Finite Group Databasebeta

← #13169147

Subgroups — #13169147

Order 1728.

1240 conjugacy classes of subgroups.

The subgroup lattice has 1160 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11723701C211yesmaximal, characteristic, complemented
2#11723519C211yesmaximal, characteristic, complemented
3#11723438C211yesmaximal, characteristic, complemented
4#11723407C211yesmaximal, characteristic, complemented
5C3×#63894C211yesmaximal, characteristic, complemented
6C3×#63890C211yesmaximal, characteristic, complemented
7C3×#63852C211yesmaximal, characteristic, complemented
8#11723007C211yesmaximal, characteristic, complemented
9#11722995C211yesmaximal, characteristic, complemented
10#11722974C211yesmaximal, characteristic, complemented
11#11722960C211yesmaximal, characteristic, complemented
12#11722957C211yesmaximal, characteristic, complemented
13#11722951C211yesmaximal, characteristic, complemented
14#11722930C211yesmaximal, characteristic, complemented
15#11722905C211yesmaximal, characteristic, complemented
16#10594639—31nomaximal
17#10594307—31nomaximal
18#10594012—31nomaximal
19C22×#1113C2211yescharacteristic
20C2×C3×C4⋊(C3⋊D3)C2211yescharacteristic
21C2×#6295C2211yescharacteristic
22C2×#6295C2211yescharacteristic
23C2×#6290C2211yescharacteristic
24C2×#6290C2211yescharacteristic, complemented
25C2×Dic3×C3⋊D3C2211yescharacteristic
26C2×C3×#627C2211yescharacteristic, complemented
27C2×C3×#626C2211yescharacteristic
28C2×C3×#626C2211yescharacteristic
29C2×C3×#624C2211yescharacteristic
30C2×C3×#624C2211yescharacteristic, complemented
31C2×C3×D3×Dic3C2211yescharacteristic, complemented
32#88857C2211yescharacteristic, complemented
33C3×#3752C2211yescharacteristic
34C3×#3752C2211yescharacteristic
35C32×(C2×D3)⋊C4C2211yescharacteristic, complemented
36C32×C4⋊Dic3C2211yescharacteristic, complemented
37C32×C4×Dic3C2211yescharacteristic, complemented
38#88814C2211yescharacteristic
39#88807C2211yescharacteristic, complemented
40#88806C2211yescharacteristic, complemented
41Dic3⋊(C3⋊Dic3)C2211yescharacteristic, complemented
42#88803C2211yescharacteristic
43#88803C2211yescharacteristic
44#88803C2211yescharacteristic
45#88803C2211yescharacteristic
46#88803C2211yescharacteristic, complemented
47Dic3×C3⋊Dic3C2211yescharacteristic, complemented
48C3×Dic3⋊Dic3C2211yescharacteristic, complemented
49C3×#3722C2211yescharacteristic
50C3×#3722C2211yescharacteristic
51C3×#3722C2211yescharacteristic
52C3×#3722C2211yescharacteristic, complemented
53C3×(C2×D3)⋊Dic3C2211yescharacteristic, complemented
54#64107—31no—
55#64093—31no—
56#64085—31no—
57C3×#894—31no—
58C3×#893—31no—
59C3×#886—31no—
60C3×#885—31no—
61C3×#875—31no—
62C3×C4×D12—31no—
63#63983—31no—
64#63978—31no—
65#63958—31no—
66#63952—31no—
67#63923—31no—
68#63922—31no—
69#63922—31no—
70#63922—31no—
71#63922—31no—
72#63921—31no—
73D3×(C2×D3)⋊C4—31no—
74D3×(C2×D3)⋊C4—31no—
75#63915—31no—
76#63908—31no—
77#63907—31no—
78#63907—31no—
79#63906—31no—
80#63906—31no—
81#63905—31no—
82C4×#625—31no—
83#63894D311yescharacteristic, complemented
84#63893—31no—
85#63890D311yescharacteristic, complemented
86#63887—31no—
87#63885—31no—
88#63885—31no—
89#63885—31no—
90#63885—61no—
91#63879—31no—
92#63871—31no—
93#63859—31no—
94#63859—31no—
95#63859—61no—
96#63858—31no—
97#63858—31no—
98#63858—61no—
99#63854—31no—
100#63852D311yescharacteristic, complemented
101#63850—31no—
102C22×C3×C3⋊D3C2311yescharacteristic
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×C33×C4C2311yescharacteristic
111C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
112C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
113C2×C3×C3⋊Dic3C2311yescharacteristic
114C2×C3×C3⋊Dic3C2311yescharacteristic
115C3×C4⋊(C3⋊D3)—22no—
116C2×C32×Dic3C2311yescharacteristic
117C2×C32×Dic3C2311yescharacteristic
118C2×C32×Dic3C2311yescharacteristic
119C2×C32×Dic3C2311yescharacteristic
120C2×C32×Dic3C2311yescharacteristic
121#6295—41no—
122#6295—41no—
123#6290—22no—
124#6290—41no—
125Dic3×C3⋊D3—41no—
126C3×#627—41no—
127C3×#626—41no—
128C3×#626—41no—
129C3×#624—41no—
130C3×#624—41no—
131C3×D3×Dic3—41no—
132#5678—91no—
133#5657—91no—
134#5560—91no—
135C22×D32—31no—
136C22×D32—31no—
137C22×D32—31no—
138C2×#638—31no—
139C2×#638—31no—
140C2×C4⋊(C3⋊D3)C2×D311yescharacteristic
141C2×C4×C3⋊D3—31no—
142C2×C3×#67—31no—
143C2×C3×#67—31no—
144C22×C3×Dic3—31no—
145C2×C3×D12—31no—
146C2×C3×D12—31no—
147C2×C3×D12—31no—
148C2×C3×D12—31no—
149C2×C3×D12—61no—
150C2×C3×C4×D3—31no—
151C2×C3×C4×D3—31no—
152C2×C3×C4×D3—31no—
153C2×C3×C4×D3—31no—
154C2×C3×C4×D3—31no—
155C2×C3×Dic6—31no—
156C2×C3×Dic6—31no—
157C2×#627C2×D311yescharacteristic, complemented
158C2×#626—31no—
159C2×#626—31no—
160C2×#626—31no—
161C2×#626—31no—
162C2×#626C2×D311yescharacteristic
163C2×#626C2×D311yescharacteristic
164C2×#625—31no—
165C2×#625—31no—
166C2×#625—31no—
167C2×#625—31no—
168C2×#625—31no—
169C2×#625—31no—
170C2×#625—61no—
171C2×#625—61no—
172C2×#624C2×D311yescharacteristic
173C2×#624C2×D311yescharacteristic, complemented
174C2×D3×Dic3—31no—
175C2×D3×Dic3—31no—
176C2×D3×Dic3—61no—
177C2×D3×Dic3C2×D311yescharacteristic, complemented
178C32×C4⋊C4—31no—
179C32×C22⋊C4—31no—
180C32×C42—31no—
181#3752—31no—
182#3752—31no—
183#3752—31no—
184#3752—31no—
185#3752—31no—
186#3752C2×D311yescharacteristic
187#3752C2×D311yescharacteristic
188C4⋊(C3⋊Dic3)—31no—
189#3750—31no—
190#3750—31no—
191#3750—31no—
192#3750—31no—
193#3750—31no—
194#3750—61no—
195#3750—61no—
196#3750—61no—
197#3750—121no—
198C4×C3⋊Dic3—31no—
199C3×#217—31no—
200C3×(C2×D3)⋊C4—21no—
201C3×(C2×D3)⋊C4—31no—
202C3×(C2×D3)⋊C4—31no—
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—31no—
211C3×(C2×D3)⋊C4—31no—
212C3×(C2×D3)⋊C4—31no—
213C3×(C2×D3)⋊C4—31no—
214C3×(C2×D3)⋊C4—61no—
215C3×(C2×D3)⋊C4—61no—
216C3×(C2×D3)⋊C4C2×D311yescharacteristic, complemented
217C3×(C2×D3)⋊C4C2×D311yescharacteristic, complemented
218C3×C4⋊Dic3—21no—
219C3×C4⋊Dic3—31no—
220C3×C4⋊Dic3C2×D311yescharacteristic, complemented
221C3×C4⋊Dic3C2×D311yescharacteristic, complemented
222C3×Dic3⋊C4—31no—
223C3×C4×Dic3—21no—
224C3×C4×Dic3C2×D311yescharacteristic, complemented
225C3×C4×Dic3C2×D311yescharacteristic, complemented
226#3724—31no—
227#3724—31no—
228#3724—61no—
229Dic3⋊Dic3—31no—
230Dic3⋊Dic3—31no—
231Dic3⋊Dic3—31no—
232Dic3⋊Dic3—31no—
233Dic3⋊Dic3—61no—
234Dic3⋊Dic3—61no—
235Dic3⋊Dic3C2×D311yescharacteristic, complemented
236#3722—31no—
237#3722C2×D311yescharacteristic
238#3722C2×D311yescharacteristic
239#3722C2×D311yescharacteristic
240#3722C2×D311yescharacteristic, complemented
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—31no—
253(C2×D3)⋊Dic3—61no—
254(C2×D3)⋊Dic3—61no—
255(C2×D3)⋊Dic3—61no—
256(C2×D3)⋊Dic3—61no—
257(C2×D3)⋊Dic3—61no—
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×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—
279C33×C4—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×#123—91no—
291C3×C4×D4—91no—
292#947—91no—
293#946—91no—
294#939—91no—
295#939—91no—
296#938—91no—
297#937—91no—
298#937—91no—
299#937—91no—
300#930—91no—
301#930—91no—
302#929—91no—
303C4×#67—91no—
304C4×#67—91no—
305C2×(C2×D3)⋊C4—91no—
306#898—91no—
307#898—91no—
308#898—181no—
309#897—91no—
310#894—31no—
311#894—91no—
312#893—31no—
313#886—31no—
314#885—31no—
315#885—91no—
316#885—91no—
317#884—91no—
318#884—91no—
319#884—91no—
320#884—91no—
321#884—181no—
322#883—91no—
323#882—91no—
324#882—91no—
325#882—91no—
326#67⋊C4—91no—
327D3×C22⋊C4—91no—
328D3×C22⋊C4—91no—
329#879—91no—
330#879—91no—
331#878—91no—
332#876—91no—
333#876—91no—
334#876—181no—
335#875—31no—
336C4×D12—31no—
337C23×C32—31no—
338C22×C3⋊D3C22×D311yescharacteristic
339C22×C3⋊D3C22×D311yescharacteristic
340C22×C3⋊D3C22×D311yescharacteristic
341C22×C3⋊D3C22×D311yescharacteristic
342C22×C3×D3—21no—
343C22×C3×D3—31no—
344C22×C3×D3—31no—
345C22×C3×D3—31no—
346C22×C3×D3—31no—
347C22×C3×D3—31no—
348C22×C3×D3—31no—
349C22×C3×D3—31no—
350C22×C3×D3—31no—
351C22×C3×D3—61no—
352C22×C3×D3—61no—
353C22×C3×D3—61no—
354C22×C3×D3—61no—
355C22×C3×D3C22×D311yescharacteristic
356C22×C3×D3C22×D311yescharacteristic
357C2×D32—62no—
358C2×D32—62no—
359C2×D32—62no—
360C2×D32—121no—
361C2×D32—121no—
362C2×D32—121no—
363C2×D32—121no—
364C2×D32—121no—
365C2×D32—121no—
366C2×C32×C4—21no—
367C2×C32×C4—21no—
368C2×C32×C4—21no—
369C2×C32×C4—31no—
370C2×C32×C4—31no—
371C2×C32×C4—31no—
372C2×C32×C4—31no—
373C2×C32×C4—31no—
374C2×C32×C4—41no—
375C2×C32×C4C22×D311yescharacteristic
376C2×C32×C4C22×D311yescharacteristic
377C2×C32×C4C22×D311yescharacteristic
378#638—62no—
379#638—121no—
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—61no—
387C2×C3⋊Dic3—61no—
388C2×C3⋊Dic3—61no—
389C2×C3⋊Dic3—61no—
390C2×C3⋊Dic3—61no—
391C2×C3⋊Dic3—61no—
392C2×C3⋊Dic3—121no—
393C2×C3⋊Dic3—121no—
394C2×C3⋊Dic3C22×D311yescharacteristic
395C2×C3⋊Dic3C22×D311yescharacteristic
396C4⋊(C3⋊D3)—22no—
397C4×C3⋊D3—121no—
398C3×#67—121no—
399C3×#67—121no—
400C2×C3×Dic3—21no—
401C2×C3×Dic3—21no—
402C2×C3×Dic3—21no—
403C2×C3×Dic3—21no—
404C2×C3×Dic3—21no—
405C2×C3×Dic3—31no—
406C2×C3×Dic3—31no—
407C2×C3×Dic3—31no—
408C2×C3×Dic3—31no—
409C2×C3×Dic3—61no—
410C2×C3×Dic3—61no—
411C2×C3×Dic3—121no—
412C2×C3×Dic3C22×D311yescharacteristic
413C2×C3×Dic3C22×D311yescharacteristic
414C2×C3×Dic3C22×D311yescharacteristic
415C2×C3×Dic3C22×D311yescharacteristic
416C2×C3×Dic3C22×D311yescharacteristic
417C2×C3×Dic3C22×D311yescharacteristic
418C2×C3×Dic3C22×D311yescharacteristic
419C2×C3×Dic3C22×D311yescharacteristic
420C2×C3×Dic3C22×D311yescharacteristic
421C2×C3×Dic3C22×D311yescharacteristic
422C3×D12—62no—
423C3×D12—62no—
424C3×D12—122no—
425C3×D12—121no—
426C3×D12—121no—
427C3×C4×D3—121no—
428C3×C4×D3—121no—
429C3×C4×D3—121no—
430C3×C4×D3—121no—
431C3×C4×D3—121no—
432C3×Dic6—121no—
433C3×Dic6—121no—
434#627—41no—
435#626—41no—
436#626—41no—
437#626—121no—
438#626—121no—
439#626—121no—
440#626—121no—
441#625—62no—
442#625—62no—
443#625—122no—
444#625—121no—
445#625—121no—
446#625—121no—
447#625—121no—
448#625—122no—
449#624—41no—
450#624—41no—
451D3×Dic3—41no—
452D3×Dic3—121no—
453D3×Dic3—121no—
454D3×Dic3—122no—
455#538—271noSylow
456C2×C33C2×#4111yescharacteristic
457C2×C33H(5,𝔽2)11yescharacteristic
458C2×C33H(5,𝔽2)11yescharacteristic
459C3×C3⋊D3—22no—
460C3×C3⋊D3—41no—
461C3×C3⋊D3—41no—
462C3×C3⋊D3—41no—
463C32×D3—41no—
464C23×D3—91no—
465C23×D3—91no—
466C23×D3—91no—
467C2×C3×Q8—91no—
468C2×C3×D4—91no—
469C2×C3×D4—91no—
470C2×C3×D4—91no—
471C22×C3×C4—91no—
472C22×C3×C4—91no—
473C22×C3×C4—91no—
474C2×#67—31no—
475C2×#67—31no—
476C2×#67—91no—
477C2×#67—91no—
478C2×#67—91no—
479C2×#67—91no—
480C2×#67—91no—
481C2×#67—91no—
482C2×#67—91no—
483C2×#67—91no—
484C2×#67—91no—
485C2×#67—91no—
486C2×#67—181no—
487C2×#67—181no—
488C22×Dic3—31no—
489C22×Dic3—91no—
490C2×D12—31no—
491C2×D12—31no—
492C2×D12—31no—
493C2×D12—31no—
494C2×D12—61no—
495C2×D12—91no—
496C2×D12—91no—
497C2×C4×D3—31no—
498C2×C4×D3—31no—
499C2×C4×D3—31no—
500C2×C4×D3—31no—
501C2×C4×D3—31no—
502C2×C4×D3—91no—
503C2×C4×D3—91no—
504C2×C4×D3—181no—
505C2×Dic6—31no—
506C2×Dic6—31no—
507C3×C4⋊C4—31no—
508C3×C4⋊C4—31no—
509C3×C4⋊C4—61no—
510C3×C4⋊C4—91no—
511C3×C22⋊C4—31no—
512C3×C22⋊C4—31no—
513C3×C22⋊C4—61no—
514C3×C22⋊C4—91no—
515C3×C22⋊C4—91no—
516C3×C22⋊C4—91no—
517C3×C22⋊C4—91no—
518C3×C22⋊C4—91no—
519C3×C22⋊C4—91no—
520C3×C22⋊C4—91no—
521C3×C42—31no—
522C3×C42—31no—
523C3×C42—61no—
524#217—31no—
525#217—91no—
526#217—91no—
527#217—91no—
528#217—91no—
529#217—91no—
530#217—91no—
531(C2×D3)⋊C4—31no—
532(C2×D3)⋊C4—31no—
533(C2×D3)⋊C4—31no—
534(C2×D3)⋊C4—31no—
535(C2×D3)⋊C4—31no—
536(C2×D3)⋊C4—31no—
537(C2×D3)⋊C4—31no—
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—61no—
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—181no—
559(C2×D3)⋊C4—181no—
560(C2×D3)⋊C4—181no—
561(C2×D3)⋊C4—181no—
562(C2×D3)⋊C4—181no—
563(C2×D3)⋊C4D3211yescharacteristic, complemented
564C4⋊Dic3—31no—
565C4⋊Dic3—91no—
566C4⋊Dic3—91no—
567C4⋊Dic3—91no—
568C4⋊Dic3—181no—
569C4⋊Dic3D3211yescharacteristic, complemented
570Dic3⋊C4—31no—
571Dic3⋊C4—91no—
572Dic3⋊C4—91no—
573Dic3⋊C4—91no—
574Dic3⋊C4—91no—
575Dic3⋊C4—91no—
576Dic3⋊C4—91no—
577Dic3⋊C4—91no—
578Dic3⋊C4—91no—
579Dic3⋊C4—91no—
580Dic3⋊C4—181no—
581Dic3⋊C4—181no—
582Dic3⋊C4—181no—
583Dic3⋊C4—181no—
584Dic3⋊C4—181no—
585Dic3⋊C4—361no—
586C4×Dic3—91no—
587C4×Dic3—91no—
588C4×Dic3—91no—
589C4×Dic3—181no—
590C4×Dic3D3211yescharacteristic, complemented
591C22×C32—21no—
592C22×C32—21no—
593C22×C32—21no—
594C22×C32—41no—
595C22×C32—61no—
596C22×C32—61no—
597C22×C32—61no—
598C22×C32C23×D311yescharacteristic
599C22×C32C23×D311yescharacteristic
600C22×C32C23×D311yescharacteristic
601C2×C3⋊D3—21no—
602C2×C3⋊D3—21no—
603C2×C3⋊D3—21no—
604C2×C3⋊D3—21no—
605C2×C3⋊D3—21no—
606C2×C3⋊D3—21no—
607C2×C3⋊D3—21no—
608C2×C3⋊D3—21no—
609C2×C3⋊D3—21no—
610C2×C3⋊D3—21no—
611C2×C3⋊D3—21no—
612C2×C3⋊D3#23512yes—
613C2×C3×D3—21no—
614C2×C3×D3—21no—
615C2×C3×D3—21no—
616C2×C3×D3—21no—
617C2×C3×D3—21no—
618C2×C3×D3—21no—
619C2×C3×D3—32no—
620C2×C3×D3—32no—
621C2×C3×D3—41no—
622C2×C3×D3—41no—
623C2×C3×D3—41no—
624C2×C3×D3—62no—
625C2×C3×D3—61no—
626C2×C3×D3—61no—
627C2×C3×D3—61no—
628C2×C3×D3—61no—
629C2×C3×D3—61no—
630C2×C3×D3—61no—
631C2×C3×D3—61no—
632C2×C3×D3—61no—
633C2×C3×D3—61no—
634C2×C3×D3—61no—
635C2×C3×D3—61no—
636C2×C3×D3—61no—
637C2×C3×D3—61no—
638C2×C3×D3—61no—
639C2×C3×D3—61no—
640C2×C3×D3—61no—
641C2×C3×D3—61no—
642C2×C3×D3—61no—
643C2×C3×D3—61no—
644C2×C3×D3—61no—
645C2×C3×D3—61no—
646C2×C3×D3—61no—
647C2×C3×D3—121no—
648C2×C3×D3—121no—
649C2×C3×D3—121no—
650C2×C3×D3—121no—
651C2×C3×D3—121no—
652C2×C3×D3—121no—
653C2×C3×D3—121no—
654C2×C3×D3—121no—
655C2×C3×D3—121no—
656C2×C3×D3—121no—
657C2×C3×D3—121no—
658D32—124no—
659D32—124no—
660D32—124no—
661C32×C4—21no—
662C32×C4—21no—
663C32×C4—21no—
664C32×C4—41no—
665C32×C4—41no—
666C32×C4—41no—
667C32×C4—61no—
668C32×C4—61no—
669C32×C4—61no—
670C32×C4—61no—
671C32×C4—61no—
672C32×C4—81no—
673C3⋊Dic3—21no—
674C3⋊Dic3—21no—
675C3⋊Dic3—61no—
676C3⋊Dic3—62no—
677C3⋊Dic3—61no—
678C3⋊Dic3—61no—
679C3⋊Dic3—61no—
680C3⋊Dic3—61no—
681C3⋊Dic3—61no—
682C3⋊Dic3—121no—
683C3⋊Dic3—121no—
684C3⋊Dic3—122no—
685C3⋊Dic3—121no—
686C3⋊Dic3—121no—
687C3⋊Dic3—121no—
688C3⋊Dic3—241no—
689C3×Dic3—21no—
690C3×Dic3—21no—
691C3×Dic3—21no—
692C3×Dic3—21no—
693C3×Dic3—21no—
694C3×Dic3—21no—
695C3×Dic3—21no—
696C3×Dic3—21no—
697C3×Dic3—21no—
698C3×Dic3—21no—
699C3×Dic3—41no—
700C3×Dic3—41no—
701C3×Dic3—41no—
702C3×Dic3—41no—
703C3×Dic3—41no—
704C3×Dic3—61no—
705C3×Dic3—61no—
706C3×Dic3—61no—
707C3×Dic3—61no—
708C3×Dic3—121no—
709C3×Dic3—121no—
710#126—271no—
711#126—271no—
712#124—91no—
713#124—271no—
714#123—91no—
715#123—271no—
716C22⋊Q8—271no—
717#121—271no—
718#121—271no—
719#121—271no—
720#120—271no—
721#120—271no—
722C4×D4—91no—
723C4×D4—271no—
724C2×C22⋊C4—271no—
725C33#53811yescharacteristic, complemented, Sylow
726C23×C3—31no—
727C23×C3—31no—
728C23×C3—61no—
729C23×C3—91no—
730C23×C3—91no—
731C23×C3—91no—
732C23×C3—91no—
733C22×D3—31no—
734C22×D3—31no—
735C22×D3—31no—
736C22×D3—31no—
737C22×D3—31no—
738C22×D3—31no—
739C22×D3—31no—
740C22×D3—31no—
741C22×D3—61no—
742C22×D3—61no—
743C22×D3—61no—
744C22×D3—61no—
745C22×D3—182no—
746C22×D3—182no—
747C22×D3—182no—
748C22×D3—361no—
749C22×D3—361no—
750C22×D3—361no—
751C22×D3—361no—
752C22×D3—361no—
753C22×D3—361no—
754C22×D3C2×D3211yescharacteristic
755C3×Q8—361no—
756C3×D4—182no—
757C3×D4—361no—
758C3×D4—361no—
759C2×C3×C4—21no—
760C2×C3×C4—21no—
761C2×C3×C4—21no—
762C2×C3×C4—31no—
763C2×C3×C4—31no—
764C2×C3×C4—31no—
765C2×C3×C4—31no—
766C2×C3×C4—31no—
767C2×C3×C4—31no—
768C2×C3×C4—31no—
769C2×C3×C4—31no—
770C2×C3×C4—31no—
771C2×C3×C4—31no—
772C2×C3×C4—41no—
773C2×C3×C4—61no—
774C2×C3×C4—61no—
775C2×C3×C4—61no—
776C2×C3×C4—61no—
777C2×C3×C4—61no—
778C2×C3×C4—91no—
779C2×C3×C4—91no—
780C2×C3×C4—361no—
781C2×C3×C4—361no—
782C2×C3×C4—361no—
783C2×C3×C4C2×D3211yescharacteristic
784C2×C3×C4C2×D3211yescharacteristic
785C2×C3×C4C2×D3211yescharacteristic
786#67—121no—
787#67—121no—
788#67—182no—
789#67—182no—
790#67—182no—
791#67—362no—
792#67—361no—
793#67—361no—
794#67—361no—
795#67—361no—
796#67—361no—
797#67—361no—
798#67—361no—
799#67—362no—
800C2×Dic3—31no—
801C2×Dic3—31no—
802C2×Dic3—31no—
803C2×Dic3—31no—
804C2×Dic3—61no—
805C2×Dic3—61no—
806C2×Dic3—91no—
807C2×Dic3—91no—
808C2×Dic3—91no—
809C2×Dic3—91no—
810C2×Dic3—91no—
811C2×Dic3—91no—
812C2×Dic3—121no—
813C2×Dic3—181no—
814C2×Dic3—181no—
815C2×Dic3—181no—
816C2×Dic3—181no—
817C2×Dic3—181no—
818C2×Dic3—181no—
819C2×Dic3—361no—
820C2×Dic3—361no—
821C2×Dic3—361no—
822C2×Dic3C2×D3211yescharacteristic
823C2×Dic3C2×D3211yescharacteristic
824C2×Dic3C2×D3211yescharacteristic
825C2×Dic3C2×D3211yescharacteristic
826C2×Dic3C2×D3211yescharacteristic
827D12—62no—
828D12—62no—
829D12—122no—
830D12—121no—
831D12—121no—
832D12—361no—
833D12—361no—
834C4×D3—121no—
835C4×D3—121no—
836C4×D3—121no—
837C4×D3—121no—
838C4×D3—121no—
839C4×D3—361no—
840C4×D3—361no—
841C4×D3—362no—
842Dic6—121no—
843Dic6—121no—
844C2×C32—21no—
845C2×C32—21no—
846C2×C32—21no—
847C2×C32—21no—
848C2×C32—21no—
849C2×C32—21no—
850C2×C32—21no—
851C2×C32—21no—
852C2×C32—21no—
853C2×C32—41no—
854C2×C32—41no—
855C2×C32—41no—
856C2×C32—121no—
857C2×C32C2×#23511yescharacteristic
858C2×C32#100411yescharacteristic
859C2×C32#100411yescharacteristic
860C2×C32#100411yescharacteristic
861C2×C32D3×#4111yescharacteristic
862C2×C32D3×#4111yescharacteristic
863C2×C32#100911yescharacteristic
864C2×C32#100911yescharacteristic
865C2×C32#100911yescharacteristic
866C3⋊D3—22no—
867C3⋊D3—41no—
868C3⋊D3—41no—
869C3⋊D3—41no—
870C3×D3—41no—
871C3×D3—41no—
872C3×D3—62no—
873C3×D3—62no—
874C3×D3—81no—
875C3×D3—122no—
876C3×D3—121no—
877C3×D3—121no—
878C3×D3—121no—
879C3×D3—121no—
880C3×D3—121no—
881C3×D3—121no—
882C3×D3—241no—
883C3×D3—241no—
884C3×D3—241no—
885C24—271no—
886C2×Q8—91no—
887C2×D4—91no—
888C2×D4—91no—
889C2×D4—91no—
890C2×D4—271no—
891C2×D4—271no—
892C2×D4—271no—
893C2×D4—271no—
894C22×C4—91no—
895C22×C4—91no—
896C22×C4—91no—
897C22×C4—271no—
898C4⋊C4—31no—
899C4⋊C4—91no—
900C4⋊C4—271no—
901C4⋊C4—271no—
902C4⋊C4—271no—
903C4⋊C4—271no—
904C22⋊C4—31no—
905C22⋊C4—91no—
906C22⋊C4—91no—
907C22⋊C4—91no—
908C22⋊C4—91no—
909C22⋊C4—91no—
910C22⋊C4—91no—
911C22⋊C4—91no—
912C22⋊C4—271no—
913C22⋊C4—271no—
914C22⋊C4—271no—
915C22⋊C4—271no—
916C22⋊C4—271no—
917C22⋊C4—271no—
918C42—31no—
919C42—271no—
920C22×C3—21no—
921C22×C3—21no—
922C22×C3—21no—
923C22×C3—41no—
924C22×C3—61no—
925C22×C3—61no—
926C22×C3—61no—
927C22×C3—61no—
928C22×C3—61no—
929C22×C3—61no—
930C22×C3—92no—
931C22×C3—121no—
932C22×C3—121no—
933C22×C3—121no—
934C22×C3—181no—
935C22×C3—181no—
936C22×C3—181no—
937C22×C3—181no—
938C22×C3—181no—
939C22×C3—181no—
940C22×C3—181no—
941C22×C3—181no—
942C22×C3—181no—
943C22×C3—181no—
944C22×C3—181no—
945C22×C3C22×D3211yescharacteristic
946C22×C3C22×D3211yescharacteristic
947C22×C3C22×D3211yescharacteristic
948C2×D3—21no—
949C2×D3—21no—
950C2×D3—21no—
951C2×D3—32no—
952C2×D3—32no—
953C2×D3—62no—
954C2×D3—61no—
955C2×D3—61no—
956C2×D3—61no—
957C2×D3—61no—
958C2×D3—61no—
959C2×D3—61no—
960C2×D3—61no—
961C2×D3—61no—
962C2×D3—61no—
963C2×D3—61no—
964C2×D3—61no—
965C2×D3—61no—
966C2×D3—61no—
967C2×D3—61no—
968C2×D3—61no—
969C2×D3—61no—
970C2×D3—61no—
971C2×D3—61no—
972C2×D3—61no—
973C2×D3—61no—
974C2×D3—61no—
975C2×D3—61no—
976C2×D3—121no—
977C2×D3—121no—
978C2×D3—121no—
979C2×D3—121no—
980C2×D3—121no—
981C2×D3—121no—
982C2×D3—121no—
983C2×D3—121no—
984C2×D3—121no—
985C2×D3—121no—
986C2×D3—121no—
987C2×D3—364no—
988C2×D3—364no—
989C2×D3—364no—
990C3×C4—21no—
991C3×C4—21no—
992C3×C4—21no—
993C3×C4—41no—
994C3×C4—41no—
995C3×C4—41no—
996C3×C4—61no—
997C3×C4—61no—
998C3×C4—61no—
999C3×C4—61no—
1000C3×C4—61no—
1001C3×C4—61no—
1002C3×C4—61no—
1003C3×C4—61no—
1004C3×C4—61no—
1005C3×C4—61no—
1006C3×C4—81no—
1007C3×C4—121no—
1008C3×C4—121no—
1009C3×C4—121no—
1010C3×C4—121no—
1011C3×C4—121no—
1012C3×C4—181no—
1013C3×C4—181no—
1014Dic3—21no—
1015Dic3—21no—
1016Dic3—21no—
1017Dic3—21no—
1018Dic3—21no—
1019Dic3—61no—
1020Dic3—61no—
1021Dic3—61no—
1022Dic3—61no—
1023Dic3—121no—
1024Dic3—121no—
1025Dic3—182no—
1026Dic3—181no—
1027Dic3—181no—
1028Dic3—181no—
1029Dic3—181no—
1030Dic3—181no—
1031Dic3—181no—
1032Dic3—361no—
1033Dic3—361no—
1034Dic3—361no—
1035Dic3—361no—
1036Dic3—361no—
1037Dic3—362no—
1038Dic3—721no—
1039C32—21no—
1040C32—21no—
1041C32—21no—
1042C32—41no—
1043C32#556011yescharacteristic, complemented
1044C32#565711yescharacteristic, complemented
1045C32#567811yescharacteristic, complemented
1046C23—31no—
1047C23—91no—
1048C23—91no—
1049C23—91no—
1050C23—91no—
1051C23—542no—
1052C23—1081no—
1053C23—1081no—
1054Q8—361no—
1055D4—182no—
1056D4—361no—
1057D4—361no—
1058D4—542no—
1059D4—1081no—
1060D4—1081no—
1061D4—1081no—
1062C2×C4—31no—
1063C2×C4—31no—
1064C2×C4—31no—
1065C2×C4—31no—
1066C2×C4—31no—
1067C2×C4—91no—
1068C2×C4—91no—
1069C2×C4—271no—
1070C2×C4—271no—
1071C2×C4—361no—
1072C2×C4—361no—
1073C2×C4—361no—
1074C2×C4—1081no—
1075C2×C4D3311yescharacteristic
1076C2×C3—21no—
1077C2×C3—21no—
1078C2×C3—21no—
1079C2×C3—21no—
1080C2×C3—21no—
1081C2×C3—21no—
1082C2×C3—21no—
1083C2×C3—21no—
1084C2×C3—21no—
1085C2×C3—41no—
1086C2×C3—41no—
1087C2×C3—41no—
1088C2×C3—121no—
1089C2×C3—121no—
1090C2×C3—182no—
1091C2×C3—241no—
1092C2×C3—361no—
1093C2×C3—361no—
1094C2×C3—361no—
1095C2×C3D3×#23511yescharacteristic
1096C2×C3D3×#23511yescharacteristic
1097C2×C3#6430711yescharacteristic
1098C2×C3#6430711yescharacteristic
1099C2×C3#6430711yescharacteristic
1100C2×C3#6431211yescharacteristic
1101C2×C3#6431311yescharacteristic
1102C2×C3#6431411yescharacteristic
1103C2×C3#6432011yescharacteristic
1104D3—41no—
1105D3—62no—
1106D3—62no—
1107D3—122no—
1108D3—121no—
1109D3—121no—
1110D3—121no—
1111D3—121no—
1112D3—121no—
1113D3—121no—
1114D3—241no—
1115D3—241no—
1116D3—241no—
1117C22—61no—
1118C22—61no—
1119C22—61no—
1120C22—92no—
1121C22—181no—
1122C22—181no—
1123C22—181no—
1124C22—181no—
1125C22—181no—
1126C22—181no—
1127C22—181no—
1128C22—181no—
1129C22—181no—
1130C22—181no—
1131C22—181no—
1132C22—1084no—
1133C22C2×D3311yescharacteristic
1134C4—21no—
1135C4—61no—
1136C4—61no—
1137C4—61no—
1138C4—61no—
1139C4—61no—
1140C4—181no—
1141C4—181no—
1142C4—541no—
1143C4—541no—
1144C3—21no—
1145C3—21no—
1146C3—21no—
1147C3—41no—
1148C3#1059401211yescharacteristic, complemented
1149C3#1059430711yescharacteristic, complemented
1150C3#1059463911yescharacteristic, complemented
1151C2—121no—
1152C2—182no—
1153C2—361no—
1154C2—361no—
1155C2—361no—
1156C2#1172438011yescharacteristic
1157C2#1172438511yescharacteristic
1158C2#1172441011yescharacteristic
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. #11723701C2semidirect
2. #11723519C2semidirect
3. #11723438C2semidirect
4. #11723407C2semidirect
5. C3×#63894C2semidirect
6. C3×#63890C2semidirect
7. C3×#63852C2semidirect
8. #11723007C2semidirect
9. #11722995C2semidirect
10. #11722974C2semidirect
11. #11722960C2semidirect
12. #11722957C2semidirect
13. #11722951C2semidirect
14. #11722930C2semidirect
15. #11722905C2semidirect
24. C2×#6290C22semidirect
26. C2×C3×#627C22semidirect
30. C2×C3×#624C22semidirect
31. C2×C3×D3×Dic3C22semidirect
32. #88857C22semidirect
35. C32×(C2×D3)⋊C4C22semidirect
36. C32×C4⋊Dic3C22semidirect
37. C32×C4×Dic3C22semidirect
39. #88807C22semidirect
40. #88806C22semidirect
41. Dic3⋊(C3⋊Dic3)C22semidirect
46. #88803C22semidirect
47. Dic3×C3⋊Dic3C22semidirect
48. C3×Dic3⋊Dic3C22semidirect
52. C3×#3722C22semidirect
53. C3×(C2×D3)⋊Dic3C22semidirect
83. #63894D3semidirect
85. #63890D3semidirect
100. #63852D3semidirect
157. C2×#627C2×D3semidirect
173. C2×#624C2×D3semidirect
177. C2×D3×Dic3C2×D3semidirect
216. C3×(C2×D3)⋊C4C2×D3semidirect
217. C3×(C2×D3)⋊C4C2×D3semidirect
220. C3×C4⋊Dic3C2×D3semidirect
221. C3×C4⋊Dic3C2×D3semidirect
224. C3×C4×Dic3C2×D3semidirect
225. C3×C4×Dic3C2×D3semidirect
235. Dic3⋊Dic3C2×D3semidirect
240. #3722C2×D3semidirect
258. (C2×D3)⋊Dic3C2×D3semidirect
563. (C2×D3)⋊C4D32semidirect
569. C4⋊Dic3D32semidirect
590. C4×Dic3D32semidirect
725. C33#538semidirect
1043. C32#5560semidirect
1044. C32#5657semidirect
1045. C32#5678semidirect
1148. C3#10594012semidirect
1149. C3#10594307semidirect
1150. C3#10594639semidirect

Maximal subgroups

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

subgroupindex
#117237012
#117235192
#117234382
#117234072
C3×#638942
C3×#638902
C3×#638522
#117230072
#117229952
#117229742
#117229602
#117229572
#117229512
#117229302
#117229052
#105946393
#105943073
#105940123