Finite Group Databasebeta

← #13169164

Subgroups — #13169164

Order 1728.

1254 conjugacy classes of subgroups.

The subgroup lattice has 1164 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11723701C211yesmaximal, characteristic, complemented
2#11723515C211yesmaximal, characteristic, complemented
3#11723483C211yesmaximal, characteristic, complemented
4#11723408C211yesmaximal, characteristic, complemented
5C3×#63904C211yesmaximal, characteristic, complemented
6C3×#63897C211yesmaximal, characteristic, complemented
7C3×#63850C211yesmaximal, characteristic, complemented
8#11723023C211yesmaximal, characteristic, complemented
9#11723010C211yesmaximal, characteristic, complemented
10#11723009C211yesmaximal, characteristic, complemented
11#11722967C211yesmaximal, characteristic, complemented
12#11722957C211yesmaximal, characteristic, complemented
13#11722951C211yesmaximal, characteristic, complemented
14#11722931C211yesmaximal, characteristic, complemented
15#11722905C211yesmaximal, characteristic, complemented
16#10595085—31nomaximal
17#10594659—31nomaximal
18#10594639—31nomaximal
19C22×#1113C2211yescharacteristic
20C2×C3×C4⋊(C3⋊D3)C2211yescharacteristic
21C2×C32×C4×D3C2211yescharacteristic, complemented
22C2×#6295C2211yescharacteristic
23C2×#6295C2211yescharacteristic
24C2×#6293C2211yescharacteristic, complemented
25C2×#6290C2211yescharacteristic
26C2×#6290C2211yescharacteristic, complemented
27C2×Dic3×C3⋊D3C2211yescharacteristic
28C2×C3×#626C2211yescharacteristic
29C2×C3×#626C2211yescharacteristic
30C2×C3×#624C2211yescharacteristic
31C2×C3×#624C2211yescharacteristic, complemented
32C4⋊(C3⋊(C3⋊Dic3))C2211yescharacteristic, complemented
33C3×#3752C2211yescharacteristic
34C3×#3752C2211yescharacteristic
35C32×Dic3⋊C4C2211yescharacteristic, complemented
36C32×Dic3⋊C4C2211yescharacteristic, complemented
37#88814C2211yescharacteristic
38#88806C2211yescharacteristic, complemented
39Dic3⋊(C3⋊Dic3)C2211yescharacteristic, complemented
40#88803C2211yescharacteristic
41#88803C2211yescharacteristic
42#88803C2211yescharacteristic
43#88803C2211yescharacteristic
44#88803C2211yescharacteristic, complemented
45Dic3×C3⋊Dic3C2211yescharacteristic, complemented
46C3×#3724C2211yescharacteristic, complemented
47C3×#3722C2211yescharacteristic
48C3×#3722C2211yescharacteristic
49C3×#3722C2211yescharacteristic
50C3×#3722C2211yescharacteristic, complemented
51C3×(C2×D3)⋊Dic3C2211yescharacteristic, complemented
52C3×(C2×D3)⋊Dic3C2211yescharacteristic, complemented
53C3×Dic32C2211yescharacteristic, complemented
54#64139—31no—
55#64107—31no—
56#64106—31no—
57C3×#929—31no—
58C3×C4×#67—31no—
59C3×#894—31no—
60C3×#894—31no—
61C3×#894—31no—
62C3×#893—31no—
63#63983—31no—
64#63971—31no—
65#63958—31no—
66#63953—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#63913—31no—
77#63913—31no—
78#63912—31no—
79#63908—31no—
80#63908—31no—
81#63908—31no—
82#63908—61no—
83#63906—31no—
84#63904—31no—
85#63904—31no—
86#63904D311yescharacteristic, complemented
87C4×#625—31no—
88#63897D311yescharacteristic, complemented
89#63893—31no—
90#63893—31no—
91#63893—61no—
92#63885—31no—
93#63868—31no—
94#63861—31no—
95#63861—31no—
96#63861—31no—
97#63861—61no—
98#63859—31no—
99#63852—31no—
100#63852—31no—
101#63850D311yescharacteristic, complemented
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)—41no—
116C2×C32×Dic3C2311yescharacteristic
117C2×C32×Dic3C2311yescharacteristic
118C2×C32×Dic3C2311yescharacteristic
119C2×C32×Dic3C2311yescharacteristic
120C2×C32×Dic3C2311yescharacteristic
121C32×C4×D3—41no—
122#6295—22no—
123#6295—41no—
124#6293—41no—
125#6290—41no—
126#6290—41no—
127Dic3×C3⋊D3—41no—
128C3×#626—22no—
129C3×#626—41no—
130C3×#624—41no—
131C3×#624—41no—
132#5657—91no—
133#5657—91no—
134#5560—91no—
135C22×D32—31no—
136C22×D32—31no—
137C22×D32—31no—
138C22×C32×C4—31no—
139C2×#638—31no—
140C2×#638—31no—
141C2×C4⋊(C3⋊D3)C2×D311yescharacteristic
142C2×C4×C3⋊D3—31no—
143C2×#634—31no—
144C2×C3×#67—31no—
145C2×C3×#67—31no—
146C2×C3×D12—31no—
147C2×C3×D12—31no—
148C2×C3×D12—31no—
149C2×C3×D12—31no—
150C2×C3×D12—61no—
151C2×C3×C4×D3—21no—
152C2×C3×C4×D3—31no—
153C2×C3×C4×D3—31no—
154C2×C3×C4×D3—31no—
155C2×C3×C4×D3—31no—
156C2×C3×C4×D3C2×D311yescharacteristic, complemented
157C2×C3×C4×D3C2×D311yescharacteristic, complemented
158C2×#627—31no—
159C2×#627—31no—
160C2×#627—61no—
161C2×#626—31no—
162C2×#626—31no—
163C2×#626—31no—
164C2×#626—31no—
165C2×#626C2×D311yescharacteristic
166C2×#626C2×D311yescharacteristic
167C2×#625—31no—
168C2×#625—31no—
169C2×#625—31no—
170C2×#625—31no—
171C2×#625—31no—
172C2×#625—31no—
173C2×#625—61no—
174C2×#625—61no—
175C2×#624C2×D311yescharacteristic
176C2×#624C2×D311yescharacteristic, complemented
177C2×D3×Dic3—31no—
178C2×D3×Dic3—31no—
179C2×D3×Dic3—61no—
180C32×C4⋊C4—31no—
181C32×C4⋊C4—31no—
182#3752—31no—
183#3752—31no—
184#3752—31no—
185#3752—31no—
186#3752—31no—
187#3752C2×D311yescharacteristic
188#3752C2×D311yescharacteristic
189C4⋊(C3⋊Dic3)—31no—
190C4⋊(C3⋊Dic3)—31no—
191C4⋊(C3⋊Dic3)—31no—
192C4⋊(C3⋊Dic3)—31no—
193C4⋊(C3⋊Dic3)—61no—
194C4⋊(C3⋊Dic3)—61no—
195C4⋊(C3⋊Dic3)—61no—
196C4⋊(C3⋊Dic3)—121no—
197#3750—31no—
198C4×C3⋊Dic3—31no—
199C3×#217—31no—
200C3×#217—31no—
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—31no—
215C3×(C2×D3)⋊C4—61no—
216C3×(C2×D3)⋊C4—61no—
217C3×Dic3⋊C4—21no—
218C3×Dic3⋊C4—21no—
219C3×Dic3⋊C4—31no—
220C3×Dic3⋊C4—31no—
221C3×Dic3⋊C4C2×D311yescharacteristic, complemented
222C3×Dic3⋊C4C2×D311yescharacteristic, complemented
223C3×Dic3⋊C4C2×D311yescharacteristic, complemented
224C3×Dic3⋊C4C2×D311yescharacteristic, complemented
225C3×C4×Dic3—31no—
226C3×C4×Dic3—31no—
227#3724—31no—
228#3724—31no—
229#3724—61no—
230#3724C2×D311yescharacteristic, complemented
231Dic3⋊Dic3—31no—
232Dic3⋊Dic3—31no—
233Dic3⋊Dic3—61no—
234#3722—31no—
235#3722C2×D311yescharacteristic
236#3722C2×D311yescharacteristic
237#3722C2×D311yescharacteristic
238#3722C2×D311yescharacteristic, complemented
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—61no—
252(C2×D3)⋊Dic3—61no—
253(C2×D3)⋊Dic3—61no—
254(C2×D3)⋊Dic3—61no—
255(C2×D3)⋊Dic3—61no—
256(C2×D3)⋊Dic3C2×D311yescharacteristic, complemented
257(C2×D3)⋊Dic3C2×D311yescharacteristic, complemented
258Dic32—31no—
259Dic32—31no—
260Dic32—61no—
261Dic32C2×D311yescharacteristic, complemented
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×#123—91no—
290C3×#123—91no—
291C3×C4×D4—91no—
292#939—91no—
293#938—91no—
294#938—91no—
295#937—91no—
296#937—91no—
297#937—91no—
298#930—91no—
299#930—91no—
300#930—91no—
301#930—181no—
302#929—31no—
303C4×#67—31no—
304C4×#67—91no—
305C4×#67—91no—
306C2×(C2×D3)⋊C4—91no—
307#898—91no—
308#898—91no—
309#898—91no—
310#898—181no—
311#897—91no—
312#897—91no—
313#897—181no—
314#894—31no—
315#894—31no—
316#894—31no—
317#893—31no—
318#893—91no—
319#885—91no—
320#885—91no—
321#885—91no—
322#885—91no—
323#885—91no—
324#884—91no—
325#884—91no—
326#884—91no—
327#882—91no—
328#882—91no—
329#882—91no—
330D3×C22⋊C4—91no—
331D3×C22⋊C4—91no—
332#879—91no—
333#879—91no—
334#878—91no—
335#876—91no—
336#875—91no—
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×C4—121no—
376C2×C32×C4C22×D311yescharacteristic
377C2×C32×C4C22×D311yescharacteristic
378C2×C32×C4C22×D311yescharacteristic
379#638—121no—
380#638—121no—
381C2×C3⋊Dic3—31no—
382C2×C3⋊Dic3—31no—
383C2×C3⋊Dic3—31no—
384C2×C3⋊Dic3—31no—
385C2×C3⋊Dic3—31no—
386C2×C3⋊Dic3—31no—
387C2×C3⋊Dic3—61no—
388C2×C3⋊Dic3—61no—
389C2×C3⋊Dic3—61no—
390C2×C3⋊Dic3—61no—
391C2×C3⋊Dic3—61no—
392C2×C3⋊Dic3—61no—
393C2×C3⋊Dic3—121no—
394C2×C3⋊Dic3—121no—
395C2×C3⋊Dic3C22×D311yescharacteristic
396C2×C3⋊Dic3C22×D311yescharacteristic
397C4⋊(C3⋊D3)—41no—
398C4×C3⋊D3—121no—
399#634—121no—
400C3×#67—62no—
401C3×#67—121no—
402C2×C3×Dic3—21no—
403C2×C3×Dic3—21no—
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—61no—
412C2×C3×Dic3—61no—
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
422C2×C3×Dic3C22×D311yescharacteristic
423C3×D12—62no—
424C3×D12—121no—
425C3×D12—121no—
426C3×D12—122no—
427C3×D12—121no—
428C3×C4×D3—41no—
429C3×C4×D3—41no—
430C3×C4×D3—42no—
431C3×C4×D3—121no—
432C3×C4×D3—121no—
433C3×C4×D3—121no—
434C3×C4×D3—121no—
435#627—121no—
436#627—121no—
437#627—122no—
438#626—22no—
439#626—41no—
440#626—62no—
441#626—62no—
442#626—121no—
443#626—121no—
444#625—62no—
445#625—121no—
446#625—121no—
447#625—121no—
448#625—121no—
449#625—121no—
450#625—122no—
451#625—122no—
452#624—41no—
453#624—41no—
454D3×Dic3—121no—
455D3×Dic3—121no—
456D3×Dic3—122no—
457#538—271noSylow
458C2×C33C2×#4111yescharacteristic
459C2×C33H(5,𝔽2)11yescharacteristic
460C2×C33H(5,𝔽2)11yescharacteristic
461C3×C3⋊D3—22no—
462C3×C3⋊D3—41no—
463C3×C3⋊D3—41no—
464C3×C3⋊D3—41no—
465C32×D3—41no—
466C23×D3—91no—
467C23×D3—91no—
468C23×D3—91no—
469C2×C3×D4—91no—
470C2×C3×D4—91no—
471C2×C3×D4—91no—
472C22×C3×C4—31no—
473C22×C3×C4—31no—
474C22×C3×C4—61no—
475C22×C3×C4—91no—
476C22×C3×C4—91no—
477C2×#67—31no—
478C2×#67—31no—
479C2×#67—91no—
480C2×#67—91no—
481C2×#67—91no—
482C2×#67—91no—
483C2×#67—91no—
484C2×#67—91no—
485C2×#67—91no—
486C2×#67—91no—
487C2×#67—91no—
488C2×#67—91no—
489C2×#67—181no—
490C2×#67—181no—
491C22×Dic3—91no—
492C2×D12—31no—
493C2×D12—31no—
494C2×D12—31no—
495C2×D12—31no—
496C2×D12—61no—
497C2×D12—91no—
498C2×D12—91no—
499C2×C4×D3—31no—
500C2×C4×D3—31no—
501C2×C4×D3—31no—
502C2×C4×D3—31no—
503C2×C4×D3—91no—
504C2×C4×D3—91no—
505C2×C4×D3—181no—
506C2×C4×D3D3211yescharacteristic, complemented
507C2×Dic6—91no—
508C2×Dic6—91no—
509C2×Dic6—91no—
510C2×Dic6—181no—
511C3×C4⋊C4—31no—
512C3×C4⋊C4—31no—
513C3×C4⋊C4—31no—
514C3×C4⋊C4—31no—
515C3×C4⋊C4—61no—
516C3×C4⋊C4—61no—
517C3×C4⋊C4—91no—
518C3×C22⋊C4—91no—
519C3×C22⋊C4—91no—
520C3×C22⋊C4—91no—
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—91no—
530#217—91no—
531#217—91no—
532#217—91no—
533#217—91no—
534#217—91no—
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—31no—
545(C2×D3)⋊C4—31no—
546(C2×D3)⋊C4—31no—
547(C2×D3)⋊C4—31no—
548(C2×D3)⋊C4—31no—
549(C2×D3)⋊C4—61no—
550(C2×D3)⋊C4—61no—
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—181no—
564(C2×D3)⋊C4—181no—
565(C2×D3)⋊C4—181no—
566(C2×D3)⋊C4—181no—
567(C2×D3)⋊C4—181no—
568C4⋊Dic3—91no—
569C4⋊Dic3—91no—
570C4⋊Dic3—91no—
571C4⋊Dic3—91no—
572C4⋊Dic3—91no—
573C4⋊Dic3—181no—
574C4⋊Dic3—181no—
575C4⋊Dic3—181no—
576C4⋊Dic3—181no—
577C4⋊Dic3—361no—
578Dic3⋊C4—31no—
579Dic3⋊C4—31no—
580Dic3⋊C4—91no—
581Dic3⋊C4—91no—
582Dic3⋊C4—91no—
583Dic3⋊C4—91no—
584Dic3⋊C4—181no—
585Dic3⋊C4D3211yescharacteristic, complemented
586Dic3⋊C4D3211yescharacteristic, complemented
587C4×Dic3—31no—
588C4×Dic3—31no—
589C4×Dic3—91no—
590C4×Dic3—91no—
591C4×Dic3—91no—
592C4×Dic3—181no—
593C22×C32—21no—
594C22×C32—21no—
595C22×C32—21no—
596C22×C32—41no—
597C22×C32—61no—
598C22×C32—61no—
599C22×C32—61no—
600C22×C32C23×D311yescharacteristic
601C22×C32C23×D311yescharacteristic
602C22×C32C23×D311yescharacteristic
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—21no—
613C2×C3⋊D3—21no—
614C2×C3⋊D3#23512yes—
615C2×C3×D3—22no—
616C2×C3×D3—21no—
617C2×C3×D3—21no—
618C2×C3×D3—21no—
619C2×C3×D3—21no—
620C2×C3×D3—21no—
621C2×C3×D3—21no—
622C2×C3×D3—32no—
623C2×C3×D3—32no—
624C2×C3×D3—41no—
625C2×C3×D3—41no—
626C2×C3×D3—62no—
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—61no—
648C2×C3×D3—61no—
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—
658C2×C3×D3—121no—
659C2×C3×D3—121no—
660D32—124no—
661D32—124no—
662D32—124no—
663C32×C4—21no—
664C32×C4—22no—
665C32×C4—21no—
666C32×C4—21no—
667C32×C4—41no—
668C32×C4—41no—
669C32×C4—42no—
670C32×C4—61no—
671C32×C4—61no—
672C32×C4—61no—
673C32×C4—61no—
674C32×C4—61no—
675C3⋊Dic3—21no—
676C3⋊Dic3—21no—
677C3⋊Dic3—61no—
678C3⋊Dic3—61no—
679C3⋊Dic3—61no—
680C3⋊Dic3—61no—
681C3⋊Dic3—61no—
682C3⋊Dic3—61no—
683C3⋊Dic3—121no—
684C3⋊Dic3—121no—
685C3⋊Dic3—121no—
686C3⋊Dic3—121no—
687C3⋊Dic3—121no—
688C3⋊Dic3—121no—
689C3⋊Dic3—241no—
690C3⋊Dic3—241no—
691C3×Dic3—22no—
692C3×Dic3—21no—
693C3×Dic3—21no—
694C3×Dic3—21no—
695C3×Dic3—21no—
696C3×Dic3—21no—
697C3×Dic3—21no—
698C3×Dic3—21no—
699C3×Dic3—21no—
700C3×Dic3—21no—
701C3×Dic3—21no—
702C3×Dic3—41no—
703C3×Dic3—41no—
704C3×Dic3—41no—
705C3×Dic3—41no—
706C3×Dic3—61no—
707C3×Dic3—61no—
708C3×Dic3—61no—
709C3×Dic3—61no—
710C3×Dic3—121no—
711C3×Dic3—121no—
712#126—271no—
713#126—271no—
714#124—271no—
715#124—271no—
716#123—91no—
717#123—91no—
718C22⋊Q8—271no—
719#121—271no—
720#121—271no—
721#121—271no—
722#120—271no—
723#120—271no—
724C4×D4—91no—
725C4×D4—271no—
726C2×C22⋊C4—271no—
727C33#53811yescharacteristic, complemented, Sylow
728C23×C3—31no—
729C23×C3—31no—
730C23×C3—61no—
731C23×C3—91no—
732C23×C3—91no—
733C23×C3—91no—
734C23×C3—91no—
735C22×D3—31no—
736C22×D3—31no—
737C22×D3—31no—
738C22×D3—31no—
739C22×D3—31no—
740C22×D3—31no—
741C22×D3—31no—
742C22×D3—31no—
743C22×D3—61no—
744C22×D3—61no—
745C22×D3—61no—
746C22×D3—61no—
747C22×D3—182no—
748C22×D3—182no—
749C22×D3—182no—
750C22×D3—361no—
751C22×D3—361no—
752C22×D3—361no—
753C22×D3—361no—
754C22×D3—361no—
755C22×D3—361no—
756C22×D3C2×D3211yescharacteristic
757C3×D4—182no—
758C3×D4—361no—
759C3×D4—361no—
760C2×C3×C4—21no—
761C2×C3×C4—21no—
762C2×C3×C4—21no—
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—31no—
773C2×C3×C4—41no—
774C2×C3×C4—61no—
775C2×C3×C4—61no—
776C2×C3×C4—61no—
777C2×C3×C4—61no—
778C2×C3×C4—61no—
779C2×C3×C4—91no—
780C2×C3×C4—91no—
781C2×C3×C4—121no—
782C2×C3×C4—121no—
783C2×C3×C4—122no—
784C2×C3×C4—361no—
785C2×C3×C4—361no—
786C2×C3×C4C2×D3211yescharacteristic
787C2×C3×C4C2×D3211yescharacteristic
788C2×C3×C4C2×D3211yescharacteristic
789#67—62no—
790#67—121no—
791#67—182no—
792#67—182no—
793#67—361no—
794#67—361no—
795#67—361no—
796#67—361no—
797#67—361no—
798#67—361no—
799#67—361no—
800#67—361no—
801#67—362no—
802#67—362no—
803C2×Dic3—31no—
804C2×Dic3—31no—
805C2×Dic3—31no—
806C2×Dic3—31no—
807C2×Dic3—61no—
808C2×Dic3—61no—
809C2×Dic3—91no—
810C2×Dic3—91no—
811C2×Dic3—91no—
812C2×Dic3—91no—
813C2×Dic3—91no—
814C2×Dic3—91no—
815C2×Dic3—181no—
816C2×Dic3—181no—
817C2×Dic3—181no—
818C2×Dic3—181no—
819C2×Dic3—181no—
820C2×Dic3—181no—
821C2×Dic3—361no—
822C2×Dic3—361no—
823C2×Dic3—361no—
824C2×Dic3C2×D3211yescharacteristic
825C2×Dic3C2×D3211yescharacteristic
826C2×Dic3C2×D3211yescharacteristic
827C2×Dic3C2×D3211yescharacteristic
828C2×Dic3C2×D3211yescharacteristic
829D12—62no—
830D12—121no—
831D12—121no—
832D12—122no—
833D12—121no—
834D12—182no—
835D12—361no—
836C4×D3—41no—
837C4×D3—121no—
838C4×D3—121no—
839C4×D3—121no—
840C4×D3—121no—
841C4×D3—361no—
842C4×D3—361no—
843C4×D3—362no—
844Dic6—361no—
845Dic6—361no—
846Dic6—361no—
847Dic6—362no—
848C2×C32—21no—
849C2×C32—21no—
850C2×C32—21no—
851C2×C32—21no—
852C2×C32—21no—
853C2×C32—21no—
854C2×C32—21no—
855C2×C32—21no—
856C2×C32—21no—
857C2×C32—41no—
858C2×C32—41no—
859C2×C32—41no—
860C2×C32—121no—
861C2×C32C2×#23511yescharacteristic
862C2×C32#100411yescharacteristic
863C2×C32#100411yescharacteristic
864C2×C32#100411yescharacteristic
865C2×C32D3×#4111yescharacteristic
866C2×C32D3×#4111yescharacteristic
867C2×C32#100911yescharacteristic
868C2×C32#100911yescharacteristic
869C2×C32#100911yescharacteristic
870C3⋊D3—22no—
871C3⋊D3—41no—
872C3⋊D3—41no—
873C3⋊D3—41no—
874C3×D3—42no—
875C3×D3—41no—
876C3×D3—41no—
877C3×D3—62no—
878C3×D3—62no—
879C3×D3—122no—
880C3×D3—121no—
881C3×D3—121no—
882C3×D3—121no—
883C3×D3—121no—
884C3×D3—121no—
885C3×D3—121no—
886C3×D3—241no—
887C3×D3—241no—
888C3×D3—241no—
889C24—271no—
890C2×Q8—271no—
891C2×D4—91no—
892C2×D4—91no—
893C2×D4—91no—
894C2×D4—271no—
895C2×D4—271no—
896C2×D4—271no—
897C2×D4—271no—
898C22×C4—31no—
899C22×C4—91no—
900C22×C4—91no—
901C22×C4—271no—
902C4⋊C4—31no—
903C4⋊C4—31no—
904C4⋊C4—91no—
905C4⋊C4—271no—
906C4⋊C4—271no—
907C4⋊C4—271no—
908C22⋊C4—91no—
909C22⋊C4—91no—
910C22⋊C4—91no—
911C22⋊C4—91no—
912C22⋊C4—91no—
913C22⋊C4—91no—
914C22⋊C4—91no—
915C22⋊C4—91no—
916C22⋊C4—271no—
917C22⋊C4—271no—
918C22⋊C4—271no—
919C22⋊C4—271no—
920C22⋊C4—271no—
921C22⋊C4—271no—
922C42—91no—
923C42—271no—
924C22×C3—21no—
925C22×C3—21no—
926C22×C3—21no—
927C22×C3—41no—
928C22×C3—62no—
929C22×C3—61no—
930C22×C3—61no—
931C22×C3—61no—
932C22×C3—61no—
933C22×C3—61no—
934C22×C3—61no—
935C22×C3—92no—
936C22×C3—121no—
937C22×C3—121no—
938C22×C3—181no—
939C22×C3—181no—
940C22×C3—181no—
941C22×C3—181no—
942C22×C3—181no—
943C22×C3—181no—
944C22×C3—181no—
945C22×C3—181no—
946C22×C3—181no—
947C22×C3—181no—
948C22×C3—181no—
949C22×C3C22×D3211yescharacteristic
950C22×C3C22×D3211yescharacteristic
951C22×C3C22×D3211yescharacteristic
952C2×D3—21no—
953C2×D3—21no—
954C2×D3—21no—
955C2×D3—32no—
956C2×D3—32no—
957C2×D3—62no—
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—61no—
977C2×D3—61no—
978C2×D3—61no—
979C2×D3—61no—
980C2×D3—121no—
981C2×D3—121no—
982C2×D3—121no—
983C2×D3—121no—
984C2×D3—121no—
985C2×D3—121no—
986C2×D3—121no—
987C2×D3—121no—
988C2×D3—121no—
989C2×D3—121no—
990C2×D3—121no—
991C2×D3—364no—
992C2×D3—364no—
993C2×D3—364no—
994C3×C4—22no—
995C3×C4—21no—
996C3×C4—21no—
997C3×C4—21no—
998C3×C4—41no—
999C3×C4—41no—
1000C3×C4—42no—
1001C3×C4—62no—
1002C3×C4—61no—
1003C3×C4—61no—
1004C3×C4—61no—
1005C3×C4—61no—
1006C3×C4—61no—
1007C3×C4—61no—
1008C3×C4—61no—
1009C3×C4—61no—
1010C3×C4—61no—
1011C3×C4—61no—
1012C3×C4—121no—
1013C3×C4—121no—
1014C3×C4—121no—
1015C3×C4—121no—
1016C3×C4—181no—
1017C3×C4—181no—
1018Dic3—21no—
1019Dic3—21no—
1020Dic3—21no—
1021Dic3—21no—
1022Dic3—21no—
1023Dic3—61no—
1024Dic3—61no—
1025Dic3—61no—
1026Dic3—61no—
1027Dic3—121no—
1028Dic3—121no—
1029Dic3—181no—
1030Dic3—181no—
1031Dic3—181no—
1032Dic3—181no—
1033Dic3—181no—
1034Dic3—181no—
1035Dic3—361no—
1036Dic3—361no—
1037Dic3—361no—
1038Dic3—361no—
1039Dic3—361no—
1040Dic3—361no—
1041Dic3—721no—
1042Dic3—721no—
1043C32—21no—
1044C32—21no—
1045C32—21no—
1046C32—41no—
1047C32#556011yescharacteristic, complemented
1048C32#565711yescharacteristic, complemented
1049C32#565711yescharacteristic, complemented
1050C23—31no—
1051C23—91no—
1052C23—91no—
1053C23—91no—
1054C23—91no—
1055C23—542no—
1056C23—1081no—
1057C23—1081no—
1058Q8—1081no—
1059D4—182no—
1060D4—361no—
1061D4—361no—
1062D4—542no—
1063D4—1081no—
1064D4—1081no—
1065D4—1081no—
1066C2×C4—31no—
1067C2×C4—31no—
1068C2×C4—31no—
1069C2×C4—31no—
1070C2×C4—31no—
1071C2×C4—91no—
1072C2×C4—91no—
1073C2×C4—121no—
1074C2×C4—271no—
1075C2×C4—271no—
1076C2×C4—361no—
1077C2×C4—361no—
1078C2×C4—1081no—
1079C2×C4D3311yescharacteristic
1080C2×C3—21no—
1081C2×C3—21no—
1082C2×C3—21no—
1083C2×C3—21no—
1084C2×C3—21no—
1085C2×C3—21no—
1086C2×C3—21no—
1087C2×C3—21no—
1088C2×C3—21no—
1089C2×C3—41no—
1090C2×C3—41no—
1091C2×C3—41no—
1092C2×C3—122no—
1093C2×C3—121no—
1094C2×C3—121no—
1095C2×C3—182no—
1096C2×C3—361no—
1097C2×C3—361no—
1098C2×C3—361no—
1099C2×C3D3×#23511yescharacteristic
1100C2×C3D3×#23511yescharacteristic
1101C2×C3#6430811yescharacteristic
1102C2×C3#6430811yescharacteristic
1103C2×C3#6431311yescharacteristic
1104C2×C3#6431311yescharacteristic
1105C2×C3#6431911yescharacteristic
1106C2×C3#6432011yescharacteristic
1107C2×C3#6433011yescharacteristic
1108D3—41no—
1109D3—62no—
1110D3—62no—
1111D3—122no—
1112D3—121no—
1113D3—121no—
1114D3—121no—
1115D3—121no—
1116D3—121no—
1117D3—121no—
1118D3—241no—
1119D3—241no—
1120D3—241no—
1121C22—61no—
1122C22—61no—
1123C22—61no—
1124C22—92no—
1125C22—181no—
1126C22—181no—
1127C22—181no—
1128C22—181no—
1129C22—181no—
1130C22—181no—
1131C22—181no—
1132C22—181no—
1133C22—181no—
1134C22—181no—
1135C22—181no—
1136C22—1084no—
1137C22C2×D3311yescharacteristic
1138C4—21no—
1139C4—61no—
1140C4—61no—
1141C4—61no—
1142C4—61no—
1143C4—61no—
1144C4—181no—
1145C4—181no—
1146C4—541no—
1147C4—541no—
1148C3—21no—
1149C3—21no—
1150C3—21no—
1151C3—41no—
1152C3#1059463911yescharacteristic, complemented
1153C3#1059465911yescharacteristic, complemented
1154C3#1059508511yescharacteristic, complemented
1155C2—121no—
1156C2—182no—
1157C2—361no—
1158C2—361no—
1159C2—361no—
1160C2#1172438911yescharacteristic
1161C2#1172439011yescharacteristic
1162C2#1172441511yescharacteristic
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. #11723515C2semidirect
3. #11723483C2semidirect
4. #11723408C2semidirect
5. C3×#63904C2semidirect
6. C3×#63897C2semidirect
7. C3×#63850C2semidirect
8. #11723023C2semidirect
9. #11723010C2semidirect
10. #11723009C2semidirect
11. #11722967C2semidirect
12. #11722957C2semidirect
13. #11722951C2semidirect
14. #11722931C2semidirect
15. #11722905C2semidirect
21. C2×C32×C4×D3C22semidirect
24. C2×#6293C22semidirect
26. C2×#6290C22semidirect
31. C2×C3×#624C22semidirect
32. C4⋊(C3⋊(C3⋊Dic3))C22semidirect
35. C32×Dic3⋊C4C22semidirect
36. C32×Dic3⋊C4C22semidirect
38. #88806C22semidirect
39. Dic3⋊(C3⋊Dic3)C22semidirect
44. #88803C22semidirect
45. Dic3×C3⋊Dic3C22semidirect
46. C3×#3724C22semidirect
50. C3×#3722C22semidirect
51. C3×(C2×D3)⋊Dic3C22semidirect
52. C3×(C2×D3)⋊Dic3C22semidirect
53. C3×Dic32C22semidirect
86. #63904D3semidirect
88. #63897D3semidirect
101. #63850D3semidirect
156. C2×C3×C4×D3C2×D3semidirect
157. C2×C3×C4×D3C2×D3semidirect
176. C2×#624C2×D3semidirect
221. C3×Dic3⋊C4C2×D3semidirect
222. C3×Dic3⋊C4C2×D3semidirect
223. C3×Dic3⋊C4C2×D3semidirect
224. C3×Dic3⋊C4C2×D3semidirect
230. #3724C2×D3semidirect
238. #3722C2×D3semidirect
256. (C2×D3)⋊Dic3C2×D3semidirect
257. (C2×D3)⋊Dic3C2×D3semidirect
261. Dic32C2×D3semidirect
506. C2×C4×D3D32semidirect
585. Dic3⋊C4D32semidirect
586. Dic3⋊C4D32semidirect
727. C33#538semidirect
1047. C32#5560semidirect
1048. C32#5657semidirect
1049. C32#5657semidirect
1152. C3#10594639semidirect
1153. C3#10594659semidirect
1154. C3#10595085semidirect

Maximal subgroups

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

subgroupindex
#117237012
#117235152
#117234832
#117234082
C3×#639042
C3×#638972
C3×#638502
#117230232
#117230102
#117230092
#117229672
#117229572
#117229512
#117229312
#117229052
#105950853
#105946593
#105946393