Finite Group Databasebeta

← #13168748

Subgroups — #13168748

Order 1728.

1300 conjugacy classes of subgroups.

The subgroup lattice has 1188 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11723676C211yesmaximal, characteristic, complemented
2#11723540C211yesmaximal, characteristic, complemented
3#11723419C211yesmaximal, characteristic, complemented
4#11723411C211yesmaximal, characteristic, complemented
5C3×#63898C211yesmaximal, characteristic, complemented
6C3×#63890C211yesmaximal, characteristic, complemented
7C3×#63885C211yesmaximal, characteristic, complemented
8#11723009C211yesmaximal, characteristic, complemented
9#11722987C211yesmaximal, characteristic, complemented
10#11722971C211yesmaximal, characteristic, complemented
11#11722958C211yesmaximal, characteristic, complemented
12#11722956C211yesmaximal, characteristic, complemented
13#11722949C211yesmaximal, characteristic, complemented
14Dic3×#625C211yesmaximal, characteristic, complemented
15D3×#3722C211yesmaximal, characteristic, complemented
16#10595221—31nomaximal
17#10594639—31nomaximal
18#10594302—31nomaximal
19C22×D3×C3⋊D3C2211yescharacteristic
20C2×C32×D12C2211yescharacteristic
21C2×#6293C2211yescharacteristic, complemented
22C2×#6291C2211yescharacteristic
23C2×#6291C2211yescharacteristic
24C2×#6290C2211yescharacteristic
25C2×C3×#626C2211yescharacteristic
26C2×C3×#625C2211yescharacteristic
27C2×C3×#625C2211yescharacteristic, complemented
28C2×C3×D3×Dic3C2211yescharacteristic
29C2×C3×D3×Dic3C2211yescharacteristic
30C2×C3×D3×Dic3C2211yescharacteristic, complemented
31C2×C3×D3×Dic3C2211yescharacteristic, complemented
32#88859C2211yescharacteristic
33C3×#3752C2211yescharacteristic
34C3×#3750C2211yescharacteristic, complemented
35C3×C4×C3⋊Dic3C2211yescharacteristic, complemented
36C32×(C2×D3)⋊C4C2211yescharacteristic, complemented
37C32×C4⋊Dic3C2211yescharacteristic, complemented
38#88815C2211yescharacteristic, complemented
39#88815C2211yescharacteristic, complemented
40#88814C2211yescharacteristic
41#88814C2211yescharacteristic
42Dic3⋊(C3⋊Dic3)C2211yescharacteristic, complemented
43#88804C2211yescharacteristic
44#88804C2211yescharacteristic
45#88804C2211yescharacteristic
46(C2×D3)⋊(C3⋊Dic3)C2211yescharacteristic
47(C2×D3)⋊(C3⋊Dic3)C2211yescharacteristic, complemented
48Dic3×C3⋊Dic3C2211yescharacteristic, complemented
49C3×Dic3⋊Dic3C2211yescharacteristic, complemented
50C3×#3722C2211yescharacteristic
51C3×(C2×D3)⋊Dic3C2211yescharacteristic
52C3×(C2×D3)⋊Dic3C2211yescharacteristic, complemented
53C3×(C2×D3)⋊Dic3C2211yescharacteristic, complemented
54#64146—31no—
55#64107—31no—
56#64094—31no—
57C3×#939—31no—
58C3×D4×Dic3—31no—
59C3×#894—31no—
60C3×#893—31no—
61C3×#886—31no—
62C3×#884—31no—
63#63983—31no—
64#63981—31no—
65#63978—31no—
66#63978—31no—
67Dic3×#67—31no—
68Dic3×#67—31no—
69#63971—31no—
70#63970—31no—
71#63966—31no—
72#63964—31no—
73C2×#3722—31no—
74#63953—31no—
75#63922—31no—
76#63922—31no—
77#63922—31no—
78#63922—61no—
79D3×(C2×D3)⋊C4—31no—
80D3×(C2×D3)⋊C4—31no—
81#63915—31no—
82#63913—31no—
83#63908—31no—
84#63906—31no—
85C4×#625—31no—
86#63898D311yescharacteristic, complemented
87#63893—31no—
88#63890—31no—
89#63890D311yescharacteristic, complemented
90#63885D311yescharacteristic, complemented
91#63868—31no—
92#63862—31no—
93#63859—31no—
94#63857—31no—
95#63852—31no—
96#63852—31no—
97#63852—61no—
98#63850—31no—
99#63848—31no—
100#63848—31no—
101#63848—61no—
102C22×C3⋊(C3⋊D3)C2311yescharacteristic
103C22×C3×C3⋊D3C2311yescharacteristic
104C22×C32×D3C2311yescharacteristic
105C22×C32×D3C2311yescharacteristic
106C22×C32×D3C2311yescharacteristic
107C2×D3×C3⋊D3—22no—
108C2×D3×C3⋊D3—41no—
109C2×D3×C3⋊D3—41no—
110C2×C33×C4C2311yescharacteristic
111C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
112C2×C3×C3⋊Dic3C2311yescharacteristic
113C2×C3×C3⋊Dic3C2311yescharacteristic
114C2×C3×C3⋊Dic3C2311yescharacteristic
115C2×C3×C3⋊Dic3C2311yescharacteristic
116C2×C3×C3⋊Dic3C2311yescharacteristic
117C2×C32×Dic3C2311yescharacteristic
118C2×C32×Dic3C2311yescharacteristic
119C2×C32×Dic3C2311yescharacteristic
120C32×D12—22no—
121#6293—41no—
122#6291—41no—
123#6291—41no—
124#6290—41no—
125C3×#626—41no—
126C3×#625—22no—
127C3×#625—41no—
128C3×D3×Dic3—41no—
129C3×D3×Dic3—41no—
130C3×D3×Dic3—41no—
131C3×D3×Dic3—41no—
132#5657—91no—
133#5617—91no—
134#5560—91no—
135C23×C3⋊D3—31no—
136C22×D32—31no—
137C22×D32—31no—
138C22×D32—61no—
139C2×C32×D4—31no—
140C2×#638—31no—
141C2×#638—31no—
142C2×#638—31no—
143C2×#634—31no—
144C2×C3×#67—31no—
145C2×C3×#67—31no—
146C2×C3×#67—31no—
147C2×C3×#67—31no—
148C2×C3×#67—31no—
149C22×C3×Dic3—31no—
150C22×C3×Dic3—31no—
151C22×C3×Dic3—31no—
152C22×C3×Dic3—31no—
153C2×C3×D12—21no—
154C2×C3×D12—31no—
155C2×C3×D12C2×D311yescharacteristic
156C2×C3×D12C2×D311yescharacteristic
157C2×C3×C4×D3—31no—
158C2×C3×C4×D3—31no—
159C2×C3×C4×D3—31no—
160C2×C3×C4×D3—31no—
161C2×#627—31no—
162C2×#627—31no—
163C2×#627—61no—
164C2×#626—31no—
165C2×#626—31no—
166C2×#626—31no—
167C2×#626—31no—
168C2×#626—61no—
169C2×#626—61no—
170C2×#626C2×D311yescharacteristic
171C2×#625—31no—
172C2×#625—31no—
173C2×#625—61no—
174C2×#625C2×D311yescharacteristic
175C2×#625C2×D311yescharacteristic, complemented
176C2×D3×Dic3C2×D311yescharacteristic
177C2×D3×Dic3C2×D311yescharacteristic
178C2×D3×Dic3C2×D311yescharacteristic, complemented
179C2×D3×Dic3C2×D311yescharacteristic, complemented
180C32×C4⋊C4—31no—
181C32×C22⋊C4—31no—
182#3757—31no—
183#3757—31no—
184#3752—31no—
185#3752—31no—
186#3752—31no—
187#3752—31no—
188#3752—31no—
189#3752—31no—
190#3752—61no—
191#3752—61no—
192#3752—61no—
193#3752—121no—
194#3752C2×D311yescharacteristic
195C4⋊(C3⋊Dic3)—31no—
196#3750C2×D311yescharacteristic, complemented
197C4×C3⋊Dic3—31no—
198C4×C3⋊Dic3C2×D311yescharacteristic, complemented
199C3×#217—31no—
200C3×#217—31no—
201C3×#217—31no—
202C3×(C2×D3)⋊C4—21no—
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×(C2×D3)⋊C4—61no—
211C3×(C2×D3)⋊C4C2×D311yescharacteristic, complemented
212C3×(C2×D3)⋊C4C2×D311yescharacteristic, complemented
213C3×C4⋊Dic3—21no—
214C3×C4⋊Dic3—31no—
215C3×C4⋊Dic3C2×D311yescharacteristic, complemented
216C3×C4⋊Dic3C2×D311yescharacteristic, complemented
217C3×Dic3⋊C4—31no—
218C3×Dic3⋊C4—31no—
219C3×Dic3⋊C4—31no—
220C3×Dic3⋊C4—61no—
221C3×C4×Dic3—31no—
222C3×C4×Dic3—31no—
223C3×C4×Dic3—61no—
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—61no—
233Dic3⋊Dic3C2×D311yescharacteristic, complemented
234#3722—31no—
235#3722—31no—
236#3722—31no—
237#3722—31no—
238#3722—31no—
239#3722—31no—
240#3722—31no—
241#3722—31no—
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—31no—
251(C2×D3)⋊Dic3—31no—
252(C2×D3)⋊Dic3—31no—
253(C2×D3)⋊Dic3—31no—
254(C2×D3)⋊Dic3—61no—
255(C2×D3)⋊Dic3—61no—
256(C2×D3)⋊Dic3C2×D311yescharacteristic
257(C2×D3)⋊Dic3C2×D311yescharacteristic, complemented
258(C2×D3)⋊Dic3C2×D311yescharacteristic, complemented
259Dic32—31no—
260Dic32—31no—
261Dic32—61no—
262C22×C33C2411yescharacteristic
263C2×C3⋊(C3⋊D3)—21no—
264C2×C3⋊(C3⋊D3)—21no—
265C2×C3⋊(C3⋊D3)—21no—
266C2×C3×C3⋊D3—21no—
267C2×C3×C3⋊D3—21no—
268C2×C3×C3⋊D3—21no—
269C2×C32×D3—21no—
270C2×C32×D3—21no—
271C2×C32×D3—21no—
272C2×C32×D3—21no—
273C2×C32×D3—21no—
274C2×C32×D3—21no—
275C2×C32×D3—21no—
276C2×C32×D3—21no—
277C2×C32×D3#4112yes—
278D3×C3⋊D3—44no—
279C33×C4—21no—
280C3⋊(C3⋊Dic3)—21no—
281C3×C3⋊Dic3—21no—
282C3×C3⋊Dic3—21no—
283C3×C3⋊Dic3—21no—
284C3×C3⋊Dic3—21no—
285C3×C3⋊Dic3—21no—
286C32×Dic3—21no—
287C32×Dic3—21no—
288C32×Dic3—21no—
289C3×#123—91no—
290C3×#121—91no—
291C3×C4×D4—91no—
292#939—31no—
293#939—91no—
294#939—91no—
295#938—91no—
296#937—91no—
297#937—91no—
298#937—91no—
299#937—91no—
300#937—181no—
301D4×Dic3—31no—
302D4×Dic3—91no—
303#930—91no—
304#930—91no—
305#929—91no—
306C4×#67—91no—
307C4×#67—91no—
308C2×(C2×D3)⋊C4—91no—
309C2×(C2×D3)⋊C4—91no—
310#924—91no—
311#898—91no—
312#898—91no—
313#898—91no—
314#898—91no—
315#898—181no—
316#897—91no—
317#894—31no—
318#894—91no—
319#893—31no—
320#886—31no—
321#886—91no—
322#885—91no—
323#885—91no—
324#885—91no—
325#885—91no—
326#885—91no—
327#885—181no—
328#884—31no—
329#884—91no—
330#882—91no—
331#882—91no—
332D3×C22⋊C4—91no—
333#879—91no—
334#878—91no—
335#876—91no—
336#875—91no—
337C23×C32—31no—
338C23×C32—31no—
339C23×C32—31no—
340C22×C3⋊D3—31no—
341C22×C3⋊D3—31no—
342C22×C3⋊D3—31no—
343C22×C3⋊D3—61no—
344C22×C3⋊D3—61no—
345C22×C3⋊D3—61no—
346C22×C3⋊D3—62no—
347C22×C3⋊D3—121no—
348C22×C3⋊D3—121no—
349C22×C3⋊D3—121no—
350C22×C3⋊D3C22×D311yescharacteristic
351C22×C3×D3—21no—
352C22×C3×D3—21no—
353C22×C3×D3—21no—
354C22×C3×D3—31no—
355C22×C3×D3—31no—
356C22×C3×D3—61no—
357C22×C3×D3C22×D311yescharacteristic
358C22×C3×D3C22×D311yescharacteristic
359C22×C3×D3C22×D311yescharacteristic
360C22×C3×D3C22×D311yescharacteristic
361C22×C3×D3C22×D311yescharacteristic
362C22×C3×D3C22×D311yescharacteristic
363C2×D32—62no—
364C2×D32—62no—
365C2×D32—122no—
366C2×D32—121no—
367C2×D32—121no—
368C2×D32—121no—
369C2×D32—121no—
370C2×D32—122no—
371C2×D32—122no—
372C32×D4—62no—
373C2×C32×C4—21no—
374C2×C32×C4—21no—
375C2×C32×C4—21no—
376C2×C32×C4—31no—
377C2×C32×C4—31no—
378C2×C32×C4—31no—
379C2×C32×C4—41no—
380C2×C32×C4C22×D311yescharacteristic
381C2×C32×C4C22×D311yescharacteristic
382C2×C32×C4C22×D311yescharacteristic
383#638—121no—
384#638—121no—
385#638—121no—
386C2×C3⋊Dic3—31no—
387C2×C3⋊Dic3—31no—
388C2×C3⋊Dic3—31no—
389C2×C3⋊Dic3—61no—
390C2×C3⋊Dic3—61no—
391C2×C3⋊Dic3—61no—
392C2×C3⋊Dic3—121no—
393C2×C3⋊Dic3C22×D311yescharacteristic
394C2×C3⋊Dic3C22×D311yescharacteristic
395C2×C3⋊Dic3C22×D311yescharacteristic
396C2×C3⋊Dic3C22×D311yescharacteristic
397C2×C3⋊Dic3C22×D311yescharacteristic
398#634—121no—
399C3×#67—62no—
400C3×#67—62no—
401C3×#67—121no—
402C3×#67—121no—
403C3×#67—121no—
404C2×C3×Dic3—21no—
405C2×C3×Dic3—21no—
406C2×C3×Dic3—21no—
407C2×C3×Dic3—31no—
408C2×C3×Dic3—31no—
409C2×C3×Dic3—31no—
410C2×C3×Dic3—31no—
411C2×C3×Dic3—31no—
412C2×C3×Dic3—31no—
413C2×C3×Dic3—31no—
414C2×C3×Dic3—31no—
415C2×C3×Dic3—31no—
416C2×C3×Dic3—31no—
417C2×C3×Dic3—61no—
418C2×C3×Dic3—61no—
419C2×C3×Dic3—61no—
420C2×C3×Dic3—61no—
421C2×C3×Dic3—61no—
422C2×C3×Dic3—121no—
423C2×C3×Dic3—121no—
424C2×C3×Dic3—121no—
425C2×C3×Dic3—121no—
426C2×C3×Dic3C22×D311yescharacteristic
427C2×C3×Dic3C22×D311yescharacteristic
428C2×C3×Dic3C22×D311yescharacteristic
429C2×C3×Dic3C22×D311yescharacteristic
430C2×C3×Dic3C22×D311yescharacteristic
431C2×C3×Dic3C22×D311yescharacteristic
432C3×D12—22no—
433C3×D12—22no—
434C3×D12—42no—
435C3×D12—121no—
436C3×C4×D3—121no—
437C3×C4×D3—121no—
438C3×C4×D3—121no—
439C3×C4×D3—121no—
440#627—121no—
441#627—121no—
442#627—122no—
443#626—41no—
444#626—121no—
445#626—121no—
446#626—121no—
447#626—121no—
448#626—122no—
449#626—122no—
450#625—22no—
451#625—41no—
452#625—121no—
453#625—121no—
454#625—122no—
455D3×Dic3—41no—
456D3×Dic3—41no—
457D3×Dic3—41no—
458D3×Dic3—41no—
459#538—271noSylow
460C2×C33C2×#4111yescharacteristic
461C2×C33H(5,𝔽2)11yescharacteristic
462C2×C33H(5,𝔽2)11yescharacteristic
463C3⋊(C3⋊D3)—41no—
464C3×C3⋊D3—41no—
465C32×D3—22no—
466C32×D3—41no—
467C32×D3—41no—
468C23×D3—91no—
469C23×D3—91no—
470C23×D3—91no—
471C23×D3—181no—
472C2×C3×D4—31no—
473C2×C3×D4—31no—
474C2×C3×D4—61no—
475C2×C3×D4—91no—
476C2×C3×D4—91no—
477C2×C3×D4—91no—
478C22×C3×C4—91no—
479C22×C3×C4—91no—
480C22×C3×C4—91no—
481C22×C3×C4—91no—
482C2×#67—31no—
483C2×#67—31no—
484C2×#67—31no—
485C2×#67—31no—
486C2×#67—31no—
487C2×#67—91no—
488C2×#67—91no—
489C2×#67—91no—
490C2×#67—91no—
491C2×#67—91no—
492C2×#67—91no—
493C2×#67—91no—
494C2×#67—181no—
495C2×#67—181no—
496C2×#67—181no—
497C22×Dic3—31no—
498C22×Dic3—31no—
499C22×Dic3—31no—
500C22×Dic3—31no—
501C2×D12—31no—
502C2×D12—91no—
503C2×D12—91no—
504C2×D12D3211yescharacteristic
505C2×C4×D3—31no—
506C2×C4×D3—31no—
507C2×C4×D3—31no—
508C2×C4×D3—31no—
509C2×Dic6—91no—
510C2×Dic6—91no—
511C2×Dic6—91no—
512C2×Dic6—181no—
513C3×C4⋊C4—31no—
514C3×C4⋊C4—31no—
515C3×C4⋊C4—61no—
516C3×C4⋊C4—91no—
517C3×C4⋊C4—91no—
518C3×C22⋊C4—31no—
519C3×C22⋊C4—31no—
520C3×C22⋊C4—61no—
521C3×C22⋊C4—91no—
522C3×C22⋊C4—91no—
523C3×C22⋊C4—91no—
524C3×C22⋊C4—91no—
525C3×C22⋊C4—91no—
526C3×C42—91no—
527#217—31no—
528#217—31no—
529#217—31no—
530#217—91no—
531#217—91no—
532#217—91no—
533#217—91no—
534#217—91no—
535#217—91no—
536#217—181no—
537#217—181no—
538(C2×D3)⋊C4—31no—
539(C2×D3)⋊C4—31no—
540(C2×D3)⋊C4—31no—
541(C2×D3)⋊C4—31no—
542(C2×D3)⋊C4—31no—
543(C2×D3)⋊C4—31no—
544(C2×D3)⋊C4—31no—
545(C2×D3)⋊C4—61no—
546(C2×D3)⋊C4—91no—
547(C2×D3)⋊C4—91no—
548(C2×D3)⋊C4—91no—
549(C2×D3)⋊C4—91no—
550(C2×D3)⋊C4—91no—
551(C2×D3)⋊C4—91no—
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—181no—
565(C2×D3)⋊C4—181no—
566(C2×D3)⋊C4—181no—
567(C2×D3)⋊C4—181no—
568(C2×D3)⋊C4—181no—
569(C2×D3)⋊C4—181no—
570(C2×D3)⋊C4—361no—
571(C2×D3)⋊C4D3211yescharacteristic, complemented
572C4⋊Dic3—31no—
573C4⋊Dic3—91no—
574C4⋊Dic3—91no—
575C4⋊Dic3—91no—
576C4⋊Dic3—91no—
577C4⋊Dic3—181no—
578C4⋊Dic3D3211yescharacteristic, complemented
579Dic3⋊C4—31no—
580Dic3⋊C4—31no—
581Dic3⋊C4—31no—
582Dic3⋊C4—61no—
583Dic3⋊C4—91no—
584Dic3⋊C4—91no—
585Dic3⋊C4—91no—
586Dic3⋊C4—91no—
587Dic3⋊C4—91no—
588C4×Dic3—31no—
589C4×Dic3—31no—
590C4×Dic3—61no—
591C4×Dic3—91no—
592C4×Dic3—91no—
593C4×Dic3—91no—
594C4×Dic3—181no—
595C22×C32—21no—
596C22×C32—21no—
597C22×C32—21no—
598C22×C32—32no—
599C22×C32—41no—
600C22×C32—61no—
601C22×C32—61no—
602C22×C32—61no—
603C22×C32—61no—
604C22×C32—61no—
605C22×C32—61no—
606C22×C32—61no—
607C22×C32—61no—
608C22×C32C23×D311yescharacteristic
609C22×C32C23×D311yescharacteristic
610C22×C32C23×D311yescharacteristic
611C2×C3⋊D3—21no—
612C2×C3⋊D3—21no—
613C2×C3⋊D3—21no—
614C2×C3⋊D3—61no—
615C2×C3⋊D3—62no—
616C2×C3⋊D3—61no—
617C2×C3⋊D3—61no—
618C2×C3⋊D3—61no—
619C2×C3⋊D3—61no—
620C2×C3⋊D3—61no—
621C2×C3⋊D3—61no—
622C2×C3⋊D3—61no—
623C2×C3⋊D3—61no—
624C2×C3⋊D3—121no—
625C2×C3⋊D3—121no—
626C2×C3⋊D3—122no—
627C2×C3⋊D3—121no—
628C2×C3⋊D3—121no—
629C2×C3⋊D3—121no—
630C2×C3⋊D3—121no—
631C2×C3⋊D3—121no—
632C2×C3⋊D3—121no—
633C2×C3⋊D3—124no—
634C2×C3⋊D3—241no—
635C2×C3⋊D3—241no—
636C2×C3×D3—21no—
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—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—22no—
653C2×C3×D3—41no—
654C2×C3×D3—41no—
655C2×C3×D3—41no—
656C2×C3×D3—41no—
657C2×C3×D3—41no—
658C2×C3×D3—41no—
659C2×C3×D3—41no—
660C2×C3×D3—41no—
661C2×C3×D3—62no—
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—121no—
669C2×C3×D3—121no—
670C2×C3×D3#23512yes—
671C2×C3×D3#23712yes—
672D32—124no—
673D32—124no—
674D32—128no—
675C32×C4—21no—
676C32×C4—21no—
677C32×C4—21no—
678C32×C4—41no—
679C32×C4—41no—
680C32×C4—41no—
681C32×C4—61no—
682C32×C4—61no—
683C32×C4—61no—
684C32×C4—81no—
685C3⋊Dic3—21no—
686C3⋊Dic3—21no—
687C3⋊Dic3—21no—
688C3⋊Dic3—21no—
689C3⋊Dic3—21no—
690C3⋊Dic3—61no—
691C3⋊Dic3—61no—
692C3⋊Dic3—61no—
693C3⋊Dic3—121no—
694C3⋊Dic3—121no—
695C3⋊Dic3—121no—
696C3⋊Dic3—241no—
697C3×Dic3—21no—
698C3×Dic3—21no—
699C3×Dic3—21no—
700C3×Dic3—21no—
701C3×Dic3—21no—
702C3×Dic3—21no—
703C3×Dic3—41no—
704C3×Dic3—41no—
705C3×Dic3—41no—
706C3×Dic3—62no—
707C3×Dic3—61no—
708C3×Dic3—61no—
709C3×Dic3—61no—
710C3×Dic3—61no—
711C3×Dic3—61no—
712C3×Dic3—61no—
713C3×Dic3—61no—
714C3×Dic3—61no—
715C3×Dic3—61no—
716C3×Dic3—61no—
717C3×Dic3—121no—
718C3×Dic3—121no—
719C3×Dic3—121no—
720C3×Dic3—121no—
721#126—271no—
722#126—271no—
723#124—271no—
724#124—271no—
725#123—91no—
726#123—271no—
727C22⋊Q8—271no—
728#121—91no—
729#121—271no—
730#121—271no—
731#120—271no—
732#120—271no—
733C4×D4—91no—
734C4×D4—271no—
735C2×C22⋊C4—271no—
736C33#53811yescharacteristic, complemented, Sylow
737C23×C3—31no—
738C23×C3—31no—
739C23×C3—31no—
740C23×C3—31no—
741C23×C3—31no—
742C23×C3—31no—
743C23×C3—61no—
744C23×C3—61no—
745C23×C3—61no—
746C23×C3—91no—
747C22×D3—31no—
748C22×D3—31no—
749C22×D3—61no—
750C22×D3—91no—
751C22×D3—91no—
752C22×D3—91no—
753C22×D3—181no—
754C22×D3—181no—
755C22×D3—181no—
756C22×D3—182no—
757C22×D3—182no—
758C22×D3—182no—
759C22×D3—361no—
760C22×D3—362no—
761C22×D3—361no—
762C22×D3—361no—
763C22×D3—361no—
764C22×D3—361no—
765C22×D3—361no—
766C22×D3—361no—
767C22×D3—362no—
768C22×D3—362no—
769C22×D3C2×D3211yescharacteristic
770C22×D3C2×D3211yescharacteristic
771C22×D3C2×D3211yescharacteristic
772C3×D4—62no—
773C3×D4—62no—
774C3×D4—122no—
775C3×D4—182no—
776C3×D4—361no—
777C3×D4—361no—
778C2×C3×C4—21no—
779C2×C3×C4—21no—
780C2×C3×C4—21no—
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—41no—
788C2×C3×C4—61no—
789C2×C3×C4—61no—
790C2×C3×C4—61no—
791C2×C3×C4—91no—
792C2×C3×C4—91no—
793C2×C3×C4—91no—
794C2×C3×C4—91no—
795C2×C3×C4—91no—
796C2×C3×C4—361no—
797C2×C3×C4—361no—
798C2×C3×C4—361no—
799C2×C3×C4—361no—
800C2×C3×C4C2×D3211yescharacteristic
801C2×C3×C4C2×D3211yescharacteristic
802C2×C3×C4C2×D3211yescharacteristic
803#67—62no—
804#67—62no—
805#67—121no—
806#67—121no—
807#67—121no—
808#67—361no—
809#67—361no—
810#67—361no—
811#67—361no—
812#67—362no—
813#67—362no—
814#67—361no—
815#67—361no—
816#67—361no—
817#67—362no—
818C2×Dic3—31no—
819C2×Dic3—31no—
820C2×Dic3—31no—
821C2×Dic3—31no—
822C2×Dic3—31no—
823C2×Dic3—31no—
824C2×Dic3—31no—
825C2×Dic3—31no—
826C2×Dic3—31no—
827C2×Dic3—31no—
828C2×Dic3—61no—
829C2×Dic3—61no—
830C2×Dic3—61no—
831C2×Dic3—61no—
832C2×Dic3—61no—
833C2×Dic3—91no—
834C2×Dic3—91no—
835C2×Dic3—91no—
836C2×Dic3—121no—
837C2×Dic3—121no—
838C2×Dic3—121no—
839C2×Dic3—121no—
840C2×Dic3—181no—
841C2×Dic3—181no—
842C2×Dic3—181no—
843C2×Dic3—361no—
844C2×Dic3C2×D3211yescharacteristic
845C2×Dic3C2×D3211yescharacteristic
846C2×Dic3C2×D3211yescharacteristic
847D12—22no—
848D12—121no—
849D12—361no—
850D12—361no—
851C4×D3—121no—
852C4×D3—121no—
853C4×D3—121no—
854C4×D3—121no—
855Dic6—361no—
856Dic6—361no—
857Dic6—361no—
858Dic6—362no—
859C2×C32—21no—
860C2×C32—21no—
861C2×C32—21no—
862C2×C32—21no—
863C2×C32—21no—
864C2×C32—21no—
865C2×C32—21no—
866C2×C32—21no—
867C2×C32—21no—
868C2×C32—41no—
869C2×C32—41no—
870C2×C32—41no—
871C2×C32—62no—
872C2×C32—121no—
873C2×C32—121no—
874C2×C32C2×#23511yescharacteristic
875C2×C32C2×#23711yescharacteristic
876C2×C32#100411yescharacteristic
877C2×C32#100411yescharacteristic
878C2×C32#100411yescharacteristic
879C2×C32D3×#4111yescharacteristic
880C2×C32#100911yescharacteristic
881C2×C32#100911yescharacteristic
882C2×C32#100911yescharacteristic
883C3⋊D3—41no—
884C3⋊D3—121no—
885C3⋊D3—122no—
886C3⋊D3—121no—
887C3⋊D3—121no—
888C3⋊D3—241no—
889C3⋊D3—241no—
890C3⋊D3—242no—
891C3×D3—22no—
892C3×D3—22no—
893C3×D3—42no—
894C3×D3—41no—
895C3×D3—41no—
896C3×D3—41no—
897C3×D3—41no—
898C3×D3—81no—
899C3×D3—81no—
900C3×D3—122no—
901C3×D3—121no—
902C3×D3—121no—
903C24—271no—
904C2×Q8—271no—
905C2×D4—31no—
906C2×D4—91no—
907C2×D4—91no—
908C2×D4—91no—
909C2×D4—271no—
910C2×D4—271no—
911C2×D4—271no—
912C22×C4—91no—
913C22×C4—91no—
914C22×C4—91no—
915C22×C4—91no—
916C4⋊C4—31no—
917C4⋊C4—91no—
918C4⋊C4—91no—
919C4⋊C4—271no—
920C4⋊C4—271no—
921C4⋊C4—271no—
922C22⋊C4—31no—
923C22⋊C4—91no—
924C22⋊C4—91no—
925C22⋊C4—91no—
926C22⋊C4—91no—
927C22⋊C4—91no—
928C22⋊C4—271no—
929C22⋊C4—271no—
930C22⋊C4—271no—
931C22⋊C4—271no—
932C22⋊C4—271no—
933C22⋊C4—271no—
934C22⋊C4—271no—
935C22⋊C4—271no—
936C42—91no—
937C42—271no—
938C22×C3—21no—
939C22×C3—21no—
940C22×C3—21no—
941C22×C3—32no—
942C22×C3—32no—
943C22×C3—41no—
944C22×C3—62no—
945C22×C3—61no—
946C22×C3—61no—
947C22×C3—61no—
948C22×C3—61no—
949C22×C3—61no—
950C22×C3—61no—
951C22×C3—61no—
952C22×C3—61no—
953C22×C3—61no—
954C22×C3—61no—
955C22×C3—61no—
956C22×C3—61no—
957C22×C3—61no—
958C22×C3—61no—
959C22×C3—61no—
960C22×C3—61no—
961C22×C3—121no—
962C22×C3—121no—
963C22×C3—121no—
964C22×C3—121no—
965C22×C3—121no—
966C22×C3—121no—
967C22×C3—121no—
968C22×C3—121no—
969C22×C3—181no—
970C22×C3—181no—
971C22×C3—181no—
972C22×C3C22×D3211yescharacteristic
973C22×C3C22×D3211yescharacteristic
974C22×C3C22×D3211yescharacteristic
975C2×D3—21no—
976C2×D3—21no—
977C2×D3—21no—
978C2×D3—21no—
979C2×D3—21no—
980C2×D3—21no—
981C2×D3—21no—
982C2×D3—21no—
983C2×D3—62no—
984C2×D3—61no—
985C2×D3—61no—
986C2×D3—61no—
987C2×D3—61no—
988C2×D3—61no—
989C2×D3—61no—
990C2×D3—121no—
991C2×D3—121no—
992C2×D3—182no—
993C2×D3—181no—
994C2×D3—181no—
995C2×D3—181no—
996C2×D3—181no—
997C2×D3—181no—
998C2×D3—181no—
999C2×D3—181no—
1000C2×D3—181no—
1001C2×D3—181no—
1002C2×D3—361no—
1003C2×D3—361no—
1004C2×D3—361no—
1005C2×D3—361no—
1006C2×D3—361no—
1007C2×D3—361no—
1008C2×D3—361no—
1009C2×D3—361no—
1010C2×D3—362no—
1011C2×D3—364no—
1012C2×D3—364no—
1013C2×D3—364no—
1014C2×D3—368no—
1015C2×D3—721no—
1016C2×D3—721no—
1017C2×D3#380412yes—
1018C3×C4—21no—
1019C3×C4—21no—
1020C3×C4—21no—
1021C3×C4—41no—
1022C3×C4—41no—
1023C3×C4—41no—
1024C3×C4—61no—
1025C3×C4—61no—
1026C3×C4—61no—
1027C3×C4—61no—
1028C3×C4—61no—
1029C3×C4—61no—
1030C3×C4—81no—
1031C3×C4—121no—
1032C3×C4—121no—
1033C3×C4—121no—
1034C3×C4—181no—
1035C3×C4—181no—
1036C3×C4—181no—
1037C3×C4—181no—
1038C3×C4—181no—
1039Dic3—21no—
1040Dic3—21no—
1041Dic3—21no—
1042Dic3—62no—
1043Dic3—61no—
1044Dic3—61no—
1045Dic3—61no—
1046Dic3—61no—
1047Dic3—61no—
1048Dic3—61no—
1049Dic3—61no—
1050Dic3—61no—
1051Dic3—61no—
1052Dic3—61no—
1053Dic3—121no—
1054Dic3—121no—
1055Dic3—121no—
1056Dic3—121no—
1057Dic3—181no—
1058Dic3—181no—
1059Dic3—181no—
1060Dic3—361no—
1061Dic3—361no—
1062Dic3—361no—
1063Dic3—721no—
1064C32—21no—
1065C32—21no—
1066C32—21no—
1067C32—41no—
1068C32#556011yescharacteristic, complemented
1069C32#561711yescharacteristic, complemented
1070C32#565711yescharacteristic, complemented
1071C23—31no—
1072C23—31no—
1073C23—31no—
1074C23—91no—
1075C23—271no—
1076C23—542no—
1077C23—1081no—
1078C23—1081no—
1079Q8—1081no—
1080D4—62no—
1081D4—182no—
1082D4—361no—
1083D4—361no—
1084D4—1081no—
1085D4—1081no—
1086D4—1081no—
1087C2×C4—31no—
1088C2×C4—31no—
1089C2×C4—31no—
1090C2×C4—91no—
1091C2×C4—91no—
1092C2×C4—91no—
1093C2×C4—91no—
1094C2×C4—91no—
1095C2×C4—271no—
1096C2×C4—361no—
1097C2×C4—361no—
1098C2×C4—361no—
1099C2×C4—361no—
1100C2×C4D3311yescharacteristic
1101C2×C3—21no—
1102C2×C3—21no—
1103C2×C3—21no—
1104C2×C3—21no—
1105C2×C3—21no—
1106C2×C3—21no—
1107C2×C3—21no—
1108C2×C3—21no—
1109C2×C3—21no—
1110C2×C3—41no—
1111C2×C3—41no—
1112C2×C3—41no—
1113C2×C3—62no—
1114C2×C3—62no—
1115C2×C3—122no—
1116C2×C3—121no—
1117C2×C3—121no—
1118C2×C3—121no—
1119C2×C3—121no—
1120C2×C3—241no—
1121C2×C3—241no—
1122C2×C3—361no—
1123C2×C3D3×#23511yescharacteristic
1124C2×C3#6430711yescharacteristic
1125C2×C3D3×#23711yescharacteristic
1126C2×C3#6431311yescharacteristic
1127C2×C3#6431411yescharacteristic
1128C2×C3#6431411yescharacteristic
1129C2×C3#6431411yescharacteristic
1130C2×C3#6432011yescharacteristic
1131C2×C3C2×#380411yescharacteristic
1132D3—22no—
1133D3—41no—
1134D3—41no—
1135D3—122no—
1136D3—121no—
1137D3—121no—
1138D3—362no—
1139D3—361no—
1140D3—361no—
1141D3—361no—
1142D3—721no—
1143D3—721no—
1144D3—722no—
1145C22—32no—
1146C22—61no—
1147C22—61no—
1148C22—61no—
1149C22—61no—
1150C22—61no—
1151C22—61no—
1152C22—61no—
1153C22—61no—
1154C22—181no—
1155C22—181no—
1156C22—181no—
1157C22—541no—
1158C22—541no—
1159C22—541no—
1160C22—1084no—
1161C22C2×D3311yescharacteristic
1162C4—21no—
1163C4—61no—
1164C4—61no—
1165C4—61no—
1166C4—181no—
1167C4—181no—
1168C4—181no—
1169C4—181no—
1170C4—181no—
1171C4—541no—
1172C3—21no—
1173C3—21no—
1174C3—21no—
1175C3—41no—
1176C3#1059430211yescharacteristic, complemented
1177C3#1059463911yescharacteristic, complemented
1178C3#1059522111yescharacteristic, complemented
1179C2—62no—
1180C2—121no—
1181C2—121no—
1182C2—361no—
1183C2—1081no—
1184C2#1172438111yescharacteristic
1185C2#1172438611yescharacteristic
1186C2D3×#380411yescharacteristic
subgroupG/H
center, FrattiniC22C2×D33
commutator, socle, cosocleC22×C33C24
FittingC2×C33×C4C23
hypercenterC2×C4D33
hypocenterC33#538
LCSG ▷ C22×C33 ▷ C33
UCSC1 ◁ C22 ◁ C2×C4

Complements

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

NH ≅ G/Ntype
1. #11723676C2semidirect
2. #11723540C2semidirect
3. #11723419C2semidirect
4. #11723411C2semidirect
5. C3×#63898C2semidirect
6. C3×#63890C2semidirect
7. C3×#63885C2semidirect
8. #11723009C2semidirect
9. #11722987C2semidirect
10. #11722971C2semidirect
11. #11722958C2semidirect
12. #11722956C2semidirect
13. #11722949C2semidirect
14. Dic3×#625C2semidirect
15. D3×#3722C2semidirect
21. C2×#6293C22semidirect
27. C2×C3×#625C22semidirect
30. C2×C3×D3×Dic3C22semidirect
31. C2×C3×D3×Dic3C22semidirect
34. C3×#3750C22semidirect
35. C3×C4×C3⋊Dic3C22semidirect
36. C32×(C2×D3)⋊C4C22semidirect
37. C32×C4⋊Dic3C22semidirect
38. #88815C22semidirect
39. #88815C22semidirect
42. Dic3⋊(C3⋊Dic3)C22semidirect
47. (C2×D3)⋊(C3⋊Dic3)C22semidirect
48. Dic3×C3⋊Dic3C22semidirect
49. C3×Dic3⋊Dic3C22semidirect
52. C3×(C2×D3)⋊Dic3C22semidirect
53. C3×(C2×D3)⋊Dic3C22semidirect
86. #63898D3semidirect
89. #63890D3semidirect
90. #63885D3semidirect
175. C2×#625C2×D3semidirect
178. C2×D3×Dic3C2×D3semidirect
179. C2×D3×Dic3C2×D3semidirect
196. #3750C2×D3semidirect
198. C4×C3⋊Dic3C2×D3semidirect
211. C3×(C2×D3)⋊C4C2×D3semidirect
212. C3×(C2×D3)⋊C4C2×D3semidirect
215. C3×C4⋊Dic3C2×D3semidirect
216. C3×C4⋊Dic3C2×D3semidirect
233. Dic3⋊Dic3C2×D3semidirect
257. (C2×D3)⋊Dic3C2×D3semidirect
258. (C2×D3)⋊Dic3C2×D3semidirect
571. (C2×D3)⋊C4D32semidirect
578. C4⋊Dic3D32semidirect
736. C33#538semidirect
1068. C32#5560semidirect
1069. C32#5617semidirect
1070. C32#5657semidirect
1176. C3#10594302semidirect
1177. C3#10594639semidirect
1178. C3#10595221semidirect

Maximal subgroups

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

subgroupindex
#117236762
#117235402
#117234192
#117234112
C3×#638982
C3×#638902
C3×#638852
#117230092
#117229872
#117229712
#117229582
#117229562
#117229492
Dic3×#6252
D3×#37222
#105952213
#105946393
#105943023