Finite Group Databasebeta

← #13148205

Subgroups — #13148205

Order 1728.

1006 conjugacy classes of subgroups.

The subgroup lattice has 802 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#88662C211yesmaximal, characteristic, complemented
2C2×#88638C211yesmaximal, characteristic, complemented
3#11721731C211yesmaximal, characteristic, complemented
4C9×#884C211yesmaximal, characteristic, complemented
5C3×#611⋊C4C211yesmaximal, characteristic, complemented
6#11721289C211yesmaximal, characteristic, complemented
7#67×Dic9C211yesmaximal, characteristic, complemented
8#11721281C211yesmaximal, characteristic, complemented
9#11721044C211yesmaximal, characteristic, complemented
10#11721034C211yesmaximal, characteristic, complemented
11#11721017C211yesmaximal, characteristic, complemented
12#11721013C211yesmaximal, characteristic, complemented
13C4×D3×Dic9C211yesmaximal, characteristic, complemented
14#11721002C211yesmaximal, characteristic, complemented
15#11720905C211yesmaximal, characteristic, complemented
16#10594058—31nomaximal
17#10589698—31nomaximal
18C2×#6233C2211yescharacteristic
19C2×#6226C2211yescharacteristic
20C2×C9×#67C2211yescharacteristic
21C2×C9×#67C2211yescharacteristic
22C2×C3×#611C2211yescharacteristic
23C22×C3×Dic9C2211yescharacteristic
24C2×C9×D12C2211yescharacteristic
25C2×C4×D3×C9C2211yescharacteristic
26C2×C3×C4×D9C2211yescharacteristic
27C2×#6195C2211yescharacteristic
28C2×#6195C2211yescharacteristic
29C2×#6194C2211yescharacteristic
30C2×#6194C2211yescharacteristic
31#88662—24no—
32C2×D3×Dic9C2211yescharacteristic
33C2×D3×Dic9C2211yescharacteristic
34C2×D3×Dic9C2211yescharacteristic
35C2×#6192C2211yescharacteristic
36C2×(C3⋊D9)⋊C4C2211yescharacteristic
37C2×#6189C2211yescharacteristic
38#88638—24no—
39C3×C9×C22⋊C4C2211yescharacteristic
40#88551C2211yescharacteristic
41#88536C2211yescharacteristic
42#88536C2211yescharacteristic
43C4×C3⋊Dic9C2211yescharacteristic
44C9×(C2×D3)⋊C4C2211yescharacteristic
45C3×(C2×D9)⋊C4C2211yescharacteristic
46C9×Dic3⋊C4C2211yescharacteristic
47C3×Dic9⋊C4C2211yescharacteristic
48C3×C4×Dic9C2211yescharacteristic
49(C2×D3)⋊Dic9C2211yescharacteristic
50(C2×D9)⋊Dic3C2211yescharacteristic
51Dic3⋊Dic9C2211yescharacteristic
52Dic9⋊Dic3C2211yescharacteristic
53Dic3×Dic9C2211yescharacteristic
54Dic3×Dic9C2211yescharacteristic
55C2×#3804—31no—
56C2×#3795—31no—
57#64094—31no—
58C3×#884D311yescharacteristic
59C3×#67⋊C4—31no—
60#63979—31no—
61Dic3×#67—31no—
62#63970—31no—
63#63915—31no—
64#63906—31no—
65#63904—31no—
66#63886—31no—
67#63880—31no—
68C4×D3×Dic3—31no—
69#63840—31no—
70C2×#3699—31no—
71C2×#3699—31no—
72C9×#121—31no—
73#63502—31no—
74#63501—31no—
75#63501—31no—
76D4×Dic9—31no—
77#63492—31no—
78C2×C4×Dic9—31no—
79#63455—31no—
80#63450—31no—
81#63447—31no—
82#63447—31no—
83#63447—61no—
84#611⋊C4—31no—
85#611⋊C4D311yescharacteristic, complemented
86C23×C3×C9C2311yescharacteristic
87C22×C3⋊D9C2311yescharacteristic
88C22×D3×C9C2311yescharacteristic
89C22×D3×C9C2311yescharacteristic
90C22×C3×D9C2311yescharacteristic
91C2×C3×C4×C9C2311yescharacteristic
92C2×C3×C4×C9C2311yescharacteristic
93#6233—22no—
94C2×C3⋊Dic9C2311yescharacteristic
95C2×C3⋊Dic9C2311yescharacteristic
96C2×C3⋊Dic9C2311yescharacteristic
97#6226—22no—
98C9×#67—22no—
99C9×#67—22no—
100C3×#611—22no—
101C2×C9×Dic3C2311yescharacteristic
102C2×C9×Dic3C2311yescharacteristic
103C2×C3×Dic9—22no—
104C2×C3×Dic9C2311yescharacteristic
105C2×C3×Dic9C2311yescharacteristic
106C2×C3×Dic9C2311yescharacteristic
107C9×D12—22no—
108C4×D3×C9—22no—
109C3×C4×D9—22no—
110#6195—22no—
111#6195—22no—
112#6194—22no—
113#6194—22no—
114D3×Dic9—22no—
115D3×Dic9—22no—
116D3×Dic9D414yescomplemented
117#6192—22no—
118(C3⋊D9)⋊C4—22no—
119#6189—22no—
120#5596—91no—
121#5548—91no—
122C2×#638—31no—
123C2×#634—31no—
124C2×C3×#67—31no—
125C2×C3×#67C2×D311yescharacteristic
126C2×C3×#67C2×D311yescharacteristic
127C22×C3×Dic3—31no—
128C2×C3×D12C2×D311yescharacteristic
129C2×C3×C4×D3—31no—
130C2×C3×C4×D3C2×D311yescharacteristic
131C2×#627—31no—
132C2×#626—31no—
133C2×#626—31no—
134C2×#626—31no—
135C2×#625—31no—
136C2×#625—31no—
137C2×#624—31no—
138#3804—64no—
139C2×D3×Dic3—31no—
140C2×D3×Dic3—31no—
141C2×D3×Dic3—31no—
142#3795—64no—
143C32×C22⋊C4C2×D311yescharacteristic
144#3757—31no—
145#3752—31no—
146#3752—31no—
147C4×C3⋊Dic3—31no—
148C3×(C2×D3)⋊C4—31no—
149C3×(C2×D3)⋊C4C2×D311yescharacteristic
150C3×Dic3⋊C4—31no—
151C3×Dic3⋊C4C2×D311yescharacteristic
152C3×C4×Dic3—31no—
153Dic3⋊Dic3—31no—
154Dic3⋊Dic3—31no—
155(C2×D3)⋊Dic3—31no—
156(C2×D3)⋊Dic3—31no—
157Dic32—31no—
158Dic32—31no—
159C2×D4×C9—31no—
160C2×D4×C9—31no—
161C2×D4×C9—31no—
162C22×C4×C9—31no—
163C2×#611—31no—
164C2×#611—31no—
165C2×#611—31no—
166C2×#611—31no—
167C2×#611—31no—
168C2×#611—61no—
169C2×#611C2×D311yescharacteristic
170C22×Dic9—31no—
171C22×Dic9—31no—
172C22×Dic9—31no—
173C22×Dic9C2×D311yescharacteristic
174#3699—64no—
175#3699—64no—
176C2×D36—31no—
177C2×C4×D9—31no—
178C2×C4×D9C2×D311yescharacteristic
179C2×Dic18—31no—
180C2×Dic18—31no—
181C2×Dic18—61no—
182C9×C4⋊C4—31no—
183C9×C22⋊C4—21no—
184C9×C22⋊C4—31no—
185C9×C22⋊C4C2×D311yescharacteristic
186#3676—31no—
187#3676—31no—
188#3676—61no—
189(C2×D9)⋊C4—31no—
190(C2×D9)⋊C4—31no—
191(C2×D9)⋊C4—31no—
192(C2×D9)⋊C4—61no—
193(C2×D9)⋊C4—61no—
194(C2×D9)⋊C4C2×D311yescharacteristic
195C4⋊Dic9—31no—
196Dic9⋊C4—31no—
197Dic9⋊C4C2×D311yescharacteristic
198C4×Dic9—31no—
199C4×Dic9—31no—
200C4×Dic9—31no—
201C4×Dic9—61no—
202C4×Dic9C2×D311yescharacteristic
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×D3×C9—21no—
211C2×D3×C9—21no—
212C2×D3×C9—21no—
213C2×D3×C9—21no—
214C2×D3×C9—21no—
215C2×D3×C9C2×D412yes—
216C2×C3×D9—21no—
217C2×C3×D9—21no—
218C2×C3×D9—21no—
219C3×C4×C9—21no—
220C3×C4×C9—21no—
221C3⋊Dic9—21no—
222C3⋊Dic9—21no—
223C3⋊Dic9C2×D412yes—
224C9×Dic3—21no—
225C9×Dic3#4112yescomplemented
226C3×Dic9—21no—
227C3×Dic9C2×D412yes—
228C3×Dic9#4112yescomplemented
229C2×#237—91no—
230C2×#237—91no—
231C2×#235—91no—
232C2×#235—91no—
233C3×#121—31no—
234C3×C4×D4—91no—
235#940—91no—
236#940—91no—
237#939—91no—
238#939—91no—
239#938—91no—
240D4×Dic3—91no—
241#930—91no—
242C4×#67—91no—
243C4×#67—91no—
244C2×C4×Dic3—91no—
245#895—91no—
246#893—91no—
247#888—91no—
248#888—91no—
249#885—91no—
250#885—91no—
251#885—91no—
252#885—91no—
253#885—181no—
254#884—91no—
255#884D911yescharacteristic, complemented
256#67⋊C4—31no—
257#67⋊C4—91no—
258C4×D12—91no—
259C42×D3—91no—
260C23×C32C22×D311yescharacteristic
261C22×C3⋊D3—31no—
262C22×C3×D3—31no—
263C22×C3×D3C22×D311yescharacteristic
264C22×C3×D3C22×D311yescharacteristic
265C2×C32×C4C22×D311yescharacteristic
266C2×C32×C4C22×D311yescharacteristic
267#638—62no—
268C2×C3⋊Dic3—31no—
269C2×C3⋊Dic3—31no—
270C2×C3⋊Dic3—31no—
271#634—62no—
272C3×#67—22no—
273C3×#67—22no—
274C3×#67—62no—
275C2×C3×Dic3—31no—
276C2×C3×Dic3—31no—
277C2×C3×Dic3—31no—
278C2×C3×Dic3—62no—
279C2×C3×Dic3C22×D311yescharacteristic
280C2×C3×Dic3C22×D311yescharacteristic
281C3×D12—22no—
282C3×C4×D3—22no—
283C3×C4×D3—62no—
284#627—62no—
285#626—62no—
286#626—62no—
287#626—62no—
288#625—62no—
289#625—62no—
290#624—62no—
291D3×Dic3—34no—
292D3×Dic3—62no—
293D3×Dic3—62no—
294C23×C9—21no—
295C23×C9—31no—
296C23×C9—31no—
297C23×C9C22×D311yescharacteristic
298C22×D9—31no—
299C22×D9—61no—
300C22×D9C22×D311yescharacteristic
301D4×C9—62no—
302D4×C9—62no—
303D4×C9—62no—
304C2×C4×C9—21no—
305C2×C4×C9—21no—
306C2×C4×C9—31no—
307C2×C4×C9—31no—
308C2×C4×C9—62no—
309C2×C4×C9C22×D311yescharacteristic
310C2×C4×C9C22×D311yescharacteristic
311#611—22no—
312#611—62no—
313#611—62no—
314#611—62no—
315#611—62no—
316#611—62no—
317#611—122no—
318C2×Dic9—22no—
319C2×Dic9—31no—
320C2×Dic9—34no—
321C2×Dic9—31no—
322C2×Dic9—31no—
323C2×Dic9—61no—
324C2×Dic9—61no—
325C2×Dic9—61no—
326C2×Dic9—62no—
327C2×Dic9—62no—
328C2×Dic9C22×D311yescharacteristic
329C2×Dic9C22×D311yescharacteristic
330C2×Dic9C22×D311yescharacteristic
331D36—62no—
332C4×D9—22no—
333C4×D9—62no—
334Dic18—62no—
335Dic18—62no—
336Dic18—122no—
337#532—271noSylow
338C2×C3×C9—41no—
339C2×C3×C9C22×D411yescharacteristic
340C2×C3×C9C2×#4111yescharacteristic
341C2×C3×C9C2×#4111yescharacteristic
342C3⋊D9—41no—
343D3×C9—22no—
344D3×C9—41no—
345C3×D9—41no—
346C2×C3×D4—31no—
347C2×C3×D4—31no—
348C2×C3×D4—31no—
349C2×C3×D4—91no—
350C22×C3×C4—31no—
351C22×C3×C4—91no—
352C22×C3×C4—91no—
353C2×#67—31no—
354C2×#67—91no—
355C2×#67—91no—
356C2×#67—91no—
357C2×#67—91no—
358C2×#67—91no—
359C2×#67—91no—
360C2×#67—91no—
361C2×#67—91no—
362C2×#67—91no—
363C2×#67—181no—
364C2×#67C2×D911yescharacteristic
365C2×#67C2×D911yescharacteristic
366C22×Dic3—31no—
367C22×Dic3—91no—
368C22×Dic3—91no—
369C22×Dic3—91no—
370#237—184no—
371#237—184no—
372#235—184no—
373#235—184no—
374C2×D12—91no—
375C2×D12—91no—
376C2×D12—91no—
377C2×D12C2×D911yescharacteristic
378C2×C4×D3—31no—
379C2×C4×D3—91no—
380C2×C4×D3—91no—
381C2×C4×D3—91no—
382C2×C4×D3—91no—
383C2×C4×D3—91no—
384C2×C4×D3C2×D911yescharacteristic
385C2×Dic6—91no—
386C2×Dic6—91no—
387C2×Dic6—91no—
388C2×Dic6—91no—
389C2×Dic6—181no—
390C3×C4⋊C4—31no—
391C3×C4⋊C4—91no—
392C3×C22⋊C4—21no—
393C3×C22⋊C4—31no—
394C3×C22⋊C4—91no—
395C3×C22⋊C4C2×D911yescharacteristic
396C3×C22⋊C4D3211yescharacteristic
397C3×C42—91no—
398#217—91no—
399#217—91no—
400#217—91no—
401#217—91no—
402#217—181no—
403(C2×D3)⋊C4—31no—
404(C2×D3)⋊C4—91no—
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—181no—
411(C2×D3)⋊C4—181no—
412(C2×D3)⋊C4C2×D911yescharacteristic
413C4⋊Dic3—91no—
414C4⋊Dic3—91no—
415Dic3⋊C4—31no—
416Dic3⋊C4—91no—
417Dic3⋊C4—91no—
418Dic3⋊C4C2×D911yescharacteristic
419C4×Dic3—31no—
420C4×Dic3—91no—
421C4×Dic3—91no—
422C4×Dic3—91no—
423C4×Dic3—91no—
424C4×Dic3—91no—
425C4×Dic3—91no—
426C4×Dic3—181no—
427C22×C32—21no—
428C22×C32—21no—
429C22×C32—21no—
430C22×C32C23×D311yescharacteristic
431C2×C3⋊D3—61no—
432C2×C3⋊D3—61no—
433C2×C3⋊D3—61no—
434C2×C3×D3—21no—
435C2×C3×D3—21no—
436C2×C3×D3—21no—
437C2×C3×D3—21no—
438C2×C3×D3—21no—
439C2×C3×D3—61no—
440C2×C3×D3—61no—
441C2×C3×D3—61no—
442C2×C3×D3D3×D412yes—
443C32×C4—21no—
444C32×C4—21no—
445C3⋊Dic3—32no—
446C3⋊Dic3—61no—
447C3⋊Dic3—61no—
448C3×Dic3—21no—
449C3×Dic3—32no—
450C3×Dic3—32no—
451C3×Dic3—61no—
452C3×Dic3#23712yes—
453C22×C9—21no—
454C22×C9—21no—
455C22×C9—21no—
456C22×C9—21no—
457C22×C9—32no—
458C22×C9—41no—
459C22×C9—41no—
460C22×C9—41no—
461C22×C9—61no—
462C22×C9—61no—
463C22×C9—61no—
464C22×C9—61no—
465C22×C9—61no—
466C22×C9C23×D311yescharacteristic
467C2×D9—21no—
468C2×D9—21no—
469C2×D9—21no—
470C2×D9—61no—
471C2×D9—61no—
472C2×D9—61no—
473C2×D9—121no—
474C2×D9—121no—
475C2×D9—121no—
476C4×C9—21no—
477C4×C9—21no—
478C4×C9—32no—
479C4×C9—41no—
480C4×C9—41no—
481C4×C9—61no—
482Dic9—21no—
483Dic9—32no—
484Dic9—62no—
485Dic9—61no—
486Dic9—61no—
487Dic9—121no—
488Dic9—121no—
489Dic9#23512yescomplemented
490Dic9D3×D412yes—
491C2×#41—271no—
492C2×#41—271no—
493C4⋊Q8—271no—
494#127—271no—
495#124—271no—
496#124—271no—
497#121—31no—
498#121—271no—
499#121—271no—
500#121—271no—
501C4×D4—91no—
502C4×D4—271no—
503C4×D4—271no—
504C4×D4—271no—
505C2×C42—271no—
506C3×C9#53211yescharacteristic, complemented, Sylow
507C23×C3—21no—
508C23×C3—31no—
509C23×C3—31no—
510C23×C3—91no—
511C23×C3C22×D911yescharacteristic
512C23×C3C2×D3211yescharacteristic
513C22×D3—31no—
514C22×D3—91no—
515C22×D3—91no—
516C22×D3—181no—
517C22×D3C22×D911yescharacteristic
518C22×D3C22×D911yescharacteristic
519C3×D4—62no—
520C3×D4—62no—
521C3×D4—62no—
522C3×D4—182no—
523C2×C3×C4—21no—
524C2×C3×C4—21no—
525C2×C3×C4—31no—
526C2×C3×C4—31no—
527C2×C3×C4—62no—
528C2×C3×C4—91no—
529C2×C3×C4—91no—
530C2×C3×C4—91no—
531C2×C3×C4—182no—
532C2×C3×C4—182no—
533C2×C3×C4C22×D911yescharacteristic
534C2×C3×C4C22×D911yescharacteristic
535C2×C3×C4C2×D3211yescharacteristic
536C2×C3×C4C2×D3211yescharacteristic
537#67—22no—
538#67—22no—
539#67—62no—
540#67—182no—
541#67—182no—
542#67—182no—
543#67—182no—
544#67—182no—
545#67—182no—
546#67—182no—
547#67—182no—
548#67—182no—
549#67—362no—
550C2×Dic3—31no—
551C2×Dic3—31no—
552C2×Dic3—31no—
553C2×Dic3—62no—
554C2×Dic3—94no—
555C2×Dic3—91no—
556C2×Dic3—91no—
557C2×Dic3—91no—
558C2×Dic3—91no—
559C2×Dic3—91no—
560C2×Dic3—91no—
561C2×Dic3—181no—
562C2×Dic3—181no—
563C2×Dic3—181no—
564C2×Dic3—182no—
565C2×Dic3—182no—
566C2×Dic3C22×D911yescharacteristic
567C2×Dic3C22×D911yescharacteristic
568D12—22no—
569D12—182no—
570D12—182no—
571D12—182no—
572C4×D3—22no—
573C4×D3—62no—
574C4×D3—94no—
575C4×D3—182no—
576C4×D3—182no—
577C4×D3—182no—
578C4×D3—182no—
579Dic6—182no—
580Dic6—182no—
581Dic6—182no—
582Dic6—182no—
583Dic6—362no—
584C2×C32—41no—
585C2×C32C2×D3×D411yescharacteristic
586C2×C32C2×#23711yescharacteristic
587C2×C32D3×#4111yescharacteristic
588C3⋊D3—121no—
589C3×D3—22no—
590C3×D3—41no—
591C3×D3—121no—
592C2×C9—21no—
593C2×C9—21no—
594C2×C9—21no—
595C2×C9—41no—
596C2×C9—62no—
597C2×C9—81no—
598C2×C9—121no—
599C2×C9C2×#23511yescharacteristic
600C2×C9C2×D3×D411yescharacteristic
601C2×C9D3×#4111yescharacteristic
602D9—41no—
603D9—121no—
604D9—241no—
605#41—544no—
606#41—544no—
607C2×Q8—271no—
608C2×Q8—271no—
609C2×D4—31no—
610C2×D4—31no—
611C2×D4—31no—
612C2×D4—91no—
613C2×D4—271no—
614C2×D4—271no—
615C2×D4—271no—
616C2×D4—271no—
617C2×D4—271no—
618C2×D4—271no—
619C22×C4—31no—
620C22×C4—91no—
621C22×C4—91no—
622C22×C4—271no—
623C22×C4—271no—
624C22×C4—271no—
625C22×C4—271no—
626C4⋊C4—31no—
627C4⋊C4—91no—
628C4⋊C4—271no—
629C4⋊C4—271no—
630C22⋊C4—31no—
631C22⋊C4—91no—
632C22⋊C4—271no—
633C22⋊C4—271no—
634C22⋊C4—271no—
635C22⋊C4—271no—
636C22⋊C4—271no—
637C22⋊C4D3×D911yescharacteristic
638C42—91no—
639C42—271no—
640C42—271no—
641C42—271no—
642C22×C3—21no—
643C22×C3—21no—
644C22×C3—21no—
645C22×C3—21no—
646C22×C3—21no—
647C22×C3—21no—
648C22×C3—21no—
649C22×C3—32no—
650C22×C3—41no—
651C22×C3—41no—
652C22×C3—41no—
653C22×C3—61no—
654C22×C3—61no—
655C22×C3—61no—
656C22×C3—61no—
657C22×C3—61no—
658C22×C3—181no—
659C22×C3—181no—
660C22×C3—181no—
661C22×C3C23×D911yescharacteristic
662C22×C3C22×D3211yescharacteristic
663C2×D3—21no—
664C2×D3—21no—
665C2×D3—21no—
666C2×D3—21no—
667C2×D3—21no—
668C2×D3—61no—
669C2×D3—61no—
670C2×D3—61no—
671C2×D3—181no—
672C2×D3—181no—
673C2×D3—181no—
674C2×D3—181no—
675C2×D3—181no—
676C2×D3—181no—
677C2×D3—361no—
678C2×D3—361no—
679C2×D3—361no—
680C2×D3D4×D912yes—
681C3×C4—21no—
682C3×C4—21no—
683C3×C4—21no—
684C3×C4—21no—
685C3×C4—32no—
686C3×C4—41no—
687C3×C4—41no—
688C3×C4—61no—
689C3×C4—92no—
690C3×C4—92no—
691C3×C4—181no—
692Dic3—21no—
693Dic3—32no—
694Dic3—32no—
695Dic3—61no—
696Dic3—92no—
697Dic3—92no—
698Dic3—182no—
699Dic3—181no—
700Dic3—181no—
701Dic3—181no—
702Dic3—181no—
703Dic3—361no—
704Dic3—361no—
705Dic3#369912yescomplemented
706C32#559611yescharacteristic
707C9—21no—
708C9#554811yescharacteristic, complemented
709C23—31no—
710C23—31no—
711C23—91no—
712C23—271no—
713C23C2×D3×D911yescharacteristic
714Q8—542no—
715Q8—542no—
716D4—62no—
717D4—62no—
718D4—62no—
719D4—182no—
720D4—542no—
721D4—542no—
722D4—542no—
723D4—542no—
724D4—542no—
725D4—542no—
726C2×C4—31no—
727C2×C4—31no—
728C2×C4—62no—
729C2×C4—91no—
730C2×C4—91no—
731C2×C4—91no—
732C2×C4—182no—
733C2×C4—182no—
734C2×C4—274no—
735C2×C4—271no—
736C2×C4—271no—
737C2×C4—271no—
738C2×C4—542no—
739C2×C4—542no—
740C2×C4—542no—
741C2×C4C2×D3×D911yescharacteristic
742C2×C4C2×D3×D911yescharacteristic
743C2×C3—21no—
744C2×C3—21no—
745C2×C3—21no—
746C2×C3—41no—
747C2×C3—41no—
748C2×C3—62no—
749C2×C3—81no—
750C2×C3—121no—
751C2×C3—361no—
752C2×C3C2×D4×D911yescharacteristic
753C2×C3C2×#369911yescharacteristic
754C2×C3#41×D911yescharacteristic
755C2×C3D3×#23511yescharacteristic
756C2×C3D32×D411yescharacteristic
757C2×C3D3×#23711yescharacteristic
758D3—22no—
759D3—41no—
760D3—121no—
761D3—361no—
762D3—361no—
763D3—721no—
764C22—21no—
765C22—21no—
766C22—21no—
767C22—32no—
768C22—61no—
769C22—61no—
770C22—61no—
771C22—61no—
772C22—61no—
773C22—181no—
774C22—181no—
775C22—181no—
776C22—541no—
777C22—541no—
778C22—541no—
779C22C22×D3×D911yescharacteristic
780C4—21no—
781C4—21no—
782C4—32no—
783C4—61no—
784C4—92no—
785C4—92no—
786C4—181no—
787C4—272no—
788C4—541no—
789C4—541no—
790C3—21no—
791C3#1058969811yescharacteristic, complemented
792C3#1059405811yescharacteristic
793C2—41no—
794C2—62no—
795C2—121no—
796C2—361no—
797C2—1081no—
798C2D9×#23511yescharacteristic
799C2D3×D4×D911yescharacteristic
800C2D3×#369911yescharacteristic
subgroupG/H
centerC22C22×D3×D9
commutator, cosocleC22×C3×C9C24
FrattiniC22×C3C22×D32
FittingC3×C9×C22⋊C4C22
socleC22×C32C23×D3
hypercenterC22⋊C4D3×D9
hypocenterC3×C9#532
LCSG ▷ C22×C3×C9 ▷ C3×C9
UCSC1 ◁ C22 ◁ C22⋊C4

Complements

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

NH ≅ G/Ntype
1. C2×#88662C2semidirect
2. C2×#88638C2semidirect
3. #11721731C2semidirect
4. C9×#884C2semidirect
5. C3×#611⋊C4C2semidirect
6. #11721289C2semidirect
7. #67×Dic9C2semidirect
8. #11721281C2semidirect
9. #11721044C2semidirect
10. #11721034C2semidirect
11. #11721017C2semidirect
12. #11721013C2semidirect
13. C4×D3×Dic9C2semidirect
14. #11721002C2semidirect
15. #11720905C2semidirect
85. #611⋊C4D3semidirect
116. D3×Dic9D4semidirect
225. C9×Dic3#41semidirect
228. C3×Dic9#41semidirect
255. #884D9semidirect
489. Dic9#235semidirect
506. C3×C9#532semidirect
705. Dic3#3699semidirect
708. C9#5548semidirect
791. C3#10589698semidirect

Maximal subgroups

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

subgroupindex
C2×#886622
C2×#886382
#117217312
C9×#8842
C3×#611⋊C42
#117212892
#67×Dic92
#117212812
#117210442
#117210342
#117210172
#117210132
C4×D3×Dic92
#117210022
#117209052
#105940583
#105896983