Finite Group Databasebeta

← #13151144

Subgroups — #13151144

Order 1728.

970 conjugacy classes of subgroups.

The subgroup lattice has 776 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C9×#237C211yesmaximal, characteristic, complemented
2C2×#88662C211yesmaximal, characteristic, complemented
3#11721839C211yesmaximal, characteristic, complemented
4C3×#63497C211yesmaximal, characteristic, complemented
5#67⋊Dic9C211yesmaximal, characteristic, complemented
6#11721282C211yesmaximal, characteristic, complemented
7#11721280C211yesmaximal, characteristic, complemented
8C2×#88442C211yesmaximal, characteristic, complemented
9#11721251C211yesmaximal, characteristic, complemented
10#11721249C211yesmaximal, characteristic, complemented
11#11721240C211yesmaximal, characteristic, complemented
12D3×Dic9⋊C4C211yesmaximal, characteristic, complemented
13#11720986C211yesmaximal, characteristic, complemented
14#11720954C211yesmaximal, characteristic, complemented
15#11720903C211yesmaximal, characteristic, complemented
16#10595149—31nomaximal
17#10589926—31nomaximal
18C2×C3×D4×C9C2211yescharacteristic
19C2×#6233C2211yescharacteristic
20C2×#6233C2211yescharacteristic
21C22×C3⋊Dic9C2211yescharacteristic
22C2×C9×#67C2211yescharacteristic
23C2×C9×#67C2211yescharacteristic
24C22×C9×Dic3C2211yescharacteristic
25C22×C9×Dic3C2211yescharacteristic
26C22×C3×Dic9C2211yescharacteristic
27C9×#237—24no—
28C2×C4×D3×C9C2211yescharacteristic
29C2×C9×Dic6C2211yescharacteristic
30C2×#6195C2211yescharacteristic
31#88662—24no—
32C2×D3×Dic9C2211yescharacteristic
33C2×D3×Dic9C2211yescharacteristic
34C2×(C3⋊D9)⋊C4C2211yescharacteristic
35C2×#6189C2211yescharacteristic
36#88551C2211yescharacteristic
37#88536C2211yescharacteristic
38#88534C2211yescharacteristic
39C3×#3676C2211yescharacteristic
40C3×#3676C2211yescharacteristic
41C3×#3676C2211yescharacteristic
42C3×Dic9⋊C4C2211yescharacteristic
43C3×Dic9⋊C4C2211yescharacteristic
44(C2×D3)⋊Dic9C2211yescharacteristic
45#88445C2211yescharacteristic
46#88445C2211yescharacteristic
47Dic3⋊Dic9C2211yescharacteristic
48#88442C2211yescharacteristic
49#88442C2211yescharacteristic
50#88442C2211yescharacteristic
51#88442C2211yescharacteristic
52Dic9⋊Dic3C2211yescharacteristic
53Dic9⋊Dic3C2211yescharacteristic
54Dic3×Dic9C2211yescharacteristic
55C2×C3×#237D311yescharacteristic
56C2×#3804—31no—
57#64148—31no—
58C3×#935—31no—
59#67⋊Dic3—31no—
60#63971—31no—
61#63969—31no—
62C2×#3724—31no—
63#63966—31no—
64#63964—31no—
65#63952—31no—
66#63888—31no—
67D3×Dic3⋊C4—31no—
68#63850—31no—
69#63839—31no—
70C2×C9×#41—31no—
71C2×#3699—31no—
72#63508—31no—
73#63506—31no—
74#63501—31no—
75#63501—31no—
76#63501—61no—
77#63497—31no—
78#63497D311yescharacteristic, complemented
79D4×Dic9—31no—
80#63491—31no—
81#63491—31no—
82C4×#611—31no—
83#63486—31no—
84C2×Dic9⋊C4—31no—
85C2×Dic9⋊C4—31no—
86C23×C3×C9C2311yescharacteristic
87C23×C3×C9C2311yescharacteristic
88C22×C3⋊D9C2311yescharacteristic
89C22×D3×C9C2311yescharacteristic
90C3×D4×C9—22no—
91C2×C3×C4×C9C2311yescharacteristic
92#6233—22no—
93#6233—22no—
94C2×C3⋊Dic9—22no—
95C2×C3⋊Dic9C2311yescharacteristic
96C2×C3⋊Dic9C2311yescharacteristic
97C2×C3⋊Dic9C2311yescharacteristic
98C9×#67—22no—
99C9×#67D414yescomplemented
100C2×C9×Dic3—22no—
101C2×C9×Dic3—22no—
102C2×C9×Dic3C2311yescharacteristic
103C2×C9×Dic3C2311yescharacteristic
104C2×C9×Dic3C2311yescharacteristic
105C2×C3×Dic9—22no—
106C2×C3×Dic9C2311yescharacteristic
107C2×C3×Dic9C2311yescharacteristic
108C2×C3×Dic9C2311yescharacteristic
109C2×C3×Dic9C2311yescharacteristic
110C4×D3×C9—22no—
111C9×Dic6—22no—
112#6195—22no—
113D3×Dic9—22no—
114D3×Dic9—22no—
115(C3⋊D9)⋊C4—22no—
116#6189—22no—
117#5824—91no—
118#5655—91no—
119C2×C32×D4C2×D311yescharacteristic
120C2×#638—31no—
121C2×#638—31no—
122C22×C3⋊Dic3—31no—
123C2×C3×#67C2×D311yescharacteristic
124C2×C3×#67C2×D311yescharacteristic
125C22×C3×Dic3—31no—
126C22×C3×Dic3C2×D311yescharacteristic
127C22×C3×Dic3C2×D311yescharacteristic
128C3×#237—24no—
129C2×C3×C4×D3C2×D311yescharacteristic
130C2×C3×Dic6C2×D311yescharacteristic
131C2×#627—31no—
132C2×#626—31no—
133C2×#624—31no—
134#3804—64no—
135C2×D3×Dic3—31no—
136C2×D3×Dic3—31no—
137#3757—31no—
138#3752—31no—
139#3750—31no—
140C3×#217—31no—
141C3×#217—31no—
142C3×#217—31no—
143C3×Dic3⋊C4—31no—
144C3×Dic3⋊C4—31no—
145#3724—31no—
146#3724—31no—
147#3724—31no—
148#3724—31no—
149Dic3⋊Dic3—31no—
150Dic3⋊Dic3—31no—
151Dic3⋊Dic3—31no—
152#3722—31no—
153#3722—31no—
154(C2×D3)⋊Dic3—31no—
155Dic32—31no—
156C9×#41—64no—
157C2×Q8×C9—31no—
158C2×D4×C9—21no—
159C2×D4×C9—31no—
160C2×D4×C9—31no—
161C2×D4×C9C2×D311yescharacteristic
162C22×C4×C9—31no—
163C22×C4×C9—31no—
164C22×C4×C9—31no—
165C2×#611—31no—
166C2×#611—31no—
167C2×#611—31no—
168C2×#611—61no—
169C2×#611—61no—
170C22×Dic9—31no—
171C22×Dic9—31no—
172C22×Dic9—31no—
173C22×Dic9—61no—
174C22×Dic9C2×D311yescharacteristic
175#3699—64no—
176C2×C4×D9—31no—
177C2×Dic18—31no—
178#3676—31no—
179#3676—31no—
180#3676—61no—
181#3676C2×D311yescharacteristic
182#3676C2×D311yescharacteristic
183#3676C2×D311yescharacteristic
184(C2×D9)⋊C4—31no—
185(C2×D9)⋊C4—31no—
186(C2×D9)⋊C4—31no—
187(C2×D9)⋊C4—61no—
188C4⋊Dic9—31no—
189Dic9⋊C4—31no—
190Dic9⋊C4—31no—
191Dic9⋊C4—31no—
192Dic9⋊C4—31no—
193Dic9⋊C4—31no—
194Dic9⋊C4—31no—
195Dic9⋊C4—31no—
196Dic9⋊C4—61no—
197Dic9⋊C4C2×D311yescharacteristic
198Dic9⋊C4C2×D311yescharacteristic
199C4×Dic9—31no—
200C22×C3×C9—21no—
201C22×C3×C9—21no—
202C22×C3×C9—21no—
203C22×C3×C9—21no—
204C22×C3×C9—21no—
205C22×C3×C9C2×D412yes—
206C22×C3×C9C2411yescharacteristic
207C2×C3⋊D9—21no—
208C2×C3⋊D9—21no—
209C2×C3⋊D9—21no—
210C2×D3×C9—21no—
211C2×D3×C9—21no—
212C2×D3×C9C2×D412yes—
213C3×C4×C9—21no—
214C3⋊Dic9—21no—
215C3⋊Dic9—21no—
216C3⋊Dic9#4112yescomplemented
217C9×Dic3—21no—
218C9×Dic3—21no—
219C9×Dic3C2×D412yes—
220C3×Dic9—21no—
221C3×Dic9—21no—
222C3×Dic9—21no—
223C3×Dic9—21no—
224C2×C3×#41—31no—
225C2×#237—91no—
226C2×#237D911yescharacteristic, complemented
227C2×#235—91no—
228C3×#123—91no—
229#946—91no—
230#944—91no—
231#939—91no—
232#939—91no—
233#939—91no—
234#939—181no—
235#935—31no—
236#935—91no—
237D4×Dic3—91no—
238#929—91no—
239#929—91no—
240C4×#67—91no—
241#924—91no—
242C2×Dic3⋊C4—91no—
243C2×Dic3⋊C4—91no—
244C2×Dic3⋊C4—91no—
245#896—91no—
246#894—91no—
247D3×C4⋊C4—91no—
248#888—91no—
249#886—91no—
250#884—91no—
251#883—91no—
252#67⋊C4—91no—
253#67⋊C4—91no—
254#878—91no—
255C23×C32C22×D311yescharacteristic
256C23×C32C22×D311yescharacteristic
257C22×C3⋊D3—31no—
258C22×C3×D3C22×D311yescharacteristic
259C32×D4—22no—
260C2×C32×C4C22×D311yescharacteristic
261#638—62no—
262#638—62no—
263C2×C3⋊Dic3—31no—
264C2×C3⋊Dic3—31no—
265C2×C3⋊Dic3—31no—
266C2×C3⋊Dic3—62no—
267C3×#67—22no—
268C3×#67#6714yes—
269C2×C3×Dic3—22no—
270C2×C3×Dic3—22no—
271C2×C3×Dic3—31no—
272C2×C3×Dic3—31no—
273C2×C3×Dic3—31no—
274C2×C3×Dic3—31no—
275C2×C3×Dic3—62no—
276C2×C3×Dic3C22×D311yescharacteristic
277C2×C3×Dic3C22×D311yescharacteristic
278C2×C3×Dic3C22×D311yescharacteristic
279C3×C4×D3—22no—
280C3×Dic6—22no—
281#627—62no—
282#626—62no—
283#624—62no—
284D3×Dic3—62no—
285D3×Dic3—62no—
286C23×C9—21no—
287C23×C9—21no—
288C23×C9—31no—
289C23×C9C22×D311yescharacteristic
290C23×C9C22×D311yescharacteristic
291C22×D9—31no—
292C22×D9—61no—
293Q8×C9—62no—
294D4×C9—22no—
295D4×C9—34no—
296D4×C9—42no—
297D4×C9—62no—
298C2×C4×C9—21no—
299C2×C4×C9—31no—
300C2×C4×C9—31no—
301C2×C4×C9—31no—
302C2×C4×C9—62no—
303C2×C4×C9—62no—
304C2×C4×C9—62no—
305C2×C4×C9C22×D311yescharacteristic
306#611—62no—
307#611—62no—
308#611—62no—
309#611—122no—
310#611—122no—
311C2×Dic9—22no—
312C2×Dic9—31no—
313C2×Dic9—31no—
314C2×Dic9—31no—
315C2×Dic9—61no—
316C2×Dic9—61no—
317C2×Dic9—61no—
318C2×Dic9—62no—
319C2×Dic9—62no—
320C2×Dic9—62no—
321C2×Dic9—122no—
322C2×Dic9C22×D311yescharacteristic
323C2×Dic9C22×D311yescharacteristic
324C2×Dic9C22×D311yescharacteristic
325C2×Dic9C22×D311yescharacteristic
326C4×D9—62no—
327Dic18—62no—
328#547—271noSylow
329C2×C3×C9—22no—
330C2×C3×C9—41no—
331C2×C3×C9C22×D411yescharacteristic
332C2×C3×C9C2×#4111yescharacteristic
333C2×C3×C92−1+411yescharacteristic
334C3⋊D9—41no—
335D3×C9—22no—
336C3×#41—64no—
337C2×C3×Q8—31no—
338C2×C3×D4—21no—
339C2×C3×D4—31no—
340C2×C3×D4—31no—
341C2×C3×D4C2×D911yescharacteristic
342C2×C3×D4D3211yescharacteristic
343C22×C3×C4—31no—
344C22×C3×C4—31no—
345C22×C3×C4—31no—
346C22×C3×C4—91no—
347C2×#67—91no—
348C2×#67—91no—
349C2×#67—91no—
350C2×#67—91no—
351C2×#67—91no—
352C2×#67—181no—
353C2×#67—181no—
354C2×#67C2×D911yescharacteristic
355C2×#67C2×D911yescharacteristic
356C22×Dic3—31no—
357C22×Dic3—91no—
358C22×Dic3—91no—
359C22×Dic3—91no—
360C22×Dic3—91no—
361C22×Dic3—181no—
362C22×Dic3C2×D911yescharacteristic
363C22×Dic3C2×D911yescharacteristic
364#237—24no—
365#237—184no—
366#235—184no—
367C2×D12—91no—
368C2×C4×D3—91no—
369C2×C4×D3—91no—
370C2×C4×D3—91no—
371C2×C4×D3—91no—
372C2×C4×D3C2×D911yescharacteristic
373C2×Dic6—91no—
374C2×Dic6—91no—
375C2×Dic6C2×D911yescharacteristic
376C3×C4⋊C4—91no—
377C3×C4⋊C4—91no—
378C3×C22⋊C4—91no—
379C3×C22⋊C4—91no—
380C3×C22⋊C4—91no—
381#217—31no—
382#217—31no—
383#217—31no—
384#217—91no—
385#217—91no—
386#217—91no—
387#217—181no—
388(C2×D3)⋊C4—91no—
389(C2×D3)⋊C4—91no—
390(C2×D3)⋊C4—91no—
391(C2×D3)⋊C4—91no—
392(C2×D3)⋊C4—91no—
393(C2×D3)⋊C4—91no—
394(C2×D3)⋊C4—91no—
395(C2×D3)⋊C4—181no—
396C4⋊Dic3—91no—
397C4⋊Dic3—91no—
398C4⋊Dic3—91no—
399Dic3⋊C4—31no—
400Dic3⋊C4—31no—
401Dic3⋊C4—91no—
402Dic3⋊C4—91no—
403Dic3⋊C4—91no—
404Dic3⋊C4—91no—
405Dic3⋊C4—91no—
406Dic3⋊C4—91no—
407Dic3⋊C4—91no—
408Dic3⋊C4—91no—
409Dic3⋊C4—91no—
410Dic3⋊C4—91no—
411Dic3⋊C4—91no—
412Dic3⋊C4—91no—
413Dic3⋊C4—91no—
414Dic3⋊C4—181no—
415C4×Dic3—91no—
416C4×Dic3—91no—
417C22×C32—21no—
418C22×C32—21no—
419C22×C32—21no—
420C22×C32—21no—
421C22×C32—21no—
422C22×C32C2×#6712yes—
423C22×C32C23×D311yescharacteristic
424C2×C3⋊D3—61no—
425C2×C3⋊D3—61no—
426C2×C3⋊D3—61no—
427C2×C3×D3—21no—
428C2×C3×D3—21no—
429C2×C3×D3C2×#6712yes—
430C32×C4—21no—
431C3⋊Dic3—32no—
432C3⋊Dic3—61no—
433C3⋊Dic3—61no—
434C3×Dic3—21no—
435C3×Dic3—21no—
436C3×Dic3—61no—
437C3×Dic3—61no—
438C3×Dic3—61no—
439C3×Dic3—61no—
440C3×Dic3C2×#6712yes—
441C22×C9—21no—
442C22×C9—21no—
443C22×C9—21no—
444C22×C9—21no—
445C22×C9—21no—
446C22×C9—21no—
447C22×C9—22no—
448C22×C9—32no—
449C22×C9—41no—
450C22×C9—41no—
451C22×C9—41no—
452C22×C9—41no—
453C22×C9—41no—
454C22×C9—61no—
455C22×C9—61no—
456C22×C9D3×D412yes—
457C22×C9C23×D311yescharacteristic
458C2×D9—61no—
459C2×D9—61no—
460C2×D9—61no—
461C2×D9—121no—
462C2×D9—121no—
463C2×D9—121no—
464C4×C9—21no—
465C4×C9—32no—
466C4×C9—41no—
467C4×C9—61no—
468C4×C9—61no—
469Dic9—21no—
470Dic9—21no—
471Dic9—21no—
472Dic9—21no—
473Dic9—32no—
474Dic9—62no—
475Dic9—61no—
476Dic9—61no—
477Dic9—121no—
478Dic9—121no—
479C2×#41—31no—
480C2×#41—271no—
481C4⋊Q8—271no—
482#123—91no—
483#123—271no—
484#123—271no—
485#123—271no—
486C22⋊Q8—271no—
487C22⋊Q8—271no—
488#121—271no—
489#121—271no—
490C4×D4—271no—
491C4×D4—271no—
492C2×C4⋊C4—271no—
493C2×C4⋊C4—271no—
494C3×C9#54711yescharacteristic, complemented, Sylow
495C23×C3—21no—
496C23×C3—21no—
497C23×C3—31no—
498C23×C3C22×D911yescharacteristic
499C23×C3C22×D911yescharacteristic
500C23×C3C2×D3211yescharacteristic
501C23×C3C2×D3211yescharacteristic
502C22×D3—91no—
503C22×D3—91no—
504C22×D3—181no—
505C22×D3C22×D911yescharacteristic
506C3×Q8—62no—
507C3×D4—22no—
508C3×D4—22no—
509C3×D4—34no—
510C3×D4—42no—
511C3×D4—62no—
512C2×C3×C4—21no—
513C2×C3×C4—31no—
514C2×C3×C4—31no—
515C2×C3×C4—31no—
516C2×C3×C4—62no—
517C2×C3×C4—62no—
518C2×C3×C4—62no—
519C2×C3×C4—91no—
520C2×C3×C4—91no—
521C2×C3×C4—91no—
522C2×C3×C4—91no—
523C2×C3×C4—182no—
524C2×C3×C4C22×D911yescharacteristic
525C2×C3×C4C2×D3211yescharacteristic
526#67—22no—
527#67—182no—
528#67—182no—
529#67—182no—
530#67—182no—
531#67—182no—
532#67—362no—
533#67—362no—
534#67#61114yescomplemented
535C2×Dic3—22no—
536C2×Dic3—22no—
537C2×Dic3—31no—
538C2×Dic3—31no—
539C2×Dic3—31no—
540C2×Dic3—31no—
541C2×Dic3—62no—
542C2×Dic3—91no—
543C2×Dic3—91no—
544C2×Dic3—91no—
545C2×Dic3—91no—
546C2×Dic3—91no—
547C2×Dic3—91no—
548C2×Dic3—181no—
549C2×Dic3—181no—
550C2×Dic3—181no—
551C2×Dic3—182no—
552C2×Dic3—182no—
553C2×Dic3—182no—
554C2×Dic3—182no—
555C2×Dic3—362no—
556C2×Dic3C22×D911yescharacteristic
557C2×Dic3C22×D911yescharacteristic
558C2×Dic3C22×D911yescharacteristic
559D12—182no—
560C4×D3—22no—
561C4×D3—182no—
562C4×D3—182no—
563C4×D3—182no—
564C4×D3—182no—
565Dic6—22no—
566Dic6—182no—
567Dic6—182no—
568C2×C32—22no—
569C2×C32—41no—
570C2×C32D3×#4111yescharacteristic
571C2×C32#101011yescharacteristic
572C2×C32C22×#6711yescharacteristic
573C3⋊D3—121no—
574C3×D3—22no—
575C2×C9—22no—
576C2×C9—21no—
577C2×C9—21no—
578C2×C9—21no—
579C2×C9—42no—
580C2×C9—41no—
581C2×C9—62no—
582C2×C9—81no—
583C2×C9C2×D3×D411yescharacteristic
584C2×C9D3×#4111yescharacteristic
585C2×C9#101011yescharacteristic
586D9—121no—
587D9—241no—
588#41—64no—
589#41—544no—
590C2×Q8—31no—
591C2×Q8—271no—
592C2×D4—31no—
593C2×D4—31no—
594C2×D4—271no—
595C2×D4—271no—
596C2×D4—271no—
597C2×D4D3×D911yescharacteristic
598C22×C4—31no—
599C22×C4—31no—
600C22×C4—31no—
601C22×C4—91no—
602C22×C4—271no—
603C22×C4—271no—
604C22×C4—271no—
605C22×C4—271no—
606C4⋊C4—91no—
607C4⋊C4—91no—
608C4⋊C4—271no—
609C4⋊C4—271no—
610C4⋊C4—271no—
611C4⋊C4—271no—
612C4⋊C4—271no—
613C4⋊C4—271no—
614C4⋊C4—271no—
615C4⋊C4—271no—
616C22⋊C4—91no—
617C22⋊C4—91no—
618C22⋊C4—91no—
619C22⋊C4—271no—
620C22⋊C4—271no—
621C22⋊C4—271no—
622C22⋊C4—271no—
623C22⋊C4—271no—
624C42—271no—
625C22×C3—21no—
626C22×C3—21no—
627C22×C3—21no—
628C22×C3—21no—
629C22×C3—21no—
630C22×C3—21no—
631C22×C3—21no—
632C22×C3—21no—
633C22×C3—21no—
634C22×C3—21no—
635C22×C3—21no—
636C22×C3—22no—
637C22×C3—32no—
638C22×C3—41no—
639C22×C3—41no—
640C22×C3—41no—
641C22×C3—41no—
642C22×C3—41no—
643C22×C3—61no—
644C22×C3—61no—
645C22×C3C2×#61112yes—
646C22×C3C23×D911yescharacteristic
647C22×C3D3×#6712yes—
648C22×C3C22×D3211yescharacteristic
649C2×D3—21no—
650C2×D3—21no—
651C2×D3—181no—
652C2×D3—181no—
653C2×D3—181no—
654C2×D3—181no—
655C2×D3—181no—
656C2×D3—181no—
657C2×D3—361no—
658C2×D3—361no—
659C2×D3—361no—
660C2×D3C2×#61112yes—
661C3×C4—21no—
662C3×C4—21no—
663C3×C4—32no—
664C3×C4—41no—
665C3×C4—61no—
666C3×C4—61no—
667C3×C4—181no—
668C3×C4—181no—
669C3×C4—181no—
670C3×C4—181no—
671Dic3—21no—
672Dic3—21no—
673Dic3—61no—
674Dic3—61no—
675Dic3—61no—
676Dic3—61no—
677Dic3—92no—
678Dic3—92no—
679Dic3—182no—
680Dic3—181no—
681Dic3—181no—
682Dic3—181no—
683Dic3—181no—
684Dic3—361no—
685Dic3—361no—
686Dic3C2×#61112yes—
687C32#582411yescharacteristic
688C9—21no—
689C9#565511yescharacteristic, complemented
690C23—31no—
691C23—271no—
692C23C2×D3×D911yescharacteristic
693C23C2×D3×D911yescharacteristic
694Q8—62no—
695Q8—542no—
696D4—22no—
697D4—34no—
698D4—62no—
699D4—542no—
700D4—542no—
701D4—542no—
702C2×C4—31no—
703C2×C4—31no—
704C2×C4—31no—
705C2×C4—62no—
706C2×C4—62no—
707C2×C4—62no—
708C2×C4—91no—
709C2×C4—91no—
710C2×C4—91no—
711C2×C4—91no—
712C2×C4—182no—
713C2×C4—271no—
714C2×C4—271no—
715C2×C4—271no—
716C2×C4—542no—
717C2×C4—542no—
718C2×C4—542no—
719C2×C4—542no—
720C2×C4C2×D3×D911yescharacteristic
721C2×C3—22no—
722C2×C3—22no—
723C2×C3—21no—
724C2×C3—21no—
725C2×C3—21no—
726C2×C3—42no—
727C2×C3—41no—
728C2×C3—41no—
729C2×C3—62no—
730C2×C3—81no—
731C2×C3#41×D911yescharacteristic
732C2×C3#6371611yescharacteristic
733C2×C3C22×#61111yescharacteristic
734C2×C3#6430911yescharacteristic
735C2×C3#6431211yescharacteristic
736C2×C3C2×D3×#6711yescharacteristic
737D3—22no—
738D3—361no—
739D3—361no—
740D3—721no—
741C22—21no—
742C22—21no—
743C22—21no—
744C22—21no—
745C22—21no—
746C22—32no—
747C22—61no—
748C22—61no—
749C22—541no—
750C22—541no—
751C22—541no—
752C22D3×#61112yes—
753C22C22×D3×D911yescharacteristic
754C4—21no—
755C4—32no—
756C4—61no—
757C4—61no—
758C4—181no—
759C4—181no—
760C4—181no—
761C4—181no—
762C4—272no—
763C4—541no—
764C4—541no—
765C3—21no—
766C3#1058992611yescharacteristic, complemented
767C3#1059514911yescharacteristic
768C2—22no—
769C2—41no—
770C2—62no—
771C2—1081no—
772C2#1172249411yescharacteristic
773C2#1172249811yescharacteristic
774C2C2×D3×#61111yescharacteristic
subgroupG/H
centerC22C22×D3×D9
commutator, cosocleC22×C3×C9C24
FrattiniC22×C3C22×D32
FittingC2×C3×D4×C9C22
socleC22×C32C23×D3
hypercenterC2×D4D3×D9
hypocenterC3×C9#547
LCSG ▷ C22×C3×C9 ▷ C3×C9
UCSC1 ◁ C22 ◁ C2×D4

Complements

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

NH ≅ G/Ntype
1. C2×C9×#237C2semidirect
2. C2×#88662C2semidirect
3. #11721839C2semidirect
4. C3×#63497C2semidirect
5. #67⋊Dic9C2semidirect
6. #11721282C2semidirect
7. #11721280C2semidirect
8. C2×#88442C2semidirect
9. #11721251C2semidirect
10. #11721249C2semidirect
11. #11721240C2semidirect
12. D3×Dic9⋊C4C2semidirect
13. #11720986C2semidirect
14. #11720954C2semidirect
15. #11720903C2semidirect
78. #63497D3semidirect
99. C9×#67D4semidirect
216. C3⋊Dic9#41semidirect
226. C2×#237D9semidirect
494. C3×C9#547semidirect
534. #67#611semidirect
689. C9#5655semidirect
766. C3#10589926semidirect

Maximal subgroups

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

subgroupindex
C2×C9×#2372
C2×#886622
#117218392
C3×#634972
#67⋊Dic92
#117212822
#117212802
C2×#884422
#117212512
#117212492
#117212402
D3×Dic9⋊C42
#117209862
#117209542
#117209032
#105951493
#105899263