Finite Group Databasebeta

← #13168482

Subgroups — #13168482

Order 1728.

1084 conjugacy classes of subgroups.

The subgroup lattice has 986 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11723665C211yesmaximal, characteristic, complemented
2#11723432C211yesmaximal, characteristic, complemented
3#11723423C211yesmaximal, characteristic, complemented
4#11723391C211yesmaximal, characteristic, complemented
5C3×#63879C211yesmaximal, characteristic
6C3×#63862C211yesmaximal, characteristic, complemented
7C3×#63851C211yesmaximal, characteristic, complemented
8#11723036C211yesmaximal, characteristic, complemented
9#11723026C211yesmaximal, characteristic, complemented
10#11723019C211yesmaximal, characteristic, complemented
11#11723006C211yesmaximal, characteristic
12#11723004C211yesmaximal, characteristic
13#11722969C211yesmaximal, characteristic, complemented
14#11722940C211yesmaximal, characteristic, complemented
15#11722914C211yesmaximal, characteristic, complemented
16#10594841—31nomaximal
17#10594554—31nomaximal
18#10594248—31nomaximal
19C2×C32×C4×D3C2211yescharacteristic
20C2×#6296C2211yescharacteristic
21C2×#6293C2211yescharacteristic
22C2×C3×#627C2211yescharacteristic
23C2×C3×#625C2211yescharacteristic
24C2×C3×D3×Dic3C2211yescharacteristic
25C4×C3⋊(C3⋊Dic3)C2211yescharacteristic
26C3×#3750C2211yescharacteristic
27C3×#3750C2211yescharacteristic
28C3×C4×C3⋊Dic3C2211yescharacteristic
29C32×(C2×D3)⋊C4C2211yescharacteristic
30C32×Dic3⋊C4C2211yescharacteristic
31#88815C2211yescharacteristic
32#88813C2211yescharacteristic
33#88813C2211yescharacteristic
34#88807C2211yescharacteristic
35#88806C2211yescharacteristic
36Dic3⋊(C3⋊Dic3)C2211yescharacteristic
37Dic3⋊(C3⋊Dic3)C2211yescharacteristic
38Dic3⋊(C3⋊Dic3)C2211yescharacteristic
39(C2×D3)⋊(C3⋊Dic3)C2211yescharacteristic
40(C2×D3)⋊(C3⋊Dic3)C2211yescharacteristic
41(C2×D3)⋊(C3⋊Dic3)C2211yescharacteristic
42(C2×D3)⋊(C3⋊Dic3)C2211yescharacteristic
43Dic3×C3⋊Dic3C2211yescharacteristic
44Dic3×C3⋊Dic3C2211yescharacteristic
45C3×Dic3⋊Dic3C2211yescharacteristic
46C3×Dic3⋊Dic3C2211yescharacteristic
47C3×Dic3⋊Dic3C2211yescharacteristic
48C3×(C2×D3)⋊Dic3C2211yescharacteristic
49C3×(C2×D3)⋊Dic3C2211yescharacteristic
50C3×(C2×D3)⋊Dic3C2211yescharacteristic
51C3×(C2×D3)⋊Dic3C2211yescharacteristic
52C3×(C2×D3)⋊Dic3C2211yescharacteristic
53C3×Dic32C2211yescharacteristic
54#64135—31no—
55#64096—31no—
56#64088—31no—
57C3×C4×#67—31no—
58C3×#924—31no—
59C3×#898—31no—
60C3×#896—31no—
61C3×#67⋊C4—31no—
62C3×#879—31no—
63#63964—31no—
64#63959—31no—
65#63959—31no—
66#63959—31no—
67#63959—31no—
68#63956—31no—
69#63956—31no—
70#63955—31no—
71#63918—31no—
72#63918—31no—
73#63915—31no—
74#63913—31no—
75#63887—31no—
76#63879D311yescharacteristic
77#63878—31no—
78#63862—31no—
79#63862—31no—
80#63862—31no—
81#63862—61no—
82#63862D311yescharacteristic, complemented
83#63861—31no—
84#63858—31no—
85#63858—31no—
86#63856—31no—
87#63855—31no—
88#63855—31no—
89#63855—61no—
90#63851D311yescharacteristic, complemented
91#63843—31no—
92Dic3×Dic6—31no—
93#63841—31no—
94#63840—31no—
95#63838—31no—
96#63838—31no—
97#63838—31no—
98#63838—61no—
99#63837—31no—
100#63837—31no—
101#63837—31no—
102C22×C32×D3C2311yescharacteristic
103C22×C32×D3C2311yescharacteristic
104C2×C33×C4C2311yescharacteristic
105C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
106C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
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×Dic3C2311yescharacteristic
114C2×C32×Dic3C2311yescharacteristic
115C2×C32×Dic3C2311yescharacteristic
116C2×C32×Dic3C2311yescharacteristic
117C32×C4×D3—22no—
118#6296—22no—
119#6293—22no—
120C3×#627—22no—
121C3×#625—22no—
122C3×D3×Dic3—22no—
123#5702—91no—
124#5641—91no—
125#5542—91no—
126C22×C32×C4—31no—
127C2×#634—31no—
128C2×C3×#67—31no—
129C2×C3×#67—31no—
130C22×C3×Dic3—31no—
131C2×C3×C4×D3—21no—
132C2×C3×C4×D3—31no—
133C2×C3×C4×D3C2×D311yescharacteristic
134C2×C3×C4×D3C2×D311yescharacteristic
135C2×C3×Dic6—31no—
136C2×C3×Dic6—31no—
137C2×#627—31no—
138C2×#627—31no—
139C2×#627—31no—
140C2×#627—31no—
141C2×#627—31no—
142C2×#627—61no—
143C2×#627C2×D311yescharacteristic
144C2×#625C2×D311yescharacteristic
145C2×D3×Dic3C2×D311yescharacteristic
146C32×C4⋊C4—31no—
147C32×C22⋊C4—31no—
148#3757—31no—
149#3757—31no—
150#3757—31no—
151#3757—31no—
152C4⋊(C3⋊Dic3)—31no—
153C4⋊(C3⋊Dic3)—31no—
154C4⋊(C3⋊Dic3)—31no—
155#3750—31no—
156#3750—31no—
157#3750C2×D311yescharacteristic
158#3750C2×D311yescharacteristic
159C4×C3⋊Dic3—31no—
160C4×C3⋊Dic3—31no—
161C4×C3⋊Dic3—31no—
162C4×C3⋊Dic3—31no—
163C4×C3⋊Dic3—31no—
164C4×C3⋊Dic3—61no—
165C4×C3⋊Dic3—61no—
166C4×C3⋊Dic3—61no—
167C4×C3⋊Dic3—121no—
168C4×C3⋊Dic3C2×D311yescharacteristic
169C3×#217—31no—
170C3×#217—31no—
171C3×#217—31no—
172C3×#217—31no—
173C3×#217—31no—
174C3×(C2×D3)⋊C4—21no—
175C3×(C2×D3)⋊C4—31no—
176C3×(C2×D3)⋊C4—31no—
177C3×(C2×D3)⋊C4—31no—
178C3×(C2×D3)⋊C4—31no—
179C3×(C2×D3)⋊C4—31no—
180C3×(C2×D3)⋊C4C2×D311yescharacteristic
181C3×(C2×D3)⋊C4C2×D311yescharacteristic
182C3×C4⋊Dic3—31no—
183C3×C4⋊Dic3—31no—
184C3×C4⋊Dic3—31no—
185C3×Dic3⋊C4—21no—
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×Dic3⋊C4—61no—
194C3×Dic3⋊C4—61no—
195C3×Dic3⋊C4C2×D311yescharacteristic
196C3×Dic3⋊C4C2×D311yescharacteristic
197C3×C4×Dic3—31no—
198C3×C4×Dic3—31no—
199C3×C4×Dic3—31no—
200C3×C4×Dic3—31no—
201C3×C4×Dic3—61no—
202#3724—31no—
203#3724—31no—
204#3724—31no—
205#3724—61no—
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—61no—
217Dic3⋊Dic3—61no—
218Dic3⋊Dic3—61no—
219Dic3⋊Dic3—61no—
220Dic3⋊Dic3C2×D311yescharacteristic
221Dic3⋊Dic3C2×D311yescharacteristic
222Dic3⋊Dic3C2×D311yescharacteristic
223(C2×D3)⋊Dic3—31no—
224(C2×D3)⋊Dic3—31no—
225(C2×D3)⋊Dic3—31no—
226(C2×D3)⋊Dic3—31no—
227(C2×D3)⋊Dic3—31no—
228(C2×D3)⋊Dic3—31no—
229(C2×D3)⋊Dic3—31no—
230(C2×D3)⋊Dic3—31no—
231(C2×D3)⋊Dic3—61no—
232(C2×D3)⋊Dic3—61no—
233(C2×D3)⋊Dic3—61no—
234(C2×D3)⋊Dic3—61no—
235(C2×D3)⋊Dic3C2×D311yescharacteristic
236(C2×D3)⋊Dic3C2×D311yescharacteristic
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×C33C2411yescharacteristic
254C2×C32×D3—21no—
255C2×C32×D3—21no—
256C2×C32×D3—21no—
257C2×C32×D3—21no—
258C2×C32×D3—21no—
259C2×C32×D3—21no—
260C33×C4—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—
268C3×C3⋊Dic3#4112yes—
269C32×Dic3—21no—
270C32×Dic3—21no—
271C32×Dic3—21no—
272C32×Dic3#4112yes—
273C3×#126—91no—
274C3×C22⋊Q8—91no—
275C3×C4×D4—91no—
276#946—91no—
277Q8×Dic3—91no—
278#936—91no—
279#936—91no—
280C4×#67—31no—
281#926—91no—
282#926—91no—
283#926—91no—
284#926—181no—
285#924—31no—
286#924—91no—
287#898—31no—
288#898—91no—
289#898—91no—
290#898—91no—
291#896—31no—
292#892—91no—
293#888—91no—
294#888—91no—
295#887—91no—
296#887—91no—
297#887—91no—
298#887—91no—
299#887—91no—
300#887—91no—
301#887—181no—
302#885—91no—
303#885—91no—
304#885—91no—
305#885—91no—
306#67⋊C4—31no—
307#879—31no—
308#879—91no—
309#879—91no—
310#879—91no—
311#879—91no—
312#879—91no—
313#879—91no—
314#879—181no—
315#878—91no—
316#877—91no—
317#872—91no—
318#869—91no—
319C4×Dic6—91no—
320C4×Dic6—91no—
321C23×C32—31no—
322C23×C32—31no—
323C22×C3×D3—21no—
324C22×C3×D3—21no—
325C22×C3×D3C22×D311yescharacteristic
326C22×C3×D3C22×D311yescharacteristic
327C22×C3×D3C22×D311yescharacteristic
328C22×C3×D3C22×D311yescharacteristic
329C2×C32×C4—21no—
330C2×C32×C4—21no—
331C2×C32×C4—21no—
332C2×C32×C4—31no—
333C2×C32×C4—31no—
334C2×C32×C4—31no—
335C2×C32×C4—31no—
336C2×C32×C4—41no—
337C2×C32×C4—62no—
338C2×C32×C4C22×D311yescharacteristic
339C2×C32×C4C22×D311yescharacteristic
340C2×C32×C4C22×D311yescharacteristic
341C2×C3⋊Dic3—31no—
342C2×C3⋊Dic3—31no—
343C2×C3⋊Dic3—31no—
344C2×C3⋊Dic3—31no—
345C2×C3⋊Dic3—31no—
346C2×C3⋊Dic3—31no—
347C2×C3⋊Dic3—61no—
348C2×C3⋊Dic3—61no—
349C2×C3⋊Dic3—61no—
350C2×C3⋊Dic3—61no—
351C2×C3⋊Dic3—61no—
352C2×C3⋊Dic3—61no—
353C2×C3⋊Dic3—121no—
354C2×C3⋊Dic3—121no—
355C2×C3⋊Dic3C22×D311yescharacteristic
356C2×C3⋊Dic3C22×D311yescharacteristic
357C2×C3⋊Dic3C22×D311yescharacteristic
358C2×C3⋊Dic3C22×D311yescharacteristic
359C2×C3⋊Dic3C22×D311yescharacteristic
360C2×C3⋊Dic3C22×D311yescharacteristic
361#634—62no—
362C3×#67—62no—
363C3×#67—62no—
364C2×C3×Dic3—21no—
365C2×C3×Dic3—21no—
366C2×C3×Dic3—21no—
367C2×C3×Dic3—21no—
368C2×C3×Dic3—31no—
369C2×C3×Dic3—31no—
370C2×C3×Dic3—31no—
371C2×C3×Dic3—31no—
372C2×C3×Dic3—31no—
373C2×C3×Dic3—31no—
374C2×C3×Dic3—31no—
375C2×C3×Dic3—31no—
376C2×C3×Dic3—31no—
377C2×C3×Dic3—31no—
378C2×C3×Dic3—31no—
379C2×C3×Dic3—31no—
380C2×C3×Dic3—61no—
381C2×C3×Dic3—61no—
382C2×C3×Dic3—61no—
383C2×C3×Dic3—61no—
384C2×C3×Dic3—61no—
385C2×C3×Dic3—61no—
386C2×C3×Dic3—62no—
387C2×C3×Dic3C22×D311yescharacteristic
388C2×C3×Dic3C22×D311yescharacteristic
389C2×C3×Dic3C22×D311yescharacteristic
390C2×C3×Dic3C22×D311yescharacteristic
391C2×C3×Dic3C22×D311yescharacteristic
392C2×C3×Dic3C22×D311yescharacteristic
393C2×C3×Dic3C22×D311yescharacteristic
394C2×C3×Dic3C22×D311yescharacteristic
395C3×C4×D3—24no—
396C3×C4×D3—22no—
397C3×C4×D3—22no—
398C3×C4×D3—62no—
399C3×Dic6—62no—
400C3×Dic6—62no—
401#627—22no—
402#627—62no—
403#627—62no—
404#627—64no—
405#627—62no—
406#627—62no—
407#627—62no—
408#625—22no—
409D3×Dic3—22no—
410#556—271noSylow
411C2×C33C2×#4111yescharacteristic
412C2×C33C2×#4111yescharacteristic
413C2×C332−1+411yescharacteristic
414C32×D3—41no—
415C32×D3—41no—
416C2×C3×Q8—91no—
417C2×C3×D4—91no—
418C22×C3×C4—31no—
419C22×C3×C4—31no—
420C22×C3×C4—61no—
421C22×C3×C4—91no—
422C2×#67—31no—
423C2×#67—31no—
424C22×Dic3—31no—
425C2×C4×D3—31no—
426C2×C4×D3D3211yescharacteristic
427C2×Dic6—31no—
428C2×Dic6—31no—
429C2×Dic6—91no—
430C2×Dic6—91no—
431C2×Dic6—91no—
432C2×Dic6—91no—
433C2×Dic6—91no—
434C2×Dic6—91no—
435C2×Dic6—181no—
436C3×C4⋊C4—31no—
437C3×C4⋊C4—31no—
438C3×C4⋊C4—61no—
439C3×C4⋊C4—91no—
440C3×C4⋊C4—91no—
441C3×C4⋊C4—91no—
442C3×C4⋊C4—91no—
443C3×C4⋊C4—91no—
444C3×C22⋊C4—31no—
445C3×C22⋊C4—31no—
446C3×C22⋊C4—61no—
447C3×C22⋊C4—91no—
448C3×C22⋊C4—91no—
449C3×C22⋊C4—91no—
450C3×C22⋊C4—91no—
451C3×C22⋊C4—91no—
452C3×C42—91no—
453C3×C42—91no—
454#217—31no—
455#217—31no—
456#217—31no—
457#217—31no—
458#217—31no—
459#217—91no—
460#217—91no—
461#217—91no—
462#217—91no—
463#217—91no—
464#217—91no—
465#217—91no—
466#217—91no—
467#217—181no—
468#217—181no—
469#217—181no—
470#217—181no—
471(C2×D3)⋊C4—31no—
472(C2×D3)⋊C4—31no—
473(C2×D3)⋊C4—31no—
474(C2×D3)⋊C4—31no—
475(C2×D3)⋊C4—31no—
476(C2×D3)⋊C4—91no—
477(C2×D3)⋊C4—91no—
478(C2×D3)⋊C4—91no—
479(C2×D3)⋊C4—91no—
480(C2×D3)⋊C4D3211yescharacteristic
481C4⋊Dic3—31no—
482C4⋊Dic3—31no—
483C4⋊Dic3—31no—
484C4⋊Dic3—91no—
485C4⋊Dic3—91no—
486C4⋊Dic3—91no—
487C4⋊Dic3—91no—
488C4⋊Dic3—91no—
489C4⋊Dic3—91no—
490C4⋊Dic3—91no—
491C4⋊Dic3—91no—
492C4⋊Dic3—181no—
493C4⋊Dic3—181no—
494C4⋊Dic3—181no—
495Dic3⋊C4—31no—
496Dic3⋊C4—31no—
497Dic3⋊C4—31no—
498Dic3⋊C4—31no—
499Dic3⋊C4—31no—
500Dic3⋊C4—31no—
501Dic3⋊C4—31no—
502Dic3⋊C4—61no—
503Dic3⋊C4—61no—
504Dic3⋊C4—91no—
505Dic3⋊C4—91no—
506Dic3⋊C4—91no—
507Dic3⋊C4—91no—
508Dic3⋊C4—91no—
509Dic3⋊C4—91no—
510Dic3⋊C4—91no—
511Dic3⋊C4—91no—
512Dic3⋊C4—91no—
513Dic3⋊C4—91no—
514Dic3⋊C4—181no—
515Dic3⋊C4—181no—
516Dic3⋊C4D3211yescharacteristic
517C4×Dic3—31no—
518C4×Dic3—31no—
519C4×Dic3—31no—
520C4×Dic3—31no—
521C4×Dic3—61no—
522C4×Dic3—91no—
523C4×Dic3—91no—
524C4×Dic3—91no—
525C4×Dic3—91no—
526C4×Dic3—91no—
527C4×Dic3—91no—
528C4×Dic3—91no—
529C4×Dic3—91no—
530C4×Dic3—91no—
531C4×Dic3—91no—
532C4×Dic3—91no—
533C4×Dic3—91no—
534C4×Dic3—91no—
535C4×Dic3—91no—
536C4×Dic3—91no—
537C4×Dic3—181no—
538C4×Dic3—181no—
539C4×Dic3—181no—
540C4×Dic3—181no—
541C4×Dic3—181no—
542C4×Dic3—361no—
543C22×C32—21no—
544C22×C32—21no—
545C22×C32—21no—
546C22×C32—41no—
547C22×C32—61no—
548C22×C32—61no—
549C22×C32—61no—
550C22×C32—61no—
551C22×C32—61no—
552C22×C32—61no—
553C22×C32C23×D311yescharacteristic
554C22×C32C23×D311yescharacteristic
555C22×C32C23×D311yescharacteristic
556C2×C3×D3—22no—
557C2×C3×D3—21no—
558C2×C3×D3—21no—
559C2×C3×D3—21no—
560C2×C3×D3—21no—
561C2×C3×D3—21no—
562C2×C3×D3—21no—
563C2×C3×D3—21no—
564C2×C3×D3—21no—
565C2×C3×D3—21no—
566C2×C3×D3—21no—
567C2×C3×D3—21no—
568C2×C3×D3—21no—
569C2×C3×D3—41no—
570C2×C3×D3—41no—
571C2×C3×D3—41no—
572C2×C3×D3—41no—
573C2×C3×D3—41no—
574C32×C4—21no—
575C32×C4—22no—
576C32×C4—21no—
577C32×C4—21no—
578C32×C4—32no—
579C32×C4—41no—
580C32×C4—41no—
581C32×C4—42no—
582C32×C4—61no—
583C32×C4—61no—
584C32×C4—61no—
585C3⋊Dic3—21no—
586C3⋊Dic3—21no—
587C3⋊Dic3—21no—
588C3⋊Dic3—21no—
589C3⋊Dic3—21no—
590C3⋊Dic3—61no—
591C3⋊Dic3—61no—
592C3⋊Dic3—62no—
593C3⋊Dic3—62no—
594C3⋊Dic3—61no—
595C3⋊Dic3—61no—
596C3⋊Dic3—61no—
597C3⋊Dic3—61no—
598C3⋊Dic3—121no—
599C3⋊Dic3—121no—
600C3⋊Dic3—121no—
601C3⋊Dic3—121no—
602C3⋊Dic3—122no—
603C3⋊Dic3—122no—
604C3⋊Dic3#23512yes—
605C3×Dic3—22no—
606C3×Dic3—21no—
607C3×Dic3—21no—
608C3×Dic3—21no—
609C3×Dic3—21no—
610C3×Dic3—21no—
611C3×Dic3—21no—
612C3×Dic3—22no—
613C3×Dic3—32no—
614C3×Dic3—32no—
615C3×Dic3—41no—
616C3×Dic3—41no—
617C3×Dic3—62no—
618C3×Dic3—61no—
619C3×Dic3—61no—
620C3×Dic3—61no—
621C3×Dic3—61no—
622C3×Dic3—61no—
623C3×Dic3—61no—
624C3×Dic3—61no—
625C3×Dic3—61no—
626C3×Dic3—61no—
627C3×Dic3—61no—
628C3×Dic3—121no—
629C3×Dic3—121no—
630C3×Dic3—121no—
631C3×Dic3—121no—
632C3×Dic3—121no—
633C3×Dic3#23712yes—
634C3×Dic3#23712yes—
635C4⋊Q8—271no—
636#126—91no—
637#126—271no—
638#126—271no—
639#126—271no—
640#124—271no—
641#124—271no—
642C22⋊Q8—91no—
643C22⋊Q8—271no—
644C4×Q8—271no—
645C4×Q8—271no—
646C4×Q8—271no—
647C4×D4—91no—
648#117—271no—
649#117—271no—
650C33#55611yescharacteristic, complemented, Sylow
651C23×C3—31no—
652C23×C3—31no—
653C23×C3—31no—
654C23×C3—31no—
655C23×C3—61no—
656C23×C3—61no—
657C22×D3C2×D3211yescharacteristic
658C22×D3C2×D3211yescharacteristic
659C3×Q8—182no—
660C3×D4—182no—
661C2×C3×C4—21no—
662C2×C3×C4—21no—
663C2×C3×C4—21no—
664C2×C3×C4—31no—
665C2×C3×C4—31no—
666C2×C3×C4—31no—
667C2×C3×C4—31no—
668C2×C3×C4—31no—
669C2×C3×C4—31no—
670C2×C3×C4—31no—
671C2×C3×C4—31no—
672C2×C3×C4—41no—
673C2×C3×C4—61no—
674C2×C3×C4—61no—
675C2×C3×C4—61no—
676C2×C3×C4—61no—
677C2×C3×C4—62no—
678C2×C3×C4—62no—
679C2×C3×C4—64no—
680C2×C3×C4—91no—
681C2×C3×C4—91no—
682C2×C3×C4—91no—
683C2×C3×C4—91no—
684C2×C3×C4—91no—
685C2×C3×C4—91no—
686C2×C3×C4—182no—
687C2×C3×C4C2×D3211yescharacteristic
688C2×C3×C4C2×D3211yescharacteristic
689C2×C3×C4C2×D3211yescharacteristic
690#67—62no—
691#67—62no—
692C2×Dic3—31no—
693C2×Dic3—31no—
694C2×Dic3—31no—
695C2×Dic3—31no—
696C2×Dic3—31no—
697C2×Dic3—31no—
698C2×Dic3—31no—
699C2×Dic3—31no—
700C2×Dic3—31no—
701C2×Dic3—31no—
702C2×Dic3—31no—
703C2×Dic3—31no—
704C2×Dic3—61no—
705C2×Dic3—61no—
706C2×Dic3—61no—
707C2×Dic3—61no—
708C2×Dic3—61no—
709C2×Dic3—61no—
710C2×Dic3—62no—
711C2×Dic3—91no—
712C2×Dic3—91no—
713C2×Dic3—91no—
714C2×Dic3—91no—
715C2×Dic3—91no—
716C2×Dic3—91no—
717C2×Dic3—181no—
718C2×Dic3—181no—
719C2×Dic3—181no—
720C2×Dic3—181no—
721C2×Dic3—181no—
722C2×Dic3—181no—
723C2×Dic3—361no—
724C2×Dic3—361no—
725C2×Dic3C2×D3211yescharacteristic
726C2×Dic3C2×D3211yescharacteristic
727C2×Dic3C2×D3211yescharacteristic
728C2×Dic3C2×D3211yescharacteristic
729C4×D3—22no—
730C4×D3—62no—
731Dic6—62no—
732Dic6—62no—
733Dic6—182no—
734Dic6—182no—
735Dic6—182no—
736Dic6—182no—
737Dic6—182no—
738Dic6—182no—
739Dic6—184no—
740C2×C32—21no—
741C2×C32—21no—
742C2×C32—21no—
743C2×C32—21no—
744C2×C32—21no—
745C2×C32—21no—
746C2×C32—21no—
747C2×C32—21no—
748C2×C32—21no—
749C2×C32—41no—
750C2×C32—41no—
751C2×C32—41no—
752C2×C32—121no—
753C2×C32—121no—
754C2×C32C2×#23511yescharacteristic
755C2×C32C2×#23711yescharacteristic
756C2×C32C2×#23711yescharacteristic
757C2×C32#100711yescharacteristic
758C2×C32D3×#4111yescharacteristic
759C2×C32D3×#4111yescharacteristic
760C2×C32D3×#4111yescharacteristic
761C2×C32#101011yescharacteristic
762C2×C32#101011yescharacteristic
763C3×D3—42no—
764C3×D3—41no—
765C3×D3—41no—
766C3×D3—41no—
767C3×D3—41no—
768C3×D3—81no—
769C2×Q8—91no—
770C2×Q8—271no—
771C2×Q8—271no—
772C2×D4—91no—
773C22×C4—31no—
774C22×C4—91no—
775C4⋊C4—31no—
776C4⋊C4—91no—
777C4⋊C4—91no—
778C4⋊C4—91no—
779C4⋊C4—91no—
780C4⋊C4—91no—
781C4⋊C4—271no—
782C4⋊C4—271no—
783C4⋊C4—271no—
784C4⋊C4—271no—
785C4⋊C4—271no—
786C4⋊C4—271no—
787C22⋊C4—31no—
788C22⋊C4—91no—
789C22⋊C4—91no—
790C22⋊C4—91no—
791C22⋊C4—91no—
792C22⋊C4—91no—
793C22⋊C4—271no—
794C22⋊C4—271no—
795C22⋊C4—271no—
796C22⋊C4—271no—
797C42—91no—
798C42—91no—
799C42—271no—
800C42—271no—
801C42—271no—
802C42—271no—
803C42—271no—
804C22×C3—21no—
805C22×C3—21no—
806C22×C3—21no—
807C22×C3—41no—
808C22×C3—62no—
809C22×C3—61no—
810C22×C3—61no—
811C22×C3—61no—
812C22×C3—61no—
813C22×C3—61no—
814C22×C3—61no—
815C22×C3—61no—
816C22×C3—61no—
817C22×C3—61no—
818C22×C3—61no—
819C22×C3—61no—
820C22×C3—61no—
821C22×C3—121no—
822C22×C3—121no—
823C22×C3—121no—
824C22×C3—121no—
825C22×C3—121no—
826C22×C3C22×D3211yescharacteristic
827C22×C3C22×D3211yescharacteristic
828C22×C3C22×D3211yescharacteristic
829C2×D3—21no—
830C2×D3—21no—
831C2×D3—21no—
832C2×D3—21no—
833C2×D3—21no—
834C2×D3—21no—
835C3×C4—22no—
836C3×C4—21no—
837C3×C4—21no—
838C3×C4—21no—
839C3×C4—32no—
840C3×C4—32no—
841C3×C4—41no—
842C3×C4—41no—
843C3×C4—42no—
844C3×C4—62no—
845C3×C4—62no—
846C3×C4—61no—
847C3×C4—61no—
848C3×C4—61no—
849C3×C4—61no—
850C3×C4—61no—
851C3×C4—61no—
852C3×C4—92no—
853C3×C4—121no—
854C3×C4—121no—
855C3×C4—181no—
856C3×C4—181no—
857C3×C4—181no—
858C3×C4—181no—
859C3×C4—181no—
860Dic3—21no—
861Dic3—21no—
862Dic3—21no—
863Dic3—32no—
864Dic3—32no—
865Dic3—62no—
866Dic3—61no—
867Dic3—61no—
868Dic3—61no—
869Dic3—61no—
870Dic3—61no—
871Dic3—61no—
872Dic3—61no—
873Dic3—61no—
874Dic3—61no—
875Dic3—61no—
876Dic3—121no—
877Dic3—121no—
878Dic3—121no—
879Dic3—121no—
880Dic3—121no—
881Dic3—182no—
882Dic3—182no—
883Dic3—181no—
884Dic3—181no—
885Dic3—181no—
886Dic3—181no—
887Dic3—181no—
888Dic3—181no—
889Dic3—361no—
890Dic3—361no—
891Dic3—361no—
892Dic3—361no—
893Dic3—362no—
894Dic3—362no—
895Dic3#380512yes—
896C32—21no—
897C32—21no—
898C32—21no—
899C32—41no—
900C32#554211yescharacteristic, complemented
901C32#564111yescharacteristic, complemented
902C32#570211yescharacteristic, complemented
903C23—31no—
904C23—31no—
905Q8—182no—
906Q8—542no—
907Q8—542no—
908D4—182no—
909C2×C4—31no—
910C2×C4—31no—
911C2×C4—31no—
912C2×C4—31no—
913C2×C4—62no—
914C2×C4—91no—
915C2×C4—91no—
916C2×C4—91no—
917C2×C4—91no—
918C2×C4—91no—
919C2×C4—91no—
920C2×C4—182no—
921C2×C4—271no—
922C2×C4—271no—
923C2×C4D3311yescharacteristic
924C2×C3—21no—
925C2×C3—21no—
926C2×C3—21no—
927C2×C3—21no—
928C2×C3—21no—
929C2×C3—21no—
930C2×C3—21no—
931C2×C3—21no—
932C2×C3—21no—
933C2×C3—41no—
934C2×C3—41no—
935C2×C3—41no—
936C2×C3—122no—
937C2×C3—121no—
938C2×C3—121no—
939C2×C3—121no—
940C2×C3—121no—
941C2×C3—241no—
942C2×C3#6429711yescharacteristic
943C2×C3D3×#23511yescharacteristic
944C2×C3D3×#23511yescharacteristic
945C2×C3#6430611yescharacteristic
946C2×C3#6430911yescharacteristic
947C2×C3D3×#23711yescharacteristic
948C2×C3D3×#23711yescharacteristic
949C2×C3#6431511yescharacteristic
950C2×C3C2×#380511yescharacteristic
951D3—41no—
952D3—41no—
953C22—61no—
954C22—61no—
955C22—61no—
956C22—61no—
957C22—61no—
958C22—61no—
959C22C2×D3311yescharacteristic
960C4—21no—
961C4—32no—
962C4—61no—
963C4—61no—
964C4—61no—
965C4—92no—
966C4—181no—
967C4—181no—
968C4—181no—
969C4—181no—
970C4—181no—
971C4—541no—
972C4—541no—
973C3—21no—
974C3—21no—
975C3—21no—
976C3—41no—
977C3#1059424811yescharacteristic, complemented
978C3#1059455411yescharacteristic, complemented
979C3#1059484111yescharacteristic, complemented
980C2—121no—
981C2—121no—
982C2#1172438711yescharacteristic
983C2#1172439311yescharacteristic
984C2D3×#380511yescharacteristic
subgroupG/H
center, FrattiniC22C2×D33
commutator, socle, cosocleC22×C33C24
FittingC2×C33×C4C23
prime radicalC2×C3×#625C22
hypercenterC2×C4D33
hypocenterC33#556
LCSG ▷ C22×C33 ▷ C33
UCSC1 ◁ C22 ◁ C2×C4

Complements

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

NH ≅ G/Ntype
1. #11723665C2semidirect
2. #11723432C2semidirect
3. #11723423C2semidirect
4. #11723391C2semidirect
6. C3×#63862C2semidirect
7. C3×#63851C2semidirect
8. #11723036C2semidirect
9. #11723026C2semidirect
10. #11723019C2semidirect
13. #11722969C2semidirect
14. #11722940C2semidirect
15. #11722914C2semidirect
82. #63862D3semidirect
90. #63851D3semidirect
650. C33#556semidirect
900. C32#5542semidirect
901. C32#5641semidirect
902. C32#5702semidirect
977. C3#10594248semidirect
978. C3#10594554semidirect
979. C3#10594841semidirect

Maximal subgroups

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

subgroupindex
#117236652
#117234322
#117234232
#117233912
C3×#638792
C3×#638622
C3×#638512
#117230362
#117230262
#117230192
#117230062
#117230042
#117229692
#117229402
#117229142
#105948413
#105945543
#105942483