Finite Group Databasebeta

← #13148005

Subgroups — #13148005

Order 1728.

1098 conjugacy classes of subgroups.

The subgroup lattice has 774 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×(C3⋊D9)⋊C4C211yesmaximal, characteristic
2C2×(C3⋊D9)⋊Q8C211yesmaximal, characteristic, complemented
3C22⋊C4×C3⋊D9C211yesmaximal, characteristic
4C9×#878C211yesmaximal, characteristic, complemented
5C3×#63440C211yesmaximal, characteristic, complemented
6#11721274C211yesmaximal, characteristic
7#11721253C211yesmaximal, characteristic, complemented
8#11721249C211yesmaximal, characteristic, complemented
9#11721000C211yesmaximal, characteristic, complemented
10#11720995C211yesmaximal, characteristic, complemented
11#11720994C211yesmaximal, characteristic, complemented
12#11720986C211yesmaximal, characteristic, complemented
13#11720985C211yesmaximal, characteristic, complemented
14#11720980C211yesmaximal, characteristic, complemented
15#11720980C211yesmaximal, characteristic, complemented
16#10594067—31nomaximal
17D9×C22⋊Q8—31nomaximal
18C23×C3⋊D9C2211yescharacteristic
19C2×C4×C3⋊D9C2211yescharacteristic
20C2×C4×C3⋊D9C2211yescharacteristic
21C22×C9×Dic3C2211yescharacteristic
22C22×C3×Dic9C2211yescharacteristic
23C2×C9×Dic6C2211yescharacteristic, complemented
24C2×C3×Dic18C2211yescharacteristic, complemented
25C2×(C3⋊D9)⋊C4—24no—
26C2×(C3⋊D9)⋊C4C2211yescharacteristic
27C2×(C3⋊D9)⋊C4C2211yescharacteristic
28C2×(C3⋊D9)⋊C4C2211yescharacteristic
29C2×(C3⋊D9)⋊C4C2211yescharacteristic
30C2×(C3⋊D9)⋊C4C2211yescharacteristic
31C2×(C3⋊D9)⋊C4C2211yescharacteristic
32C2×#6189C2211yescharacteristic, complemented
33C2×#6189C2211yescharacteristic, complemented
34(C3⋊D9)⋊Q8—24no—
35C3×C9×C22⋊C4C2211yescharacteristic
36#88551C2211yescharacteristic
37#88536C2211yescharacteristic
38#88536C2211yescharacteristic
39C9×#217C2211yescharacteristic
40C3×#3676C2211yescharacteristic
41C9×C4⋊Dic3C2211yescharacteristic, complemented
42C9×Dic3⋊C4C2211yescharacteristic, complemented
43C9×Dic3⋊C4C2211yescharacteristic, complemented
44C3×C4⋊Dic9C2211yescharacteristic, complemented
45C3×Dic9⋊C4C2211yescharacteristic, complemented
46C3×Dic9⋊C4C2211yescharacteristic, complemented
47#88445C2211yescharacteristic
48#88445C2211yescharacteristic
49Dic3⋊Dic9C2211yescharacteristic, complemented
50Dic3⋊Dic9C2211yescharacteristic, complemented
51#88442C2211yescharacteristic, complemented
52#88442C2211yescharacteristic, complemented
53Dic9⋊Dic3C2211yescharacteristic, complemented
54Dic9⋊Dic3C2211yescharacteristic, complemented
55C22×#624—31no—
56C2×#3797—31no—
57C22⋊C4×C3⋊D3—31no—
58C3×#878—31no—
59C3×#878D311yescharacteristic
60#63974—31no—
61#63964—31no—
62#63964—31no—
63#63900—31no—
64#63895—31no—
65#63895—31no—
66#63888—31no—
67#63888—31no—
68#63883—31no—
69#63883—31no—
70C2×Q8×D9—31no—
71C22×C4×D9—31no—
72C9×C22⋊Q8—31no—
73#63508—31no—
74#63486—31no—
75#63459—31no—
76#63458—31no—
77#63458—31no—
78C4⋊C4×D9—31no—
79C4⋊C4×D9—31no—
80C4⋊C4×D9—31no—
81C22⋊C4×D9—31no—
82C22⋊C4×D9—31no—
83C22⋊C4×D9—61no—
84#63440—31no—
85#63440D311yescharacteristic, complemented
86C23×C3×C9C2311yescharacteristic
87C22×C3⋊D9—22no—
88C22×C3⋊D9—22no—
89C22×C3⋊D9Q814yescomplemented
90C22×C3⋊D9C2311yescharacteristic
91C22×C3⋊D9C2311yescharacteristic
92C2×C3×C4×C9C2311yescharacteristic
93C2×C3×C4×C9C2311yescharacteristic
94C2×C3⋊Dic9C2311yescharacteristic
95C2×C3⋊Dic9C2311yescharacteristic
96C4×C3⋊D9—22no—
97C4×C3⋊D9—22no—
98C2×C9×Dic3—22no—
99C2×C9×Dic3C2311yescharacteristic
100C2×C9×Dic3C2311yescharacteristic
101C2×C9×Dic3C2311yescharacteristic
102C2×C9×Dic3C2311yescharacteristic
103C2×C3×Dic9—22no—
104C2×C3×Dic9C2311yescharacteristic
105C2×C3×Dic9C2311yescharacteristic
106C2×C3×Dic9C2311yescharacteristic
107C2×C3×Dic9C2311yescharacteristic
108C9×Dic6—22no—
109C3×Dic18—22no—
110(C3⋊D9)⋊C4—22no—
111(C3⋊D9)⋊C4—22no—
112(C3⋊D9)⋊C4—22no—
113(C3⋊D9)⋊C4—22no—
114(C3⋊D9)⋊C4—22no—
115(C3⋊D9)⋊C4D414yes—
116#6189—22no—
117#6189—22no—
118D3×C22⋊Q8—91no—
119D3×C22⋊Q8—91no—
120C23×C3⋊D3—31no—
121C2×C4×C3⋊D3—31no—
122C2×C4×C3⋊D3—31no—
123C22×C3×Dic3—31no—
124C22×C3×Dic3C2×D311yescharacteristic
125C2×C3×Dic6—31no—
126C2×C3×Dic6C2×D311yescharacteristic
127C2×#627—31no—
128C2×#627—31no—
129C2×#624—31no—
130C2×#624—31no—
131C2×#624—31no—
132C2×#624—31no—
133C2×#624—31no—
134C2×#624—31no—
135C2×#624—64no—
136#3797—64no—
137C23×D9—31no—
138C23×D9—61no—
139C32×C22⋊C4C2×D311yescharacteristic
140#3757—31no—
141#3752—31no—
142#3752—31no—
143C3×#217—31no—
144C3×#217C2×D311yescharacteristic
145C3×C4⋊Dic3—31no—
146C3×C4⋊Dic3C2×D311yescharacteristic
147C3×Dic3⋊C4—31no—
148C3×Dic3⋊C4—31no—
149C3×Dic3⋊C4C2×D311yescharacteristic
150C3×Dic3⋊C4C2×D311yescharacteristic
151#3724—31no—
152#3724—31no—
153Dic3⋊Dic3—31no—
154Dic3⋊Dic3—31no—
155Dic3⋊Dic3—31no—
156Dic3⋊Dic3—31no—
157#3722—31no—
158#3722—31no—
159C2×Q8×C9—31no—
160C22×C4×C9—31no—
161C22×Dic9C2×D311yescharacteristic
162Q8×D9—64no—
163C2×C4×D9—31no—
164C2×C4×D9—31no—
165C2×C4×D9—31no—
166C2×C4×D9—31no—
167C2×C4×D9—31no—
168C2×C4×D9—31no—
169C2×C4×D9—31no—
170C2×C4×D9—31no—
171C2×C4×D9—64no—
172C2×C4×D9—61no—
173C2×C4×D9—61no—
174C2×Dic18—31no—
175C2×Dic18—31no—
176C2×Dic18C2×D311yescharacteristic, complemented
177C9×C4⋊C4—31no—
178C9×C4⋊C4—31no—
179C9×C4⋊C4—31no—
180C9×C22⋊C4—21no—
181C9×C22⋊C4—31no—
182C9×C22⋊C4C2×D311yescharacteristic
183#3676—31no—
184#3676—61no—
185#3676C2×D311yescharacteristic
186(C2×D9)⋊C4—31no—
187(C2×D9)⋊C4—31no—
188(C2×D9)⋊C4—31no—
189(C2×D9)⋊C4—31no—
190(C2×D9)⋊C4—61no—
191(C2×D9)⋊C4—61no—
192C4⋊Dic9—31no—
193C4⋊Dic9—31no—
194C4⋊Dic9C2×D311yescharacteristic, complemented
195Dic9⋊C4—31no—
196Dic9⋊C4—31no—
197Dic9⋊C4—31no—
198Dic9⋊C4—31no—
199Dic9⋊C4C2×D311yescharacteristic, complemented
200Dic9⋊C4C2×D311yescharacteristic, complemented
201C22×C3×C9—21no—
202C22×C3×C9—21no—
203C22×C3×C9C2×Q812yescomplemented
204C22×C3×C9C2411yescharacteristic
205C2×C3⋊D9—21no—
206C2×C3⋊D9—21no—
207C2×C3⋊D9—28no—
208C2×C3⋊D9C2×D412yes—
209C2×C3⋊D9C2×Q812yes—
210C2×C3⋊D9C2×Q812yescomplemented
211C2×C3⋊D9#4112yes—
212C3×C4×C9—21no—
213C3×C4×C9—21no—
214C3⋊Dic9—21no—
215C3⋊Dic9—21no—
216C9×Dic3—21no—
217C9×Dic3—21no—
218C9×Dic3—21no—
219C9×Dic3C2×D412yes—
220C3×Dic9—21no—
221C3×Dic9—21no—
222C3×Dic9—21no—
223C3×Dic9C2×D412yes—
224C2×D3×Q8—91no—
225C2×D3×Q8—91no—
226C22×C4×D3—91no—
227C22×C4×D3—91no—
228C3×C22⋊Q8—31no—
229C3×C22⋊Q8—91no—
230#946—91no—
231#946—91no—
232#924—91no—
233#924—91no—
234#897—91no—
235#897—91no—
236#896—91no—
237#896—91no—
238#896—91no—
239#896—91no—
240D3×C4⋊C4—91no—
241D3×C4⋊C4—91no—
242D3×C4⋊C4—91no—
243D3×C4⋊C4—91no—
244D3×C4⋊C4—91no—
245D3×C4⋊C4—91no—
246D3×C22⋊C4—91no—
247D3×C22⋊C4—91no—
248D3×C22⋊C4—91no—
249D3×C22⋊C4—91no—
250D3×C22⋊C4—181no—
251#878—31no—
252#878—91no—
253#878—91no—
254#878D911yescharacteristic, complemented
255C23×C32C22×D311yescharacteristic
256C22×C3⋊D3—31no—
257C22×C3⋊D3—34no—
258C22×C3⋊D3—31no—
259C22×C3⋊D3—62no—
260C22×C3⋊D3—62no—
261C2×C32×C4C22×D311yescharacteristic
262C2×C32×C4C22×D311yescharacteristic
263C2×C3⋊Dic3—31no—
264C2×C3⋊Dic3—31no—
265C4×C3⋊D3—62no—
266C4×C3⋊D3—62no—
267C2×C3×Dic3—22no—
268C2×C3×Dic3—31no—
269C2×C3×Dic3—31no—
270C2×C3×Dic3—31no—
271C2×C3×Dic3—31no—
272C2×C3×Dic3—62no—
273C2×C3×Dic3C22×D311yescharacteristic
274C2×C3×Dic3C22×D311yescharacteristic
275C2×C3×Dic3C22×D311yescharacteristic
276C2×C3×Dic3C22×D311yescharacteristic
277C3×Dic6—22no—
278C3×Dic6—62no—
279#627—62no—
280#627—62no—
281#624—34no—
282#624—62no—
283#624—62no—
284#624—62no—
285#624—62no—
286#624—62no—
287C23×C9—21no—
288C23×C9C22×D311yescharacteristic
289C22×D9—31no—
290C22×D9—34no—
291C22×D9—31no—
292C22×D9—61no—
293C22×D9—61no—
294C22×D9—64no—
295C22×D9—62no—
296C22×D9—62no—
297C22×D9—122no—
298C22×D9—122no—
299Q8×C9—62no—
300C2×C4×C9—21no—
301C2×C4×C9—21no—
302C2×C4×C9—31no—
303C2×C4×C9—31no—
304C2×C4×C9—31no—
305C2×C4×C9—31no—
306C2×C4×C9—62no—
307C2×C4×C9C22×D311yescharacteristic
308C2×C4×C9C22×D311yescharacteristic
309C2×Dic9—22no—
310C2×Dic9—31no—
311C2×Dic9—31no—
312C2×Dic9—61no—
313C2×Dic9—61no—
314C2×Dic9C22×D311yescharacteristic
315C2×Dic9C22×D311yescharacteristic
316C2×Dic9C22×D311yescharacteristic
317C2×Dic9C22×D311yescharacteristic
318C4×D9—34no—
319C4×D9—62no—
320C4×D9—62no—
321C4×D9—62no—
322C4×D9—62no—
323C4×D9—62no—
324C4×D9—62no—
325C4×D9—62no—
326C4×D9—122no—
327C4×D9—122no—
328Dic18—22no—
329Dic18—62no—
330Dic18—62no—
331C2×C22⋊Q8—271noSylow
332C2×C3×C9—22no—
333C2×C3×C9C22×D411yescharacteristic
334C2×C3×C9C22×Q811yescharacteristic
335C2×C3×C9C2×#4111yescharacteristic
336C3⋊D9—22no—
337C3⋊D9C22⋊Q814yescomplemented
338C23×D3—91no—
339C23×D3—91no—
340C23×D3—181no—
341C2×C3×Q8—31no—
342C2×C3×Q8—91no—
343C22×C3×C4—31no—
344C22×C3×C4—91no—
345C22×Dic3—31no—
346C22×Dic3C2×D911yescharacteristic
347D3×Q8—184no—
348D3×Q8—184no—
349C2×C4×D3—91no—
350C2×C4×D3—91no—
351C2×C4×D3—91no—
352C2×C4×D3—91no—
353C2×C4×D3—91no—
354C2×C4×D3—91no—
355C2×C4×D3—91no—
356C2×C4×D3—91no—
357C2×C4×D3—91no—
358C2×C4×D3—91no—
359C2×C4×D3—91no—
360C2×C4×D3—91no—
361C2×C4×D3—91no—
362C2×C4×D3—91no—
363C2×C4×D3—91no—
364C2×C4×D3—91no—
365C2×C4×D3—181no—
366C2×C4×D3—181no—
367C2×C4×D3—184no—
368C2×C4×D3—184no—
369C2×Dic6—31no—
370C2×Dic6—91no—
371C2×Dic6—91no—
372C2×Dic6—91no—
373C2×Dic6—91no—
374C2×Dic6C2×D911yescharacteristic, complemented
375C3×C4⋊C4—31no—
376C3×C4⋊C4—31no—
377C3×C4⋊C4—31no—
378C3×C4⋊C4—91no—
379C3×C4⋊C4—91no—
380C3×C4⋊C4—91no—
381C3×C22⋊C4—21no—
382C3×C22⋊C4—31no—
383C3×C22⋊C4—91no—
384C3×C22⋊C4C2×D911yescharacteristic
385C3×C22⋊C4D3211yescharacteristic
386#217—31no—
387#217—91no—
388#217—91no—
389#217—181no—
390#217C2×D911yescharacteristic
391(C2×D3)⋊C4—91no—
392(C2×D3)⋊C4—91no—
393(C2×D3)⋊C4—91no—
394(C2×D3)⋊C4—91no—
395(C2×D3)⋊C4—91no—
396(C2×D3)⋊C4—91no—
397(C2×D3)⋊C4—91no—
398(C2×D3)⋊C4—91no—
399(C2×D3)⋊C4—181no—
400(C2×D3)⋊C4—181no—
401C4⋊Dic3—31no—
402C4⋊Dic3—91no—
403C4⋊Dic3—91no—
404C4⋊Dic3—91no—
405C4⋊Dic3—91no—
406C4⋊Dic3C2×D911yescharacteristic, complemented
407Dic3⋊C4—31no—
408Dic3⋊C4—31no—
409Dic3⋊C4—91no—
410Dic3⋊C4—91no—
411Dic3⋊C4—91no—
412Dic3⋊C4—91no—
413Dic3⋊C4—91no—
414Dic3⋊C4—91no—
415Dic3⋊C4—91no—
416Dic3⋊C4—91no—
417Dic3⋊C4C2×D911yescharacteristic, complemented
418Dic3⋊C4C2×D911yescharacteristic, complemented
419C22×C32—21no—
420C22×C32—21no—
421C22×C32D3×Q812yes—
422C22×C32C23×D311yescharacteristic
423C2×C3⋊D3—32no—
424C2×C3⋊D3—32no—
425C2×C3⋊D3—32no—
426C2×C3⋊D3—32no—
427C2×C3⋊D3—68no—
428C2×C3⋊D3—61no—
429C2×C3⋊D3—61no—
430C32×C4—21no—
431C32×C4—21no—
432C3⋊Dic3—61no—
433C3⋊Dic3—61no—
434C3×Dic3—21no—
435C3×Dic3—21no—
436C3×Dic3—21no—
437C3×Dic3—32no—
438C3×Dic3—61no—
439C3×Dic3—61no—
440C3×Dic3—61no—
441C3×Dic3D3×D412yes—
442C22×C9—21no—
443C22×C9—21no—
444C22×C9—21no—
445C22×C9—22no—
446C22×C9—41no—
447C22×C9—41no—
448C22×C9D3×Q812yescomplemented
449C22×C9C23×D311yescharacteristic
450C2×D9—32no—
451C2×D9—32no—
452C2×D9—32no—
453C2×D9—32no—
454C2×D9—62no—
455C2×D9—62no—
456C2×D9—62no—
457C2×D9—62no—
458C2×D9—68no—
459C2×D9—61no—
460C2×D9—61no—
461C2×D9—128no—
462C2×D9—121no—
463C2×D9—121no—
464C4×C9—21no—
465C4×C9—21no—
466C4×C9—32no—
467C4×C9—41no—
468C4×C9—41no—
469C4×C9—61no—
470C4×C9—61no—
471C4×C9—61no—
472Dic9—21no—
473Dic9—21no—
474Dic9—21no—
475Dic9—61no—
476Dic9—61no—
477Dic9—121no—
478Dic9—121no—
479Dic9D3×D412yes—
480C22×Q8—271no—
481C23×C4—271no—
482C22⋊Q8—31no—
483C22⋊Q8—91no—
484C22⋊Q8—271no—
485C22⋊Q8—271no—
486C22⋊Q8—271no—
487C22⋊Q8—271no—
488C22⋊Q8—271no—
489C22⋊Q8—271no—
490C2×C4⋊C4—271no—
491C2×C4⋊C4—271no—
492C2×C4⋊C4—271no—
493C2×C22⋊C4—271no—
494C2×C22⋊C4—271no—
495C3×C9C2×C22⋊Q811yescharacteristic, complemented, Sylow
496C23×C3—21no—
497C23×C3C22×D911yescharacteristic
498C23×C3C2×D3211yescharacteristic
499C22×D3—91no—
500C22×D3—91no—
501C22×D3—91no—
502C22×D3—94no—
503C22×D3—91no—
504C22×D3—94no—
505C22×D3—181no—
506C22×D3—181no—
507C22×D3—184no—
508C22×D3—182no—
509C22×D3—182no—
510C22×D3—182no—
511C22×D3—182no—
512C22×D3—362no—
513C22×D3—362no—
514C3×Q8—62no—
515C3×Q8—182no—
516C2×C3×C4—21no—
517C2×C3×C4—21no—
518C2×C3×C4—31no—
519C2×C3×C4—31no—
520C2×C3×C4—31no—
521C2×C3×C4—31no—
522C2×C3×C4—62no—
523C2×C3×C4—91no—
524C2×C3×C4—91no—
525C2×C3×C4—91no—
526C2×C3×C4—91no—
527C2×C3×C4—182no—
528C2×C3×C4C22×D911yescharacteristic
529C2×C3×C4C22×D911yescharacteristic
530C2×C3×C4C2×D3211yescharacteristic
531C2×C3×C4C2×D3211yescharacteristic
532C2×Dic3—22no—
533C2×Dic3—31no—
534C2×Dic3—31no—
535C2×Dic3—31no—
536C2×Dic3—31no—
537C2×Dic3—62no—
538C2×Dic3—91no—
539C2×Dic3—91no—
540C2×Dic3—91no—
541C2×Dic3—91no—
542C2×Dic3—181no—
543C2×Dic3—181no—
544C2×Dic3C22×D911yescharacteristic
545C2×Dic3C22×D911yescharacteristic
546C2×Dic3C22×D911yescharacteristic
547C2×Dic3C22×D911yescharacteristic
548C4×D3—94no—
549C4×D3—94no—
550C4×D3—182no—
551C4×D3—182no—
552C4×D3—182no—
553C4×D3—182no—
554C4×D3—182no—
555C4×D3—182no—
556C4×D3—182no—
557C4×D3—182no—
558C4×D3—182no—
559C4×D3—182no—
560C4×D3—182no—
561C4×D3—182no—
562C4×D3—182no—
563C4×D3—182no—
564C4×D3—362no—
565C4×D3—362no—
566Dic6—22no—
567Dic6—62no—
568Dic6—182no—
569Dic6—182no—
570Dic6—182no—
571Dic6—182no—
572C2×C32—22no—
573C2×C32C2×D3×D411yescharacteristic
574C2×C32C2×D3×Q811yescharacteristic
575C2×C32D3×#4111yescharacteristic
576C3⋊D3—34no—
577C3⋊D3—62no—
578C2×C9—22no—
579C2×C9—21no—
580C2×C9—21no—
581C2×C9—21no—
582C2×C9—42no—
583C2×C9C2×D3×D411yescharacteristic
584C2×C9C2×D3×Q811yescharacteristic
585C2×C9D3×#4111yescharacteristic
586D9—34no—
587D9—64no—
588D9—62no—
589D9—122no—
590C24—271no—
591C2×Q8—31no—
592C2×Q8—91no—
593C2×Q8—271no—
594C2×Q8—271no—
595C2×Q8—544no—
596C22×C4—31no—
597C22×C4—91no—
598C22×C4—271no—
599C22×C4—271no—
600C22×C4—271no—
601C22×C4—271no—
602C22×C4—271no—
603C22×C4—271no—
604C22×C4—271no—
605C22×C4—271no—
606C22×C4—544no—
607C4⋊C4—31no—
608C4⋊C4—31no—
609C4⋊C4—31no—
610C4⋊C4—91no—
611C4⋊C4—91no—
612C4⋊C4—91no—
613C4⋊C4—271no—
614C4⋊C4—271no—
615C4⋊C4—271no—
616C4⋊C4—271no—
617C4⋊C4—271no—
618C4⋊C4—271no—
619C22⋊C4—31no—
620C22⋊C4—91no—
621C22⋊C4—271no—
622C22⋊C4—271no—
623C22⋊C4—271no—
624C22⋊C4—271no—
625C22⋊C4—271no—
626C22⋊C4D3×D911yescharacteristic
627C22×C3—21no—
628C22×C3—21no—
629C22×C3—21no—
630C22×C3—21no—
631C22×C3—22no—
632C22×C3—21no—
633C22×C3—41no—
634C22×C3—41no—
635C22×C3Q8×D912yescomplemented
636C22×C3C23×D911yescharacteristic
637C22×C3#379712yes—
638C22×C3C22×D3211yescharacteristic
639C2×D3—92no—
640C2×D3—92no—
641C2×D3—92no—
642C2×D3—92no—
643C2×D3—92no—
644C2×D3—92no—
645C2×D3—92no—
646C2×D3—92no—
647C2×D3—182no—
648C2×D3—182no—
649C2×D3—182no—
650C2×D3—182no—
651C2×D3—188no—
652C2×D3—188no—
653C2×D3—181no—
654C2×D3—181no—
655C2×D3—181no—
656C2×D3—181no—
657C2×D3—368no—
658C2×D3—361no—
659C2×D3—361no—
660C3×C4—21no—
661C3×C4—21no—
662C3×C4—21no—
663C3×C4—21no—
664C3×C4—32no—
665C3×C4—41no—
666C3×C4—41no—
667C3×C4—61no—
668C3×C4—61no—
669C3×C4—61no—
670C3×C4—92no—
671C3×C4—181no—
672C3×C4—181no—
673C3×C4—181no—
674Dic3—21no—
675Dic3—21no—
676Dic3—21no—
677Dic3—32no—
678Dic3—61no—
679Dic3—61no—
680Dic3—61no—
681Dic3—181no—
682Dic3—181no—
683Dic3—181no—
684Dic3—181no—
685Dic3—361no—
686Dic3—361no—
687Dic3D4×D912yes—
688C32D3×C22⋊Q811yescharacteristic
689C9—21no—
690C9D3×C22⋊Q811yescharacteristic, complemented
691C23—271no—
692C23—274no—
693C23—271no—
694C23—542no—
695C23—542no—
696C23C2×D3×D911yescharacteristic
697Q8—62no—
698Q8—182no—
699Q8—542no—
700Q8—542no—
701C2×C4—31no—
702C2×C4—31no—
703C2×C4—31no—
704C2×C4—31no—
705C2×C4—62no—
706C2×C4—91no—
707C2×C4—91no—
708C2×C4—91no—
709C2×C4—91no—
710C2×C4—182no—
711C2×C4—274no—
712C2×C4—271no—
713C2×C4—271no—
714C2×C4—542no—
715C2×C4—542no—
716C2×C4—542no—
717C2×C4—542no—
718C2×C4—542no—
719C2×C4—542no—
720C2×C4—542no—
721C2×C4C2×D3×D911yescharacteristic
722C2×C4C2×D3×D911yescharacteristic
723C2×C3—22no—
724C2×C3—22no—
725C2×C3—21no—
726C2×C3—21no—
727C2×C3—21no—
728C2×C3—42no—
729C2×C3C2×D4×D911yescharacteristic
730C2×C3C2×Q8×D911yescharacteristic
731C2×C3#41×D911yescharacteristic
732C2×C3C2×#379711yescharacteristic
733C2×C3D32×D411yescharacteristic
734C2×C3#6431211yescharacteristic
735D3—94no—
736D3—94no—
737D3—184no—
738D3—182no—
739D3—182no—
740D3—362no—
741C22—21no—
742C22—21no—
743C22—272no—
744C22—272no—
745C22—272no—
746C22—272no—
747C22—548no—
748C22—541no—
749C22—541no—
750C22(C3⋊D9)⋊Q812yescomplemented
751C22C22×D3×D911yescharacteristic
752C4—21no—
753C4—21no—
754C4—32no—
755C4—61no—
756C4—61no—
757C4—61no—
758C4—92no—
759C4—181no—
760C4—181no—
761C4—181no—
762C4—541no—
763C4—541no—
764C3—21no—
765C3D9×C22⋊Q811yescharacteristic, complemented
766C3#1059406711yescharacteristic
767C2—22no—
768C2—274no—
769C2—542no—
770C2C2×(C3⋊D9)⋊Q811yescharacteristic
771C2D3×D4×D911yescharacteristic
772C2#1172249811yescharacteristic
subgroupG/H
centerC22C22×D3×D9
commutator, cosocleC22×C3×C9C24
FrattiniC22×C3C22×D32
FittingC3×C9×C22⋊C4C22
socleC22×C32C23×D3
prime radicalC23×C3⋊D9C22
hypercenterC22⋊C4D3×D9
hypocenterC3×C9C2×C22⋊Q8
LCSG ▷ C22×C3×C9 ▷ C3×C9
UCSC1 ◁ C22 ◁ C22⋊C4

Complements

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

NH ≅ G/Ntype
2. C2×(C3⋊D9)⋊Q8C2semidirect
4. C9×#878C2semidirect
5. C3×#63440C2semidirect
7. #11721253C2semidirect
8. #11721249C2semidirect
9. #11721000C2semidirect
10. #11720995C2semidirect
11. #11720994C2semidirect
12. #11720986C2semidirect
13. #11720985C2semidirect
14. #11720980C2semidirect
15. #11720980C2semidirect
23. C2×C9×Dic6C22semidirect
24. C2×C3×Dic18C22semidirect
32. C2×#6189C22semidirect
33. C2×#6189C22semidirect
41. C9×C4⋊Dic3C22semidirect
42. C9×Dic3⋊C4C22semidirect
43. C9×Dic3⋊C4C22semidirect
44. C3×C4⋊Dic9C22semidirect
45. C3×Dic9⋊C4C22semidirect
46. C3×Dic9⋊C4C22semidirect
49. Dic3⋊Dic9C22semidirect
50. Dic3⋊Dic9C22semidirect
51. #88442C22semidirect
52. #88442C22semidirect
53. Dic9⋊Dic3C22semidirect
54. Dic9⋊Dic3C22semidirect
85. #63440D3semidirect
89. C22×C3⋊D9Q8semidirect
176. C2×Dic18C2×D3semidirect
194. C4⋊Dic9C2×D3semidirect
199. Dic9⋊C4C2×D3semidirect
200. Dic9⋊C4C2×D3semidirect
203. C22×C3×C9C2×Q8semidirect
210. C2×C3⋊D9C2×Q8semidirect
254. #878D9semidirect
337. C3⋊D9C22⋊Q8semidirect
374. C2×Dic6C2×D9semidirect
406. C4⋊Dic3C2×D9semidirect
417. Dic3⋊C4C2×D9semidirect
418. Dic3⋊C4C2×D9semidirect
448. C22×C9D3×Q8semidirect
495. C3×C9C2×C22⋊Q8semidirect
635. C22×C3Q8×D9semidirect
690. C9D3×C22⋊Q8semidirect
750. C22(C3⋊D9)⋊Q8semidirect
765. C3D9×C22⋊Q8semidirect

Maximal subgroups

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

subgroupindex
C22×(C3⋊D9)⋊C42
C2×(C3⋊D9)⋊Q82
C22⋊C4×C3⋊D92
C9×#8782
C3×#634402
#117212742
#117212532
#117212492
#117210002
#117209952
#117209942
#117209862
#117209852
#117209802
#105940673
D9×C22⋊Q83