Finite Group Databasebeta

← #13175481

Subgroups — #13175481

Order 1728.

2500 conjugacy classes of subgroups.

The subgroup lattice has 830 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#6289C211yesmaximal, characteristic, complemented
2C2×#89022C211yesmaximal, characteristic, complemented
3#11723923C211yesmaximal, characteristic, complemented
4C3×#64087C211yesmaximal, characteristic, complemented
5C32×#67⋊C4C211yesmaximal, characteristic, complemented
6#11723638C211yesmaximal, characteristic, complemented
7#11723635C211yesmaximal, characteristic, complemented
8#11723618C211yesmaximal, characteristic, complemented
9#11723525C211yesmaximal, characteristic, complemented
10#11723510C211yesmaximal, characteristic, complemented
11#11723498C211yesmaximal, characteristic, complemented
12#11723489C211yesmaximal, characteristic, complemented
13#11723484C211yesmaximal, characteristic, complemented
14#11723468C211yesmaximal, characteristic, complemented
15#11723422C211yesmaximal, characteristic, complemented
16#10596018—31nomaximal
17#10594066—34nomaximal
18C23×C3⋊(C3⋊D3)C2211yescharacteristic
19C2×#6312C2211yescharacteristic
20C2×C4⋊(C3⋊(C3⋊D3))C2211yescharacteristic
21C2×C4⋊(C3⋊(C3⋊D3))C2211yescharacteristic
22C22×C3×C3⋊Dic3C2211yescharacteristic
23C2×C3×#634C2211yescharacteristic, complemented
24C2×C32×#67C2211yescharacteristic
25C22×C32×Dic3C2211yescharacteristic
26C2×C32×C4×D3C2211yescharacteristic, complemented
27C2×#6291C2211yescharacteristic
28C2×#6291C2211yescharacteristic
29C2×#6291C2211yescharacteristic, complemented
30C2×#6289—24no—
31C2×#6289C2211yescharacteristic
32C2×#6289C2211yescharacteristic
33C2×#6289C2211yescharacteristic
34C2×#6289C2211yescharacteristic
35C2×#6289C2211yescharacteristic, complemented
36#89022—24no—
37C33×C22⋊C4C2211yescharacteristic
38#88859C2211yescharacteristic
39#88859C2211yescharacteristic
40C3×#3757C2211yescharacteristic
41C3×C4⋊(C3⋊Dic3)C2211yescharacteristic, complemented
42C3×#3750C2211yescharacteristic, complemented
43C3×#3750C2211yescharacteristic, complemented
44C32×(C2×D3)⋊C4C2211yescharacteristic, complemented
45C32×Dic3⋊C4C2211yescharacteristic, complemented
46C32×C4×Dic3C2211yescharacteristic, complemented
47#88807C2211yescharacteristic, complemented
48#88806C2211yescharacteristic, complemented
49#88804C2211yescharacteristic
50#88804C2211yescharacteristic
51#88804C2211yescharacteristic, complemented
52#88804C2211yescharacteristic, complemented
53(C2×D3)⋊(C3⋊Dic3)C2211yescharacteristic, complemented
54Dic3×C3⋊Dic3C2211yescharacteristic, complemented
55C2×#3828—31no—
56C22×C4×C3⋊D3—31no—
57C22×#624—34no—
58C2×#3799—34no—
59C32×C4×D4—31no—
60#64148—31no—
61#64146—31no—
62C4×#638—31no—
63C4×#638—31no—
64#64105—31no—
65#64103—31no—
66#64093—31no—
67#64092—31no—
68#64091—31no—
69#64091—34no—
70#64091—64no—
71#64087D311yescharacteristic, complemented
72C4×C4⋊(C3⋊D3)—31no—
73#64081—31no—
74C3×#67⋊C4D314yescomplemented
75C3×#878—34no—
76#63981—34no—
77#63978—34no—
78#63952—34no—
79#63910—34no—
80#63904—34no—
81#63897—34no—
82#63894—34no—
83#63888—34no—
84#63854—34no—
85#63836—34no—
86C23×C33C2311yescharacteristic
87C22×C3⋊(C3⋊D3)—22no—
88C22×C3⋊(C3⋊D3)—22no—
89C22×C3⋊(C3⋊D3)—22no—
90C22×C3⋊(C3⋊D3)C2311yescharacteristic
91C22×C3⋊(C3⋊D3)C2311yescharacteristic
92C22×C3⋊(C3⋊D3)C2311yescharacteristic
93C22×C32×D3C2311yescharacteristic
94C2×C33×C4C2311yescharacteristic
95C2×C33×C4C2311yescharacteristic
96#6312—22no—
97C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
98C4⋊(C3⋊(C3⋊D3))—22no—
99C4⋊(C3⋊(C3⋊D3))—22no—
100C2×C3×C3⋊Dic3—22no—
101C2×C3×C3⋊Dic3C2311yescharacteristic
102C2×C3×C3⋊Dic3C2311yescharacteristic
103C2×C3×C3⋊Dic3C2311yescharacteristic
104C2×C3×C3⋊Dic3C2311yescharacteristic
105C3×#634—22no—
106C32×#67—22no—
107C2×C32×Dic3—22no—
108C2×C32×Dic3C2311yescharacteristic
109C2×C32×Dic3C2311yescharacteristic
110C2×C32×Dic3C2311yescharacteristic
111C32×C4×D3—22no—
112#6291—22no—
113#6291—22no—
114#6291—22no—
115#6289—22no—
116#6289—22no—
117#6289—22no—
118#6289—22no—
119#6289D414yescomplemented
120#5627—91no—
121#5547—94no—
122C23×C3⋊D3—31no—
123C23×C3⋊D3—34no—
124C23×C3⋊D3—64no—
125C2×C32×D4—31no—
126C22×C32×C4—31no—
127C22×C32×C4—31no—
128C2×#638—31no—
129C2×#638—34no—
130C2×#638—31no—
131C2×#638—31no—
132C2×#638—31no—
133C2×#638—64no—
134C22×C3⋊Dic3C2×D311yescharacteristic
135#3828—64no—
136C2×C4⋊(C3⋊D3)—31no—
137C2×C4⋊(C3⋊D3)—31no—
138C2×C4⋊(C3⋊D3)—34no—
139C2×C4⋊(C3⋊D3)—34no—
140C2×C4⋊(C3⋊D3)—64no—
141C2×C4⋊(C3⋊D3)—64no—
142C2×C4×C3⋊D3—31no—
143C2×C4×C3⋊D3—31no—
144C2×C4×C3⋊D3—31no—
145C2×C4×C3⋊D3—31no—
146C2×C4×C3⋊D3—31no—
147C2×C4×C3⋊D3—64no—
148C2×#634C2×D311yescharacteristic, complemented
149C2×C3×#67C2×D314yes—
150C22×C3×Dic3—34no—
151C22×C3×Dic3C2×D314yes—
152C2×C3×C4×D3C2×D314yescomplemented
153C2×C3×Dic6—34no—
154C2×#626—34no—
155C2×#626—34no—
156C2×#626—34no—
157C2×#624—34no—
158C2×#624—34no—
159C2×#624—34no—
160C2×#624—34no—
161C2×#624—34no—
162C2×#624—616no—
163#3799—616no—
164C32×C4⋊C4—31no—
165C32×C22⋊C4—24no—
166C32×C22⋊C4—31no—
167C32×C22⋊C4C2×D314yes—
168C32×C22⋊C4C2×D311yescharacteristic
169C32×C42—31no—
170#3757—31no—
171#3757C2×D311yescharacteristic
172#3752—31no—
173#3752—31no—
174#3752—34no—
175#3752—34no—
176#3752—31no—
177#3752—31no—
178#3752—31no—
179#3752—31no—
180#3752—64no—
181#3752—64no—
182C4⋊(C3⋊Dic3)C2×D311yescharacteristic, complemented
183#3750—31no—
184#3750—31no—
185#3750C2×D311yescharacteristic, complemented
186#3750C2×D311yescharacteristic, complemented
187C4×C3⋊Dic3—31no—
188C3×#217—34no—
189C3×(C2×D3)⋊C4C2×D314yescomplemented
190C3×C4⋊Dic3—34no—
191C3×Dic3⋊C4—34no—
192C3×Dic3⋊C4—34no—
193C3×Dic3⋊C4C2×D314yescomplemented
194C3×C4×Dic3C2×D314yescomplemented
195#3724—34no—
196Dic3⋊Dic3—34no—
197#3722—34no—
198#3722—34no—
199#3722—34no—
200#3722—34no—
201(C2×D3)⋊Dic3—34no—
202Dic32—34no—
203C22×C33—21no—
204C22×C33—21no—
205C22×C33#4112yescomplemented
206C22×C33C2411yescharacteristic
207C2×C3⋊(C3⋊D3)—28no—
208C2×C3⋊(C3⋊D3)—21no—
209C2×C3⋊(C3⋊D3)—21no—
210C2×C3⋊(C3⋊D3)—21no—
211C2×C3⋊(C3⋊D3)—21no—
212C2×C3⋊(C3⋊D3)—21no—
213C2×C3⋊(C3⋊D3)—21no—
214C2×C3⋊(C3⋊D3)—21no—
215C2×C3⋊(C3⋊D3)C2×D412yes—
216C2×C3⋊(C3⋊D3)#4112yescomplemented
217C2×C32×D3—21no—
218C2×C32×D3—21no—
219C2×C32×D3—21no—
220C33×C4—21no—
221C33×C4—21no—
222C3⋊(C3⋊Dic3)—21no—
223C3×C3⋊Dic3—21no—
224C3×C3⋊Dic3—21no—
225C3×C3⋊Dic3—21no—
226C3×C3⋊Dic3C2×D412yes—
227C32×Dic3—21no—
228C32×Dic3—21no—
229C32×Dic3C2×D412yes—
230C2×#239—91no—
231C2×#235—94no—
232C22×C4×D3—94no—
233C22×C4×D3—91no—
234C3×C22⋊Q8—91no—
235C3×C4×D4—34no—
236#946—91no—
237#939—94no—
238#937—94no—
239#930—91no—
240C4×#67—94no—
241C4×#67—94no—
242#896—94no—
243#895—91no—
244#894—94no—
245#894—91no—
246#894—91no—
247#893—91no—
248#893—91no—
249#892—91no—
250#884—94no—
251#883—94no—
252#882—91no—
253#882—94no—
254#882—91no—
255#882—184no—
256#67⋊C4—91no—
257#67⋊C4C3⋊D311yescharacteristic, complemented
258#878—34no—
259C4×D12—94no—
260#872—94no—
261C23×C32—24no—
262C23×C32—31no—
263C23×C32C22×D314yes—
264C23×C32C22×D311yescharacteristic
265C22×C3⋊D3—31no—
266C22×C3⋊D3—31no—
267C22×C3⋊D3—31no—
268C22×C3⋊D3—34no—
269C22×C3⋊D3—34no—
270C22×C3⋊D3—34no—
271C22×C3⋊D3—64no—
272C22×C3⋊D3—64no—
273C22×C3⋊D3—64no—
274C22×C3⋊D3—62no—
275C22×C3⋊D3—62no—
276C22×C3⋊D3—62no—
277C22×C3⋊D3—68no—
278C22×C3⋊D3—68no—
279C22×C3⋊D3—68no—
280C22×C3⋊D3—128no—
281C22×C3⋊D3—128no—
282C22×C3⋊D3—128no—
283C22×C3×D3C22×D314yes—
284C32×D4—62no—
285C2×C32×C4—24no—
286C2×C32×C4—24no—
287C2×C32×C4—31no—
288C2×C32×C4—31no—
289C2×C32×C4—31no—
290C2×C32×C4—62no—
291C2×C32×C4—62no—
292C2×C32×C4C22×D314yes—
293C2×C32×C4C22×D314yes—
294C2×C32×C4C22×D311yescharacteristic
295C2×C32×C4C22×D311yescharacteristic
296#638—62no—
297#638—62no—
298#638—62no—
299#638—62no—
300#638—68no—
301#638—128no—
302C2×C3⋊Dic3—22no—
303C2×C3⋊Dic3—31no—
304C2×C3⋊Dic3—34no—
305C2×C3⋊Dic3—64no—
306C2×C3⋊Dic3C22×D311yescharacteristic
307C2×C3⋊Dic3C22×D311yescharacteristic
308C2×C3⋊Dic3C22×D311yescharacteristic
309C2×C3⋊Dic3C22×D311yescharacteristic
310C4⋊(C3⋊D3)—62no—
311C4⋊(C3⋊D3)—62no—
312C4⋊(C3⋊D3)—68no—
313C4⋊(C3⋊D3)—68no—
314C4⋊(C3⋊D3)—128no—
315C4⋊(C3⋊D3)—128no—
316C4×C3⋊D3—34no—
317C4×C3⋊D3—62no—
318C4×C3⋊D3—62no—
319C4×C3⋊D3—62no—
320C4×C3⋊D3—62no—
321#634—22no—
322C3×#67—28no—
323C2×C3×Dic3—28no—
324C2×C3×Dic3—34no—
325C2×C3×Dic3—34no—
326C2×C3×Dic3—34no—
327C2×C3×Dic3—34no—
328C2×C3×Dic3—68no—
329C2×C3×Dic3C22×D314yes—
330C2×C3×Dic3C22×D314yes—
331C2×C3×Dic3C22×D314yes—
332C3×C4×D3—28no—
333C3×Dic6—68no—
334#626—68no—
335#626—68no—
336#626—68no—
337#624—316no—
338#624—68no—
339#624—68no—
340#624—68no—
341#624—68no—
342#525—271noSylow
343C2×C33—22no—
344C2×C33C22×D411yescharacteristic
345C2×C33C2×#4111yescharacteristic
346C2×C33C2×#4111yescharacteristic
347C3⋊(C3⋊D3)—22no—
348C3⋊(C3⋊D3)—22no—
349C3⋊(C3⋊D3)—41no—
350C32×D3—41no—
351C23×D3—94no—
352C23×D3—91no—
353C23×D3—184no—
354C2×C3×Q8—91no—
355C2×C3×D4—34no—
356C22×C3×C4—34no—
357C22×C3×C4—34no—
358C22×C3×C4—91no—
359C2×#67—94no—
360C2×#67—94no—
361C2×#67—94no—
362C2×#67—94no—
363C2×#67—91no—
364C2×#67—184no—
365C2×#67C2×C3⋊D311yescharacteristic
366C22×Dic3—34no—
367C22×Dic3C2×C3⋊D311yescharacteristic
368#239—184no—
369#235—1816no—
370C2×D12—91no—
371C2×D12—91no—
372C2×D12—91no—
373C2×D12—94no—
374C2×D12—94no—
375C2×D12—91no—
376C2×D12—91no—
377C2×D12—184no—
378C2×D12—184no—
379C2×C4×D3—94no—
380C2×C4×D3—91no—
381C2×C4×D3—94no—
382C2×C4×D3—94no—
383C2×C4×D3—94no—
384C2×C4×D3—94no—
385C2×C4×D3—91no—
386C2×C4×D3—91no—
387C2×C4×D3—91no—
388C2×C4×D3—91no—
389C2×C4×D3—184no—
390C2×C4×D3—1816no—
391C2×C4×D3C2×C3⋊D311yescharacteristic, complemented
392C2×Dic6—34no—
393C3×C4⋊C4—34no—
394C3×C4⋊C4—91no—
395C3×C4⋊C4—91no—
396C3×C4⋊C4—91no—
397C3×C22⋊C4—24no—
398C3×C22⋊C4—34no—
399C3×C22⋊C4—91no—
400C3×C22⋊C4D3214yes—
401C3×C22⋊C4C2×C3⋊D311yescharacteristic
402C3×C42—34no—
403#217—34no—
404#217—94no—
405(C2×D3)⋊C4—94no—
406(C2×D3)⋊C4—94no—
407(C2×D3)⋊C4—94no—
408(C2×D3)⋊C4—94no—
409(C2×D3)⋊C4—91no—
410(C2×D3)⋊C4—94no—
411(C2×D3)⋊C4—94no—
412(C2×D3)⋊C4—91no—
413(C2×D3)⋊C4—91no—
414(C2×D3)⋊C4—91no—
415(C2×D3)⋊C4—91no—
416(C2×D3)⋊C4—91no—
417(C2×D3)⋊C4—91no—
418(C2×D3)⋊C4—184no—
419(C2×D3)⋊C4—184no—
420(C2×D3)⋊C4C2×C3⋊D311yescharacteristic, complemented
421C4⋊Dic3—34no—
422C4⋊Dic3—91no—
423Dic3⋊C4—34no—
424Dic3⋊C4—34no—
425Dic3⋊C4—94no—
426Dic3⋊C4—94no—
427Dic3⋊C4—91no—
428Dic3⋊C4C2×C3⋊D311yescharacteristic, complemented
429C4×Dic3—94no—
430C4×Dic3—91no—
431C4×Dic3C2×C3⋊D311yescharacteristic, complemented
432C22×C32—21no—
433C22×C32—21no—
434C22×C32—24no—
435C22×C32—28no—
436C22×C32—24no—
437C22×C32—24no—
438C22×C32—44no—
439C22×C32—44no—
440C22×C32—61no—
441C22×C32—61no—
442C22×C32—61no—
443C22×C32#23518yescomplemented
444C22×C32#23912yescomplemented
445C22×C32C23×D314yes—
446C22×C32C23×D311yescharacteristic
447C2×C3⋊D3—32no—
448C2×C3⋊D3—32no—
449C2×C3⋊D3—38no—
450C2×C3⋊D3—38no—
451C2×C3⋊D3—68no—
452C2×C3⋊D3—68no—
453C2×C3⋊D3—68no—
454C2×C3⋊D3—61no—
455C2×C3⋊D3—61no—
456C2×C3⋊D3—61no—
457C2×C3⋊D3—61no—
458C2×C3⋊D3—61no—
459C2×C3⋊D3—61no—
460C2×C3⋊D3—61no—
461C2×C3⋊D3—632no—
462C2×C3⋊D3—64no—
463C2×C3⋊D3—64no—
464C2×C3⋊D3—64no—
465C2×C3⋊D3—64no—
466C2×C3⋊D3—64no—
467C2×C3⋊D3—64no—
468C2×C3⋊D3—64no—
469C2×C3⋊D3—124no—
470C2×C3⋊D3—124no—
471C2×C3⋊D3—124no—
472C2×C3⋊D3—124no—
473C2×C3⋊D3—1232no—
474C2×C3⋊D3—124no—
475C2×C3⋊D3—124no—
476C2×C3⋊D3—124no—
477C2×C3×D3—24no—
478C2×C3×D3—24no—
479C2×C3×D3—24no—
480C32×C4—21no—
481C32×C4—21no—
482C32×C4—24no—
483C32×C4—24no—
484C32×C4—32no—
485C32×C4—44no—
486C32×C4—44no—
487C32×C4—61no—
488C32×C4—61no—
489C3⋊Dic3—21no—
490C3⋊Dic3—21no—
491C3⋊Dic3—21no—
492C3⋊Dic3—61no—
493C3⋊Dic3—64no—
494C3⋊Dic3—124no—
495C3⋊Dic3D3×D412yes—
496C3×Dic3—24no—
497C3×Dic3—24no—
498C3×Dic3—38no—
499C3×Dic3—64no—
500C3×Dic3—64no—
501C3×Dic3—64no—
502C3×Dic3D3×D418yes—
503C2×#41—271no—
504C23×C4—271no—
505#123—271no—
506#123—271no—
507C22⋊Q8—91no—
508C22⋊Q8—271no—
509#121—271no—
510#121—271no—
511#120—271no—
512#120—271no—
513C4×D4—31no—
514C4×D4—271no—
515C4×D4—271no—
516C4×D4—271no—
517#117—271no—
518C33#52511yescharacteristic, complemented, Sylow
519C23×C3—24no—
520C23×C3—34no—
521C23×C3C2×D3214yes—
522C23×C3C22×C3⋊D311yescharacteristic
523C22×D3—94no—
524C22×D3—94no—
525C22×D3—91no—
526C22×D3—91no—
527C22×D3—94no—
528C22×D3—91no—
529C22×D3—184no—
530C22×D3—184no—
531C22×D3—184no—
532C22×D3—182no—
533C22×D3—182no—
534C22×D3—188no—
535C22×D3—188no—
536C22×D3—188no—
537C22×D3—182no—
538C22×D3—368no—
539C22×D3—368no—
540C22×D3—368no—
541C22×D3C22×C3⋊D311yescharacteristic
542C3×Q8—182no—
543C3×D4—68no—
544C2×C3×C4—24no—
545C2×C3×C4—24no—
546C2×C3×C4—34no—
547C2×C3×C4—34no—
548C2×C3×C4—34no—
549C2×C3×C4—68no—
550C2×C3×C4—68no—
551C2×C3×C4—91no—
552C2×C3×C4—91no—
553C2×C3×C4—91no—
554C2×C3×C4—91no—
555C2×C3×C4—182no—
556C2×C3×C4C2×D3214yes—
557C2×C3×C4C2×D3214yes—
558C2×C3×C4C22×C3⋊D311yescharacteristic
559C2×C3×C4C22×C3⋊D311yescharacteristic
560#67—22no—
561#67—188no—
562#67—188no—
563#67—188no—
564#67—188no—
565#67—182no—
566#67—368no—
567C2×Dic3—22no—
568C2×Dic3—34no—
569C2×Dic3—34no—
570C2×Dic3—34no—
571C2×Dic3—34no—
572C2×Dic3—68no—
573C2×Dic3—94no—
574C2×Dic3—91no—
575C2×Dic3—184no—
576C2×Dic3C22×C3⋊D311yescharacteristic
577C2×Dic3C22×C3⋊D311yescharacteristic
578C2×Dic3C22×C3⋊D311yescharacteristic
579D12—182no—
580D12—182no—
581D12—188no—
582D12—188no—
583D12—182no—
584D12—182no—
585D12—182no—
586D12—368no—
587D12—368no—
588C4×D3—22no—
589C4×D3—916no—
590C4×D3—94no—
591C4×D3—182no—
592C4×D3—182no—
593C4×D3—188no—
594C4×D3—188no—
595C4×D3—188no—
596C4×D3—188no—
597C4×D3—182no—
598C4×D3—182no—
599Dic6—68no—
600C2×C32—22no—
601C2×C32—24no—
602C2×C32—24no—
603C2×C32—24no—
604C2×C32—28no—
605C2×C32—48no—
606C2×C32—121no—
607C2×C32C2×#23514yes—
608C2×C32C2×D3×D414yes—
609C2×C32C2×D3×D411yescharacteristic
610C2×C32C2×#23911yescharacteristic
611C2×C32D3×#4114yes—
612C2×C32D3×#4111yescharacteristic
613C3⋊D3—62no—
614C3⋊D3—62no—
615C3⋊D3—68no—
616C3⋊D3—68no—
617C3⋊D3—128no—
618C3⋊D3—128no—
619C3⋊D3—121no—
620C3⋊D3—124no—
621C3⋊D3—244no—
622C3×D3—44no—
623C24—271no—
624#41—544no—
625C2×Q8—91no—
626C2×D4—31no—
627C2×D4—271no—
628C2×D4—271no—
629C2×D4—271no—
630C2×D4—271no—
631C2×D4—271no—
632C2×D4—271no—
633C22×C4—31no—
634C22×C4—31no—
635C22×C4—91no—
636C22×C4—271no—
637C22×C4—271no—
638C22×C4—271no—
639C22×C4—271no—
640C22×C4—271no—
641C22×C4—544no—
642C4⋊C4—31no—
643C4⋊C4—91no—
644C4⋊C4—91no—
645C4⋊C4—91no—
646C4⋊C4—271no—
647C4⋊C4—271no—
648C22⋊C4—31no—
649C22⋊C4—91no—
650C22⋊C4—271no—
651C22⋊C4—271no—
652C22⋊C4—271no—
653C22⋊C4—271no—
654C22⋊C4—271no—
655C22⋊C4—271no—
656C22⋊C4—271no—
657C22⋊C4D3×C3⋊D311yescharacteristic
658C42—31no—
659C42—271no—
660C22×C3—24no—
661C22×C3—24no—
662C22×C3—21no—
663C22×C3—21no—
664C22×C3—24no—
665C22×C3—28no—
666C22×C3—44no—
667C22×C3—44no—
668C22×C3—64no—
669C22×C3—64no—
670C22×C3—64no—
671C22×C3#379918yescomplemented
672C22×C3#382812yescomplemented
673C22×C3C22×D3214yes—
674C22×C3C23×C3⋊D311yescharacteristic
675C2×D3—21no—
676C2×D3—21no—
677C2×D3—21no—
678C2×D3—98no—
679C2×D3—98no—
680C2×D3—92no—
681C2×D3—92no—
682C2×D3—188no—
683C2×D3—188no—
684C2×D3—188no—
685C2×D3—1832no—
686C2×D3—184no—
687C2×D3—184no—
688C2×D3—184no—
689C2×D3—184no—
690C2×D3—181no—
691C2×D3—181no—
692C2×D3—181no—
693C2×D3—181no—
694C2×D3—184no—
695C2×D3—184no—
696C2×D3—184no—
697C2×D3—181no—
698C2×D3—181no—
699C2×D3—181no—
700C2×D3—364no—
701C2×D3—364no—
702C2×D3—364no—
703C2×D3—364no—
704C2×D3—3632no—
705C2×D3—364no—
706C2×D3—364no—
707C2×D3—364no—
708C3×C4—24no—
709C3×C4—24no—
710C3×C4—21no—
711C3×C4—21no—
712C3×C4—38no—
713C3×C4—44no—
714C3×C4—44no—
715C3×C4—64no—
716C3×C4—64no—
717C3×C4—92no—
718C3×C4—181no—
719C3×C4—181no—
720C3×C4—181no—
721Dic3—21no—
722Dic3—21no—
723Dic3—38no—
724Dic3—64no—
725Dic3—64no—
726Dic3—64no—
727Dic3—184no—
728Dic3—181no—
729Dic3—364no—
730Dic3D4×C3⋊D312yes—
731C32—24no—
732C32#554714yescomplemented
733C32#562711yescharacteristic, complemented
734C23—31no—
735C23—271no—
736C23—271no—
737C23—271no—
738C23—542no—
739C23—542no—
740C23—542no—
741C23C2×D3×C3⋊D311yescharacteristic
742Q8—182no—
743D4—62no—
744D4—542no—
745D4—542no—
746D4—542no—
747D4—542no—
748D4—542no—
749D4—542no—
750C2×C4—31no—
751C2×C4—31no—
752C2×C4—31no—
753C2×C4—62no—
754C2×C4—62no—
755C2×C4—91no—
756C2×C4—91no—
757C2×C4—91no—
758C2×C4—91no—
759C2×C4—182no—
760C2×C4—274no—
761C2×C4—271no—
762C2×C4—542no—
763C2×C4—542no—
764C2×C4—542no—
765C2×C4—542no—
766C2×C4C2×D3×C3⋊D311yescharacteristic
767C2×C4C2×D3×C3⋊D311yescharacteristic
768C2×C3—28no—
769C2×C3—22no—
770C2×C3—24no—
771C2×C3—24no—
772C2×C3—24no—
773C2×C3—48no—
774C2×C3—124no—
775C2×C3C2×#379914yes—
776C2×C3D32×D414yes—
777C2×C3#6431214yes—
778C2×C3C2×#382811yescharacteristic
779C2×C3C2×D4×C3⋊D311yescharacteristic
780C2×C3#41×C3⋊D311yescharacteristic
781D3—41no—
782D3—188no—
783D3—188no—
784D3—182no—
785D3—182no—
786D3—368no—
787D3—368no—
788D3—364no—
789D3—361no—
790D3—724no—
791C22—21no—
792C22—21no—
793C22—61no—
794C22—61no—
795C22—61no—
796C22—272no—
797C22—272no—
798C22—548no—
799C22—541no—
800C22—541no—
801C22—541no—
802C22—541no—
803C22—541no—
804C22—541no—
805C22—541no—
806C22#8902212yescomplemented
807C22C22×D3×C3⋊D311yescharacteristic
808C4—21no—
809C4—21no—
810C4—32no—
811C4—61no—
812C4—61no—
813C4—92no—
814C4—181no—
815C4—181no—
816C4—181no—
817C4—541no—
818C3—24no—
819C3#1059406614yescomplemented
820C3#1059601811yescharacteristic, complemented
821C2—22no—
822C2—121no—
823C2—542no—
824C2—542no—
825C2—1081no—
826C2C2×#8902211yescharacteristic
827C2D3×D4×C3⋊D311yescharacteristic
828C2#1172458611yescharacteristic
subgroupG/H
center, FrattiniC22C22×D3×C3⋊D3
commutator, socle, cosocleC22×C33C24
FittingC33×C22⋊C4C22
hypercenterC22⋊C4D3×C3⋊D3
hypocenterC33#525
LCSG ▷ C22×C33 ▷ C33
UCSC1 ◁ C22 ◁ C22⋊C4

Complements

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

NH ≅ G/Ntype
1. C22×#6289C2semidirect
2. C2×#89022C2semidirect
3. #11723923C2semidirect
4. C3×#64087C2semidirect
5. C32×#67⋊C4C2semidirect
6. #11723638C2semidirect
7. #11723635C2semidirect
8. #11723618C2semidirect
9. #11723525C2semidirect
10. #11723510C2semidirect
11. #11723498C2semidirect
12. #11723489C2semidirect
13. #11723484C2semidirect
14. #11723468C2semidirect
15. #11723422C2semidirect
23. C2×C3×#634C22semidirect
26. C2×C32×C4×D3C22semidirect
29. C2×#6291C22semidirect
35. C2×#6289C22semidirect
41. C3×C4⋊(C3⋊Dic3)C22semidirect
42. C3×#3750C22semidirect
43. C3×#3750C22semidirect
44. C32×(C2×D3)⋊C4C22semidirect
45. C32×Dic3⋊C4C22semidirect
46. C32×C4×Dic3C22semidirect
47. #88807C22semidirect
48. #88806C22semidirect
51. #88804C22semidirect
52. #88804C22semidirect
53. (C2×D3)⋊(C3⋊Dic3)C22semidirect
54. Dic3×C3⋊Dic3C22semidirect
71. #64087D3semidirect
74. C3×#67⋊C4D3semidirect
119. #6289D4semidirect
148. C2×#634C2×D3semidirect
152. C2×C3×C4×D3C2×D3semidirect
182. C4⋊(C3⋊Dic3)C2×D3semidirect
185. #3750C2×D3semidirect
186. #3750C2×D3semidirect
189. C3×(C2×D3)⋊C4C2×D3semidirect
193. C3×Dic3⋊C4C2×D3semidirect
194. C3×C4×Dic3C2×D3semidirect
205. C22×C33#41semidirect
216. C2×C3⋊(C3⋊D3)#41semidirect
257. #67⋊C4C3⋊D3semidirect
391. C2×C4×D3C2×C3⋊D3semidirect
420. (C2×D3)⋊C4C2×C3⋊D3semidirect
428. Dic3⋊C4C2×C3⋊D3semidirect
431. C4×Dic3C2×C3⋊D3semidirect
443. C22×C32#235semidirect
444. C22×C32#239semidirect
518. C33#525semidirect
671. C22×C3#3799semidirect
672. C22×C3#3828semidirect
732. C32#5547semidirect
733. C32#5627semidirect
806. C22#89022semidirect
819. C3#10594066semidirect
820. C3#10596018semidirect

Maximal subgroups

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

subgroupindex
C22×#62892
C2×#890222
#117239232
C3×#640872
C32×#67⋊C42
#117236382
#117236352
#117236182
#117235252
#117235102
#117234982
#117234892
#117234842
#117234682
#117234222
#105960183
#105940663