Finite Group Databasebeta

← #13172232

Subgroups — #13172232

Order 1728.

1248 conjugacy classes of subgroups.

The subgroup lattice has 1070 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11723721C211yesmaximal, characteristic, complemented
2#11723622C211yesmaximal, characteristic
3#11723618C211yesmaximal, characteristic
4#11723618C211yesmaximal, characteristic
5C2×C3×Dic3⋊Dic3C211yesmaximal, characteristic, complemented
6C3×#63964C211yesmaximal, characteristic, complemented
7C3×#63964C211yesmaximal, characteristic, complemented
8#11723035C211yesmaximal, characteristic, complemented
9#11723016C211yesmaximal, characteristic, complemented
10#11723016C211yesmaximal, characteristic, complemented
11#11722982C211yesmaximal, characteristic, complemented
12#11722973C211yesmaximal, characteristic, complemented
13#11722973C211yesmaximal, characteristic, complemented
14#11722941C211yesmaximal, characteristic, complemented
15#11722912C211yesmaximal, characteristic, complemented
16#10594991—31nomaximal
17#10594956—31nomaximal
18#10594141—31nomaximal
19C2×#6312C2211yescharacteristic
20C22×C3×C3⋊Dic3C2211yescharacteristic
21C22×C32×Dic3C2211yescharacteristic
22C22×C32×Dic3C2211yescharacteristic
23C2×#6296C2211yescharacteristic
24C2×#6289C2211yescharacteristic
25C2×#6289C2211yescharacteristic
26C2×#6289C2211yescharacteristic
27C2×C3×#627C2211yescharacteristic
28C2×C3×#627C2211yescharacteristic
29C3×#3757C2211yescharacteristic
30C3×#3757C2211yescharacteristic
31C32×#217C2211yescharacteristic
32#88815C2211yescharacteristic
33#88815C2211yescharacteristic
34#88815C2211yescharacteristic
35#88806C2211yescharacteristic
36#88806C2211yescharacteristic
37#88806C2211yescharacteristic
38#88804C2211yescharacteristic
39#88804C2211yescharacteristic
40#88804C2211yescharacteristic
41Dic3×C3⋊Dic3C2211yescharacteristic
42Dic3×C3⋊Dic3C2211yescharacteristic
43Dic3×C3⋊Dic3C2211yescharacteristic
44C3×#3724C2211yescharacteristic
45C3×#3724C2211yescharacteristic
46C3×Dic3⋊Dic3C2211yescharacteristic
47C3×Dic3⋊Dic3C2211yescharacteristic
48C3×Dic3⋊Dic3C2211yescharacteristic
49C3×Dic3⋊Dic3C2211yescharacteristic
50C3×Dic3⋊Dic3C2211yescharacteristic
51C3×Dic3⋊Dic3C2211yescharacteristic
52C3×Dic3⋊Dic3C2211yescharacteristic
53C3×Dic3⋊Dic3C2211yescharacteristic
54C4×#638—31no—
55C4×#638—31no—
56#64090—31no—
57C2×C3×C4⋊Dic3—31no—
58C3×#924—31no—
59C3×#924—31no—
60C2×C3×Dic3⋊C4—31no—
61C3×#878—31no—
62C3×#878—31no—
63#63982—31no—
64C2×Dic3⋊Dic3D311yescharacteristic, complemented
65#63964—31no—
66#63964—31no—
67#63964D311yescharacteristic, complemented
68#63964D311yescharacteristic, complemented
69#63952—31no—
70#63952—31no—
71#63952—31no—
72#63952—31no—
73#63952—31no—
74#63952—31no—
75#63952—61no—
76#63952—61no—
77#63952—61no—
78#63919—31no—
79#63900—31no—
80#63895—31no—
81#63895—31no—
82#63895—31no—
83#63895—31no—
84#63888—31no—
85#63888—31no—
86#63883—31no—
87#63883—31no—
88#63871—31no—
89#63871—31no—
90#63870—31no—
91#63870—31no—
92#63865—31no—
93#63847—31no—
94#63847—31no—
95#63847—31no—
96#63847—31no—
97#63843—31no—
98#63843—31no—
99#63839—31no—
100#63839—31no—
101#63838—31no—
102C23×C33C2311yescharacteristic
103C22×C3⋊(C3⋊D3)C2311yescharacteristic
104#6312Q814yescomplemented
105C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
106C2×C3×C3⋊Dic3—41no—
107C2×C3×C3⋊Dic3C2311yescharacteristic
108C2×C3×C3⋊Dic3C2311yescharacteristic
109C2×C3×C3⋊Dic3C2311yescharacteristic
110C2×C3×C3⋊Dic3C2311yescharacteristic
111C2×C3×C3⋊Dic3C2311yescharacteristic
112C2×C3×C3⋊Dic3C2311yescharacteristic
113C2×C32×Dic3—22no—
114C2×C32×Dic3—41no—
115C2×C32×Dic3C2311yescharacteristic
116C2×C32×Dic3C2311yescharacteristic
117C2×C32×Dic3C2311yescharacteristic
118C2×C32×Dic3C2311yescharacteristic
119C2×C32×Dic3C2311yescharacteristic
120C2×C32×Dic3C2311yescharacteristic
121#6296—41no—
122#6289—22no—
123#6289—41no—
124#6289—41no—
125C3×#627—22no—
126C3×#627—41no—
127#5636—91no—
128#5635—91no—
129#5511—91no—
130C22×C32×C4—31no—
131C22×C32×C4—31no—
132C2×#638—31no—
133C2×#638—31no—
134C2×#638—31no—
135C2×#638—61no—
136C2×#638—61no—
137C2×#638—61no—
138C2×#638—121no—
139C22×C3⋊Dic3C2×D311yescharacteristic
140C2×C4×C3⋊D3—31no—
141C2×C4×C3⋊D3—31no—
142C2×C4×C3⋊D3—31no—
143C22×C3×Dic3—21no—
144C22×C3×Dic3—21no—
145C22×C3×Dic3—31no—
146C22×C3×Dic3—31no—
147C22×C3×Dic3—61no—
148C22×C3×Dic3C2×D311yescharacteristic
149C22×C3×Dic3C2×D311yescharacteristic
150C22×C3×Dic3C2×D311yescharacteristic
151C22×C3×Dic3C2×D311yescharacteristic
152C2×C3×Dic6—31no—
153C2×C3×Dic6—31no—
154C2×C3×Dic6—31no—
155C2×C3×Dic6—31no—
156C2×#627—31no—
157C2×#627—31no—
158C2×#627—31no—
159C2×#627C2×D311yescharacteristic
160C2×#627C2×D311yescharacteristic
161C2×#624—31no—
162C2×#624—31no—
163C2×#624—31no—
164C2×#624—31no—
165C2×#624—31no—
166C2×#624—31no—
167C2×#624—61no—
168C2×#624—61no—
169C2×#624—61no—
170C32×C22⋊C4—31no—
171#3757C2×D311yescharacteristic
172#3757C2×D311yescharacteristic
173#3752—31no—
174#3752—31no—
175#3752—31no—
176#3750—31no—
177#3750—31no—
178#3750—31no—
179C4×C3⋊Dic3—31no—
180C4×C3⋊Dic3—31no—
181C4×C3⋊Dic3—31no—
182C3×#217—21no—
183C3×#217—31no—
184C3×#217—31no—
185C3×#217—31no—
186C3×#217—31no—
187C3×#217—61no—
188C3×#217—61no—
189C3×#217C2×D311yescharacteristic
190C3×#217C2×D311yescharacteristic
191C3×C4⋊Dic3—31no—
192C3×C4⋊Dic3—31no—
193C3×C4⋊Dic3—31no—
194C3×C4⋊Dic3—31no—
195C3×C4⋊Dic3—31no—
196C3×C4⋊Dic3—31no—
197C3×C4⋊Dic3—31no—
198C3×C4⋊Dic3—31no—
199C3×Dic3⋊C4—31no—
200C3×Dic3⋊C4—31no—
201C3×Dic3⋊C4—31no—
202C3×Dic3⋊C4—31no—
203C3×Dic3⋊C4—31no—
204C3×Dic3⋊C4—31no—
205C3×Dic3⋊C4—31no—
206C3×Dic3⋊C4—31no—
207C3×Dic3⋊C4—31no—
208C3×Dic3⋊C4—31no—
209C3×Dic3⋊C4—31no—
210C3×Dic3⋊C4—31no—
211#3724—31no—
212#3724—31no—
213#3724—31no—
214#3724—31no—
215#3724—31no—
216#3724—31no—
217#3724—31no—
218#3724—31no—
219#3724—31no—
220#3724—61no—
221#3724—61no—
222#3724—61no—
223#3724C2×D311yescharacteristic
224#3724C2×D311yescharacteristic
225Dic3⋊Dic3—31no—
226Dic3⋊Dic3—31no—
227Dic3⋊Dic3—31no—
228Dic3⋊Dic3—31no—
229Dic3⋊Dic3—31no—
230Dic3⋊Dic3—31no—
231Dic3⋊Dic3C2×D311yescharacteristic
232Dic3⋊Dic3C2×D311yescharacteristic
233Dic3⋊Dic3C2×D311yescharacteristic
234Dic3⋊Dic3C2×D311yescharacteristic
235Dic3⋊Dic3C2×D311yescharacteristic
236Dic3⋊Dic3C2×D311yescharacteristic
237Dic3⋊Dic3C2×D311yescharacteristic
238Dic3⋊Dic3C2×D311yescharacteristic
239#3722—31no—
240#3722—31no—
241#3722—31no—
242#3722—31no—
243#3722—31no—
244#3722—31no—
245#3722—61no—
246#3722—61no—
247#3722—61no—
248Dic32—31no—
249Dic32—31no—
250Dic32—31no—
251Dic32—31no—
252Dic32—31no—
253Dic32—31no—
254Dic32—61no—
255Dic32—61no—
256Dic32—61no—
257C22×C33—21no—
258C22×C33—21no—
259C22×C33C2×Q812yes—
260C22×C33C2411yescharacteristic
261C2×C3⋊(C3⋊D3)—21no—
262C2×C3⋊(C3⋊D3)—21no—
263C2×C3⋊(C3⋊D3)C2×Q812yes—
264C3⋊(C3⋊Dic3)C2×Q812yes—
265C3×C3⋊Dic3—21no—
266C3×C3⋊Dic3—21no—
267C3×C3⋊Dic3—21no—
268C3×C3⋊Dic3—21no—
269C3×C3⋊Dic3—21no—
270C3×C3⋊Dic3—21no—
271C32×Dic3—21no—
272C32×Dic3—21no—
273C32×Dic3—21no—
274C32×Dic3—21no—
275C32×Dic3—21no—
276C32×Dic3#4112yes—
277C3×C22⋊Q8—91no—
278C3×C22⋊Q8—91no—
279C2×C3×C4⋊C4—91no—
280#946—91no—
281#946—91no—
282Q8×Dic3—91no—
283#944—91no—
284C4×#67—91no—
285C4×#67—91no—
286C4×#67—91no—
287C4×#67—91no—
288C4×#67—91no—
289C4×#67—181no—
290C4×#67—181no—
291C2×C4⋊Dic3—31no—
292#924—31no—
293#924—31no—
294#924—91no—
295C2×Dic3⋊C4—31no—
296#897—91no—
297#897—91no—
298#897—91no—
299#896—91no—
300#896—91no—
301#896—91no—
302#896—91no—
303D3×C4⋊C4—91no—
304D3×C4⋊C4—91no—
305D3×C4⋊C4—91no—
306#889—91no—
307#889—91no—
308#889—91no—
309#889—91no—
310#889—91no—
311#889—91no—
312#888—91no—
313#888—91no—
314#887—91no—
315#887—91no—
316#67⋊C4—91no—
317#67⋊C4—91no—
318#67⋊C4—91no—
319#67⋊C4—91no—
320#67⋊C4—181no—
321#878—31no—
322#878—31no—
323#878—91no—
324#878—91no—
325C23×C32—21no—
326C23×C32—21no—
327C23×C32—21no—
328C23×C32—41no—
329C23×C32C22×D311yescharacteristic
330C23×C32C22×D311yescharacteristic
331C23×C32C22×D311yescharacteristic
332C22×C3⋊D3—31no—
333C22×C3⋊D3—31no—
334C22×C3⋊D3—31no—
335C22×C3⋊D3—61no—
336C22×C3⋊D3—61no—
337C22×C3⋊D3—61no—
338C22×C3⋊D3—121no—
339C2×C32×C4—31no—
340C2×C32×C4—31no—
341C2×C32×C4—31no—
342C2×C32×C4—31no—
343C2×C32×C4—31no—
344C2×C32×C4—31no—
345C2×C32×C4—62no—
346C2×C32×C4—121no—
347#638—34no—
348#638—34no—
349#638—34no—
350#638—64no—
351#638—64no—
352#638—64no—
353#638—124no—
354C2×C3⋊Dic3—31no—
355C2×C3⋊Dic3—31no—
356C2×C3⋊Dic3—31no—
357C2×C3⋊Dic3—41no—
358C2×C3⋊Dic3—61no—
359C2×C3⋊Dic3—61no—
360C2×C3⋊Dic3—61no—
361C2×C3⋊Dic3—121no—
362C2×C3⋊Dic3C22×D311yescharacteristic
363C2×C3⋊Dic3C22×D311yescharacteristic
364C2×C3⋊Dic3C22×D311yescharacteristic
365C2×C3⋊Dic3C22×D311yescharacteristic
366C2×C3⋊Dic3C22×D311yescharacteristic
367C2×C3⋊Dic3C22×D311yescharacteristic
368C4×C3⋊D3—62no—
369C4×C3⋊D3—121no—
370C4×C3⋊D3—121no—
371C2×C3×Dic3—22no—
372C2×C3×Dic3—22no—
373C2×C3×Dic3—21no—
374C2×C3×Dic3—21no—
375C2×C3×Dic3—21no—
376C2×C3×Dic3—21no—
377C2×C3×Dic3—21no—
378C2×C3×Dic3—21no—
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—31no—
386C2×C3×Dic3—31no—
387C2×C3×Dic3—31no—
388C2×C3×Dic3—31no—
389C2×C3×Dic3—31no—
390C2×C3×Dic3—31no—
391C2×C3×Dic3—42no—
392C2×C3×Dic3—41no—
393C2×C3×Dic3—41no—
394C2×C3×Dic3—42no—
395C2×C3×Dic3—61no—
396C2×C3×Dic3—61no—
397C2×C3×Dic3—61no—
398C2×C3×Dic3—61no—
399C2×C3×Dic3—61no—
400C2×C3×Dic3—61no—
401C2×C3×Dic3—121no—
402C2×C3×Dic3—121no—
403C2×C3×Dic3—122no—
404C2×C3×Dic3C22×D311yescharacteristic
405C2×C3×Dic3C22×D311yescharacteristic
406C2×C3×Dic3C22×D311yescharacteristic
407C2×C3×Dic3C22×D311yescharacteristic
408C2×C3×Dic3C22×D311yescharacteristic
409C2×C3×Dic3C22×D311yescharacteristic
410C2×C3×Dic3C22×D311yescharacteristic
411C2×C3×Dic3C22×D311yescharacteristic
412C2×C3×Dic3C22×D311yescharacteristic
413C2×C3×Dic3C22×D311yescharacteristic
414C2×C3×Dic3C22×D311yescharacteristic
415C2×C3×Dic3C22×D311yescharacteristic
416C3×Dic6—62no—
417C3×Dic6—62no—
418C3×Dic6—121no—
419C3×Dic6—121no—
420#627—22no—
421#627—41no—
422#627—121no—
423#627—121no—
424#627—121no—
425#624—62no—
426#624—62no—
427#624—122no—
428#624—121no—
429#624—121no—
430#624—121no—
431#624—121no—
432#624—122no—
433#624—122no—
434#554—271noSylow
435C2×C33—22no—
436C2×C33C22×Q811yescharacteristic
437C2×C33C2×#4111yescharacteristic
438C2×C33H(5,𝔽2)11yescharacteristic
439C3⋊(C3⋊D3)—22no—
440C2×C3×Q8—91no—
441C2×C3×Q8—91no—
442C22×C3×C4—31no—
443C22×C3×C4—31no—
444C22×C3×C4—31no—
445C22×C3×C4—31no—
446C22×C3×C4—61no—
447C22×C3×C4—61no—
448C22×C3×C4—91no—
449C2×#67—91no—
450C2×#67—91no—
451C2×#67—91no—
452C2×#67—181no—
453C2×#67—181no—
454C2×#67—181no—
455C2×#67—361no—
456C22×Dic3—31no—
457C22×Dic3—31no—
458C22×Dic3—61no—
459C22×Dic3D3211yescharacteristic
460C22×Dic3D3211yescharacteristic
461C2×C4×D3—91no—
462C2×C4×D3—91no—
463C2×C4×D3—91no—
464C2×C4×D3—91no—
465C2×C4×D3—91no—
466C2×C4×D3—91no—
467C2×C4×D3—91no—
468C2×C4×D3—91no—
469C2×C4×D3—91no—
470C2×C4×D3—181no—
471C2×C4×D3—181no—
472C2×C4×D3—181no—
473C2×Dic6—31no—
474C2×Dic6—31no—
475C2×Dic6—31no—
476C2×Dic6—31no—
477C2×Dic6—91no—
478C2×Dic6—91no—
479C2×Dic6—91no—
480C3×C4⋊C4—91no—
481C3×C4⋊C4—91no—
482C3×C4⋊C4—91no—
483C3×C4⋊C4—91no—
484C3×C4⋊C4—91no—
485C3×C4⋊C4—91no—
486C3×C4⋊C4—91no—
487C3×C4⋊C4—91no—
488C3×C4⋊C4—91no—
489C3×C4⋊C4—91no—
490C3×C22⋊C4—31no—
491C3×C22⋊C4—31no—
492C3×C22⋊C4—61no—
493C3×C22⋊C4—91no—
494C3×C22⋊C4—91no—
495#217—31no—
496#217—31no—
497#217—31no—
498#217—31no—
499#217—61no—
500#217—61no—
501#217D3211yescharacteristic
502(C2×D3)⋊C4—91no—
503(C2×D3)⋊C4—91no—
504(C2×D3)⋊C4—91no—
505(C2×D3)⋊C4—91no—
506(C2×D3)⋊C4—91no—
507(C2×D3)⋊C4—91no—
508(C2×D3)⋊C4—91no—
509(C2×D3)⋊C4—91no—
510(C2×D3)⋊C4—91no—
511(C2×D3)⋊C4—181no—
512(C2×D3)⋊C4—181no—
513(C2×D3)⋊C4—181no—
514C4⋊Dic3—31no—
515C4⋊Dic3—31no—
516C4⋊Dic3—31no—
517C4⋊Dic3—31no—
518C4⋊Dic3—31no—
519C4⋊Dic3—31no—
520C4⋊Dic3—31no—
521C4⋊Dic3—31no—
522C4⋊Dic3—91no—
523C4⋊Dic3—91no—
524C4⋊Dic3—91no—
525Dic3⋊C4—31no—
526Dic3⋊C4—31no—
527Dic3⋊C4—31no—
528Dic3⋊C4—31no—
529Dic3⋊C4—31no—
530Dic3⋊C4—31no—
531Dic3⋊C4—31no—
532Dic3⋊C4—31no—
533Dic3⋊C4—31no—
534Dic3⋊C4—31no—
535Dic3⋊C4—31no—
536Dic3⋊C4—31no—
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—181no—
553Dic3⋊C4—181no—
554Dic3⋊C4—181no—
555C4×Dic3—91no—
556C4×Dic3—91no—
557C4×Dic3—91no—
558C4×Dic3—91no—
559C4×Dic3—91no—
560C4×Dic3—91no—
561C4×Dic3—91no—
562C4×Dic3—91no—
563C4×Dic3—91no—
564C4×Dic3—181no—
565C4×Dic3—181no—
566C4×Dic3—181no—
567C22×C32—21no—
568C22×C32—21no—
569C22×C32—21no—
570C22×C32—21no—
571C22×C32—21no—
572C22×C32—21no—
573C22×C32—21no—
574C22×C32—21no—
575C22×C32—21no—
576C22×C32—22no—
577C22×C32—22no—
578C22×C32—22no—
579C22×C32—41no—
580C22×C32—42no—
581C22×C32—41no—
582C22×C32—41no—
583C22×C32—41no—
584C22×C32—41no—
585C22×C32—41no—
586C22×C32—41no—
587C22×C32—81no—
588C22×C32—81no—
589C22×C32D3×Q812yes—
590C22×C32D3×Q812yes—
591C22×C32D3×Q812yes—
592C22×C32C23×D311yescharacteristic
593C22×C32C23×D311yescharacteristic
594C22×C32C23×D311yescharacteristic
595C2×C3⋊D3—32no—
596C2×C3⋊D3—32no—
597C2×C3⋊D3—32no—
598C2×C3⋊D3—62no—
599C2×C3⋊D3—62no—
600C2×C3⋊D3—62no—
601C2×C3⋊D3—61no—
602C2×C3⋊D3—61no—
603C2×C3⋊D3—61no—
604C2×C3⋊D3—61no—
605C2×C3⋊D3—61no—
606C2×C3⋊D3—61no—
607C2×C3⋊D3—122no—
608C2×C3⋊D3—121no—
609C2×C3⋊D3—121no—
610C2×C3⋊D3—121no—
611C2×C3⋊D3—121no—
612C2×C3⋊D3—121no—
613C2×C3⋊D3—121no—
614C2×C3⋊D3—241no—
615C2×C3⋊D3—241no—
616C32×C4—32no—
617C32×C4—61no—
618C32×C4—61no—
619C32×C4—61no—
620C32×C4—61no—
621C32×C4—61no—
622C3⋊Dic3—21no—
623C3⋊Dic3—21no—
624C3⋊Dic3—21no—
625C3⋊Dic3—21no—
626C3⋊Dic3—21no—
627C3⋊Dic3—21no—
628C3⋊Dic3—32no—
629C3⋊Dic3—32no—
630C3⋊Dic3—32no—
631C3⋊Dic3—62no—
632C3⋊Dic3—62no—
633C3⋊Dic3—62no—
634C3⋊Dic3—122no—
635C3×Dic3—22no—
636C3×Dic3—21no—
637C3×Dic3—21no—
638C3×Dic3—21no—
639C3×Dic3—21no—
640C3×Dic3—21no—
641C3×Dic3—21no—
642C3×Dic3—21no—
643C3×Dic3—21no—
644C3×Dic3—21no—
645C3×Dic3—21no—
646C3×Dic3—22no—
647C3×Dic3—41no—
648C3×Dic3—41no—
649C3×Dic3—41no—
650C3×Dic3—41no—
651C3×Dic3—62no—
652C3×Dic3—61no—
653C3×Dic3—61no—
654C3×Dic3—61no—
655C3×Dic3—61no—
656C3×Dic3—61no—
657C3×Dic3—61no—
658C3×Dic3—61no—
659C3×Dic3—61no—
660C3×Dic3—61no—
661C3×Dic3—61no—
662C3×Dic3—61no—
663C3×Dic3—61no—
664C3×Dic3—121no—
665C3×Dic3—121no—
666C3×Dic3—121no—
667C3×Dic3—121no—
668C3×Dic3—121no—
669C3×Dic3#23512yes—
670C3×Dic3#23712yes—
671C4⋊Q8—271no—
672#125—271no—
673#125—271no—
674C22⋊Q8—91no—
675C22⋊Q8—91no—
676C22⋊Q8—271no—
677C22⋊Q8—271no—
678C22⋊Q8—271no—
679C22⋊Q8—271no—
680C4×Q8—271no—
681C4×D4—271no—
682C4×D4—271no—
683C4×D4—271no—
684C2×C4⋊C4—91no—
685C2×C4⋊C4—271no—
686C33#55411yescharacteristic, complemented, Sylow
687C23×C3—21no—
688C23×C3—21no—
689C23×C3—21no—
690C23×C3—41no—
691C23×C3C2×D3211yescharacteristic
692C23×C3C2×D3211yescharacteristic
693C23×C3C2×D3211yescharacteristic
694C22×D3—91no—
695C22×D3—91no—
696C22×D3—91no—
697C22×D3—181no—
698C22×D3—181no—
699C22×D3—181no—
700C22×D3—361no—
701C3×Q8—182no—
702C3×Q8—361no—
703C2×C3×C4—31no—
704C2×C3×C4—31no—
705C2×C3×C4—31no—
706C2×C3×C4—31no—
707C2×C3×C4—31no—
708C2×C3×C4—31no—
709C2×C3×C4—31no—
710C2×C3×C4—31no—
711C2×C3×C4—31no—
712C2×C3×C4—31no—
713C2×C3×C4—31no—
714C2×C3×C4—31no—
715C2×C3×C4—61no—
716C2×C3×C4—61no—
717C2×C3×C4—61no—
718C2×C3×C4—61no—
719C2×C3×C4—61no—
720C2×C3×C4—61no—
721C2×C3×C4—62no—
722C2×C3×C4—62no—
723C2×C3×C4—91no—
724C2×C3×C4—91no—
725C2×C3×C4—91no—
726C2×C3×C4—91no—
727C2×C3×C4—91no—
728C2×C3×C4—91no—
729C2×C3×C4—122no—
730C2×C3×C4—121no—
731C2×C3×C4—121no—
732C2×C3×C4—122no—
733C2×C3×C4—361no—
734#67—94no—
735#67—94no—
736#67—94no—
737#67—184no—
738#67—184no—
739#67—184no—
740#67—364no—
741C2×Dic3—22no—
742C2×Dic3—31no—
743C2×Dic3—31no—
744C2×Dic3—31no—
745C2×Dic3—31no—
746C2×Dic3—31no—
747C2×Dic3—31no—
748C2×Dic3—31no—
749C2×Dic3—31no—
750C2×Dic3—31no—
751C2×Dic3—31no—
752C2×Dic3—31no—
753C2×Dic3—31no—
754C2×Dic3—41no—
755C2×Dic3—61no—
756C2×Dic3—61no—
757C2×Dic3—61no—
758C2×Dic3—61no—
759C2×Dic3—61no—
760C2×Dic3—61no—
761C2×Dic3—91no—
762C2×Dic3—91no—
763C2×Dic3—91no—
764C2×Dic3—121no—
765C2×Dic3—121no—
766C2×Dic3—122no—
767C2×Dic3—181no—
768C2×Dic3—181no—
769C2×Dic3—181no—
770C2×Dic3—361no—
771C2×Dic3C2×D3211yescharacteristic
772C2×Dic3C2×D3211yescharacteristic
773C2×Dic3C2×D3211yescharacteristic
774C2×Dic3C2×D3211yescharacteristic
775C2×Dic3C2×D3211yescharacteristic
776C2×Dic3C2×D3211yescharacteristic
777C4×D3—182no—
778C4×D3—182no—
779C4×D3—182no—
780C4×D3—362no—
781C4×D3—361no—
782C4×D3—361no—
783C4×D3—361no—
784C4×D3—361no—
785C4×D3—361no—
786C4×D3—361no—
787C4×D3—362no—
788C4×D3—362no—
789Dic6—62no—
790Dic6—62no—
791Dic6—121no—
792Dic6—121no—
793Dic6—361no—
794Dic6—361no—
795Dic6—361no—
796C2×C32—22no—
797C2×C32—22no—
798C2×C32—22no—
799C2×C32—21no—
800C2×C32—21no—
801C2×C32—21no—
802C2×C32—21no—
803C2×C32—21no—
804C2×C32—21no—
805C2×C32—21no—
806C2×C32—21no—
807C2×C32—21no—
808C2×C32—41no—
809C2×C32—41no—
810C2×C32—41no—
811C2×C32—42no—
812C2×C32—42no—
813C2×C32—42no—
814C2×C32—82no—
815C2×C32C2×#23511yescharacteristic
816C2×C32C2×#23711yescharacteristic
817C2×C32#100411yescharacteristic
818C2×C32#100411yescharacteristic
819C2×C32C2×D3×Q811yescharacteristic
820C2×C32C2×D3×Q811yescharacteristic
821C2×C32C2×D3×Q811yescharacteristic
822C2×C32D3×#4111yescharacteristic
823C2×C32#100911yescharacteristic
824C3⋊D3—62no—
825C3⋊D3—62no—
826C3⋊D3—62no—
827C3⋊D3—122no—
828C3⋊D3—122no—
829C3⋊D3—122no—
830C3⋊D3—242no—
831C2×Q8—91no—
832C2×Q8—91no—
833C2×Q8—271no—
834C2×D4—271no—
835C22×C4—31no—
836C22×C4—31no—
837C22×C4—91no—
838C22×C4—271no—
839C22×C4—271no—
840C22×C4—271no—
841C4⋊C4—91no—
842C4⋊C4—91no—
843C4⋊C4—91no—
844C4⋊C4—91no—
845C4⋊C4—91no—
846C4⋊C4—91no—
847C4⋊C4—91no—
848C4⋊C4—91no—
849C4⋊C4—91no—
850C4⋊C4—91no—
851C4⋊C4—271no—
852C4⋊C4—271no—
853C4⋊C4—271no—
854C4⋊C4—271no—
855C4⋊C4—271no—
856C4⋊C4—271no—
857C22⋊C4—31no—
858C22⋊C4—91no—
859C22⋊C4—91no—
860C22⋊C4—271no—
861C22⋊C4—271no—
862C22⋊C4—271no—
863C42—271no—
864C42—271no—
865C42—271no—
866C22×C3—21no—
867C22×C3—21no—
868C22×C3—21no—
869C22×C3—21no—
870C22×C3—21no—
871C22×C3—21no—
872C22×C3—21no—
873C22×C3—21no—
874C22×C3—21no—
875C22×C3—22no—
876C22×C3—22no—
877C22×C3—22no—
878C22×C3—41no—
879C22×C3—41no—
880C22×C3—41no—
881C22×C3—41no—
882C22×C3—41no—
883C22×C3—41no—
884C22×C3—41no—
885C22×C3—42no—
886C22×C3—81no—
887C22×C3—81no—
888C22×C3#379712yes—
889C22×C3#379712yes—
890C22×C3#379712yes—
891C22×C3C22×D3211yescharacteristic
892C22×C3C22×D3211yescharacteristic
893C22×C3C22×D3211yescharacteristic
894C2×D3—92no—
895C2×D3—92no—
896C2×D3—92no—
897C2×D3—182no—
898C2×D3—182no—
899C2×D3—182no—
900C2×D3—181no—
901C2×D3—181no—
902C2×D3—181no—
903C2×D3—181no—
904C2×D3—181no—
905C2×D3—181no—
906C2×D3—362no—
907C2×D3—361no—
908C2×D3—361no—
909C2×D3—361no—
910C2×D3—361no—
911C2×D3—361no—
912C2×D3—361no—
913C2×D3—721no—
914C2×D3—721no—
915C3×C4—32no—
916C3×C4—32no—
917C3×C4—62no—
918C3×C4—62no—
919C3×C4—61no—
920C3×C4—61no—
921C3×C4—61no—
922C3×C4—61no—
923C3×C4—61no—
924C3×C4—61no—
925C3×C4—61no—
926C3×C4—61no—
927C3×C4—61no—
928C3×C4—61no—
929C3×C4—121no—
930C3×C4—121no—
931C3×C4—121no—
932C3×C4—121no—
933C3×C4—181no—
934C3×C4—181no—
935C3×C4—181no—
936C3×C4—181no—
937C3×C4—181no—
938C3×C4—181no—
939Dic3—21no—
940Dic3—21no—
941Dic3—21no—
942Dic3—21no—
943Dic3—21no—
944Dic3—62no—
945Dic3—61no—
946Dic3—61no—
947Dic3—61no—
948Dic3—61no—
949Dic3—61no—
950Dic3—61no—
951Dic3—61no—
952Dic3—61no—
953Dic3—61no—
954Dic3—61no—
955Dic3—61no—
956Dic3—61no—
957Dic3—92no—
958Dic3—92no—
959Dic3—92no—
960Dic3—121no—
961Dic3—121no—
962Dic3—121no—
963Dic3—121no—
964Dic3—121no—
965Dic3—182no—
966Dic3—182no—
967Dic3—182no—
968Dic3—362no—
969Dic3#380412yes—
970C32—21no—
971C32—21no—
972C32—21no—
973C32—41no—
974C32#551111yescharacteristic, complemented
975C32#563511yescharacteristic, complemented
976C32#563611yescharacteristic, complemented
977C23—271no—
978C23D3311yescharacteristic
979Q8—182no—
980Q8—361no—
981Q8—1081no—
982D4—274no—
983C2×C4—31no—
984C2×C4—31no—
985C2×C4—31no—
986C2×C4—31no—
987C2×C4—31no—
988C2×C4—31no—
989C2×C4—62no—
990C2×C4—91no—
991C2×C4—91no—
992C2×C4—91no—
993C2×C4—91no—
994C2×C4—91no—
995C2×C4—91no—
996C2×C4—121no—
997C2×C4—271no—
998C2×C4—361no—
999C2×C4—542no—
1000C2×C4—1081no—
1001C2×C4—1081no—
1002C2×C3—22no—
1003C2×C3—22no—
1004C2×C3—22no—
1005C2×C3—21no—
1006C2×C3—21no—
1007C2×C3—21no—
1008C2×C3—21no—
1009C2×C3—21no—
1010C2×C3—21no—
1011C2×C3—21no—
1012C2×C3—21no—
1013C2×C3—21no—
1014C2×C3—42no—
1015C2×C3—42no—
1016C2×C3—42no—
1017C2×C3—41no—
1018C2×C3—41no—
1019C2×C3—41no—
1020C2×C3—82no—
1021C2×C3C2×#379711yescharacteristic
1022C2×C3C2×#379711yescharacteristic
1023C2×C3C2×#379711yescharacteristic
1024C2×C3D3×#23511yescharacteristic
1025C2×C3#6430711yescharacteristic
1026C2×C3D3×#23711yescharacteristic
1027C2×C3#6431411yescharacteristic
1028C2×C3C2×#380411yescharacteristic
1029C2×C3#6433011yescharacteristic
1030D3—182no—
1031D3—182no—
1032D3—182no—
1033D3—362no—
1034D3—362no—
1035D3—362no—
1036D3—722no—
1037C22—21no—
1038C22—21no—
1039C22—272no—
1040C22—541no—
1041C22—541no—
1042C22#8895812yes—
1043C22C2×D3311yescharacteristic
1044C4—32no—
1045C4—61no—
1046C4—61no—
1047C4—61no—
1048C4—61no—
1049C4—61no—
1050C4—181no—
1051C4—181no—
1052C4—181no—
1053C4—181no—
1054C4—181no—
1055C4—181no—
1056C4—272no—
1057C3—21no—
1058C3—21no—
1059C3—21no—
1060C3—41no—
1061C3#1059414111yescharacteristic, complemented
1062C3#1059495611yescharacteristic, complemented
1063C3#1059499111yescharacteristic, complemented
1064C2—22no—
1065C2—542no—
1066C2D3×#380411yescharacteristic
1067C2#1172441811yescharacteristic
1068C2C2×#8895811yescharacteristic
subgroupG/H
center, FrattiniC22C2×D33
commutator, socle, cosocleC22×C33C24
FittingC23×C33C23
prime radicalC2×#6312C22
hypercenterC23D33
hypocenterC33#554
LCSG ▷ C22×C33 ▷ C33
UCSC1 ◁ C22 ◁ C23

Complements

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

NH ≅ G/Ntype
1. #11723721C2semidirect
5. C2×C3×Dic3⋊Dic3C2semidirect
6. C3×#63964C2semidirect
7. C3×#63964C2semidirect
8. #11723035C2semidirect
9. #11723016C2semidirect
10. #11723016C2semidirect
11. #11722982C2semidirect
12. #11722973C2semidirect
13. #11722973C2semidirect
14. #11722941C2semidirect
15. #11722912C2semidirect
64. C2×Dic3⋊Dic3D3semidirect
67. #63964D3semidirect
68. #63964D3semidirect
104. #6312Q8semidirect
686. C33#554semidirect
974. C32#5511semidirect
975. C32#5635semidirect
976. C32#5636semidirect
1061. C3#10594141semidirect
1062. C3#10594956semidirect
1063. C3#10594991semidirect

Maximal subgroups

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

subgroupindex
#117237212
#117236222
#117236182
C2×C3×Dic3⋊Dic32
C3×#639642
#117230352
#117230162
#117229822
#117229732
#117229412
#117229122
#105949913
#105949563
#105941413