Finite Group Databasebeta

← #13150988

Subgroups — #13150988

Order 1728.

976 conjugacy classes of subgroups.

The subgroup lattice has 812 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C9×#237C211yesmaximal, characteristic, complemented
2C2×#88658C211yesmaximal, characteristic, complemented
3#11721839C211yesmaximal, characteristic, complemented
4C3×#63501C211yesmaximal, characteristic, complemented
5#11721290C211yesmaximal, characteristic, complemented
6#11721288C211yesmaximal, characteristic, complemented
7#11721277C211yesmaximal, characteristic, complemented
8#11721270C211yesmaximal, characteristic, complemented
9#11721262C211yesmaximal, characteristic, complemented
10C2×Dic3⋊Dic9C211yesmaximal, characteristic, complemented
11#11721249C211yesmaximal, characteristic, complemented
12#11721034C211yesmaximal, characteristic, complemented
13#11720986C211yesmaximal, characteristic, complemented
14#11720984C211yesmaximal, characteristic, complemented
15#11720955C211yesmaximal, characteristic, complemented
16#10595156—31nomaximal
17#10589935—31nomaximal
18C2×C3×D4×C9C2211yescharacteristic
19C2×#6233C2211yescharacteristic
20C2×#6233C2211yescharacteristic
21C22×C3⋊Dic9C2211yescharacteristic
22C2×C9×#67C2211yescharacteristic
23C2×C9×#67C2211yescharacteristic
24C2×C3×#611C2211yescharacteristic
25C2×C3×#611C2211yescharacteristic
26C22×C9×Dic3C2211yescharacteristic
27C22×C9×Dic3C2211yescharacteristic
28C22×C3×Dic9C2211yescharacteristic
29C9×#237—24no—
30C2×C4×D3×C9C2211yescharacteristic
31C2×C9×Dic6C2211yescharacteristic
32C2×#6195C2211yescharacteristic
33C2×#6194C2211yescharacteristic
34C2×#6192C2211yescharacteristic
35C2×(C3⋊D9)⋊C4C2211yescharacteristic
36#88658—24no—
37C2×Dic3×D9C2211yescharacteristic
38C2×#6189C2211yescharacteristic
39#88551C2211yescharacteristic
40#88536C2211yescharacteristic
41#88534C2211yescharacteristic
42C3×#3676C2211yescharacteristic
43C3×(C2×D9)⋊C4C2211yescharacteristic
44C3×Dic9⋊C4C2211yescharacteristic
45(C2×D3)⋊Dic9C2211yescharacteristic
46(C2×D3)⋊Dic9C2211yescharacteristic
47#88445C2211yescharacteristic
48(C2×D9)⋊Dic3C2211yescharacteristic
49Dic3⋊Dic9C2211yescharacteristic
50Dic3⋊Dic9C2211yescharacteristic
51Dic3⋊Dic9C2211yescharacteristic
52Dic3⋊Dic9C2211yescharacteristic
53#88442C2211yescharacteristic
54Dic9⋊Dic3C2211yescharacteristic
55C2×C3×#237D311yescharacteristic
56C2×#3804—31no—
57#64148—31no—
58C3×#939—31no—
59#63980—31no—
60#63978—31no—
61#63978—31no—
62#63970—31no—
63C2×Dic3⋊Dic3—31no—
64#63964—31no—
65#63958—31no—
66#63906—31no—
67#63888—31no—
68#63887—31no—
69#63851—31no—
70C2×C9×#41—31no—
71C2×#3697—31no—
72#63508—31no—
73#63508—31no—
74#63501—31no—
75#63501—31no—
76#63501—31no—
77#63501—61no—
78#63501D311yescharacteristic, complemented
79#63500—31no—
80#63500—31no—
81#63492—31no—
82#63492—31no—
83C2×C4⋊Dic9—31no—
84#63486—31no—
85#63486—31no—
86C23×C3×C9C2311yescharacteristic
87C23×C3×C9C2311yescharacteristic
88C22×C3⋊D9C2311yescharacteristic
89C22×D3×C9C2311yescharacteristic
90C22×C3×D9C2311yescharacteristic
91C3×D4×C9—22no—
92C2×C3×C4×C9C2311yescharacteristic
93#6233—22no—
94#6233—41no—
95C2×C3⋊Dic9—41no—
96C2×C3⋊Dic9C2311yescharacteristic
97C2×C3⋊Dic9C2311yescharacteristic
98C2×C3⋊Dic9C2311yescharacteristic
99C9×#67—22no—
100C9×#67—22no—
101C3×#611—22no—
102C3×#611—41no—
103C2×C9×Dic3—22no—
104C2×C9×Dic3D414yescomplemented
105C2×C9×Dic3C2311yescharacteristic
106C2×C9×Dic3C2311yescharacteristic
107C2×C9×Dic3C2311yescharacteristic
108C2×C3×Dic9—41no—
109C2×C3×Dic9C2311yescharacteristic
110C2×C3×Dic9C2311yescharacteristic
111C2×C3×Dic9C2311yescharacteristic
112C4×D3×C9—22no—
113C9×Dic6—22no—
114#6195—41no—
115#6194—41no—
116#6192—22no—
117(C3⋊D9)⋊C4—22no—
118Dic3×D9—22no—
119#6189—22no—
120#5833—91no—
121#5597—91no—
122C2×C32×D4C2×D311yescharacteristic
123C2×#638—31no—
124C2×#638—31no—
125C22×C3⋊Dic3—31no—
126C2×C3×#67—31no—
127C2×C3×#67—31no—
128C2×C3×#67C2×D311yescharacteristic
129C2×C3×#67C2×D311yescharacteristic
130C22×C3×Dic3—31no—
131C22×C3×Dic3C2×D311yescharacteristic
132C22×C3×Dic3C2×D311yescharacteristic
133C3×#237—24no—
134C2×C3×C4×D3C2×D311yescharacteristic
135C2×C3×Dic6C2×D311yescharacteristic
136C2×#627—31no—
137C2×#626—31no—
138C2×#626—31no—
139C2×#625—31no—
140C2×#624—31no—
141#3804—64no—
142C2×D3×Dic3—31no—
143#3757—31no—
144#3752—31no—
145#3750—31no—
146C3×#217—31no—
147C3×(C2×D3)⋊C4—31no—
148C3×Dic3⋊C4—31no—
149#3724—31no—
150Dic3⋊Dic3—31no—
151Dic3⋊Dic3—31no—
152Dic3⋊Dic3—31no—
153Dic3⋊Dic3—31no—
154Dic3⋊Dic3—31no—
155#3722—31no—
156(C2×D3)⋊Dic3—31no—
157(C2×D3)⋊Dic3—31no—
158(C2×D3)⋊Dic3—31no—
159C9×#41—64no—
160C2×Q8×C9—31no—
161C2×D4×C9—21no—
162C2×D4×C9—31no—
163C2×D4×C9—31no—
164C2×D4×C9C2×D311yescharacteristic
165C22×C4×C9—31no—
166C22×C4×C9—31no—
167C22×C4×C9—31no—
168C2×#611—31no—
169C2×#611—31no—
170C2×#611—31no—
171C2×#611—31no—
172C2×#611—61no—
173C2×#611—61no—
174C2×#611C2×D311yescharacteristic
175C2×#611C2×D311yescharacteristic
176C22×Dic9—31no—
177C22×Dic9—61no—
178C22×Dic9C2×D311yescharacteristic
179#3697—64no—
180C2×D36—31no—
181C2×C4×D9—31no—
182C2×C4×D9—31no—
183C2×Dic18—31no—
184#3676—31no—
185#3676—31no—
186#3676—31no—
187#3676—61no—
188#3676C2×D311yescharacteristic
189(C2×D9)⋊C4—31no—
190(C2×D9)⋊C4—31no—
191(C2×D9)⋊C4—31no—
192(C2×D9)⋊C4—61no—
193(C2×D9)⋊C4C2×D311yescharacteristic
194C4⋊Dic9—31no—
195C4⋊Dic9—31no—
196C4⋊Dic9—31no—
197C4⋊Dic9—31no—
198Dic9⋊C4—31no—
199Dic9⋊C4—31no—
200Dic9⋊C4—31no—
201Dic9⋊C4—61no—
202Dic9⋊C4C2×D311yescharacteristic
203C22×C3×C9—21no—
204C22×C3×C9—21no—
205C22×C3×C9—21no—
206C22×C3×C9—21no—
207C22×C3×C9—21no—
208C22×C3×C9C2×D412yes—
209C22×C3×C9C2411yescharacteristic
210C2×C3⋊D9—21no—
211C2×C3⋊D9—21no—
212C2×C3⋊D9—21no—
213C2×D3×C9—21no—
214C2×D3×C9—21no—
215C2×D3×C9—21no—
216C2×C3×D9—21no—
217C2×C3×D9—21no—
218C2×C3×D9—21no—
219C3×C4×C9—21no—
220C3⋊Dic9—21no—
221C3⋊Dic9—21no—
222C3⋊Dic9—21no—
223C9×Dic3—21no—
224C9×Dic3C2×D412yes—
225C9×Dic3C2×D412yes—
226C3×Dic9—21no—
227C3×Dic9—21no—
228C3×Dic9—21no—
229C2×C3×#41—31no—
230C2×#237—91no—
231C2×#237D911yescharacteristic, complemented
232C2×#235—91no—
233C3×#121—91no—
234#946—91no—
235#946—91no—
236#939—31no—
237#939—91no—
238#939—91no—
239#939—91no—
240#939—91no—
241#939—91no—
242#939—91no—
243#939—91no—
244#939—181no—
245#938—91no—
246#938—91no—
247#930—91no—
248#930—91no—
249#930—91no—
250C2×C4⋊Dic3—91no—
251#924—91no—
252#924—91no—
253C2×Dic3⋊C4—91no—
254#896—91no—
255#896—91no—
256#884—91no—
257#884—91no—
258#878—91no—
259#878—91no—
260C23×C32C22×D311yescharacteristic
261C23×C32C22×D311yescharacteristic
262C22×C3⋊D3—31no—
263C22×C3×D3—31no—
264C22×C3×D3C22×D311yescharacteristic
265C32×D4—22no—
266C2×C32×C4C22×D311yescharacteristic
267#638—62no—
268#638—121no—
269C2×C3⋊Dic3—31no—
270C2×C3⋊Dic3—31no—
271C2×C3⋊Dic3—31no—
272C2×C3⋊Dic3—121no—
273C3×#67—22no—
274C3×#67—22no—
275C3×#67—62no—
276C3×#67—121no—
277C2×C3×Dic3—22no—
278C2×C3×Dic3—31no—
279C2×C3×Dic3—31no—
280C2×C3×Dic3—31no—
281C2×C3×Dic3—121no—
282C2×C3×Dic3#6714yes—
283C2×C3×Dic3C22×D311yescharacteristic
284C2×C3×Dic3C22×D311yescharacteristic
285C2×C3×Dic3C22×D311yescharacteristic
286C3×C4×D3—22no—
287C3×Dic6—22no—
288#627—62no—
289#626—62no—
290#626—121no—
291#625—121no—
292#624—62no—
293D3×Dic3—62no—
294C23×C9—21no—
295C23×C9—21no—
296C23×C9—31no—
297C23×C9C22×D311yescharacteristic
298C23×C9C22×D311yescharacteristic
299C22×D9—31no—
300C22×D9—61no—
301C22×D9C22×D311yescharacteristic
302Q8×C9—62no—
303D4×C9—22no—
304D4×C9—42no—
305D4×C9—62no—
306D4×C9—62no—
307C2×C4×C9—21no—
308C2×C4×C9—34no—
309C2×C4×C9—31no—
310C2×C4×C9—31no—
311C2×C4×C9—31no—
312C2×C4×C9—62no—
313C2×C4×C9—62no—
314C2×C4×C9C22×D311yescharacteristic
315#611—22no—
316#611—41no—
317#611—62no—
318#611—122no—
319#611—121no—
320#611—121no—
321#611—121no—
322#611—122no—
323C2×Dic9—31no—
324C2×Dic9—31no—
325C2×Dic9—31no—
326C2×Dic9—41no—
327C2×Dic9—61no—
328C2×Dic9—61no—
329C2×Dic9—61no—
330C2×Dic9—121no—
331C2×Dic9—122no—
332C2×Dic9C22×D311yescharacteristic
333C2×Dic9C22×D311yescharacteristic
334C2×Dic9C22×D311yescharacteristic
335D36—62no—
336C4×D9—62no—
337C4×D9—62no—
338Dic18—62no—
339#537—271noSylow
340C2×C3×C9—22no—
341C2×C3×C9—41no—
342C2×C3×C9C22×D411yescharacteristic
343C2×C3×C9H(5,𝔽2)11yescharacteristic
344C2×C3×C92−1+411yescharacteristic
345C3⋊D9—41no—
346D3×C9—41no—
347C3×D9—41no—
348C3×#41—64no—
349C2×C3×Q8—31no—
350C2×C3×D4—21no—
351C2×C3×D4—31no—
352C2×C3×D4—31no—
353C2×C3×D4—91no—
354C2×C3×D4—91no—
355C2×C3×D4C2×D911yescharacteristic
356C2×C3×D4D3211yescharacteristic
357C22×C3×C4—31no—
358C22×C3×C4—31no—
359C22×C3×C4—31no—
360C22×C3×C4—91no—
361C2×#67—31no—
362C2×#67—31no—
363C2×#67—91no—
364C2×#67—91no—
365C2×#67—91no—
366C2×#67—91no—
367C2×#67—91no—
368C2×#67—91no—
369C2×#67—91no—
370C2×#67—91no—
371C2×#67—181no—
372C2×#67—181no—
373C2×#67C2×D911yescharacteristic
374C2×#67C2×D911yescharacteristic
375C22×Dic3—31no—
376C22×Dic3—91no—
377C22×Dic3—91no—
378C22×Dic3—91no—
379C22×Dic3—181no—
380C22×Dic3C2×D911yescharacteristic
381C22×Dic3C2×D911yescharacteristic
382#237—24no—
383#237—184no—
384#235—184no—
385C2×D12—91no—
386C2×D12—91no—
387C2×C4×D3—91no—
388C2×C4×D3—91no—
389C2×C4×D3—91no—
390C2×C4×D3C2×D911yescharacteristic
391C2×Dic6—91no—
392C2×Dic6—91no—
393C2×Dic6C2×D911yescharacteristic
394C3×C4⋊C4—91no—
395C3×C22⋊C4—91no—
396C3×C22⋊C4—91no—
397#217—31no—
398#217—91no—
399#217—91no—
400#217—91no—
401#217—91no—
402#217—91no—
403#217—181no—
404(C2×D3)⋊C4—31no—
405(C2×D3)⋊C4—91no—
406(C2×D3)⋊C4—91no—
407(C2×D3)⋊C4—91no—
408(C2×D3)⋊C4—91no—
409(C2×D3)⋊C4—91no—
410(C2×D3)⋊C4—91no—
411(C2×D3)⋊C4—91no—
412(C2×D3)⋊C4—181no—
413C4⋊Dic3—91no—
414C4⋊Dic3—91no—
415C4⋊Dic3—91no—
416C4⋊Dic3—91no—
417C4⋊Dic3—91no—
418Dic3⋊C4—31no—
419Dic3⋊C4—91no—
420Dic3⋊C4—91no—
421Dic3⋊C4—91no—
422Dic3⋊C4—91no—
423Dic3⋊C4—91no—
424Dic3⋊C4—91no—
425Dic3⋊C4—91no—
426Dic3⋊C4—91no—
427Dic3⋊C4—91no—
428Dic3⋊C4—181no—
429C22×C32—21no—
430C22×C32—21no—
431C22×C32—21no—
432C22×C32—21no—
433C22×C32—21no—
434C22×C32C2×#6712yes—
435C22×C32C23×D311yescharacteristic
436C2×C3⋊D3—61no—
437C2×C3⋊D3—61no—
438C2×C3⋊D3—61no—
439C2×C3×D3—21no—
440C2×C3×D3—21no—
441C2×C3×D3—21no—
442C2×C3×D3—61no—
443C2×C3×D3—61no—
444C2×C3×D3—61no—
445C32×C4—21no—
446C3⋊Dic3—61no—
447C3⋊Dic3—61no—
448C3⋊Dic3—61no—
449C3×Dic3—21no—
450C3×Dic3—61no—
451C3×Dic3—61no—
452C3×Dic3—61no—
453C3×Dic3C2×#6712yes—
454C3×Dic3C2×#6712yes—
455C22×C9—21no—
456C22×C9—21no—
457C22×C9—21no—
458C22×C9—21no—
459C22×C9—21no—
460C22×C9—21no—
461C22×C9—22no—
462C22×C9—41no—
463C22×C9—41no—
464C22×C9—41no—
465C22×C9—41no—
466C22×C9—41no—
467C22×C9—61no—
468C22×C9—61no—
469C22×C9—61no—
470C22×C9D3×D412yes—
471C22×C9C23×D311yescharacteristic
472C2×D9—21no—
473C2×D9—21no—
474C2×D9—21no—
475C2×D9—61no—
476C2×D9—61no—
477C2×D9—61no—
478C2×D9—121no—
479C2×D9—121no—
480C2×D9—121no—
481C4×C9—21no—
482C4×C9—32no—
483C4×C9—32no—
484C4×C9—41no—
485C4×C9—61no—
486Dic9—21no—
487Dic9—21no—
488Dic9—21no—
489Dic9—62no—
490Dic9—61no—
491Dic9—61no—
492Dic9—61no—
493Dic9—121no—
494Dic9—121no—
495C2×#41—31no—
496C2×#41—271no—
497C22⋊Q8—271no—
498C22⋊Q8—271no—
499C22⋊Q8—271no—
500C22⋊Q8—271no—
501#121—91no—
502#121—271no—
503#121—271no—
504#121—271no—
505#121—271no—
506#121—271no—
507#121—271no—
508#121—271no—
509C2×C4⋊C4—271no—
510C3×C9#53711yescharacteristic, complemented, Sylow
511C23×C3—21no—
512C23×C3—21no—
513C23×C3—31no—
514C23×C3—91no—
515C23×C3C22×D911yescharacteristic
516C23×C3C22×D911yescharacteristic
517C23×C3C2×D3211yescharacteristic
518C23×C3C2×D3211yescharacteristic
519C22×D3—31no—
520C22×D3—91no—
521C22×D3—91no—
522C22×D3—181no—
523C22×D3C22×D911yescharacteristic
524C3×Q8—62no—
525C3×D4—22no—
526C3×D4—22no—
527C3×D4—42no—
528C3×D4—62no—
529C3×D4—62no—
530C3×D4—182no—
531C3×D4—361no—
532C2×C3×C4—21no—
533C2×C3×C4—31no—
534C2×C3×C4—31no—
535C2×C3×C4—34no—
536C2×C3×C4—31no—
537C2×C3×C4—62no—
538C2×C3×C4—62no—
539C2×C3×C4—91no—
540C2×C3×C4—91no—
541C2×C3×C4—91no—
542C2×C3×C4—361no—
543C2×C3×C4C22×D911yescharacteristic
544C2×C3×C4C2×D3211yescharacteristic
545#67—22no—
546#67—22no—
547#67—62no—
548#67—121no—
549#67—182no—
550#67—182no—
551#67—182no—
552#67—362no—
553#67—361no—
554#67—361no—
555#67—361no—
556#67—361no—
557#67—361no—
558#67—362no—
559C2×Dic3—22no—
560C2×Dic3—31no—
561C2×Dic3—31no—
562C2×Dic3—31no—
563C2×Dic3—91no—
564C2×Dic3—91no—
565C2×Dic3—91no—
566C2×Dic3—91no—
567C2×Dic3—91no—
568C2×Dic3—91no—
569C2×Dic3—121no—
570C2×Dic3—181no—
571C2×Dic3—181no—
572C2×Dic3—181no—
573C2×Dic3—182no—
574C2×Dic3—361no—
575C2×Dic3—361no—
576C2×Dic3—362no—
577C2×Dic3#61114yescomplemented
578C2×Dic3C22×D911yescharacteristic
579C2×Dic3C22×D911yescharacteristic
580C2×Dic3C22×D911yescharacteristic
581D12—182no—
582D12—361no—
583C4×D3—22no—
584C4×D3—182no—
585C4×D3—182no—
586C4×D3—182no—
587Dic6—22no—
588Dic6—182no—
589Dic6—182no—
590C2×C32—22no—
591C2×C32—41no—
592C2×C32#100911yescharacteristic
593C2×C32#101011yescharacteristic
594C2×C32C22×#6711yescharacteristic
595C3⋊D3—121no—
596C3×D3—41no—
597C3×D3—121no—
598C2×C9—22no—
599C2×C9—21no—
600C2×C9—21no—
601C2×C9—21no—
602C2×C9—42no—
603C2×C9—41no—
604C2×C9—81no—
605C2×C9—121no—
606C2×C9C2×D3×D411yescharacteristic
607C2×C9#100411yescharacteristic
608C2×C9#101011yescharacteristic
609D9—41no—
610D9—121no—
611D9—241no—
612#41—64no—
613#41—544no—
614C2×Q8—31no—
615C2×Q8—271no—
616C2×D4—31no—
617C2×D4—31no—
618C2×D4—91no—
619C2×D4—91no—
620C2×D4—271no—
621C2×D4—271no—
622C2×D4—271no—
623C2×D4—271no—
624C2×D4—271no—
625C2×D4D3×D911yescharacteristic
626C22×C4—31no—
627C22×C4—31no—
628C22×C4—31no—
629C22×C4—91no—
630C22×C4—271no—
631C22×C4—271no—
632C22×C4—271no—
633C4⋊C4—91no—
634C4⋊C4—271no—
635C4⋊C4—271no—
636C4⋊C4—271no—
637C4⋊C4—271no—
638C4⋊C4—271no—
639C4⋊C4—271no—
640C4⋊C4—271no—
641C22⋊C4—91no—
642C22⋊C4—91no—
643C22⋊C4—271no—
644C22⋊C4—271no—
645C22⋊C4—271no—
646C22⋊C4—271no—
647C22⋊C4—271no—
648C22⋊C4—271no—
649C22×C3—21no—
650C22×C3—21no—
651C22×C3—21no—
652C22×C3—21no—
653C22×C3—21no—
654C22×C3—21no—
655C22×C3—21no—
656C22×C3—21no—
657C22×C3—21no—
658C22×C3—21no—
659C22×C3—21no—
660C22×C3—22no—
661C22×C3—41no—
662C22×C3—41no—
663C22×C3—41no—
664C22×C3—41no—
665C22×C3—41no—
666C22×C3—61no—
667C22×C3—61no—
668C22×C3—61no—
669C22×C3—181no—
670C22×C3—181no—
671C22×C3—181no—
672C22×C3C2×#61112yes—
673C22×C3C23×D911yescharacteristic
674C22×C3D3×#6712yes—
675C22×C3C22×D3211yescharacteristic
676C2×D3—21no—
677C2×D3—21no—
678C2×D3—21no—
679C2×D3—61no—
680C2×D3—61no—
681C2×D3—61no—
682C2×D3—181no—
683C2×D3—181no—
684C2×D3—181no—
685C2×D3—181no—
686C2×D3—181no—
687C2×D3—181no—
688C2×D3—361no—
689C2×D3—361no—
690C2×D3—361no—
691C3×C4—21no—
692C3×C4—21no—
693C3×C4—32no—
694C3×C4—32no—
695C3×C4—41no—
696C3×C4—61no—
697C3×C4—181no—
698C3×C4—181no—
699C3×C4—181no—
700Dic3—21no—
701Dic3—61no—
702Dic3—61no—
703Dic3—61no—
704Dic3—182no—
705Dic3—181no—
706Dic3—181no—
707Dic3—181no—
708Dic3—181no—
709Dic3—181no—
710Dic3—181no—
711Dic3—361no—
712Dic3—361no—
713Dic3C2×#61112yes—
714Dic3C2×#61112yes—
715C32#583311yescharacteristic
716C9—21no—
717C9#559711yescharacteristic, complemented
718C23—31no—
719C23—91no—
720C23—271no—
721C23C2×D3×D911yescharacteristic
722C23C2×D3×D911yescharacteristic
723Q8—62no—
724Q8—542no—
725D4—22no—
726D4—62no—
727D4—62no—
728D4—182no—
729D4—361no—
730D4—542no—
731D4—542no—
732D4—1081no—
733D4—1081no—
734D4—1081no—
735C2×C4—31no—
736C2×C4—31no—
737C2×C4—34no—
738C2×C4—31no—
739C2×C4—62no—
740C2×C4—62no—
741C2×C4—91no—
742C2×C4—91no—
743C2×C4—91no—
744C2×C4—271no—
745C2×C4—271no—
746C2×C4—271no—
747C2×C4—361no—
748C2×C4—542no—
749C2×C4—542no—
750C2×C4—1081no—
751C2×C4C2×D3×D911yescharacteristic
752C2×C3—22no—
753C2×C3—22no—
754C2×C3—21no—
755C2×C3—21no—
756C2×C3—21no—
757C2×C3—42no—
758C2×C3—41no—
759C2×C3—41no—
760C2×C3—81no—
761C2×C3—121no—
762C2×C3—361no—
763C2×C3#6371511yescharacteristic
764C2×C3#6371611yescharacteristic
765C2×C3C22×#61111yescharacteristic
766C2×C3#6430911yescharacteristic
767C2×C3#6431411yescharacteristic
768C2×C3C2×D3×#6711yescharacteristic
769D3—41no—
770D3—121no—
771D3—361no—
772D3—361no—
773D3—721no—
774C22—21no—
775C22—21no—
776C22—21no—
777C22—21no—
778C22—21no—
779C22—61no—
780C22—61no—
781C22—61no—
782C22—181no—
783C22—181no—
784C22—181no—
785C22—541no—
786C22—541no—
787C22—541no—
788C22D3×#61112yes—
789C22C22×D3×D911yescharacteristic
790C4—21no—
791C4—32no—
792C4—32no—
793C4—61no—
794C4—181no—
795C4—181no—
796C4—181no—
797C4—541no—
798C4—541no—
799C4—541no—
800C3—21no—
801C3#1058993511yescharacteristic, complemented
802C3#1059515611yescharacteristic
803C2—22no—
804C2—41no—
805C2—121no—
806C2—361no—
807C2—1081no—
808C2#1172249411yescharacteristic
809C2#1172250111yescharacteristic
810C2C2×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#537
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×#88658C2semidirect
3. #11721839C2semidirect
4. C3×#63501C2semidirect
5. #11721290C2semidirect
6. #11721288C2semidirect
7. #11721277C2semidirect
8. #11721270C2semidirect
9. #11721262C2semidirect
10. C2×Dic3⋊Dic9C2semidirect
11. #11721249C2semidirect
12. #11721034C2semidirect
13. #11720986C2semidirect
14. #11720984C2semidirect
15. #11720955C2semidirect
78. #63501D3semidirect
104. C2×C9×Dic3D4semidirect
231. C2×#237D9semidirect
510. C3×C9#537semidirect
577. C2×Dic3#611semidirect
717. C9#5597semidirect
801. C3#10589935semidirect

Maximal subgroups

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

subgroupindex
C2×C9×#2372
C2×#886582
#117218392
C3×#635012
#117212902
#117212882
#117212772
#117212702
#117212622
C2×Dic3⋊Dic92
#117212492
#117210342
#117209862
#117209842
#117209552
#105951563
#105899353