Finite Group Databasebeta

← #13171935

Subgroups — #13171935

Order 1728.

1156 conjugacy classes of subgroups.

The subgroup lattice has 1014 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11723715C211yesmaximal, characteristic, complemented
2C2×Dic3⋊(C3⋊Dic3)C211yesmaximal, characteristic, complemented
3#11723603C211yesmaximal, characteristic
4#11723598C211yesmaximal, characteristic, complemented
5C3×Dic3×#67C211yesmaximal, characteristic
6C3×#63964C211yesmaximal, characteristic, complemented
7C3×#63962C211yesmaximal, characteristic
8#11723026C211yesmaximal, characteristic, complemented
9#11723022C211yesmaximal, characteristic, complemented
10#11723017C211yesmaximal, characteristic, complemented
11#11723013C211yesmaximal, characteristic, complemented
12#11723012C211yesmaximal, characteristic, complemented
13#11722969C211yesmaximal, characteristic, complemented
14#11722940C211yesmaximal, characteristic, complemented
15#11722914C211yesmaximal, characteristic, complemented
16#10595117—31nomaximal
17#10594853—31nomaximal
18#10594135—31nomaximal
19C22×C3⋊(C3⋊Dic3)C2211yescharacteristic
20C22×C3×C3⋊Dic3C2211yescharacteristic
21C2×C32×#67C2211yescharacteristic
22C22×C32×Dic3C2211yescharacteristic
23C2×C3×#627C2211yescharacteristic
24C2×C3×D3×Dic3C2211yescharacteristic
25C3×#3757C2211yescharacteristic
26C3×#3757C2211yescharacteristic
27C32×#217C2211yescharacteristic
28#88815C2211yescharacteristic
29#88815C2211yescharacteristic
30#88813C2211yescharacteristic
31#88813C2211yescharacteristic
32#88807C2211yescharacteristic
33#88807C2211yescharacteristic
34#88806C2211yescharacteristic
35#88806C2211yescharacteristic
36Dic3⋊(C3⋊Dic3)C2211yescharacteristic
37Dic3⋊(C3⋊Dic3)C2211yescharacteristic
38Dic3⋊(C3⋊Dic3)C2211yescharacteristic
39Dic3⋊(C3⋊Dic3)C2211yescharacteristic
40(C2×D3)⋊(C3⋊Dic3)C2211yescharacteristic
41(C2×D3)⋊(C3⋊Dic3)C2211yescharacteristic
42Dic3×C3⋊Dic3C2211yescharacteristic
43Dic3×C3⋊Dic3C2211yescharacteristic
44C3×#3724C2211yescharacteristic
45C3×Dic3⋊Dic3C2211yescharacteristic
46C3×Dic3⋊Dic3C2211yescharacteristic
47C3×Dic3⋊Dic3C2211yescharacteristic
48C3×Dic3⋊Dic3C2211yescharacteristic
49C3×Dic3⋊Dic3C2211yescharacteristic
50C3×(C2×D3)⋊Dic3C2211yescharacteristic
51C3×(C2×D3)⋊Dic3C2211yescharacteristic
52C3×(C2×D3)⋊Dic3C2211yescharacteristic
53C3×Dic32C2211yescharacteristic
54#64144—31no—
55C2×C4⋊(C3⋊Dic3)—31no—
56#64086—31no—
57C3×#935—31no—
58C3×D4×Dic3—31no—
59C3×C4×#67—31no—
60C3×#924—31no—
61C3×#886—31no—
62C3×#878—31no—
63Dic3×#67D311yescharacteristic
64C2×Dic3⋊Dic3—31no—
65C2×Dic3⋊Dic3—31no—
66C2×Dic3⋊Dic3—61no—
67#63964—31no—
68#63964D311yescharacteristic, complemented
69#63962—31no—
70#63962—31no—
71#63962—61no—
72#63962D311yescharacteristic
73#63957—31no—
74#63957—31no—
75#63957—31no—
76#63957—61no—
77#63956—31no—
78#63956—31no—
79#63955—31no—
80#63955—31no—
81#63955—31no—
82#63887—31no—
83#63878—31no—
84#63872—31no—
85#63869—31no—
86#63867—31no—
87#63862—31no—
88#63861—31no—
89#63861—31no—
90#63858—31no—
91#63856—31no—
92#63847—31no—
93#63846—31no—
94#63846—31no—
95#63846—31no—
96#63845—31no—
97#63845—31no—
98#63843—31no—
99Dic3×Dic6—31no—
100#63841—31no—
101#63837—31no—
102C23×C33C2311yescharacteristic
103C22×C32×D3C2311yescharacteristic
104C2×C3⋊(C3⋊Dic3)—22no—
105C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
106C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
107C2×C3×C3⋊Dic3—22no—
108C2×C3×C3⋊Dic3C2311yescharacteristic
109C2×C3×C3⋊Dic3C2311yescharacteristic
110C2×C3×C3⋊Dic3C2311yescharacteristic
111C2×C3×C3⋊Dic3C2311yescharacteristic
112C2×C3×C3⋊Dic3C2311yescharacteristic
113C2×C3×C3⋊Dic3C2311yescharacteristic
114C32×#67—22no—
115C2×C32×Dic3—22no—
116C2×C32×Dic3C2311yescharacteristic
117C2×C32×Dic3C2311yescharacteristic
118C2×C32×Dic3C2311yescharacteristic
119C2×C32×Dic3C2311yescharacteristic
120C2×C32×Dic3C2311yescharacteristic
121C3×#627—22no—
122C3×D3×Dic3—22no—
123#5650—91no—
124#5642—91no—
125#5541—91no—
126C2×C32×D4—31no—
127C22×C32×C4—31no—
128C22×C3⋊Dic3—31no—
129C22×C3⋊Dic3—31no—
130C22×C3⋊Dic3—31no—
131C22×C3⋊Dic3—61no—
132C22×C3⋊Dic3—61no—
133C22×C3⋊Dic3—61no—
134C22×C3⋊Dic3—121no—
135C22×C3⋊Dic3C2×D311yescharacteristic
136C2×C3×#67—21no—
137C2×C3×#67C2×D311yescharacteristic
138C2×C3×#67C2×D311yescharacteristic
139C22×C3×Dic3—21no—
140C22×C3×Dic3—31no—
141C22×C3×Dic3—31no—
142C22×C3×Dic3—31no—
143C22×C3×Dic3—61no—
144C22×C3×Dic3C2×D311yescharacteristic
145C22×C3×Dic3C2×D311yescharacteristic
146C2×C3×C4×D3—31no—
147C2×C3×Dic6—31no—
148C2×C3×Dic6—31no—
149C2×#627C2×D311yescharacteristic
150C2×D3×Dic3C2×D311yescharacteristic
151C32×C22⋊C4—31no—
152#3757—31no—
153#3757—31no—
154#3757C2×D311yescharacteristic
155#3757C2×D311yescharacteristic
156C4⋊(C3⋊Dic3)—31no—
157C4⋊(C3⋊Dic3)—31no—
158C4⋊(C3⋊Dic3)—31no—
159C4⋊(C3⋊Dic3)—31no—
160#3750—31no—
161#3750—31no—
162#3750—31no—
163#3750—31no—
164C4×C3⋊Dic3—31no—
165C4×C3⋊Dic3—31no—
166C3×#217—21no—
167C3×#217—31no—
168C3×#217—31no—
169C3×#217—31no—
170C3×#217—31no—
171C3×#217—31no—
172C3×#217—31no—
173C3×#217—31no—
174C3×#217—61no—
175C3×#217—61no—
176C3×#217C2×D311yescharacteristic
177C3×#217C2×D311yescharacteristic
178C3×(C2×D3)⋊C4—31no—
179C3×(C2×D3)⋊C4—31no—
180C3×(C2×D3)⋊C4—31no—
181C3×C4⋊Dic3—31no—
182C3×C4⋊Dic3—31no—
183C3×C4⋊Dic3—31no—
184C3×C4⋊Dic3—31no—
185C3×C4⋊Dic3—31no—
186C3×Dic3⋊C4—31no—
187C3×Dic3⋊C4—31no—
188C3×Dic3⋊C4—31no—
189C3×Dic3⋊C4—31no—
190C3×Dic3⋊C4—31no—
191C3×Dic3⋊C4—31no—
192C3×Dic3⋊C4—31no—
193C3×C4×Dic3—31no—
194C3×C4×Dic3—31no—
195#3724—31no—
196#3724—31no—
197#3724—31no—
198#3724—31no—
199#3724—31no—
200#3724—31no—
201#3724—61no—
202#3724—61no—
203#3724C2×D311yescharacteristic
204Dic3⋊Dic3—31no—
205Dic3⋊Dic3—31no—
206Dic3⋊Dic3—31no—
207Dic3⋊Dic3—31no—
208Dic3⋊Dic3—31no—
209Dic3⋊Dic3—31no—
210Dic3⋊Dic3—31no—
211Dic3⋊Dic3—31no—
212Dic3⋊Dic3—31no—
213Dic3⋊Dic3—31no—
214Dic3⋊Dic3—31no—
215Dic3⋊Dic3—31no—
216Dic3⋊Dic3—31no—
217Dic3⋊Dic3—31no—
218Dic3⋊Dic3—31no—
219Dic3⋊Dic3—31no—
220Dic3⋊Dic3—61no—
221Dic3⋊Dic3—61no—
222Dic3⋊Dic3—61no—
223Dic3⋊Dic3—61no—
224Dic3⋊Dic3—61no—
225Dic3⋊Dic3—61no—
226Dic3⋊Dic3C2×D311yescharacteristic
227Dic3⋊Dic3C2×D311yescharacteristic
228Dic3⋊Dic3C2×D311yescharacteristic
229Dic3⋊Dic3C2×D311yescharacteristic
230Dic3⋊Dic3C2×D311yescharacteristic
231(C2×D3)⋊Dic3—31no—
232(C2×D3)⋊Dic3—31no—
233(C2×D3)⋊Dic3—31no—
234(C2×D3)⋊Dic3—31no—
235(C2×D3)⋊Dic3—61no—
236(C2×D3)⋊Dic3—61no—
237(C2×D3)⋊Dic3C2×D311yescharacteristic
238(C2×D3)⋊Dic3C2×D311yescharacteristic
239(C2×D3)⋊Dic3C2×D311yescharacteristic
240Dic32—31no—
241Dic32—31no—
242Dic32—31no—
243Dic32—31no—
244Dic32—31no—
245Dic32—31no—
246Dic32—31no—
247Dic32—31no—
248Dic32—31no—
249Dic32—31no—
250Dic32—61no—
251Dic32—61no—
252Dic32C2×D311yescharacteristic
253C22×C33—21no—
254C22×C33—21no—
255C22×C33#4112yes—
256C22×C33C2411yescharacteristic
257C2×C32×D3—21no—
258C2×C32×D3—21no—
259C2×C32×D3—21no—
260C3⋊(C3⋊Dic3)—21no—
261C3⋊(C3⋊Dic3)—21no—
262C3×C3⋊Dic3—21no—
263C3×C3⋊Dic3—21no—
264C3×C3⋊Dic3—21no—
265C3×C3⋊Dic3—21no—
266C3×C3⋊Dic3—21no—
267C3×C3⋊Dic3—21no—
268C32×Dic3—21no—
269C32×Dic3—21no—
270C32×Dic3—21no—
271C32×Dic3—21no—
272C32×Dic3#4112yes—
273C3×#123—91no—
274C3×C22⋊Q8—91no—
275C3×C4×D4—91no—
276#946—91no—
277Q8×Dic3—91no—
278#935—31no—
279#935—91no—
280#935—91no—
281#935—181no—
282D4×Dic3—31no—
283C4×#67—31no—
284#926—91no—
285#926—91no—
286C2×C4⋊Dic3—91no—
287C2×C4⋊Dic3—91no—
288C2×C4⋊Dic3—181no—
289#924—31no—
290#924—91no—
291C2×Dic3⋊C4—91no—
292#898—91no—
293#898—91no—
294#892—91no—
295#890—91no—
296#890—91no—
297#890—91no—
298#890—91no—
299#889—91no—
300#889—91no—
301#889—91no—
302#889—91no—
303#887—91no—
304#886—31no—
305#886—91no—
306#879—91no—
307#879—91no—
308#879—91no—
309#879—91no—
310#878—31no—
311#878—91no—
312#877—91no—
313#877—91no—
314#877—91no—
315#877—91no—
316#877—91no—
317#877—91no—
318#877—181no—
319#870—91no—
320C4×Dic6—91no—
321C23×C32—21no—
322C23×C32—21no—
323C23×C32—21no—
324C23×C32—31no—
325C23×C32—41no—
326C23×C32C22×D311yescharacteristic
327C23×C32C22×D311yescharacteristic
328C23×C32C22×D311yescharacteristic
329C22×C3×D3—21no—
330C22×C3×D3C22×D311yescharacteristic
331C22×C3×D3C22×D311yescharacteristic
332C32×D4—62no—
333C2×C32×C4—31no—
334C2×C32×C4—31no—
335C2×C32×C4—31no—
336C2×C32×C4—31no—
337C2×C32×C4—31no—
338C2×C32×C4—62no—
339C2×C3⋊Dic3—22no—
340C2×C3⋊Dic3—31no—
341C2×C3⋊Dic3—31no—
342C2×C3⋊Dic3—31no—
343C2×C3⋊Dic3—31no—
344C2×C3⋊Dic3—31no—
345C2×C3⋊Dic3—31no—
346C2×C3⋊Dic3—61no—
347C2×C3⋊Dic3—61no—
348C2×C3⋊Dic3—61no—
349C2×C3⋊Dic3—61no—
350C2×C3⋊Dic3—61no—
351C2×C3⋊Dic3—61no—
352C2×C3⋊Dic3—62no—
353C2×C3⋊Dic3—64no—
354C2×C3⋊Dic3—62no—
355C2×C3⋊Dic3—62no—
356C2×C3⋊Dic3—121no—
357C2×C3⋊Dic3—121no—
358C2×C3⋊Dic3—122no—
359C2×C3⋊Dic3—122no—
360C2×C3⋊Dic3—124no—
361C2×C3⋊Dic3C22×D311yescharacteristic
362C2×C3⋊Dic3C22×D311yescharacteristic
363C2×C3⋊Dic3C22×D311yescharacteristic
364C2×C3⋊Dic3C22×D311yescharacteristic
365C2×C3⋊Dic3C22×D311yescharacteristic
366C2×C3⋊Dic3C22×D311yescharacteristic
367C3×#67—22no—
368C3×#67—22no—
369C3×#67—42no—
370C2×C3×Dic3—24no—
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—31no—
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—61no—
391C2×C3×Dic3—61no—
392C2×C3×Dic3—61no—
393C2×C3×Dic3—61no—
394C2×C3×Dic3—61no—
395C2×C3×Dic3—61no—
396C2×C3×Dic3—62no—
397C2×C3×Dic3—62no—
398C2×C3×Dic3—62no—
399C2×C3×Dic3—122no—
400C2×C3×Dic3C22×D311yescharacteristic
401C2×C3×Dic3C22×D311yescharacteristic
402C2×C3×Dic3C22×D311yescharacteristic
403C2×C3×Dic3C22×D311yescharacteristic
404C2×C3×Dic3C22×D311yescharacteristic
405C2×C3×Dic3C22×D311yescharacteristic
406C2×C3×Dic3C22×D311yescharacteristic
407C2×C3×Dic3C22×D311yescharacteristic
408C2×C3×Dic3C22×D311yescharacteristic
409C2×C3×Dic3C22×D311yescharacteristic
410C3×C4×D3—62no—
411C3×Dic6—62no—
412C3×Dic6—62no—
413#627—22no—
414D3×Dic3—22no—
415#552—271noSylow
416C2×C33—22no—
417C2×C33C2×#4111yescharacteristic
418C2×C33C2×#4111yescharacteristic
419C2×C332−1+411yescharacteristic
420C32×D3—41no—
421C2×C3×Q8—91no—
422C2×C3×D4—31no—
423C2×C3×D4—31no—
424C2×C3×D4—61no—
425C22×C3×C4—31no—
426C22×C3×C4—31no—
427C22×C3×C4—61no—
428C22×C3×C4—91no—
429C22×C3×C4—91no—
430C2×#67D3211yescharacteristic
431C22×Dic3—31no—
432C22×Dic3—31no—
433C22×Dic3—31no—
434C22×Dic3—61no—
435C22×Dic3—91no—
436C22×Dic3—91no—
437C22×Dic3—91no—
438C22×Dic3—181no—
439C22×Dic3—181no—
440C22×Dic3—181no—
441C22×Dic3—361no—
442C22×Dic3D3211yescharacteristic
443C2×C4×D3—31no—
444C2×Dic6—31no—
445C2×Dic6—31no—
446C3×C4⋊C4—91no—
447C3×C4⋊C4—91no—
448C3×C4⋊C4—91no—
449C3×C4⋊C4—91no—
450C3×C4⋊C4—91no—
451C3×C4⋊C4—91no—
452C3×C22⋊C4—31no—
453C3×C22⋊C4—31no—
454C3×C22⋊C4—61no—
455C3×C22⋊C4—91no—
456C3×C22⋊C4—91no—
457C3×C22⋊C4—91no—
458C3×C22⋊C4—91no—
459C3×C22⋊C4—91no—
460C3×C42—91no—
461#217—31no—
462#217—31no—
463#217—31no—
464#217—31no—
465#217—31no—
466#217—31no—
467#217—31no—
468#217—61no—
469#217—61no—
470#217—91no—
471#217—91no—
472#217—91no—
473#217—91no—
474#217—181no—
475#217—181no—
476#217D3211yescharacteristic
477(C2×D3)⋊C4—31no—
478(C2×D3)⋊C4—31no—
479(C2×D3)⋊C4—31no—
480(C2×D3)⋊C4—91no—
481(C2×D3)⋊C4—91no—
482C4⋊Dic3—31no—
483C4⋊Dic3—31no—
484C4⋊Dic3—31no—
485C4⋊Dic3—31no—
486C4⋊Dic3—31no—
487C4⋊Dic3—91no—
488C4⋊Dic3—91no—
489C4⋊Dic3—91no—
490C4⋊Dic3—91no—
491C4⋊Dic3—91no—
492C4⋊Dic3—91no—
493C4⋊Dic3—91no—
494C4⋊Dic3—91no—
495C4⋊Dic3—91no—
496C4⋊Dic3—91no—
497C4⋊Dic3—91no—
498C4⋊Dic3—91no—
499C4⋊Dic3—181no—
500C4⋊Dic3—181no—
501C4⋊Dic3—181no—
502C4⋊Dic3—181no—
503Dic3⋊C4—31no—
504Dic3⋊C4—31no—
505Dic3⋊C4—31no—
506Dic3⋊C4—31no—
507Dic3⋊C4—31no—
508Dic3⋊C4—31no—
509Dic3⋊C4—31no—
510Dic3⋊C4—91no—
511Dic3⋊C4—91no—
512Dic3⋊C4—91no—
513Dic3⋊C4—91no—
514Dic3⋊C4—91no—
515Dic3⋊C4—91no—
516Dic3⋊C4—91no—
517Dic3⋊C4—91no—
518Dic3⋊C4—91no—
519Dic3⋊C4—91no—
520Dic3⋊C4—91no—
521Dic3⋊C4—91no—
522Dic3⋊C4—91no—
523Dic3⋊C4—91no—
524Dic3⋊C4—91no—
525Dic3⋊C4—91no—
526Dic3⋊C4—91no—
527Dic3⋊C4—91no—
528Dic3⋊C4—181no—
529Dic3⋊C4—181no—
530Dic3⋊C4—181no—
531Dic3⋊C4—181no—
532C4×Dic3—31no—
533C4×Dic3—31no—
534C4×Dic3—91no—
535C4×Dic3—91no—
536C4×Dic3—91no—
537C4×Dic3—91no—
538C4×Dic3—91no—
539C4×Dic3—91no—
540C4×Dic3—91no—
541C4×Dic3—91no—
542C4×Dic3—91no—
543C4×Dic3—91no—
544C4×Dic3—91no—
545C4×Dic3—91no—
546C4×Dic3—181no—
547C4×Dic3—181no—
548C22×C32—21no—
549C22×C32—21no—
550C22×C32—22no—
551C22×C32—22no—
552C22×C32—21no—
553C22×C32—21no—
554C22×C32—21no—
555C22×C32—21no—
556C22×C32—21no—
557C22×C32—21no—
558C22×C32—21no—
559C22×C32—22no—
560C22×C32—22no—
561C22×C32—22no—
562C22×C32—42no—
563C22×C32—41no—
564C22×C32—41no—
565C22×C32—41no—
566C22×C32—41no—
567C22×C32—41no—
568C22×C32—42no—
569C22×C32—42no—
570C22×C32—61no—
571C22×C32—61no—
572C22×C32—61no—
573C22×C32#23512yes—
574C22×C32#23712yes—
575C22×C32#23912yes—
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—21no—
584C2×C3×D3—21no—
585C2×C3×D3—41no—
586C2×C3×D3—41no—
587C2×C3×D3—41no—
588C32×C4—32no—
589C32×C4—61no—
590C32×C4—61no—
591C32×C4—61no—
592C32×C4—61no—
593C3⋊Dic3—21no—
594C3⋊Dic3—21no—
595C3⋊Dic3—21no—
596C3⋊Dic3—21no—
597C3⋊Dic3—21no—
598C3⋊Dic3—21no—
599C3⋊Dic3—61no—
600C3⋊Dic3—61no—
601C3⋊Dic3—62no—
602C3⋊Dic3—62no—
603C3⋊Dic3—61no—
604C3⋊Dic3—61no—
605C3⋊Dic3—61no—
606C3⋊Dic3—61no—
607C3⋊Dic3—121no—
608C3⋊Dic3—121no—
609C3⋊Dic3—121no—
610C3⋊Dic3—121no—
611C3⋊Dic3—122no—
612C3⋊Dic3—122no—
613C3×Dic3—22no—
614C3×Dic3—21no—
615C3×Dic3—21no—
616C3×Dic3—21no—
617C3×Dic3—21no—
618C3×Dic3—21no—
619C3×Dic3—21no—
620C3×Dic3—21no—
621C3×Dic3—21no—
622C3×Dic3—22no—
623C3×Dic3—41no—
624C3×Dic3—41no—
625C3×Dic3—41no—
626C3×Dic3—61no—
627C3×Dic3—61no—
628C3×Dic3—61no—
629C3×Dic3—61no—
630C3×Dic3—61no—
631C3×Dic3—61no—
632C3×Dic3—61no—
633C3×Dic3—61no—
634C3×Dic3—61no—
635C3×Dic3—61no—
636C3×Dic3—61no—
637C3×Dic3—61no—
638C3×Dic3—121no—
639C3×Dic3—121no—
640C3×Dic3—121no—
641C3×Dic3—121no—
642C3×Dic3—121no—
643C3×Dic3—121no—
644C3×Dic3#23712yes—
645C3×Dic3#23712yes—
646#126—271no—
647#126—271no—
648#125—271no—
649#125—271no—
650#125—271no—
651#123—91no—
652#123—271no—
653C22⋊Q8—91no—
654C22⋊Q8—271no—
655C4×Q8—271no—
656C4×D4—91no—
657#117—271no—
658#117—271no—
659#117—271no—
660C2×C4⋊C4—271no—
661C33#55211yescharacteristic, complemented, Sylow
662C23×C3—21no—
663C23×C3—21no—
664C23×C3—21no—
665C23×C3—31no—
666C23×C3—31no—
667C23×C3—41no—
668C23×C3—61no—
669C23×C3C2×D3211yescharacteristic
670C23×C3C2×D3211yescharacteristic
671C23×C3C2×D3211yescharacteristic
672C22×D3C2×D3211yescharacteristic
673C3×Q8—182no—
674C3×D4—62no—
675C3×D4—62no—
676C3×D4—122no—
677C2×C3×C4—31no—
678C2×C3×C4—31no—
679C2×C3×C4—31no—
680C2×C3×C4—31no—
681C2×C3×C4—31no—
682C2×C3×C4—31no—
683C2×C3×C4—31no—
684C2×C3×C4—31no—
685C2×C3×C4—31no—
686C2×C3×C4—31no—
687C2×C3×C4—61no—
688C2×C3×C4—61no—
689C2×C3×C4—61no—
690C2×C3×C4—61no—
691C2×C3×C4—61no—
692C2×C3×C4—62no—
693C2×C3×C4—62no—
694C2×C3×C4—64no—
695C2×C3×C4—91no—
696C2×C3×C4—91no—
697C2×C3×C4—91no—
698C2×C3×C4—91no—
699C2×C3×C4—91no—
700C2×C3×C4—91no—
701C2×C3×C4—182no—
702C2×C3×C4—182no—
703#67—22no—
704C2×Dic3—22no—
705C2×Dic3—31no—
706C2×Dic3—31no—
707C2×Dic3—31no—
708C2×Dic3—31no—
709C2×Dic3—31no—
710C2×Dic3—31no—
711C2×Dic3—31no—
712C2×Dic3—31no—
713C2×Dic3—31no—
714C2×Dic3—31no—
715C2×Dic3—31no—
716C2×Dic3—31no—
717C2×Dic3—61no—
718C2×Dic3—61no—
719C2×Dic3—61no—
720C2×Dic3—61no—
721C2×Dic3—61no—
722C2×Dic3—61no—
723C2×Dic3—62no—
724C2×Dic3—62no—
725C2×Dic3—62no—
726C2×Dic3—91no—
727C2×Dic3—91no—
728C2×Dic3—91no—
729C2×Dic3—91no—
730C2×Dic3—91no—
731C2×Dic3—91no—
732C2×Dic3—122no—
733C2×Dic3—181no—
734C2×Dic3—181no—
735C2×Dic3—181no—
736C2×Dic3—181no—
737C2×Dic3—181no—
738C2×Dic3—181no—
739C2×Dic3—184no—
740C2×Dic3—182no—
741C2×Dic3—182no—
742C2×Dic3—182no—
743C2×Dic3—361no—
744C2×Dic3—361no—
745C2×Dic3—362no—
746C2×Dic3—362no—
747C2×Dic3—364no—
748C2×Dic3C2×D3211yescharacteristic
749C2×Dic3C2×D3211yescharacteristic
750C2×Dic3C2×D3211yescharacteristic
751C2×Dic3C2×D3211yescharacteristic
752C2×Dic3C2×D3211yescharacteristic
753C4×D3—62no—
754Dic6—62no—
755Dic6—62no—
756C2×C32—22no—
757C2×C32—24no—
758C2×C32—22no—
759C2×C32—22no—
760C2×C32—21no—
761C2×C32—21no—
762C2×C32—21no—
763C2×C32—21no—
764C2×C32—21no—
765C2×C32—21no—
766C2×C32—21no—
767C2×C32—21no—
768C2×C32—21no—
769C2×C32—41no—
770C2×C32—41no—
771C2×C32—41no—
772C2×C32—42no—
773C2×C32—42no—
774C2×C32—44no—
775C2×C32—121no—
776C2×C32C2×#23511yescharacteristic
777C2×C32C2×#23711yescharacteristic
778C2×C32C2×#23711yescharacteristic
779C2×C32C2×#23711yescharacteristic
780C2×C32C2×#23911yescharacteristic
781C2×C32D3×#4111yescharacteristic
782C2×C32#101011yescharacteristic
783C2×C32#101011yescharacteristic
784C2×C32#101011yescharacteristic
785C3×D3—41no—
786C3×D3—41no—
787C3×D3—81no—
788C2×Q8—91no—
789C2×D4—31no—
790C22×C4—31no—
791C22×C4—91no—
792C22×C4—91no—
793C22×C4—271no—
794C4⋊C4—91no—
795C4⋊C4—91no—
796C4⋊C4—91no—
797C4⋊C4—91no—
798C4⋊C4—91no—
799C4⋊C4—91no—
800C4⋊C4—271no—
801C4⋊C4—271no—
802C4⋊C4—271no—
803C4⋊C4—271no—
804C4⋊C4—271no—
805C4⋊C4—271no—
806C4⋊C4—271no—
807C4⋊C4—271no—
808C4⋊C4—271no—
809C4⋊C4—271no—
810C22⋊C4—31no—
811C22⋊C4—91no—
812C22⋊C4—91no—
813C22⋊C4—91no—
814C22⋊C4—91no—
815C22⋊C4—91no—
816C22⋊C4—271no—
817C22⋊C4—271no—
818C42—91no—
819C42—271no—
820C42—271no—
821C42—271no—
822C42—271no—
823C22×C3—22no—
824C22×C3—22no—
825C22×C3—21no—
826C22×C3—21no—
827C22×C3—21no—
828C22×C3—21no—
829C22×C3—21no—
830C22×C3—21no—
831C22×C3—21no—
832C22×C3—21no—
833C22×C3—21no—
834C22×C3—22no—
835C22×C3—22no—
836C22×C3—22no—
837C22×C3—41no—
838C22×C3—41no—
839C22×C3—41no—
840C22×C3—41no—
841C22×C3—42no—
842C22×C3—42no—
843C22×C3—41no—
844C22×C3—42no—
845C22×C3—61no—
846C22×C3—61no—
847C22×C3—61no—
848C22×C3—61no—
849C22×C3—61no—
850C22×C3—61no—
851C22×C3—121no—
852C22×C3—121no—
853C22×C3—121no—
854C22×C3#379612yes—
855C22×C3#379912yes—
856C22×C3#380412yes—
857C22×C3C22×D3211yescharacteristic
858C22×C3C22×D3211yescharacteristic
859C22×C3C22×D3211yescharacteristic
860C2×D3—21no—
861C2×D3—21no—
862C2×D3—21no—
863C3×C4—32no—
864C3×C4—32no—
865C3×C4—62no—
866C3×C4—62no—
867C3×C4—61no—
868C3×C4—61no—
869C3×C4—61no—
870C3×C4—61no—
871C3×C4—61no—
872C3×C4—61no—
873C3×C4—61no—
874C3×C4—61no—
875C3×C4—121no—
876C3×C4—121no—
877C3×C4—121no—
878C3×C4—181no—
879C3×C4—181no—
880C3×C4—181no—
881C3×C4—181no—
882C3×C4—181no—
883C3×C4—181no—
884Dic3—21no—
885Dic3—21no—
886Dic3—21no—
887Dic3—21no—
888Dic3—61no—
889Dic3—61no—
890Dic3—61no—
891Dic3—61no—
892Dic3—61no—
893Dic3—61no—
894Dic3—61no—
895Dic3—61no—
896Dic3—61no—
897Dic3—61no—
898Dic3—61no—
899Dic3—61no—
900Dic3—121no—
901Dic3—121no—
902Dic3—121no—
903Dic3—121no—
904Dic3—121no—
905Dic3—121no—
906Dic3—182no—
907Dic3—182no—
908Dic3—181no—
909Dic3—181no—
910Dic3—181no—
911Dic3—181no—
912Dic3—181no—
913Dic3—181no—
914Dic3—361no—
915Dic3—361no—
916Dic3—361no—
917Dic3—361no—
918Dic3—362no—
919Dic3—362no—
920Dic3#380512yes—
921C32—21no—
922C32—21no—
923C32—21no—
924C32—41no—
925C32#554111yescharacteristic, complemented
926C32#564211yescharacteristic, complemented
927C32#565011yescharacteristic, complemented
928C23—31no—
929C23D3311yescharacteristic
930Q8—182no—
931D4—62no—
932C2×C4—31no—
933C2×C4—31no—
934C2×C4—31no—
935C2×C4—31no—
936C2×C4—31no—
937C2×C4—62no—
938C2×C4—91no—
939C2×C4—91no—
940C2×C4—91no—
941C2×C4—91no—
942C2×C4—91no—
943C2×C4—91no—
944C2×C4—182no—
945C2×C4—182no—
946C2×C4—271no—
947C2×C4—271no—
948C2×C4—542no—
949C2×C3—24no—
950C2×C3—22no—
951C2×C3—22no—
952C2×C3—22no—
953C2×C3—21no—
954C2×C3—21no—
955C2×C3—21no—
956C2×C3—21no—
957C2×C3—21no—
958C2×C3—21no—
959C2×C3—21no—
960C2×C3—21no—
961C2×C3—21no—
962C2×C3—42no—
963C2×C3—42no—
964C2×C3—44no—
965C2×C3—41no—
966C2×C3—41no—
967C2×C3—41no—
968C2×C3—121no—
969C2×C3—121no—
970C2×C3—241no—
971C2×C3C2×#379611yescharacteristic
972C2×C3#6429811yescharacteristic
973C2×C3C2×#379911yescharacteristic
974C2×C3#6430911yescharacteristic
975C2×C3#6430911yescharacteristic
976C2×C3D3×#23711yescharacteristic
977C2×C3D3×#23711yescharacteristic
978C2×C3C2×#380411yescharacteristic
979C2×C3C2×#380511yescharacteristic
980D3—41no—
981C22—21no—
982C22—21no—
983C22—61no—
984C22—61no—
985C22—61no—
986C22#8896212yes—
987C22C2×D3311yescharacteristic
988C4—32no—
989C4—61no—
990C4—61no—
991C4—61no—
992C4—61no—
993C4—181no—
994C4—181no—
995C4—181no—
996C4—181no—
997C4—181no—
998C4—181no—
999C4—541no—
1000C4—541no—
1001C3—21no—
1002C3—21no—
1003C3—21no—
1004C3—41no—
1005C3#1059413511yescharacteristic, complemented
1006C3#1059485311yescharacteristic, complemented
1007C3#1059511711yescharacteristic, complemented
1008C2—22no—
1009C2—121no—
1010C2D3×#380511yescharacteristic
1011C2#1172442711yescharacteristic
1012C2C2×#8896211yescharacteristic
subgroupG/H
center, FrattiniC22C2×D33
commutator, socle, cosocleC22×C33C24
FittingC23×C33C23
prime radicalC2×C32×#67C22
hypercenterC23D33
hypocenterC33#552
LCSG ▷ C22×C33 ▷ C33
UCSC1 ◁ C22 ◁ C23

Complements

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

NH ≅ G/Ntype
1. #11723715C2semidirect
2. C2×Dic3⋊(C3⋊Dic3)C2semidirect
4. #11723598C2semidirect
6. C3×#63964C2semidirect
8. #11723026C2semidirect
9. #11723022C2semidirect
10. #11723017C2semidirect
11. #11723013C2semidirect
12. #11723012C2semidirect
13. #11722969C2semidirect
14. #11722940C2semidirect
15. #11722914C2semidirect
68. #63964D3semidirect
661. C33#552semidirect
925. C32#5541semidirect
926. C32#5642semidirect
927. C32#5650semidirect
1005. C3#10594135semidirect
1006. C3#10594853semidirect
1007. C3#10595117semidirect

Maximal subgroups

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

subgroupindex
#117237152
C2×Dic3⋊(C3⋊Dic3)2
#117236032
#117235982
C3×Dic3×#672
C3×#639642
C3×#639622
#117230262
#117230222
#117230172
#117230132
#117230122
#117229692
#117229402
#117229142
#105951173
#105948533
#105941353