Finite Group Databasebeta

← #13167960

Subgroups — #13167960

Order 1728.

1134 conjugacy classes of subgroups.

The subgroup lattice has 966 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11723666C211yesmaximal, characteristic, complemented
2#11723460C211yesmaximal, characteristic
3#11723410C211yesmaximal, characteristic, complemented
4#11723391C211yesmaximal, characteristic, complemented
5C3×#63899C211yesmaximal, characteristic
6C3×#63896C211yesmaximal, characteristic
7C3×#63847C211yesmaximal, characteristic, complemented
8#11723034C211yesmaximal, characteristic, complemented
9#11723014C211yesmaximal, characteristic, complemented
10#11722978C211yesmaximal, characteristic
11#11722975C211yesmaximal, characteristic
12#11722945C211yesmaximal, characteristic, complemented
13#11722941C211yesmaximal, characteristic, complemented
14#11722917C211yesmaximal, characteristic
15D3×Dic32C211yesmaximal, characteristic
16#10594388—31nomaximal
17#10594388—31nomaximal
18#10594030—31nomaximal
19C2×C3×#634C2211yescharacteristic
20C2×#6296C2211yescharacteristic
21C2×#6293C2211yescharacteristic
22C2×D3×C3⋊Dic3C2211yescharacteristic
23C2×C3×#627C2211yescharacteristic
24C2×C3×D3×Dic3C2211yescharacteristic
25C2×C3×D3×Dic3C2211yescharacteristic
26C4×C3⋊(C3⋊Dic3)C2211yescharacteristic
27C3×#3750C2211yescharacteristic
28C3×#3750C2211yescharacteristic
29C32×(C2×D3)⋊C4C2211yescharacteristic
30C32×C4⋊Dic3C2211yescharacteristic
31C32×Dic3⋊C4C2211yescharacteristic
32#88815C2211yescharacteristic
33#88815C2211yescharacteristic
34#88813C2211yescharacteristic
35#88807C2211yescharacteristic
36#88807C2211yescharacteristic
37#88807C2211yescharacteristic
38#88806C2211yescharacteristic
39(C2×D3)⋊(C3⋊Dic3)C2211yescharacteristic
40Dic3×C3⋊Dic3C2211yescharacteristic
41Dic3×C3⋊Dic3C2211yescharacteristic
42Dic3×C3⋊Dic3C2211yescharacteristic
43Dic3×C3⋊Dic3C2211yescharacteristic
44Dic3×C3⋊Dic3C2211yescharacteristic
45C3×#3724C2211yescharacteristic
46C3×#3724C2211yescharacteristic
47C3×#3724C2211yescharacteristic
48C3×#3724C2211yescharacteristic
49C3×Dic3⋊Dic3C2211yescharacteristic
50C3×Dic3⋊Dic3C2211yescharacteristic
51C3×(C2×D3)⋊Dic3C2211yescharacteristic
52C3×(C2×D3)⋊Dic3C2211yescharacteristic
53C3×Dic32C2211yescharacteristic
54#64096—31no—
55#64096—31no—
56#64086—31no—
57C3×#896—31no—
58C3×#896—31no—
59C3×#889—31no—
60C3×#889—31no—
61C3×#878—31no—
62C3×#878—31no—
63#63964—31no—
64#63964—31no—
65#63957—31no—
66C2×Dic32—31no—
67#63899—31no—
68#63899D311yescharacteristic
69#63896—31no—
70#63896D311yescharacteristic
71#63878—31no—
72#63878—31no—
73#63878—31no—
74#63878—31no—
75#63878—61no—
76C4×D3×Dic3—31no—
77C4×D3×Dic3—31no—
78#63867—31no—
79#63867—31no—
80#63851—31no—
81#63851—31no—
82#63847—31no—
83#63847D311yescharacteristic, complemented
84#63843—31no—
85#63843—31no—
86#63843—31no—
87#63843—31no—
88#63843—61no—
89#63840—31no—
90#63840—31no—
91#63839—31no—
92#63839—31no—
93#63839—31no—
94#63839—31no—
95#63838—31no—
96#63838—31no—
97#63838—31no—
98#63838—31no—
99#63838—31no—
100#63838—31no—
101#63838—61no—
102C22×C32×D3C2311yescharacteristic
103C2×C33×C4C2311yescharacteristic
104C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
105C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
106C2×C3×C3⋊Dic3C2311yescharacteristic
107C2×C3×C3⋊Dic3C2311yescharacteristic
108C2×C3×C3⋊Dic3C2311yescharacteristic
109C2×C3×C3⋊Dic3C2311yescharacteristic
110C2×C3×C3⋊Dic3C2311yescharacteristic
111C2×C3×C3⋊Dic3C2311yescharacteristic
112C3×#634—22no—
113C2×C32×Dic3C2311yescharacteristic
114C2×C32×Dic3C2311yescharacteristic
115C2×C32×Dic3C2311yescharacteristic
116C2×C32×Dic3C2311yescharacteristic
117C2×C32×Dic3C2311yescharacteristic
118#6296—22no—
119#6293—22no—
120D3×C3⋊Dic3Q814yescomplemented
121C3×#627—22no—
122C3×D3×Dic3—22no—
123C3×D3×Dic3—22no—
124#5688—91no—
125#5622—91no—
126#5622—91no—
127C22×C3⋊Dic3—31no—
128C2×#634—31no—
129C2×#634C2×D311yescharacteristic
130C22×C3×Dic3—31no—
131C22×C3×Dic3—31no—
132C2×C3×C4×D3—31no—
133C2×C3×C4×D3—31no—
134C2×C3×Dic6—31no—
135C2×C3×Dic6—31no—
136C2×C3×Dic6—31no—
137C2×C3×Dic6—31no—
138C2×C3×Dic6—61no—
139C2×#627—31no—
140C2×#627—31no—
141C2×#627—31no—
142C2×#627—31no—
143C2×#627—31no—
144C2×#627—61no—
145C2×#627C2×D311yescharacteristic
146C2×D3×Dic3—31no—
147C2×D3×Dic3—31no—
148C2×D3×Dic3—61no—
149C2×D3×Dic3C2×D311yescharacteristic
150C2×D3×Dic3C2×D311yescharacteristic
151C32×C4⋊C4—31no—
152C32×C4⋊C4—31no—
153C32×C22⋊C4—31no—
154#3757—31no—
155#3750—31no—
156#3750—31no—
157#3750—31no—
158#3750—31no—
159#3750C2×D311yescharacteristic
160#3750C2×D311yescharacteristic
161C4×C3⋊Dic3—31no—
162C4×C3⋊Dic3—31no—
163C4×C3⋊Dic3—31no—
164C4×C3⋊Dic3—31no—
165C4×C3⋊Dic3—31no—
166C4×C3⋊Dic3—31no—
167C4×C3⋊Dic3—31no—
168C4×C3⋊Dic3—31no—
169C4×C3⋊Dic3—61no—
170C4×C3⋊Dic3—61no—
171C4×C3⋊Dic3—61no—
172C4×C3⋊Dic3—121no—
173C3×#217—31no—
174C3×#217—31no—
175C3×(C2×D3)⋊C4—21no—
176C3×(C2×D3)⋊C4—31no—
177C3×(C2×D3)⋊C4—31no—
178C3×(C2×D3)⋊C4C2×D311yescharacteristic
179C3×(C2×D3)⋊C4C2×D311yescharacteristic
180C3×C4⋊Dic3—21no—
181C3×C4⋊Dic3—31no—
182C3×C4⋊Dic3—31no—
183C3×C4⋊Dic3C2×D311yescharacteristic
184C3×C4⋊Dic3C2×D311yescharacteristic
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—31no—
194C3×Dic3⋊C4—31no—
195C3×Dic3⋊C4—31no—
196C3×Dic3⋊C4—31no—
197C3×Dic3⋊C4—31no—
198C3×Dic3⋊C4—31no—
199C3×Dic3⋊C4—31no—
200C3×Dic3⋊C4—61no—
201C3×Dic3⋊C4—61no—
202C3×Dic3⋊C4C2×D311yescharacteristic
203C3×Dic3⋊C4C2×D311yescharacteristic
204C3×C4×Dic3—31no—
205C3×C4×Dic3—31no—
206#3724—31no—
207#3724—31no—
208#3724—31no—
209#3724—31no—
210#3724—61no—
211#3724C2×D311yescharacteristic
212#3724C2×D311yescharacteristic
213#3724C2×D311yescharacteristic
214#3724C2×D311yescharacteristic
215Dic3⋊Dic3—31no—
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—61no—
226Dic3⋊Dic3—61no—
227Dic3⋊Dic3—61no—
228Dic3⋊Dic3C2×D311yescharacteristic
229Dic3⋊Dic3C2×D311yescharacteristic
230(C2×D3)⋊Dic3—31no—
231(C2×D3)⋊Dic3—31no—
232(C2×D3)⋊Dic3—61no—
233(C2×D3)⋊Dic3C2×D311yescharacteristic
234(C2×D3)⋊Dic3C2×D311yescharacteristic
235Dic32—31no—
236Dic32—31no—
237Dic32—31no—
238Dic32—31no—
239Dic32—31no—
240Dic32—31no—
241Dic32—31no—
242Dic32—31no—
243Dic32—31no—
244Dic32—31no—
245Dic32—31no—
246Dic32—31no—
247Dic32—31no—
248Dic32—61no—
249Dic32—61no—
250Dic32—61no—
251Dic32—61no—
252Dic32—61no—
253Dic32C2×D311yescharacteristic
254C22×C33C2411yescharacteristic
255C2×C32×D3—21no—
256C2×C32×D3—21no—
257C2×C32×D3C2×Q812yes—
258C33×C4—21no—
259C3⋊(C3⋊Dic3)—21no—
260C3⋊(C3⋊Dic3)C2×Q812yes—
261C3×C3⋊Dic3—21no—
262C3×C3⋊Dic3—21no—
263C3×C3⋊Dic3—21no—
264C3×C3⋊Dic3C2×Q812yes—
265C3×C3⋊Dic3#4112yes—
266C3×C3⋊Dic3#4112yes—
267C32×Dic3—21no—
268C32×Dic3—21no—
269C32×Dic3—21no—
270C32×Dic3—21no—
271C32×Dic3—21no—
272C3×#125—91no—
273C3×C22⋊Q8—91no—
274C3×C22⋊Q8—91no—
275Q8×Dic3—91no—
276Q8×Dic3—91no—
277#944—91no—
278#944—91no—
279#924—91no—
280#924—91no—
281C2×C4×Dic3—91no—
282C2×C4×Dic3—91no—
283#896—31no—
284#896—31no—
285#896—91no—
286#896—91no—
287#892—91no—
288#892—91no—
289#889—31no—
290#889—31no—
291#889—91no—
292#889—91no—
293#888—91no—
294#888—91no—
295#888—91no—
296#888—91no—
297#887—91no—
298#887—91no—
299#887—91no—
300#887—91no—
301#887—91no—
302#887—91no—
303#887—91no—
304#887—91no—
305#887—91no—
306#887—91no—
307#887—181no—
308#887—181no—
309#878—31no—
310#878—31no—
311#878—91no—
312#878—91no—
313#877—91no—
314#877—91no—
315#877—91no—
316#877—91no—
317#877—181no—
318C42×D3—91no—
319#870—91no—
320C23×C32—31no—
321C22×C3×D3—21no—
322C22×C3×D3C22×D311yescharacteristic
323C22×C3×D3C22×D311yescharacteristic
324C2×C32×C4—21no—
325C2×C32×C4—21no—
326C2×C32×C4—21no—
327C2×C32×C4—31no—
328C2×C32×C4—31no—
329C2×C32×C4—31no—
330C2×C32×C4—31no—
331C2×C32×C4—31no—
332C2×C32×C4—41no—
333C2×C32×C4C22×D311yescharacteristic
334C2×C32×C4C22×D311yescharacteristic
335C2×C32×C4C22×D311yescharacteristic
336C2×C3⋊Dic3—31no—
337C2×C3⋊Dic3—31no—
338C2×C3⋊Dic3—31no—
339C2×C3⋊Dic3—34no—
340C2×C3⋊Dic3—31no—
341C2×C3⋊Dic3—31no—
342C2×C3⋊Dic3—31no—
343C2×C3⋊Dic3—61no—
344C2×C3⋊Dic3—61no—
345C2×C3⋊Dic3—61no—
346C2×C3⋊Dic3—61no—
347C2×C3⋊Dic3—61no—
348C2×C3⋊Dic3—61no—
349C2×C3⋊Dic3—121no—
350C2×C3⋊Dic3—121no—
351C2×C3⋊Dic3C22×D311yescharacteristic
352C2×C3⋊Dic3C22×D311yescharacteristic
353C2×C3⋊Dic3C22×D311yescharacteristic
354C2×C3⋊Dic3C22×D311yescharacteristic
355C2×C3⋊Dic3C22×D311yescharacteristic
356C2×C3⋊Dic3C22×D311yescharacteristic
357#634—22no—
358#634—62no—
359C2×C3×Dic3—21no—
360C2×C3×Dic3—21no—
361C2×C3×Dic3—21no—
362C2×C3×Dic3—21no—
363C2×C3×Dic3—21no—
364C2×C3×Dic3—31no—
365C2×C3×Dic3—31no—
366C2×C3×Dic3—31no—
367C2×C3×Dic3—31no—
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—61no—
377C2×C3×Dic3—61no—
378C2×C3×Dic3—61no—
379C2×C3×Dic3—61no—
380C2×C3×Dic3—61no—
381C2×C3×Dic3—61no—
382C2×C3×Dic3—62no—
383C2×C3×Dic3—62no—
384C2×C3×Dic3C22×D311yescharacteristic
385C2×C3×Dic3C22×D311yescharacteristic
386C2×C3×Dic3C22×D311yescharacteristic
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
394C3×C4×D3—62no—
395C3×C4×D3—62no—
396C3×Dic6—62no—
397C3×Dic6—62no—
398C3×Dic6—62no—
399C3×Dic6—62no—
400C3×Dic6—64no—
401#627—22no—
402#627—62no—
403#627—62no—
404#627—64no—
405#627—62no—
406#627—62no—
407#627—62no—
408D3×Dic3—22no—
409D3×Dic3—22no—
410D3×Dic3—34no—
411D3×Dic3—34no—
412D3×Dic3—64no—
413#533—271noSylow
414C2×C33C22×Q811yescharacteristic
415C2×C33C2×#4111yescharacteristic
416C2×C33C2×#4111yescharacteristic
417C32×D3—22no—
418C2×C3×Q8—91no—
419C2×C3×Q8—91no—
420C22×C3×C4—91no—
421C22×C3×C4—91no—
422C22×Dic3—31no—
423C22×Dic3—31no—
424C22×Dic3—91no—
425C22×Dic3—91no—
426C22×Dic3—181no—
427C2×C4×D3—31no—
428C2×C4×D3—31no—
429C2×C4×D3—91no—
430C2×Dic6—31no—
431C2×Dic6—31no—
432C2×Dic6—31no—
433C2×Dic6—31no—
434C2×Dic6—61no—
435C2×Dic6—91no—
436C2×Dic6—91no—
437C2×Dic6—91no—
438C2×Dic6—91no—
439C2×Dic6—91no—
440C2×Dic6—91no—
441C2×Dic6—181no—
442C3×C4⋊C4—31no—
443C3×C4⋊C4—31no—
444C3×C4⋊C4—31no—
445C3×C4⋊C4—31no—
446C3×C4⋊C4—61no—
447C3×C4⋊C4—61no—
448C3×C4⋊C4—91no—
449C3×C4⋊C4—91no—
450C3×C4⋊C4—91no—
451C3×C4⋊C4—91no—
452C3×C4⋊C4—91no—
453C3×C4⋊C4—91no—
454C3×C4⋊C4—91no—
455C3×C4⋊C4—91no—
456C3×C22⋊C4—31no—
457C3×C22⋊C4—31no—
458C3×C22⋊C4—61no—
459C3×C22⋊C4—91no—
460C3×C22⋊C4—91no—
461C3×C42—91no—
462#217—31no—
463#217—31no—
464#217—91no—
465#217—91no—
466#217—181no—
467(C2×D3)⋊C4—31no—
468(C2×D3)⋊C4—31no—
469(C2×D3)⋊C4—91no—
470(C2×D3)⋊C4D3211yescharacteristic
471C4⋊Dic3—31no—
472C4⋊Dic3—31no—
473C4⋊Dic3—91no—
474C4⋊Dic3—91no—
475C4⋊Dic3—91no—
476C4⋊Dic3—91no—
477C4⋊Dic3—91no—
478C4⋊Dic3D3211yescharacteristic
479Dic3⋊C4—31no—
480Dic3⋊C4—31no—
481Dic3⋊C4—31no—
482Dic3⋊C4—31no—
483Dic3⋊C4—31no—
484Dic3⋊C4—31no—
485Dic3⋊C4—31no—
486Dic3⋊C4—31no—
487Dic3⋊C4—31no—
488Dic3⋊C4—31no—
489Dic3⋊C4—31no—
490Dic3⋊C4—31no—
491Dic3⋊C4—31no—
492Dic3⋊C4—31no—
493Dic3⋊C4—61no—
494Dic3⋊C4—61no—
495Dic3⋊C4—91no—
496Dic3⋊C4—91no—
497Dic3⋊C4—91no—
498Dic3⋊C4—91no—
499Dic3⋊C4—91no—
500Dic3⋊C4—91no—
501Dic3⋊C4—91no—
502Dic3⋊C4—91no—
503Dic3⋊C4—91no—
504Dic3⋊C4—91no—
505Dic3⋊C4—91no—
506Dic3⋊C4—91no—
507Dic3⋊C4—91no—
508Dic3⋊C4—181no—
509Dic3⋊C4—181no—
510Dic3⋊C4—181no—
511Dic3⋊C4—181no—
512Dic3⋊C4D3211yescharacteristic
513C4×Dic3—31no—
514C4×Dic3—31no—
515C4×Dic3—91no—
516C4×Dic3—91no—
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—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—181no—
537C4×Dic3—181no—
538C4×Dic3—181no—
539C4×Dic3—181no—
540C4×Dic3—181no—
541C4×Dic3—181no—
542C4×Dic3—181no—
543C4×Dic3—181no—
544C4×Dic3—361no—
545C22×C32—21no—
546C22×C32—21no—
547C22×C32—21no—
548C22×C32—32no—
549C22×C32—41no—
550C22×C32—61no—
551C22×C32—61no—
552C22×C32C23×D311yescharacteristic
553C22×C32C23×D311yescharacteristic
554C22×C32C23×D311yescharacteristic
555C2×C3×D3—21no—
556C2×C3×D3—21no—
557C2×C3×D3—21no—
558C2×C3×D3—21no—
559C2×C3×D3—22no—
560C2×C3×D3—41no—
561C2×C3×D3—41no—
562C2×C3×D3D3×Q812yes—
563C2×C3×D3D3×Q812yes—
564C32×C4—21no—
565C32×C4—22no—
566C32×C4—21no—
567C32×C4—21no—
568C32×C4—41no—
569C32×C4—41no—
570C32×C4—42no—
571C32×C4—61no—
572C32×C4—61no—
573C32×C4—61no—
574C32×C4—61no—
575C32×C4—61no—
576C3⋊Dic3—21no—
577C3⋊Dic3—21no—
578C3⋊Dic3—21no—
579C3⋊Dic3—32no—
580C3⋊Dic3—32no—
581C3⋊Dic3—32no—
582C3⋊Dic3—62no—
583C3⋊Dic3—62no—
584C3⋊Dic3—62no—
585C3⋊Dic3—61no—
586C3⋊Dic3—62no—
587C3⋊Dic3—61no—
588C3⋊Dic3—61no—
589C3⋊Dic3—122no—
590C3⋊Dic3—121no—
591C3⋊Dic3—121no—
592C3⋊Dic3—122no—
593C3⋊Dic3#23712yes—
594C3⋊Dic3#23712yes—
595C3⋊Dic3D3×Q812yes—
596C3×Dic3—22no—
597C3×Dic3—21no—
598C3×Dic3—21no—
599C3×Dic3—21no—
600C3×Dic3—21no—
601C3×Dic3—21no—
602C3×Dic3—21no—
603C3×Dic3—21no—
604C3×Dic3—21no—
605C3×Dic3—21no—
606C3×Dic3—21no—
607C3×Dic3—32no—
608C3×Dic3—32no—
609C3×Dic3—32no—
610C3×Dic3—32no—
611C3×Dic3—32no—
612C3×Dic3—32no—
613C3×Dic3—41no—
614C3×Dic3—41no—
615C3×Dic3—41no—
616C3×Dic3—41no—
617C3×Dic3—62no—
618C3×Dic3—62no—
619C3×Dic3—62no—
620C3×Dic3—62no—
621C3×Dic3—61no—
622C3×Dic3—61no—
623C3×Dic3—61no—
624C3×Dic3—61no—
625C3×Dic3—61no—
626C3×Dic3—61no—
627C3×Dic3—121no—
628C3×Dic3—121no—
629C4⋊Q8—271no—
630C4⋊Q8—271no—
631#125—91no—
632#125—271no—
633C22⋊Q8—91no—
634C22⋊Q8—91no—
635C22⋊Q8—271no—
636C22⋊Q8—271no—
637C4×Q8—271no—
638C4×Q8—271no—
639C4×Q8—271no—
640C4×Q8—271no—
641#117—271no—
642#117—271no—
643C2×C42—271no—
644C33#53311yescharacteristic, complemented, Sylow
645C23×C3—31no—
646C23×C3—31no—
647C23×C3—61no—
648C22×D3C2×D3211yescharacteristic
649C3×Q8—182no—
650C3×Q8—182no—
651C2×C3×C4—21no—
652C2×C3×C4—21no—
653C2×C3×C4—21no—
654C2×C3×C4—31no—
655C2×C3×C4—31no—
656C2×C3×C4—31no—
657C2×C3×C4—31no—
658C2×C3×C4—31no—
659C2×C3×C4—31no—
660C2×C3×C4—31no—
661C2×C3×C4—31no—
662C2×C3×C4—31no—
663C2×C3×C4—31no—
664C2×C3×C4—41no—
665C2×C3×C4—61no—
666C2×C3×C4—61no—
667C2×C3×C4—61no—
668C2×C3×C4—61no—
669C2×C3×C4—61no—
670C2×C3×C4—91no—
671C2×C3×C4—91no—
672C2×C3×C4—91no—
673C2×C3×C4—91no—
674C2×C3×C4—91no—
675C2×C3×C4—91no—
676C2×C3×C4—182no—
677C2×C3×C4—182no—
678C2×C3×C4C2×D3211yescharacteristic
679C2×C3×C4C2×D3211yescharacteristic
680C2×C3×C4C2×D3211yescharacteristic
681C2×Dic3—31no—
682C2×Dic3—31no—
683C2×Dic3—31no—
684C2×Dic3—31no—
685C2×Dic3—31no—
686C2×Dic3—31no—
687C2×Dic3—31no—
688C2×Dic3—31no—
689C2×Dic3—31no—
690C2×Dic3—31no—
691C2×Dic3—31no—
692C2×Dic3—31no—
693C2×Dic3—61no—
694C2×Dic3—61no—
695C2×Dic3—61no—
696C2×Dic3—61no—
697C2×Dic3—61no—
698C2×Dic3—61no—
699C2×Dic3—62no—
700C2×Dic3—62no—
701C2×Dic3—94no—
702C2×Dic3—94no—
703C2×Dic3—91no—
704C2×Dic3—91no—
705C2×Dic3—91no—
706C2×Dic3—91no—
707C2×Dic3—91no—
708C2×Dic3—91no—
709C2×Dic3—184no—
710C2×Dic3—181no—
711C2×Dic3—181no—
712C2×Dic3—181no—
713C2×Dic3—181no—
714C2×Dic3—181no—
715C2×Dic3—181no—
716C2×Dic3—361no—
717C2×Dic3—361no—
718C2×Dic3C2×D3211yescharacteristic
719C2×Dic3C2×D3211yescharacteristic
720C2×Dic3C2×D3211yescharacteristic
721C2×Dic3C2×D3211yescharacteristic
722C2×Dic3C2×D3211yescharacteristic
723C4×D3—62no—
724C4×D3—62no—
725C4×D3—94no—
726Dic6—62no—
727Dic6—62no—
728Dic6—62no—
729Dic6—62no—
730Dic6—64no—
731Dic6—182no—
732Dic6—182no—
733Dic6—182no—
734Dic6—182no—
735Dic6—182no—
736Dic6—182no—
737Dic6—184no—
738C2×C32—21no—
739C2×C32—21no—
740C2×C32—21no—
741C2×C32—21no—
742C2×C32—21no—
743C2×C32—21no—
744C2×C32—21no—
745C2×C32—21no—
746C2×C32—21no—
747C2×C32—41no—
748C2×C32—41no—
749C2×C32—41no—
750C2×C32—62no—
751C2×C32C2×#23711yescharacteristic
752C2×C32C2×#23711yescharacteristic
753C2×C32C2×D3×Q811yescharacteristic
754C2×C32C2×D3×Q811yescharacteristic
755C2×C32C2×D3×Q811yescharacteristic
756C2×C32D3×#4111yescharacteristic
757C2×C32D3×#4111yescharacteristic
758C2×C32D3×#4111yescharacteristic
759C2×C32D3×#4111yescharacteristic
760C3×D3—22no—
761C3×D3—22no—
762C3×D3—42no—
763C2×Q8—91no—
764C2×Q8—91no—
765C2×Q8—271no—
766C2×Q8—271no—
767C22×C4—91no—
768C22×C4—91no—
769C22×C4—271no—
770C4⋊C4—31no—
771C4⋊C4—31no—
772C4⋊C4—91no—
773C4⋊C4—91no—
774C4⋊C4—91no—
775C4⋊C4—91no—
776C4⋊C4—91no—
777C4⋊C4—91no—
778C4⋊C4—91no—
779C4⋊C4—91no—
780C4⋊C4—271no—
781C4⋊C4—271no—
782C4⋊C4—271no—
783C4⋊C4—271no—
784C4⋊C4—271no—
785C4⋊C4—271no—
786C22⋊C4—31no—
787C22⋊C4—91no—
788C22⋊C4—91no—
789C22⋊C4—271no—
790C42—91no—
791C42—271no—
792C42—271no—
793C42—271no—
794C42—271no—
795C42—271no—
796C42—271no—
797C42—271no—
798C22×C3—21no—
799C22×C3—21no—
800C22×C3—21no—
801C22×C3—32no—
802C22×C3—32no—
803C22×C3—41no—
804C22×C3—62no—
805C22×C3—61no—
806C22×C3—61no—
807C22×C3—61no—
808C22×C3—61no—
809C22×C3—121no—
810C22×C3—121no—
811C22×C3C22×D3211yescharacteristic
812C22×C3C22×D3211yescharacteristic
813C22×C3C22×D3211yescharacteristic
814C2×D3—21no—
815C2×D3—21no—
816C2×D3#379712yes—
817C3×C4—22no—
818C3×C4—21no—
819C3×C4—21no—
820C3×C4—21no—
821C3×C4—41no—
822C3×C4—41no—
823C3×C4—42no—
824C3×C4—62no—
825C3×C4—61no—
826C3×C4—61no—
827C3×C4—61no—
828C3×C4—61no—
829C3×C4—61no—
830C3×C4—61no—
831C3×C4—61no—
832C3×C4—61no—
833C3×C4—61no—
834C3×C4—61no—
835C3×C4—92no—
836C3×C4—92no—
837C3×C4—92no—
838C3×C4—121no—
839C3×C4—121no—
840C3×C4—121no—
841C3×C4—121no—
842C3×C4—181no—
843C3×C4—181no—
844C3×C4—181no—
845Dic3—21no—
846Dic3—21no—
847Dic3—21no—
848Dic3—21no—
849Dic3—21no—
850Dic3—32no—
851Dic3—32no—
852Dic3—32no—
853Dic3—32no—
854Dic3—32no—
855Dic3—32no—
856Dic3—62no—
857Dic3—62no—
858Dic3—62no—
859Dic3—62no—
860Dic3—61no—
861Dic3—61no—
862Dic3—61no—
863Dic3—61no—
864Dic3—61no—
865Dic3—61no—
866Dic3—92no—
867Dic3—92no—
868Dic3—92no—
869Dic3—121no—
870Dic3—121no—
871Dic3—182no—
872Dic3—182no—
873Dic3—182no—
874Dic3—182no—
875Dic3—181no—
876Dic3—181no—
877Dic3—181no—
878Dic3—362no—
879Dic3—361no—
880Dic3—361no—
881Dic3—362no—
882C32—21no—
883C32—21no—
884C32—21no—
885C32—41no—
886C32#562211yescharacteristic, complemented
887C32#562211yescharacteristic, complemented
888C32#568811yescharacteristic, complemented
889C23—31no—
890Q8—182no—
891Q8—182no—
892Q8—542no—
893Q8—542no—
894C2×C4—31no—
895C2×C4—31no—
896C2×C4—31no—
897C2×C4—31no—
898C2×C4—31no—
899C2×C4—91no—
900C2×C4—91no—
901C2×C4—91no—
902C2×C4—91no—
903C2×C4—91no—
904C2×C4—91no—
905C2×C4—182no—
906C2×C4—182no—
907C2×C4—274no—
908C2×C4—271no—
909C2×C4—271no—
910C2×C4D3311yescharacteristic
911C2×C3—21no—
912C2×C3—21no—
913C2×C3—21no—
914C2×C3—21no—
915C2×C3—21no—
916C2×C3—21no—
917C2×C3—21no—
918C2×C3—21no—
919C2×C3—21no—
920C2×C3—41no—
921C2×C3—41no—
922C2×C3—41no—
923C2×C3—62no—
924C2×C3—62no—
925C2×C3—122no—
926C2×C3C2×#379711yescharacteristic
927C2×C3#6430611yescharacteristic
928C2×C3#6430611yescharacteristic
929C2×C3D3×#23711yescharacteristic
930C2×C3D3×#23711yescharacteristic
931C2×C3D3×#23711yescharacteristic
932C2×C3D3×#23711yescharacteristic
933C2×C3D32×Q811yescharacteristic
934C2×C3D32×Q811yescharacteristic
935D3—22no—
936C22—32no—
937C22—61no—
938C22—61no—
939C22C2×D3311yescharacteristic
940C4—21no—
941C4—61no—
942C4—61no—
943C4—61no—
944C4—61no—
945C4—61no—
946C4—92no—
947C4—92no—
948C4—92no—
949C4—181no—
950C4—181no—
951C4—181no—
952C4—272no—
953C4—541no—
954C3—21no—
955C3—21no—
956C3—21no—
957C3—41no—
958C3#1059403011yescharacteristic, complemented
959C3#1059438811yescharacteristic, complemented
960C3#1059438811yescharacteristic, complemented
961C2—62no—
962C2#1172437311yescharacteristic
963C2D3×#379711yescharacteristic
964C2#1172440711yescharacteristic
subgroupG/H
center, FrattiniC22C2×D33
commutator, socle, cosocleC22×C33C24
FittingC2×C33×C4C23
prime radicalC22×C32×D3C23
hypercenterC2×C4D33
hypocenterC33#533
LCSG ▷ C22×C33 ▷ C33
UCSC1 ◁ C22 ◁ C2×C4

Complements

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

NH ≅ G/Ntype
1. #11723666C2semidirect
3. #11723410C2semidirect
4. #11723391C2semidirect
7. C3×#63847C2semidirect
8. #11723034C2semidirect
9. #11723014C2semidirect
12. #11722945C2semidirect
13. #11722941C2semidirect
83. #63847D3semidirect
120. D3×C3⋊Dic3Q8semidirect
644. C33#533semidirect
886. C32#5622semidirect
887. C32#5622semidirect
888. C32#5688semidirect
958. C3#10594030semidirect
959. C3#10594388semidirect
960. C3#10594388semidirect

Maximal subgroups

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

subgroupindex
#117236662
#117234602
#117234102
#117233912
C3×#638992
C3×#638962
C3×#638472
#117230342
#117230142
#117229782
#117229752
#117229452
#117229412
#117229172
D3×Dic322
#105943883
#105940303