Finite Group Databasebeta

← #13170789

Subgroups — #13170789

Order 1728.

1658 conjugacy classes of subgroups.

The subgroup lattice has 1168 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#88958C211yesmaximal, characteristic, complemented
2C2×D3×#624C211yesmaximal, characteristic
3#11723692C211yesmaximal, characteristic, complemented
4#11723539C211yesmaximal, characteristic
5#11723503C211yesmaximal, characteristic, complemented
6#11723470C211yesmaximal, characteristic, complemented
7C3×#63899C211yesmaximal, characteristic, complemented
8C3×#63895C211yesmaximal, characteristic, complemented
9C3×#63893C211yesmaximal, characteristic, complemented
10#11722979C211yesmaximal, characteristic, complemented
11#11722978C211yesmaximal, characteristic, complemented
12#11722970C211yesmaximal, characteristic, complemented
13#11722969C211yesmaximal, characteristic, complemented
14#11722912C211yesmaximal, characteristic, complemented
15#11722906C211yesmaximal, characteristic
16#10594631—31nomaximal
17#10594624—31nomaximal
18#10594067—31nomaximal
19C22×D3×C3⋊D3C2211yescharacteristic
20C2×C4×C3⋊(C3⋊D3)C2211yescharacteristic
21C2×#6296C2211yescharacteristic, complemented
22C2×#6294C2211yescharacteristic
23C2×#6289C2211yescharacteristic
24C2×#6289C2211yescharacteristic
25C2×#6289C2211yescharacteristic
26C2×#6289C2211yescharacteristic
27C2×#6289C2211yescharacteristic
28C2×C3×#627C2211yescharacteristic, complemented
29C2×C3×#627C2211yescharacteristic, complemented
30C2×C3×#627C2211yescharacteristic, complemented
31C2×C3×#624C2211yescharacteristic
32C2×C3×D3×Dic3C2211yescharacteristic
33C2×C3×D3×Dic3C2211yescharacteristic
34#88958—24no—
35D3×#624—24no—
36C3×#3752C2211yescharacteristic
37C3×C4⋊(C3⋊Dic3)C2211yescharacteristic, complemented
38C3×#3750C2211yescharacteristic, complemented
39C32×(C2×D3)⋊C4C2211yescharacteristic
40C32×C4⋊Dic3C2211yescharacteristic, complemented
41C32×Dic3⋊C4C2211yescharacteristic, complemented
42#88815C2211yescharacteristic, complemented
43#88814C2211yescharacteristic
44#88807C2211yescharacteristic, complemented
45#88806C2211yescharacteristic, complemented
46#88806C2211yescharacteristic, complemented
47Dic3⋊(C3⋊Dic3)C2211yescharacteristic, complemented
48#88803C2211yescharacteristic
49(C2×D3)⋊(C3⋊Dic3)C2211yescharacteristic
50C3×#3724C2211yescharacteristic, complemented
51C3×Dic3⋊Dic3C2211yescharacteristic, complemented
52C3×Dic3⋊Dic3C2211yescharacteristic, complemented
53C3×#3722C2211yescharacteristic
54C3×(C2×D3)⋊Dic3C2211yescharacteristic
55C3×(C2×D3)⋊Dic3C2211yescharacteristic
56C22×#624—31no—
57C2×C4×D32—31no—
58C2×C4×D32—31no—
59C2×#3797—31no—
60C2×#3797—31no—
61C2×#3797—31no—
62C4⋊C4×C3⋊D3—31no—
63C4⋊C4×C3⋊D3—31no—
64C22⋊C4×C3⋊D3—31no—
65C3×#897—31no—
66C3×#897—31no—
67C3×#896—31no—
68C3×#896—31no—
69C3×#878—31no—
70C3×#878—31no—
71#63974—31no—
72#63964—31no—
73#63964—31no—
74#63921—31no—
75#63921—31no—
76#63921—31no—
77#63921—31no—
78#63921—61no—
79#63900—31no—
80#63900—31no—
81#63900—31no—
82#63900—61no—
83#63899—31no—
84#63899—31no—
85#63899—31no—
86#63899D311yescharacteristic, complemented
87#63895—31no—
88#63895D311yescharacteristic, complemented
89#63893—31no—
90#63893D311yescharacteristic, complemented
91#63888—31no—
92#63888—31no—
93#63887—31no—
94#63887—31no—
95#63883—31no—
96#63883—31no—
97#63883—31no—
98#63883—31no—
99#63883—61no—
100#63856—31no—
101#63856—31no—
102#63851—31no—
103#63851—31no—
104C22×C3⋊(C3⋊D3)C2311yescharacteristic
105C22×C3×C3⋊D3C2311yescharacteristic
106C22×C32×D3C2311yescharacteristic
107C2×D3×C3⋊D3—22no—
108C2×D3×C3⋊D3—22no—
109C2×D3×C3⋊D3Q814yescomplemented
110C2×C33×C4C2311yescharacteristic
111C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
112C4×C3⋊(C3⋊D3)—22no—
113C2×C3×C3⋊Dic3C2311yescharacteristic
114C2×C3×C3⋊Dic3C2311yescharacteristic
115C2×C3×C3⋊Dic3C2311yescharacteristic
116C2×C3×C3⋊Dic3C2311yescharacteristic
117C2×C3×C3⋊Dic3C2311yescharacteristic
118C2×C32×Dic3C2311yescharacteristic
119C2×C32×Dic3C2311yescharacteristic
120C2×C32×Dic3C2311yescharacteristic
121C2×C32×Dic3C2311yescharacteristic
122C2×C32×Dic3C2311yescharacteristic
123#6296—22no—
124#6294—22no—
125#6289—22no—
126#6289—22no—
127#6289—22no—
128#6289—22no—
129#6289D414yes—
130C3×#627—22no—
131C3×#627—22no—
132C3×#627—22no—
133C3×#624—22no—
134C3×D3×Dic3—22no—
135C3×D3×Dic3—22no—
136D3×C22⋊Q8—91no—
137D3×C22⋊Q8—91no—
138D3×C22⋊Q8—91no—
139C23×C3⋊D3—31no—
140C22×D32—31no—
141C22×D32—31no—
142C22×D32—61no—
143C2×C4×C3⋊D3—31no—
144C2×C4×C3⋊D3—31no—
145C2×C4×C3⋊D3—31no—
146C2×C4×C3⋊D3—31no—
147C2×C4×C3⋊D3—31no—
148C2×C4×C3⋊D3—31no—
149C2×C4×C3⋊D3—31no—
150C2×C4×C3⋊D3—31no—
151C2×C4×C3⋊D3—61no—
152C2×C4×C3⋊D3—61no—
153C2×C4×C3⋊D3—61no—
154C2×C4×C3⋊D3—121no—
155C22×C3×Dic3—31no—
156C22×C3×Dic3—31no—
157C2×C3×C4×D3—31no—
158C2×C3×C4×D3—31no—
159C2×C3×C4×D3—31no—
160C2×C3×C4×D3—31no—
161C2×C3×Dic6—31no—
162C2×C3×Dic6—31no—
163C2×C3×Dic6—31no—
164C2×C3×Dic6—31no—
165C2×C3×Dic6—31no—
166C2×C3×Dic6—31no—
167C2×#627—31no—
168C2×#627—31no—
169C2×#627—31no—
170C2×#627C2×D311yescharacteristic, complemented
171C2×#627C2×D311yescharacteristic, complemented
172C2×#627C2×D311yescharacteristic, complemented
173C2×#624—31no—
174C2×#624—31no—
175C2×#624—31no—
176C2×#624—31no—
177C2×#624—31no—
178C2×#624—31no—
179C2×#624—31no—
180C2×#624—31no—
181C2×#624—31no—
182C2×#624—31no—
183C2×#624—31no—
184C2×#624—64no—
185C2×#624—61no—
186C2×#624—61no—
187C2×#624—61no—
188C2×#624—61no—
189C2×#624—61no—
190C2×#624C2×D311yescharacteristic
191C2×D3×Dic3—31no—
192C2×D3×Dic3—31no—
193C2×D3×Dic3C2×D311yescharacteristic
194C2×D3×Dic3C2×D311yescharacteristic
195C4×D32—64no—
196C4×D32—64no—
197#3797—64no—
198#3797—64no—
199#3797—64no—
200C32×C4⋊C4—31no—
201C32×C4⋊C4—31no—
202C32×C22⋊C4—31no—
203#3757—31no—
204#3752—31no—
205#3752C2×D311yescharacteristic
206C4⋊(C3⋊Dic3)—31no—
207C4⋊(C3⋊Dic3)C2×D311yescharacteristic, complemented
208#3750—31no—
209#3750—31no—
210#3750—31no—
211#3750C2×D311yescharacteristic, complemented
212C3×#217—31no—
213C3×#217—31no—
214C3×(C2×D3)⋊C4—21no—
215C3×(C2×D3)⋊C4—31no—
216C3×(C2×D3)⋊C4—31no—
217C3×(C2×D3)⋊C4—31no—
218C3×(C2×D3)⋊C4—31no—
219C3×(C2×D3)⋊C4—31no—
220C3×(C2×D3)⋊C4—31no—
221C3×(C2×D3)⋊C4—61no—
222C3×(C2×D3)⋊C4C2×D311yescharacteristic
223C3×(C2×D3)⋊C4C2×D311yescharacteristic
224C3×C4⋊Dic3—21no—
225C3×C4⋊Dic3—31no—
226C3×C4⋊Dic3—31no—
227C3×C4⋊Dic3—31no—
228C3×C4⋊Dic3—31no—
229C3×C4⋊Dic3—61no—
230C3×C4⋊Dic3C2×D311yescharacteristic, complemented
231C3×C4⋊Dic3C2×D311yescharacteristic, complemented
232C3×Dic3⋊C4—21no—
233C3×Dic3⋊C4—31no—
234C3×Dic3⋊C4—31no—
235C3×Dic3⋊C4—31no—
236C3×Dic3⋊C4—31no—
237C3×Dic3⋊C4—31no—
238C3×Dic3⋊C4—31no—
239C3×Dic3⋊C4—61no—
240C3×Dic3⋊C4C2×D311yescharacteristic, complemented
241C3×Dic3⋊C4C2×D311yescharacteristic, complemented
242#3724—31no—
243#3724—31no—
244#3724—31no—
245#3724—31no—
246#3724—31no—
247#3724—61no—
248#3724—61no—
249#3724C2×D311yescharacteristic, complemented
250Dic3⋊Dic3—31no—
251Dic3⋊Dic3—31no—
252Dic3⋊Dic3—31no—
253Dic3⋊Dic3—31no—
254Dic3⋊Dic3—31no—
255Dic3⋊Dic3—31no—
256Dic3⋊Dic3—61no—
257Dic3⋊Dic3—61no—
258Dic3⋊Dic3C2×D311yescharacteristic, complemented
259Dic3⋊Dic3C2×D311yescharacteristic, complemented
260#3722—31no—
261#3722C2×D311yescharacteristic
262(C2×D3)⋊Dic3—31no—
263(C2×D3)⋊Dic3—31no—
264(C2×D3)⋊Dic3—31no—
265(C2×D3)⋊Dic3—31no—
266(C2×D3)⋊Dic3—31no—
267(C2×D3)⋊Dic3—31no—
268(C2×D3)⋊Dic3—61no—
269(C2×D3)⋊Dic3—61no—
270(C2×D3)⋊Dic3C2×D311yescharacteristic
271(C2×D3)⋊Dic3C2×D311yescharacteristic
272C22×C33C2411yescharacteristic
273C2×C3⋊(C3⋊D3)C2×D412yes—
274C2×C3⋊(C3⋊D3)C2×Q812yes—
275C2×C3⋊(C3⋊D3)#4112yes—
276C2×C3×C3⋊D3—21no—
277C2×C3×C3⋊D3—21no—
278C2×C3×C3⋊D3C2×Q812yescomplemented
279C2×C32×D3—21no—
280C2×C32×D3—21no—
281C2×C32×D3C2×Q812yescomplemented
282D3×C3⋊D3—28no—
283C33×C4—21no—
284C3⋊(C3⋊Dic3)—21no—
285C3×C3⋊Dic3—21no—
286C3×C3⋊Dic3—21no—
287C3×C3⋊Dic3—21no—
288C3×C3⋊Dic3—21no—
289C3×C3⋊Dic3C2×D412yes—
290C32×Dic3—21no—
291C32×Dic3—21no—
292C32×Dic3—21no—
293C32×Dic3—21no—
294C32×Dic3C2×D412yes—
295C2×D3×Q8—91no—
296C2×D3×Q8—91no—
297C2×D3×Q8—91no—
298C22×C4×D3—91no—
299C22×C4×D3—91no—
300C22×C4×D3—91no—
301C3×C22⋊Q8—91no—
302C3×C22⋊Q8—91no—
303C3×C22⋊Q8—91no—
304#946—91no—
305#946—91no—
306#946—91no—
307#924—91no—
308#924—91no—
309#924—91no—
310#897—31no—
311#897—31no—
312#897—91no—
313#896—31no—
314#896—31no—
315#896—91no—
316#896—91no—
317#896—91no—
318#896—91no—
319D3×C4⋊C4—91no—
320D3×C4⋊C4—91no—
321D3×C4⋊C4—91no—
322D3×C4⋊C4—91no—
323D3×C4⋊C4—91no—
324D3×C4⋊C4—91no—
325D3×C4⋊C4—91no—
326D3×C4⋊C4—91no—
327D3×C4⋊C4—91no—
328D3×C4⋊C4—181no—
329D3×C4⋊C4—181no—
330D3×C22⋊C4—91no—
331D3×C22⋊C4—91no—
332D3×C22⋊C4—91no—
333D3×C22⋊C4—91no—
334D3×C22⋊C4—91no—
335D3×C22⋊C4—91no—
336D3×C22⋊C4—181no—
337#878—31no—
338#878—31no—
339#878—91no—
340#878—91no—
341#878—91no—
342#878—91no—
343C23×C32—31no—
344C22×C3⋊D3—31no—
345C22×C3⋊D3—31no—
346C22×C3⋊D3—31no—
347C22×C3⋊D3—34no—
348C22×C3⋊D3—61no—
349C22×C3⋊D3—61no—
350C22×C3⋊D3—61no—
351C22×C3⋊D3—62no—
352C22×C3⋊D3—62no—
353C22×C3⋊D3—121no—
354C22×C3⋊D3C22×D311yescharacteristic
355C22×C3×D3—21no—
356C22×C3×D3—31no—
357C22×C3×D3—31no—
358C22×C3×D3—61no—
359C22×C3×D3C22×D311yescharacteristic
360C22×C3×D3C22×D311yescharacteristic
361C2×D32—34no—
362C2×D32—34no—
363C2×D32—64no—
364C2×D32—62no—
365C2×D32—62no—
366C2×D32—62no—
367C2×D32—62no—
368C2×D32—122no—
369C2×D32—122no—
370C2×C32×C4—21no—
371C2×C32×C4—21no—
372C2×C32×C4—21no—
373C2×C32×C4—31no—
374C2×C32×C4—31no—
375C2×C32×C4—31no—
376C2×C32×C4—31no—
377C2×C32×C4—31no—
378C2×C32×C4—41no—
379C2×C32×C4C22×D311yescharacteristic
380C2×C32×C4C22×D311yescharacteristic
381C2×C32×C4C22×D311yescharacteristic
382C2×C3⋊Dic3—31no—
383C2×C3⋊Dic3—31no—
384C2×C3⋊Dic3—31no—
385C2×C3⋊Dic3—61no—
386C2×C3⋊Dic3—61no—
387C2×C3⋊Dic3—61no—
388C2×C3⋊Dic3—121no—
389C2×C3⋊Dic3C22×D311yescharacteristic
390C2×C3⋊Dic3C22×D311yescharacteristic
391C2×C3⋊Dic3C22×D311yescharacteristic
392C2×C3⋊Dic3C22×D311yescharacteristic
393C2×C3⋊Dic3C22×D311yescharacteristic
394C4×C3⋊D3—34no—
395C4×C3⋊D3—62no—
396C4×C3⋊D3—62no—
397C4×C3⋊D3—62no—
398C4×C3⋊D3—62no—
399C4×C3⋊D3—62no—
400C4×C3⋊D3—62no—
401C4×C3⋊D3—62no—
402C4×C3⋊D3—64no—
403C4×C3⋊D3—122no—
404C4×C3⋊D3—122no—
405C4×C3⋊D3—124no—
406C2×C3×Dic3—21no—
407C2×C3×Dic3—21no—
408C2×C3×Dic3—21no—
409C2×C3×Dic3—21no—
410C2×C3×Dic3—21no—
411C2×C3×Dic3—31no—
412C2×C3×Dic3—31no—
413C2×C3×Dic3—31no—
414C2×C3×Dic3—31no—
415C2×C3×Dic3—31no—
416C2×C3×Dic3—31no—
417C2×C3×Dic3—31no—
418C2×C3×Dic3—31no—
419C2×C3×Dic3—31no—
420C2×C3×Dic3—31no—
421C2×C3×Dic3—61no—
422C2×C3×Dic3—61no—
423C2×C3×Dic3—61no—
424C2×C3×Dic3—61no—
425C2×C3×Dic3—61no—
426C2×C3×Dic3—62no—
427C2×C3×Dic3—62no—
428C2×C3×Dic3C22×D311yescharacteristic
429C2×C3×Dic3C22×D311yescharacteristic
430C2×C3×Dic3C22×D311yescharacteristic
431C2×C3×Dic3C22×D311yescharacteristic
432C2×C3×Dic3C22×D311yescharacteristic
433C2×C3×Dic3C22×D311yescharacteristic
434C2×C3×Dic3C22×D311yescharacteristic
435C2×C3×Dic3C22×D311yescharacteristic
436C2×C3×Dic3C22×D311yescharacteristic
437C2×C3×Dic3C22×D311yescharacteristic
438C3×C4×D3—62no—
439C3×C4×D3—62no—
440C3×C4×D3—62no—
441C3×C4×D3—62no—
442C3×Dic6—62no—
443C3×Dic6—62no—
444C3×Dic6—62no—
445C3×Dic6—62no—
446C3×Dic6—62no—
447C3×Dic6—62no—
448#627—22no—
449#627—22no—
450#627—22no—
451#627—62no—
452#627—62no—
453#627—62no—
454#624—22no—
455#624—34no—
456#624—34no—
457#624—64no—
458#624—62no—
459#624—62no—
460#624—62no—
461#624—62no—
462#624—62no—
463#624—62no—
464#624—62no—
465#624—62no—
466#624—62no—
467#624—122no—
468#624—122no—
469#624—122no—
470#624—122no—
471D3×Dic3—22no—
472D3×Dic3—22no—
473D3×Dic3—62no—
474D3×Dic3—62no—
475C2×C22⋊Q8—271noSylow
476C2×C33C22×D411yescharacteristic
477C2×C33C22×Q811yescharacteristic
478C2×C33C2×#4111yescharacteristic
479C3⋊(C3⋊D3)C22⋊Q814yescomplemented
480C3×C3⋊D3—22no—
481C32×D3—22no—
482C23×D3—91no—
483C23×D3—91no—
484C23×D3—91no—
485C23×D3—181no—
486C2×C3×Q8—91no—
487C2×C3×Q8—91no—
488C2×C3×Q8—91no—
489C22×C3×C4—91no—
490C22×C3×C4—91no—
491C22×C3×C4—91no—
492C22×Dic3—31no—
493C22×Dic3—31no—
494C22×Dic3—91no—
495D3×Q8—184no—
496D3×Q8—184no—
497D3×Q8—184no—
498C2×C4×D3—31no—
499C2×C4×D3—31no—
500C2×C4×D3—31no—
501C2×C4×D3—31no—
502C2×C4×D3—91no—
503C2×C4×D3—91no—
504C2×C4×D3—91no—
505C2×C4×D3—91no—
506C2×C4×D3—91no—
507C2×C4×D3—91no—
508C2×C4×D3—91no—
509C2×C4×D3—91no—
510C2×C4×D3—91no—
511C2×C4×D3—91no—
512C2×C4×D3—91no—
513C2×C4×D3—91no—
514C2×C4×D3—91no—
515C2×C4×D3—91no—
516C2×C4×D3—91no—
517C2×C4×D3—91no—
518C2×C4×D3—91no—
519C2×C4×D3—91no—
520C2×C4×D3—91no—
521C2×C4×D3—91no—
522C2×C4×D3—181no—
523C2×C4×D3—181no—
524C2×C4×D3—181no—
525C2×C4×D3—181no—
526C2×C4×D3—181no—
527C2×C4×D3—181no—
528C2×C4×D3—181no—
529C2×C4×D3—181no—
530C2×C4×D3—184no—
531C2×C4×D3—184no—
532C2×C4×D3—184no—
533C2×C4×D3—361no—
534C2×Dic6—31no—
535C2×Dic6—31no—
536C2×Dic6—31no—
537C2×Dic6—31no—
538C2×Dic6—31no—
539C2×Dic6—31no—
540C2×Dic6—91no—
541C2×Dic6—91no—
542C2×Dic6—91no—
543C3×C4⋊C4—31no—
544C3×C4⋊C4—31no—
545C3×C4⋊C4—31no—
546C3×C4⋊C4—31no—
547C3×C4⋊C4—61no—
548C3×C4⋊C4—61no—
549C3×C4⋊C4—91no—
550C3×C4⋊C4—91no—
551C3×C4⋊C4—91no—
552C3×C4⋊C4—91no—
553C3×C4⋊C4—91no—
554C3×C22⋊C4—31no—
555C3×C22⋊C4—31no—
556C3×C22⋊C4—61no—
557C3×C22⋊C4—91no—
558C3×C22⋊C4—91no—
559C3×C22⋊C4—91no—
560C3×C22⋊C4—91no—
561#217—31no—
562#217—31no—
563#217—91no—
564#217—91no—
565#217—91no—
566#217—91no—
567#217—181no—
568(C2×D3)⋊C4—31no—
569(C2×D3)⋊C4—31no—
570(C2×D3)⋊C4—31no—
571(C2×D3)⋊C4—31no—
572(C2×D3)⋊C4—31no—
573(C2×D3)⋊C4—31no—
574(C2×D3)⋊C4—61no—
575(C2×D3)⋊C4—91no—
576(C2×D3)⋊C4—91no—
577(C2×D3)⋊C4—91no—
578(C2×D3)⋊C4—91no—
579(C2×D3)⋊C4—91no—
580(C2×D3)⋊C4—181no—
581(C2×D3)⋊C4D3211yescharacteristic
582C4⋊Dic3—31no—
583C4⋊Dic3—31no—
584C4⋊Dic3—31no—
585C4⋊Dic3—31no—
586C4⋊Dic3—61no—
587C4⋊Dic3—91no—
588C4⋊Dic3—91no—
589C4⋊Dic3—91no—
590C4⋊Dic3—91no—
591C4⋊Dic3—181no—
592C4⋊Dic3D3211yescharacteristic, complemented
593Dic3⋊C4—31no—
594Dic3⋊C4—31no—
595Dic3⋊C4—31no—
596Dic3⋊C4—31no—
597Dic3⋊C4—31no—
598Dic3⋊C4—31no—
599Dic3⋊C4—61no—
600Dic3⋊C4—91no—
601Dic3⋊C4—91no—
602Dic3⋊C4—91no—
603Dic3⋊C4—91no—
604Dic3⋊C4—91no—
605Dic3⋊C4—91no—
606Dic3⋊C4—91no—
607Dic3⋊C4—91no—
608Dic3⋊C4—91no—
609Dic3⋊C4—91no—
610Dic3⋊C4—91no—
611Dic3⋊C4—181no—
612Dic3⋊C4—181no—
613Dic3⋊C4—181no—
614Dic3⋊C4D3211yescharacteristic, complemented
615C22×C32—21no—
616C22×C32—21no—
617C22×C32—21no—
618C22×C32—32no—
619C22×C32—41no—
620C22×C32—61no—
621C22×C32—61no—
622C22×C32C23×D311yescharacteristic
623C22×C32C23×D311yescharacteristic
624C22×C32C23×D311yescharacteristic
625C2×C3⋊D3—21no—
626C2×C3⋊D3—21no—
627C2×C3⋊D3—32no—
628C2×C3⋊D3—32no—
629C2×C3⋊D3—32no—
630C2×C3⋊D3—32no—
631C2×C3⋊D3—32no—
632C2×C3⋊D3—32no—
633C2×C3⋊D3—32no—
634C2×C3⋊D3—32no—
635C2×C3⋊D3—32no—
636C2×C3⋊D3—62no—
637C2×C3⋊D3—62no—
638C2×C3⋊D3—62no—
639C2×C3⋊D3—62no—
640C2×C3⋊D3—62no—
641C2×C3⋊D3—62no—
642C2×C3⋊D3—62no—
643C2×C3⋊D3—62no—
644C2×C3⋊D3—62no—
645C2×C3⋊D3—68no—
646C2×C3⋊D3—122no—
647C2×C3⋊D3—122no—
648C2×C3⋊D3—122no—
649C2×C3⋊D3D3×Q812yescomplemented
650C2×C3×D3—21no—
651C2×C3×D3—21no—
652C2×C3×D3—21no—
653C2×C3×D3—21no—
654C2×C3×D3—22no—
655C2×C3×D3—32no—
656C2×C3×D3—32no—
657C2×C3×D3—41no—
658C2×C3×D3—41no—
659C2×C3×D3—62no—
660C2×C3×D3—61no—
661C2×C3×D3—61no—
662C2×C3×D3—61no—
663C2×C3×D3—61no—
664C2×C3×D3—121no—
665C2×C3×D3—121no—
666C2×C3×D3D3×Q812yescomplemented
667C2×C3×D3D3×Q812yescomplemented
668D32—68no—
669D32—68no—
670D32—128no—
671C32×C4—21no—
672C32×C4—22no—
673C32×C4—21no—
674C32×C4—21no—
675C32×C4—32no—
676C32×C4—41no—
677C32×C4—41no—
678C32×C4—42no—
679C32×C4—61no—
680C32×C4—61no—
681C32×C4—61no—
682C32×C4—61no—
683C3⋊Dic3—21no—
684C3⋊Dic3—21no—
685C3⋊Dic3—21no—
686C3⋊Dic3—21no—
687C3⋊Dic3—61no—
688C3⋊Dic3—62no—
689C3⋊Dic3—61no—
690C3⋊Dic3—61no—
691C3⋊Dic3—121no—
692C3⋊Dic3—121no—
693C3⋊Dic3—122no—
694C3⋊Dic3D3×D412yes—
695C3×Dic3—21no—
696C3×Dic3—21no—
697C3×Dic3—21no—
698C3×Dic3—21no—
699C3×Dic3—21no—
700C3×Dic3—21no—
701C3×Dic3—21no—
702C3×Dic3—21no—
703C3×Dic3—22no—
704C3×Dic3—32no—
705C3×Dic3—32no—
706C3×Dic3—41no—
707C3×Dic3—41no—
708C3×Dic3—41no—
709C3×Dic3—41no—
710C3×Dic3—62no—
711C3×Dic3—61no—
712C3×Dic3—61no—
713C3×Dic3—61no—
714C3×Dic3—61no—
715C3×Dic3—61no—
716C3×Dic3—61no—
717C3×Dic3—61no—
718C3×Dic3—61no—
719C3×Dic3—121no—
720C3×Dic3—121no—
721C3×Dic3—121no—
722C3×Dic3—121no—
723C3×Dic3D3×D412yes—
724C3×Dic3D3×D412yes—
725C22×Q8—271no—
726C23×C4—271no—
727C22⋊Q8—91no—
728C22⋊Q8—91no—
729C22⋊Q8—91no—
730C22⋊Q8—271no—
731C22⋊Q8—271no—
732C22⋊Q8—271no—
733C22⋊Q8—271no—
734C22⋊Q8—271no—
735C2×C4⋊C4—271no—
736C2×C4⋊C4—271no—
737C2×C4⋊C4—271no—
738C2×C22⋊C4—271no—
739C2×C22⋊C4—271no—
740C33C2×C22⋊Q811yescharacteristic, complemented, Sylow
741C23×C3—31no—
742C23×C3—31no—
743C23×C3—61no—
744C23×C3—91no—
745C22×D3—31no—
746C22×D3—31no—
747C22×D3—61no—
748C22×D3—94no—
749C22×D3—94no—
750C22×D3—91no—
751C22×D3—91no—
752C22×D3—91no—
753C22×D3—94no—
754C22×D3—184no—
755C22×D3—181no—
756C22×D3—181no—
757C22×D3—181no—
758C22×D3—182no—
759C22×D3—182no—
760C22×D3—182no—
761C22×D3—182no—
762C22×D3—182no—
763C22×D3—182no—
764C22×D3—361no—
765C22×D3—362no—
766C22×D3—362no—
767C22×D3C2×D3211yescharacteristic
768C3×Q8—182no—
769C3×Q8—182no—
770C3×Q8—182no—
771C2×C3×C4—21no—
772C2×C3×C4—21no—
773C2×C3×C4—21no—
774C2×C3×C4—31no—
775C2×C3×C4—31no—
776C2×C3×C4—31no—
777C2×C3×C4—31no—
778C2×C3×C4—31no—
779C2×C3×C4—31no—
780C2×C3×C4—31no—
781C2×C3×C4—31no—
782C2×C3×C4—31no—
783C2×C3×C4—31no—
784C2×C3×C4—41no—
785C2×C3×C4—61no—
786C2×C3×C4—61no—
787C2×C3×C4—61no—
788C2×C3×C4—61no—
789C2×C3×C4—61no—
790C2×C3×C4—91no—
791C2×C3×C4—91no—
792C2×C3×C4—91no—
793C2×C3×C4—91no—
794C2×C3×C4—91no—
795C2×C3×C4—182no—
796C2×C3×C4—182no—
797C2×C3×C4—182no—
798C2×C3×C4C2×D3211yescharacteristic
799C2×C3×C4C2×D3211yescharacteristic
800C2×C3×C4C2×D3211yescharacteristic
801C2×Dic3—31no—
802C2×Dic3—31no—
803C2×Dic3—31no—
804C2×Dic3—31no—
805C2×Dic3—31no—
806C2×Dic3—31no—
807C2×Dic3—31no—
808C2×Dic3—31no—
809C2×Dic3—31no—
810C2×Dic3—31no—
811C2×Dic3—61no—
812C2×Dic3—61no—
813C2×Dic3—61no—
814C2×Dic3—61no—
815C2×Dic3—61no—
816C2×Dic3—62no—
817C2×Dic3—62no—
818C2×Dic3—91no—
819C2×Dic3—91no—
820C2×Dic3—91no—
821C2×Dic3—181no—
822C2×Dic3—181no—
823C2×Dic3—181no—
824C2×Dic3—182no—
825C2×Dic3—361no—
826C2×Dic3C2×D3211yescharacteristic
827C2×Dic3C2×D3211yescharacteristic
828C2×Dic3C2×D3211yescharacteristic
829C2×Dic3C2×D3211yescharacteristic
830C2×Dic3C2×D3211yescharacteristic
831C4×D3—62no—
832C4×D3—62no—
833C4×D3—62no—
834C4×D3—62no—
835C4×D3—94no—
836C4×D3—94no—
837C4×D3—94no—
838C4×D3—184no—
839C4×D3—182no—
840C4×D3—182no—
841C4×D3—182no—
842C4×D3—182no—
843C4×D3—182no—
844C4×D3—182no—
845C4×D3—182no—
846C4×D3—182no—
847C4×D3—182no—
848C4×D3—182no—
849C4×D3—182no—
850C4×D3—182no—
851C4×D3—182no—
852C4×D3—182no—
853C4×D3—182no—
854C4×D3—182no—
855C4×D3—182no—
856C4×D3—184no—
857C4×D3—362no—
858C4×D3—362no—
859C4×D3—362no—
860C4×D3—362no—
861C4×D3—362no—
862C4×D3—362no—
863C4×D3—364no—
864Dic6—62no—
865Dic6—62no—
866Dic6—62no—
867Dic6—62no—
868Dic6—62no—
869Dic6—62no—
870Dic6—182no—
871Dic6—182no—
872Dic6—182no—
873C2×C32—21no—
874C2×C32—21no—
875C2×C32—21no—
876C2×C32—21no—
877C2×C32—21no—
878C2×C32—21no—
879C2×C32—21no—
880C2×C32—21no—
881C2×C32—21no—
882C2×C32—41no—
883C2×C32—41no—
884C2×C32—41no—
885C2×C32—62no—
886C2×C32C2×D3×D411yescharacteristic
887C2×C32C2×D3×D411yescharacteristic
888C2×C32C2×D3×D411yescharacteristic
889C2×C32C2×D3×Q811yescharacteristic
890C2×C32C2×D3×Q811yescharacteristic
891C2×C32C2×D3×Q811yescharacteristic
892C2×C32D3×#4111yescharacteristic
893C2×C32D3×#4111yescharacteristic
894C2×C32D3×#4111yescharacteristic
895C3⋊D3—22no—
896C3⋊D3—34no—
897C3⋊D3—34no—
898C3⋊D3—34no—
899C3⋊D3—64no—
900C3⋊D3—64no—
901C3⋊D3—64no—
902C3⋊D3—124no—
903C3×D3—22no—
904C3×D3—22no—
905C3×D3—42no—
906C3×D3—62no—
907C3×D3—62no—
908C3×D3—122no—
909C24—271no—
910C2×Q8—91no—
911C2×Q8—91no—
912C2×Q8—91no—
913C2×Q8—271no—
914C2×Q8—544no—
915C22×C4—91no—
916C22×C4—91no—
917C22×C4—91no—
918C22×C4—271no—
919C22×C4—271no—
920C22×C4—271no—
921C22×C4—271no—
922C22×C4—271no—
923C22×C4—271no—
924C22×C4—271no—
925C22×C4—544no—
926C4⋊C4—31no—
927C4⋊C4—31no—
928C4⋊C4—91no—
929C4⋊C4—91no—
930C4⋊C4—91no—
931C4⋊C4—91no—
932C4⋊C4—91no—
933C4⋊C4—271no—
934C4⋊C4—271no—
935C4⋊C4—271no—
936C4⋊C4—271no—
937C4⋊C4—271no—
938C22⋊C4—31no—
939C22⋊C4—91no—
940C22⋊C4—91no—
941C22⋊C4—91no—
942C22⋊C4—91no—
943C22⋊C4—271no—
944C22⋊C4—271no—
945C22⋊C4—271no—
946C22×C3—21no—
947C22×C3—21no—
948C22×C3—21no—
949C22×C3—32no—
950C22×C3—32no—
951C22×C3—41no—
952C22×C3—62no—
953C22×C3—61no—
954C22×C3—61no—
955C22×C3—61no—
956C22×C3—61no—
957C22×C3—92no—
958C22×C3—121no—
959C22×C3—121no—
960C22×C3—181no—
961C22×C3—181no—
962C22×C3C22×D3211yescharacteristic
963C22×C3C22×D3211yescharacteristic
964C22×C3C22×D3211yescharacteristic
965C2×D3—21no—
966C2×D3—21no—
967C2×D3—32no—
968C2×D3—32no—
969C2×D3—62no—
970C2×D3—61no—
971C2×D3—61no—
972C2×D3—61no—
973C2×D3—61no—
974C2×D3—92no—
975C2×D3—92no—
976C2×D3—92no—
977C2×D3—92no—
978C2×D3—92no—
979C2×D3—92no—
980C2×D3—92no—
981C2×D3—92no—
982C2×D3—92no—
983C2×D3—121no—
984C2×D3—121no—
985C2×D3—182no—
986C2×D3—182no—
987C2×D3—182no—
988C2×D3—182no—
989C2×D3—182no—
990C2×D3—182no—
991C2×D3—182no—
992C2×D3—182no—
993C2×D3—182no—
994C2×D3—188no—
995C2×D3—188no—
996C2×D3—188no—
997C2×D3—362no—
998C2×D3—362no—
999C2×D3—362no—
1000C2×D3—368no—
1001C2×D3#379712yescomplemented
1002C3×C4—22no—
1003C3×C4—21no—
1004C3×C4—21no—
1005C3×C4—21no—
1006C3×C4—32no—
1007C3×C4—32no—
1008C3×C4—41no—
1009C3×C4—41no—
1010C3×C4—42no—
1011C3×C4—62no—
1012C3×C4—61no—
1013C3×C4—61no—
1014C3×C4—61no—
1015C3×C4—61no—
1016C3×C4—61no—
1017C3×C4—61no—
1018C3×C4—61no—
1019C3×C4—61no—
1020C3×C4—92no—
1021C3×C4—121no—
1022C3×C4—121no—
1023C3×C4—121no—
1024C3×C4—121no—
1025C3×C4—181no—
1026C3×C4—181no—
1027C3×C4—181no—
1028C3×C4—181no—
1029Dic3—21no—
1030Dic3—21no—
1031Dic3—21no—
1032Dic3—21no—
1033Dic3—32no—
1034Dic3—32no—
1035Dic3—62no—
1036Dic3—61no—
1037Dic3—61no—
1038Dic3—61no—
1039Dic3—61no—
1040Dic3—61no—
1041Dic3—61no—
1042Dic3—61no—
1043Dic3—61no—
1044Dic3—121no—
1045Dic3—121no—
1046Dic3—121no—
1047Dic3—121no—
1048Dic3—182no—
1049Dic3—181no—
1050Dic3—181no—
1051Dic3—181no—
1052Dic3—361no—
1053Dic3—361no—
1054Dic3—362no—
1055Dic3#380212yes—
1056C32—21no—
1057C32—21no—
1058C32—21no—
1059C32—41no—
1060C32D3×C22⋊Q811yescharacteristic, complemented
1061C32D3×C22⋊Q811yescharacteristic, complemented
1062C32D3×C22⋊Q811yescharacteristic, complemented
1063C23—31no—
1064C23—91no—
1065C23—274no—
1066C23—271no—
1067C23—542no—
1068C23—542no—
1069Q8—182no—
1070Q8—182no—
1071Q8—182no—
1072Q8—542no—
1073C2×C4—31no—
1074C2×C4—31no—
1075C2×C4—31no—
1076C2×C4—31no—
1077C2×C4—31no—
1078C2×C4—91no—
1079C2×C4—91no—
1080C2×C4—91no—
1081C2×C4—91no—
1082C2×C4—91no—
1083C2×C4—182no—
1084C2×C4—182no—
1085C2×C4—182no—
1086C2×C4—274no—
1087C2×C4—271no—
1088C2×C4—542no—
1089C2×C4—542no—
1090C2×C4—542no—
1091C2×C4—542no—
1092C2×C4—542no—
1093C2×C4—542no—
1094C2×C4D3311yescharacteristic
1095C2×C3—21no—
1096C2×C3—21no—
1097C2×C3—21no—
1098C2×C3—21no—
1099C2×C3—21no—
1100C2×C3—21no—
1101C2×C3—21no—
1102C2×C3—21no—
1103C2×C3—21no—
1104C2×C3—41no—
1105C2×C3—41no—
1106C2×C3—41no—
1107C2×C3—62no—
1108C2×C3—62no—
1109C2×C3—122no—
1110C2×C3—182no—
1111C2×C3C2×#379711yescharacteristic
1112C2×C3C2×#380211yescharacteristic
1113C2×C3#6430611yescharacteristic
1114C2×C3D32×D411yescharacteristic
1115C2×C3D32×D411yescharacteristic
1116C2×C3#6431211yescharacteristic
1117C2×C3#6431211yescharacteristic
1118C2×C3D32×Q811yescharacteristic
1119C2×C3D32×Q811yescharacteristic
1120D3—22no—
1121D3—62no—
1122D3—62no—
1123D3—94no—
1124D3—94no—
1125D3—94no—
1126D3—122no—
1127D3—184no—
1128D3—184no—
1129D3—184no—
1130D3—364no—
1131C22—32no—
1132C22—61no—
1133C22—61no—
1134C22—92no—
1135C22—181no—
1136C22—181no—
1137C22—272no—
1138C22—272no—
1139C22—272no—
1140C22—548no—
1141C22C2×D3311yescharacteristic
1142C4—21no—
1143C4—32no—
1144C4—61no—
1145C4—61no—
1146C4—61no—
1147C4—61no—
1148C4—92no—
1149C4—181no—
1150C4—181no—
1151C4—181no—
1152C4—181no—
1153C4—541no—
1154C3—21no—
1155C3—21no—
1156C3—21no—
1157C3—41no—
1158C3#1059406711yescharacteristic, complemented
1159C3#1059462411yescharacteristic, complemented
1160C3#1059463111yescharacteristic, complemented
1161C2—62no—
1162C2—182no—
1163C2—274no—
1164C2D3×#379711yescharacteristic
1165C2D3×#380211yescharacteristic
1166C2#1172441111yescharacteristic
subgroupG/H
center, FrattiniC22C2×D33
commutator, socle, cosocleC22×C33C24
FittingC2×C33×C4C23
prime radicalC22×D3×C3⋊D3C22
hypercenterC2×C4D33
hypocenterC33C2×C22⋊Q8
LCSG ▷ C22×C33 ▷ C33
UCSC1 ◁ C22 ◁ C2×C4

Complements

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

NH ≅ G/Ntype
1. C2×#88958C2semidirect
3. #11723692C2semidirect
5. #11723503C2semidirect
6. #11723470C2semidirect
7. C3×#63899C2semidirect
8. C3×#63895C2semidirect
9. C3×#63893C2semidirect
10. #11722979C2semidirect
11. #11722978C2semidirect
12. #11722970C2semidirect
13. #11722969C2semidirect
14. #11722912C2semidirect
21. C2×#6296C22semidirect
28. C2×C3×#627C22semidirect
29. C2×C3×#627C22semidirect
30. C2×C3×#627C22semidirect
37. C3×C4⋊(C3⋊Dic3)C22semidirect
38. C3×#3750C22semidirect
40. C32×C4⋊Dic3C22semidirect
41. C32×Dic3⋊C4C22semidirect
42. #88815C22semidirect
44. #88807C22semidirect
45. #88806C22semidirect
46. #88806C22semidirect
47. Dic3⋊(C3⋊Dic3)C22semidirect
50. C3×#3724C22semidirect
51. C3×Dic3⋊Dic3C22semidirect
52. C3×Dic3⋊Dic3C22semidirect
86. #63899D3semidirect
88. #63895D3semidirect
90. #63893D3semidirect
109. C2×D3×C3⋊D3Q8semidirect
170. C2×#627C2×D3semidirect
171. C2×#627C2×D3semidirect
172. C2×#627C2×D3semidirect
207. C4⋊(C3⋊Dic3)C2×D3semidirect
211. #3750C2×D3semidirect
230. C3×C4⋊Dic3C2×D3semidirect
231. C3×C4⋊Dic3C2×D3semidirect
240. C3×Dic3⋊C4C2×D3semidirect
241. C3×Dic3⋊C4C2×D3semidirect
249. #3724C2×D3semidirect
258. Dic3⋊Dic3C2×D3semidirect
259. Dic3⋊Dic3C2×D3semidirect
278. C2×C3×C3⋊D3C2×Q8semidirect
281. C2×C32×D3C2×Q8semidirect
479. C3⋊(C3⋊D3)C22⋊Q8semidirect
592. C4⋊Dic3D32semidirect
614. Dic3⋊C4D32semidirect
649. C2×C3⋊D3D3×Q8semidirect
666. C2×C3×D3D3×Q8semidirect
667. C2×C3×D3D3×Q8semidirect
740. C33C2×C22⋊Q8semidirect
1001. C2×D3#3797semidirect
1060. C32D3×C22⋊Q8semidirect
1061. C32D3×C22⋊Q8semidirect
1062. C32D3×C22⋊Q8semidirect
1158. C3#10594067semidirect
1159. C3#10594624semidirect
1160. C3#10594631semidirect

Maximal subgroups

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

subgroupindex
C2×#889582
C2×D3×#6242
#117236922
#117235392
#117235032
#117234702
C3×#638992
C3×#638952
C3×#638932
#117229792
#117229782
#117229702
#117229692
#117229122
#117229062
#105946313
#105946243
#105940673