Finite Group Databasebeta

← #13168114

Subgroups — #13168114

Order 1728.

1282 conjugacy classes of subgroups.

The subgroup lattice has 1186 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11723691C211yesmaximal, characteristic, complemented
2#11723482C211yesmaximal, characteristic, complemented
3#11723422C211yesmaximal, characteristic, complemented
4#11723419C211yesmaximal, characteristic, complemented
5C3×#63923C211yesmaximal, characteristic, complemented
6C3×#63862C211yesmaximal, characteristic, complemented
7C3×#63861C211yesmaximal, characteristic, complemented
8#11723002C211yesmaximal, characteristic, complemented
9#11722994C211yesmaximal, characteristic, complemented
10#11722983C211yesmaximal, characteristic, complemented
11#11722966C211yesmaximal, characteristic, complemented
12#11722963C211yesmaximal, characteristic, complemented
13#11722948C211yesmaximal, characteristic, complemented
14#11722937C211yesmaximal, characteristic, complemented
15#11722902C211yesmaximal, characteristic, complemented
16#10594658—31nomaximal
17#10594127—31nomaximal
18#10594126—31nomaximal
19C22×C3×D32C2211yescharacteristic
20C2×C3×C4⋊(C3⋊D3)C2211yescharacteristic
21C2×#6294C2211yescharacteristic
22C2×#6294C2211yescharacteristic, complemented
23C2×#6293C2211yescharacteristic, complemented
24C2×#6292C2211yescharacteristic
25C2×#6292C2211yescharacteristic, complemented
26C2×#6291C2211yescharacteristic
27C2×#6291C2211yescharacteristic
28C2×#6289C2211yescharacteristic, complemented
29C2×Dic3×C3⋊D3C2211yescharacteristic
30C2×C3×#626C2211yescharacteristic
31C2×C3×#626C2211yescharacteristic
32#88859C2211yescharacteristic, complemented
33C3×C4⋊(C3⋊Dic3)C2211yescharacteristic, complemented
34C3×C4×C3⋊Dic3C2211yescharacteristic, complemented
35C32×(C2×D3)⋊C4C2211yescharacteristic
36C32×(C2×D3)⋊C4C2211yescharacteristic
37C32×Dic3⋊C4C2211yescharacteristic, complemented
38#88814C2211yescharacteristic
39#88814C2211yescharacteristic, complemented
40#88806C2211yescharacteristic, complemented
41#88804C2211yescharacteristic, complemented
42#88803C2211yescharacteristic, complemented
43(C2×D3)⋊(C3⋊Dic3)C2211yescharacteristic
44(C2×D3)⋊(C3⋊Dic3)C2211yescharacteristic
45C3×#3724C2211yescharacteristic, complemented
46C3×Dic3⋊Dic3C2211yescharacteristic, complemented
47C3×Dic3⋊Dic3C2211yescharacteristic, complemented
48C3×#3722C2211yescharacteristic
49C3×(C2×D3)⋊Dic3C2211yescharacteristic
50C3×(C2×D3)⋊Dic3C2211yescharacteristic
51C3×(C2×D3)⋊Dic3C2211yescharacteristic
52C3×(C2×D3)⋊Dic3C2211yescharacteristic
53C3×Dic32C2211yescharacteristic, complemented
54#64104—31no—
55#64094—31no—
56#64092—31no—
57C3×#898—31no—
58C3×#898—31no—
59C3×#882—31no—
60C3×#882—31no—
61C3×#879—31no—
62C3×#879—31no—
63#63977—31no—
64#63977—31no—
65#63971—31no—
66#63969—31no—
67D3×#217—31no—
68D3×#217—31no—
69#63959—31no—
70#63958—31no—
71#63923—31no—
72#63923D311yescharacteristic, complemented
73#63921—31no—
74#63916—31no—
75#63910—31no—
76#63910—31no—
77#63899—31no—
78#63898—31no—
79#63896—31no—
80#63894—31no—
81#63894—31no—
82Dic3×D12—31no—
83#63886—31no—
84#63886—31no—
85#63886—31no—
86#63886—61no—
87#63884—31no—
88#63881—31no—
89#63880—31no—
90#63865—31no—
91#63862D311yescharacteristic, complemented
92#63861D311yescharacteristic, complemented
93#63860—31no—
94#63854—31no—
95#63854—31no—
96#63854—31no—
97#63854—61no—
98#63852—31no—
99#63852—31no—
100#63852—31no—
101#63852—61no—
102C22×C3⋊(C3⋊D3)C2311yescharacteristic
103C22×C3×C3⋊D3C2311yescharacteristic
104C22×C3×C3⋊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⋊Dic3C2311yescharacteristic
113C2×C3×C3⋊Dic3C2311yescharacteristic
114C2×C3×C3⋊Dic3C2311yescharacteristic
115C2×C3×C3⋊Dic3C2311yescharacteristic
116C3×C4⋊(C3⋊D3)—22no—
117C2×C32×Dic3C2311yescharacteristic
118C2×C32×Dic3C2311yescharacteristic
119C2×C32×Dic3C2311yescharacteristic
120C2×C32×Dic3C2311yescharacteristic
121#6294—41no—
122#6294—41no—
123#6293—41no—
124#6292—22no—
125#6292—41no—
126#6291—41no—
127#6291—41no—
128#6289—41no—
129Dic3×C3⋊D3—41no—
130C3×#626—41no—
131C3×#626—41no—
132#5704—91no—
133#5704—91no—
134#5593—91no—
135C23×C3×D3—31no—
136C23×C3×D3—31no—
137C22×D32C2×D311yescharacteristic
138C2×#638—31no—
139C2×#638—31no—
140C2×C4⋊(C3⋊D3)—31no—
141C2×C4⋊(C3⋊D3)—31no—
142C2×C4⋊(C3⋊D3)C2×D311yescharacteristic
143C2×C4×C3⋊D3—31no—
144C2×C4×C3⋊D3—31no—
145C2×#634—31no—
146C2×C3×#67—31no—
147C2×C3×#67—31no—
148C2×C3×D12—31no—
149C2×C3×D12—31no—
150C2×C3×D12—31no—
151C2×C3×D12—31no—
152C2×C3×D12—61no—
153C2×#627—31no—
154C2×#627—31no—
155C2×#627—61no—
156C2×#626—31no—
157C2×#626—31no—
158C2×#626—31no—
159C2×#626—31no—
160C2×#626—31no—
161C2×#626—31no—
162C2×#626—31no—
163C2×#626—31no—
164C2×#626—61no—
165C2×#626—61no—
166C2×#626—61no—
167C2×#626—61no—
168C2×#626C2×D311yescharacteristic
169C2×#626C2×D311yescharacteristic
170C2×#624—31no—
171C2×#624—31no—
172C2×#624—31no—
173C2×#624—31no—
174C2×#624—61no—
175C2×D3×Dic3—31no—
176C2×D3×Dic3—31no—
177C2×D3×Dic3—31no—
178C2×D3×Dic3—31no—
179C2×D3×Dic3—31no—
180C2×D3×Dic3—31no—
181C2×D3×Dic3—61no—
182C32×C4⋊C4—31no—
183C32×C22⋊C4—31no—
184C32×C22⋊C4—31no—
185#3757—31no—
186#3757—31no—
187#3752—31no—
188#3752—31no—
189#3752—31no—
190#3752—31no—
191#3752—31no—
192#3752—61no—
193#3752—61no—
194#3752—61no—
195#3752—121no—
196C4⋊(C3⋊Dic3)C2×D311yescharacteristic, complemented
197#3750—31no—
198C4×C3⋊Dic3C2×D311yescharacteristic, complemented
199C3×#217—31no—
200C3×#217—31no—
201C3×#217—31no—
202C3×#217—31no—
203C3×(C2×D3)⋊C4—21no—
204C3×(C2×D3)⋊C4—21no—
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)⋊C4C2×D311yescharacteristic
212C3×(C2×D3)⋊C4C2×D311yescharacteristic
213C3×(C2×D3)⋊C4C2×D311yescharacteristic
214C3×(C2×D3)⋊C4C2×D311yescharacteristic
215C3×C4⋊Dic3—31no—
216C3×C4⋊Dic3—31no—
217C3×C4⋊Dic3—31no—
218C3×C4⋊Dic3—31no—
219C3×C4⋊Dic3—61no—
220C3×Dic3⋊C4—21no—
221C3×Dic3⋊C4—31no—
222C3×Dic3⋊C4—31no—
223C3×Dic3⋊C4—31no—
224C3×Dic3⋊C4—31no—
225C3×Dic3⋊C4C2×D311yescharacteristic, complemented
226C3×Dic3⋊C4C2×D311yescharacteristic, complemented
227C3×C4×Dic3—31no—
228C3×C4×Dic3—31no—
229C3×C4×Dic3—31no—
230C3×C4×Dic3—31no—
231C3×C4×Dic3—61no—
232#3724—31no—
233#3724—31no—
234#3724—61no—
235#3724C2×D311yescharacteristic, complemented
236Dic3⋊Dic3C2×D311yescharacteristic, complemented
237Dic3⋊Dic3C2×D311yescharacteristic, complemented
238#3722—31no—
239#3722—31no—
240#3722—31no—
241#3722—31no—
242#3722—61no—
243#3722C2×D311yescharacteristic
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—31no—
254(C2×D3)⋊Dic3—61no—
255(C2×D3)⋊Dic3—61no—
256(C2×D3)⋊Dic3—61no—
257(C2×D3)⋊Dic3C2×D311yescharacteristic
258(C2×D3)⋊Dic3C2×D311yescharacteristic
259(C2×D3)⋊Dic3C2×D311yescharacteristic
260(C2×D3)⋊Dic3C2×D311yescharacteristic
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#4112yes—
272C2×C32×D3—21no—
273C2×C32×D3—21no—
274C2×C32×D3—21no—
275C2×C32×D3—21no—
276C2×C32×D3—21no—
277C2×C32×D3—21no—
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—
285C32×Dic3—21no—
286C32×Dic3—21no—
287C32×Dic3—21no—
288C32×Dic3—21no—
289C3×#126—91no—
290C3×#126—91no—
291C3×#120—91no—
292#953—91no—
293C2×#217—91no—
294#939—91no—
295#939—91no—
296#938—91no—
297#936—91no—
298#935—91no—
299D4×Dic3—91no—
300#898—31no—
301#898—31no—
302#896—91no—
303#896—91no—
304#895—91no—
305#895—91no—
306#895—91no—
307#895—91no—
308#895—181no—
309#894—91no—
310#894—91no—
311#893—91no—
312#893—91no—
313#885—91no—
314#885—91no—
315#885—91no—
316#885—181no—
317#884—91no—
318#884—91no—
319#883—91no—
320#883—91no—
321#883—91no—
322#883—181no—
323#882—31no—
324#882—31no—
325#882—91no—
326#882—91no—
327#67⋊C4—91no—
328D3×C22⋊C4—91no—
329D3×C22⋊C4—91no—
330#879—31no—
331#879—31no—
332#878—91no—
333#875—91no—
334#875—91no—
335C4×D12—91no—
336C4×D12—91no—
337C23×C32—31no—
338C23×C32—31no—
339C22×C3⋊D3—31no—
340C22×C3⋊D3—31no—
341C22×C3⋊D3—31no—
342C22×C3⋊D3—61no—
343C22×C3⋊D3—61no—
344C22×C3⋊D3—61no—
345C22×C3⋊D3—121no—
346C22×C3⋊D3C22×D311yescharacteristic
347C22×C3⋊D3C22×D311yescharacteristic
348C22×C3×D3—21no—
349C22×C3×D3—21no—
350C22×C3×D3—31no—
351C22×C3×D3—31no—
352C22×C3×D3—31no—
353C22×C3×D3—31no—
354C22×C3×D3—61no—
355C22×C3×D3—61no—
356C22×C3×D3—62no—
357C22×C3×D3—62no—
358C22×C3×D3—121no—
359C22×C3×D3—121no—
360C22×C3×D3—121no—
361C22×C3×D3—121no—
362C22×C3×D3C22×D311yescharacteristic
363C22×C3×D3C22×D311yescharacteristic
364C22×C3×D3C22×D311yescharacteristic
365C22×C3×D3C22×D311yescharacteristic
366C2×D32—22no—
367C2×D32—41no—
368C2×D32—41no—
369C2×C32×C4—21no—
370C2×C32×C4—21no—
371C2×C32×C4—21no—
372C2×C32×C4—31no—
373C2×C32×C4—31no—
374C2×C32×C4—31no—
375C2×C32×C4—31no—
376C2×C32×C4—41no—
377C2×C32×C4C22×D311yescharacteristic
378C2×C32×C4C22×D311yescharacteristic
379C2×C32×C4C22×D311yescharacteristic
380#638—121no—
381#638—121no—
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—121no—
389C2×C3⋊Dic3C22×D311yescharacteristic
390C2×C3⋊Dic3C22×D311yescharacteristic
391C2×C3⋊Dic3C22×D311yescharacteristic
392C2×C3⋊Dic3C22×D311yescharacteristic
393C4⋊(C3⋊D3)—22no—
394C4⋊(C3⋊D3)—62no—
395C4⋊(C3⋊D3)—121no—
396C4×C3⋊D3—121no—
397C4×C3⋊D3—121no—
398#634—121no—
399C3×#67—121no—
400C3×#67—121no—
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—31no—
410C2×C3×Dic3—31no—
411C2×C3×Dic3—31no—
412C2×C3×Dic3—31no—
413C2×C3×Dic3—61no—
414C2×C3×Dic3—61no—
415C2×C3×Dic3—61no—
416C2×C3×Dic3—61no—
417C2×C3×Dic3C22×D311yescharacteristic
418C2×C3×Dic3C22×D311yescharacteristic
419C2×C3×Dic3C22×D311yescharacteristic
420C2×C3×Dic3C22×D311yescharacteristic
421C2×C3×Dic3C22×D311yescharacteristic
422C2×C3×Dic3C22×D311yescharacteristic
423C2×C3×Dic3C22×D311yescharacteristic
424C2×C3×Dic3C22×D311yescharacteristic
425C3×D12—62no—
426C3×D12—62no—
427C3×D12—122no—
428C3×D12—121no—
429C3×D12—121no—
430#627—121no—
431#627—121no—
432#627—122no—
433#626—41no—
434#626—41no—
435#626—62no—
436#626—62no—
437#626—122no—
438#626—121no—
439#626—121no—
440#626—122no—
441#626—121no—
442#626—121no—
443#626—121no—
444#626—121no—
445#626—122no—
446#626—122no—
447#624—121no—
448#624—121no—
449#624—122no—
450#624—121no—
451#624—121no—
452D3×Dic3—121no—
453D3×Dic3—121no—
454D3×Dic3—122no—
455D3×Dic3—121no—
456D3×Dic3—121no—
457D3×Dic3—121no—
458D3×Dic3—121no—
459#538—271noSylow
460C2×C33C2×#4111yescharacteristic
461C2×C33H(5,𝔽2)11yescharacteristic
462C2×C33H(5,𝔽2)11yescharacteristic
463C3⋊(C3⋊D3)—41no—
464C3×C3⋊D3—22no—
465C3×C3⋊D3—41no—
466C32×D3—41no—
467C32×D3—41no—
468C24×C3—91no—
469C23×D3—31no—
470C23×D3—31no—
471C2×C3×D4—91no—
472C2×C3×D4—91no—
473C2×C3×D4—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—181no—
483C2×#67—181no—
484C22×Dic3—91no—
485C22×Dic3—91no—
486C22×Dic3—91no—
487C2×D12—31no—
488C2×D12—31no—
489C2×D12—31no—
490C2×D12—31no—
491C2×D12—61no—
492C2×D12—91no—
493C2×D12—91no—
494C2×D12—91no—
495C2×D12—91no—
496C2×D12—91no—
497C2×D12—91no—
498C2×D12—181no—
499C2×D12—181no—
500C2×C4×D3—91no—
501C2×C4×D3—91no—
502C2×C4×D3—91no—
503C2×C4×D3—91no—
504C2×C4×D3—91no—
505C2×C4×D3—91no—
506C2×C4×D3—91no—
507C2×C4×D3—91no—
508C2×C4×D3—91no—
509C2×C4×D3—181no—
510C2×C4×D3—181no—
511C2×Dic6—91no—
512C2×Dic6—91no—
513C2×Dic6—91no—
514C2×Dic6—181no—
515C3×C4⋊C4—31no—
516C3×C4⋊C4—31no—
517C3×C4⋊C4—61no—
518C3×C4⋊C4—91no—
519C3×C4⋊C4—91no—
520C3×C4⋊C4—91no—
521C3×C4⋊C4—91no—
522C3×C22⋊C4—31no—
523C3×C22⋊C4—31no—
524C3×C22⋊C4—31no—
525C3×C22⋊C4—31no—
526C3×C22⋊C4—61no—
527C3×C22⋊C4—61no—
528C3×C22⋊C4—91no—
529C3×C22⋊C4—91no—
530C3×C22⋊C4—91no—
531C3×C22⋊C4—91no—
532C3×C22⋊C4—91no—
533C3×C42—91no—
534C3×C42—91no—
535#217—31no—
536#217—31no—
537#217—31no—
538#217—31no—
539#217—91no—
540#217—91no—
541#217—91no—
542#217—91no—
543#217—91no—
544#217—91no—
545#217—91no—
546#217—181no—
547#217—181no—
548(C2×D3)⋊C4—31no—
549(C2×D3)⋊C4—31no—
550(C2×D3)⋊C4—31no—
551(C2×D3)⋊C4—31no—
552(C2×D3)⋊C4—31no—
553(C2×D3)⋊C4—31no—
554(C2×D3)⋊C4—91no—
555(C2×D3)⋊C4—91no—
556(C2×D3)⋊C4—91no—
557(C2×D3)⋊C4—91no—
558(C2×D3)⋊C4—91no—
559(C2×D3)⋊C4—91no—
560(C2×D3)⋊C4—91no—
561(C2×D3)⋊C4—91no—
562(C2×D3)⋊C4—91no—
563(C2×D3)⋊C4—91no—
564(C2×D3)⋊C4—91no—
565(C2×D3)⋊C4—91no—
566(C2×D3)⋊C4—91no—
567(C2×D3)⋊C4—91no—
568(C2×D3)⋊C4—181no—
569(C2×D3)⋊C4—181no—
570(C2×D3)⋊C4—181no—
571(C2×D3)⋊C4—181no—
572(C2×D3)⋊C4—181no—
573(C2×D3)⋊C4—361no—
574(C2×D3)⋊C4D3211yescharacteristic
575(C2×D3)⋊C4D3211yescharacteristic
576C4⋊Dic3—31no—
577C4⋊Dic3—31no—
578C4⋊Dic3—31no—
579C4⋊Dic3—31no—
580C4⋊Dic3—61no—
581Dic3⋊C4—31no—
582Dic3⋊C4—31no—
583Dic3⋊C4—31no—
584Dic3⋊C4—31no—
585Dic3⋊C4—91no—
586Dic3⋊C4—91no—
587Dic3⋊C4—91no—
588Dic3⋊C4—181no—
589Dic3⋊C4D3211yescharacteristic, complemented
590C4×Dic3—31no—
591C4×Dic3—31no—
592C4×Dic3—31no—
593C4×Dic3—31no—
594C4×Dic3—61no—
595C22×C32—21no—
596C22×C32—21no—
597C22×C32—21no—
598C22×C32—41no—
599C22×C32—61no—
600C22×C32—61no—
601C22×C32—61no—
602C22×C32—61no—
603C22×C32—61no—
604C22×C32—61no—
605C22×C32C23×D311yescharacteristic
606C22×C32C23×D311yescharacteristic
607C22×C32C23×D311yescharacteristic
608C2×C3⋊D3—21no—
609C2×C3⋊D3—21no—
610C2×C3⋊D3—21no—
611C2×C3⋊D3—21no—
612C2×C3⋊D3—21no—
613C2×C3⋊D3—61no—
614C2×C3⋊D3—62no—
615C2×C3⋊D3—61no—
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—121no—
624C2×C3⋊D3—121no—
625C2×C3⋊D3—122no—
626C2×C3⋊D3—121no—
627C2×C3⋊D3—121no—
628C2×C3⋊D3—121no—
629C2×C3⋊D3—121no—
630C2×C3⋊D3—121no—
631C2×C3⋊D3—121no—
632C2×C3⋊D3—241no—
633C2×C3⋊D3—241no—
634C2×C3⋊D3#23712yes—
635C2×C3×D3—21no—
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—32no—
648C2×C3×D3—32no—
649C2×C3×D3—41no—
650C2×C3×D3—41no—
651C2×C3×D3—41no—
652C2×C3×D3—41no—
653C2×C3×D3—41no—
654C2×C3×D3—41no—
655C2×C3×D3—62no—
656C2×C3×D3—61no—
657C2×C3×D3—61no—
658C2×C3×D3—61no—
659C2×C3×D3—61no—
660C2×C3×D3—61no—
661C2×C3×D3—61no—
662C2×C3×D3—61no—
663C2×C3×D3—61no—
664C2×C3×D3—61no—
665C2×C3×D3—61no—
666C2×C3×D3—121no—
667C2×C3×D3—121no—
668C2×C3×D3—121no—
669C2×C3×D3—121no—
670C2×C3×D3—121no—
671C2×C3×D3—124no—
672C2×C3×D3—124no—
673D32—44no—
674C32×C4—21no—
675C32×C4—21no—
676C32×C4—21no—
677C32×C4—41no—
678C32×C4—41no—
679C32×C4—41no—
680C32×C4—61no—
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—61no—
690C3⋊Dic3—61no—
691C3⋊Dic3—61no—
692C3⋊Dic3—121no—
693C3⋊Dic3—121no—
694C3⋊Dic3—121no—
695C3⋊Dic3—241no—
696C3×Dic3—22no—
697C3×Dic3—21no—
698C3×Dic3—21no—
699C3×Dic3—21no—
700C3×Dic3—21no—
701C3×Dic3—21no—
702C3×Dic3—21no—
703C3×Dic3—21no—
704C3×Dic3—21no—
705C3×Dic3—41no—
706C3×Dic3—41no—
707C3×Dic3—41no—
708C3×Dic3—62no—
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—
720#126—91no—
721#126—91no—
722#124—271no—
723#124—271no—
724#123—271no—
725#123—271no—
726C22⋊Q8—271no—
727#121—271no—
728#121—271no—
729#121—271no—
730#120—91no—
731#120—271no—
732C4×D4—271no—
733C4×D4—271no—
734C2×C22⋊C4—271no—
735C33#53811yescharacteristic, complemented, Sylow
736C23×C3—31no—
737C23×C3—31no—
738C23×C3—31no—
739C23×C3—31no—
740C23×C3—61no—
741C23×C3—61no—
742C23×C3—91no—
743C23×C3—91no—
744C23×C3—182no—
745C23×C3—361no—
746C23×C3—361no—
747C22×D3—31no—
748C22×D3—31no—
749C22×D3—31no—
750C22×D3—31no—
751C22×D3—61no—
752C22×D3—61no—
753C22×D3—62no—
754C22×D3—62no—
755C22×D3—91no—
756C22×D3—91no—
757C22×D3—91no—
758C22×D3—121no—
759C22×D3—121no—
760C22×D3—121no—
761C22×D3—121no—
762C22×D3—181no—
763C22×D3—181no—
764C22×D3—181no—
765C22×D3—361no—
766C22×D3C2×D3211yescharacteristic
767C22×D3C2×D3211yescharacteristic
768C3×D4—182no—
769C3×D4—361no—
770C3×D4—361no—
771C2×C3×C4—21no—
772C2×C3×C4—21no—
773C2×C3×C4—21no—
774C2×C3×C4—31no—
775C2×C3×C4—31no—
776C2×C3×C4—31no—
777C2×C3×C4—31no—
778C2×C3×C4—31no—
779C2×C3×C4—31no—
780C2×C3×C4—31no—
781C2×C3×C4—31no—
782C2×C3×C4—41no—
783C2×C3×C4—61no—
784C2×C3×C4—61no—
785C2×C3×C4—61no—
786C2×C3×C4—61no—
787C2×C3×C4—91no—
788C2×C3×C4—91no—
789C2×C3×C4—91no—
790C2×C3×C4—91no—
791C2×C3×C4C2×D3211yescharacteristic
792C2×C3×C4C2×D3211yescharacteristic
793C2×C3×C4C2×D3211yescharacteristic
794#67—121no—
795#67—121no—
796#67—182no—
797#67—361no—
798#67—361no—
799#67—361no—
800#67—361no—
801#67—361no—
802#67—362no—
803#67—362no—
804C2×Dic3—31no—
805C2×Dic3—31no—
806C2×Dic3—31no—
807C2×Dic3—31no—
808C2×Dic3—31no—
809C2×Dic3—31no—
810C2×Dic3—31no—
811C2×Dic3—31no—
812C2×Dic3—61no—
813C2×Dic3—61no—
814C2×Dic3—61no—
815C2×Dic3—61no—
816C2×Dic3—91no—
817C2×Dic3—91no—
818C2×Dic3—91no—
819C2×Dic3—181no—
820C2×Dic3—181no—
821C2×Dic3—181no—
822C2×Dic3—361no—
823C2×Dic3—361no—
824C2×Dic3—361no—
825C2×Dic3—361no—
826C2×Dic3C2×D3211yescharacteristic
827C2×Dic3C2×D3211yescharacteristic
828C2×Dic3C2×D3211yescharacteristic
829C2×Dic3C2×D3211yescharacteristic
830D12—62no—
831D12—62no—
832D12—122no—
833D12—121no—
834D12—121no—
835D12—182no—
836D12—182no—
837D12—362no—
838D12—361no—
839D12—361no—
840D12—362no—
841D12—361no—
842D12—361no—
843C4×D3—361no—
844C4×D3—361no—
845C4×D3—361no—
846C4×D3—361no—
847C4×D3—361no—
848C4×D3—361no—
849C4×D3—361no—
850C4×D3—362no—
851C4×D3—361no—
852C4×D3—361no—
853C4×D3—362no—
854Dic6—361no—
855Dic6—361no—
856Dic6—361no—
857Dic6—362no—
858C2×C32—21no—
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—41no—
868C2×C32—41no—
869C2×C32—41no—
870C2×C32—121no—
871C2×C32—121no—
872C2×C32C2×#23711yescharacteristic
873C2×C32#100411yescharacteristic
874C2×C32#100411yescharacteristic
875C2×C32D3×#4111yescharacteristic
876C2×C32D3×#4111yescharacteristic
877C2×C32#100911yescharacteristic
878C2×C32#100911yescharacteristic
879C2×C32#100911yescharacteristic
880C2×C32#100911yescharacteristic
881C3⋊D3—22no—
882C3⋊D3—41no—
883C3⋊D3—121no—
884C3⋊D3—122no—
885C3⋊D3—121no—
886C3⋊D3—121no—
887C3⋊D3—241no—
888C3⋊D3—241no—
889C3⋊D3—242no—
890C3×D3—41no—
891C3×D3—41no—
892C3×D3—41no—
893C3×D3—41no—
894C3×D3—62no—
895C3×D3—62no—
896C3×D3—81no—
897C3×D3—81no—
898C3×D3—122no—
899C3×D3—121no—
900C3×D3—121no—
901C3×D3—241no—
902C24—91no—
903C2×Q8—271no—
904C2×D4—91no—
905C2×D4—91no—
906C2×D4—91no—
907C2×D4—271no—
908C2×D4—271no—
909C2×D4—271no—
910C2×D4—271no—
911C22×C4—271no—
912C22×C4—271no—
913C22×C4—271no—
914C22×C4—271no—
915C4⋊C4—31no—
916C4⋊C4—91no—
917C4⋊C4—91no—
918C4⋊C4—91no—
919C4⋊C4—91no—
920C4⋊C4—271no—
921C22⋊C4—31no—
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—
935C42—91no—
936C42—91no—
937C22×C3—21no—
938C22×C3—21no—
939C22×C3—21no—
940C22×C3—41no—
941C22×C3—61no—
942C22×C3—61no—
943C22×C3—61no—
944C22×C3—61no—
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—92no—
954C22×C3—121no—
955C22×C3—121no—
956C22×C3—121no—
957C22×C3—121no—
958C22×C3—121no—
959C22×C3—121no—
960C22×C3—181no—
961C22×C3—181no—
962C22×C3—181no—
963C22×C3—181no—
964C22×C3—181no—
965C22×C3—364no—
966C22×C3C22×D3211yescharacteristic
967C22×C3C22×D3211yescharacteristic
968C22×C3C22×D3211yescharacteristic
969C2×D3—21no—
970C2×D3—21no—
971C2×D3—21no—
972C2×D3—21no—
973C2×D3—21no—
974C2×D3—21no—
975C2×D3—32no—
976C2×D3—32no—
977C2×D3—62no—
978C2×D3—61no—
979C2×D3—61no—
980C2×D3—61no—
981C2×D3—61no—
982C2×D3—61no—
983C2×D3—61no—
984C2×D3—61no—
985C2×D3—61no—
986C2×D3—61no—
987C2×D3—61no—
988C2×D3—121no—
989C2×D3—121no—
990C2×D3—121no—
991C2×D3—121no—
992C2×D3—121no—
993C2×D3—124no—
994C2×D3—124no—
995C2×D3—182no—
996C2×D3—181no—
997C2×D3—181no—
998C2×D3—181no—
999C2×D3—181no—
1000C2×D3—181no—
1001C2×D3—181no—
1002C2×D3—181no—
1003C2×D3—181no—
1004C2×D3—181no—
1005C2×D3—361no—
1006C2×D3—361no—
1007C2×D3—361no—
1008C2×D3—361no—
1009C2×D3—361no—
1010C2×D3—361no—
1011C2×D3—361no—
1012C2×D3—361no—
1013C2×D3—362no—
1014C2×D3—721no—
1015C2×D3—721no—
1016C3×C4—21no—
1017C3×C4—21no—
1018C3×C4—21no—
1019C3×C4—41no—
1020C3×C4—41no—
1021C3×C4—41no—
1022C3×C4—62no—
1023C3×C4—61no—
1024C3×C4—61no—
1025C3×C4—61no—
1026C3×C4—61no—
1027C3×C4—61no—
1028C3×C4—61no—
1029C3×C4—61no—
1030C3×C4—61no—
1031C3×C4—81no—
1032C3×C4—121no—
1033C3×C4—121no—
1034C3×C4—121no—
1035C3×C4—181no—
1036C3×C4—181no—
1037C3×C4—181no—
1038C3×C4—181no—
1039Dic3—21no—
1040Dic3—21no—
1041Dic3—21no—
1042Dic3—21no—
1043Dic3—62no—
1044Dic3—61no—
1045Dic3—61no—
1046Dic3—61no—
1047Dic3—61no—
1048Dic3—61no—
1049Dic3—61no—
1050Dic3—61no—
1051Dic3—61no—
1052Dic3—121no—
1053Dic3—121no—
1054Dic3—121no—
1055Dic3—181no—
1056Dic3—181no—
1057Dic3—181no—
1058Dic3—361no—
1059Dic3—361no—
1060Dic3—361no—
1061Dic3—721no—
1062C32—21no—
1063C32—21no—
1064C32—21no—
1065C32—41no—
1066C32#559311yescharacteristic, complemented
1067C32#570411yescharacteristic, complemented
1068C32#570411yescharacteristic, complemented
1069C23—31no—
1070C23—31no—
1071C23—91no—
1072C23—91no—
1073C23—182no—
1074C23—271no—
1075C23—361no—
1076C23—361no—
1077Q8—1081no—
1078D4—182no—
1079D4—361no—
1080D4—361no—
1081D4—542no—
1082D4—1081no—
1083D4—1081no—
1084D4—1081no—
1085C2×C4—31no—
1086C2×C4—31no—
1087C2×C4—31no—
1088C2×C4—31no—
1089C2×C4—91no—
1090C2×C4—91no—
1091C2×C4—91no—
1092C2×C4—91no—
1093C2×C4—271no—
1094C2×C4—1081no—
1095C2×C4—1081no—
1096C2×C4—1081no—
1097C2×C4—1081no—
1098C2×C4D3311yescharacteristic
1099C2×C3—21no—
1100C2×C3—21no—
1101C2×C3—21no—
1102C2×C3—21no—
1103C2×C3—21no—
1104C2×C3—21no—
1105C2×C3—21no—
1106C2×C3—21no—
1107C2×C3—21no—
1108C2×C3—41no—
1109C2×C3—41no—
1110C2×C3—41no—
1111C2×C3—121no—
1112C2×C3—121no—
1113C2×C3—121no—
1114C2×C3—121no—
1115C2×C3—182no—
1116C2×C3—241no—
1117C2×C3—241no—
1118C2×C3—361no—
1119C2×C3#6430711yescharacteristic
1120C2×C3#6430711yescharacteristic
1121C2×C3#6430811yescharacteristic
1122C2×C3D3×#23711yescharacteristic
1123C2×C3D3×#23711yescharacteristic
1124C2×C3#6431211yescharacteristic
1125C2×C3#6431411yescharacteristic
1126C2×C3#6431411yescharacteristic
1127C2×C3#6432011yescharacteristic
1128D3—41no—
1129D3—41no—
1130D3—62no—
1131D3—62no—
1132D3—122no—
1133D3—121no—
1134D3—121no—
1135D3—241no—
1136D3—362no—
1137D3—361no—
1138D3—361no—
1139D3—361no—
1140D3—721no—
1141D3—721no—
1142D3—722no—
1143C22—61no—
1144C22—61no—
1145C22—61no—
1146C22—61no—
1147C22—61no—
1148C22—61no—
1149C22—92no—
1150C22—181no—
1151C22—181no—
1152C22—181no—
1153C22—181no—
1154C22—181no—
1155C22—364no—
1156C22—541no—
1157C22—541no—
1158C22—541no—
1159C22C2×D3311yescharacteristic
1160C4—21no—
1161C4—61no—
1162C4—61no—
1163C4—61no—
1164C4—61no—
1165C4—181no—
1166C4—181no—
1167C4—181no—
1168C4—181no—
1169C4—541no—
1170C3—21no—
1171C3—21no—
1172C3—21no—
1173C3—41no—
1174C3#1059412611yescharacteristic, complemented
1175C3#1059412711yescharacteristic, complemented
1176C3#1059465811yescharacteristic, complemented
1177C2—121no—
1178C2—121no—
1179C2—182no—
1180C2—361no—
1181C2—1081no—
1182C2#1172438411yescharacteristic
1183C2#1172438511yescharacteristic
1184C2#1172440811yescharacteristic
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. #11723691C2semidirect
2. #11723482C2semidirect
3. #11723422C2semidirect
4. #11723419C2semidirect
5. C3×#63923C2semidirect
6. C3×#63862C2semidirect
7. C3×#63861C2semidirect
8. #11723002C2semidirect
9. #11722994C2semidirect
10. #11722983C2semidirect
11. #11722966C2semidirect
12. #11722963C2semidirect
13. #11722948C2semidirect
14. #11722937C2semidirect
15. #11722902C2semidirect
22. C2×#6294C22semidirect
23. C2×#6293C22semidirect
25. C2×#6292C22semidirect
28. C2×#6289C22semidirect
32. #88859C22semidirect
33. C3×C4⋊(C3⋊Dic3)C22semidirect
34. C3×C4×C3⋊Dic3C22semidirect
37. C32×Dic3⋊C4C22semidirect
39. #88814C22semidirect
40. #88806C22semidirect
41. #88804C22semidirect
42. #88803C22semidirect
45. C3×#3724C22semidirect
46. C3×Dic3⋊Dic3C22semidirect
47. C3×Dic3⋊Dic3C22semidirect
53. C3×Dic32C22semidirect
72. #63923D3semidirect
91. #63862D3semidirect
92. #63861D3semidirect
196. C4⋊(C3⋊Dic3)C2×D3semidirect
198. C4×C3⋊Dic3C2×D3semidirect
225. C3×Dic3⋊C4C2×D3semidirect
226. C3×Dic3⋊C4C2×D3semidirect
235. #3724C2×D3semidirect
236. Dic3⋊Dic3C2×D3semidirect
237. Dic3⋊Dic3C2×D3semidirect
261. Dic32C2×D3semidirect
589. Dic3⋊C4D32semidirect
735. C33#538semidirect
1066. C32#5593semidirect
1067. C32#5704semidirect
1068. C32#5704semidirect
1174. C3#10594126semidirect
1175. C3#10594127semidirect
1176. C3#10594658semidirect

Maximal subgroups

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

subgroupindex
#117236912
#117234822
#117234222
#117234192
C3×#639232
C3×#638622
C3×#638612
#117230022
#117229942
#117229832
#117229662
#117229632
#117229482
#117229372
#117229022
#105946583
#105941273
#105941263