Finite Group Databasebeta

← #13176558

Subgroups — #13176558

Order 1728.

1748 conjugacy classes of subgroups.

The subgroup lattice has 718 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11723937C211yesmaximal, characteristic, complemented
2C3×#64105C211yesmaximal, characteristic, complemented
3C32×#897C211yesmaximal, characteristic, complemented
4#11723539C211yesmaximal, characteristic
5C3⋊D3×(C2×D3)⋊C4C211yesmaximal, characteristic
6D3×#3752C211yesmaximal, characteristic
7#11723502C211yesmaximal, characteristic, complemented
8#11723496C211yesmaximal, characteristic, complemented
9#11723495C211yesmaximal, characteristic, complemented
10#11723487C211yesmaximal, characteristic, complemented
11#11723477C211yesmaximal, characteristic, complemented
12#11723476C211yesmaximal, characteristic, complemented
13#11723449C211yesmaximal, characteristic, complemented
14#11723431C211yesmaximal, characteristic, complemented
15#11723415C211yesmaximal, characteristic, complemented
16#10596105—31nomaximal
17#10594635—34nomaximal
18C22×D3×C3⋊D3C2211yescharacteristic
19C2×C4×C3⋊(C3⋊D3)C2211yescharacteristic
20C2×#6308C2211yescharacteristic, complemented
21C2×C3×C4×C3⋊D3C2211yescharacteristic
22C2×C3×#634C2211yescharacteristic, complemented
23C2×C32×C4×D3C2211yescharacteristic
24C2×C32×Dic6C2211yescharacteristic, complemented
25C2×#6293C2211yescharacteristic, complemented
26C2×#6289C2211yescharacteristic
27C2×Dic3×C3⋊D3C2211yescharacteristic
28C2×D3×C3⋊Dic3C2211yescharacteristic
29C33×C4⋊C4C2211yescharacteristic, complemented
30#88859C2211yescharacteristic
31#88859C2211yescharacteristic
32#88857C2211yescharacteristic, complemented
33#88857C2211yescharacteristic, complemented
34C3×#3752C2211yescharacteristic
35C3×#3752C2211yescharacteristic
36C3×#3750C2211yescharacteristic, complemented
37C3×#3750C2211yescharacteristic, complemented
38C32×(C2×D3)⋊C4C2211yescharacteristic
39C32×(C2×D3)⋊C4C2211yescharacteristic
40C32×C4⋊Dic3C2211yescharacteristic, complemented
41C32×C4⋊Dic3C2211yescharacteristic, complemented
42#88807C2211yescharacteristic, complemented
43#88806C2211yescharacteristic, complemented
44Dic3⋊(C3⋊Dic3)C2211yescharacteristic, complemented
45Dic3⋊(C3⋊Dic3)C2211yescharacteristic, complemented
46Dic3⋊(C3⋊Dic3)C2211yescharacteristic, complemented
47#88804C2211yescharacteristic
48#88804C2211yescharacteristic
49#88803C2211yescharacteristic
50#88803C2211yescharacteristic
51(C2×D3)⋊(C3⋊Dic3)C2211yescharacteristic
52(C2×D3)⋊(C3⋊Dic3)C2211yescharacteristic
53C32×C22⋊Q8—31no—
54#64155—31no—
55#64155—31no—
56C2×#3752—31no—
57#64133—31no—
58#64106—31no—
59#64106—31no—
60#64105—31no—
61#64105—31no—
62#64105—31no—
63#64105—34no—
64#64105—64no—
65#64105D311yescharacteristic, complemented
66C22⋊C4×C3⋊D3—31no—
67C22⋊C4×C3⋊D3—31no—
68#64087—31no—
69#64087—31no—
70C3×#897D314yescomplemented
71C3×#896—34no—
72#63921—34no—
73D3×(C2×D3)⋊C4—34no—
74D3×(C2×D3)⋊C4—34no—
75#63899—34no—
76#63896—34no—
77#63895—34no—
78#63888—34no—
79#63887—34no—
80#63887—34no—
81#63871—34no—
82#63857—34no—
83#63851—34no—
84C22×C3⋊(C3⋊D3)C2311yescharacteristic
85C22×C3×C3⋊D3C2311yescharacteristic
86C22×C32×D3C2311yescharacteristic
87C2×D3×C3⋊D3—41no—
88C2×D3×C3⋊D3—41no—
89C2×D3×C3⋊D3Q814yescomplemented
90C2×C33×C4C2311yescharacteristic
91C2×C33×C4C2311yescharacteristic
92C2×C33×C4C2311yescharacteristic
93C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
94C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
95C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
96C4×C3⋊(C3⋊D3)—41no—
97#6308—41no—
98C2×C3×C3⋊Dic3C2311yescharacteristic
99C2×C3×C3⋊Dic3C2311yescharacteristic
100C2×C3×C3⋊Dic3C2311yescharacteristic
101C3×C4×C3⋊D3—41no—
102C3×#634—41no—
103C2×C32×Dic3C2311yescharacteristic
104C2×C32×Dic3C2311yescharacteristic
105C2×C32×Dic3C2311yescharacteristic
106C32×C4×D3—41no—
107C32×Dic6—41no—
108#6293—41no—
109#6289—41no—
110Dic3×C3⋊D3—41no—
111D3×C3⋊Dic3—41no—
112#5634—94no—
113#5634—91no—
114C23×C3⋊D3—31no—
115C22×D32—34no—
116C2×C32×Q8—31no—
117C22×C32×C4—31no—
118C22×C3⋊Dic3—31no—
119C2×C4×C3⋊D3—31no—
120C2×C4×C3⋊D3—31no—
121C2×C4×C3⋊D3—34no—
122C2×C4×C3⋊D3—31no—
123C2×C4×C3⋊D3—64no—
124C2×C4×C3⋊D3C2×D311yescharacteristic
125C2×#634—31no—
126C2×#634—34no—
127C2×#634—31no—
128C2×#634—64no—
129C2×#634C2×D311yescharacteristic, complemented
130C2×C3×C4×D3—34no—
131C2×C3×C4×D3C2×D314yes—
132C2×C3×Dic6—34no—
133C2×C3×Dic6C2×D314yescomplemented
134C2×#627—34no—
135C2×#624—34no—
136C2×D3×Dic3—34no—
137C2×D3×Dic3—34no—
138C32×C4⋊C4—24no—
139C32×C4⋊C4—31no—
140C32×C4⋊C4—31no—
141C32×C4⋊C4C2×D314yescomplemented
142C32×C4⋊C4C2×D311yescharacteristic, complemented
143C32×C22⋊C4—31no—
144C32×C22⋊C4—31no—
145#3757—31no—
146#3757—31no—
147#3752—31no—
148#3752—31no—
149#3752—31no—
150#3752—31no—
151#3752—34no—
152#3752—34no—
153#3752—31no—
154#3752—31no—
155#3752—64no—
156#3752—64no—
157#3752C2×D311yescharacteristic
158#3752C2×D311yescharacteristic
159C4⋊(C3⋊Dic3)—31no—
160C4⋊(C3⋊Dic3)—31no—
161C4⋊(C3⋊Dic3)—31no—
162#3750—31no—
163#3750—31no—
164#3750—34no—
165#3750—34no—
166#3750—31no—
167#3750—31no—
168#3750—64no—
169#3750—64no—
170#3750C2×D311yescharacteristic, complemented
171#3750C2×D311yescharacteristic, complemented
172C3×(C2×D3)⋊C4—34no—
173C3×(C2×D3)⋊C4—34no—
174C3×(C2×D3)⋊C4C2×D314yes—
175C3×(C2×D3)⋊C4C2×D314yes—
176C3×C4⋊Dic3C2×D314yescomplemented
177C3×C4⋊Dic3C2×D314yescomplemented
178C3×Dic3⋊C4—34no—
179C3×Dic3⋊C4—34no—
180#3724—34no—
181Dic3⋊Dic3—34no—
182Dic3⋊Dic3—34no—
183Dic3⋊Dic3—34no—
184Dic3⋊Dic3—34no—
185#3722—34no—
186#3722—34no—
187(C2×D3)⋊Dic3—34no—
188(C2×D3)⋊Dic3—34no—
189(C2×D3)⋊Dic3—34no—
190(C2×D3)⋊Dic3—34no—
191C22×C33C2411yescharacteristic
192C2×C3⋊(C3⋊D3)—21no—
193C2×C3⋊(C3⋊D3)—21no—
194C2×C3⋊(C3⋊D3)C2×Q812yes—
195C2×C3×C3⋊D3—21no—
196C2×C3×C3⋊D3—21no—
197C2×C3×C3⋊D3C2×Q812yes—
198C2×C32×D3—21no—
199C2×C32×D3—21no—
200C2×C32×D3C2×Q812yes—
201D3×C3⋊D3—44no—
202C33×C4—21no—
203C33×C4—21no—
204C33×C4—21no—
205C3⋊(C3⋊Dic3)—21no—
206C3⋊(C3⋊Dic3)—21no—
207C3⋊(C3⋊Dic3)—21no—
208C3×C3⋊Dic3—21no—
209C3×C3⋊Dic3—21no—
210C3×C3⋊Dic3—21no—
211C32×Dic3—21no—
212C32×Dic3—21no—
213C32×Dic3—21no—
214C3×C22⋊Q8—34no—
215C3×C22⋊Q8—91no—
216#946—94no—
217#946—94no—
218#946—91no—
219#946—91no—
220C2×(C2×D3)⋊C4—94no—
221C2×(C2×D3)⋊C4—91no—
222#924—94no—
223#924—91no—
224#897—94no—
225#897—94no—
226#897—91no—
227#897C3⋊D311yescharacteristic, complemented
228#896—34no—
229#896—94no—
230#896—94no—
231#896—91no—
232#896—91no—
233#896—94no—
234#896—91no—
235#896—91no—
236#896—184no—
237D3×C22⋊C4—94no—
238D3×C22⋊C4—94no—
239D3×C22⋊C4—91no—
240D3×C22⋊C4—91no—
241#878—94no—
242#878—94no—
243#878—91no—
244#878—91no—
245C23×C32—31no—
246C22×C3⋊D3—31no—
247C22×C3⋊D3—34no—
248C22×C3⋊D3—34no—
249C22×C3⋊D3—64no—
250C22×C3⋊D3—121no—
251C22×C3⋊D3—121no—
252C22×C3⋊D3C22×D311yescharacteristic
253C22×C3×D3—34no—
254C22×C3×D3C22×D314yes—
255C2×D32—316no—
256C2×D32—124no—
257C2×D32—124no—
258C32×Q8—121no—
259C2×C32×C4—24no—
260C2×C32×C4—24no—
261C2×C32×C4—24no—
262C2×C32×C4—31no—
263C2×C32×C4—31no—
264C2×C32×C4—31no—
265C2×C32×C4—121no—
266C2×C32×C4C22×D314yes—
267C2×C32×C4C22×D314yes—
268C2×C32×C4C22×D314yes—
269C2×C32×C4C22×D311yescharacteristic
270C2×C32×C4C22×D311yescharacteristic
271C2×C32×C4C22×D311yescharacteristic
272C2×C3⋊Dic3—31no—
273C2×C3⋊Dic3—31no—
274C2×C3⋊Dic3—31no—
275C2×C3⋊Dic3—34no—
276C2×C3⋊Dic3—34no—
277C2×C3⋊Dic3—34no—
278C2×C3⋊Dic3—64no—
279C2×C3⋊Dic3—64no—
280C2×C3⋊Dic3—64no—
281C2×C3⋊Dic3—121no—
282C2×C3⋊Dic3C22×D311yescharacteristic
283C2×C3⋊Dic3C22×D311yescharacteristic
284C2×C3⋊Dic3C22×D311yescharacteristic
285C4×C3⋊D3—41no—
286C4×C3⋊D3—121no—
287C4×C3⋊D3—121no—
288C4×C3⋊D3—124no—
289C4×C3⋊D3—128no—
290C4×C3⋊D3—121no—
291#634—41no—
292#634—121no—
293#634—121no—
294#634—124no—
295#634—128no—
296C2×C3×Dic3—34no—
297C2×C3×Dic3—34no—
298C2×C3×Dic3—34no—
299C2×C3×Dic3C22×D314yes—
300C2×C3×Dic3C22×D314yes—
301C2×C3×Dic3C22×D314yes—
302C3×C4×D3—44no—
303C3×C4×D3—124no—
304C3×Dic6—44no—
305C3×Dic6—124no—
306#627—124no—
307#624—124no—
308D3×Dic3—124no—
309D3×Dic3—124no—
310#543—271noSylow
311C2×C33C22×Q811yescharacteristic
312C2×C33H(5,𝔽2)11yescharacteristic
313C2×C33H(5,𝔽2)11yescharacteristic
314C3⋊(C3⋊D3)—22no—
315C3×C3⋊D3—22no—
316C32×D3—22no—
317C23×D3—94no—
318C23×D3—91no—
319C2×C3×Q8—34no—
320C2×C3×Q8—91no—
321C22×C3×C4—34no—
322C22×C3×C4—91no—
323C22×Dic3—94no—
324C22×Dic3—91no—
325C2×C4×D3—34no—
326C2×C4×D3—94no—
327C2×C4×D3—94no—
328C2×C4×D3—91no—
329C2×C4×D3—94no—
330C2×C4×D3—91no—
331C2×C4×D3—91no—
332C2×C4×D3—184no—
333C2×C4×D3C2×C3⋊D311yescharacteristic
334C2×Dic6—34no—
335C2×Dic6—94no—
336C2×Dic6—94no—
337C2×Dic6—91no—
338C2×Dic6—91no—
339C2×Dic6—184no—
340C2×Dic6C2×C3⋊D311yescharacteristic, complemented
341C3×C4⋊C4—24no—
342C3×C4⋊C4—34no—
343C3×C4⋊C4—34no—
344C3×C4⋊C4—91no—
345C3×C4⋊C4—91no—
346C3×C4⋊C4D3214yescomplemented
347C3×C4⋊C4C2×C3⋊D311yescharacteristic, complemented
348C3×C22⋊C4—34no—
349C3×C22⋊C4—34no—
350C3×C22⋊C4—91no—
351C3×C22⋊C4—91no—
352#217—94no—
353#217—94no—
354#217—91no—
355#217—91no—
356(C2×D3)⋊C4—34no—
357(C2×D3)⋊C4—34no—
358(C2×D3)⋊C4—94no—
359(C2×D3)⋊C4—94no—
360(C2×D3)⋊C4—94no—
361(C2×D3)⋊C4—94no—
362(C2×D3)⋊C4—91no—
363(C2×D3)⋊C4—91no—
364(C2×D3)⋊C4—94no—
365(C2×D3)⋊C4—94no—
366(C2×D3)⋊C4—91no—
367(C2×D3)⋊C4—91no—
368(C2×D3)⋊C4—91no—
369(C2×D3)⋊C4—91no—
370(C2×D3)⋊C4—184no—
371(C2×D3)⋊C4—184no—
372(C2×D3)⋊C4C2×C3⋊D311yescharacteristic
373(C2×D3)⋊C4C2×C3⋊D311yescharacteristic
374C4⋊Dic3—94no—
375C4⋊Dic3—94no—
376C4⋊Dic3—94no—
377C4⋊Dic3—91no—
378C4⋊Dic3C2×C3⋊D311yescharacteristic, complemented
379C4⋊Dic3C2×C3⋊D311yescharacteristic, complemented
380Dic3⋊C4—34no—
381Dic3⋊C4—34no—
382Dic3⋊C4—94no—
383Dic3⋊C4—94no—
384Dic3⋊C4—94no—
385Dic3⋊C4—94no—
386Dic3⋊C4—91no—
387Dic3⋊C4—91no—
388Dic3⋊C4—91no—
389Dic3⋊C4—91no—
390Dic3⋊C4—91no—
391Dic3⋊C4—91no—
392Dic3⋊C4—184no—
393Dic3⋊C4—184no—
394C22×C32—24no—
395C22×C32—32no—
396C22×C32—61no—
397C22×C32—61no—
398C22×C32C23×D314yes—
399C22×C32C23×D311yescharacteristic
400C2×C3⋊D3—21no—
401C2×C3⋊D3—21no—
402C2×C3⋊D3—32no—
403C2×C3⋊D3—38no—
404C2×C3⋊D3—68no—
405C2×C3⋊D3—61no—
406C2×C3⋊D3—61no—
407C2×C3⋊D3—64no—
408C2×C3⋊D3—64no—
409C2×C3⋊D3—124no—
410C2×C3⋊D3—124no—
411C2×C3⋊D3—124no—
412C2×C3⋊D3D3×Q812yes—
413C2×C3×D3—24no—
414C2×C3×D3—24no—
415C2×C3×D3—38no—
416C2×C3×D3—64no—
417C2×C3×D3—64no—
418C2×C3×D3D3×Q818yes—
419D32—1216no—
420C32×C4—21no—
421C32×C4—21no—
422C32×C4—21no—
423C32×C4—24no—
424C32×C4—24no—
425C32×C4—24no—
426C32×C4—44no—
427C32×C4—44no—
428C32×C4—44no—
429C32×C4—61no—
430C32×C4—61no—
431C32×C4—61no—
432C3⋊Dic3—21no—
433C3⋊Dic3—21no—
434C3⋊Dic3—21no—
435C3⋊Dic3—68no—
436C3⋊Dic3—61no—
437C3⋊Dic3—61no—
438C3⋊Dic3—64no—
439C3⋊Dic3—61no—
440C3⋊Dic3—64no—
441C3⋊Dic3—64no—
442C3⋊Dic3—124no—
443C3⋊Dic3—124no—
444C3×Dic3—24no—
445C3×Dic3—24no—
446C3×Dic3—24no—
447C3×Dic3—64no—
448C3×Dic3—64no—
449C3×Dic3—64no—
450C22⋊Q8—31no—
451C22⋊Q8—91no—
452C22⋊Q8—271no—
453C22⋊Q8—271no—
454C22⋊Q8—271no—
455C22⋊Q8—271no—
456C22⋊Q8—271no—
457C22⋊Q8—271no—
458C22⋊Q8—271no—
459C22⋊Q8—271no—
460C22⋊Q8—271no—
461C22⋊Q8—271no—
462C2×C22⋊C4—271no—
463C2×C22⋊C4—271no—
464C2×C22⋊C4—271no—
465C33#54311yescharacteristic, complemented, Sylow
466C23×C3—34no—
467C23×C3—91no—
468C22×D3—34no—
469C22×D3—916no—
470C22×D3—94no—
471C22×D3—91no—
472C22×D3—94no—
473C22×D3—184no—
474C22×D3—361no—
475C22×D3—361no—
476C22×D3—364no—
477C22×D3—364no—
478C22×D3C22×C3⋊D311yescharacteristic
479C3×Q8—124no—
480C3×Q8—361no—
481C2×C3×C4—24no—
482C2×C3×C4—24no—
483C2×C3×C4—24no—
484C2×C3×C4—34no—
485C2×C3×C4—34no—
486C2×C3×C4—34no—
487C2×C3×C4—91no—
488C2×C3×C4—91no—
489C2×C3×C4—91no—
490C2×C3×C4—124no—
491C2×C3×C4—361no—
492C2×C3×C4C2×D3214yes—
493C2×C3×C4C2×D3214yes—
494C2×C3×C4C2×D3214yes—
495C2×C3×C4C22×C3⋊D311yescharacteristic
496C2×C3×C4C22×C3⋊D311yescharacteristic
497C2×C3×C4C22×C3⋊D311yescharacteristic
498C2×Dic3—34no—
499C2×Dic3—34no—
500C2×Dic3—34no—
501C2×Dic3—94no—
502C2×Dic3—94no—
503C2×Dic3—94no—
504C2×Dic3—91no—
505C2×Dic3—91no—
506C2×Dic3—91no—
507C2×Dic3—184no—
508C2×Dic3—184no—
509C2×Dic3—184no—
510C2×Dic3—361no—
511C2×Dic3—364no—
512C2×Dic3C22×C3⋊D311yescharacteristic
513C2×Dic3C22×C3⋊D311yescharacteristic
514C2×Dic3C22×C3⋊D311yescharacteristic
515C4×D3—41no—
516C4×D3—124no—
517C4×D3—361no—
518C4×D3—364no—
519C4×D3—364no—
520C4×D3—361no—
521C4×D3—368no—
522C4×D3—364no—
523C4×D3—361no—
524Dic6—41no—
525Dic6—124no—
526Dic6—361no—
527Dic6—364no—
528Dic6—364no—
529Dic6—361no—
530Dic6—368no—
531C2×C32—24no—
532C2×C32—24no—
533C2×C32—24no—
534C2×C32—62no—
535C2×C32#100414yes—
536C2×C32#100411yescharacteristic
537C2×C32C2×D3×Q814yes—
538C2×C32C2×D3×Q811yescharacteristic
539C2×C32#100914yes—
540C2×C32#100911yescharacteristic
541C3⋊D3—22no—
542C3⋊D3—62no—
543C3⋊D3—68no—
544C3⋊D3—128no—
545C3×D3—28no—
546C3×D3—68no—
547C24—271no—
548C2×Q8—31no—
549C2×Q8—91no—
550C2×Q8—271no—
551C2×Q8—271no—
552C22×C4—31no—
553C22×C4—91no—
554C22×C4—271no—
555C22×C4—271no—
556C22×C4—271no—
557C22×C4—271no—
558C4⋊C4—31no—
559C4⋊C4—31no—
560C4⋊C4—91no—
561C4⋊C4—91no—
562C4⋊C4—271no—
563C4⋊C4—271no—
564C4⋊C4—271no—
565C4⋊C4—271no—
566C4⋊C4—271no—
567C4⋊C4—271no—
568C4⋊C4—271no—
569C4⋊C4D3×C3⋊D311yescharacteristic, complemented
570C22⋊C4—31no—
571C22⋊C4—31no—
572C22⋊C4—91no—
573C22⋊C4—91no—
574C22⋊C4—271no—
575C22⋊C4—271no—
576C22⋊C4—271no—
577C22⋊C4—271no—
578C22⋊C4—271no—
579C22⋊C4—271no—
580C22⋊C4—271no—
581C22⋊C4—271no—
582C22×C3—24no—
583C22×C3—38no—
584C22×C3—64no—
585C22×C3—64no—
586C22×C3—92no—
587C22×C3—181no—
588C22×C3—181no—
589C22×C3C22×D3214yes—
590C22×C3C23×C3⋊D311yescharacteristic
591C2×D3—21no—
592C2×D3—21no—
593C2×D3—38no—
594C2×D3—64no—
595C2×D3—64no—
596C2×D3—98no—
597C2×D3—92no—
598C2×D3—188no—
599C2×D3—184no—
600C2×D3—184no—
601C2×D3—181no—
602C2×D3—181no—
603C2×D3—364no—
604C2×D3—364no—
605C2×D3—364no—
606C2×D3—3616no—
607C2×D3Q8×C3⋊D312yes—
608C3×C4—24no—
609C3×C4—24no—
610C3×C4—24no—
611C3×C4—21no—
612C3×C4—21no—
613C3×C4—21no—
614C3×C4—44no—
615C3×C4—44no—
616C3×C4—44no—
617C3×C4—64no—
618C3×C4—64no—
619C3×C4—64no—
620C3×C4—181no—
621C3×C4—181no—
622C3×C4—181no—
623Dic3—21no—
624Dic3—21no—
625Dic3—21no—
626Dic3—64no—
627Dic3—64no—
628Dic3—64no—
629Dic3—188no—
630Dic3—184no—
631Dic3—184no—
632Dic3—184no—
633Dic3—181no—
634Dic3—181no—
635Dic3—181no—
636Dic3—364no—
637Dic3—364no—
638C32—24no—
639C32#563414yescomplemented
640C32#563411yescharacteristic, complemented
641C23—31no—
642C23—91no—
643C23—274no—
644C23—271no—
645C23—1081no—
646C23—1081no—
647Q8—121no—
648Q8—361no—
649Q8—1081no—
650Q8—1081no—
651C2×C4—31no—
652C2×C4—31no—
653C2×C4—31no—
654C2×C4—91no—
655C2×C4—91no—
656C2×C4—91no—
657C2×C4—121no—
658C2×C4—271no—
659C2×C4—271no—
660C2×C4—271no—
661C2×C4—361no—
662C2×C4—1081no—
663C2×C4—1081no—
664C2×C4—1081no—
665C2×C4—1081no—
666C2×C4C2×D3×C3⋊D311yescharacteristic
667C2×C4C2×D3×C3⋊D311yescharacteristic
668C2×C4C2×D3×C3⋊D311yescharacteristic
669C2×C3—24no—
670C2×C3—24no—
671C2×C3—24no—
672C2×C3—68no—
673C2×C3—182no—
674C2×C3#6430714yes—
675C2×C3#6431414yes—
676C2×C3D32×Q814yes—
677C2×C3#6436111yescharacteristic
678C2×C3C2×Q8×C3⋊D311yescharacteristic
679C2×C3#6436611yescharacteristic
680D3—22no—
681D3—68no—
682D3—182no—
683D3—188no—
684D3—368no—
685C22—32no—
686C22—61no—
687C22—61no—
688C22—92no—
689C22—181no—
690C22—181no—
691C22—272no—
692C22—541no—
693C22—541no—
694C22—1084no—
695C22C22×D3×C3⋊D311yescharacteristic
696C4—21no—
697C4—21no—
698C4—21no—
699C4—61no—
700C4—61no—
701C4—61no—
702C4—181no—
703C4—181no—
704C4—181no—
705C4—541no—
706C4—541no—
707C4—541no—
708C3—24no—
709C3#1059463514yescomplemented
710C3#1059610511yescharacteristic, complemented
711C2—62no—
712C2—182no—
713C2—542no—
714C2#1172457911yescharacteristic
715C2#1172458911yescharacteristic
716C2D3×Q8×C3⋊D311yescharacteristic
subgroupG/H
center, FrattiniC22C22×D3×C3⋊D3
commutator, socle, cosocleC22×C33C24
FittingC33×C4⋊C4C22
prime radicalC22×D3×C3⋊D3C22
hypercenterC4⋊C4D3×C3⋊D3
hypocenterC33#543
LCSG ▷ C22×C33 ▷ C33
UCSC1 ◁ C22 ◁ C4⋊C4

Complements

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

NH ≅ G/Ntype
1. #11723937C2semidirect
2. C3×#64105C2semidirect
3. C32×#897C2semidirect
7. #11723502C2semidirect
8. #11723496C2semidirect
9. #11723495C2semidirect
10. #11723487C2semidirect
11. #11723477C2semidirect
12. #11723476C2semidirect
13. #11723449C2semidirect
14. #11723431C2semidirect
15. #11723415C2semidirect
20. C2×#6308C22semidirect
22. C2×C3×#634C22semidirect
24. C2×C32×Dic6C22semidirect
25. C2×#6293C22semidirect
29. C33×C4⋊C4C22semidirect
32. #88857C22semidirect
33. #88857C22semidirect
36. C3×#3750C22semidirect
37. C3×#3750C22semidirect
40. C32×C4⋊Dic3C22semidirect
41. C32×C4⋊Dic3C22semidirect
42. #88807C22semidirect
43. #88806C22semidirect
44. Dic3⋊(C3⋊Dic3)C22semidirect
45. Dic3⋊(C3⋊Dic3)C22semidirect
46. Dic3⋊(C3⋊Dic3)C22semidirect
65. #64105D3semidirect
70. C3×#897D3semidirect
89. C2×D3×C3⋊D3Q8semidirect
129. C2×#634C2×D3semidirect
133. C2×C3×Dic6C2×D3semidirect
141. C32×C4⋊C4C2×D3semidirect
142. C32×C4⋊C4C2×D3semidirect
170. #3750C2×D3semidirect
171. #3750C2×D3semidirect
176. C3×C4⋊Dic3C2×D3semidirect
177. C3×C4⋊Dic3C2×D3semidirect
227. #897C3⋊D3semidirect
340. C2×Dic6C2×C3⋊D3semidirect
346. C3×C4⋊C4D32semidirect
347. C3×C4⋊C4C2×C3⋊D3semidirect
378. C4⋊Dic3C2×C3⋊D3semidirect
379. C4⋊Dic3C2×C3⋊D3semidirect
465. C33#543semidirect
569. C4⋊C4D3×C3⋊D3semidirect
639. C32#5634semidirect
640. C32#5634semidirect
709. C3#10594635semidirect
710. C3#10596105semidirect

Maximal subgroups

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

subgroupindex
#117239372
C3×#641052
C32×#8972
#117235392
C3⋊D3×(C2×D3)⋊C42
D3×#37522
#117235022
#117234962
#117234952
#117234872
#117234772
#117234762
#117234492
#117234312
#117234152
#105961053
#105946353