Finite Group Databasebeta

← #13168164

Subgroups — #13168164

Order 1728.

1036 conjugacy classes of subgroups.

The subgroup lattice has 964 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4⋊#6296C211yesmaximal, characteristic, complemented
2#11723500C211yesmaximal, characteristic
3#11723445C211yesmaximal, characteristic, complemented
4#11723401C211yesmaximal, characteristic, complemented
5C3×#63893C211yesmaximal, characteristic
6C3×#63878C211yesmaximal, characteristic
7C3×#63845C211yesmaximal, characteristic, complemented
8#11723036C211yesmaximal, characteristic, complemented
9#11723035C211yesmaximal, characteristic, complemented
10#11723033C211yesmaximal, characteristic, complemented
11#11723014C211yesmaximal, characteristic, complemented
12#11722981C211yesmaximal, characteristic
13#11722978C211yesmaximal, characteristic
14#11722913C211yesmaximal, characteristic
15D3×Dic3⋊Dic3C211yesmaximal, characteristic
16#10594505—31nomaximal
17#10594389—31nomaximal
18#10594035—31nomaximal
19C2×#6296C2211yescharacteristic
20C2×#6296C2211yescharacteristic
21C2×#6293C2211yescharacteristic
22C2×D3×C3⋊Dic3C2211yescharacteristic
23C2×C3×#627C2211yescharacteristic
24C2×C3×D3×Dic3C2211yescharacteristic
25C2×C3×D3×Dic3C2211yescharacteristic
26#88857C2211yescharacteristic
27C3×C4⋊(C3⋊Dic3)C2211yescharacteristic
28C3×C4⋊(C3⋊Dic3)C2211yescharacteristic
29C3×C4×C3⋊Dic3C2211yescharacteristic
30C32×(C2×D3)⋊C4C2211yescharacteristic
31C32×Dic3⋊C4C2211yescharacteristic
32C32×Dic3⋊C4C2211yescharacteristic
33#88815C2211yescharacteristic
34#88815C2211yescharacteristic
35#88807C2211yescharacteristic
36#88807C2211yescharacteristic
37#88807C2211yescharacteristic
38#88806C2211yescharacteristic
39#88806C2211yescharacteristic
40Dic3⋊(C3⋊Dic3)C2211yescharacteristic
41Dic3⋊(C3⋊Dic3)C2211yescharacteristic
42Dic3⋊(C3⋊Dic3)C2211yescharacteristic
43(C2×D3)⋊(C3⋊Dic3)C2211yescharacteristic
44Dic3×C3⋊Dic3C2211yescharacteristic
45C3×#3724C2211yescharacteristic
46C3×Dic3⋊Dic3C2211yescharacteristic
47C3×Dic3⋊Dic3C2211yescharacteristic
48C3×Dic3⋊Dic3C2211yescharacteristic
49C3×Dic3⋊Dic3C2211yescharacteristic
50C3×(C2×D3)⋊Dic3C2211yescharacteristic
51C3×(C2×D3)⋊Dic3C2211yescharacteristic
52C3×Dic32C2211yescharacteristic
53C3×Dic32C2211yescharacteristic
54#64099—31no—
55#64098—31no—
56#64087—31no—
57C3×#897—31no—
58C3×#892—31no—
59C3×#890—31no—
60C3×#889—31no—
61C3×#878—31no—
62C3×#877—31no—
63#63982—31no—
64C2×Dic3⋊Dic3—31no—
65#63964—31no—
66#63955—31no—
67#63919—31no—
68#63919—31no—
69#63918—31no—
70#63918—31no—
71#63918—31no—
72#63918—31no—
73#63918—31no—
74#63899—31no—
75#63899—31no—
76#63899—31no—
77#63899—61no—
78#63893—31no—
79#63893—31no—
80#63893D311yescharacteristic
81D3×C4⋊Dic3—31no—
82#63878D311yescharacteristic
83#63877—31no—
84D3×Dic3⋊C4—31no—
85#63867—31no—
86#63867—31no—
87#63867—31no—
88#63867—31no—
89#63867—61no—
90#63866—31no—
91#63855—31no—
92#63851—31no—
93#63847—31no—
94#63846—31no—
95#63846—31no—
96#63846—61no—
97#63845D311yescharacteristic, complemented
98#63840—31no—
99#63839—31no—
100#63839—31no—
101#63839—31no—
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
112C2×C32×Dic3C2311yescharacteristic
113C2×C32×Dic3C2311yescharacteristic
114C2×C32×Dic3C2311yescharacteristic
115C2×C32×Dic3C2311yescharacteristic
116C2×C32×Dic3C2311yescharacteristic
117#6296—41no—
118#6296—41no—
119#6293—41no—
120D3×C3⋊Dic3—41no—
121C3×#627—41no—
122C3×D3×Dic3—41no—
123C3×D3×Dic3Q814yescomplemented
124#5689—91no—
125#5623—91no—
126#5519—91no—
127C22×C3⋊Dic3—31no—
128C2×#634—31no—
129C22×C3×Dic3—31no—
130C22×C3×Dic3—31no—
131C2×C3×C4×D3—31no—
132C2×C3×C4×D3—31no—
133C2×C3×Dic6—31no—
134C2×C3×Dic6—31no—
135C2×#627—31no—
136C2×#627—31no—
137C2×#627—31no—
138C2×#627—31no—
139C2×#627—31no—
140C2×#627—31no—
141C2×#627—31no—
142C2×#627—31no—
143C2×#627—61no—
144C2×#627C2×D311yescharacteristic
145C2×D3×Dic3—31no—
146C2×D3×Dic3—31no—
147C2×D3×Dic3—61no—
148C2×D3×Dic3C2×D311yescharacteristic
149C2×D3×Dic3C2×D311yescharacteristic
150C32×C4⋊C4—31no—
151C32×C4⋊C4—31no—
152C32×C22⋊C4—31no—
153#3757—31no—
154C4⋊(C3⋊Dic3)—31no—
155C4⋊(C3⋊Dic3)—31no—
156C4⋊(C3⋊Dic3)—31no—
157C4⋊(C3⋊Dic3)C2×D311yescharacteristic
158C4⋊(C3⋊Dic3)C2×D311yescharacteristic
159#3750—31no—
160#3750—31no—
161#3750—31no—
162#3750—31no—
163#3750—31no—
164#3750—31no—
165#3750—31no—
166#3750—31no—
167#3750—61no—
168#3750—61no—
169#3750—61no—
170#3750—121no—
171C4×C3⋊Dic3—31no—
172C4×C3⋊Dic3C2×D311yescharacteristic
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—31no—
181C3×C4⋊Dic3—31no—
182C3×C4⋊Dic3—31no—
183C3×C4⋊Dic3—31no—
184C3×C4⋊Dic3—31no—
185C3×C4⋊Dic3—31no—
186C3×C4⋊Dic3—31no—
187C3×C4⋊Dic3—31no—
188C3×C4⋊Dic3—61no—
189C3×C4⋊Dic3—61no—
190C3×Dic3⋊C4—21no—
191C3×Dic3⋊C4—21no—
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⋊C4C2×D311yescharacteristic
199C3×Dic3⋊C4C2×D311yescharacteristic
200C3×Dic3⋊C4C2×D311yescharacteristic
201C3×Dic3⋊C4C2×D311yescharacteristic
202C3×C4×Dic3—31no—
203C3×C4×Dic3—31no—
204C3×C4×Dic3—31no—
205C3×C4×Dic3—31no—
206C3×C4×Dic3—31no—
207C3×C4×Dic3—31no—
208C3×C4×Dic3—61no—
209#3724—31no—
210#3724—31no—
211#3724—31no—
212#3724—31no—
213#3724—31no—
214#3724—31no—
215#3724—61no—
216#3724—61no—
217#3724C2×D311yescharacteristic
218Dic3⋊Dic3—31no—
219Dic3⋊Dic3—31no—
220Dic3⋊Dic3—31no—
221Dic3⋊Dic3—31no—
222Dic3⋊Dic3—31no—
223Dic3⋊Dic3—31no—
224Dic3⋊Dic3—31no—
225Dic3⋊Dic3—31no—
226Dic3⋊Dic3—31no—
227Dic3⋊Dic3—31no—
228Dic3⋊Dic3—31no—
229Dic3⋊Dic3—31no—
230Dic3⋊Dic3—31no—
231Dic3⋊Dic3—31no—
232Dic3⋊Dic3—31no—
233Dic3⋊Dic3—31no—
234Dic3⋊Dic3—61no—
235Dic3⋊Dic3—61no—
236Dic3⋊Dic3—61no—
237Dic3⋊Dic3—61no—
238Dic3⋊Dic3—61no—
239Dic3⋊Dic3—61no—
240Dic3⋊Dic3C2×D311yescharacteristic
241Dic3⋊Dic3C2×D311yescharacteristic
242Dic3⋊Dic3C2×D311yescharacteristic
243Dic3⋊Dic3C2×D311yescharacteristic
244(C2×D3)⋊Dic3—31no—
245(C2×D3)⋊Dic3—31no—
246(C2×D3)⋊Dic3—61no—
247(C2×D3)⋊Dic3C2×D311yescharacteristic
248(C2×D3)⋊Dic3C2×D311yescharacteristic
249Dic32—31no—
250Dic32—31no—
251Dic32—61no—
252Dic32C2×D311yescharacteristic
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)—21no—
261C3×C3⋊Dic3—21no—
262C3×C3⋊Dic3—21no—
263C3×C3⋊Dic3—21no—
264C3×C3⋊Dic3—21no—
265C3×C3⋊Dic3—21no—
266C3×C3⋊Dic3C2×Q812yes—
267C32×Dic3—21no—
268C32×Dic3—21no—
269C32×Dic3—21no—
270C32×Dic3—21no—
271C32×Dic3C2×Q812yes—
272C3×#125—91no—
273C3×C22⋊Q8—91no—
274C3×#117—91no—
275#944—91no—
276#944—91no—
277#926—91no—
278C2×C4⋊Dic3—91no—
279#924—91no—
280C2×Dic3⋊C4—91no—
281#897—31no—
282#897—91no—
283#896—91no—
284#896—91no—
285#892—31no—
286D3×C4⋊C4—91no—
287#890—31no—
288#890—91no—
289#890—91no—
290#890—181no—
291#889—31no—
292#889—91no—
293#889—91no—
294#889—91no—
295#889—91no—
296#889—91no—
297#889—181no—
298#888—91no—
299#888—91no—
300#888—91no—
301#888—91no—
302#888—91no—
303#888—91no—
304#888—91no—
305#878—31no—
306#878—91no—
307#878—91no—
308#878—91no—
309#878—91no—
310#878—91no—
311#878—181no—
312#877—31no—
313#877—91no—
314#872—91no—
315#870—91no—
316#870—91no—
317#869—91no—
318#869—91no—
319#869—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—31no—
340C2×C3⋊Dic3—31no—
341C2×C3⋊Dic3—31no—
342C2×C3⋊Dic3—61no—
343C2×C3⋊Dic3—61no—
344C2×C3⋊Dic3—61no—
345C2×C3⋊Dic3—61no—
346C2×C3⋊Dic3—61no—
347C2×C3⋊Dic3—61no—
348C2×C3⋊Dic3—121no—
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—121no—
358C2×C3×Dic3—21no—
359C2×C3×Dic3—21no—
360C2×C3×Dic3—21no—
361C2×C3×Dic3—21no—
362C2×C3×Dic3—21no—
363C2×C3×Dic3—31no—
364C2×C3×Dic3—31no—
365C2×C3×Dic3—34no—
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—121no—
383C2×C3×Dic3C22×D311yescharacteristic
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
393C3×C4×D3—34no—
394C3×C4×D3—121no—
395C3×Dic6—121no—
396C3×Dic6—121no—
397#627—41no—
398#627—121no—
399#627—121no—
400#627—122no—
401#627—121no—
402#627—121no—
403#627—121no—
404#627—121no—
405#627—121no—
406#627—121no—
407D3×Dic3—41no—
408D3×Dic3—121no—
409D3×Dic3—121no—
410D3×Dic3—122no—
411D3×Dic3Dic614yescomplemented
412#544—271noSylow
413C2×C33C22×Q811yescharacteristic
414C2×C33H(5,𝔽2)11yescharacteristic
415C2×C332−1+411yescharacteristic
416C32×D3—22no—
417C2×C3×Q8—91no—
418C22×C3×C4—91no—
419C22×C3×C4—91no—
420C22×Dic3—31no—
421C22×Dic3—31no—
422C22×Dic3—91no—
423C22×Dic3—91no—
424C22×Dic3—181no—
425C2×C4×D3—31no—
426C2×C4×D3—31no—
427C2×C4×D3—91no—
428C2×Dic6—31no—
429C2×Dic6—31no—
430C2×Dic6—91no—
431C2×Dic6—91no—
432C2×Dic6—91no—
433C2×Dic6—91no—
434C2×Dic6—91no—
435C2×Dic6—91no—
436C2×Dic6—91no—
437C2×Dic6—91no—
438C2×Dic6—91no—
439C2×Dic6—181no—
440C3×C4⋊C4—31no—
441C3×C4⋊C4—31no—
442C3×C4⋊C4—31no—
443C3×C4⋊C4—31no—
444C3×C4⋊C4—61no—
445C3×C4⋊C4—61no—
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×C4⋊C4—91no—
453C3×C22⋊C4—31no—
454C3×C22⋊C4—31no—
455C3×C22⋊C4—61no—
456C3×C22⋊C4—91no—
457C3×C22⋊C4—91no—
458C3×C42—91no—
459C3×C42—91no—
460C3×C42—91no—
461#217—31no—
462#217—31no—
463#217—91no—
464#217—91no—
465#217—181no—
466(C2×D3)⋊C4—31no—
467(C2×D3)⋊C4—31no—
468(C2×D3)⋊C4—91no—
469(C2×D3)⋊C4D3211yescharacteristic
470C4⋊Dic3—31no—
471C4⋊Dic3—31no—
472C4⋊Dic3—31no—
473C4⋊Dic3—31no—
474C4⋊Dic3—31no—
475C4⋊Dic3—31no—
476C4⋊Dic3—31no—
477C4⋊Dic3—31no—
478C4⋊Dic3—61no—
479C4⋊Dic3—61no—
480C4⋊Dic3—91no—
481C4⋊Dic3—91no—
482C4⋊Dic3—91no—
483C4⋊Dic3—91no—
484C4⋊Dic3—91no—
485C4⋊Dic3—91no—
486C4⋊Dic3—91no—
487C4⋊Dic3—91no—
488C4⋊Dic3—91no—
489C4⋊Dic3—91no—
490C4⋊Dic3—91no—
491C4⋊Dic3—181no—
492C4⋊Dic3—181no—
493C4⋊Dic3—181no—
494Dic3⋊C4—31no—
495Dic3⋊C4—31no—
496Dic3⋊C4—31no—
497Dic3⋊C4—31no—
498Dic3⋊C4—31no—
499Dic3⋊C4—31no—
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—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—
527Dic3⋊C4—181no—
528Dic3⋊C4—181no—
529Dic3⋊C4—181no—
530Dic3⋊C4—361no—
531Dic3⋊C4D3211yescharacteristic
532Dic3⋊C4D3211yescharacteristic
533C4×Dic3—31no—
534C4×Dic3—31no—
535C4×Dic3—31no—
536C4×Dic3—31no—
537C4×Dic3—31no—
538C4×Dic3—31no—
539C4×Dic3—61no—
540C4×Dic3—91no—
541C4×Dic3—91no—
542C4×Dic3—91no—
543C4×Dic3—181no—
544C22×C32—21no—
545C22×C32—21no—
546C22×C32—21no—
547C22×C32—32no—
548C22×C32—41no—
549C22×C32—61no—
550C22×C32—61no—
551C22×C32C23×D311yescharacteristic
552C22×C32C23×D311yescharacteristic
553C22×C32C23×D311yescharacteristic
554C2×C3×D3—21no—
555C2×C3×D3—21no—
556C2×C3×D3—21no—
557C2×C3×D3—21no—
558C2×C3×D3—22no—
559C2×C3×D3—41no—
560C2×C3×D3—41no—
561C2×C3×D3C2×Dic612yes—
562C2×C3×D3D3×Q812yes—
563C32×C4—21no—
564C32×C4—21no—
565C32×C4—21no—
566C32×C4—32no—
567C32×C4—41no—
568C32×C4—41no—
569C32×C4—41no—
570C32×C4—61no—
571C32×C4—61no—
572C32×C4—61no—
573C32×C4—61no—
574C32×C4—81no—
575C3⋊Dic3—21no—
576C3⋊Dic3—21no—
577C3⋊Dic3—21no—
578C3⋊Dic3—21no—
579C3⋊Dic3—21no—
580C3⋊Dic3—61no—
581C3⋊Dic3—62no—
582C3⋊Dic3—61no—
583C3⋊Dic3—61no—
584C3⋊Dic3—61no—
585C3⋊Dic3—61no—
586C3⋊Dic3—61no—
587C3⋊Dic3—121no—
588C3⋊Dic3—121no—
589C3⋊Dic3—122no—
590C3⋊Dic3—121no—
591C3⋊Dic3—121no—
592C3⋊Dic3—121no—
593C3⋊Dic3—241no—
594C3⋊Dic3C2×Dic612yes—
595C3×Dic3—21no—
596C3×Dic3—21no—
597C3×Dic3—21no—
598C3×Dic3—21no—
599C3×Dic3—21no—
600C3×Dic3—21no—
601C3×Dic3—21no—
602C3×Dic3—21no—
603C3×Dic3—22no—
604C3×Dic3—32no—
605C3×Dic3—32no—
606C3×Dic3—41no—
607C3×Dic3—41no—
608C3×Dic3—41no—
609C3×Dic3—41no—
610C3×Dic3—62no—
611C3×Dic3—61no—
612C3×Dic3—61no—
613C3×Dic3—61no—
614C3×Dic3—61no—
615C3×Dic3—61no—
616C3×Dic3—61no—
617C3×Dic3—61no—
618C3×Dic3—61no—
619C3×Dic3—61no—
620C3×Dic3—61no—
621C3×Dic3—121no—
622C3×Dic3—121no—
623C3×Dic3—121no—
624C3×Dic3—121no—
625C3×Dic3—121no—
626C3×Dic3C2×Dic612yes—
627C3×Dic3D3×Q812yes—
628C4⋊Q8—271no—
629C4⋊Q8—271no—
630C4⋊Q8—271no—
631C4⋊Q8—271no—
632#125—91no—
633#125—271no—
634#125—271no—
635#125—271no—
636C22⋊Q8—91no—
637C22⋊Q8—271no—
638C22⋊Q8—271no—
639C22⋊Q8—271no—
640#117—91no—
641#117—271no—
642C2×C4⋊C4—271no—
643C33#54411yescharacteristic, complemented, Sylow
644C23×C3—31no—
645C23×C3—31no—
646C23×C3—61no—
647C22×D3C2×D3211yescharacteristic
648C3×Q8—361no—
649C2×C3×C4—21no—
650C2×C3×C4—21no—
651C2×C3×C4—21no—
652C2×C3×C4—31no—
653C2×C3×C4—31no—
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—41no—
663C2×C3×C4—61no—
664C2×C3×C4—61no—
665C2×C3×C4—61no—
666C2×C3×C4—61no—
667C2×C3×C4—61no—
668C2×C3×C4—94no—
669C2×C3×C4—91no—
670C2×C3×C4—91no—
671C2×C3×C4—91no—
672C2×C3×C4—91no—
673C2×C3×C4—91no—
674C2×C3×C4—91no—
675C2×C3×C4—361no—
676C2×C3×C4C2×D3211yescharacteristic
677C2×C3×C4C2×D3211yescharacteristic
678C2×C3×C4C2×D3211yescharacteristic
679C2×Dic3—31no—
680C2×Dic3—31no—
681C2×Dic3—34no—
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—61no—
693C2×Dic3—61no—
694C2×Dic3—61no—
695C2×Dic3—61no—
696C2×Dic3—61no—
697C2×Dic3—61no—
698C2×Dic3—91no—
699C2×Dic3—91no—
700C2×Dic3—91no—
701C2×Dic3—91no—
702C2×Dic3—91no—
703C2×Dic3—91no—
704C2×Dic3—121no—
705C2×Dic3—181no—
706C2×Dic3—181no—
707C2×Dic3—181no—
708C2×Dic3—181no—
709C2×Dic3—181no—
710C2×Dic3—181no—
711C2×Dic3—361no—
712C2×Dic3—361no—
713C2×Dic3—361no—
714C2×Dic3—361no—
715C2×Dic3—362no—
716C2×Dic3C2×D3211yescharacteristic
717C2×Dic3C2×D3211yescharacteristic
718C2×Dic3C2×D3211yescharacteristic
719C2×Dic3C2×D3211yescharacteristic
720C2×Dic3C2×D3211yescharacteristic
721C4×D3—34no—
722C4×D3—121no—
723C4×D3—361no—
724Dic6—121no—
725Dic6—121no—
726Dic6—361no—
727Dic6—361no—
728Dic6—361no—
729Dic6—361no—
730Dic6—361no—
731Dic6—361no—
732Dic6—361no—
733Dic6—361no—
734Dic6—361no—
735Dic6—362no—
736C2×C32—21no—
737C2×C32—21no—
738C2×C32—21no—
739C2×C32—21no—
740C2×C32—21no—
741C2×C32—21no—
742C2×C32—21no—
743C2×C32—21no—
744C2×C32—21no—
745C2×C32—41no—
746C2×C32—41no—
747C2×C32—41no—
748C2×C32—62no—
749C2×C32C22×Dic611yescharacteristic
750C2×C32#100411yescharacteristic
751C2×C32C2×D3×Q811yescharacteristic
752C2×C32C2×D3×Q811yescharacteristic
753C2×C32#100911yescharacteristic
754C2×C32#100911yescharacteristic
755C2×C32#101011yescharacteristic
756C2×C32#101011yescharacteristic
757C2×C32#101011yescharacteristic
758C3×D3—22no—
759C3×D3—22no—
760C3×D3—42no—
761C2×Q8—91no—
762C2×Q8—271no—
763C2×Q8—271no—
764C2×Q8—271no—
765C22×C4—91no—
766C22×C4—91no—
767C22×C4—271no—
768C4⋊C4—31no—
769C4⋊C4—31no—
770C4⋊C4—91no—
771C4⋊C4—91no—
772C4⋊C4—91no—
773C4⋊C4—91no—
774C4⋊C4—91no—
775C4⋊C4—91no—
776C4⋊C4—91no—
777C4⋊C4—271no—
778C4⋊C4—271no—
779C4⋊C4—271no—
780C4⋊C4—271no—
781C4⋊C4—271no—
782C4⋊C4—271no—
783C4⋊C4—271no—
784C4⋊C4—271no—
785C4⋊C4—271no—
786C4⋊C4—271no—
787C4⋊C4—271no—
788C22⋊C4—31no—
789C22⋊C4—91no—
790C22⋊C4—91no—
791C22⋊C4—271no—
792C42—91no—
793C42—91no—
794C42—91no—
795C42—271no—
796C22×C3—21no—
797C22×C3—21no—
798C22×C3—21no—
799C22×C3—32no—
800C22×C3—32no—
801C22×C3—41no—
802C22×C3—62no—
803C22×C3—61no—
804C22×C3—61no—
805C22×C3—61no—
806C22×C3—61no—
807C22×C3—121no—
808C22×C3—121no—
809C22×C3C22×D3211yescharacteristic
810C22×C3C22×D3211yescharacteristic
811C22×C3C22×D3211yescharacteristic
812C2×D3—21no—
813C2×D3—21no—
814C2×D3D3×Dic612yes—
815C3×C4—21no—
816C3×C4—21no—
817C3×C4—21no—
818C3×C4—32no—
819C3×C4—32no—
820C3×C4—41no—
821C3×C4—41no—
822C3×C4—41no—
823C3×C4—62no—
824C3×C4—61no—
825C3×C4—61no—
826C3×C4—61no—
827C3×C4—61no—
828C3×C4—61no—
829C3×C4—61no—
830C3×C4—61no—
831C3×C4—61no—
832C3×C4—81no—
833C3×C4—92no—
834C3×C4—121no—
835C3×C4—121no—
836C3×C4—121no—
837C3×C4—121no—
838C3×C4—181no—
839C3×C4—181no—
840C3×C4—181no—
841C3×C4—181no—
842C3×C4—181no—
843Dic3—21no—
844Dic3—21no—
845Dic3—21no—
846Dic3—21no—
847Dic3—32no—
848Dic3—32no—
849Dic3—62no—
850Dic3—61no—
851Dic3—61no—
852Dic3—61no—
853Dic3—61no—
854Dic3—61no—
855Dic3—61no—
856Dic3—61no—
857Dic3—61no—
858Dic3—61no—
859Dic3—61no—
860Dic3—121no—
861Dic3—121no—
862Dic3—121no—
863Dic3—121no—
864Dic3—121no—
865Dic3—182no—
866Dic3—181no—
867Dic3—181no—
868Dic3—181no—
869Dic3—181no—
870Dic3—181no—
871Dic3—181no—
872Dic3—361no—
873Dic3—361no—
874Dic3—361no—
875Dic3—361no—
876Dic3—361no—
877Dic3—362no—
878Dic3—721no—
879Dic3D3×Dic612yes—
880C32—21no—
881C32—21no—
882C32—21no—
883C32—41no—
884C32#551911yescharacteristic, complemented
885C32#562311yescharacteristic, complemented
886C32#568911yescharacteristic, complemented
887C23—31no—
888Q8—361no—
889Q8—1081no—
890Q8—1081no—
891Q8—1081no—
892C2×C4—31no—
893C2×C4—31no—
894C2×C4—31no—
895C2×C4—31no—
896C2×C4—31no—
897C2×C4—94no—
898C2×C4—91no—
899C2×C4—91no—
900C2×C4—91no—
901C2×C4—91no—
902C2×C4—91no—
903C2×C4—91no—
904C2×C4—271no—
905C2×C4—271no—
906C2×C4—361no—
907C2×C4—1081no—
908C2×C4D3311yescharacteristic
909C2×C3—21no—
910C2×C3—21no—
911C2×C3—21no—
912C2×C3—21no—
913C2×C3—21no—
914C2×C3—21no—
915C2×C3—21no—
916C2×C3—21no—
917C2×C3—21no—
918C2×C3—41no—
919C2×C3—41no—
920C2×C3—41no—
921C2×C3—62no—
922C2×C3—62no—
923C2×C3—122no—
924C2×C3C2×D3×Dic611yescharacteristic
925C2×C3C2×D3×Dic611yescharacteristic
926C2×C3#6430711yescharacteristic
927C2×C3#6430911yescharacteristic
928C2×C3#6430911yescharacteristic
929C2×C3#6430911yescharacteristic
930C2×C3#6431411yescharacteristic
931C2×C3D32×Q811yescharacteristic
932C2×C3#6432011yescharacteristic
933D3—22no—
934C22—32no—
935C22—61no—
936C22—61no—
937C22C2×D3311yescharacteristic
938C4—21no—
939C4—32no—
940C4—61no—
941C4—61no—
942C4—61no—
943C4—61no—
944C4—92no—
945C4—181no—
946C4—181no—
947C4—181no—
948C4—181no—
949C4—181no—
950C4—541no—
951C4—541no—
952C3—21no—
953C3—21no—
954C3—21no—
955C3—41no—
956C3#1059403511yescharacteristic, complemented
957C3#1059438911yescharacteristic, complemented
958C3#1059450511yescharacteristic, complemented
959C2—62no—
960C2D32×Dic611yescharacteristic
961C2#1172438511yescharacteristic
962C2#1172442811yescharacteristic
subgroupG/H
center, FrattiniC22C2×D33
commutator, socle, cosocleC22×C33C24
FittingC2×C33×C4C23
prime radicalC22×C32×D3C23
hypercenterC2×C4D33
hypocenterC33#544
LCSG ▷ C22×C33 ▷ C33
UCSC1 ◁ C22 ◁ C2×C4

Complements

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

NH ≅ G/Ntype
1. C4⋊#6296C2semidirect
3. #11723445C2semidirect
4. #11723401C2semidirect
7. C3×#63845C2semidirect
8. #11723036C2semidirect
9. #11723035C2semidirect
10. #11723033C2semidirect
11. #11723014C2semidirect
97. #63845D3semidirect
123. C3×D3×Dic3Q8semidirect
411. D3×Dic3Dic6semidirect
643. C33#544semidirect
884. C32#5519semidirect
885. C32#5623semidirect
886. C32#5689semidirect
956. C3#10594035semidirect
957. C3#10594389semidirect
958. C3#10594505semidirect

Maximal subgroups

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

subgroupindex
C4⋊#62962
#117235002
#117234452
#117234012
C3×#638932
C3×#638782
C3×#638452
#117230362
#117230352
#117230332
#117230142
#117229812
#117229782
#117229132
D3×Dic3⋊Dic32
#105945053
#105943893
#105940353