Finite Group Databasebeta

← #13148927

Subgroups — #13148927

Order 1728.

808 conjugacy classes of subgroups.

The subgroup lattice has 740 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11721751C211yesmaximal, characteristic, complemented
2C9×#898C211yesmaximal, characteristic, complemented
3C3×#63451C211yesmaximal, characteristic, complemented
4#11721039C211yesmaximal, characteristic, complemented
5#11721039C211yesmaximal, characteristic, complemented
6#11721039C211yesmaximal, characteristic, complemented
7#11721020C211yesmaximal, characteristic, complemented
8#11721014C211yesmaximal, characteristic, complemented
9#11721013C211yesmaximal, characteristic, complemented
10#11720997C211yesmaximal, characteristic, complemented
11#11720993C211yesmaximal, characteristic, complemented
12#11720992C211yesmaximal, characteristic, complemented
13#11720980C211yesmaximal, characteristic, complemented
14#11720920C211yesmaximal, characteristic, complemented
15#11720898C211yesmaximal, characteristic, complemented
16#10594468—31nomaximal
17#10589811—31nomaximal
18C2×C4⋊(C3⋊D9)C2211yescharacteristic
19C2×C4⋊(C3⋊D9)C2211yescharacteristic
20C2×C4⋊(C3⋊D9)C2211yescharacteristic
21C2×C4×C3⋊D9C2211yescharacteristic
22C2×#6195C2211yescharacteristic
23C2×#6195C2211yescharacteristic
24C2×#6195C2211yescharacteristic
25C2×D3×Dic9C2211yescharacteristic
26C2×(C3⋊D9)⋊C4C2211yescharacteristic
27C2×(C3⋊D9)⋊C4C2211yescharacteristic
28C2×(C3⋊D9)⋊C4C2211yescharacteristic
29C2×(C3⋊D9)⋊C4C2211yescharacteristic
30C3×C9×C4⋊C4C2211yescharacteristic
31#88536C2211yescharacteristic
32#88536C2211yescharacteristic
33C9×(C2×D3)⋊C4C2211yescharacteristic
34C9×(C2×D3)⋊C4C2211yescharacteristic
35C9×(C2×D3)⋊C4C2211yescharacteristic
36C9×C4⋊Dic3C2211yescharacteristic
37C9×Dic3⋊C4C2211yescharacteristic
38C4×C9×Dic3C2211yescharacteristic
39C3×C4⋊Dic9C2211yescharacteristic
40C3×Dic9⋊C4C2211yescharacteristic
41C3×Dic9⋊C4C2211yescharacteristic
42C3×Dic9⋊C4C2211yescharacteristic
43C3×Dic9⋊C4C2211yescharacteristic
44C3×C4×Dic9C2211yescharacteristic
45#88445C2211yescharacteristic
46#88445C2211yescharacteristic
47#88445C2211yescharacteristic
48#88445C2211yescharacteristic
49#88445C2211yescharacteristic
50Dic3⋊Dic9C2211yescharacteristic
51Dic9⋊Dic3C2211yescharacteristic
52Dic3×Dic9C2211yescharacteristic
53#64104—31no—
54C3×#898D311yescharacteristic
55C3×#889—31no—
56#63910—31no—
57#63910—31no—
58#63910—31no—
59#63897—31no—
60#63894—31no—
61#63894—31no—
62#63890—31no—
63#63883—31no—
64#63881—31no—
65#63880—31no—
66#63848—31no—
67#63836—31no—
68C9×#126—31no—
69#63460—31no—
70#63457—31no—
71#63457—61no—
72#63456—31no—
73#63455—31no—
74C4⋊C4×D9—31no—
75#63451D311yescharacteristic, complemented
76#63448—31no—
77#63446—31no—
78#63446—31no—
79#63446—31no—
80#611⋊C4—31no—
81#611⋊C4—31no—
82C4×D36—31no—
83#63434—31no—
84C22×C3⋊D9C2311yescharacteristic
85C22×C3⋊D9C2311yescharacteristic
86C22×C3⋊D9C2311yescharacteristic
87C22×D3×C9C2311yescharacteristic
88C2×C3×C4×C9C2311yescharacteristic
89C2×C3×C4×C9C2311yescharacteristic
90C2×C3×C4×C9C2311yescharacteristic
91C2×C3⋊Dic9C2311yescharacteristic
92C4⋊(C3⋊D9)—22no—
93C4⋊(C3⋊D9)—22no—
94C4⋊(C3⋊D9)—41no—
95C4×C3⋊D9—41no—
96C2×C9×Dic3C2311yescharacteristic
97C2×C9×Dic3C2311yescharacteristic
98C2×C9×Dic3C2311yescharacteristic
99C2×C3×Dic9C2311yescharacteristic
100C2×C3×Dic9C2311yescharacteristic
101C2×C3×Dic9C2311yescharacteristic
102C2×C3×Dic9C2311yescharacteristic
103#6195—22no—
104#6195—22no—
105#6195—41no—
106D3×Dic9—41no—
107(C3⋊D9)⋊C4—22no—
108(C3⋊D9)⋊C4—22no—
109(C3⋊D9)⋊C4—41no—
110(C3⋊D9)⋊C4—41no—
111#5709—91no—
112#5695—91no—
113C2×C4⋊(C3⋊D3)—31no—
114C2×C4⋊(C3⋊D3)—31no—
115C2×C4⋊(C3⋊D3)—31no—
116C2×C4×C3⋊D3—31no—
117C2×#626—31no—
118C2×#626—31no—
119C2×#626—31no—
120C2×#624—31no—
121C2×#624—31no—
122C2×#624—31no—
123C2×#624—31no—
124C2×D3×Dic3—31no—
125C32×C4⋊C4C2×D311yescharacteristic
126#3752—31no—
127#3752—31no—
128C3×(C2×D3)⋊C4C2×D311yescharacteristic
129C3×(C2×D3)⋊C4C2×D311yescharacteristic
130C3×(C2×D3)⋊C4C2×D311yescharacteristic
131C3×C4⋊Dic3—31no—
132C3×C4⋊Dic3C2×D311yescharacteristic
133C3×Dic3⋊C4—31no—
134C3×Dic3⋊C4—31no—
135C3×Dic3⋊C4—31no—
136C3×Dic3⋊C4—31no—
137C3×Dic3⋊C4C2×D311yescharacteristic
138C3×C4×Dic3—31no—
139C3×C4×Dic3C2×D311yescharacteristic
140Dic3⋊Dic3—31no—
141Dic3⋊Dic3—31no—
142#3722—31no—
143#3722—31no—
144#3722—31no—
145#3722—31no—
146#3722—31no—
147Dic32—31no—
148C2×#611—31no—
149C2×#611—31no—
150C2×#611—31no—
151C22×Dic9—31no—
152C2×D36—31no—
153C2×D36—31no—
154C2×D36—31no—
155C2×D36—61no—
156C2×D36—61no—
157C2×D36—61no—
158C2×C4×D9—31no—
159C2×C4×D9—31no—
160C2×C4×D9—31no—
161C2×C4×D9—31no—
162C2×C4×D9—31no—
163C2×C4×D9—61no—
164C9×C4⋊C4—21no—
165C9×C4⋊C4—31no—
166C9×C4⋊C4—31no—
167C9×C4⋊C4C2×D311yescharacteristic
168C9×C22⋊C4—31no—
169C9×C22⋊C4—31no—
170C9×C22⋊C4—31no—
171C42×C9—31no—
172(C2×D9)⋊C4—31no—
173(C2×D9)⋊C4—31no—
174(C2×D9)⋊C4—31no—
175(C2×D9)⋊C4—31no—
176(C2×D9)⋊C4—31no—
177(C2×D9)⋊C4—31no—
178(C2×D9)⋊C4—31no—
179(C2×D9)⋊C4—61no—
180(C2×D9)⋊C4—61no—
181C4⋊Dic9—31no—
182C4⋊Dic9C2×D311yescharacteristic
183Dic9⋊C4—31no—
184Dic9⋊C4C2×D311yescharacteristic
185Dic9⋊C4C2×D311yescharacteristic
186Dic9⋊C4C2×D311yescharacteristic
187Dic9⋊C4C2×D311yescharacteristic
188C4×Dic9—31no—
189C4×Dic9C2×D311yescharacteristic
190C22×C3×C9C2411yescharacteristic
191C2×C3⋊D9—21no—
192C2×C3⋊D9—21no—
193C2×C3⋊D9—21no—
194C2×C3⋊D9—21no—
195C2×C3⋊D9—21no—
196C2×C3⋊D9—21no—
197C2×C3⋊D9—21no—
198C2×C3⋊D9—21no—
199C2×C3⋊D9#4112yes—
200C2×D3×C9—21no—
201C2×D3×C9—21no—
202C2×D3×C9—21no—
203C3×C4×C9—21no—
204C3×C4×C9—21no—
205C3×C4×C9—21no—
206C3⋊Dic9—21no—
207C9×Dic3—21no—
208C9×Dic3—21no—
209C9×Dic3—21no—
210C3×Dic9—21no—
211C3×Dic9—21no—
212C3×Dic9—21no—
213C3×Dic9#4112yes—
214C3×#126—31no—
215C3×#125—91no—
216#898—91no—
217#898—91no—
218#898D911yescharacteristic, complemented
219#895—91no—
220#895—91no—
221#895—91no—
222#895—91no—
223#895—91no—
224#895—181no—
225#894—91no—
226#894—91no—
227#894—91no—
228#893—91no—
229#893—91no—
230#893—91no—
231#892—91no—
232D3×C4⋊C4—91no—
233D3×C4⋊C4—91no—
234#889—31no—
235#886—91no—
236#884—91no—
237#884—91no—
238#884—91no—
239#67⋊C4—91no—
240#67⋊C4—91no—
241C4×D12—91no—
242C4×D12—91no—
243C4×D12—91no—
244#872—91no—
245C22×C3⋊D3—31no—
246C22×C3⋊D3—31no—
247C22×C3⋊D3—31no—
248C22×C3×D3C22×D311yescharacteristic
249C2×C32×C4C22×D311yescharacteristic
250C2×C32×C4C22×D311yescharacteristic
251C2×C32×C4C22×D311yescharacteristic
252C2×C3⋊Dic3—31no—
253C4⋊(C3⋊D3)—62no—
254C4⋊(C3⋊D3)—62no—
255C4⋊(C3⋊D3)—121no—
256C4×C3⋊D3—121no—
257C2×C3×Dic3—31no—
258C2×C3×Dic3—31no—
259C2×C3×Dic3—31no—
260C2×C3×Dic3—31no—
261C2×C3×Dic3C22×D311yescharacteristic
262C2×C3×Dic3C22×D311yescharacteristic
263C2×C3×Dic3C22×D311yescharacteristic
264#626—62no—
265#626—62no—
266#626—121no—
267#624—62no—
268#624—62no—
269#624—121no—
270#624—121no—
271D3×Dic3—121no—
272C23×C9—31no—
273C22×D9—31no—
274C22×D9—31no—
275C22×D9—31no—
276C22×D9—61no—
277C22×D9—61no—
278C22×D9—61no—
279C2×C4×C9—21no—
280C2×C4×C9—21no—
281C2×C4×C9—21no—
282C2×C4×C9—31no—
283C2×C4×C9—31no—
284C2×C4×C9—31no—
285C2×C4×C9C22×D311yescharacteristic
286C2×C4×C9C22×D311yescharacteristic
287C2×C4×C9C22×D311yescharacteristic
288#611—62no—
289#611—62no—
290#611—121no—
291C2×Dic9—31no—
292C2×Dic9—61no—
293C2×Dic9—121no—
294C2×Dic9C22×D311yescharacteristic
295C2×Dic9C22×D311yescharacteristic
296C2×Dic9C22×D311yescharacteristic
297C2×Dic9C22×D311yescharacteristic
298D36—62no—
299D36—62no—
300D36—122no—
301D36—122no—
302D36—121no—
303D36—122no—
304C4×D9—62no—
305C4×D9—62no—
306C4×D9—121no—
307C4×D9—121no—
308C4×D9—121no—
309C4×D9—122no—
310#553—271noSylow
311C2×C3×C9C2×#4111yescharacteristic
312C2×C3×C9C2×#4111yescharacteristic
313C2×C3×C9H(5,𝔽2)11yescharacteristic
314C3⋊D9—22no—
315C3⋊D9—41no—
316C3⋊D9—41no—
317D3×C9—41no—
318C2×#67—91no—
319C2×#67—91no—
320C2×#67—91no—
321C22×Dic3—91no—
322C2×D12—91no—
323C2×D12—91no—
324C2×D12—91no—
325C2×D12—91no—
326C2×D12—91no—
327C2×D12—91no—
328C2×D12—91no—
329C2×D12—91no—
330C2×D12—91no—
331C2×D12—181no—
332C2×D12—181no—
333C2×D12—181no—
334C2×C4×D3—91no—
335C2×C4×D3—91no—
336C2×C4×D3—91no—
337C2×C4×D3—91no—
338C2×C4×D3—91no—
339C2×C4×D3—91no—
340C2×C4×D3—91no—
341C2×C4×D3—91no—
342C2×C4×D3—91no—
343C2×C4×D3—91no—
344C2×C4×D3—91no—
345C2×C4×D3—181no—
346C3×C4⋊C4—21no—
347C3×C4⋊C4—31no—
348C3×C4⋊C4—31no—
349C3×C4⋊C4—91no—
350C3×C4⋊C4—91no—
351C3×C4⋊C4—91no—
352C3×C4⋊C4—91no—
353C3×C4⋊C4—91no—
354C3×C4⋊C4C2×D911yescharacteristic
355C3×C4⋊C4D3211yescharacteristic
356C3×C22⋊C4—31no—
357C3×C22⋊C4—31no—
358C3×C22⋊C4—31no—
359C3×C42—31no—
360C3×C42—91no—
361(C2×D3)⋊C4—91no—
362(C2×D3)⋊C4—91no—
363(C2×D3)⋊C4—91no—
364(C2×D3)⋊C4—91no—
365(C2×D3)⋊C4—91no—
366(C2×D3)⋊C4—91no—
367(C2×D3)⋊C4—91no—
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—91no—
375(C2×D3)⋊C4—181no—
376(C2×D3)⋊C4—181no—
377(C2×D3)⋊C4C2×D911yescharacteristic
378(C2×D3)⋊C4C2×D911yescharacteristic
379(C2×D3)⋊C4C2×D911yescharacteristic
380C4⋊Dic3—31no—
381C4⋊Dic3—91no—
382C4⋊Dic3—91no—
383C4⋊Dic3C2×D911yescharacteristic
384Dic3⋊C4—31no—
385Dic3⋊C4—31no—
386Dic3⋊C4—31no—
387Dic3⋊C4—31no—
388Dic3⋊C4—91no—
389Dic3⋊C4—91no—
390Dic3⋊C4C2×D911yescharacteristic
391C4×Dic3—31no—
392C4×Dic3—91no—
393C4×Dic3—91no—
394C4×Dic3C2×D911yescharacteristic
395C22×C32C23×D311yescharacteristic
396C2×C3⋊D3—32no—
397C2×C3⋊D3—61no—
398C2×C3⋊D3—61no—
399C2×C3⋊D3—61no—
400C2×C3⋊D3—61no—
401C2×C3⋊D3—61no—
402C2×C3⋊D3—61no—
403C2×C3⋊D3—61no—
404C2×C3⋊D3—61no—
405C2×C3×D3—21no—
406C2×C3×D3—21no—
407C2×C3×D3—21no—
408C32×C4—21no—
409C32×C4—21no—
410C32×C4—21no—
411C3⋊Dic3—61no—
412C3×Dic3—21no—
413C3×Dic3—21no—
414C3×Dic3—21no—
415C3×Dic3—32no—
416C3×Dic3—61no—
417C3×Dic3—61no—
418C3×Dic3—61no—
419C22×C9—21no—
420C22×C9—61no—
421C22×C9—61no—
422C22×C9—61no—
423C22×C9C23×D311yescharacteristic
424C2×D9—32no—
425C2×D9—62no—
426C2×D9—61no—
427C2×D9—61no—
428C2×D9—61no—
429C2×D9—61no—
430C2×D9—61no—
431C2×D9—61no—
432C2×D9—61no—
433C2×D9—61no—
434C2×D9—121no—
435C2×D9—121no—
436C2×D9—121no—
437C2×D9—121no—
438C2×D9—121no—
439C2×D9—121no—
440C2×D9—121no—
441C2×D9—121no—
442C4×C9—22no—
443C4×C9—21no—
444C4×C9—21no—
445C4×C9—21no—
446C4×C9—41no—
447C4×C9—41no—
448C4×C9—61no—
449C4×C9—61no—
450C4×C9—61no—
451Dic9—21no—
452Dic9—21no—
453Dic9—21no—
454Dic9—61no—
455Dic9—121no—
456Dic9#23912yes—
457#126—31no—
458#126—271no—
459#125—91no—
460#123—271no—
461#123—271no—
462#121—271no—
463#121—271no—
464#121—271no—
465#121—271no—
466C4×D4—271no—
467C4×D4—271no—
468C4×D4—271no—
469C4×D4—271no—
470#117—271no—
471C2×C4⋊C4—271no—
472C3×C9#55311yescharacteristic, complemented, Sylow
473C23×C3—31no—
474C22×D3—91no—
475C22×D3—91no—
476C22×D3—91no—
477C22×D3—91no—
478C22×D3—91no—
479C22×D3—91no—
480C22×D3—181no—
481C22×D3—181no—
482C22×D3—181no—
483C22×D3C22×D911yescharacteristic
484C2×C3×C4—21no—
485C2×C3×C4—21no—
486C2×C3×C4—21no—
487C2×C3×C4—31no—
488C2×C3×C4—31no—
489C2×C3×C4—31no—
490C2×C3×C4—91no—
491C2×C3×C4—91no—
492C2×C3×C4—91no—
493C2×C3×C4—91no—
494C2×C3×C4C22×D911yescharacteristic
495C2×C3×C4C22×D911yescharacteristic
496C2×C3×C4C22×D911yescharacteristic
497C2×C3×C4C2×D3211yescharacteristic
498C2×C3×C4C2×D3211yescharacteristic
499C2×C3×C4C2×D3211yescharacteristic
500#67—182no—
501#67—182no—
502#67—361no—
503C2×Dic3—31no—
504C2×Dic3—31no—
505C2×Dic3—31no—
506C2×Dic3—31no—
507C2×Dic3—91no—
508C2×Dic3—91no—
509C2×Dic3—181no—
510C2×Dic3—361no—
511C2×Dic3C22×D911yescharacteristic
512C2×Dic3C22×D911yescharacteristic
513C2×Dic3C22×D911yescharacteristic
514D12—182no—
515D12—182no—
516D12—182no—
517D12—182no—
518D12—182no—
519D12—182no—
520D12—362no—
521D12—362no—
522D12—361no—
523D12—361no—
524D12—362no—
525D12—361no—
526C4×D3—182no—
527C4×D3—182no—
528C4×D3—182no—
529C4×D3—182no—
530C4×D3—361no—
531C4×D3—361no—
532C4×D3—361no—
533C4×D3—361no—
534C4×D3—361no—
535C4×D3—361no—
536C4×D3—361no—
537C4×D3—362no—
538C2×C32D3×#4111yescharacteristic
539C2×C32D3×#4111yescharacteristic
540C2×C32#100911yescharacteristic
541C3⋊D3—62no—
542C3⋊D3—121no—
543C3⋊D3—121no—
544C3×D3—41no—
545C2×C9—21no—
546C2×C9—21no—
547C2×C9—21no—
548C2×C9—121no—
549C2×C9C2×#23911yescharacteristic
550C2×C9D3×#4111yescharacteristic
551C2×C9#100911yescharacteristic
552D9—62no—
553D9—122no—
554D9—121no—
555D9—121no—
556D9—241no—
557D9—241no—
558C2×D4—271no—
559C2×D4—271no—
560C2×D4—271no—
561C2×D4—271no—
562C2×D4—271no—
563C2×D4—271no—
564C22×C4—271no—
565C22×C4—271no—
566C22×C4—271no—
567C22×C4—271no—
568C22×C4—271no—
569C22×C4—271no—
570C4⋊C4—31no—
571C4⋊C4—31no—
572C4⋊C4—91no—
573C4⋊C4—91no—
574C4⋊C4—91no—
575C4⋊C4—91no—
576C4⋊C4—91no—
577C4⋊C4—271no—
578C4⋊C4—271no—
579C4⋊C4D3×D911yescharacteristic
580C22⋊C4—31no—
581C22⋊C4—31no—
582C22⋊C4—31no—
583C22⋊C4—271no—
584C22⋊C4—271no—
585C22⋊C4—271no—
586C22⋊C4—271no—
587C22⋊C4—271no—
588C22⋊C4—271no—
589C22⋊C4—271no—
590C42—31no—
591C42—91no—
592C42—271no—
593C22×C3—21no—
594C22×C3—61no—
595C22×C3—61no—
596C22×C3—61no—
597C22×C3C23×D911yescharacteristic
598C22×C3C22×D3211yescharacteristic
599C2×D3—21no—
600C2×D3—21no—
601C2×D3—21no—
602C2×D3—92no—
603C2×D3—92no—
604C2×D3—182no—
605C2×D3—181no—
606C2×D3—181no—
607C2×D3—181no—
608C2×D3—181no—
609C2×D3—181no—
610C2×D3—181no—
611C2×D3—181no—
612C2×D3—181no—
613C2×D3—181no—
614C2×D3—181no—
615C2×D3—181no—
616C2×D3—181no—
617C2×D3—181no—
618C2×D3—181no—
619C2×D3—181no—
620C2×D3—181no—
621C2×D3—361no—
622C2×D3—361no—
623C2×D3—361no—
624C2×D3—361no—
625C2×D3—361no—
626C2×D3—361no—
627C2×D3—361no—
628C2×D3—361no—
629C3×C4—22no—
630C3×C4—21no—
631C3×C4—21no—
632C3×C4—21no—
633C3×C4—21no—
634C3×C4—21no—
635C3×C4—21no—
636C3×C4—41no—
637C3×C4—41no—
638C3×C4—61no—
639C3×C4—61no—
640C3×C4—61no—
641C3×C4—92no—
642C3×C4—181no—
643C3×C4—181no—
644C3×C4—181no—
645Dic3—21no—
646Dic3—21no—
647Dic3—21no—
648Dic3—32no—
649Dic3—61no—
650Dic3—61no—
651Dic3—61no—
652Dic3—181no—
653Dic3—181no—
654Dic3—361no—
655C32#570911yescharacteristic
656C9—21no—
657C9#569511yescharacteristic, complemented
658C23—31no—
659C23—271no—
660C23—271no—
661C23—271no—
662D4—542no—
663D4—542no—
664D4—542no—
665D4—542no—
666D4—1081no—
667D4—1081no—
668C2×C4—31no—
669C2×C4—31no—
670C2×C4—31no—
671C2×C4—91no—
672C2×C4—91no—
673C2×C4—91no—
674C2×C4—91no—
675C2×C4—271no—
676C2×C4—542no—
677C2×C4—542no—
678C2×C4—1081no—
679C2×C4—1081no—
680C2×C4—1081no—
681C2×C4—1081no—
682C2×C4C2×D3×D911yescharacteristic
683C2×C4C2×D3×D911yescharacteristic
684C2×C4C2×D3×D911yescharacteristic
685C2×C3—21no—
686C2×C3—21no—
687C2×C3—21no—
688C2×C3—121no—
689C2×C3#41×D911yescharacteristic
690C2×C3#41×D911yescharacteristic
691C2×C3#6371511yescharacteristic
692C2×C3#6430811yescharacteristic
693C2×C3#6431211yescharacteristic
694C2×C3D3×#23911yescharacteristic
695D3—41no—
696D3—182no—
697D3—182no—
698D3—362no—
699D3—361no—
700D3—361no—
701D3—361no—
702D3—361no—
703D3—721no—
704D3—721no—
705C22—61no—
706C22—61no—
707C22—61no—
708C22—272no—
709C22—541no—
710C22—541no—
711C22—541no—
712C22—541no—
713C22—541no—
714C22—541no—
715C22—541no—
716C22—541no—
717C22C22×D3×D911yescharacteristic
718C4—21no—
719C4—21no—
720C4—21no—
721C4—61no—
722C4—61no—
723C4—61no—
724C4—92no—
725C4—181no—
726C4—181no—
727C4—181no—
728C4—541no—
729C3—21no—
730C3#1058981111yescharacteristic, complemented
731C3#1059446811yescharacteristic
732C2—121no—
733C2—542no—
734C2—1081no—
735C2—1081no—
736C2#1172247811yescharacteristic
737C2#1172249811yescharacteristic
738C2D9×#23911yescharacteristic
subgroupG/H
centerC22C22×D3×D9
commutator, cosocleC22×C3×C9C24
FrattiniC22×C3C22×D32
FittingC3×C9×C4⋊C4C22
socleC22×C32C23×D3
hypercenterC4⋊C4D3×D9
hypocenterC3×C9#553
LCSG ▷ C22×C3×C9 ▷ C3×C9
UCSC1 ◁ C22 ◁ C4⋊C4

Complements

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

NH ≅ G/Ntype
1. #11721751C2semidirect
2. C9×#898C2semidirect
3. C3×#63451C2semidirect
4. #11721039C2semidirect
5. #11721039C2semidirect
6. #11721039C2semidirect
7. #11721020C2semidirect
8. #11721014C2semidirect
9. #11721013C2semidirect
10. #11720997C2semidirect
11. #11720993C2semidirect
12. #11720992C2semidirect
13. #11720980C2semidirect
14. #11720920C2semidirect
15. #11720898C2semidirect
75. #63451D3semidirect
218. #898D9semidirect
472. C3×C9#553semidirect
657. C9#5695semidirect
730. C3#10589811semidirect

Maximal subgroups

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

subgroupindex
#117217512
C9×#8982
C3×#634512
#117210392
#117210202
#117210142
#117210132
#117209972
#117209932
#117209922
#117209802
#117209202
#117208982
#105944683
#105898113