Finite Group Databasebeta

← #13176586

Subgroups — #13176586

Order 1728.

1800 conjugacy classes of subgroups.

The subgroup lattice has 736 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11723935C211yesmaximal, characteristic, complemented
2C3×#64107C211yesmaximal, characteristic, complemented
3C32×#892C211yesmaximal, characteristic, complemented
4#11723542C211yesmaximal, characteristic
5#11723539C211yesmaximal, characteristic, complemented
6D3×#3752C211yesmaximal, characteristic, complemented
7#11723504C211yesmaximal, characteristic, complemented
8#11723500C211yesmaximal, characteristic, complemented
9#11723495C211yesmaximal, characteristic, complemented
10#11723484C211yesmaximal, characteristic, complemented
11#11723461C211yesmaximal, characteristic, complemented
12#11723452C211yesmaximal, characteristic, complemented
13#11723438C211yesmaximal, characteristic, complemented
14#11723416C211yesmaximal, characteristic, complemented
15#11723414C211yesmaximal, characteristic, complemented
16#10595998—31nomaximal
17#10594643—34nomaximal
18C22×D3×C3⋊D3C2211yescharacteristic
19C2×C4⋊(C3⋊(C3⋊D3))C2211yescharacteristic
20C2×C4×C3⋊(C3⋊D3)C2211yescharacteristic
21C2×C32×C4×D3C2211yescharacteristic
22C2×#6293C2211yescharacteristic, complemented
23C2×#6292C2211yescharacteristic
24C2×#6291C2211yescharacteristic
25C2×#6289C2211yescharacteristic
26C2×#6289C2211yescharacteristic, complemented
27C2×D3×C3⋊Dic3C2211yescharacteristic
28C33×C4⋊C4C2211yescharacteristic, complemented
29#88859C2211yescharacteristic
30#88859C2211yescharacteristic, complemented
31#88859C2211yescharacteristic, complemented
32#88857C2211yescharacteristic, complemented
33C3×#3752C2211yescharacteristic
34C3×#3752C2211yescharacteristic
35C3×#3752C2211yescharacteristic
36C3×C4⋊(C3⋊Dic3)C2211yescharacteristic, complemented
37C3×#3750C2211yescharacteristic, complemented
38C3×C4×C3⋊Dic3C2211yescharacteristic, complemented
39C32×(C2×D3)⋊C4C2211yescharacteristic
40C32×(C2×D3)⋊C4C2211yescharacteristic
41C32×C4⋊Dic3C2211yescharacteristic, complemented
42C32×C4×Dic3C2211yescharacteristic, complemented
43C32×C4×Dic3C2211yescharacteristic, complemented
44#88807C2211yescharacteristic, complemented
45#88806C2211yescharacteristic, complemented
46#88806C2211yescharacteristic, complemented
47#88804C2211yescharacteristic
48#88804C2211yescharacteristic
49#88804C2211yescharacteristic, complemented
50#88803C2211yescharacteristic
51#88803C2211yescharacteristic
52(C2×D3)⋊(C3⋊Dic3)C2211yescharacteristic
53C32×#117—31no—
54#64138—31no—
55C2×#3752—31no—
56#64107D311yescharacteristic, complemented
57#64105—31no—
58#64103—31no—
59#64103—31no—
60#64103—34no—
61#64103—64no—
62#64091—31no—
63#64090—31no—
64C22⋊C4×C3⋊D3—31no—
65#64087—31no—
66#64085—31no—
67#64084—31no—
68C4×C4⋊(C3⋊D3)—31no—
69#64081—31no—
70C3×#898—34no—
71C3×#892D314yescomplemented
72#63923—34no—
73#63921—34no—
74D3×(C2×D3)⋊C4—34no—
75#63899—34no—
76#63895—34no—
77#63894—34no—
78#63880—34no—
79#63874—34no—
80#63859—34no—
81#63854—34no—
82#63852—34no—
83#63850—34no—
84C22×C3⋊(C3⋊D3)C2311yescharacteristic
85C22×C3⋊(C3⋊D3)C2311yescharacteristic
86C22×C3×C3⋊D3C2311yescharacteristic
87C22×C32×D3C2311yescharacteristic
88C2×D3×C3⋊D3—22no—
89C2×D3×C3⋊D3—22no—
90C2×D3×C3⋊D3—41no—
91C2×C33×C4C2311yescharacteristic
92C2×C33×C4C2311yescharacteristic
93C2×C33×C4C2311yescharacteristic
94C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
95C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
96C4⋊(C3⋊(C3⋊D3))—22no—
97C4×C3⋊(C3⋊D3)—22no—
98C2×C3×C3⋊Dic3C2311yescharacteristic
99C2×C3×C3⋊Dic3C2311yescharacteristic
100C2×C3×C3⋊Dic3C2311yescharacteristic
101C2×C32×Dic3C2311yescharacteristic
102C2×C32×Dic3C2311yescharacteristic
103C2×C32×Dic3C2311yescharacteristic
104C32×C4×D3—22no—
105#6293—41no—
106#6292—41no—
107#6291—22no—
108#6289—41no—
109#6289—41no—
110D3×C3⋊Dic3—41no—
111#5705—91no—
112#5527—94no—
113C23×C3⋊D3—31no—
114C22×D32—34no—
115C22×C32×C4—31no—
116C2×#638—31no—
117C22×C3⋊Dic3—31no—
118C2×C4⋊(C3⋊D3)—31no—
119C2×C4⋊(C3⋊D3)—34no—
120C2×C4⋊(C3⋊D3)—31no—
121C2×C4⋊(C3⋊D3)—64no—
122C2×C4×C3⋊D3—31no—
123C2×C4×C3⋊D3—34no—
124C2×C4×C3⋊D3—31no—
125C2×C4×C3⋊D3—31no—
126C2×C4×C3⋊D3—64no—
127C2×#634—31no—
128C2×C3×C4×D3C2×D314yes—
129C2×#627—34no—
130C2×#626—34no—
131C2×#626—34no—
132C2×#624—34no—
133C2×#624—34no—
134C2×D3×Dic3—34no—
135C32×C4⋊C4—24no—
136C32×C4⋊C4—31no—
137C32×C4⋊C4C2×D314yescomplemented
138C32×C4⋊C4C2×D311yescharacteristic, complemented
139C32×C22⋊C4—31no—
140C32×C22⋊C4—31no—
141C32×C42—31no—
142C32×C42—31no—
143#3757—31no—
144#3752—31no—
145#3752—31no—
146#3752—31no—
147#3752—31no—
148#3752—31no—
149#3752—34no—
150#3752—34no—
151#3752—34no—
152#3752—31no—
153#3752—31no—
154#3752—31no—
155#3752—64no—
156#3752—64no—
157#3752—64no—
158#3752C2×D311yescharacteristic
159#3752C2×D311yescharacteristic
160#3752C2×D311yescharacteristic
161C4⋊(C3⋊Dic3)C2×D311yescharacteristic, complemented
162#3750—31no—
163#3750—34no—
164#3750—31no—
165#3750—31no—
166#3750—31no—
167#3750—64no—
168#3750C2×D311yescharacteristic, complemented
169C4×C3⋊Dic3C2×D311yescharacteristic, complemented
170C3×(C2×D3)⋊C4—34no—
171C3×(C2×D3)⋊C4—34no—
172C3×(C2×D3)⋊C4—34no—
173C3×(C2×D3)⋊C4C2×D314yes—
174C3×(C2×D3)⋊C4C2×D314yes—
175C3×C4⋊Dic3—34no—
176C3×C4⋊Dic3C2×D314yescomplemented
177C3×Dic3⋊C4—34no—
178C3×C4×Dic3—34no—
179C3×C4×Dic3C2×D314yescomplemented
180C3×C4×Dic3C2×D314yescomplemented
181#3724—34no—
182#3724—34no—
183Dic3⋊Dic3—34no—
184#3722—34no—
185#3722—34no—
186#3722—34no—
187(C2×D3)⋊Dic3—34no—
188(C2×D3)⋊Dic3—34no—
189(C2×D3)⋊Dic3—34no—
190C22×C33C2411yescharacteristic
191C2×C3⋊(C3⋊D3)—21no—
192C2×C3⋊(C3⋊D3)—21no—
193C2×C3⋊(C3⋊D3)—21no—
194C2×C3⋊(C3⋊D3)—21no—
195C2×C3⋊(C3⋊D3)—21no—
196C2×C3⋊(C3⋊D3)#4112yes—
197C2×C3×C3⋊D3—21no—
198C2×C3×C3⋊D3—21no—
199C2×C3×C3⋊D3—21no—
200C2×C32×D3—21no—
201C2×C32×D3—21no—
202C2×C32×D3#4112yes—
203D3×C3⋊D3—44no—
204C33×C4—21no—
205C33×C4—21no—
206C33×C4—21no—
207C3⋊(C3⋊Dic3)—21no—
208C3⋊(C3⋊Dic3)—21no—
209C3×C3⋊Dic3—21no—
210C3×C3⋊Dic3—21no—
211C3×C3⋊Dic3—21no—
212C32×Dic3—21no—
213C32×Dic3—21no—
214C32×Dic3—21no—
215C3×#126—91no—
216C3×#117—34no—
217#929—94no—
218C2×(C2×D3)⋊C4—94no—
219#898—34no—
220#897—91no—
221#896—94no—
222#896—91no—
223#894—94no—
224#894—91no—
225#894—94no—
226#894—91no—
227#894—184no—
228#893—91no—
229#892C3⋊D311yescharacteristic, complemented
230#885—91no—
231#883—91no—
232#882—94no—
233#882—91no—
234#67⋊C4—94no—
235D3×C22⋊C4—94no—
236D3×C22⋊C4—91no—
237D3×C22⋊C4—91no—
238#879—91no—
239#878—94no—
240#876—94no—
241#875—94no—
242C4×D12—94no—
243C4×D12—91no—
244#872—94no—
245#872—91no—
246C23×C32—31no—
247C22×C3⋊D3—31no—
248C22×C3⋊D3—31no—
249C22×C3⋊D3—34no—
250C22×C3⋊D3—34no—
251C22×C3⋊D3—64no—
252C22×C3⋊D3—64no—
253C22×C3⋊D3—62no—
254C22×C3⋊D3—62no—
255C22×C3⋊D3—121no—
256C22×C3⋊D3C22×D311yescharacteristic
257C22×C3×D3—34no—
258C22×C3×D3C22×D314yes—
259C2×D32—68no—
260C2×D32—68no—
261C2×D32—124no—
262C2×C32×C4—24no—
263C2×C32×C4—24no—
264C2×C32×C4—24no—
265C2×C32×C4—31no—
266C2×C32×C4—31no—
267C2×C32×C4—31no—
268C2×C32×C4—62no—
269C2×C32×C4C22×D314yes—
270C2×C32×C4C22×D314yes—
271C2×C32×C4C22×D314yes—
272C2×C32×C4C22×D311yescharacteristic
273C2×C32×C4C22×D311yescharacteristic
274C2×C32×C4C22×D311yescharacteristic
275#638—62no—
276C2×C3⋊Dic3—31no—
277C2×C3⋊Dic3—31no—
278C2×C3⋊Dic3—34no—
279C2×C3⋊Dic3—34no—
280C2×C3⋊Dic3—64no—
281C2×C3⋊Dic3—64no—
282C2×C3⋊Dic3—121no—
283C2×C3⋊Dic3C22×D311yescharacteristic
284C2×C3⋊Dic3C22×D311yescharacteristic
285C2×C3⋊Dic3C22×D311yescharacteristic
286C4⋊(C3⋊D3)—62no—
287C4⋊(C3⋊D3)—68no—
288C4⋊(C3⋊D3)—128no—
289C4⋊(C3⋊D3)—121no—
290C4×C3⋊D3—62no—
291C4×C3⋊D3—68no—
292C4×C3⋊D3—128no—
293C4×C3⋊D3—121no—
294C4×C3⋊D3—121no—
295#634—121no—
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—28no—
303#627—124no—
304#626—68no—
305#626—124no—
306#624—124no—
307#624—124no—
308D3×Dic3—124no—
309#551—271noSylow
310C2×C33C2×#4111yescharacteristic
311C2×C33C2×#4111yescharacteristic
312C2×C33H(5,𝔽2)11yescharacteristic
313C3⋊(C3⋊D3)—22no—
314C3⋊(C3⋊D3)—41no—
315C3×C3⋊D3—41no—
316C32×D3—22no—
317C23×D3—94no—
318C23×D3—91no—
319C22×C3×C4—34no—
320C2×#67—94no—
321C2×#67—91no—
322C22×Dic3—94no—
323C2×D12—91no—
324C2×D12—94no—
325C2×D12—91no—
326C2×D12—94no—
327C2×D12—184no—
328C2×C4×D3—94no—
329C2×C4×D3—91no—
330C2×C4×D3—94no—
331C2×C4×D3—94no—
332C2×C4×D3—91no—
333C2×C4×D3—91no—
334C2×C4×D3—91no—
335C2×C4×D3—184no—
336C2×C4×D3C2×C3⋊D311yescharacteristic
337C2×Dic6—94no—
338C2×Dic6—91no—
339C3×C4⋊C4—24no—
340C3×C4⋊C4—34no—
341C3×C4⋊C4—91no—
342C3×C4⋊C4—91no—
343C3×C4⋊C4D3214yescomplemented
344C3×C4⋊C4C2×C3⋊D311yescharacteristic, complemented
345C3×C22⋊C4—34no—
346C3×C22⋊C4—34no—
347C3×C22⋊C4—91no—
348C3×C22⋊C4—91no—
349C3×C22⋊C4—91no—
350C3×C42—34no—
351C3×C42—34no—
352C3×C42—91no—
353#217—94no—
354#217—91no—
355#217—91no—
356(C2×D3)⋊C4—34no—
357(C2×D3)⋊C4—34no—
358(C2×D3)⋊C4—34no—
359(C2×D3)⋊C4—94no—
360(C2×D3)⋊C4—94no—
361(C2×D3)⋊C4—94no—
362(C2×D3)⋊C4—94no—
363(C2×D3)⋊C4—94no—
364(C2×D3)⋊C4—91no—
365(C2×D3)⋊C4—94no—
366(C2×D3)⋊C4—94no—
367(C2×D3)⋊C4—94no—
368(C2×D3)⋊C4—91no—
369(C2×D3)⋊C4—91no—
370(C2×D3)⋊C4—91no—
371(C2×D3)⋊C4—91no—
372(C2×D3)⋊C4—91no—
373(C2×D3)⋊C4—91no—
374(C2×D3)⋊C4—184no—
375(C2×D3)⋊C4—184no—
376(C2×D3)⋊C4—184no—
377(C2×D3)⋊C4C2×C3⋊D311yescharacteristic
378(C2×D3)⋊C4C2×C3⋊D311yescharacteristic
379C4⋊Dic3—34no—
380C4⋊Dic3—91no—
381C4⋊Dic3C2×C3⋊D311yescharacteristic, complemented
382Dic3⋊C4—34no—
383Dic3⋊C4—94no—
384Dic3⋊C4—94no—
385Dic3⋊C4—94no—
386Dic3⋊C4—94no—
387Dic3⋊C4—91no—
388Dic3⋊C4—91no—
389Dic3⋊C4—91no—
390Dic3⋊C4—184no—
391C4×Dic3—34no—
392C4×Dic3C2×C3⋊D311yescharacteristic, complemented
393C4×Dic3C2×C3⋊D311yescharacteristic, complemented
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—21no—
403C2×C3⋊D3—32no—
404C2×C3⋊D3—38no—
405C2×C3⋊D3—68no—
406C2×C3⋊D3—61no—
407C2×C3⋊D3—61no—
408C2×C3⋊D3—61no—
409C2×C3⋊D3—61no—
410C2×C3⋊D3—61no—
411C2×C3⋊D3—64no—
412C2×C3⋊D3—64no—
413C2×C3⋊D3—64no—
414C2×C3⋊D3—64no—
415C2×C3⋊D3—64no—
416C2×C3⋊D3—124no—
417C2×C3⋊D3—124no—
418C2×C3⋊D3—124no—
419C2×C3⋊D3—124no—
420C2×C3⋊D3—124no—
421C2×C3⋊D3—124no—
422C2×C3×D3—24no—
423C2×C3×D3—24no—
424C2×C3×D3—64no—
425C2×C3×D3—64no—
426C2×C3×D3—64no—
427C2×C3×D3#23518yes—
428D32—1216no—
429C32×C4—21no—
430C32×C4—21no—
431C32×C4—21no—
432C32×C4—24no—
433C32×C4—24no—
434C32×C4—24no—
435C32×C4—44no—
436C32×C4—44no—
437C32×C4—44no—
438C32×C4—61no—
439C32×C4—61no—
440C32×C4—61no—
441C3⋊Dic3—21no—
442C3⋊Dic3—21no—
443C3⋊Dic3—21no—
444C3⋊Dic3—61no—
445C3⋊Dic3—61no—
446C3⋊Dic3—64no—
447C3⋊Dic3—64no—
448C3⋊Dic3—124no—
449C3⋊Dic3—124no—
450C3×Dic3—24no—
451C3×Dic3—24no—
452C3×Dic3—24no—
453C3×Dic3—64no—
454C3×Dic3—64no—
455C3×Dic3—64no—
456#126—91no—
457#126—271no—
458#124—271no—
459#123—271no—
460#123—271no—
461#123—271no—
462C22⋊Q8—271no—
463C22⋊Q8—271no—
464#120—271no—
465C4×D4—271no—
466C4×D4—271no—
467#117—31no—
468#117—271no—
469C2×C22⋊C4—271no—
470C2×C22⋊C4—271no—
471C33#55111yescharacteristic, complemented, Sylow
472C23×C3—34no—
473C23×C3—91no—
474C22×D3—34no—
475C22×D3—94no—
476C22×D3—91no—
477C22×D3—94no—
478C22×D3—91no—
479C22×D3—184no—
480C22×D3—184no—
481C22×D3—182no—
482C22×D3—188no—
483C22×D3—188no—
484C22×D3—182no—
485C22×D3—361no—
486C22×D3—364no—
487C22×D3C22×C3⋊D311yescharacteristic
488C2×C3×C4—24no—
489C2×C3×C4—24no—
490C2×C3×C4—24no—
491C2×C3×C4—34no—
492C2×C3×C4—34no—
493C2×C3×C4—34no—
494C2×C3×C4—68no—
495C2×C3×C4—91no—
496C2×C3×C4—91no—
497C2×C3×C4—91no—
498C2×C3×C4C2×D3214yes—
499C2×C3×C4C2×D3214yes—
500C2×C3×C4C2×D3214yes—
501C2×C3×C4C22×C3⋊D311yescharacteristic
502C2×C3×C4C22×C3⋊D311yescharacteristic
503C2×C3×C4C22×C3⋊D311yescharacteristic
504#67—188no—
505#67—361no—
506C2×Dic3—34no—
507C2×Dic3—34no—
508C2×Dic3—34no—
509C2×Dic3—94no—
510C2×Dic3—94no—
511C2×Dic3—91no—
512C2×Dic3—91no—
513C2×Dic3—184no—
514C2×Dic3—184no—
515C2×Dic3—364no—
516C2×Dic3C22×C3⋊D311yescharacteristic
517C2×Dic3C22×C3⋊D311yescharacteristic
518C2×Dic3C22×C3⋊D311yescharacteristic
519D12—182no—
520D12—188no—
521D12—182no—
522D12—368no—
523D12—364no—
524C4×D3—22no—
525C4×D3—182no—
526C4×D3—188no—
527C4×D3—368no—
528C4×D3—361no—
529C4×D3—361no—
530C4×D3—364no—
531C4×D3—364no—
532C4×D3—361no—
533Dic6—361no—
534Dic6—364no—
535C2×C32—24no—
536C2×C32—24no—
537C2×C32—24no—
538C2×C32—62no—
539C2×C32C2×#23514yes—
540C2×C32D3×#4114yes—
541C2×C32D3×#4111yescharacteristic
542C2×C32D3×#4111yescharacteristic
543C2×C32#100914yes—
544C2×C32#100911yescharacteristic
545C3⋊D3—41no—
546C3⋊D3—62no—
547C3⋊D3—68no—
548C3⋊D3—128no—
549C3⋊D3—121no—
550C3⋊D3—124no—
551C3⋊D3—244no—
552C3×D3—28no—
553C3×D3—124no—
554C24—271no—
555C2×Q8—271no—
556C2×D4—271no—
557C2×D4—271no—
558C2×D4—271no—
559C22×C4—31no—
560C22×C4—271no—
561C22×C4—271no—
562C22×C4—271no—
563C22×C4—271no—
564C4⋊C4—31no—
565C4⋊C4—91no—
566C4⋊C4—91no—
567C4⋊C4—271no—
568C4⋊C4—271no—
569C4⋊C4—271no—
570C4⋊C4—271no—
571C4⋊C4D3×C3⋊D311yescharacteristic, complemented
572C22⋊C4—31no—
573C22⋊C4—31no—
574C22⋊C4—91no—
575C22⋊C4—91no—
576C22⋊C4—91no—
577C22⋊C4—271no—
578C22⋊C4—271no—
579C22⋊C4—271no—
580C22⋊C4—271no—
581C22⋊C4—271no—
582C22⋊C4—271no—
583C22⋊C4—271no—
584C22⋊C4—271no—
585C22⋊C4—271no—
586C42—31no—
587C42—31no—
588C42—91no—
589C22×C3—24no—
590C22×C3—38no—
591C22×C3—64no—
592C22×C3—64no—
593C22×C3—181no—
594C22×C3—181no—
595C22×C3—181no—
596C22×C3C22×D3214yes—
597C22×C3C23×C3⋊D311yescharacteristic
598C2×D3—21no—
599C2×D3—21no—
600C2×D3—64no—
601C2×D3—64no—
602C2×D3—64no—
603C2×D3—98no—
604C2×D3—92no—
605C2×D3—188no—
606C2×D3—184no—
607C2×D3—184no—
608C2×D3—181no—
609C2×D3—181no—
610C2×D3—184no—
611C2×D3—184no—
612C2×D3—184no—
613C2×D3—181no—
614C2×D3—181no—
615C2×D3—181no—
616C2×D3—364no—
617C2×D3—364no—
618C2×D3—364no—
619C2×D3—364no—
620C2×D3—364no—
621C2×D3—364no—
622C2×D3—3616no—
623C2×D3#382812yes—
624C3×C4—24no—
625C3×C4—24no—
626C3×C4—24no—
627C3×C4—21no—
628C3×C4—21no—
629C3×C4—21no—
630C3×C4—44no—
631C3×C4—44no—
632C3×C4—44no—
633C3×C4—64no—
634C3×C4—64no—
635C3×C4—64no—
636C3×C4—181no—
637C3×C4—181no—
638C3×C4—181no—
639Dic3—21no—
640Dic3—21no—
641Dic3—21no—
642Dic3—64no—
643Dic3—64no—
644Dic3—64no—
645Dic3—184no—
646Dic3—184no—
647Dic3—181no—
648Dic3—181no—
649Dic3—364no—
650Dic3—364no—
651C32—24no—
652C32#552714yescomplemented
653C32#570511yescharacteristic, complemented
654C23—31no—
655C23—91no—
656C23—271no—
657C23—271no—
658C23—542no—
659C23—542no—
660C23—1081no—
661Q8—1081no—
662D4—542no—
663D4—542no—
664D4—1081no—
665C2×C4—31no—
666C2×C4—31no—
667C2×C4—31no—
668C2×C4—62no—
669C2×C4—91no—
670C2×C4—91no—
671C2×C4—91no—
672C2×C4—271no—
673C2×C4—271no—
674C2×C4—542no—
675C2×C4—1081no—
676C2×C4—1081no—
677C2×C4—1081no—
678C2×C4C2×D3×C3⋊D311yescharacteristic
679C2×C4C2×D3×C3⋊D311yescharacteristic
680C2×C4C2×D3×C3⋊D311yescharacteristic
681C2×C3—24no—
682C2×C3—24no—
683C2×C3—24no—
684C2×C3—68no—
685C2×C3—361no—
686C2×C3D3×#23514yes—
687C2×C3#6431214yes—
688C2×C3#6432014yes—
689C2×C3C2×#382811yescharacteristic
690C2×C3#41×C3⋊D311yescharacteristic
691C2×C3#6436611yescharacteristic
692D3—22no—
693D3—124no—
694D3—188no—
695D3—182no—
696D3—368no—
697D3—364no—
698D3—361no—
699D3—724no—
700C22—32no—
701C22—61no—
702C22—61no—
703C22—181no—
704C22—181no—
705C22—181no—
706C22—272no—
707C22—541no—
708C22—541no—
709C22—541no—
710C22—541no—
711C22—541no—
712C22—1084no—
713C22C22×D3×C3⋊D311yescharacteristic
714C4—21no—
715C4—21no—
716C4—21no—
717C4—61no—
718C4—61no—
719C4—61no—
720C4—181no—
721C4—181no—
722C4—181no—
723C4—541no—
724C4—541no—
725C3—24no—
726C3#1059464314yescomplemented
727C3#1059599811yescharacteristic, complemented
728C2—62no—
729C2—361no—
730C2—542no—
731C2—1081no—
732C2D3×#382811yescharacteristic
733C2#1172458611yescharacteristic
734C2#1172459711yescharacteristic
subgroupG/H
center, FrattiniC22C22×D3×C3⋊D3
commutator, socle, cosocleC22×C33C24
FittingC33×C4⋊C4C22
prime radical#11723542C2
hypercenterC4⋊C4D3×C3⋊D3
hypocenterC33#551
LCSG ▷ C22×C33 ▷ C33
UCSC1 ◁ C22 ◁ C4⋊C4

Complements

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

NH ≅ G/Ntype
1. #11723935C2semidirect
2. C3×#64107C2semidirect
3. C32×#892C2semidirect
5. #11723539C2semidirect
6. D3×#3752C2semidirect
7. #11723504C2semidirect
8. #11723500C2semidirect
9. #11723495C2semidirect
10. #11723484C2semidirect
11. #11723461C2semidirect
12. #11723452C2semidirect
13. #11723438C2semidirect
14. #11723416C2semidirect
15. #11723414C2semidirect
22. C2×#6293C22semidirect
26. C2×#6289C22semidirect
28. C33×C4⋊C4C22semidirect
30. #88859C22semidirect
31. #88859C22semidirect
32. #88857C22semidirect
36. C3×C4⋊(C3⋊Dic3)C22semidirect
37. C3×#3750C22semidirect
38. C3×C4×C3⋊Dic3C22semidirect
41. C32×C4⋊Dic3C22semidirect
42. C32×C4×Dic3C22semidirect
43. C32×C4×Dic3C22semidirect
44. #88807C22semidirect
45. #88806C22semidirect
46. #88806C22semidirect
49. #88804C22semidirect
56. #64107D3semidirect
71. C3×#892D3semidirect
137. C32×C4⋊C4C2×D3semidirect
138. C32×C4⋊C4C2×D3semidirect
161. C4⋊(C3⋊Dic3)C2×D3semidirect
168. #3750C2×D3semidirect
169. C4×C3⋊Dic3C2×D3semidirect
176. C3×C4⋊Dic3C2×D3semidirect
179. C3×C4×Dic3C2×D3semidirect
180. C3×C4×Dic3C2×D3semidirect
229. #892C3⋊D3semidirect
343. C3×C4⋊C4D32semidirect
344. C3×C4⋊C4C2×C3⋊D3semidirect
381. C4⋊Dic3C2×C3⋊D3semidirect
392. C4×Dic3C2×C3⋊D3semidirect
393. C4×Dic3C2×C3⋊D3semidirect
471. C33#551semidirect
571. C4⋊C4D3×C3⋊D3semidirect
652. C32#5527semidirect
653. C32#5705semidirect
726. C3#10594643semidirect
727. C3#10595998semidirect

Maximal subgroups

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

subgroupindex
#117239352
C3×#641072
C32×#8922
#117235422
#117235392
D3×#37522
#117235042
#117235002
#117234952
#117234842
#117234612
#117234522
#117234382
#117234162
#117234142
#105959983
#105946433