Finite Group Databasebeta

← #13148016

Subgroups — #13148016

Order 1728.

1122 conjugacy classes of subgroups.

The subgroup lattice has 828 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#88668C211yesmaximal, characteristic
2C2×(C3⋊D9)⋊Q8C211yesmaximal, characteristic, complemented
3C22⋊C4×C3⋊D9C211yesmaximal, characteristic, complemented
4C9×#885C211yesmaximal, characteristic, complemented
5C3×#63447C211yesmaximal, characteristic, complemented
6#11721274C211yesmaximal, characteristic, complemented
7#11721263C211yesmaximal, characteristic, complemented
8#11721257C211yesmaximal, characteristic, complemented
9#11721048C211yesmaximal, characteristic, complemented
10#11721048C211yesmaximal, characteristic, complemented
11#11721035C211yesmaximal, characteristic, complemented
12#11721003C211yesmaximal, characteristic, complemented
13C4×(C3⋊D9)⋊C4C211yesmaximal, characteristic, complemented
14#11720956C211yesmaximal, characteristic, complemented
15#11720940C211yesmaximal, characteristic, complemented
16#10594288—31nomaximal
17D9×#124—31nomaximal
18C23×C3⋊D9C2211yescharacteristic
19C22×D3×D9C2211yescharacteristic
20C2×C4×C3⋊D9C2211yescharacteristic
21C2×C4×C3⋊D9C2211yescharacteristic
22C2×C9×#67C2211yescharacteristic
23C2×C3×#611C2211yescharacteristic
24C2×C9×Dic6C2211yescharacteristic, complemented
25C2×C3×Dic18C2211yescharacteristic, complemented
26#88668—24no—
27C2×#6195C2211yescharacteristic
28C2×#6192C2211yescharacteristic
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, complemented
36#88551C2211yescharacteristic, complemented
37#88536C2211yescharacteristic, complemented
38#88536C2211yescharacteristic, complemented
39C9×#217C2211yescharacteristic, complemented
40C3×#3676C2211yescharacteristic, complemented
41C9×(C2×D3)⋊C4C2211yescharacteristic, complemented
42C9×(C2×D3)⋊C4C2211yescharacteristic, complemented
43C3×(C2×D9)⋊C4C2211yescharacteristic, complemented
44C3×(C2×D9)⋊C4C2211yescharacteristic, complemented
45C4×C9×Dic3C2211yescharacteristic, complemented
46C3×C4×Dic9C2211yescharacteristic, complemented
47(C2×D3)⋊Dic9C2211yescharacteristic, complemented
48(C2×D3)⋊Dic9C2211yescharacteristic, complemented
49#88445C2211yescharacteristic, complemented
50#88445C2211yescharacteristic, complemented
51(C2×D9)⋊Dic3C2211yescharacteristic, complemented
52(C2×D9)⋊Dic3C2211yescharacteristic, complemented
53Dic3×Dic9C2211yescharacteristic, complemented
54Dic3×Dic9C2211yescharacteristic, complemented
55C2×#3811—31no—
56C2×#3797—31no—
57C22⋊C4×C3⋊D3—31no—
58C3×#885—31no—
59C3×#885D311yescharacteristic
60#63974—31no—
61#63959—31no—
62#63959—31no—
63#63921—31no—
64#63921—31no—
65#63907—31no—
66#63907—31no—
67C4×#624—31no—
68#63852—31no—
69#63852—31no—
70C2×Q8×D9—31no—
71C2×D4×D9—31no—
72C9×#124—31no—
73#63509—31no—
74#63498—31no—
75#63447—31no—
76#63447—31no—
77#63447—31no—
78#63447D311yescharacteristic, complemented
79C22⋊C4×D9—31no—
80C22⋊C4×D9—31no—
81C22⋊C4×D9—31no—
82C22⋊C4×D9—31no—
83C22⋊C4×D9—61no—
84#63437—31no—
85C42×D9—31no—
86C23×C3×C9C2311yescharacteristic
87C22×C3⋊D9—22no—
88C22×C3⋊D9—22no—
89C22×C3⋊D9—22no—
90C22×C3⋊D9C2311yescharacteristic
91C22×C3⋊D9C2311yescharacteristic
92C22×D3×C9C2311yescharacteristic
93C22×C3×D9C2311yescharacteristic
94C2×D3×D9—22no—
95C2×D3×D9—22no—
96C2×D3×D9—22no—
97C2×C3×C4×C9C2311yescharacteristic
98C2×C3×C4×C9C2311yescharacteristic
99C2×C3⋊Dic9C2311yescharacteristic
100C2×C3⋊Dic9C2311yescharacteristic
101C4×C3⋊D9—22no—
102C4×C3⋊D9—22no—
103C9×#67—22no—
104C3×#611—22no—
105C2×C9×Dic3C2311yescharacteristic
106C2×C9×Dic3C2311yescharacteristic
107C2×C9×Dic3C2311yescharacteristic
108C2×C3×Dic9C2311yescharacteristic
109C2×C3×Dic9C2311yescharacteristic
110C2×C3×Dic9C2311yescharacteristic
111C9×Dic6—22no—
112C3×Dic18—22no—
113#6195—22no—
114#6192—22no—
115(C3⋊D9)⋊C4—22no—
116(C3⋊D9)⋊C4—22no—
117(C3⋊D9)⋊C4D414yes—
118#6189—22no—
119#6189—22no—
120D3×#124—91no—
121D3×#124—91no—
122C23×C3⋊D3—31no—
123C22×D32—31no—
124C2×C4×C3⋊D3—31no—
125C2×C4×C3⋊D3—31no—
126C2×C3×#67—31no—
127C2×C3×#67C2×D311yescharacteristic
128C2×C3×Dic6—31no—
129C2×C3×Dic6C2×D311yescharacteristic
130#3811—64no—
131C2×#627—31no—
132C2×#627—31no—
133C2×#626—31no—
134C2×#626—31no—
135C2×#624—31no—
136C2×#624—31no—
137C2×#624—31no—
138#3797—64no—
139C23×D9—31no—
140C23×D9—31no—
141C23×D9—61no—
142C32×C22⋊C4C2×D311yescharacteristic
143#3757—31no—
144#3752—31no—
145#3752—31no—
146C3×#217—31no—
147C3×#217C2×D311yescharacteristic
148C3×(C2×D3)⋊C4—31no—
149C3×(C2×D3)⋊C4—31no—
150C3×(C2×D3)⋊C4C2×D311yescharacteristic
151C3×(C2×D3)⋊C4C2×D311yescharacteristic
152C3×C4×Dic3—31no—
153C3×C4×Dic3C2×D311yescharacteristic
154#3722—31no—
155#3722—31no—
156(C2×D3)⋊Dic3—31no—
157(C2×D3)⋊Dic3—31no—
158(C2×D3)⋊Dic3—31no—
159(C2×D3)⋊Dic3—31no—
160Dic32—31no—
161Dic32—31no—
162C2×Q8×C9—31no—
163C2×D4×C9—31no—
164C2×#611—31no—
165C2×#611C2×D311yescharacteristic
166Q8×D9—64no—
167D4×D9—64no—
168C2×D36—31no—
169C2×C4×D9—31no—
170C2×C4×D9—31no—
171C2×C4×D9—31no—
172C2×C4×D9—31no—
173C2×C4×D9—31no—
174C2×C4×D9—61no—
175C2×C4×D9—61no—
176C2×Dic18—31no—
177C2×Dic18—31no—
178C2×Dic18C2×D311yescharacteristic, complemented
179C9×C22⋊C4—21no—
180C9×C22⋊C4—31no—
181C9×C22⋊C4—31no—
182C9×C22⋊C4—31no—
183C9×C22⋊C4C2×D311yescharacteristic, complemented
184C42×C9—31no—
185#3676—31no—
186#3676—31no—
187#3676—31no—
188#3676—61no—
189#3676C2×D311yescharacteristic, complemented
190(C2×D9)⋊C4—31no—
191(C2×D9)⋊C4—31no—
192(C2×D9)⋊C4—31no—
193(C2×D9)⋊C4—31no—
194(C2×D9)⋊C4—31no—
195(C2×D9)⋊C4—31no—
196(C2×D9)⋊C4—61no—
197(C2×D9)⋊C4—61no—
198(C2×D9)⋊C4C2×D311yescharacteristic, complemented
199(C2×D9)⋊C4C2×D311yescharacteristic, complemented
200C4×Dic9—31no—
201C4×Dic9—31no—
202C4×Dic9C2×D311yescharacteristic, complemented
203C22×C3×C9—21no—
204C22×C3×C9—21no—
205C22×C3×C9—21no—
206C22×C3×C9C2411yescharacteristic
207C2×C3⋊D9—21no—
208C2×C3⋊D9—21no—
209C2×C3⋊D9—21no—
210C2×C3⋊D9—44no—
211C2×C3⋊D9C2×D412yes—
212C2×C3⋊D9#4112yes—
213C2×C3⋊D9#4112yes—
214C2×D3×C9—21no—
215C2×D3×C9—21no—
216C2×D3×C9—21no—
217C2×C3×D9—21no—
218C2×C3×D9—21no—
219C2×C3×D9—21no—
220D3×D9—44no—
221C3×C4×C9—21no—
222C3×C4×C9—21no—
223C3⋊Dic9—21no—
224C3⋊Dic9—21no—
225C9×Dic3—21no—
226C9×Dic3—21no—
227C9×Dic3C2×D412yes—
228C3×Dic9—21no—
229C3×Dic9—21no—
230C3×Dic9C2×D412yes—
231C2×D3×Q8—91no—
232C2×D3×Q8—91no—
233C2×D3×D4—91no—
234C2×D3×D4—91no—
235C3×#124—31no—
236C3×#124—91no—
237#947—91no—
238#947—91no—
239#936—91no—
240#936—91no—
241#885—31no—
242#885—91no—
243#885—91no—
244#885—91no—
245#885—91no—
246#885—91no—
247#885—91no—
248#885D911yescharacteristic, complemented
249D3×C22⋊C4—91no—
250D3×C22⋊C4—91no—
251D3×C22⋊C4—91no—
252D3×C22⋊C4—91no—
253D3×C22⋊C4—91no—
254D3×C22⋊C4—91no—
255D3×C22⋊C4—91no—
256D3×C22⋊C4—91no—
257D3×C22⋊C4—181no—
258#875—91no—
259#875—91no—
260C42×D3—91no—
261C42×D3—91no—
262C23×C32C22×D311yescharacteristic
263C22×C3⋊D3—31no—
264C22×C3⋊D3—31no—
265C22×C3⋊D3—62no—
266C22×C3⋊D3—62no—
267C22×C3⋊D3—62no—
268C22×C3×D3—31no—
269C22×C3×D3C22×D311yescharacteristic
270C2×D32—62no—
271C2×D32—62no—
272C2×D32—62no—
273C2×C32×C4C22×D311yescharacteristic
274C2×C32×C4C22×D311yescharacteristic
275C2×C3⋊Dic3—31no—
276C2×C3⋊Dic3—31no—
277C4×C3⋊D3—62no—
278C4×C3⋊D3—62no—
279C3×#67—22no—
280C3×#67—62no—
281C2×C3×Dic3—31no—
282C2×C3×Dic3—31no—
283C2×C3×Dic3—31no—
284C2×C3×Dic3C22×D311yescharacteristic
285C2×C3×Dic3C22×D311yescharacteristic
286C2×C3×Dic3C22×D311yescharacteristic
287C3×Dic6—22no—
288C3×Dic6—62no—
289#627—62no—
290#627—62no—
291#626—62no—
292#626—62no—
293#624—34no—
294#624—62no—
295#624—62no—
296C23×C9—21no—
297C23×C9—31no—
298C23×C9C22×D311yescharacteristic
299C22×D9—31no—
300C22×D9—31no—
301C22×D9—61no—
302C22×D9—61no—
303C22×D9—62no—
304C22×D9—62no—
305C22×D9—62no—
306C22×D9—62no—
307C22×D9—62no—
308C22×D9—62no—
309C22×D9—64no—
310C22×D9—122no—
311C22×D9—122no—
312C22×D9C22×D311yescharacteristic
313Q8×C9—62no—
314D4×C9—62no—
315C2×C4×C9—21no—
316C2×C4×C9—21no—
317C2×C4×C9—31no—
318C2×C4×C9—31no—
319C2×C4×C9—31no—
320C2×C4×C9C22×D311yescharacteristic
321C2×C4×C9C22×D311yescharacteristic
322#611—22no—
323#611—62no—
324C2×Dic9—31no—
325C2×Dic9—31no—
326C2×Dic9—61no—
327C2×Dic9—61no—
328C2×Dic9C22×D311yescharacteristic
329C2×Dic9C22×D311yescharacteristic
330C2×Dic9C22×D311yescharacteristic
331D36—62no—
332C4×D9—34no—
333C4×D9—62no—
334C4×D9—62no—
335C4×D9—62no—
336C4×D9—62no—
337C4×D9—122no—
338C4×D9—122no—
339Dic18—22no—
340Dic18—62no—
341Dic18—62no—
342C2×#124—271noSylow
343C2×C3×C9—41no—
344C2×C3×C9C22×D411yescharacteristic
345C2×C3×C9C2×#4111yescharacteristic
346C2×C3×C9C2×#4111yescharacteristic
347C3⋊D9—41no—
348C3⋊D9#12414yescomplemented
349D3×C9—41no—
350C3×D9—41no—
351C23×D3—91no—
352C23×D3—91no—
353C23×D3—91no—
354C23×D3—91no—
355C23×D3—181no—
356C2×C3×Q8—31no—
357C2×C3×Q8—91no—
358C2×C3×D4—31no—
359C2×C3×D4—91no—
360C2×#67—31no—
361C2×#67—91no—
362C2×#67—91no—
363C2×#67C2×D911yescharacteristic
364D3×Q8—184no—
365D3×Q8—184no—
366D3×D4—184no—
367D3×D4—184no—
368C2×D12—91no—
369C2×D12—91no—
370C2×C4×D3—91no—
371C2×C4×D3—91no—
372C2×C4×D3—91no—
373C2×C4×D3—91no—
374C2×C4×D3—91no—
375C2×C4×D3—91no—
376C2×C4×D3—91no—
377C2×C4×D3—91no—
378C2×C4×D3—91no—
379C2×C4×D3—91no—
380C2×C4×D3—181no—
381C2×C4×D3—181no—
382C2×Dic6—31no—
383C2×Dic6—91no—
384C2×Dic6—91no—
385C2×Dic6—91no—
386C2×Dic6—91no—
387C2×Dic6C2×D911yescharacteristic, complemented
388C3×C22⋊C4—21no—
389C3×C22⋊C4—31no—
390C3×C22⋊C4—31no—
391C3×C22⋊C4—31no—
392C3×C22⋊C4—91no—
393C3×C22⋊C4—91no—
394C3×C22⋊C4—91no—
395C3×C22⋊C4C2×D911yescharacteristic, complemented
396C3×C22⋊C4D3211yescharacteristic
397C3×C42—31no—
398C3×C42—91no—
399#217—31no—
400#217—91no—
401#217—91no—
402#217—91no—
403#217—91no—
404#217—91no—
405#217—91no—
406#217—181no—
407#217C2×D911yescharacteristic, complemented
408(C2×D3)⋊C4—31no—
409(C2×D3)⋊C4—31no—
410(C2×D3)⋊C4—91no—
411(C2×D3)⋊C4—91no—
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—91no—
419(C2×D3)⋊C4—91no—
420(C2×D3)⋊C4—91no—
421(C2×D3)⋊C4—91no—
422(C2×D3)⋊C4—181no—
423(C2×D3)⋊C4—181no—
424(C2×D3)⋊C4C2×D911yescharacteristic, complemented
425(C2×D3)⋊C4C2×D911yescharacteristic, complemented
426C4×Dic3—31no—
427C4×Dic3—91no—
428C4×Dic3—91no—
429C4×Dic3—91no—
430C4×Dic3—91no—
431C4×Dic3C2×D911yescharacteristic, complemented
432C22×C32—21no—
433C22×C32—21no—
434C22×C32—21no—
435C22×C32C23×D311yescharacteristic
436C2×C3⋊D3—32no—
437C2×C3⋊D3—32no—
438C2×C3⋊D3—32no—
439C2×C3⋊D3—61no—
440C2×C3⋊D3—61no—
441C2×C3⋊D3—61no—
442C2×C3⋊D3—124no—
443C2×C3×D3—21no—
444C2×C3×D3—21no—
445C2×C3×D3—21no—
446C2×C3×D3—61no—
447C2×C3×D3—61no—
448C2×C3×D3—61no—
449D32—124no—
450C32×C4—21no—
451C32×C4—21no—
452C3⋊Dic3—61no—
453C3⋊Dic3—61no—
454C3×Dic3—21no—
455C3×Dic3—21no—
456C3×Dic3—32no—
457C3×Dic3—61no—
458C3×Dic3—61no—
459C3×Dic3D3×D412yes—
460C22×C9—22no—
461C22×C9—21no—
462C22×C9—21no—
463C22×C9—21no—
464C22×C9—21no—
465C22×C9—41no—
466C22×C9—41no—
467C22×C9—61no—
468C22×C9—61no—
469C22×C9—61no—
470C22×C9C23×D311yescharacteristic
471C2×D9—21no—
472C2×D9—21no—
473C2×D9—21no—
474C2×D9—32no—
475C2×D9—32no—
476C2×D9—32no—
477C2×D9—62no—
478C2×D9—62no—
479C2×D9—62no—
480C2×D9—62no—
481C2×D9—61no—
482C2×D9—61no—
483C2×D9—61no—
484C2×D9—121no—
485C2×D9—121no—
486C2×D9—124no—
487C2×D9—124no—
488C2×D9—128no—
489C4×C9—21no—
490C4×C9—21no—
491C4×C9—32no—
492C4×C9—41no—
493C4×C9—41no—
494C4×C9—61no—
495C4×C9—61no—
496Dic9—21no—
497Dic9—21no—
498Dic9—61no—
499Dic9—61no—
500Dic9—121no—
501Dic9—121no—
502Dic9D3×D412yes—
503C22×Q8—271no—
504C22×D4—271no—
505#124—31no—
506#124—91no—
507#124—271no—
508#124—271no—
509#124—271no—
510#124—271no—
511#124—271no—
512#124—271no—
513C2×C22⋊C4—271no—
514C2×C22⋊C4—271no—
515C2×C22⋊C4—271no—
516C2×C22⋊C4—271no—
517C2×C42—271no—
518C3×C9C2×#12411yescharacteristic, complemented, Sylow
519C23×C3—21no—
520C23×C3—31no—
521C23×C3—91no—
522C23×C3C22×D911yescharacteristic
523C23×C3C2×D3211yescharacteristic
524C22×D3—31no—
525C22×D3—91no—
526C22×D3—91no—
527C22×D3—91no—
528C22×D3—91no—
529C22×D3—181no—
530C22×D3—181no—
531C22×D3—182no—
532C22×D3—182no—
533C22×D3—182no—
534C22×D3—182no—
535C22×D3—182no—
536C22×D3—182no—
537C22×D3—182no—
538C22×D3—182no—
539C22×D3—182no—
540C22×D3—182no—
541C22×D3—182no—
542C22×D3—182no—
543C22×D3—184no—
544C22×D3—362no—
545C22×D3—362no—
546C22×D3C22×D911yescharacteristic
547C3×Q8—62no—
548C3×Q8—182no—
549C3×D4—62no—
550C3×D4—182no—
551C2×C3×C4—21no—
552C2×C3×C4—21no—
553C2×C3×C4—31no—
554C2×C3×C4—31no—
555C2×C3×C4—31no—
556C2×C3×C4—91no—
557C2×C3×C4—91no—
558C2×C3×C4—91no—
559C2×C3×C4C22×D911yescharacteristic
560C2×C3×C4C22×D911yescharacteristic
561C2×C3×C4C2×D3211yescharacteristic
562C2×C3×C4C2×D3211yescharacteristic
563#67—22no—
564#67—62no—
565#67—182no—
566#67—182no—
567C2×Dic3—31no—
568C2×Dic3—31no—
569C2×Dic3—31no—
570C2×Dic3—91no—
571C2×Dic3—91no—
572C2×Dic3—91no—
573C2×Dic3—91no—
574C2×Dic3—181no—
575C2×Dic3—181no—
576C2×Dic3C22×D911yescharacteristic
577C2×Dic3C22×D911yescharacteristic
578C2×Dic3C22×D911yescharacteristic
579D12—182no—
580D12—182no—
581C4×D3—94no—
582C4×D3—94no—
583C4×D3—182no—
584C4×D3—182no—
585C4×D3—182no—
586C4×D3—182no—
587C4×D3—182no—
588C4×D3—182no—
589C4×D3—182no—
590C4×D3—182no—
591C4×D3—362no—
592C4×D3—362no—
593Dic6—22no—
594Dic6—62no—
595Dic6—182no—
596Dic6—182no—
597Dic6—182no—
598Dic6—182no—
599C2×C32—41no—
600C2×C32C2×D3×D411yescharacteristic
601C2×C32D3×#4111yescharacteristic
602C2×C32D3×#4111yescharacteristic
603C3⋊D3—34no—
604C3⋊D3—121no—
605C3×D3—41no—
606C3×D3—121no—
607C2×C9—21no—
608C2×C9—21no—
609C2×C9—21no—
610C2×C9—42no—
611C2×C9—41no—
612C2×C9—121no—
613C2×C9C2×D3×D411yescharacteristic
614C2×C9D3×#4111yescharacteristic
615C2×C9D3×#4111yescharacteristic
616D9—34no—
617D9—41no—
618D9—64no—
619D9—122no—
620D9—121no—
621C24—271no—
622C24—271no—
623C2×Q8—31no—
624C2×Q8—91no—
625C2×Q8—271no—
626C2×Q8—271no—
627C2×Q8—544no—
628C2×D4—31no—
629C2×D4—91no—
630C2×D4—271no—
631C2×D4—271no—
632C2×D4—544no—
633C22×C4—271no—
634C22×C4—271no—
635C22×C4—271no—
636C22×C4—271no—
637C22×C4—271no—
638C22⋊C4—31no—
639C22⋊C4—31no—
640C22⋊C4—31no—
641C22⋊C4—91no—
642C22⋊C4—91no—
643C22⋊C4—91no—
644C22⋊C4—271no—
645C22⋊C4—271no—
646C22⋊C4—271no—
647C22⋊C4—271no—
648C22⋊C4—271no—
649C22⋊C4—271no—
650C22⋊C4—271no—
651C22⋊C4—271no—
652C22⋊C4—271no—
653C22⋊C4D3×D911yescharacteristic, complemented
654C42—31no—
655C42—91no—
656C42—271no—
657C42—271no—
658C22×C3—22no—
659C22×C3—21no—
660C22×C3—21no—
661C22×C3—21no—
662C22×C3—21no—
663C22×C3—21no—
664C22×C3—21no—
665C22×C3—21no—
666C22×C3—41no—
667C22×C3—41no—
668C22×C3—61no—
669C22×C3—61no—
670C22×C3—61no—
671C22×C3—181no—
672C22×C3—181no—
673C22×C3—181no—
674C22×C3C23×D911yescharacteristic
675C22×C3C22×D3211yescharacteristic
676C2×D3—21no—
677C2×D3—21no—
678C2×D3—21no—
679C2×D3—61no—
680C2×D3—61no—
681C2×D3—61no—
682C2×D3—92no—
683C2×D3—92no—
684C2×D3—92no—
685C2×D3—92no—
686C2×D3—92no—
687C2×D3—92no—
688C2×D3—182no—
689C2×D3—182no—
690C2×D3—182no—
691C2×D3—182no—
692C2×D3—181no—
693C2×D3—181no—
694C2×D3—181no—
695C2×D3—181no—
696C2×D3—181no—
697C2×D3—181no—
698C2×D3—361no—
699C2×D3—361no—
700C2×D3—364no—
701C2×D3—364no—
702C2×D3—364no—
703C2×D3—364no—
704C2×D3—368no—
705C3×C4—21no—
706C3×C4—21no—
707C3×C4—21no—
708C3×C4—21no—
709C3×C4—32no—
710C3×C4—41no—
711C3×C4—41no—
712C3×C4—61no—
713C3×C4—61no—
714C3×C4—92no—
715C3×C4—181no—
716C3×C4—181no—
717Dic3—21no—
718Dic3—21no—
719Dic3—32no—
720Dic3—61no—
721Dic3—61no—
722Dic3—181no—
723Dic3—181no—
724Dic3—181no—
725Dic3—181no—
726Dic3—361no—
727Dic3—361no—
728Dic3D4×D912yes—
729C32D3×#12411yescharacteristic
730C9—21no—
731C9D3×#12411yescharacteristic, complemented
732C23—31no—
733C23—91no—
734C23—271no—
735C23—271no—
736C23—542no—
737C23—542no—
738C23—542no—
739C23—542no—
740C23—542no—
741C23—542no—
742C23C2×D3×D911yescharacteristic
743Q8—62no—
744Q8—182no—
745Q8—542no—
746Q8—542no—
747D4—62no—
748D4—182no—
749D4—542no—
750D4—542no—
751C2×C4—31no—
752C2×C4—31no—
753C2×C4—31no—
754C2×C4—91no—
755C2×C4—91no—
756C2×C4—91no—
757C2×C4—274no—
758C2×C4—271no—
759C2×C4—271no—
760C2×C4—542no—
761C2×C4—542no—
762C2×C4—542no—
763C2×C4—542no—
764C2×C4C2×D3×D911yescharacteristic
765C2×C4C2×D3×D911yescharacteristic
766C2×C3—21no—
767C2×C3—21no—
768C2×C3—21no—
769C2×C3—42no—
770C2×C3—41no—
771C2×C3—41no—
772C2×C3—121no—
773C2×C3—361no—
774C2×C3C2×D4×D911yescharacteristic
775C2×C3#41×D911yescharacteristic
776C2×C3#41×D911yescharacteristic
777C2×C3#6430611yescharacteristic
778C2×C3D32×D411yescharacteristic
779C2×C3#6431211yescharacteristic
780D3—41no—
781D3—94no—
782D3—94no—
783D3—121no—
784D3—184no—
785D3—362no—
786D3—361no—
787D3—361no—
788C22—21no—
789C22—21no—
790C22—21no—
791C22—61no—
792C22—61no—
793C22—61no—
794C22—181no—
795C22—181no—
796C22—181no—
797C22—272no—
798C22—272no—
799C22—272no—
800C22—541no—
801C22—541no—
802C22—541no—
803C22—1084no—
804C22—1084no—
805C22C22×D3×D911yescharacteristic
806C4—21no—
807C4—21no—
808C4—32no—
809C4—61no—
810C4—61no—
811C4—92no—
812C4—181no—
813C4—181no—
814C4—541no—
815C4—541no—
816C3—21no—
817C3D9×#12411yescharacteristic, complemented
818C3#1059428811yescharacteristic
819C2—41no—
820C2—121no—
821C2—274no—
822C2—361no—
823C2—1081no—
824C2#1172247511yescharacteristic
825C2D3×D4×D911yescharacteristic
826C2#1172249811yescharacteristic
subgroupG/H
centerC22C22×D3×D9
commutator, cosocleC22×C3×C9C24
FrattiniC22×C3C22×D32
FittingC3×C9×C22⋊C4C22
socleC22×C32C23×D3
prime radicalC2×#88668C2
hypercenterC22⋊C4D3×D9
hypocenterC3×C9C2×#124
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
3. C22⋊C4×C3⋊D9C2semidirect
4. C9×#885C2semidirect
5. C3×#63447C2semidirect
6. #11721274C2semidirect
7. #11721263C2semidirect
8. #11721257C2semidirect
9. #11721048C2semidirect
10. #11721048C2semidirect
11. #11721035C2semidirect
12. #11721003C2semidirect
13. C4×(C3⋊D9)⋊C4C2semidirect
14. #11720956C2semidirect
15. #11720940C2semidirect
24. C2×C9×Dic6C22semidirect
25. C2×C3×Dic18C22semidirect
32. C2×#6189C22semidirect
33. C2×#6189C22semidirect
35. C3×C9×C22⋊C4C22semidirect
36. #88551C22semidirect
37. #88536C22semidirect
38. #88536C22semidirect
39. C9×#217C22semidirect
40. C3×#3676C22semidirect
41. C9×(C2×D3)⋊C4C22semidirect
42. C9×(C2×D3)⋊C4C22semidirect
43. C3×(C2×D9)⋊C4C22semidirect
44. C3×(C2×D9)⋊C4C22semidirect
45. C4×C9×Dic3C22semidirect
46. C3×C4×Dic9C22semidirect
47. (C2×D3)⋊Dic9C22semidirect
48. (C2×D3)⋊Dic9C22semidirect
49. #88445C22semidirect
50. #88445C22semidirect
51. (C2×D9)⋊Dic3C22semidirect
52. (C2×D9)⋊Dic3C22semidirect
53. Dic3×Dic9C22semidirect
54. Dic3×Dic9C22semidirect
78. #63447D3semidirect
178. C2×Dic18C2×D3semidirect
183. C9×C22⋊C4C2×D3semidirect
189. #3676C2×D3semidirect
198. (C2×D9)⋊C4C2×D3semidirect
199. (C2×D9)⋊C4C2×D3semidirect
202. C4×Dic9C2×D3semidirect
248. #885D9semidirect
348. C3⋊D9#124semidirect
387. C2×Dic6C2×D9semidirect
395. C3×C22⋊C4C2×D9semidirect
407. #217C2×D9semidirect
424. (C2×D3)⋊C4C2×D9semidirect
425. (C2×D3)⋊C4C2×D9semidirect
431. C4×Dic3C2×D9semidirect
518. C3×C9C2×#124semidirect
653. C22⋊C4D3×D9semidirect
731. C9D3×#124semidirect
817. C3D9×#124semidirect

Maximal subgroups

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

subgroupindex
C2×#886682
C2×(C3⋊D9)⋊Q82
C22⋊C4×C3⋊D92
C9×#8852
C3×#634472
#117212742
#117212632
#117212572
#117210482
#117210352
#117210032
C4×(C3⋊D9)⋊C42
#117209562
#117209402
#105942883
D9×#1243