Finite Group Databasebeta

← #13178206

Subgroups — #13178206

Order 1728.

1260 conjugacy classes of subgroups.

The subgroup lattice has 1180 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#64093C211yesmaximal, characteristic, complemented
2C3×#64092C211yesmaximal, characteristic, complemented
3C3×#64090C211yesmaximal, characteristic, complemented
4#11723728C211yesmaximal, characteristic, complemented
5#11723725C211yesmaximal, characteristic, complemented
6#11723720C211yesmaximal, characteristic, complemented
7#11723717C211yesmaximal, characteristic, complemented
8#11723696C211yesmaximal, characteristic, complemented
9#11723695C211yesmaximal, characteristic, complemented
10#11723694C211yesmaximal, characteristic, complemented
11#11723694C211yesmaximal, characteristic, complemented
12C4×#6295C211yesmaximal, characteristic, complemented
13#11723687C211yesmaximal, characteristic, complemented
14#11723683C211yesmaximal, characteristic, complemented
15#11723669C211yesmaximal, characteristic, complemented
16#10594202—31nomaximal
17#10594151—31nomaximal
18#10594100—31nomaximal
19C2×C3×#638C2211yescharacteristic
20C2×C3×#638C2211yescharacteristic
21C2×C3×#638C2211yescharacteristic
22C2×C3×#638C2211yescharacteristic
23C22×C3×C3⋊Dic3C2211yescharacteristic
24C2×C3×C4⋊(C3⋊D3)C2211yescharacteristic
25C2×C3×C4×C3⋊D3C2211yescharacteristic
26C2×C3×C4×C3⋊D3C2211yescharacteristic
27C2×C3×C4×C3⋊D3C2211yescharacteristic
28C2×#6295C2211yescharacteristic
29C2×#6295C2211yescharacteristic
30C2×#6295C2211yescharacteristic
31C2×#6295C2211yescharacteristic
32C2×#6295C2211yescharacteristic
33C2×#6294C2211yescharacteristic
34C33×C22⋊C4C2211yescharacteristic
35C3×#3757C2211yescharacteristic
36C3×#3752C2211yescharacteristic
37C3×#3752C2211yescharacteristic
38C3×#3752C2211yescharacteristic
39C3×C4⋊(C3⋊Dic3)C2211yescharacteristic
40C3×#3750C2211yescharacteristic
41C3×#3750C2211yescharacteristic
42C3×#3750C2211yescharacteristic
43C3×C4×C3⋊Dic3C2211yescharacteristic
44#88815C2211yescharacteristic
45#88815C2211yescharacteristic
46#88815C2211yescharacteristic
47#88815C2211yescharacteristic
48#88814C2211yescharacteristic
49#88814C2211yescharacteristic
50#88814C2211yescharacteristic
51#88814C2211yescharacteristic
52#88814C2211yescharacteristic
53#88813C2211yescharacteristic
54#64093D311yescharacteristic, complemented
55#64092D311yescharacteristic, complemented
56#64090D311yescharacteristic, complemented
57C3×#884—31no—
58C3×#884—31no—
59C3×#884—61no—
60C3×#883—31no—
61C3×#883—31no—
62C3×#883—61no—
63C3×#67⋊C4—31no—
64C3×#67⋊C4—31no—
65C3×#67⋊C4—61no—
66#63980—31no—
67#63979—31no—
68#63979—31no—
69#63979—31no—
70#63978—31no—
71#63978—31no—
72#63971—31no—
73#63970—31no—
74#63966—31no—
75#63962—31no—
76#63961—31no—
77#63958—31no—
78#63916—31no—
79#63912—31no—
80#63910—31no—
81#63909—31no—
82#63908—31no—
83#63906—31no—
84#63906—31no—
85#63905—31no—
86#63905—31no—
87C4×#626—31no—
88C4×#626—31no—
89C4×#625—31no—
90#63886—31no—
91#63885—31no—
92#63878—31no—
93#63877—31no—
94#63853—31no—
95#63853—31no—
96#63850—31no—
97#63850—31no—
98#63847—31no—
99#63846—31no—
100#63845—31no—
101#63836—31no—
102C23×C33C2311yescharacteristic
103C22×C3×C3⋊D3C2311yescharacteristic
104C22×C3×C3⋊D3C2311yescharacteristic
105C22×C3×C3⋊D3C2311yescharacteristic
106C22×C3×C3⋊D3C2311yescharacteristic
107C2×C33×C4C2311yescharacteristic
108C2×C33×C4C2311yescharacteristic
109C3×#638—22no—
110C3×#638—41no—
111C3×#638—41no—
112C3×#638—41no—
113C2×C3×C3⋊Dic3—41no—
114C2×C3×C3⋊Dic3C2311yescharacteristic
115C2×C3×C3⋊Dic3C2311yescharacteristic
116C2×C3×C3⋊Dic3C2311yescharacteristic
117C2×C3×C3⋊Dic3C2311yescharacteristic
118C2×C3×C3⋊Dic3C2311yescharacteristic
119C2×C3×C3⋊Dic3C2311yescharacteristic
120C2×C3×C3⋊Dic3C2311yescharacteristic
121C2×C3×C3⋊Dic3C2311yescharacteristic
122C3×C4⋊(C3⋊D3)—41no—
123C3×C4×C3⋊D3—41no—
124C3×C4×C3⋊D3—41no—
125C3×C4×C3⋊D3—41no—
126#6295—22no—
127#6295—41no—
128#6295—41no—
129#6295—41no—
130#6295—41no—
131#6294—22no—
132#5663—91no—
133#5615—91no—
134#5562—91no—
135C2×#638C2×D311yescharacteristic
136C2×#638C2×D311yescharacteristic
137C2×#638C2×D311yescharacteristic
138C2×#638C2×D311yescharacteristic
139C22×C3⋊Dic3C2×D311yescharacteristic
140C2×C4⋊(C3⋊D3)C2×D311yescharacteristic
141C2×C4×C3⋊D3C2×D311yescharacteristic
142C2×C4×C3⋊D3C2×D311yescharacteristic
143C2×C4×C3⋊D3C2×D311yescharacteristic
144C2×C3×#67—31no—
145C2×C3×#67—31no—
146C2×C3×#67—31no—
147C2×C3×#67—31no—
148C2×C3×#67—31no—
149C2×C3×#67—31no—
150C2×C3×#67—31no—
151C2×C3×#67—31no—
152C2×C3×#67—61no—
153C2×C3×#67—61no—
154C2×C3×#67—61no—
155C2×C3×#67—61no—
156C22×C3×Dic3—31no—
157C22×C3×Dic3—31no—
158C22×C3×Dic3—61no—
159C2×C3×D12—31no—
160C2×C3×D12—31no—
161C2×C3×D12—61no—
162C2×C3×C4×D3—31no—
163C2×C3×C4×D3—31no—
164C2×C3×C4×D3—31no—
165C2×C3×C4×D3—31no—
166C2×C3×C4×D3—31no—
167C2×C3×C4×D3—31no—
168C2×C3×C4×D3—61no—
169C2×C3×C4×D3—61no—
170C2×C3×C4×D3—61no—
171C2×#626—31no—
172C2×#626—31no—
173C2×#626—31no—
174C2×#626—31no—
175C2×#626—31no—
176C2×#626—31no—
177C2×#626—31no—
178C2×#626—31no—
179C2×#626—31no—
180C2×#626—31no—
181C2×#625—31no—
182C2×#625—31no—
183C2×#625—31no—
184C2×#625—31no—
185C2×#625—31no—
186C2×#624—31no—
187C2×D3×Dic3—31no—
188C2×D3×Dic3—31no—
189C32×C22⋊C4—21no—
190C32×C22⋊C4—21no—
191C32×C22⋊C4—21no—
192C32×C22⋊C4—41no—
193C32×C22⋊C4C2×D311yescharacteristic
194C32×C22⋊C4C2×D311yescharacteristic
195C32×C22⋊C4C2×D311yescharacteristic
196#3757C2×D311yescharacteristic
197#3752C2×D311yescharacteristic
198#3752C2×D311yescharacteristic
199#3752C2×D311yescharacteristic
200C4⋊(C3⋊Dic3)C2×D311yescharacteristic
201#3750C2×D311yescharacteristic
202#3750C2×D311yescharacteristic
203#3750C2×D311yescharacteristic
204C4×C3⋊Dic3C2×D311yescharacteristic
205C3×#217—31no—
206C3×#217—31no—
207C3×#217—61no—
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)⋊C4—61no—
217C3×C4⋊Dic3—31no—
218C3×C4⋊Dic3—31no—
219C3×C4⋊Dic3—61no—
220C3×Dic3⋊C4—31no—
221C3×Dic3⋊C4—31no—
222C3×Dic3⋊C4—31no—
223C3×Dic3⋊C4—31no—
224C3×Dic3⋊C4—31no—
225C3×Dic3⋊C4—31no—
226C3×Dic3⋊C4—61no—
227C3×Dic3⋊C4—61no—
228C3×Dic3⋊C4—61no—
229C3×C4×Dic3—31no—
230C3×C4×Dic3—31no—
231C3×C4×Dic3—61no—
232#3724—31no—
233#3724—31no—
234#3724—31no—
235#3724—31no—
236Dic3⋊Dic3—31no—
237Dic3⋊Dic3—31no—
238Dic3⋊Dic3—31no—
239Dic3⋊Dic3—31no—
240Dic3⋊Dic3—31no—
241Dic3⋊Dic3—31no—
242Dic3⋊Dic3—31no—
243Dic3⋊Dic3—31no—
244#3722—31no—
245#3722—31no—
246#3722—31no—
247#3722—31no—
248#3722—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—31no—
255(C2×D3)⋊Dic3—31no—
256(C2×D3)⋊Dic3—31no—
257(C2×D3)⋊Dic3—31no—
258(C2×D3)⋊Dic3—31no—
259Dic32—31no—
260Dic32—31no—
261Dic32—31no—
262C22×C33—21no—
263C22×C33—21no—
264C22×C33—21no—
265C22×C33C2411yescharacteristic
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—21no—
275C2×C3×C3⋊D3—21no—
276C2×C3×C3⋊D3—21no—
277C2×C3×C3⋊D3—21no—
278C33×C4—21no—
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—
286C3×C3⋊Dic3—21no—
287C3×C3⋊Dic3#4112yes—
288C3×#123—91no—
289C3×#121—91no—
290C3×C4×D4—91no—
291#940—91no—
292#940—91no—
293#940—91no—
294#939—91no—
295#939—91no—
296#939—91no—
297#939—91no—
298#938—91no—
299#938—91no—
300#935—91no—
301#930—91no—
302#930—91no—
303#930—91no—
304#929—91no—
305#929—91no—
306#929—91no—
307C4×#67—91no—
308C4×#67—91no—
309#895—91no—
310#895—91no—
311#894—91no—
312#894—91no—
313#892—91no—
314#890—91no—
315#889—91no—
316#889—91no—
317#886—91no—
318#884—31no—
319#884—31no—
320#884—61no—
321#884—91no—
322#884—91no—
323#884—91no—
324#884—91no—
325#883—31no—
326#883—31no—
327#883—61no—
328#883—91no—
329#883—91no—
330#67⋊C4—31no—
331#67⋊C4—31no—
332#67⋊C4—61no—
333#877—91no—
334C4×D12—91no—
335#872—91no—
336C23×C32—21no—
337C23×C32—21no—
338C23×C32—21no—
339C23×C32—41no—
340C23×C32C22×D311yescharacteristic
341C23×C32C22×D311yescharacteristic
342C23×C32C22×D311yescharacteristic
343C22×C3⋊D3C22×D311yescharacteristic
344C22×C3⋊D3C22×D311yescharacteristic
345C22×C3⋊D3C22×D311yescharacteristic
346C22×C3⋊D3C22×D311yescharacteristic
347C22×C3×D3—31no—
348C22×C3×D3—31no—
349C22×C3×D3—31no—
350C22×C3×D3—31no—
351C22×C3×D3—31no—
352C22×C3×D3—31no—
353C22×C3×D3—31no—
354C22×C3×D3—31no—
355C22×C3×D3—61no—
356C22×C3×D3—61no—
357C22×C3×D3—61no—
358C22×C3×D3—61no—
359C2×C32×C4—21no—
360C2×C32×C4—21no—
361C2×C32×C4—21no—
362C2×C32×C4—21no—
363C2×C32×C4—21no—
364C2×C32×C4—21no—
365C2×C32×C4—41no—
366C2×C32×C4—41no—
367C2×C32×C4C22×D311yescharacteristic
368C2×C32×C4C22×D311yescharacteristic
369C2×C32×C4C22×D311yescharacteristic
370C2×C32×C4C22×D311yescharacteristic
371C2×C32×C4C22×D311yescharacteristic
372C2×C32×C4C22×D311yescharacteristic
373#638—22no—
374#638—41no—
375#638—41no—
376#638—41no—
377C2×C3⋊Dic3—41no—
378C2×C3⋊Dic3C22×D311yescharacteristic
379C2×C3⋊Dic3C22×D311yescharacteristic
380C2×C3⋊Dic3C22×D311yescharacteristic
381C2×C3⋊Dic3C22×D311yescharacteristic
382C2×C3⋊Dic3C22×D311yescharacteristic
383C2×C3⋊Dic3C22×D311yescharacteristic
384C2×C3⋊Dic3C22×D311yescharacteristic
385C2×C3⋊Dic3C22×D311yescharacteristic
386C4⋊(C3⋊D3)—41no—
387C4×C3⋊D3—41no—
388C4×C3⋊D3—41no—
389C4×C3⋊D3—41no—
390C3×#67—62no—
391C3×#67—62no—
392C3×#67—64no—
393C3×#67—121no—
394C3×#67—121no—
395C3×#67—121no—
396C3×#67—121no—
397C3×#67—121no—
398C3×#67—121no—
399C3×#67—122no—
400C3×#67—122no—
401C3×#67—122no—
402C2×C3×Dic3—31no—
403C2×C3×Dic3—31no—
404C2×C3×Dic3—31no—
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—31no—
414C2×C3×Dic3—31no—
415C2×C3×Dic3—31no—
416C2×C3×Dic3—31no—
417C2×C3×Dic3—31no—
418C2×C3×Dic3—61no—
419C2×C3×Dic3—61no—
420C2×C3×Dic3—61no—
421C2×C3×Dic3—61no—
422C2×C3×Dic3—61no—
423C2×C3×Dic3—61no—
424C2×C3×Dic3—61no—
425C2×C3×Dic3—61no—
426C2×C3×Dic3—121no—
427C2×C3×Dic3—121no—
428C2×C3×Dic3—122no—
429C3×D12—121no—
430C3×D12—121no—
431C3×D12—122no—
432C3×C4×D3—121no—
433C3×C4×D3—121no—
434C3×C4×D3—121no—
435C3×C4×D3—121no—
436C3×C4×D3—121no—
437C3×C4×D3—121no—
438C3×C4×D3—122no—
439C3×C4×D3—122no—
440C3×C4×D3—122no—
441#626—62no—
442#626—62no—
443#626—121no—
444#626—121no—
445#626—121no—
446#626—121no—
447#626—121no—
448#626—121no—
449#626—121no—
450#626—121no—
451#625—62no—
452#625—121no—
453#625—121no—
454#625—121no—
455#625—121no—
456#624—62no—
457D3×Dic3—62no—
458D3×Dic3—62no—
459#540—271noSylow
460C2×C33—41no—
461C2×C33C2×#4111yescharacteristic
462C2×C33H(5,𝔽2)11yescharacteristic
463C2×C33H(5,𝔽2)11yescharacteristic
464C3×C3⋊D3—41no—
465C3×C3⋊D3—41no—
466C3×C3⋊D3—41no—
467C3×C3⋊D3—41no—
468C2×C3×D4—91no—
469C2×C3×D4—91no—
470C2×C3×D4—91no—
471C2×C3×D4—91no—
472C2×C3×D4—91no—
473C22×C3×C4—91no—
474C22×C3×C4—91no—
475C22×C3×C4—91no—
476C22×C3×C4—91no—
477C2×#67—31no—
478C2×#67—31no—
479C2×#67—31no—
480C2×#67—31no—
481C2×#67—31no—
482C2×#67—31no—
483C2×#67—31no—
484C2×#67—31no—
485C2×#67—61no—
486C2×#67—61no—
487C2×#67—61no—
488C2×#67—61no—
489C2×#67—91no—
490C2×#67—91no—
491C2×#67—91no—
492C2×#67—91no—
493C2×#67—91no—
494C2×#67—91no—
495C2×#67—91no—
496C2×#67—91no—
497C2×#67—91no—
498C2×#67—91no—
499C22×Dic3—31no—
500C22×Dic3—31no—
501C22×Dic3—61no—
502C22×Dic3—91no—
503C2×D12—31no—
504C2×D12—31no—
505C2×D12—61no—
506C2×D12—91no—
507C2×D12—91no—
508C2×D12—91no—
509C2×D12—91no—
510C2×D12—91no—
511C2×C4×D3—31no—
512C2×C4×D3—31no—
513C2×C4×D3—31no—
514C2×C4×D3—31no—
515C2×C4×D3—31no—
516C2×C4×D3—31no—
517C2×C4×D3—61no—
518C2×C4×D3—61no—
519C2×C4×D3—61no—
520C2×C4×D3—91no—
521C2×C4×D3—91no—
522C3×C4⋊C4—91no—
523C3×C4⋊C4—91no—
524C3×C4⋊C4—91no—
525C3×C4⋊C4—91no—
526C3×C22⋊C4—21no—
527C3×C22⋊C4—21no—
528C3×C22⋊C4—21no—
529C3×C22⋊C4—41no—
530C3×C22⋊C4—91no—
531C3×C22⋊C4—91no—
532C3×C22⋊C4—91no—
533C3×C22⋊C4—91no—
534C3×C22⋊C4D3211yescharacteristic
535C3×C22⋊C4D3211yescharacteristic
536C3×C22⋊C4D3211yescharacteristic
537C3×C42—91no—
538#217—31no—
539#217—31no—
540#217—61no—
541#217—91no—
542#217—91no—
543#217—91no—
544#217—91no—
545#217—91no—
546(C2×D3)⋊C4—31no—
547(C2×D3)⋊C4—31no—
548(C2×D3)⋊C4—31no—
549(C2×D3)⋊C4—31no—
550(C2×D3)⋊C4—31no—
551(C2×D3)⋊C4—31no—
552(C2×D3)⋊C4—61no—
553(C2×D3)⋊C4—61no—
554(C2×D3)⋊C4—61no—
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—
565C4⋊Dic3—31no—
566C4⋊Dic3—31no—
567C4⋊Dic3—61no—
568C4⋊Dic3—91no—
569C4⋊Dic3—91no—
570C4⋊Dic3—91no—
571C4⋊Dic3—91no—
572Dic3⋊C4—31no—
573Dic3⋊C4—31no—
574Dic3⋊C4—31no—
575Dic3⋊C4—31no—
576Dic3⋊C4—31no—
577Dic3⋊C4—31no—
578Dic3⋊C4—61no—
579Dic3⋊C4—61no—
580Dic3⋊C4—61no—
581Dic3⋊C4—91no—
582Dic3⋊C4—91no—
583Dic3⋊C4—91no—
584Dic3⋊C4—91no—
585Dic3⋊C4—91no—
586Dic3⋊C4—91no—
587Dic3⋊C4—91no—
588Dic3⋊C4—91no—
589C4×Dic3—31no—
590C4×Dic3—31no—
591C4×Dic3—61no—
592C4×Dic3—91no—
593C4×Dic3—91no—
594C4×Dic3—91no—
595C22×C32—21no—
596C22×C32—22no—
597C22×C32—21no—
598C22×C32—21no—
599C22×C32—21no—
600C22×C32—21no—
601C22×C32—21no—
602C22×C32—21no—
603C22×C32—21no—
604C22×C32—21no—
605C22×C32—21no—
606C22×C32—21no—
607C22×C32—21no—
608C22×C32—41no—
609C22×C32—41no—
610C22×C32—41no—
611C22×C32—42no—
612C22×C32—41no—
613C22×C32—41no—
614C22×C32—41no—
615C22×C32—41no—
616C22×C32—41no—
617C22×C32—41no—
618C22×C32—81no—
619C22×C32—81no—
620C22×C32C23×D311yescharacteristic
621C22×C32C23×D311yescharacteristic
622C22×C32C23×D311yescharacteristic
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—21no—
633C2×C3⋊D3—21no—
634C2×C3⋊D3—21no—
635C2×C3×D3—62no—
636C2×C3×D3—62no—
637C2×C3×D3—62no—
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—61no—
650C2×C3×D3—61no—
651C2×C3×D3—61no—
652C2×C3×D3—61no—
653C2×C3×D3—61no—
654C2×C3×D3—61no—
655C2×C3×D3—61no—
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—121no—
663C2×C3×D3—121no—
664C2×C3×D3—121no—
665C2×C3×D3—121no—
666C2×C3×D3—121no—
667C2×C3×D3—121no—
668C2×C3×D3—121no—
669C2×C3×D3—121no—
670C2×C3×D3—121no—
671C32×C4—21no—
672C32×C4—21no—
673C32×C4—21no—
674C32×C4—21no—
675C32×C4—21no—
676C32×C4—21no—
677C32×C4—41no—
678C32×C4—41no—
679C32×C4—41no—
680C32×C4—41no—
681C32×C4—41no—
682C32×C4—41no—
683C32×C4—81no—
684C32×C4—81no—
685C3⋊Dic3—21no—
686C3⋊Dic3—21no—
687C3⋊Dic3—21no—
688C3⋊Dic3—21no—
689C3⋊Dic3—21no—
690C3⋊Dic3—21no—
691C3⋊Dic3—21no—
692C3⋊Dic3#23512yes—
693C3×Dic3—32no—
694C3×Dic3—32no—
695C3×Dic3—62no—
696C3×Dic3—62no—
697C3×Dic3—62no—
698C3×Dic3—61no—
699C3×Dic3—61no—
700C3×Dic3—61no—
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—61no—
710C3×Dic3—61no—
711C3×Dic3—61no—
712C3×Dic3—121no—
713C3×Dic3—121no—
714C3×Dic3—121no—
715C3×Dic3—121no—
716C3×Dic3—121no—
717#127—271no—
718#125—271no—
719#123—91no—
720#123—271no—
721#123—271no—
722#123—271no—
723#121—91no—
724#121—271no—
725#121—271no—
726#121—271no—
727#121—271no—
728#121—271no—
729C4×D4—91no—
730C4×D4—271no—
731#117—271no—
732C33#54011yescharacteristic, complemented, Sylow
733C23×C3—21no—
734C23×C3—21no—
735C23×C3—21no—
736C23×C3—41no—
737C23×C3—91no—
738C23×C3—91no—
739C23×C3—91no—
740C23×C3—91no—
741C23×C3C2×D3211yescharacteristic
742C23×C3C2×D3211yescharacteristic
743C23×C3C2×D3211yescharacteristic
744C22×D3—31no—
745C22×D3—31no—
746C22×D3—31no—
747C22×D3—31no—
748C22×D3—31no—
749C22×D3—31no—
750C22×D3—31no—
751C22×D3—31no—
752C22×D3—61no—
753C22×D3—61no—
754C22×D3—61no—
755C22×D3—61no—
756C3×D4—182no—
757C3×D4—361no—
758C3×D4—361no—
759C3×D4—361no—
760C3×D4—361no—
761C2×C3×C4—21no—
762C2×C3×C4—21no—
763C2×C3×C4—21no—
764C2×C3×C4—21no—
765C2×C3×C4—21no—
766C2×C3×C4—21no—
767C2×C3×C4—41no—
768C2×C3×C4—41no—
769C2×C3×C4—91no—
770C2×C3×C4—91no—
771C2×C3×C4—91no—
772C2×C3×C4—91no—
773C2×C3×C4—91no—
774C2×C3×C4—91no—
775C2×C3×C4—91no—
776C2×C3×C4—91no—
777C2×C3×C4—361no—
778C2×C3×C4—361no—
779C2×C3×C4—361no—
780C2×C3×C4—361no—
781C2×C3×C4C2×D3211yescharacteristic
782C2×C3×C4C2×D3211yescharacteristic
783C2×C3×C4C2×D3211yescharacteristic
784C2×C3×C4C2×D3211yescharacteristic
785C2×C3×C4C2×D3211yescharacteristic
786C2×C3×C4C2×D3211yescharacteristic
787#67—62no—
788#67—62no—
789#67—64no—
790#67—121no—
791#67—121no—
792#67—121no—
793#67—121no—
794#67—121no—
795#67—121no—
796#67—122no—
797#67—122no—
798#67—122no—
799#67—182no—
800#67—182no—
801#67—361no—
802#67—361no—
803#67—361no—
804#67—361no—
805#67—361no—
806#67—361no—
807#67—361no—
808#67—361no—
809C2×Dic3—31no—
810C2×Dic3—31no—
811C2×Dic3—31no—
812C2×Dic3—31no—
813C2×Dic3—31no—
814C2×Dic3—31no—
815C2×Dic3—31no—
816C2×Dic3—31no—
817C2×Dic3—31no—
818C2×Dic3—31no—
819C2×Dic3—31no—
820C2×Dic3—31no—
821C2×Dic3—31no—
822C2×Dic3—31no—
823C2×Dic3—31no—
824C2×Dic3—31no—
825C2×Dic3—61no—
826C2×Dic3—61no—
827C2×Dic3—61no—
828C2×Dic3—61no—
829C2×Dic3—61no—
830C2×Dic3—61no—
831C2×Dic3—61no—
832C2×Dic3—61no—
833C2×Dic3—121no—
834C2×Dic3—121no—
835C2×Dic3—122no—
836C2×Dic3—182no—
837D12—121no—
838D12—121no—
839D12—122no—
840D12—182no—
841D12—361no—
842D12—361no—
843D12—361no—
844D12—361no—
845C4×D3—121no—
846C4×D3—121no—
847C4×D3—121no—
848C4×D3—121no—
849C4×D3—121no—
850C4×D3—121no—
851C4×D3—122no—
852C4×D3—122no—
853C4×D3—122no—
854C4×D3—182no—
855C4×D3—182no—
856C2×C32—21no—
857C2×C32—21no—
858C2×C32—21no—
859C2×C32—21no—
860C2×C32—21no—
861C2×C32—21no—
862C2×C32—21no—
863C2×C32—21no—
864C2×C32—21no—
865C2×C32—41no—
866C2×C32—41no—
867C2×C32—41no—
868C2×C32—41no—
869C2×C32—42no—
870C2×C32—41no—
871C2×C32—41no—
872C2×C32—81no—
873C2×C32—81no—
874C2×C32—82no—
875C2×C32C2×#23511yescharacteristic
876C2×C32#100411yescharacteristic
877C2×C32#100411yescharacteristic
878C2×C32#100411yescharacteristic
879C2×C32#100411yescharacteristic
880C2×C32D3×#4111yescharacteristic
881C2×C32D3×#4111yescharacteristic
882C2×C32#100911yescharacteristic
883C2×C32#100911yescharacteristic
884C3⋊D3—41no—
885C3⋊D3—41no—
886C3⋊D3—41no—
887C3⋊D3—41no—
888C3×D3—122no—
889C3×D3—122no—
890C3×D3—122no—
891C3×D3—121no—
892C3×D3—121no—
893C3×D3—121no—
894C3×D3—121no—
895C3×D3—121no—
896C3×D3—121no—
897C3×D3—121no—
898C3×D3—121no—
899C3×D3—241no—
900C2×D4—91no—
901C2×D4—91no—
902C2×D4—91no—
903C2×D4—91no—
904C2×D4—91no—
905C2×D4—271no—
906C2×D4—271no—
907C2×D4—271no—
908C2×D4—271no—
909C2×D4—271no—
910C22×C4—91no—
911C22×C4—91no—
912C22×C4—91no—
913C22×C4—91no—
914C22×C4—271no—
915C4⋊C4—91no—
916C4⋊C4—91no—
917C4⋊C4—91no—
918C4⋊C4—91no—
919C4⋊C4—271no—
920C4⋊C4—271no—
921C4⋊C4—271no—
922C4⋊C4—271no—
923C22⋊C4—91no—
924C22⋊C4—91no—
925C22⋊C4—91no—
926C22⋊C4—91no—
927C22⋊C4—271no—
928C22⋊C4—271no—
929C22⋊C4—271no—
930C22⋊C4—271no—
931C22⋊C4—271no—
932C22⋊C4#111311yescharacteristic
933C42—91no—
934C42—271no—
935C22×C3—22no—
936C22×C3—21no—
937C22×C3—21no—
938C22×C3—21no—
939C22×C3—21no—
940C22×C3—21no—
941C22×C3—21no—
942C22×C3—21no—
943C22×C3—21no—
944C22×C3—21no—
945C22×C3—21no—
946C22×C3—21no—
947C22×C3—21no—
948C22×C3—41no—
949C22×C3—41no—
950C22×C3—41no—
951C22×C3—41no—
952C22×C3—41no—
953C22×C3—41no—
954C22×C3—41no—
955C22×C3—41no—
956C22×C3—42no—
957C22×C3—41no—
958C22×C3—81no—
959C22×C3—81no—
960C22×C3—181no—
961C22×C3—181no—
962C22×C3—181no—
963C22×C3—181no—
964C22×C3—181no—
965C22×C3—181no—
966C22×C3—181no—
967C22×C3—181no—
968C22×C3—181no—
969C22×C3—181no—
970C22×C3—181no—
971C22×C3—181no—
972C22×C3C22×D3211yescharacteristic
973C22×C3C22×D3211yescharacteristic
974C22×C3C22×D3211yescharacteristic
975C2×D3—62no—
976C2×D3—62no—
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—61no—
989C2×D3—61no—
990C2×D3—61no—
991C2×D3—61no—
992C2×D3—61no—
993C2×D3—61no—
994C2×D3—61no—
995C2×D3—61no—
996C2×D3—61no—
997C2×D3—61no—
998C2×D3—61no—
999C2×D3—61no—
1000C2×D3—61no—
1001C2×D3—61no—
1002C2×D3—121no—
1003C2×D3—121no—
1004C2×D3—121no—
1005C2×D3—121no—
1006C2×D3—121no—
1007C2×D3—121no—
1008C2×D3—121no—
1009C2×D3—121no—
1010C2×D3—121no—
1011C3×C4—21no—
1012C3×C4—21no—
1013C3×C4—21no—
1014C3×C4—21no—
1015C3×C4—21no—
1016C3×C4—21no—
1017C3×C4—41no—
1018C3×C4—41no—
1019C3×C4—41no—
1020C3×C4—41no—
1021C3×C4—41no—
1022C3×C4—41no—
1023C3×C4—81no—
1024C3×C4—81no—
1025C3×C4—92no—
1026C3×C4—181no—
1027C3×C4—181no—
1028C3×C4—181no—
1029C3×C4—181no—
1030C3×C4—181no—
1031C3×C4—181no—
1032C3×C4—181no—
1033Dic3—32no—
1034Dic3—32no—
1035Dic3—62no—
1036Dic3—62no—
1037Dic3—62no—
1038Dic3—61no—
1039Dic3—61no—
1040Dic3—61no—
1041Dic3—61no—
1042Dic3—61no—
1043Dic3—61no—
1044Dic3—61no—
1045Dic3—61no—
1046Dic3—61no—
1047Dic3—61no—
1048Dic3—61no—
1049Dic3—61no—
1050Dic3—61no—
1051Dic3—61no—
1052Dic3—121no—
1053Dic3—121no—
1054Dic3—121no—
1055Dic3—121no—
1056Dic3—121no—
1057C32—21no—
1058C32—21no—
1059C32—21no—
1060C32—41no—
1061C32#556211yescharacteristic, complemented
1062C32#561511yescharacteristic, complemented
1063C32#566311yescharacteristic, complemented
1064C23—91no—
1065C23—91no—
1066C23—91no—
1067C23—91no—
1068C23C2×#111311yescharacteristic
1069D4—182no—
1070D4—361no—
1071D4—361no—
1072D4—361no—
1073D4—361no—
1074D4—542no—
1075D4—1081no—
1076D4—1081no—
1077D4—1081no—
1078D4—1081no—
1079C2×C4—91no—
1080C2×C4—91no—
1081C2×C4—91no—
1082C2×C4—91no—
1083C2×C4—91no—
1084C2×C4—91no—
1085C2×C4—91no—
1086C2×C4—91no—
1087C2×C4—361no—
1088C2×C4—361no—
1089C2×C4—361no—
1090C2×C4—361no—
1091C2×C4—542no—
1092C2×C4C2×#111311yescharacteristic
1093C2×C4C2×#111311yescharacteristic
1094C2×C3—21no—
1095C2×C3—21no—
1096C2×C3—21no—
1097C2×C3—21no—
1098C2×C3—21no—
1099C2×C3—21no—
1100C2×C3—21no—
1101C2×C3—21no—
1102C2×C3—21no—
1103C2×C3—42no—
1104C2×C3—41no—
1105C2×C3—41no—
1106C2×C3—41no—
1107C2×C3—41no—
1108C2×C3—41no—
1109C2×C3—41no—
1110C2×C3—81no—
1111C2×C3—81no—
1112C2×C3—82no—
1113C2×C3—361no—
1114C2×C3—361no—
1115C2×C3—361no—
1116C2×C3—361no—
1117C2×C3D3×#23511yescharacteristic
1118C2×C3D3×#23511yescharacteristic
1119C2×C3#6430611yescharacteristic
1120C2×C3#6431311yescharacteristic
1121C2×C3#6431311yescharacteristic
1122C2×C3#6431411yescharacteristic
1123C2×C3#6431411yescharacteristic
1124C2×C3#6431411yescharacteristic
1125C2×C3#6431411yescharacteristic
1126D3—122no—
1127D3—122no—
1128D3—122no—
1129D3—121no—
1130D3—121no—
1131D3—121no—
1132D3—121no—
1133D3—121no—
1134D3—121no—
1135D3—121no—
1136D3—121no—
1137D3—241no—
1138C22—21no—
1139C22—21no—
1140C22—21no—
1141C22—181no—
1142C22—181no—
1143C22—181no—
1144C22—181no—
1145C22—181no—
1146C22—181no—
1147C22—181no—
1148C22—181no—
1149C22—181no—
1150C22—181no—
1151C22—181no—
1152C22—181no—
1153C22C22×#111311yescharacteristic
1154C4—21no—
1155C4—21no—
1156C4—92no—
1157C4—181no—
1158C4—181no—
1159C4—181no—
1160C4—181no—
1161C4—181no—
1162C4—181no—
1163C4—181no—
1164C3—21no—
1165C3—21no—
1166C3—21no—
1167C3—41no—
1168C3#1059410011yescharacteristic, complemented
1169C3#1059415111yescharacteristic, complemented
1170C3#1059420211yescharacteristic, complemented
1171C2—41no—
1172C2—361no—
1173C2—361no—
1174C2—361no—
1175C2—361no—
1176C2#1172461811yescharacteristic
1177C2#1172462311yescharacteristic
1178C2#1172462311yescharacteristic
subgroupG/H
center, FrattiniC22C22×#1113
commutator, socle, cosocleC22×C33C24
FittingC33×C22⋊C4C22
hypercenterC22⋊C4#1113
hypocenterC33#540
LCSG ▷ C22×C33 ▷ C33
UCSC1 ◁ C22 ◁ C22⋊C4

Complements

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

NH ≅ G/Ntype
1. C3×#64093C2semidirect
2. C3×#64092C2semidirect
3. C3×#64090C2semidirect
4. #11723728C2semidirect
5. #11723725C2semidirect
6. #11723720C2semidirect
7. #11723717C2semidirect
8. #11723696C2semidirect
9. #11723695C2semidirect
10. #11723694C2semidirect
11. #11723694C2semidirect
12. C4×#6295C2semidirect
13. #11723687C2semidirect
14. #11723683C2semidirect
15. #11723669C2semidirect
54. #64093D3semidirect
55. #64092D3semidirect
56. #64090D3semidirect
732. C33#540semidirect
1061. C32#5562semidirect
1062. C32#5615semidirect
1063. C32#5663semidirect
1168. C3#10594100semidirect
1169. C3#10594151semidirect
1170. C3#10594202semidirect

Maximal subgroups

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

subgroupindex
C3×#640932
C3×#640922
C3×#640902
#117237282
#117237252
#117237202
#117237172
#117236962
#117236952
#117236942
C4×#62952
#117236872
#117236832
#117236692
#105942023
#105941513
#105941003