×#638—22no—
114C3×#638—41no—
115C3×#638—41no—
116C2×C3×C3⋊Dic3C2311yescharacteristic
117C2×C3×C3⋊Dic3C2311yescharacteristic
118C2×C3×C3⋊Dic3C2311yescharacteristic
119C32×#67—41no—
120C2×C32×Dic3C2311yescharacteristic
121C2×C32×Dic3C2311yescharacteristic
122C2×C32×Dic3C2311yescharacteristic
123C2×C32×Dic3C2311yescharacteristic
124C2×C32×Dic3C2311yescharacteristic
125#6290—41no—
126Dic3×C3⋊D3—41no—
127C3×#627—41no—
128C3×#626—22no—
129C3×#626—41no—
130C3×#624—41no—
131C3×D3×Dic3—41no—
132#5678—91no—
133#5617—91no—
134#5613—91no—
135C22×D32—31no—
136C22×D32—31no—
137C22×D32—31no—
138C2×C32×D4—31no—
139C2×#638—31no—
140C2×#638C2×D311yescharacteristic
141C2×#638C2×D311yescharacteristic
142C2×#638C2×D311yescharacteristic
143C22×C3⋊Dic3—31no—
144C22×C3⋊Dic3—31no—
145C22×C3⋊Dic3—31no—
146C22×C3⋊Dic3—61no—
147C22×C3⋊Dic3—61no—
148C22×C3⋊Dic3—61no—
149C22×C3⋊Dic3—121no—
150C2×C4×C3⋊D3—31no—
151C2×C3×#67—21no—
152C2×C3×#67—31no—
153C2×C3×#67—31no—
154C2×C3×#67—31no—
155C2×C3×#67—31no—
156C2×C3×#67—31no—
157C2×C3×#67—31no—
158C2×C3×#67—31no—
159C2×C3×#67—31no—
160C2×C3×#67—61no—
161C2×C3×#67—61no—
162C2×C3×#67—61no—
163C2×C3×#67C2×D311yescharacteristic, complemented
164C2×C3×#67C2×D311yescharacteristic, complemented
165C22×C3×Dic3—31no—
166C2×C3×D12—31no—
167C2×C3×D12—31no—
168C2×C3×C4×D3—31no—
169C2×C3×C4×D3—31no—
170C2×C3×C4×D3—31no—
171C2×C3×Dic6—31no—
172C2×C3×Dic6—31no—
173C2×#627C2×D311yescharacteristic, complemented
174C2×#626C2×D311yescharacteristic
175C2×#626C2×D311yescharacteristic
176C2×#625—31no—
177C2×#625—31no—
178C2×#625—61no—
179C2×#624C2×D311yescharacteristic
180C2×D3×Dic3—31no—
181C2×D3×Dic3—31no—
182C2×D3×Dic3—61no—
183C2×D3×Dic3C2×D311yescharacteristic, complemented
184C32×C22⋊C4—31no—
185C32×C22⋊C4—31no—
186#3757—31no—
187#3752—31no—
188#3752—31no—
189#3752—31no—
190#3752—31no—
191C4⋊(C3⋊Dic3)—31no—
192C4⋊(C3⋊Dic3)—31no—
193#3750—31no—
194#3750—31no—
195C4×C3⋊Dic3—31no—
196C3×#217—21no—
197C3×#217—21no—
198C3×#217—31no—
199C3×#217C2×D311yescharacteristic, complemented
200C3×#217C2×D311yescharacteristic, complemented
201C3×#217C2×D311yescharacteristic, complemented
202C3×#217C2×D311yescharacteristic, complemented
203C3×(C2×D3)⋊C4—31no—
204C3×(C2×D3)⋊C4—31no—
205C3×(C2×D3)⋊C4—31no—
206C3×(C2×D3)⋊C4—31no—
207C3×(C2×D3)⋊C4—31no—
208C3×(C2×D3)⋊C4—31no—
209C3×(C2×D3)⋊C4—31no—
210C3×C4⋊Dic3—31no—
211C3×Dic3⋊C4—31no—
212C3×Dic3⋊C4—31no—
213C3×Dic3⋊C4—31no—
214C3×C4×Dic3—31no—
215C3×C4×Dic3—31no—
216#3724—31no—
217#3724—31no—
218#3724—61no—
219#3724C2×D311yescharacteristic, complemented
220Dic3⋊Dic3—31no—
221Dic3⋊Dic3—31no—
222Dic3⋊Dic3—31no—
223Dic3⋊Dic3—31no—
224Dic3⋊Dic3—31no—
225Dic3⋊Dic3—31no—
226Dic3⋊Dic3—61no—
227Dic3⋊Dic3—61no—
228Dic3⋊Dic3—61no—
229Dic3⋊Dic3C2×D311yescharacteristic, complemented
230#3722—31no—
231#3722—31no—
232#3722—31no—
233#3722C2×D311yescharacteristic
234#3722C2×D311yescharacteristic
235#3722C2×D311yescharacteristic
236(C2×D3)⋊Dic3—31no—
237(C2×D3)⋊Dic3—31no—
238(C2×D3)⋊Dic3—31no—
239(C2×D3)⋊Dic3—31no—
240(C2×D3)⋊Dic3—31no—
241(C2×D3)⋊Dic3—31no—
242(C2×D3)⋊Dic3—31no—
243(C2×D3)⋊Dic3—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—61no—
253(C2×D3)⋊Dic3—61no—
254(C2×D3)⋊Dic3—61no—
255(C2×D3)⋊Dic3—61no—
256(C2×D3)⋊Dic3—61no—
257(C2×D3)⋊Dic3C2×D311yescharacteristic, complemented
258Dic32—31no—
259Dic32—31no—
260Dic32—61no—
261Dic32C2×D311yescharacteristic, complemented
262C22×C33—21no—
263C22×C33—21no—
264C22×C33—21no—
265C22×C33C2411yescharacteristic
266C2×C3×C3⋊D3—21no—
267C2×C3×C3⋊D3—21no—
268C2×C3×C3⋊D3—21no—
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#4112yes—
275C2×C32×D3—21no—
276C2×C32×D3—21no—
277C2×C32×D3—21no—
278#1113—44no—
279C3⋊(C3⋊Dic3)—21no—
280C3⋊(C3⋊Dic3)—21no—
281C3×C3⋊Dic3—21no—
282C3×C3⋊Dic3—21no—
283C3×C3⋊Dic3—21no—
284C32×Dic3—21no—
285C32×Dic3—21no—
286C32×Dic3—21no—
287C32×Dic3—21no—
288C32×Dic3—21no—
289C3×#124—91no—
290C3×#121—91no—
291C3×#121—91no—
292#947—91no—
293#946—91no—
294#939—31no—
295#939—91no—
296#939—91no—
297#939—91no—
298#939—181no—
299#938—31no—
300#937—91no—
301#937—91no—
302#937—91no—
303#937—91no—
304#937—91no—
305#936—91no—
306#935—91no—
307D4×Dic3—91no—
308D4×Dic3—91no—
309#929—91no—
310C4×#67—91no—
311C2×(C2×D3)⋊C4—91no—
312#924—91no—
313#898—91no—
314#898—91no—
315#898—91no—
316#896—91no—
317#886—91no—
318#886—91no—
319#886—91no—
320#886—181no—
321#885—31no—
322#885—31no—
323#885—91no—
324#884—31no—
325#884—31no—
326#883—91no—
327#882—91no—
328#67⋊C4—91no—
329#67⋊C4—91no—
330#67⋊C4—181no—
331D3×C22⋊C4—91no—
332D3×C22⋊C4—91no—
333#879—91no—
334#879—91no—
335#876—91no—
336C4×D12—91no—
337C23×C32—21no—
338C23×C32—21no—
339C23×C32—21no—
340C23×C32—31no—
341C23×C32—41no—
342C23×C32C22×D311yescharacteristic
343C23×C32C22×D311yescharacteristic
344C23×C32C22×D311yescharacteristic
345C22×C3⋊D3C22×D311yescharacteristic
346C22×C3⋊D3C22×D311yescharacteristic
347C22×C3⋊D3C22×D311yescharacteristic
348C22×C3×D3—21no—
349C22×C3×D3—31no—
350C22×C3×D3—31no—
351C22×C3×D3—31no—
352C22×C3×D3—31no—
353C22×C3×D3—31no—
354C22×C3×D3—31no—
355C22×C3×D3—61no—
356C22×C3×D3—61no—
357C22×C3×D3—61no—
358C22×C3×D3C22×D311yescharacteristic
359C22×C3×D3C22×D311yescharacteristic
360C2×D32—62no—
361C2×D32—62no—
362C2×D32—62no—
363C2×D32—121no—
364C2×D32—121no—
365C2×D32—121no—
366C2×D32—121no—
367C2×D32—121no—
368C2×D32—121no—
369C32×D4—121no—
370C2×C32×C4—31no—
371C2×C32×C4—31no—
372C2×C32×C4—31no—
373C2×C32×C4—31no—
374C2×C32×C4—31no—
375#638—22no—
376#638—41no—
377#638—41no—
378#638—121no—
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—61no—
386C2×C3⋊Dic3—61no—
387C2×C3⋊Dic3—61no—
388C2×C3⋊Dic3—61no—
389C2×C3⋊Dic3—61no—
390C2×C3⋊Dic3—61no—
391C2×C3⋊Dic3—121no—
392C2×C3⋊Dic3—121no—
393C2×C3⋊Dic3—121no—
394C2×C3⋊Dic3—121no—
395C2×C3⋊Dic3—121no—
396C2×C3⋊Dic3—122no—
397C2×C3⋊Dic3—122no—
398C2×C3⋊Dic3—122no—
399C2×C3⋊Dic3—124no—
400C2×C3⋊Dic3C22×D311yescharacteristic
401C2×C3⋊Dic3C22×D311yescharacteristic
402C2×C3⋊Dic3C22×D311yescharacteristic
403C4×C3⋊D3—121no—
404C3×#67—41no—
405C3×#67—41no—
406C3×#67—42no—
407C3×#67—62no—
408C3×#67—62no—
409C3×#67—62no—
410C3×#67—64no—
411C3×#67—121no—
412C3×#67—121no—
413C3×#67—121no—
414C3×#67—121no—
415C3×#67—121no—
416C3×#67—122no—
417C3×#67—122no—
418C2×C3×Dic3—21no—
419C2×C3×Dic3—21no—
420C2×C3×Dic3—21no—
421C2×C3×Dic3—21no—
422C2×C3×Dic3—21no—
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—61no—
430C2×C3×Dic3—61no—
431C2×C3×Dic3—61no—
432C2×C3×Dic3—121no—
433C2×C3×Dic3C22×D311yescharacteristic
434C2×C3×Dic3C22×D311yescharacteristic
435C2×C3×Dic3C22×D311yescharacteristic
436C2×C3×Dic3C22×D311yescharacteristic
437C2×C3×Dic3C22×D311yescharacteristic
438C2×C3×Dic3C22×D311yescharacteristic
439C2×C3×Dic3C22×D311yescharacteristic
440C2×C3×Dic3C22×D311yescharacteristic
441C2×C3×Dic3C22×D311yescharacteristic
442C2×C3×Dic3C22×D311yescharacteristic
443C3×D12—62no—
444C3×D12—121no—
445C3×C4×D3—121no—
446C3×C4×D3—121no—
447C3×C4×D3—121no—
448C3×Dic6—121no—
449C3×Dic6—121no—
450#627—41no—
451#626—22no—
452#626—41no—
453#625—121no—
454#625—121no—
455#625—122no—
456#624—41no—
457D3×Dic3—41no—
458D3×Dic3—121no—
459D3×Dic3—121no—
460D3×Dic3—122no—
461#538—271noSylow
462C2×C33—41no—
463C2×C33C2×#4111yescharacteristic
464C2×C33H(5,𝔽2)11yescharacteristic
465C2×C33H(5,𝔽2)11yescharacteristic
466C3×C3⋊D3—22no—
467C3×C3⋊D3—41no—
468C3×C3⋊D3—41no—
469C32×D3—41no—
470C23×D3—91no—
471C23×D3—91no—
472C23×D3—91no—
473C2×C3×Q8—91no—
474C2×C3×D4—31no—
475C2×C3×D4—31no—
476C2×C3×D4—61no—
477C2×C3×D4—91no—
478C2×C3×D4—91no—
479C2×C3×D4—91no—
480C2×C3×D4—91no—
481C2×C3×D4—91no—
482C22×C3×C4—91no—
483C22×C3×C4—91no—
484C2×#67—31no—
485C2×#67—31no—
486C2×#67—31no—
487C2×#67—31no—
488C2×#67—31no—
489C2×#67—31no—
490C2×#67—31no—
491C2×#67—31no—
492C2×#67—61no—
493C2×#67—61no—
494C2×#67—61no—
495C2×#67—91no—
496C2×#67—91no—
497C2×#67—91no—
498C2×#67—181no—
499C2×#67D3211yescharacteristic, complemented
500C22×Dic3—31no—
501C22×Dic3—91no—
502C22×Dic3—91no—
503C22×Dic3—91no—
504C22×Dic3—91no—
505C22×Dic3—181no—
506C22×Dic3—181no—
507C22×Dic3—181no—
508C22×Dic3—361no—
509C2×D12—31no—
510C2×D12—31no—
511C2×C4×D3—31no—
512C2×C4×D3—31no—
513C2×C4×D3—31no—
514C2×C4×D3—91no—
515C2×C4×D3—91no—
516C2×C4×D3—181no—
517C2×Dic6—31no—
518C2×Dic6—31no—
519C3×C4⋊C4—91no—
520C3×C4⋊C4—91no—
521C3×C22⋊C4—31no—
522C3×C22⋊C4—31no—
523C3×C22⋊C4—31no—
524C3×C22⋊C4—31no—
525C3×C22⋊C4—61no—
526C3×C22⋊C4—61no—
527C3×C22⋊C4—91no—
528C3×C22⋊C4—91no—
529C3×C22⋊C4—91no—
530C3×C22⋊C4—91no—
531C3×C42—91no—
532#217—31no—
533#217—91no—
534#217—91no—
535#217—91no—
536#217—91no—
537#217—91no—
538#217—91no—
539#217—91no—
540#217—91no—
541#217—91no—
542#217—181no—
543#217D3211yescharacteristic, complemented
544#217D3211yescharacteristic, complemented
545(C2×D3)⋊C4—31no—
546(C2×D3)⋊C4—31no—
547(C2×D3)⋊C4—31no—
548(C2×D3)⋊C4—31no—
549(C2×D3)⋊C4—31no—
550(C2×D3)⋊C4—31no—
551(C2×D3)⋊C4—31no—
552(C2×D3)⋊C4—91no—
553(C2×D3)⋊C4—91no—
554(C2×D3)⋊C4—91no—
555(C2×D3)⋊C4—91no—
556(C2×D3)⋊C4—91no—
557(C2×D3)⋊C4—91no—
558(C2×D3)⋊C4—91no—
559(C2×D3)⋊C4—91no—
560(C2×D3)⋊C4—91no—
561(C2×D3)⋊C4—91no—
562(C2×D3)⋊C4—91no—
563(C2×D3)⋊C4—91no—
564(C2×D3)⋊C4—91no—
565(C2×D3)⋊C4—91no—
566(C2×D3)⋊C4—91no—
567(C2×D3)⋊C4—181no—
568(C2×D3)⋊C4—181no—
569(C2×D3)⋊C4—181no—
570(C2×D3)⋊C4—181no—
571C4⋊Dic3—31no—
572C4⋊Dic3—91no—
573C4⋊Dic3—91no—
574C4⋊Dic3—91no—
575C4⋊Dic3—91no—
576C4⋊Dic3—91no—
577C4⋊Dic3—181no—
578C4⋊Dic3—181no—
579Dic3⋊C4—31no—
580Dic3⋊C4—31no—
581Dic3⋊C4—31no—
582Dic3⋊C4—91no—
583Dic3⋊C4—91no—
584Dic3⋊C4—91no—
585Dic3⋊C4—91no—
586Dic3⋊C4—91no—
587Dic3⋊C4—91no—
588Dic3⋊C4—91no—
589Dic3⋊C4—181no—
590Dic3⋊C4—181no—
591C4×Dic3—31no—
592C4×Dic3—31no—
593C4×Dic3—91no—
594C4×Dic3—91no—
595C4×Dic3—91no—
596C4×Dic3—181no—
597C22×C32—21no—
598C22×C32—21no—
599C22×C32—21no—
600C22×C32—22no—
601C22×C32—22no—
602C22×C32—22no—
603C22×C32—21no—
604C22×C32—21no—
605C22×C32—21no—
606C22×C32—21no—
607C22×C32—21no—
608C22×C32—21no—
609C22×C32—21no—
610C22×C32—21no—
611C22×C32—21no—
612C22×C32—41no—
613C22×C32—41no—
614C22×C32—41no—
615C22×C32—41no—
616C22×C32—41no—
617C22×C32—41no—
618C22×C32—41no—
619C22×C32—42no—
620C22×C32—42no—
621C22×C32—42no—
622C22×C32—61no—
623C22×C32—61no—
624C22×C32—61no—
625C22×C32C23×D311yescharacteristic
626C22×C32C23×D311yescharacteristic
627C22×C32C23×D311yescharacteristic
628C2×C3⋊D3—21no—
629C2×C3⋊D3—21no—
630C2×C3⋊D3—21no—
631C2×C3⋊D3—21no—
632C2×C3⋊D3—21no—
633C2×C3⋊D3—21no—
634C2×C3⋊D3—21no—
635C2×C3⋊D3—21no—
636C2×C3⋊D3#23712yes—
637C2×C3×D3—21no—
638C2×C3×D3—21no—
639C2×C3×D3—21no—
640C2×C3×D3—21no—
641C2×C3×D3—21no—
642C2×C3×D3—21no—
643C2×C3×D3—32no—
644C2×C3×D3—32no—
645C2×C3×D3—41no—
646C2×C3×D3—41no—
647C2×C3×D3—41no—
648C2×C3×D3—62no—
649C2×C3×D3—61no—
650C2×C3×D3—61no—
651C2×C3×D3—61no—
652C2×C3×D3—61no—
653C2×C3×D3—61no—
654C2×C3×D3—61no—
655C2×C3×D3—61no—
656C2×C3×D3—61no—
657C2×C3×D3—61no—
658C2×C3×D3—61no—
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—121no—
666C2×C3×D3—121no—
667C2×C3×D3—121no—
668C2×C3×D3—121no—
669C2×C3×D3—121no—
670C2×C3×D3—121no—
671C2×C3×D3—121no—
672C2×C3×D3—121no—
673D32—124no—
674D32—124no—
675D32—124no—
676C32×C4—61no—
677C32×C4—61no—
678C32×C4—61no—
679C32×C4—61no—
680C32×C4—61no—
681C3⋊Dic3—21no—
682C3⋊Dic3—21no—
683C3⋊Dic3—21no—
684C3⋊Dic3—61no—
685C3⋊Dic3—61no—
686C3⋊Dic3—62no—
687C3⋊Dic3—62no—
688C3⋊Dic3—61no—
689C3⋊Dic3—61no—
690C3⋊Dic3—61no—
691C3⋊Dic3—61no—
692C3⋊Dic3—121no—
693C3⋊Dic3—121no—
694C3⋊Dic3—121no—
695C3⋊Dic3—121no—
696C3⋊Dic3—122no—
697C3⋊Dic3—122no—
698C3×Dic3—21no—
699C3×Dic3—21no—
700C3×Dic3—21no—
701C3×Dic3—21no—
702C3×Dic3—21no—
703C3×Dic3—21no—
704C3×Dic3—21no—
705C3×Dic3—21no—
706C3×Dic3—21no—
707C3×Dic3—21no—
708C3×Dic3—41no—
709C3×Dic3—41no—
710C3×Dic3—41no—
711C3×Dic3—41no—
712C3×Dic3—41no—
713C3×Dic3—62no—
714C3×Dic3—61no—
715C3×Dic3—61no—
716C3×Dic3—61no—
717C3×Dic3—61no—
718C3×Dic3—61no—
719C3×Dic3—61no—
720C3×Dic3—121no—
721C3×Dic3—121no—
722#126—271no—
723#126—271no—
724#124—91no—
725#124—271no—
726#123—271no—
727#123—271no—
728C22⋊Q8—271no—
729#121—91no—
730#121—91no—
731#121—271no—
732#120—271no—
733#120—271no—
734C4×D4—271no—
735C4×D4—271no—
736C2×C22⋊C4—271no—
737C33#53811yescharacteristic, complemented, Sylow
738C23×C3—21no—
739C23×C3—21no—
740C23×C3—21no—
741C23×C3—31no—
742C23×C3—31no—
743C23×C3—41no—
744C23×C3—61no—
745C23×C3—91no—
746C23×C3—91no—
747C23×C3—91no—
748C23×C3C2×D3211yescharacteristic
749C23×C3C2×D3211yescharacteristic
750C23×C3C2×D3211yescharacteristic
751C22×D3—31no—
752C22×D3—31no—
753C22×D3—31no—
754C22×D3—31no—
755C22×D3—31no—
756C22×D3—31no—
757C22×D3—61no—
758C22×D3—61no—
759C22×D3—61no—
760C22×D3—182no—
761C22×D3—182no—
762C22×D3—182no—
763C22×D3—361no—
764C22×D3—361no—
765C22×D3—361no—
766C22×D3—361no—
767C22×D3—361no—
768C22×D3—361no—
769C22×D3C2×D3211yescharacteristic
770C3×Q8—361no—
771C3×D4—121no—
772C3×D4—121no—
773C3×D4—122no—
774C3×D4—182no—
775C3×D4—182no—
776C3×D4—361no—
777C3×D4—361no—
778C3×D4—361no—
779C2×C3×C4—31no—
780C2×C3×C4—31no—
781C2×C3×C4—31no—
782C2×C3×C4—31no—
783C2×C3×C4—31no—
784C2×C3×C4—31no—
785C2×C3×C4—31no—
786C2×C3×C4—31no—
787C2×C3×C4—31no—
788C2×C3×C4—31no—
789C2×C3×C4—61no—
790C2×C3×C4—61no—
791C2×C3×C4—61no—
792C2×C3×C4—61no—
793C2×C3×C4—61no—
794C2×C3×C4—91no—
795C2×C3×C4—91no—
796C2×C3×C4—91no—
797C2×C3×C4—361no—
798C2×C3×C4—361no—
799#67—41no—
800#67—62no—
801#67—62no—
802#67—62no—
803#67—64no—
804#67—121no—
805#67—121no—
806#67—121no—
807#67—121no—
808#67—121no—
809#67—122no—
810#67—122no—
811#67—361no—
812#67—361no—
813#67—361no—
814#67—362no—
815C2×Dic3—31no—
816C2×Dic3—31no—
817C2×Dic3—31no—
818C2×Dic3—31no—
819C2×Dic3—31no—
820C2×Dic3—31no—
821C2×Dic3—61no—
822C2×Dic3—61no—
823C2×Dic3—61no—
824C2×Dic3—91no—
825C2×Dic3—91no—
826C2×Dic3—91no—
827C2×Dic3—91no—
828C2×Dic3—91no—
829C2×Dic3—91no—
830C2×Dic3—121no—
831C2×Dic3—181no—
832C2×Dic3—181no—
833C2×Dic3—181no—
834C2×Dic3—181no—
835C2×Dic3—181no—
836C2×Dic3—181no—
837C2×Dic3—361no—
838C2×Dic3—361no—
839C2×Dic3—361no—
840C2×Dic3—361no—
841C2×Dic3—361no—
842C2×Dic3—361no—
843C2×Dic3—362no—
844C2×Dic3—362no—
845C2×Dic3—362no—
846C2×Dic3—364no—
847C2×Dic3C2×D3211yescharacteristic
848C2×Dic3C2×D3211yescharacteristic
849C2×Dic3C2×D3211yescharacteristic
850C2×Dic3C2×D3211yescharacteristic
851C2×Dic3C2×D3211yescharacteristic
852D12—62no—
853D12—121no—
854C4×D3—121no—
855C4×D3—121no—
856C4×D3—121no—
857C4×D3—361no—
858C4×D3—361no—
859C4×D3—362no—
860Dic6—121no—
861Dic6—121no—
862C2×C32—21no—
863C2×C32—21no—
864C2×C32—21no—
865C2×C32—21no—
866C2×C32—21no—
867C2×C32—21no—
868C2×C32—21no—
869C2×C32—21no—
870C2×C32—21no—
871C2×C32—41no—
872C2×C32—41no—
873C2×C32—41no—
874C2×C32—42no—
875C2×C32—42no—
876C2×C32—42no—
877C2×C32—44no—
878C2×C32—41no—
879C2×C32—41no—
880C2×C32—41no—
881C2×C32—121no—
882C2×C32C2×#23711yescharacteristic
883C2×C32#100411yescharacteristic
884C2×C32#100411yescharacteristic
885C2×C32#100411yescharacteristic
886C2×C32#100411yescharacteristic
887C2×C32D3×#4111yescharacteristic
888C2×C32D3×#4111yescharacteristic
889C2×C32#100911yescharacteristic
890C2×C32#100911yescharacteristic
891C3⋊D3—22no—
892C3⋊D3—41no—
893C3⋊D3—41no—
894C3×D3—41no—
895C3×D3—41no—
896C3×D3—62no—
897C3×D3—62no—
898C3×D3—81no—
899C3×D3—122no—
900C3×D3—121no—
901C3×D3—121no—
902C3×D3—121no—
903C3×D3—121no—
904C3×D3—241no—
905C3×D3—241no—
906C24—271no—
907C2×Q8—91no—
908C2×D4—31no—
909C2×D4—91no—
910C2×D4—91no—
911C2×D4—91no—
912C2×D4—91no—
913C2×D4—91no—
914C2×D4—271no—
915C22×C4—91no—
916C22×C4—91no—
917C22×C4—271no—
918C22×C4—271no—
919C4⋊C4—91no—
920C4⋊C4—91no—
921C4⋊C4—271no—
922C4⋊C4—271no—
923C4⋊C4—271no—
924C4⋊C4—271no—
925C22⋊C4—31no—
926C22⋊C4—31no—
927C22⋊C4—91no—
928C22⋊C4—91no—
929C22⋊C4—91no—
930C22⋊C4—91no—
931C22⋊C4—271no—
932C22⋊C4—271no—
933C22⋊C4—271no—
934C22⋊C4—271no—
935C22⋊C4—271no—
936C22⋊C4—271no—
937C22⋊C4—271no—
938C22⋊C4—271no—
939C42—91no—
940C42—271no—
941C22×C3—22no—
942C22×C3—22no—
943C22×C3—22no—
944C22×C3—21no—
945C22×C3—21no—
946C22×C3—21no—
947C22×C3—21no—
948C22×C3—21no—
949C22×C3—21no—
950C22×C3—21no—
951C22×C3—21no—
952C22×C3—21no—
953C22×C3—21no—
954C22×C3—21no—
955C22×C3—21no—
956C22×C3—41no—
957C22×C3—41no—
958C22×C3—41no—
959C22×C3—41no—
960C22×C3—41no—
961C22×C3—41no—
962C22×C3—42no—
963C22×C3—42no—
964C22×C3—42no—
965C22×C3—41no—
966C22×C3—61no—
967C22×C3—61no—
968C22×C3—61no—
969C22×C3—61no—
970C22×C3—61no—
971C22×C3—61no—
972C22×C3—92no—
973C22×C3—121no—
974C22×C3—121no—
975C22×C3—121no—
976C22×C3—181no—
977C22×C3—181no—
978C22×C3—181no—
979C22×C3—181no—
980C22×C3—181no—
981C22×C3—181no—
982C22×C3—181no—
983C22×C3—181no—
984C22×C3C22×D3211yescharacteristic
985C22×C3C22×D3211yescharacteristic
986C22×C3C22×D3211yescharacteristic
987C2×D3—21no—
988C2×D3—21no—
989C2×D3—21no—
990C2×D3—32no—
991C2×D3—32no—
992C2×D3—62no—
993C2×D3—61no—
994C2×D3—61no—
995C2×D3—61no—
996C2×D3—61no—
997C2×D3—61no—
998C2×D3—61no—
999C2×D3—61no—
1000C2×D3—61no—
1001C2×D3—61no—
1002C2×D3—61no—
1003C2×D3—61no—
1004C2×D3—61no—
1005C2×D3—61no—
1006C2×D3—61no—
1007C2×D3—61no—
1008C2×D3—61no—
1009C2×D3—121no—
1010C2×D3—121no—
1011C2×D3—121no—
1012C2×D3—121no—
1013C2×D3—121no—
1014C2×D3—121no—
1015C2×D3—121no—
1016C2×D3—121no—
1017C2×D3—364no—
1018C2×D3—364no—
1019C2×D3—364no—
1020C3×C4—61no—
1021C3×C4—61no—
1022C3×C4—61no—
1023C3×C4—61no—
1024C3×C4—61no—
1025C3×C4—61no—
1026C3×C4—61no—
1027C3×C4—61no—
1028C3×C4—61no—
1029C3×C4—61no—
1030C3×C4—121no—
1031C3×C4—121no—
1032C3×C4—121no—
1033C3×C4—121no—
1034C3×C4—121no—
1035C3×C4—181no—
1036C3×C4—181no—
1037C3×C4—181no—
1038Dic3—21no—
1039Dic3—21no—
1040Dic3—21no—
1041Dic3—21no—
1042Dic3—21no—
1043Dic3—62no—
1044Dic3—61no—
1045Dic3—61no—
1046Dic3—61no—
1047Dic3—61no—
1048Dic3—61no—
1049Dic3—61no—
1050Dic3—121no—
1051Dic3—121no—
1052Dic3—182no—
1053Dic3—182no—
1054Dic3—181no—
1055Dic3—181no—
1056Dic3—181no—
1057Dic3—181no—
1058Dic3—181no—
1059Dic3—181no—
1060Dic3—361no—
1061Dic3—361no—
1062Dic3—361no—
1063Dic3—361no—
1064Dic3—362no—
1065Dic3—362no—
1066C32—21no—
1067C32—21no—
1068C32—21no—
1069C32—41no—
1070C32#561311yescharacteristic, complemented
1071C32#561711yescharacteristic, complemented
1072C32#567811yescharacteristic, complemented
1073C23—31no—
1074C23—91no—
1075C23—91no—
1076C23—91no—
1077C23—542no—
1078C23—1081no—
1079C23—1081no—
1080C23D3311yescharacteristic
1081Q8—361no—
1082D4—121no—
1083D4—182no—
1084D4—182no—
1085D4—361no—
1086D4—361no—
1087D4—361no—
1088D4—1081no—
1089C2×C4—31no—
1090C2×C4—31no—
1091C2×C4—31no—
1092C2×C4—31no—
1093C2×C4—31no—
1094C2×C4—91no—
1095C2×C4—91no—
1096C2×C4—91no—
1097C2×C4—271no—
1098C2×C4—271no—
1099C2×C4—361no—
1100C2×C4—361no—
1101C2×C4—1081no—
1102C2×C4—1081no—
1103C2×C3—21no—
1104C2×C3—21no—
1105C2×C3—21no—
1106C2×C3—21no—
1107C2×C3—21no—
1108C2×C3—21no—
1109C2×C3—21no—
1110C2×C3—21no—
1111C2×C3—21no—
1112C2×C3—42no—
1113C2×C3—42no—
1114C2×C3—42no—
1115C2×C3—44no—
1116C2×C3—41no—
1117C2×C3—41no—
1118C2×C3—41no—
1119C2×C3—41no—
1120C2×C3—41no—
1121C2×C3—41no—
1122C2×C3—121no—
1123C2×C3—121no—
1124C2×C3—182no—
1125C2×C3—241no—
1126C2×C3—361no—
1127C2×C3—361no—
1128C2×C3#6430611yescharacteristic
1129C2×C3#6430811yescharacteristic
1130C2×C3D3×#23711yescharacteristic
1131C2×C3D3×#23711yescharacteristic
1132C2×C3#6431311yescharacteristic
1133C2×C3#6431311yescharacteristic
1134C2×C3#6431411yescharacteristic
1135C2×C3#6431411yescharacteristic
1136C2×C3#6433011yescharacteristic
1137D3—41no—
1138D3—62no—
1139D3—62no—
1140D3—122no—
1141D3—121no—
1142D3—121no—
1143D3—121no—
1144D3—121no—
1145D3—241no—
1146D3—241no—
1147C22—21no—
1148C22—21no—
1149C22—21no—
1150C22—61no—
1151C22—61no—
1152C22—61no—
1153C22—92no—
1154C22—181no—
1155C22—181no—
1156C22—181no—
1157C22—181no—
1158C22—181no—
1159C22—181no—
1160C22—181no—
1161C22—181no—
1162C22—1084no—
1163C22C2×D3311yescharacteristic
1164C4—61no—
1165C4—61no—
1166C4—61no—
1167C4—61no—
1168C4—61no—
1169C4—181no—
1170C4—181no—
1171C4—181no—
1172C4—541no—
1173C4—541no—
1174C3—21no—
1175C3—21no—
1176C3—21no—
1177C3—41no—
1178C3#1059430111yescharacteristic, complemented
1179C3#1059430611yescharacteristic, complemented
1180C3#1059531011yescharacteristic, complemented
1181C2—41no—
1182C2—121no—
1183C2—182no—
1184C2—361no—
1185C2—361no—
1186C2#1172440711yescharacteristic
1187C2#1172441511yescharacteristic
1188C2#1172442011yescharacteristic
subgroupG/H
center, FrattiniC22C2×D33
commutator, socle, cosocleC22×C33C24
FittingC23×C33C23
hypercenterC23D33
hypocenterC33#538
LCSG ▷ C22×C33 ▷ C33
UCSC1 ◁ C22 ◁ C23

Complements

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

NH ≅ G/Ntype
1. #11723729C2semidirect
2. #11723637C2semidirect
3. #11723626C2semidirect
4. #11723609C2semidirect
5. C3×#63971C2semidirect
6. C3×#63958C2semidirect
7. C3×#63953C2semidirect
8. #11723027C2semidirect
9. #11723024C2semidirect
10. #11723001C2semidirect
11. #11722988C2semidirect
12. #11722970C2semidirect
13. #11722951C2semidirect
14. Dic3×#626C2semidirect
15. #11722905C2semidirect
20. C22×C3⋊(C3⋊Dic3)C22semidirect
24. C2×C32×#67C22semidirect
27. C2×C3×#627C22semidirect
31. C2×C3×D3×Dic3C22semidirect
32. C32×#217C22semidirect
33. C32×#217C22semidirect
37. #88807C22semidirect
38. #88806C22semidirect
39. Dic3⋊(C3⋊Dic3)C22semidirect
40. Dic3⋊(C3⋊Dic3)C22semidirect
45. (C2×D3)⋊(C3⋊Dic3)C22semidirect
46. Dic3×C3⋊Dic3C22semidirect
47. C3×#3724C22semidirect
48. C3×Dic3⋊Dic3C22semidirect
52. C3×(C2×D3)⋊Dic3C22semidirect
53. C3×Dic32C22semidirect
74. #63971D3semidirect
80. #63958D3semidirect
81. #63953D3semidirect
163. C2×C3×#67C2×D3semidirect
164. C2×C3×#67C2×D3semidirect
173. C2×#627C2×D3semidirect
183. C2×D3×Dic3C2×D3semidirect
199. C3×#217C2×D3semidirect
200. C3×#217C2×D3semidirect
201. C3×#217C2×D3semidirect
202. C3×#217C2×D3semidirect
219. #3724C2×D3semidirect
229. Dic3⋊Dic3C2×D3semidirect
257. (C2×D3)⋊Dic3C2×D3semidirect
261. Dic32C2×D3semidirect
499. C2×#67D32semidirect
543. #217D32semidirect
544. #217D32semidirect
737. C33#538semidirect
1070. C32#5613semidirect
1071. C32#5617semidirect
1072. C32#5678semidirect
1178. C3#10594301semidirect
1179. C3#10594306semidirect
1180. C3#10595310semidirect

Maximal subgroups

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

subgroupindex
#117237292
#117236372
#117236262
#117236092
C3×#639712
C3×#639582
C3×#639532
#117230272
#117230242
#117230012
#117229882
#117229702
#117229512
Dic3×#6262
#117229052
#105953103
#105943063
#105943013