Finite Group Databasebeta

← #13168185

Subgroups — #13168185

Order 1728.

1132 conjugacy classes of subgroups.

The subgroup lattice has 1050 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11723669C211yesmaximal, characteristic, complemented
2#11723496C211yesmaximal, characteristic, complemented
3#11723496C211yesmaximal, characteristic, complemented
4#11723426C211yesmaximal, characteristic, complemented
5C3×#63905C211yesmaximal, characteristic, complemented
6C3×#63891C211yesmaximal, characteristic, complemented
7C3×#63879C211yesmaximal, characteristic, complemented
8#11723026C211yesmaximal, characteristic, complemented
9#11723020C211yesmaximal, characteristic, complemented
10#11723012C211yesmaximal, characteristic, complemented
11#11722989C211yesmaximal, characteristic, complemented
12#11722985C211yesmaximal, characteristic, complemented
13#11722953C211yesmaximal, characteristic
14#11722924C211yesmaximal, characteristic, complemented
15D3×Dic3⋊Dic3C211yesmaximal, characteristic, complemented
16#10594935—31nomaximal
17#10594177—31nomaximal
18#10594121—31nomaximal
19C2×#6308C2211yescharacteristic
20C2×C32×C4×D3C2211yescharacteristic
21C2×D3×C3⋊Dic3C2211yescharacteristic
22C2×D3×C3⋊Dic3C2211yescharacteristic
23C2×C3×#625C2211yescharacteristic
24C2×C3×#625C2211yescharacteristic
25C2×C3×#625C2211yescharacteristic
26C2×C3×D3×Dic3C2211yescharacteristic
27C2×C3×D3×Dic3C2211yescharacteristic
28C3×C4⋊(C3⋊Dic3)C2211yescharacteristic
29C3×#3750C2211yescharacteristic
30C3×#3750C2211yescharacteristic
31C32×(C2×D3)⋊C4C2211yescharacteristic
32C32×(C2×D3)⋊C4C2211yescharacteristic
33#88815C2211yescharacteristic
34#88815C2211yescharacteristic
35#88815C2211yescharacteristic
36#88813C2211yescharacteristic
37#88807C2211yescharacteristic
38#88807C2211yescharacteristic
39#88806C2211yescharacteristic
40#88806C2211yescharacteristic
41Dic3⋊(C3⋊Dic3)C2211yescharacteristic
42Dic3⋊(C3⋊Dic3)C2211yescharacteristic
43(C2×D3)⋊(C3⋊Dic3)C2211yescharacteristic
44(C2×D3)⋊(C3⋊Dic3)C2211yescharacteristic
45(C2×D3)⋊(C3⋊Dic3)C2211yescharacteristic
46(C2×D3)⋊(C3⋊Dic3)C2211yescharacteristic
47C3×Dic3⋊Dic3C2211yescharacteristic
48C3×Dic3⋊Dic3C2211yescharacteristic
49C3×(C2×D3)⋊Dic3C2211yescharacteristic
50C3×(C2×D3)⋊Dic3C2211yescharacteristic
51C3×(C2×D3)⋊Dic3C2211yescharacteristic
52C3×(C2×D3)⋊Dic3C2211yescharacteristic
53C3×Dic32C2211yescharacteristic
54#64133—31no—
55#64087—31no—
56#64087—31no—
57C3×#929—31no—
58C3×C4×#67—31no—
59C3×#886—31no—
60C3×#883—31no—
61C3×#883—31no—
62C3×#67⋊C4—31no—
63#63980—31no—
64#67⋊Dic3—31no—
65Dic3×#67—31no—
66#63970—31no—
67#63970—31no—
68#63969—31no—
69#63969—31no—
70C2×Dic3⋊Dic3—31no—
71#63962—31no—
72#63961—31no—
73#63956—31no—
74#63956—31no—
75#63905—31no—
76#63905D311yescharacteristic, complemented
77#63896—31no—
78#63896—31no—
79#63896—31no—
80#63896—31no—
81#63896—61no—
82#63896—61no—
83#63891—31no—
84#63891D311yescharacteristic, complemented
85D3×C4⋊Dic3—31no—
86#63879—31no—
87#63879D311yescharacteristic, complemented
88D3×Dic3⋊C4—31no—
89#63869—31no—
90#63867—31no—
91#63861—31no—
92#63859—31no—
93#63859—31no—
94#63858—31no—
95#63857—31no—
96#63857—31no—
97#63857—61no—
98#63847—31no—
99#63846—31no—
100#63846—31no—
101#63845—31no—
102C22×C32×D3C2311yescharacteristic
103C22×C32×D3C2311yescharacteristic
104C22×C32×D3C2311yescharacteristic
105C2×C33×C4C2311yescharacteristic
106C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
107C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
108#6308—41no—
109C2×C3×C3⋊Dic3C2311yescharacteristic
110C2×C3×C3⋊Dic3C2311yescharacteristic
111C2×C3×C3⋊Dic3C2311yescharacteristic
112C2×C3×C3⋊Dic3C2311yescharacteristic
113C2×C3×C3⋊Dic3C2311yescharacteristic
114C2×C3×C3⋊Dic3C2311yescharacteristic
115C2×C32×Dic3C2311yescharacteristic
116C2×C32×Dic3C2311yescharacteristic
117C2×C32×Dic3C2311yescharacteristic
118C32×C4×D3—41no—
119D3×C3⋊Dic3—41no—
120D3×C3⋊Dic3—41no—
121C3×#625—22no—
122C3×#625—22no—
123C3×#625—41no—
124C3×D3×Dic3—22no—
125C3×D3×Dic3—41no—
126#5665—91no—
127#5660—91no—
128#5564—91no—
129C22×C32×C4—31no—
130C22×C3⋊Dic3—31no—
131C22×C3⋊Dic3—31no—
132C2×#634—31no—
133C2×#634—31no—
134C2×#634—31no—
135C2×#634—61no—
136C2×#634—61no—
137C2×#634—61no—
138C2×#634—121no—
139C2×C3×#67—31no—
140C2×C3×#67—31no—
141C2×C3×#67—31no—
142C2×C3×#67—31no—
143C2×C3×#67—31no—
144C2×C3×#67—31no—
145C22×C3×Dic3—31no—
146C22×C3×Dic3—31no—
147C2×C3×C4×D3—21no—
148C2×C3×C4×D3—31no—
149C2×C3×C4×D3—31no—
150C2×C3×C4×D3C2×D311yescharacteristic
151C2×C3×C4×D3C2×D311yescharacteristic
152C2×#625C2×D311yescharacteristic
153C2×#625C2×D311yescharacteristic
154C2×#625C2×D311yescharacteristic
155C2×D3×Dic3—31no—
156C2×D3×Dic3—31no—
157C2×D3×Dic3—31no—
158C2×D3×Dic3—31no—
159C2×D3×Dic3—61no—
160C2×D3×Dic3—61no—
161C2×D3×Dic3C2×D311yescharacteristic
162C2×D3×Dic3C2×D311yescharacteristic
163C32×C22⋊C4—31no—
164C32×C22⋊C4—31no—
165#3757—31no—
166#3757—31no—
167#3757—31no—
168#3757—31no—
169C4⋊(C3⋊Dic3)—31no—
170C4⋊(C3⋊Dic3)—31no—
171C4⋊(C3⋊Dic3)C2×D311yescharacteristic
172#3750—31no—
173#3750—31no—
174#3750—31no—
175#3750—31no—
176#3750C2×D311yescharacteristic
177#3750C2×D311yescharacteristic
178C3×#217—31no—
179C3×#217—31no—
180C3×#217—31no—
181C3×#217—31no—
182C3×(C2×D3)⋊C4—21no—
183C3×(C2×D3)⋊C4—21no—
184C3×(C2×D3)⋊C4—31no—
185C3×(C2×D3)⋊C4—31no—
186C3×(C2×D3)⋊C4—31no—
187C3×(C2×D3)⋊C4—31no—
188C3×(C2×D3)⋊C4C2×D311yescharacteristic
189C3×(C2×D3)⋊C4C2×D311yescharacteristic
190C3×(C2×D3)⋊C4C2×D311yescharacteristic
191C3×(C2×D3)⋊C4C2×D311yescharacteristic
192C3×C4⋊Dic3—31no—
193C3×C4⋊Dic3—31no—
194C3×C4⋊Dic3—31no—
195C3×C4⋊Dic3—31no—
196C3×C4⋊Dic3—61no—
197C3×Dic3⋊C4—31no—
198C3×Dic3⋊C4—31no—
199C3×Dic3⋊C4—31no—
200C3×Dic3⋊C4—31no—
201C3×Dic3⋊C4—31no—
202C3×Dic3⋊C4—31no—
203C3×Dic3⋊C4—61no—
204C3×Dic3⋊C4—61no—
205C3×C4×Dic3—31no—
206C3×C4×Dic3—31no—
207#3724—31no—
208#3724—31no—
209#3724—31no—
210#3724—31no—
211#3724—31no—
212#3724—31no—
213#3724—31no—
214#3724—61no—
215#3724—61no—
216Dic3⋊Dic3—31no—
217Dic3⋊Dic3—31no—
218Dic3⋊Dic3—31no—
219Dic3⋊Dic3—31no—
220Dic3⋊Dic3—31no—
221Dic3⋊Dic3—31no—
222Dic3⋊Dic3—31no—
223Dic3⋊Dic3—31no—
224Dic3⋊Dic3—31no—
225Dic3⋊Dic3—31no—
226Dic3⋊Dic3—31no—
227Dic3⋊Dic3—31no—
228Dic3⋊Dic3—31no—
229Dic3⋊Dic3—31no—
230Dic3⋊Dic3—61no—
231Dic3⋊Dic3—61no—
232Dic3⋊Dic3—61no—
233Dic3⋊Dic3—61no—
234Dic3⋊Dic3C2×D311yescharacteristic
235Dic3⋊Dic3C2×D311yescharacteristic
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—61no—
245(C2×D3)⋊Dic3—61no—
246(C2×D3)⋊Dic3—61no—
247(C2×D3)⋊Dic3—61no—
248(C2×D3)⋊Dic3C2×D311yescharacteristic
249(C2×D3)⋊Dic3C2×D311yescharacteristic
250(C2×D3)⋊Dic3C2×D311yescharacteristic
251(C2×D3)⋊Dic3C2×D311yescharacteristic
252Dic32—31no—
253Dic32—31no—
254Dic32—31no—
255Dic32C2×D311yescharacteristic
256C22×C33C2411yescharacteristic
257C2×C32×D3—21no—
258C2×C32×D3—21no—
259C2×C32×D3—21no—
260C2×C32×D3—21no—
261C2×C32×D3—21no—
262C2×C32×D3—21no—
263C2×C32×D3—21no—
264C2×C32×D3—21no—
265C2×C32×D3#4112yes—
266C33×C4—21no—
267C3⋊(C3⋊Dic3)—21no—
268C3⋊(C3⋊Dic3)—21no—
269C3×C3⋊Dic3—21no—
270C3×C3⋊Dic3—21no—
271C3×C3⋊Dic3—21no—
272C3×C3⋊Dic3—21no—
273C3×C3⋊Dic3—21no—
274C3×C3⋊Dic3—21no—
275C32×Dic3—21no—
276C32×Dic3—21no—
277C32×Dic3—21no—
278C3×#123—91no—
279C3×#123—91no—
280C3×C4×D4—91no—
281#939—91no—
282#939—91no—
283#938—91no—
284#935—91no—
285#935—91no—
286D4×Dic3—91no—
287#929—31no—
288#929—91no—
289C4×#67—31no—
290C4×#67—91no—
291C2×C4⋊Dic3—91no—
292#924—91no—
293#924—91no—
294#924—181no—
295C2×Dic3⋊C4—91no—
296#898—91no—
297#897—91no—
298#896—91no—
299#896—91no—
300D3×C4⋊C4—91no—
301#890—91no—
302#890—91no—
303#889—91no—
304#889—91no—
305#889—91no—
306#886—31no—
307#886—91no—
308#883—31no—
309#883—31no—
310#883—91no—
311#883—91no—
312#67⋊C4—31no—
313#67⋊C4—91no—
314#879—91no—
315#879—91no—
316#879—91no—
317#879—91no—
318#878—91no—
319#878—91no—
320#878—91no—
321#878—91no—
322#878—181no—
323#878—181no—
324#876—91no—
325#870—91no—
326C23×C32—31no—
327C23×C32—31no—
328C23×C32—31no—
329C22×C3×D3—21no—
330C22×C3×D3—21no—
331C22×C3×D3—21no—
332C22×C3×D3C22×D311yescharacteristic
333C22×C3×D3C22×D311yescharacteristic
334C22×C3×D3C22×D311yescharacteristic
335C22×C3×D3C22×D311yescharacteristic
336C22×C3×D3C22×D311yescharacteristic
337C22×C3×D3C22×D311yescharacteristic
338C2×C32×C4—21no—
339C2×C32×C4—21no—
340C2×C32×C4—21no—
341C2×C32×C4—31no—
342C2×C32×C4—31no—
343C2×C32×C4—31no—
344C2×C32×C4—41no—
345C2×C32×C4—121no—
346C2×C32×C4C22×D311yescharacteristic
347C2×C32×C4C22×D311yescharacteristic
348C2×C32×C4C22×D311yescharacteristic
349C2×C3⋊Dic3—31no—
350C2×C3⋊Dic3—31no—
351C2×C3⋊Dic3—31no—
352C2×C3⋊Dic3—31no—
353C2×C3⋊Dic3—31no—
354C2×C3⋊Dic3—31no—
355C2×C3⋊Dic3—61no—
356C2×C3⋊Dic3—61no—
357C2×C3⋊Dic3—61no—
358C2×C3⋊Dic3—61no—
359C2×C3⋊Dic3—61no—
360C2×C3⋊Dic3—61no—
361C2×C3⋊Dic3—121no—
362C2×C3⋊Dic3—121no—
363C2×C3⋊Dic3—121no—
364C2×C3⋊Dic3—121no—
365C2×C3⋊Dic3C22×D311yescharacteristic
366C2×C3⋊Dic3C22×D311yescharacteristic
367C2×C3⋊Dic3C22×D311yescharacteristic
368C2×C3⋊Dic3C22×D311yescharacteristic
369C2×C3⋊Dic3C22×D311yescharacteristic
370C2×C3⋊Dic3C22×D311yescharacteristic
371#634—121no—
372#634—121no—
373#634—121no—
374#634—122no—
375#634—122no—
376#634—122no—
377#634—124no—
378C3×#67—62no—
379C3×#67—62no—
380C3×#67—62no—
381C3×#67—62no—
382C3×#67—121no—
383C3×#67—121no—
384C2×C3×Dic3—21no—
385C2×C3×Dic3—21no—
386C2×C3×Dic3—21no—
387C2×C3×Dic3—31no—
388C2×C3×Dic3—31no—
389C2×C3×Dic3—31no—
390C2×C3×Dic3—31no—
391C2×C3×Dic3—31no—
392C2×C3×Dic3—31no—
393C2×C3×Dic3—31no—
394C2×C3×Dic3—31no—
395C2×C3×Dic3—31no—
396C2×C3×Dic3—31no—
397C2×C3×Dic3—31no—
398C2×C3×Dic3—31no—
399C2×C3×Dic3—61no—
400C2×C3×Dic3—61no—
401C2×C3×Dic3—61no—
402C2×C3×Dic3—61no—
403C2×C3×Dic3—61no—
404C2×C3×Dic3—61no—
405C2×C3×Dic3—62no—
406C2×C3×Dic3—121no—
407C2×C3×Dic3C22×D311yescharacteristic
408C2×C3×Dic3C22×D311yescharacteristic
409C2×C3×Dic3C22×D311yescharacteristic
410C2×C3×Dic3C22×D311yescharacteristic
411C2×C3×Dic3C22×D311yescharacteristic
412C2×C3×Dic3C22×D311yescharacteristic
413C3×C4×D3—41no—
414C3×C4×D3—41no—
415C3×C4×D3—42no—
416C3×C4×D3—62no—
417C3×C4×D3—121no—
418#625—22no—
419#625—22no—
420#625—41no—
421D3×Dic3—22no—
422D3×Dic3—41no—
423D3×Dic3—121no—
424D3×Dic3—121no—
425D3×Dic3—121no—
426D3×Dic3—121no—
427D3×Dic3—122no—
428D3×Dic3—122no—
429#539—271noSylow
430C2×C33C2×#4111yescharacteristic
431C2×C33H(5,𝔽2)11yescharacteristic
432C2×C332−1+411yescharacteristic
433C32×D3—22no—
434C32×D3—41no—
435C32×D3—41no—
436C2×C3×D4—91no—
437C2×C3×D4—91no—
438C2×C3×D4—91no—
439C22×C3×C4—31no—
440C22×C3×C4—31no—
441C22×C3×C4—61no—
442C22×C3×C4—91no—
443C22×C3×C4—91no—
444C2×#67—31no—
445C2×#67—31no—
446C2×#67—31no—
447C2×#67—31no—
448C2×#67—31no—
449C2×#67—31no—
450C22×Dic3—31no—
451C22×Dic3—31no—
452C22×Dic3—91no—
453C22×Dic3—91no—
454C22×Dic3—91no—
455C22×Dic3—91no—
456C22×Dic3—181no—
457C22×Dic3—181no—
458C2×C4×D3—31no—
459C2×C4×D3—31no—
460C2×C4×D3—91no—
461C2×C4×D3—91no—
462C2×C4×D3D3211yescharacteristic
463C2×Dic6—91no—
464C2×Dic6—91no—
465C2×Dic6—91no—
466C2×Dic6—181no—
467C2×Dic6—181no—
468C2×Dic6—181no—
469C2×Dic6—361no—
470C3×C4⋊C4—91no—
471C3×C4⋊C4—91no—
472C3×C4⋊C4—91no—
473C3×C4⋊C4—91no—
474C3×C4⋊C4—91no—
475C3×C22⋊C4—31no—
476C3×C22⋊C4—31no—
477C3×C22⋊C4—31no—
478C3×C22⋊C4—31no—
479C3×C22⋊C4—61no—
480C3×C22⋊C4—61no—
481C3×C22⋊C4—91no—
482C3×C22⋊C4—91no—
483C3×C22⋊C4—91no—
484C3×C22⋊C4—91no—
485C3×C42—91no—
486#217—31no—
487#217—31no—
488#217—31no—
489#217—31no—
490#217—91no—
491#217—91no—
492#217—91no—
493#217—91no—
494#217—91no—
495#217—91no—
496#217—91no—
497#217—91no—
498#217—181no—
499#217—181no—
500#217—181no—
501#217—181no—
502(C2×D3)⋊C4—31no—
503(C2×D3)⋊C4—31no—
504(C2×D3)⋊C4—31no—
505(C2×D3)⋊C4—31no—
506(C2×D3)⋊C4—91no—
507(C2×D3)⋊C4—91no—
508(C2×D3)⋊C4—91no—
509(C2×D3)⋊C4—91no—
510(C2×D3)⋊C4D3211yescharacteristic
511(C2×D3)⋊C4D3211yescharacteristic
512C4⋊Dic3—31no—
513C4⋊Dic3—31no—
514C4⋊Dic3—31no—
515C4⋊Dic3—31no—
516C4⋊Dic3—61no—
517C4⋊Dic3—91no—
518C4⋊Dic3—91no—
519C4⋊Dic3—91no—
520C4⋊Dic3—91no—
521C4⋊Dic3—91no—
522C4⋊Dic3—91no—
523C4⋊Dic3—91no—
524C4⋊Dic3—91no—
525C4⋊Dic3—91no—
526C4⋊Dic3—181no—
527C4⋊Dic3—181no—
528Dic3⋊C4—31no—
529Dic3⋊C4—31no—
530Dic3⋊C4—31no—
531Dic3⋊C4—31no—
532Dic3⋊C4—31no—
533Dic3⋊C4—31no—
534Dic3⋊C4—61no—
535Dic3⋊C4—61no—
536Dic3⋊C4—91no—
537Dic3⋊C4—91no—
538Dic3⋊C4—91no—
539Dic3⋊C4—91no—
540Dic3⋊C4—91no—
541Dic3⋊C4—91no—
542Dic3⋊C4—91no—
543Dic3⋊C4—91no—
544Dic3⋊C4—91no—
545Dic3⋊C4—91no—
546Dic3⋊C4—91no—
547Dic3⋊C4—91no—
548Dic3⋊C4—91no—
549Dic3⋊C4—91no—
550Dic3⋊C4—91no—
551Dic3⋊C4—91no—
552Dic3⋊C4—91no—
553Dic3⋊C4—91no—
554Dic3⋊C4—181no—
555Dic3⋊C4—181no—
556Dic3⋊C4—181no—
557Dic3⋊C4—181no—
558C4×Dic3—31no—
559C4×Dic3—31no—
560C4×Dic3—91no—
561C4×Dic3—91no—
562C4×Dic3—91no—
563C22×C32—21no—
564C22×C32—21no—
565C22×C32—21no—
566C22×C32—32no—
567C22×C32—41no—
568C22×C32—61no—
569C22×C32—61no—
570C22×C32—61no—
571C22×C32—61no—
572C22×C32—61no—
573C22×C32—61no—
574C22×C32—61no—
575C22×C32—61no—
576C22×C32C23×D311yescharacteristic
577C22×C32C23×D311yescharacteristic
578C22×C32C23×D311yescharacteristic
579C2×C3×D3—21no—
580C2×C3×D3—21no—
581C2×C3×D3—21no—
582C2×C3×D3—21no—
583C2×C3×D3—22no—
584C2×C3×D3—22no—
585C2×C3×D3—21no—
586C2×C3×D3—21no—
587C2×C3×D3—21no—
588C2×C3×D3—21no—
589C2×C3×D3—21no—
590C2×C3×D3—21no—
591C2×C3×D3—21no—
592C2×C3×D3—21no—
593C2×C3×D3—21no—
594C2×C3×D3—21no—
595C2×C3×D3—21no—
596C2×C3×D3—21no—
597C2×C3×D3—22no—
598C2×C3×D3—41no—
599C2×C3×D3—41no—
600C2×C3×D3—41no—
601C2×C3×D3—41no—
602C2×C3×D3—41no—
603C2×C3×D3—41no—
604C2×C3×D3#23512yes—
605C2×C3×D3#23712yes—
606C32×C4—21no—
607C32×C4—22no—
608C32×C4—21no—
609C32×C4—21no—
610C32×C4—41no—
611C32×C4—41no—
612C32×C4—42no—
613C32×C4—61no—
614C32×C4—61no—
615C32×C4—61no—
616C3⋊Dic3—21no—
617C3⋊Dic3—21no—
618C3⋊Dic3—21no—
619C3⋊Dic3—21no—
620C3⋊Dic3—21no—
621C3⋊Dic3—21no—
622C3⋊Dic3—61no—
623C3⋊Dic3—61no—
624C3⋊Dic3—62no—
625C3⋊Dic3—62no—
626C3⋊Dic3—61no—
627C3⋊Dic3—61no—
628C3⋊Dic3—61no—
629C3⋊Dic3—61no—
630C3⋊Dic3—121no—
631C3⋊Dic3—121no—
632C3⋊Dic3—121no—
633C3⋊Dic3—121no—
634C3⋊Dic3—122no—
635C3⋊Dic3—122no—
636C3×Dic3—21no—
637C3×Dic3—21no—
638C3×Dic3—21no—
639C3×Dic3—21no—
640C3×Dic3—21no—
641C3×Dic3—21no—
642C3×Dic3—41no—
643C3×Dic3—41no—
644C3×Dic3—41no—
645C3×Dic3—61no—
646C3×Dic3—61no—
647C3×Dic3—61no—
648C3×Dic3—61no—
649C3×Dic3—61no—
650C3×Dic3—61no—
651C3×Dic3—61no—
652C3×Dic3—61no—
653C3×Dic3—61no—
654C3×Dic3—61no—
655C3×Dic3—61no—
656C3×Dic3—61no—
657C3×Dic3—121no—
658C3×Dic3—121no—
659C3×Dic3—121no—
660C3×Dic3—121no—
661C3×Dic3—121no—
662C3×Dic3—121no—
663#126—271no—
664#126—271no—
665#125—271no—
666#125—271no—
667#123—91no—
668#123—91no—
669#123—271no—
670#123—271no—
671C22⋊Q8—271no—
672C22⋊Q8—271no—
673C22⋊Q8—271no—
674#121—271no—
675C4×D4—91no—
676C4×D4—271no—
677C2×C4⋊C4—271no—
678C33#53911yescharacteristic, complemented, Sylow
679C23×C3—31no—
680C23×C3—31no—
681C23×C3—31no—
682C23×C3—31no—
683C23×C3—31no—
684C23×C3—31no—
685C23×C3—61no—
686C23×C3—61no—
687C23×C3—61no—
688C22×D3C2×D3211yescharacteristic
689C22×D3C2×D3211yescharacteristic
690C22×D3C2×D3211yescharacteristic
691C3×D4—182no—
692C3×D4—182no—
693C3×D4—361no—
694C2×C3×C4—21no—
695C2×C3×C4—21no—
696C2×C3×C4—21no—
697C2×C3×C4—31no—
698C2×C3×C4—31no—
699C2×C3×C4—31no—
700C2×C3×C4—31no—
701C2×C3×C4—31no—
702C2×C3×C4—31no—
703C2×C3×C4—41no—
704C2×C3×C4—61no—
705C2×C3×C4—61no—
706C2×C3×C4—61no—
707C2×C3×C4—91no—
708C2×C3×C4—91no—
709C2×C3×C4—91no—
710C2×C3×C4—91no—
711C2×C3×C4—91no—
712C2×C3×C4—91no—
713C2×C3×C4—121no—
714C2×C3×C4—121no—
715C2×C3×C4—122no—
716C2×C3×C4—182no—
717C2×C3×C4—361no—
718C2×C3×C4C2×D3211yescharacteristic
719C2×C3×C4C2×D3211yescharacteristic
720C2×C3×C4C2×D3211yescharacteristic
721#67—62no—
722#67—62no—
723#67—62no—
724#67—62no—
725#67—121no—
726#67—121no—
727C2×Dic3—31no—
728C2×Dic3—31no—
729C2×Dic3—31no—
730C2×Dic3—31no—
731C2×Dic3—31no—
732C2×Dic3—31no—
733C2×Dic3—31no—
734C2×Dic3—31no—
735C2×Dic3—31no—
736C2×Dic3—31no—
737C2×Dic3—31no—
738C2×Dic3—31no—
739C2×Dic3—61no—
740C2×Dic3—61no—
741C2×Dic3—61no—
742C2×Dic3—61no—
743C2×Dic3—61no—
744C2×Dic3—61no—
745C2×Dic3—62no—
746C2×Dic3—91no—
747C2×Dic3—91no—
748C2×Dic3—91no—
749C2×Dic3—91no—
750C2×Dic3—91no—
751C2×Dic3—91no—
752C2×Dic3—121no—
753C2×Dic3—181no—
754C2×Dic3—181no—
755C2×Dic3—181no—
756C2×Dic3—181no—
757C2×Dic3—181no—
758C2×Dic3—181no—
759C2×Dic3—361no—
760C2×Dic3—361no—
761C2×Dic3—361no—
762C2×Dic3—361no—
763C2×Dic3—361no—
764C2×Dic3—361no—
765C2×Dic3—362no—
766C2×Dic3—362no—
767C2×Dic3C2×D3211yescharacteristic
768C2×Dic3C2×D3211yescharacteristic
769C2×Dic3C2×D3211yescharacteristic
770C4×D3—41no—
771C4×D3—62no—
772C4×D3—121no—
773C4×D3—361no—
774C4×D3—361no—
775Dic6—361no—
776Dic6—361no—
777Dic6—361no—
778Dic6—362no—
779Dic6—362no—
780Dic6—362no—
781Dic6—364no—
782C2×C32—21no—
783C2×C32—21no—
784C2×C32—21no—
785C2×C32—21no—
786C2×C32—21no—
787C2×C32—21no—
788C2×C32—21no—
789C2×C32—21no—
790C2×C32—21no—
791C2×C32—41no—
792C2×C32—41no—
793C2×C32—41no—
794C2×C32—62no—
795C2×C32—121no—
796C2×C32—121no—
797C2×C32C2×#23511yescharacteristic
798C2×C32C2×#23711yescharacteristic
799C2×C32#100411yescharacteristic
800C2×C32#100411yescharacteristic
801C2×C32D3×#4111yescharacteristic
802C2×C32#100911yescharacteristic
803C2×C32#101011yescharacteristic
804C2×C32#101011yescharacteristic
805C2×C32#101011yescharacteristic
806C3×D3—22no—
807C3×D3—22no—
808C3×D3—42no—
809C3×D3—42no—
810C3×D3—42no—
811C3×D3—41no—
812C3×D3—41no—
813C3×D3—41no—
814C3×D3—41no—
815C2×Q8—271no—
816C2×D4—91no—
817C2×D4—91no—
818C2×D4—91no—
819C22×C4—31no—
820C22×C4—91no—
821C22×C4—91no—
822C22×C4—271no—
823C22×C4—271no—
824C4⋊C4—91no—
825C4⋊C4—91no—
826C4⋊C4—91no—
827C4⋊C4—91no—
828C4⋊C4—91no—
829C4⋊C4—271no—
830C4⋊C4—271no—
831C4⋊C4—271no—
832C4⋊C4—271no—
833C4⋊C4—271no—
834C4⋊C4—271no—
835C4⋊C4—271no—
836C4⋊C4—271no—
837C4⋊C4—271no—
838C22⋊C4—31no—
839C22⋊C4—31no—
840C22⋊C4—91no—
841C22⋊C4—91no—
842C22⋊C4—91no—
843C22⋊C4—91no—
844C22⋊C4—271no—
845C22⋊C4—271no—
846C22⋊C4—271no—
847C22⋊C4—271no—
848C42—91no—
849C42—271no—
850C22×C3—21no—
851C22×C3—21no—
852C22×C3—21no—
853C22×C3—32no—
854C22×C3—32no—
855C22×C3—41no—
856C22×C3—62no—
857C22×C3—62no—
858C22×C3—62no—
859C22×C3—61no—
860C22×C3—61no—
861C22×C3—61no—
862C22×C3—61no—
863C22×C3—61no—
864C22×C3—61no—
865C22×C3—61no—
866C22×C3—61no—
867C22×C3—61no—
868C22×C3—61no—
869C22×C3—61no—
870C22×C3—61no—
871C22×C3—61no—
872C22×C3—61no—
873C22×C3—61no—
874C22×C3—61no—
875C22×C3—121no—
876C22×C3—121no—
877C22×C3—121no—
878C22×C3—121no—
879C22×C3—121no—
880C22×C3—121no—
881C22×C3C22×D3211yescharacteristic
882C22×C3C22×D3211yescharacteristic
883C22×C3C22×D3211yescharacteristic
884C2×D3—21no—
885C2×D3—21no—
886C2×D3—21no—
887C2×D3—21no—
888C2×D3—21no—
889C2×D3—21no—
890C2×D3—21no—
891C2×D3—21no—
892C2×D3#379512yes—
893C3×C4—22no—
894C3×C4—21no—
895C3×C4—21no—
896C3×C4—21no—
897C3×C4—41no—
898C3×C4—41no—
899C3×C4—42no—
900C3×C4—61no—
901C3×C4—61no—
902C3×C4—61no—
903C3×C4—61no—
904C3×C4—61no—
905C3×C4—61no—
906C3×C4—121no—
907C3×C4—121no—
908C3×C4—121no—
909C3×C4—181no—
910C3×C4—181no—
911C3×C4—181no—
912C3×C4—181no—
913C3×C4—181no—
914C3×C4—181no—
915Dic3—21no—
916Dic3—21no—
917Dic3—21no—
918Dic3—61no—
919Dic3—61no—
920Dic3—61no—
921Dic3—61no—
922Dic3—61no—
923Dic3—61no—
924Dic3—61no—
925Dic3—61no—
926Dic3—61no—
927Dic3—61no—
928Dic3—61no—
929Dic3—61no—
930Dic3—121no—
931Dic3—121no—
932Dic3—121no—
933Dic3—121no—
934Dic3—121no—
935Dic3—121no—
936Dic3—182no—
937Dic3—182no—
938Dic3—181no—
939Dic3—181no—
940Dic3—181no—
941Dic3—181no—
942Dic3—181no—
943Dic3—181no—
944Dic3—361no—
945Dic3—361no—
946Dic3—361no—
947Dic3—361no—
948Dic3—362no—
949Dic3—362no—
950C32—21no—
951C32—21no—
952C32—21no—
953C32—41no—
954C32#556411yescharacteristic, complemented
955C32#566011yescharacteristic, complemented
956C32#566511yescharacteristic, complemented
957C23—31no—
958C23—31no—
959C23—31no—
960Q8—1081no—
961D4—182no—
962D4—182no—
963D4—361no—
964C2×C4—31no—
965C2×C4—31no—
966C2×C4—31no—
967C2×C4—91no—
968C2×C4—91no—
969C2×C4—91no—
970C2×C4—91no—
971C2×C4—91no—
972C2×C4—91no—
973C2×C4—121no—
974C2×C4—182no—
975C2×C4—271no—
976C2×C4—271no—
977C2×C4—361no—
978C2×C4—1081no—
979C2×C4—1081no—
980C2×C4D3311yescharacteristic
981C2×C3—21no—
982C2×C3—21no—
983C2×C3—21no—
984C2×C3—21no—
985C2×C3—21no—
986C2×C3—21no—
987C2×C3—21no—
988C2×C3—21no—
989C2×C3—21no—
990C2×C3—41no—
991C2×C3—41no—
992C2×C3—41no—
993C2×C3—62no—
994C2×C3—62no—
995C2×C3—122no—
996C2×C3—122no—
997C2×C3—122no—
998C2×C3—121no—
999C2×C3—121no—
1000C2×C3—121no—
1001C2×C3—121no—
1002C2×C3C2×#379511yescharacteristic
1003C2×C3#6429811yescharacteristic
1004C2×C3#6429811yescharacteristic
1005C2×C3D3×#23511yescharacteristic
1006C2×C3#6430911yescharacteristic
1007C2×C3D3×#23711yescharacteristic
1008C2×C3#6431411yescharacteristic
1009C2×C3#6431411yescharacteristic
1010C2×C3#6433011yescharacteristic
1011D3—22no—
1012D3—41no—
1013D3—41no—
1014C22—32no—
1015C22—61no—
1016C22—61no—
1017C22—61no—
1018C22—61no—
1019C22—61no—
1020C22—61no—
1021C22—61no—
1022C22—61no—
1023C22C2×D3311yescharacteristic
1024C4—21no—
1025C4—61no—
1026C4—61no—
1027C4—61no—
1028C4—181no—
1029C4—181no—
1030C4—181no—
1031C4—181no—
1032C4—181no—
1033C4—181no—
1034C4—541no—
1035C4—541no—
1036C3—21no—
1037C3—21no—
1038C3—21no—
1039C3—41no—
1040C3#1059412111yescharacteristic, complemented
1041C3#1059417711yescharacteristic, complemented
1042C3#1059493511yescharacteristic, complemented
1043C2—62no—
1044C2—121no—
1045C2—121no—
1046C2D3×#379511yescharacteristic
1047C2#1172439211yescharacteristic
1048C2#1172441911yescharacteristic
subgroupG/H
center, FrattiniC22C2×D33
commutator, socle, cosocleC22×C33C24
FittingC2×C33×C4C23
prime radical#11722953C2
hypercenterC2×C4D33
hypocenterC33#539
LCSG ▷ C22×C33 ▷ C33
UCSC1 ◁ C22 ◁ C2×C4

Complements

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

NH ≅ G/Ntype
1. #11723669C2semidirect
2. #11723496C2semidirect
3. #11723496C2semidirect
4. #11723426C2semidirect
5. C3×#63905C2semidirect
6. C3×#63891C2semidirect
7. C3×#63879C2semidirect
8. #11723026C2semidirect
9. #11723020C2semidirect
10. #11723012C2semidirect
11. #11722989C2semidirect
12. #11722985C2semidirect
14. #11722924C2semidirect
15. D3×Dic3⋊Dic3C2semidirect
76. #63905D3semidirect
84. #63891D3semidirect
87. #63879D3semidirect
678. C33#539semidirect
954. C32#5564semidirect
955. C32#5660semidirect
956. C32#5665semidirect
1040. C3#10594121semidirect
1041. C3#10594177semidirect
1042. C3#10594935semidirect

Maximal subgroups

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

subgroupindex
#117236692
#117234962
#117234262
C3×#639052
C3×#638912
C3×#638792
#117230262
#117230202
#117230122
#117229892
#117229852
#117229532
#117229242
D3×Dic3⋊Dic32
#105949353
#105941773
#105941213