Finite Group Databasebeta

← #13172250

Subgroups — #13172250

Order 1728.

1104 conjugacy classes of subgroups.

The subgroup lattice has 1006 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11723726C211yesmaximal, characteristic
2#11723621C211yesmaximal, characteristic
3#11723597C211yesmaximal, characteristic, complemented
4#11723595C211yesmaximal, characteristic, complemented
5C3×#63982C211yesmaximal, characteristic, complemented
6C3×#63975C211yesmaximal, characteristic
7C3×#63956C211yesmaximal, characteristic, complemented
8#11723017C211yesmaximal, characteristic, complemented
9#11723016C211yesmaximal, characteristic, complemented
10#11723013C211yesmaximal, characteristic, complemented
11#11722979C211yesmaximal, characteristic, complemented
12#11722940C211yesmaximal, characteristic, complemented
13#11722921C211yesmaximal, characteristic, complemented
14#11722915C211yesmaximal, characteristic, complemented
15#11722910C211yesmaximal, characteristic, complemented
16#10594120—31nomaximal
17#10594118—31nomaximal
18#10594026—31nomaximal
19C2×C3×#638C2211yescharacteristic
20C22×C3×C3⋊Dic3C2211yescharacteristic
21C2×#6294C2211yescharacteristic
22C2×Dic3×C3⋊D3C2211yescharacteristic
23C2×C3×#627C2211yescharacteristic
24C2×C3×#624C2211yescharacteristic
25#88864C2211yescharacteristic
26C3×#3757C2211yescharacteristic
27C32×#217C2211yescharacteristic
28C32×#217C2211yescharacteristic
29C32×#217C2211yescharacteristic
30#88815C2211yescharacteristic
31#88814C2211yescharacteristic
32#88813C2211yescharacteristic
33#88807C2211yescharacteristic
34#88807C2211yescharacteristic
35#88807C2211yescharacteristic
36#88806C2211yescharacteristic
37#88806C2211yescharacteristic
38Dic3⋊(C3⋊Dic3)C2211yescharacteristic
39Dic3⋊(C3⋊Dic3)C2211yescharacteristic
40#88803C2211yescharacteristic
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×#3722C2211yescharacteristic
53C3×Dic32C2211yescharacteristic
54#64092—31no—
55#64088—31no—
56#64086—31no—
57C3×#883—31no—
58C3×#883—31no—
59C3×#879—31no—
60C3×#879—31no—
61C3×#878—31no—
62C3×#878—31no—
63#63982D311yescharacteristic, complemented
64#63975D311yescharacteristic
65#67⋊Dic3—31no—
66Dic3×#67—31no—
67#63969—31no—
68#63969—31no—
69#63969—61no—
70#63956—31no—
71#63956—31no—
72#63956—61no—
73#63956D311yescharacteristic, complemented
74#63955—31no—
75#63955—31no—
76#63955—61no—
77#63952—31no—
78#63899—31no—
79#63888—31no—
80#63887—31no—
81#63883—31no—
82#63878—31no—
83#63878—31no—
84D3×Dic3⋊C4—31no—
85D3×Dic3⋊C4—31no—
86#63872—31no—
87#63870—31no—
88#63855—31no—
89#63849—31no—
90#63847—31no—
91#63847—31no—
92#63847—31no—
93#63846—31no—
94#63846—31no—
95#63845—31no—
96#63845—31no—
97#63843—31no—
98Dic3×Dic6—31no—
99#63841—31no—
100#63837—31no—
101#63836—31no—
102C23×C33C2311yescharacteristic
103C22×C3×C3⋊D3C2311yescharacteristic
104C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
105C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
106C3×#638—22no—
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×C32×Dic3C2311yescharacteristic
114C2×C32×Dic3C2311yescharacteristic
115C2×C32×Dic3C2311yescharacteristic
116C2×C32×Dic3C2311yescharacteristic
117C2×C32×Dic3C2311yescharacteristic
118C2×C32×Dic3C2311yescharacteristic
119#6294—22no—
120Dic3×C3⋊D3—22no—
121C3×#627—22no—
122C3×#624—22no—
123#5708—91no—
124#5650—91no—
125#5639—91no—
126C2×#638C2×D311yescharacteristic
127C22×C3⋊Dic3C2×D311yescharacteristic
128C2×C4×C3⋊D3—31no—
129C2×C3×#67—31no—
130C2×C3×#67—31no—
131C2×C3×#67—61no—
132C22×C3×Dic3—31no—
133C22×C3×Dic3—31no—
134C22×C3×Dic3—61no—
135C2×C3×C4×D3—31no—
136C2×C3×C4×D3—31no—
137C2×C3×Dic6—31no—
138C2×C3×Dic6—31no—
139C2×#627C2×D311yescharacteristic
140C2×#624—31no—
141C2×#624C2×D311yescharacteristic
142C2×D3×Dic3—31no—
143C2×D3×Dic3—31no—
144C2×D3×Dic3—31no—
145C2×D3×Dic3—31no—
146C2×D3×Dic3—61no—
147C32×C22⋊C4—31no—
148C32×C22⋊C4—31no—
149C32×C22⋊C4—31no—
150#3757—31no—
151#3757—31no—
152#3757—31no—
153#3757—61no—
154#3757—61no—
155#3757—61no—
156#3757—121no—
157#3757C2×D311yescharacteristic
158#3752—31no—
159C4⋊(C3⋊Dic3)—31no—
160C4⋊(C3⋊Dic3)—31no—
161#3750—31no—
162#3750—31no—
163#3750—31no—
164#3750—31no—
165#3750—31no—
166C4×C3⋊Dic3—31no—
167C4×C3⋊Dic3—31no—
168C4×C3⋊Dic3—31no—
169C3×#217—21no—
170C3×#217—21no—
171C3×#217—21no—
172C3×#217—31no—
173C3×#217—31no—
174C3×#217—61no—
175C3×#217C2×D311yescharacteristic
176C3×#217C2×D311yescharacteristic
177C3×#217C2×D311yescharacteristic
178C3×#217C2×D311yescharacteristic
179C3×#217C2×D311yescharacteristic
180C3×#217C2×D311yescharacteristic
181C3×(C2×D3)⋊C4—31no—
182C3×(C2×D3)⋊C4—31no—
183C3×C4⋊Dic3—31no—
184C3×C4⋊Dic3—31no—
185C3×C4⋊Dic3—31no—
186C3×C4⋊Dic3—31no—
187C3×C4⋊Dic3—31no—
188C3×C4⋊Dic3—31no—
189C3×Dic3⋊C4—31no—
190C3×Dic3⋊C4—31no—
191C3×Dic3⋊C4—31no—
192C3×Dic3⋊C4—31no—
193C3×Dic3⋊C4—31no—
194C3×Dic3⋊C4—31no—
195C3×Dic3⋊C4—31no—
196C3×Dic3⋊C4—31no—
197C3×Dic3⋊C4—31no—
198C3×Dic3⋊C4—31no—
199C3×C4×Dic3—31no—
200C3×C4×Dic3—31no—
201#3724—31no—
202#3724—31no—
203#3724—31no—
204#3724—31no—
205#3724—31no—
206#3724—61no—
207#3724—61no—
208#3724C2×D311yescharacteristic
209#3724C2×D311yescharacteristic
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—31no—
221Dic3⋊Dic3—31no—
222Dic3⋊Dic3—61no—
223Dic3⋊Dic3—61no—
224Dic3⋊Dic3—61no—
225Dic3⋊Dic3—61no—
226Dic3⋊Dic3—61no—
227Dic3⋊Dic3C2×D311yescharacteristic
228Dic3⋊Dic3C2×D311yescharacteristic
229Dic3⋊Dic3C2×D311yescharacteristic
230Dic3⋊Dic3C2×D311yescharacteristic
231Dic3⋊Dic3C2×D311yescharacteristic
232Dic3⋊Dic3C2×D311yescharacteristic
233#3722—31no—
234#3722C2×D311yescharacteristic
235(C2×D3)⋊Dic3—31no—
236(C2×D3)⋊Dic3—31no—
237(C2×D3)⋊Dic3—31no—
238(C2×D3)⋊Dic3—31no—
239(C2×D3)⋊Dic3—61no—
240Dic32—31no—
241Dic32—31no—
242Dic32—31no—
243Dic32—31no—
244Dic32—31no—
245Dic32—31no—
246Dic32—31no—
247Dic32—31no—
248Dic32—31no—
249Dic32—61no—
250Dic32—61no—
251Dic32—61no—
252Dic32C2×D311yescharacteristic
253C22×C33—21no—
254C22×C33—21no—
255C22×C33—21no—
256C22×C33C2411yescharacteristic
257C2×C3×C3⋊D3—21no—
258C2×C3×C3⋊D3—21no—
259C2×C3×C3⋊D3#4112yes—
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#4112yes—
267C32×Dic3—21no—
268C32×Dic3—21no—
269C32×Dic3—21no—
270C32×Dic3—21no—
271C32×Dic3—21no—
272C32×Dic3—21no—
273C3×#126—91no—
274C3×#123—91no—
275C3×C22⋊Q8—91no—
276#946—91no—
277Q8×Dic3—91no—
278#935—91no—
279D4×Dic3—91no—
280C4×#67—91no—
281#926—91no—
282#926—91no—
283C2×Dic3⋊C4—91no—
284#896—91no—
285#892—91no—
286#892—91no—
287#892—91no—
288D3×C4⋊C4—91no—
289D3×C4⋊C4—91no—
290#890—91no—
291#890—91no—
292#890—91no—
293#889—91no—
294#889—91no—
295#889—91no—
296#889—91no—
297#889—91no—
298#889—91no—
299#887—91no—
300#883—31no—
301#883—31no—
302#883—91no—
303#883—91no—
304#883—181no—
305#67⋊C4—91no—
306#879—31no—
307#879—31no—
308#879—91no—
309#879—91no—
310#879—91no—
311#879—181no—
312#878—31no—
313#878—31no—
314#878—91no—
315#877—91no—
316#877—91no—
317#877—91no—
318#877—181no—
319#872—91no—
320C4×Dic6—91no—
321C23×C32—21no—
322C23×C32—21no—
323C23×C32—21no—
324C23×C32—41no—
325C23×C32C22×D311yescharacteristic
326C23×C32C22×D311yescharacteristic
327C23×C32C22×D311yescharacteristic
328C22×C3⋊D3C22×D311yescharacteristic
329C22×C3×D3—31no—
330C22×C3×D3—31no—
331C22×C3×D3—61no—
332C2×C32×C4—31no—
333C2×C32×C4—31no—
334C2×C32×C4—31no—
335C2×C32×C4—31no—
336C2×C32×C4—31no—
337C2×C32×C4—31no—
338#638—22no—
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—121no—
353C2×C3⋊Dic3—121no—
354C2×C3⋊Dic3C22×D311yescharacteristic
355C2×C3⋊Dic3C22×D311yescharacteristic
356C2×C3⋊Dic3C22×D311yescharacteristic
357C2×C3⋊Dic3C22×D311yescharacteristic
358C2×C3⋊Dic3C22×D311yescharacteristic
359C4×C3⋊D3—62no—
360C3×#67—62no—
361C3×#67—62no—
362C3×#67—122no—
363C2×C3×Dic3—21no—
364C2×C3×Dic3—21no—
365C2×C3×Dic3—21no—
366C2×C3×Dic3—21no—
367C2×C3×Dic3—21no—
368C2×C3×Dic3—21no—
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—61no—
380C2×C3×Dic3—61no—
381C2×C3×Dic3—61no—
382C2×C3×Dic3—61no—
383C2×C3×Dic3—61no—
384C2×C3×Dic3—62no—
385C2×C3×Dic3—62no—
386C2×C3×Dic3—64no—
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
395C2×C3×Dic3C22×D311yescharacteristic
396C2×C3×Dic3C22×D311yescharacteristic
397C2×C3×Dic3C22×D311yescharacteristic
398C2×C3×Dic3C22×D311yescharacteristic
399C3×C4×D3—62no—
400C3×C4×D3—62no—
401C3×Dic6—62no—
402C3×Dic6—62no—
403#627—22no—
404#624—22no—
405#624—62no—
406D3×Dic3—62no—
407D3×Dic3—62no—
408D3×Dic3—62no—
409D3×Dic3—62no—
410D3×Dic3—122no—
411#552—271noSylow
412C2×C33—41no—
413C2×C33C2×#4111yescharacteristic
414C2×C33C2×#4111yescharacteristic
415C2×C332−1+411yescharacteristic
416C3×C3⋊D3—22no—
417C2×C3×Q8—91no—
418C2×C3×D4—91no—
419C22×C3×C4—91no—
420C22×C3×C4—91no—
421C2×#67—31no—
422C2×#67—31no—
423C2×#67—61no—
424C22×Dic3—31no—
425C22×Dic3—31no—
426C22×Dic3—61no—
427C22×Dic3—91no—
428C22×Dic3—91no—
429C2×C4×D3—31no—
430C2×C4×D3—31no—
431C2×C4×D3—91no—
432C2×C4×D3—91no—
433C2×C4×D3—91no—
434C2×C4×D3—91no—
435C2×C4×D3—181no—
436C2×Dic6—31no—
437C2×Dic6—31no—
438C3×C4⋊C4—91no—
439C3×C4⋊C4—91no—
440C3×C4⋊C4—91no—
441C3×C4⋊C4—91no—
442C3×C4⋊C4—91no—
443C3×C4⋊C4—91no—
444C3×C4⋊C4—91no—
445C3×C4⋊C4—91no—
446C3×C22⋊C4—31no—
447C3×C22⋊C4—31no—
448C3×C22⋊C4—31no—
449C3×C22⋊C4—31no—
450C3×C22⋊C4—31no—
451C3×C22⋊C4—31no—
452C3×C22⋊C4—61no—
453C3×C22⋊C4—61no—
454C3×C22⋊C4—61no—
455C3×C22⋊C4—91no—
456C3×C22⋊C4—91no—
457C3×C42—91no—
458#217—31no—
459#217—31no—
460#217—61no—
461#217—91no—
462#217—91no—
463#217—91no—
464#217—91no—
465#217—91no—
466#217—181no—
467#217—181no—
468#217—181no—
469#217—361no—
470#217D3211yescharacteristic
471#217D3211yescharacteristic
472#217D3211yescharacteristic
473(C2×D3)⋊C4—31no—
474(C2×D3)⋊C4—31no—
475(C2×D3)⋊C4—91no—
476(C2×D3)⋊C4—91no—
477(C2×D3)⋊C4—91no—
478(C2×D3)⋊C4—91no—
479(C2×D3)⋊C4—181no—
480C4⋊Dic3—31no—
481C4⋊Dic3—31no—
482C4⋊Dic3—31no—
483C4⋊Dic3—31no—
484C4⋊Dic3—31no—
485C4⋊Dic3—31no—
486C4⋊Dic3—91no—
487C4⋊Dic3—91no—
488C4⋊Dic3—91no—
489C4⋊Dic3—91no—
490C4⋊Dic3—91no—
491C4⋊Dic3—91no—
492C4⋊Dic3—91no—
493C4⋊Dic3—91no—
494C4⋊Dic3—181no—
495C4⋊Dic3—181no—
496Dic3⋊C4—31no—
497Dic3⋊C4—31no—
498Dic3⋊C4—31no—
499Dic3⋊C4—31no—
500Dic3⋊C4—31no—
501Dic3⋊C4—31no—
502Dic3⋊C4—31no—
503Dic3⋊C4—31no—
504Dic3⋊C4—31no—
505Dic3⋊C4—31no—
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—91no—
515Dic3⋊C4—91no—
516Dic3⋊C4—91no—
517Dic3⋊C4—91no—
518Dic3⋊C4—91no—
519Dic3⋊C4—91no—
520Dic3⋊C4—91no—
521Dic3⋊C4—91no—
522Dic3⋊C4—181no—
523Dic3⋊C4—181no—
524Dic3⋊C4—181no—
525Dic3⋊C4—181no—
526Dic3⋊C4—181no—
527C4×Dic3—31no—
528C4×Dic3—31no—
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—91no—
538C4×Dic3—91no—
539C4×Dic3—91no—
540C4×Dic3—91no—
541C4×Dic3—181no—
542C4×Dic3—181no—
543C4×Dic3—181no—
544C22×C32—21no—
545C22×C32—22no—
546C22×C32—21no—
547C22×C32—21no—
548C22×C32—21no—
549C22×C32—21no—
550C22×C32—21no—
551C22×C32—21no—
552C22×C32—21no—
553C22×C32—21no—
554C22×C32—21no—
555C22×C32—21no—
556C22×C32—21no—
557C22×C32—41no—
558C22×C32—41no—
559C22×C32—41no—
560C22×C32—42no—
561C22×C32—41no—
562C22×C32—41no—
563C22×C32—41no—
564C22×C32—41no—
565C22×C32—41no—
566C22×C32—41no—
567C22×C32—81no—
568C22×C32—81no—
569C22×C32C23×D311yescharacteristic
570C22×C32C23×D311yescharacteristic
571C22×C32C23×D311yescharacteristic
572C2×C3⋊D3—21no—
573C2×C3⋊D3—21no—
574C2×C3⋊D3#23712yes—
575C2×C3×D3—32no—
576C2×C3×D3—32no—
577C2×C3×D3—62no—
578C2×C3×D3—61no—
579C2×C3×D3—61no—
580C2×C3×D3—61no—
581C2×C3×D3—61no—
582C2×C3×D3—121no—
583C2×C3×D3—121no—
584C32×C4—61no—
585C32×C4—61no—
586C32×C4—61no—
587C32×C4—61no—
588C32×C4—61no—
589C32×C4—61no—
590C3⋊Dic3—21no—
591C3⋊Dic3—21no—
592C3⋊Dic3—21no—
593C3⋊Dic3—21no—
594C3⋊Dic3—61no—
595C3⋊Dic3—61no—
596C3⋊Dic3—61no—
597C3⋊Dic3—61no—
598C3⋊Dic3—61no—
599C3⋊Dic3—61no—
600C3⋊Dic3—121no—
601C3⋊Dic3—121no—
602C3⋊Dic3—121no—
603C3⋊Dic3—121no—
604C3⋊Dic3—121no—
605C3⋊Dic3—121no—
606C3⋊Dic3—241no—
607C3⋊Dic3—241no—
608C3⋊Dic3#23712yes—
609C3×Dic3—21no—
610C3×Dic3—21no—
611C3×Dic3—21no—
612C3×Dic3—21no—
613C3×Dic3—21no—
614C3×Dic3—21no—
615C3×Dic3—21no—
616C3×Dic3—21no—
617C3×Dic3—21no—
618C3×Dic3—21no—
619C3×Dic3—21no—
620C3×Dic3—21no—
621C3×Dic3—32no—
622C3×Dic3—32no—
623C3×Dic3—41no—
624C3×Dic3—41no—
625C3×Dic3—41no—
626C3×Dic3—41no—
627C3×Dic3—41no—
628C3×Dic3—41no—
629C3×Dic3—62no—
630C3×Dic3—62no—
631C3×Dic3—61no—
632C3×Dic3—61no—
633C3×Dic3—61no—
634C3×Dic3—61no—
635C3×Dic3—61no—
636C3×Dic3—61no—
637C3×Dic3—61no—
638C3×Dic3—61no—
639C3×Dic3—121no—
640C3×Dic3—121no—
641C3×Dic3—121no—
642#126—91no—
643#126—271no—
644#125—271no—
645#125—271no—
646#125—271no—
647#123—91no—
648#123—271no—
649C22⋊Q8—91no—
650C22⋊Q8—271no—
651C4×Q8—271no—
652C4×D4—271no—
653#117—271no—
654#117—271no—
655#117—271no—
656C2×C4⋊C4—271no—
657C33#55211yescharacteristic, complemented, Sylow
658C23×C3—21no—
659C23×C3—21no—
660C23×C3—21no—
661C23×C3—41no—
662C23×C3—91no—
663C23×C3C2×D3211yescharacteristic
664C23×C3C2×D3211yescharacteristic
665C23×C3C2×D3211yescharacteristic
666C22×D3—31no—
667C22×D3—31no—
668C22×D3—61no—
669C3×Q8—182no—
670C3×D4—182no—
671C2×C3×C4—31no—
672C2×C3×C4—31no—
673C2×C3×C4—31no—
674C2×C3×C4—31no—
675C2×C3×C4—31no—
676C2×C3×C4—31no—
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—61no—
684C2×C3×C4—61no—
685C2×C3×C4—61no—
686C2×C3×C4—61no—
687C2×C3×C4—61no—
688C2×C3×C4—61no—
689C2×C3×C4—91no—
690C2×C3×C4—91no—
691C2×C3×C4—91no—
692C2×C3×C4—91no—
693C2×C3×C4—91no—
694C2×C3×C4—182no—
695C2×C3×C4—182no—
696#67—62no—
697#67—62no—
698#67—122no—
699C2×Dic3—31no—
700C2×Dic3—31no—
701C2×Dic3—31no—
702C2×Dic3—31no—
703C2×Dic3—31no—
704C2×Dic3—31no—
705C2×Dic3—31no—
706C2×Dic3—31no—
707C2×Dic3—31no—
708C2×Dic3—31no—
709C2×Dic3—61no—
710C2×Dic3—61no—
711C2×Dic3—61no—
712C2×Dic3—61no—
713C2×Dic3—61no—
714C2×Dic3—62no—
715C2×Dic3—62no—
716C2×Dic3—64no—
717C2×Dic3—91no—
718C2×Dic3—91no—
719C2×Dic3—91no—
720C2×Dic3—91no—
721C2×Dic3—91no—
722C2×Dic3—91no—
723C2×Dic3—181no—
724C2×Dic3—181no—
725C2×Dic3—181no—
726C2×Dic3—181no—
727C2×Dic3—181no—
728C2×Dic3—181no—
729C2×Dic3—182no—
730C2×Dic3—182no—
731C2×Dic3—361no—
732C2×Dic3—361no—
733C2×Dic3C2×D3211yescharacteristic
734C2×Dic3C2×D3211yescharacteristic
735C2×Dic3C2×D3211yescharacteristic
736C2×Dic3C2×D3211yescharacteristic
737C2×Dic3C2×D3211yescharacteristic
738C2×Dic3C2×D3211yescharacteristic
739C4×D3—62no—
740C4×D3—62no—
741C4×D3—182no—
742C4×D3—182no—
743C4×D3—182no—
744C4×D3—182no—
745C4×D3—362no—
746Dic6—62no—
747Dic6—62no—
748C2×C32—21no—
749C2×C32—21no—
750C2×C32—21no—
751C2×C32—21no—
752C2×C32—21no—
753C2×C32—21no—
754C2×C32—21no—
755C2×C32—21no—
756C2×C32—21no—
757C2×C32—41no—
758C2×C32—41no—
759C2×C32—41no—
760C2×C32—41no—
761C2×C32—42no—
762C2×C32—41no—
763C2×C32—41no—
764C2×C32—81no—
765C2×C32—81no—
766C2×C32—82no—
767C2×C32C2×#23711yescharacteristic
768C2×C32C2×#23711yescharacteristic
769C2×C32#100711yescharacteristic
770C2×C32D3×#4111yescharacteristic
771C2×C32D3×#4111yescharacteristic
772C2×C32D3×#4111yescharacteristic
773C2×C32D3×#4111yescharacteristic
774C2×C32#101011yescharacteristic
775C2×C32#101011yescharacteristic
776C3⋊D3—22no—
777C3×D3—62no—
778C3×D3—62no—
779C3×D3—122no—
780C2×Q8—91no—
781C2×D4—91no—
782C22×C4—91no—
783C22×C4—91no—
784C22×C4—271no—
785C22×C4—271no—
786C4⋊C4—91no—
787C4⋊C4—91no—
788C4⋊C4—91no—
789C4⋊C4—91no—
790C4⋊C4—91no—
791C4⋊C4—91no—
792C4⋊C4—91no—
793C4⋊C4—91no—
794C4⋊C4—271no—
795C4⋊C4—271no—
796C4⋊C4—271no—
797C4⋊C4—271no—
798C4⋊C4—271no—
799C4⋊C4—271no—
800C4⋊C4—271no—
801C4⋊C4—271no—
802C22⋊C4—31no—
803C22⋊C4—31no—
804C22⋊C4—31no—
805C22⋊C4—91no—
806C22⋊C4—91no—
807C22⋊C4—271no—
808C22⋊C4—271no—
809C22⋊C4—271no—
810C42—91no—
811C42—271no—
812C42—271no—
813C42—271no—
814C42—271no—
815C22×C3—22no—
816C22×C3—21no—
817C22×C3—21no—
818C22×C3—21no—
819C22×C3—21no—
820C22×C3—21no—
821C22×C3—21no—
822C22×C3—21no—
823C22×C3—21no—
824C22×C3—21no—
825C22×C3—21no—
826C22×C3—21no—
827C22×C3—21no—
828C22×C3—41no—
829C22×C3—41no—
830C22×C3—41no—
831C22×C3—41no—
832C22×C3—41no—
833C22×C3—41no—
834C22×C3—41no—
835C22×C3—41no—
836C22×C3—42no—
837C22×C3—41no—
838C22×C3—81no—
839C22×C3—81no—
840C22×C3—92no—
841C22×C3—181no—
842C22×C3—181no—
843C22×C3C22×D3211yescharacteristic
844C22×C3C22×D3211yescharacteristic
845C22×C3C22×D3211yescharacteristic
846C2×D3—32no—
847C2×D3—32no—
848C2×D3—62no—
849C2×D3—61no—
850C2×D3—61no—
851C2×D3—61no—
852C2×D3—61no—
853C2×D3—121no—
854C2×D3—121no—
855C3×C4—61no—
856C3×C4—61no—
857C3×C4—61no—
858C3×C4—61no—
859C3×C4—61no—
860C3×C4—61no—
861C3×C4—61no—
862C3×C4—61no—
863C3×C4—61no—
864C3×C4—61no—
865C3×C4—61no—
866C3×C4—61no—
867C3×C4—92no—
868C3×C4—121no—
869C3×C4—121no—
870C3×C4—121no—
871C3×C4—121no—
872C3×C4—121no—
873C3×C4—121no—
874C3×C4—181no—
875C3×C4—181no—
876C3×C4—181no—
877C3×C4—181no—
878Dic3—21no—
879Dic3—21no—
880Dic3—21no—
881Dic3—21no—
882Dic3—21no—
883Dic3—21no—
884Dic3—32no—
885Dic3—32no—
886Dic3—62no—
887Dic3—62no—
888Dic3—61no—
889Dic3—61no—
890Dic3—61no—
891Dic3—61no—
892Dic3—61no—
893Dic3—61no—
894Dic3—61no—
895Dic3—61no—
896Dic3—121no—
897Dic3—121no—
898Dic3—121no—
899Dic3—181no—
900Dic3—181no—
901Dic3—181no—
902Dic3—181no—
903Dic3—181no—
904Dic3—181no—
905Dic3—361no—
906Dic3—361no—
907Dic3—361no—
908Dic3—361no—
909Dic3—361no—
910Dic3—361no—
911Dic3—721no—
912Dic3—721no—
913C32—21no—
914C32—21no—
915C32—21no—
916C32—41no—
917C32#563911yescharacteristic, complemented
918C32#565011yescharacteristic, complemented
919C32#570811yescharacteristic, complemented
920C23—91no—
921C23D3311yescharacteristic
922Q8—182no—
923D4—182no—
924C2×C4—31no—
925C2×C4—31no—
926C2×C4—31no—
927C2×C4—31no—
928C2×C4—31no—
929C2×C4—31no—
930C2×C4—91no—
931C2×C4—91no—
932C2×C4—91no—
933C2×C4—91no—
934C2×C4—91no—
935C2×C4—182no—
936C2×C4—182no—
937C2×C4—271no—
938C2×C4—271no—
939C2×C4—542no—
940C2×C4—542no—
941C2×C3—21no—
942C2×C3—21no—
943C2×C3—21no—
944C2×C3—21no—
945C2×C3—21no—
946C2×C3—21no—
947C2×C3—21no—
948C2×C3—21no—
949C2×C3—21no—
950C2×C3—42no—
951C2×C3—41no—
952C2×C3—41no—
953C2×C3—41no—
954C2×C3—41no—
955C2×C3—41no—
956C2×C3—41no—
957C2×C3—81no—
958C2×C3—81no—
959C2×C3—82no—
960C2×C3—182no—
961C2×C3#6429711yescharacteristic
962C2×C3#6429711yescharacteristic
963C2×C3#6430611yescharacteristic
964C2×C3#6430911yescharacteristic
965C2×C3D3×#23711yescharacteristic
966C2×C3D3×#23711yescharacteristic
967C2×C3D3×#23711yescharacteristic
968C2×C3D3×#23711yescharacteristic
969C2×C3#6431211yescharacteristic
970D3—62no—
971D3—62no—
972D3—122no—
973C22—21no—
974C22—21no—
975C22—21no—
976C22—92no—
977C22—181no—
978C22—181no—
979C22C2×D3311yescharacteristic
980C4—61no—
981C4—61no—
982C4—61no—
983C4—61no—
984C4—61no—
985C4—61no—
986C4—92no—
987C4—181no—
988C4—181no—
989C4—181no—
990C4—181no—
991C4—541no—
992C4—541no—
993C3—21no—
994C3—21no—
995C3—21no—
996C3—41no—
997C3#1059402611yescharacteristic, complemented
998C3#1059411811yescharacteristic, complemented
999C3#1059412011yescharacteristic, complemented
1000C2—41no—
1001C2—182no—
1002C2#1172440711yescharacteristic
1003C2#1172440811yescharacteristic
1004C2#1172442611yescharacteristic
subgroupG/H
center, FrattiniC22C2×D33
commutator, socle, cosocleC22×C33C24
FittingC23×C33C23
prime radicalC2×C3×#638C22
hypercenterC23D33
hypocenterC33#552
LCSG ▷ C22×C33 ▷ C33
UCSC1 ◁ C22 ◁ C23

Complements

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

NH ≅ G/Ntype
3. #11723597C2semidirect
4. #11723595C2semidirect
5. C3×#63982C2semidirect
7. C3×#63956C2semidirect
8. #11723017C2semidirect
9. #11723016C2semidirect
10. #11723013C2semidirect
11. #11722979C2semidirect
12. #11722940C2semidirect
13. #11722921C2semidirect
14. #11722915C2semidirect
15. #11722910C2semidirect
63. #63982D3semidirect
73. #63956D3semidirect
657. C33#552semidirect
917. C32#5639semidirect
918. C32#5650semidirect
919. C32#5708semidirect
997. C3#10594026semidirect
998. C3#10594118semidirect
999. C3#10594120semidirect

Maximal subgroups

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

subgroupindex
#117237262
#117236212
#117235972
#117235952
C3×#639822
C3×#639752
C3×#639562
#117230172
#117230162
#117230132
#117229792
#117229402
#117229212
#117229152
#117229102
#105941203
#105941183
#105940263