Finite Group Databasebeta

← #13168026

Subgroups — #13168026

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#11723686C211yesmaximal, characteristic, complemented
2#11723515C211yesmaximal, characteristic, complemented
3#11723491C211yesmaximal, characteristic, complemented
4#11723430C211yesmaximal, characteristic, complemented
5C3×#63923C211yesmaximal, characteristic, complemented
6C3×#63905C211yesmaximal, characteristic, complemented
7C3×#63879C211yesmaximal, characteristic, complemented
8#11723024C211yesmaximal, characteristic, complemented
9#11723009C211yesmaximal, characteristic, complemented
10#11723002C211yesmaximal, characteristic, complemented
11#11722965C211yesmaximal, characteristic, complemented
12#11722954C211yesmaximal, characteristic, complemented
13#11722946C211yesmaximal, characteristic, complemented
14#11722927C211yesmaximal, characteristic, complemented
15D3×(C2×D3)⋊Dic3C211yesmaximal, characteristic, complemented
16#10595085—31nomaximal
17#10594238—31nomaximal
18#10594213—31nomaximal
19C22×C3×D32C2211yescharacteristic
20C2×C3×C4⋊(C3⋊D3)C2211yescharacteristic
21C2×C32×C4×D3C2211yescharacteristic, complemented
22C2×#6294C2211yescharacteristic, complemented
23C2×#6293C2211yescharacteristic, complemented
24C2×#6290C2211yescharacteristic
25C2×#6290C2211yescharacteristic, complemented
26C2×D3×C3⋊Dic3C2211yescharacteristic
27C2×C3×#626C2211yescharacteristic
28C2×C3×#626C2211yescharacteristic
29C2×C3×#625C2211yescharacteristic
30C2×C3×#625C2211yescharacteristic
31C2×C3×D3×Dic3C2211yescharacteristic
32C4⋊(C3⋊(C3⋊Dic3))C2211yescharacteristic, complemented
33C3×#3750C2211yescharacteristic, complemented
34C3×#3750C2211yescharacteristic, complemented
35C32×(C2×D3)⋊C4C2211yescharacteristic
36C32×(C2×D3)⋊C4C2211yescharacteristic
37#88814C2211yescharacteristic
38#88814C2211yescharacteristic
39#88814C2211yescharacteristic, complemented
40#88807C2211yescharacteristic, complemented
41#88806C2211yescharacteristic, complemented
42#88803C2211yescharacteristic
43#88803C2211yescharacteristic, complemented
44(C2×D3)⋊(C3⋊Dic3)C2211yescharacteristic
45(C2×D3)⋊(C3⋊Dic3)C2211yescharacteristic
46(C2×D3)⋊(C3⋊Dic3)C2211yescharacteristic
47Dic3×C3⋊Dic3C2211yescharacteristic, complemented
48C3×Dic3⋊Dic3C2211yescharacteristic, complemented
49C3×#3722C2211yescharacteristic
50C3×(C2×D3)⋊Dic3C2211yescharacteristic
51C3×(C2×D3)⋊Dic3C2211yescharacteristic, complemented
52C3×(C2×D3)⋊Dic3C2211yescharacteristic, complemented
53C3×Dic32C2211yescharacteristic, complemented
54#64139—31no—
55#64088—31no—
56#64087—31no—
57C3×#929—31no—
58C3×C4×#67—31no—
59C3×#883—31no—
60C3×#882—31no—
61C3×#882—31no—
62C3×#67⋊C4—31no—
63#63983—31no—
64#63980—31no—
65#63976—31no—
66#63976—31no—
67Dic3×#67—31no—
68#63971—31no—
69#63970—31no—
70D3×#217—31no—
71C2×(C2×D3)⋊Dic3—31no—
72#63959—31no—
73#63958—31no—
74#63953—31no—
75#63923D311yescharacteristic, complemented
76D3×(C2×D3)⋊C4—31no—
77#63915—31no—
78#63913—31no—
79#63908—31no—
80#63908—31no—
81#63908—61no—
82#63905D311yescharacteristic, complemented
83#63904—31no—
84#63898—31no—
85#63897—31no—
86#63893—31no—
87#63893—31no—
88#63893—61no—
89#63885—31no—
90#63885—31no—
91#63884—31no—
92#63884—31no—
93#63879D311yescharacteristic, complemented
94#63868—31no—
95#63861—31no—
96#63861—31no—
97#63861—61no—
98#63860—31no—
99#63859—31no—
100#63858—31no—
101#63852—31no—
102C22×C3×C3⋊D3C2311yescharacteristic
103C22×C3×C3⋊D3C2311yescharacteristic
104C22×C32×D3C2311yescharacteristic
105C22×C32×D3C2311yescharacteristic
106C22×C32×D3C2311yescharacteristic
107C2×C3×D32—22no—
108C2×C3×D32—41no—
109C2×C3×D32—41no—
110C2×C33×C4C2311yescharacteristic
111C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
112C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
113C2×C3×C3⋊Dic3C2311yescharacteristic
114C2×C3×C3⋊Dic3C2311yescharacteristic
115C2×C3×C3⋊Dic3C2311yescharacteristic
116C2×C3×C3⋊Dic3C2311yescharacteristic
117C3×C4⋊(C3⋊D3)—41no—
118C2×C32×Dic3C2311yescharacteristic
119C2×C32×Dic3C2311yescharacteristic
120C2×C32×Dic3C2311yescharacteristic
121C32×C4×D3—41no—
122#6294—41no—
123#6293—41no—
124#6290—41no—
125#6290—41no—
126D3×C3⋊Dic3—41no—
127C3×#626—22no—
128C3×#626—41no—
129C3×#625—22no—
130C3×#625—41no—
131C3×D3×Dic3—41no—
132#5657—91no—
133#5593—91no—
134#5560—91no—
135C23×C3×D3—31no—
136C23×C3×D3—31no—
137C22×D32C2×D311yescharacteristic
138C22×C32×C4—31no—
139C2×#638—31no—
140C2×#638—31no—
141C22×C3⋊Dic3—31no—
142C2×C4⋊(C3⋊D3)C2×D311yescharacteristic
143C2×#634—31no—
144C2×C3×#67—31no—
145C2×C3×#67—31no—
146C2×C3×#67—31no—
147C2×C3×#67—31no—
148C2×C3×#67—31no—
149C2×C3×#67—31no—
150C22×C3×Dic3—31no—
151C2×C3×D12—31no—
152C2×C3×D12—31no—
153C2×C3×D12—31no—
154C2×C3×D12—31no—
155C2×C3×D12—61no—
156C2×C3×C4×D3—21no—
157C2×C3×C4×D3—31no—
158C2×C3×C4×D3C2×D311yescharacteristic, complemented
159C2×C3×C4×D3C2×D311yescharacteristic, complemented
160C2×#627—31no—
161C2×#627—31no—
162C2×#627—61no—
163C2×#626C2×D311yescharacteristic
164C2×#626C2×D311yescharacteristic
165C2×#625—31no—
166C2×#625—31no—
167C2×#625—31no—
168C2×#625—31no—
169C2×#625—61no—
170C2×#625—61no—
171C2×#625C2×D311yescharacteristic
172C2×#625C2×D311yescharacteristic
173C2×#624—31no—
174C2×D3×Dic3—31no—
175C2×D3×Dic3—31no—
176C2×D3×Dic3—31no—
177C2×D3×Dic3—31no—
178C2×D3×Dic3—61no—
179C2×D3×Dic3C2×D311yescharacteristic
180C32×C22⋊C4—31no—
181C32×C22⋊C4—31no—
182#3757—31no—
183#3757—31no—
184#3757—31no—
185#3752—31no—
186#3752—31no—
187C4⋊(C3⋊Dic3)—31no—
188C4⋊(C3⋊Dic3)—31no—
189C4⋊(C3⋊Dic3)—31no—
190C4⋊(C3⋊Dic3)—61no—
191C4⋊(C3⋊Dic3)—61no—
192C4⋊(C3⋊Dic3)—61no—
193C4⋊(C3⋊Dic3)—121no—
194#3750—31no—
195#3750—31no—
196#3750C2×D311yescharacteristic, complemented
197#3750C2×D311yescharacteristic, complemented
198C4×C3⋊Dic3—31no—
199C3×#217—31no—
200C3×#217—31no—
201C3×#217—31no—
202C3×(C2×D3)⋊C4—21no—
203C3×(C2×D3)⋊C4—21no—
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)⋊C4C2×D311yescharacteristic
210C3×(C2×D3)⋊C4C2×D311yescharacteristic
211C3×(C2×D3)⋊C4C2×D311yescharacteristic
212C3×(C2×D3)⋊C4C2×D311yescharacteristic
213C3×C4⋊Dic3—31no—
214C3×Dic3⋊C4—31no—
215C3×Dic3⋊C4—31no—
216C3×Dic3⋊C4—31no—
217C3×Dic3⋊C4—31no—
218C3×Dic3⋊C4—31no—
219C3×Dic3⋊C4—61no—
220C3×Dic3⋊C4—61no—
221C3×C4×Dic3—31no—
222C3×C4×Dic3—31no—
223#3724—31no—
224#3724—31no—
225#3724—61no—
226Dic3⋊Dic3—31no—
227Dic3⋊Dic3—31no—
228Dic3⋊Dic3—61no—
229Dic3⋊Dic3C2×D311yescharacteristic, complemented
230#3722—31no—
231#3722—31no—
232#3722—31no—
233#3722C2×D311yescharacteristic
234(C2×D3)⋊Dic3—31no—
235(C2×D3)⋊Dic3—31no—
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—61no—
251(C2×D3)⋊Dic3—61no—
252(C2×D3)⋊Dic3—61no—
253(C2×D3)⋊Dic3—61no—
254(C2×D3)⋊Dic3—61no—
255(C2×D3)⋊Dic3C2×D311yescharacteristic
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×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—
278C3×D32—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×#120—91no—
291C3×C4×D4—91no—
292#953—91no—
293C2×#217—91no—
294#939—91no—
295#939—91no—
296#939—91no—
297#938—91no—
298#938—91no—
299#937—91no—
300#937—91no—
301#936—91no—
302#935—91no—
303D4×Dic3—91no—
304#930—91no—
305#930—91no—
306#930—181no—
307#929—31no—
308C4×#67—31no—
309C4×#67—91no—
310C2×(C2×D3)⋊C4—91no—
311#898—91no—
312#898—91no—
313#897—91no—
314#894—91no—
315#894—91no—
316#893—91no—
317#885—91no—
318#885—91no—
319#885—91no—
320#885—91no—
321#884—91no—
322#884—91no—
323#883—31no—
324#882—31no—
325#882—31no—
326#67⋊C4—31no—
327D3×C22⋊C4—91no—
328#879—91no—
329#879—91no—
330#879—91no—
331#879—181no—
332#878—91no—
333#878—91no—
334#878—181no—
335#876—91no—
336#875—91no—
337C23×C32—31no—
338C23×C32—31no—
339C23×C32—31no—
340C22×C3⋊D3C22×D311yescharacteristic
341C22×C3⋊D3C22×D311yescharacteristic
342C22×C3×D3—21no—
343C22×C3×D3—21no—
344C22×C3×D3—21no—
345C22×C3×D3—31no—
346C22×C3×D3—31no—
347C22×C3×D3—31no—
348C22×C3×D3—31no—
349C22×C3×D3—61no—
350C22×C3×D3—61no—
351C22×C3×D3—62no—
352C22×C3×D3—62no—
353C22×C3×D3—121no—
354C22×C3×D3—121no—
355C22×C3×D3—121no—
356C22×C3×D3—121no—
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—22no—
364C2×D32—41no—
365C2×D32—41no—
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—41no—
373C2×C32×C4—121no—
374C2×C32×C4C22×D311yescharacteristic
375C2×C32×C4C22×D311yescharacteristic
376C2×C32×C4C22×D311yescharacteristic
377#638—121no—
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⋊Dic3C22×D311yescharacteristic
395C2×C3⋊Dic3C22×D311yescharacteristic
396C2×C3⋊Dic3C22×D311yescharacteristic
397C2×C3⋊Dic3C22×D311yescharacteristic
398C4⋊(C3⋊D3)—41no—
399#634—121no—
400C3×#67—62no—
401C3×#67—62no—
402C3×#67—62no—
403C3×#67—121no—
404C3×#67—121no—
405C3×#67—121no—
406C2×C3×Dic3—21no—
407C2×C3×Dic3—21no—
408C2×C3×Dic3—21no—
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—121no—
422C2×C3×Dic3C22×D311yescharacteristic
423C2×C3×Dic3C22×D311yescharacteristic
424C2×C3×Dic3C22×D311yescharacteristic
425C2×C3×Dic3C22×D311yescharacteristic
426C2×C3×Dic3C22×D311yescharacteristic
427C2×C3×Dic3C22×D311yescharacteristic
428C3×D12—62no—
429C3×D12—121no—
430C3×D12—121no—
431C3×D12—122no—
432C3×D12—121no—
433C3×C4×D3—41no—
434C3×C4×D3—41no—
435C3×C4×D3—42no—
436C3×C4×D3—121no—
437#627—121no—
438#627—121no—
439#627—122no—
440#626—22no—
441#626—41no—
442#625—22no—
443#625—41no—
444#625—121no—
445#625—121no—
446#625—121no—
447#625—121no—
448#625—122no—
449#625—122no—
450#624—121no—
451D3×Dic3—41no—
452D3×Dic3—121no—
453D3×Dic3—121no—
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—41no—
462C3×C3⋊D3—41no—
463C32×D3—22no—
464C32×D3—41no—
465C32×D3—41no—
466C24×C3—91no—
467C23×D3—31no—
468C23×D3—31no—
469C2×C3×D4—91no—
470C2×C3×D4—91no—
471C2×C3×D4—91no—
472C2×C3×D4—91no—
473C2×C3×D4—91no—
474C22×C3×C4—31no—
475C22×C3×C4—31no—
476C22×C3×C4—61no—
477C22×C3×C4—91no—
478C2×#67—31no—
479C2×#67—31no—
480C2×#67—31no—
481C2×#67—31no—
482C2×#67—31no—
483C2×#67—31no—
484C2×#67—91no—
485C2×#67—91no—
486C2×#67—91no—
487C2×#67—91no—
488C2×#67—91no—
489C2×#67—91no—
490C2×#67—181no—
491C2×#67—181no—
492C22×Dic3—31no—
493C22×Dic3—91no—
494C22×Dic3—91no—
495C22×Dic3—91no—
496C22×Dic3—181no—
497C2×D12—31no—
498C2×D12—31no—
499C2×D12—31no—
500C2×D12—31no—
501C2×D12—61no—
502C2×C4×D3—31no—
503C2×C4×D3—91no—
504C2×C4×D3—91no—
505C2×C4×D3—91no—
506C2×C4×D3D3211yescharacteristic, complemented
507C2×Dic6—91no—
508C2×Dic6—91no—
509C2×Dic6—91no—
510C2×Dic6—181no—
511C3×C4⋊C4—91no—
512C3×C4⋊C4—91no—
513C3×C4⋊C4—91no—
514C3×C22⋊C4—31no—
515C3×C22⋊C4—31no—
516C3×C22⋊C4—31no—
517C3×C22⋊C4—31no—
518C3×C22⋊C4—61no—
519C3×C22⋊C4—61no—
520C3×C22⋊C4—91no—
521C3×C22⋊C4—91no—
522C3×C22⋊C4—91no—
523C3×C22⋊C4—91no—
524C3×C42—91no—
525#217—31no—
526#217—31no—
527#217—31no—
528#217—91no—
529#217—91no—
530#217—91no—
531#217—91no—
532#217—91no—
533#217—91no—
534#217—91no—
535#217—91no—
536#217—91no—
537#217—91no—
538#217—91no—
539#217—181no—
540#217—181no—
541#217—181no—
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—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—181no—
561(C2×D3)⋊C4—181no—
562(C2×D3)⋊C4D3211yescharacteristic
563(C2×D3)⋊C4D3211yescharacteristic
564C4⋊Dic3—31no—
565C4⋊Dic3—91no—
566C4⋊Dic3—91no—
567C4⋊Dic3—91no—
568C4⋊Dic3—91no—
569C4⋊Dic3—181no—
570C4⋊Dic3—181no—
571C4⋊Dic3—181no—
572C4⋊Dic3—361no—
573Dic3⋊C4—31no—
574Dic3⋊C4—31no—
575Dic3⋊C4—31no—
576Dic3⋊C4—31no—
577Dic3⋊C4—31no—
578Dic3⋊C4—61no—
579Dic3⋊C4—61no—
580Dic3⋊C4—91no—
581Dic3⋊C4—91no—
582Dic3⋊C4—91no—
583Dic3⋊C4—91no—
584Dic3⋊C4—91no—
585Dic3⋊C4—181no—
586Dic3⋊C4—181no—
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—32no—
597C22×C32—41no—
598C22×C32—61no—
599C22×C32—61no—
600C22×C32—61no—
601C22×C32—61no—
602C22×C32—61no—
603C22×C32—61no—
604C22×C32—61no—
605C22×C32—61no—
606C22×C32C23×D311yescharacteristic
607C22×C32C23×D311yescharacteristic
608C22×C32C23×D311yescharacteristic
609C2×C3⋊D3—21no—
610C2×C3⋊D3—21no—
611C2×C3⋊D3—21no—
612C2×C3⋊D3—21no—
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—22no—
620C2×C3×D3—21no—
621C2×C3×D3—21no—
622C2×C3×D3—21no—
623C2×C3×D3—21no—
624C2×C3×D3—21no—
625C2×C3×D3—21no—
626C2×C3×D3—21no—
627C2×C3×D3—21no—
628C2×C3×D3—21no—
629C2×C3×D3—21no—
630C2×C3×D3—21no—
631C2×C3×D3—21no—
632C2×C3×D3—22no—
633C2×C3×D3—41no—
634C2×C3×D3—41no—
635C2×C3×D3—41no—
636C2×C3×D3—41no—
637C2×C3×D3—41no—
638C2×C3×D3—41no—
639C2×C3×D3—41no—
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—61no—
650C2×C3×D3—61no—
651C2×C3×D3—61no—
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—124no—
659C2×C3×D3—124no—
660C2×C3×D3#23512yes—
661C2×C3×D3#23712yes—
662D32—44no—
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—
673C3⋊Dic3—21no—
674C3⋊Dic3—21no—
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—21no—
692C3×Dic3—21no—
693C3×Dic3—21no—
694C3×Dic3—21no—
695C3×Dic3—21no—
696C3×Dic3—21no—
697C3×Dic3—41no—
698C3×Dic3—41no—
699C3×Dic3—41no—
700C3×Dic3—62no—
701C3×Dic3—61no—
702C3×Dic3—61no—
703C3×Dic3—61no—
704C3×Dic3—61no—
705C3×Dic3—61no—
706C3×Dic3—61no—
707C3×Dic3—61no—
708C3×Dic3—61no—
709C3×Dic3—121no—
710C3×Dic3—121no—
711C3×Dic3—121no—
712#126—271no—
713#126—271no—
714#124—271no—
715#124—271no—
716#123—91no—
717#123—271no—
718C22⋊Q8—271no—
719#121—271no—
720#121—271no—
721#121—271no—
722#120—91no—
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—31no—
731C23×C3—31no—
732C23×C3—31no—
733C23×C3—31no—
734C23×C3—61no—
735C23×C3—61no—
736C23×C3—61no—
737C23×C3—91no—
738C23×C3—91no—
739C23×C3—182no—
740C23×C3—361no—
741C23×C3—361no—
742C22×D3—31no—
743C22×D3—31no—
744C22×D3—31no—
745C22×D3—31no—
746C22×D3—61no—
747C22×D3—61no—
748C22×D3—62no—
749C22×D3—62no—
750C22×D3—121no—
751C22×D3—121no—
752C22×D3—121no—
753C22×D3—121no—
754C22×D3C2×D3211yescharacteristic
755C22×D3C2×D3211yescharacteristic
756C22×D3C2×D3211yescharacteristic
757C3×D4—182no—
758C3×D4—182no—
759C3×D4—361no—
760C3×D4—361no—
761C3×D4—361no—
762C2×C3×C4—21no—
763C2×C3×C4—21no—
764C2×C3×C4—21no—
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—41no—
772C2×C3×C4—61no—
773C2×C3×C4—61no—
774C2×C3×C4—61no—
775C2×C3×C4—91no—
776C2×C3×C4—91no—
777C2×C3×C4—91no—
778C2×C3×C4—91no—
779C2×C3×C4—121no—
780C2×C3×C4—121no—
781C2×C3×C4—122no—
782C2×C3×C4—361no—
783C2×C3×C4C2×D3211yescharacteristic
784C2×C3×C4C2×D3211yescharacteristic
785C2×C3×C4C2×D3211yescharacteristic
786#67—62no—
787#67—62no—
788#67—62no—
789#67—121no—
790#67—121no—
791#67—121no—
792#67—361no—
793#67—361no—
794#67—361no—
795#67—361no—
796#67—361no—
797#67—361no—
798#67—362no—
799#67—362no—
800C2×Dic3—31no—
801C2×Dic3—31no—
802C2×Dic3—31no—
803C2×Dic3—31no—
804C2×Dic3—31no—
805C2×Dic3—31no—
806C2×Dic3—31no—
807C2×Dic3—31no—
808C2×Dic3—61no—
809C2×Dic3—61no—
810C2×Dic3—61no—
811C2×Dic3—61no—
812C2×Dic3—91no—
813C2×Dic3—91no—
814C2×Dic3—91no—
815C2×Dic3—91no—
816C2×Dic3—91no—
817C2×Dic3—91no—
818C2×Dic3—121no—
819C2×Dic3—181no—
820C2×Dic3—181no—
821C2×Dic3—181no—
822C2×Dic3—181no—
823C2×Dic3—181no—
824C2×Dic3—181no—
825C2×Dic3—361no—
826C2×Dic3—361no—
827C2×Dic3—361no—
828C2×Dic3—361no—
829C2×Dic3—361no—
830C2×Dic3—362no—
831C2×Dic3C2×D3211yescharacteristic
832C2×Dic3C2×D3211yescharacteristic
833C2×Dic3C2×D3211yescharacteristic
834D12—62no—
835D12—121no—
836D12—121no—
837D12—122no—
838D12—121no—
839C4×D3—41no—
840C4×D3—121no—
841C4×D3—361no—
842C4×D3—361no—
843C4×D3—361no—
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—62no—
861C2×C32—121no—
862C2×C32—121no—
863C2×C32C2×#23511yescharacteristic
864C2×C32C2×#23711yescharacteristic
865C2×C32#100411yescharacteristic
866C2×C32#100411yescharacteristic
867C2×C32#100411yescharacteristic
868C2×C32#100411yescharacteristic
869C2×C32D3×#4111yescharacteristic
870C2×C32#100911yescharacteristic
871C2×C32#100911yescharacteristic
872C3⋊D3—41no—
873C3⋊D3—41no—
874C3×D3—22no—
875C3×D3—22no—
876C3×D3—42no—
877C3×D3—42no—
878C3×D3—41no—
879C3×D3—41no—
880C3×D3—41no—
881C3×D3—41no—
882C3×D3—81no—
883C3×D3—121no—
884C3×D3—121no—
885C3×D3—121no—
886C3×D3—121no—
887C3×D3—241no—
888C3×D3—241no—
889C24—91no—
890C2×Q8—271no—
891C2×D4—91no—
892C2×D4—91no—
893C2×D4—91no—
894C2×D4—91no—
895C2×D4—91no—
896C2×D4—271no—
897C2×D4—271no—
898C22×C4—31no—
899C22×C4—91no—
900C22×C4—271no—
901C22×C4—271no—
902C4⋊C4—91no—
903C4⋊C4—91no—
904C4⋊C4—91no—
905C4⋊C4—271no—
906C4⋊C4—271no—
907C4⋊C4—271no—
908C22⋊C4—31no—
909C22⋊C4—31no—
910C22⋊C4—91no—
911C22⋊C4—91no—
912C22⋊C4—91no—
913C22⋊C4—91no—
914C22⋊C4—271no—
915C22⋊C4—271no—
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—32no—
928C22×C3—32no—
929C22×C3—41no—
930C22×C3—62no—
931C22×C3—62no—
932C22×C3—61no—
933C22×C3—61no—
934C22×C3—61no—
935C22×C3—61no—
936C22×C3—61no—
937C22×C3—61no—
938C22×C3—61no—
939C22×C3—61no—
940C22×C3—61no—
941C22×C3—61no—
942C22×C3—61no—
943C22×C3—61no—
944C22×C3—61no—
945C22×C3—61no—
946C22×C3—61no—
947C22×C3—61no—
948C22×C3—121no—
949C22×C3—121no—
950C22×C3—121no—
951C22×C3—121no—
952C22×C3—121no—
953C22×C3—121no—
954C22×C3—121no—
955C22×C3—181no—
956C22×C3—181no—
957C22×C3—181no—
958C22×C3—181no—
959C22×C3—181no—
960C22×C3—181no—
961C22×C3—364no—
962C22×C3C22×D3211yescharacteristic
963C22×C3C22×D3211yescharacteristic
964C22×C3C22×D3211yescharacteristic
965C2×D3—21no—
966C2×D3—21no—
967C2×D3—21no—
968C2×D3—21no—
969C2×D3—21no—
970C2×D3—21no—
971C2×D3—21no—
972C2×D3—21no—
973C2×D3—61no—
974C2×D3—61no—
975C2×D3—61no—
976C2×D3—61no—
977C2×D3—61no—
978C2×D3—61no—
979C2×D3—61no—
980C2×D3—61no—
981C2×D3—61no—
982C2×D3—61no—
983C2×D3—61no—
984C2×D3—61no—
985C2×D3—121no—
986C2×D3—121no—
987C2×D3—121no—
988C2×D3—121no—
989C2×D3—121no—
990C2×D3—121no—
991C2×D3—124no—
992C2×D3—124no—
993C2×D3#379512yes—
994C3×C4—22no—
995C3×C4—21no—
996C3×C4—21no—
997C3×C4—21no—
998C3×C4—41no—
999C3×C4—41no—
1000C3×C4—42no—
1001C3×C4—61no—
1002C3×C4—61no—
1003C3×C4—61no—
1004C3×C4—61no—
1005C3×C4—61no—
1006C3×C4—61no—
1007C3×C4—121no—
1008C3×C4—121no—
1009C3×C4—121no—
1010C3×C4—181no—
1011C3×C4—181no—
1012C3×C4—181no—
1013C3×C4—181no—
1014Dic3—21no—
1015Dic3—21no—
1016Dic3—21no—
1017Dic3—62no—
1018Dic3—61no—
1019Dic3—61no—
1020Dic3—61no—
1021Dic3—61no—
1022Dic3—61no—
1023Dic3—61no—
1024Dic3—61no—
1025Dic3—61no—
1026Dic3—121no—
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#559311yescharacteristic, complemented
1049C32#565711yescharacteristic, complemented
1050C23—31no—
1051C23—31no—
1052C23—31no—
1053C23—91no—
1054C23—91no—
1055C23—182no—
1056C23—361no—
1057C23—361no—
1058Q8—1081no—
1059D4—182no—
1060D4—182no—
1061D4—361no—
1062D4—361no—
1063D4—361no—
1064D4—1081no—
1065D4—1081no—
1066C2×C4—31no—
1067C2×C4—31no—
1068C2×C4—31no—
1069C2×C4—91no—
1070C2×C4—91no—
1071C2×C4—91no—
1072C2×C4—91no—
1073C2×C4—121no—
1074C2×C4—271no—
1075C2×C4—271no—
1076C2×C4—361no—
1077C2×C4—1081no—
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—62no—
1093C2×C3—62no—
1094C2×C3—122no—
1095C2×C3—122no—
1096C2×C3—121no—
1097C2×C3—121no—
1098C2×C3—121no—
1099C2×C3—121no—
1100C2×C3—241no—
1101C2×C3—361no—
1102C2×C3—361no—
1103C2×C3C2×#379511yescharacteristic
1104C2×C3D3×#23511yescharacteristic
1105C2×C3#6430711yescharacteristic
1106C2×C3#6430811yescharacteristic
1107C2×C3D3×#23711yescharacteristic
1108C2×C3#6431311yescharacteristic
1109C2×C3#6431311yescharacteristic
1110C2×C3#6431411yescharacteristic
1111C2×C3#6433011yescharacteristic
1112D3—22no—
1113D3—41no—
1114D3—41no—
1115D3—121no—
1116D3—121no—
1117D3—121no—
1118D3—121no—
1119D3—241no—
1120D3—241no—
1121C22—32no—
1122C22—61no—
1123C22—61no—
1124C22—61no—
1125C22—61no—
1126C22—61no—
1127C22—61no—
1128C22—61no—
1129C22—61no—
1130C22—181no—
1131C22—181no—
1132C22—181no—
1133C22—181no—
1134C22—181no—
1135C22—181no—
1136C22—364no—
1137C22C2×D3311yescharacteristic
1138C4—21no—
1139C4—61no—
1140C4—61no—
1141C4—61no—
1142C4—181no—
1143C4—181no—
1144C4—181no—
1145C4—181no—
1146C4—541no—
1147C4—541no—
1148C3—21no—
1149C3—21no—
1150C3—21no—
1151C3—41no—
1152C3#1059421311yescharacteristic, complemented
1153C3#1059423811yescharacteristic, complemented
1154C3#1059508511yescharacteristic, complemented
1155C2—62no—
1156C2—121no—
1157C2—121no—
1158C2—361no—
1159C2—361no—
1160C2D3×#379511yescharacteristic
1161C2#1172438411yescharacteristic
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. #11723686C2semidirect
2. #11723515C2semidirect
3. #11723491C2semidirect
4. #11723430C2semidirect
5. C3×#63923C2semidirect
6. C3×#63905C2semidirect
7. C3×#63879C2semidirect
8. #11723024C2semidirect
9. #11723009C2semidirect
10. #11723002C2semidirect
11. #11722965C2semidirect
12. #11722954C2semidirect
13. #11722946C2semidirect
14. #11722927C2semidirect
15. D3×(C2×D3)⋊Dic3C2semidirect
21. C2×C32×C4×D3C22semidirect
22. C2×#6294C22semidirect
23. C2×#6293C22semidirect
25. C2×#6290C22semidirect
32. C4⋊(C3⋊(C3⋊Dic3))C22semidirect
33. C3×#3750C22semidirect
34. C3×#3750C22semidirect
39. #88814C22semidirect
40. #88807C22semidirect
41. #88806C22semidirect
43. #88803C22semidirect
47. Dic3×C3⋊Dic3C22semidirect
48. C3×Dic3⋊Dic3C22semidirect
51. C3×(C2×D3)⋊Dic3C22semidirect
52. C3×(C2×D3)⋊Dic3C22semidirect
53. C3×Dic32C22semidirect
75. #63923D3semidirect
82. #63905D3semidirect
93. #63879D3semidirect
158. C2×C3×C4×D3C2×D3semidirect
159. C2×C3×C4×D3C2×D3semidirect
196. #3750C2×D3semidirect
197. #3750C2×D3semidirect
229. Dic3⋊Dic3C2×D3semidirect
256. (C2×D3)⋊Dic3C2×D3semidirect
257. (C2×D3)⋊Dic3C2×D3semidirect
261. Dic32C2×D3semidirect
506. C2×C4×D3D32semidirect
727. C33#538semidirect
1047. C32#5560semidirect
1048. C32#5593semidirect
1049. C32#5657semidirect
1152. C3#10594213semidirect
1153. C3#10594238semidirect
1154. C3#10595085semidirect

Maximal subgroups

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

subgroupindex
#117236862
#117235152
#117234912
#117234302
C3×#639232
C3×#639052
C3×#638792
#117230242
#117230092
#117230022
#117229652
#117229542
#117229462
#117229272
D3×(C2×D3)⋊Dic32
#105950853
#105942383
#105942133