Finite Group Databasebeta

← #13148451

Subgroups — #13148451

Order 1728.

856 conjugacy classes of subgroups.

The subgroup lattice has 814 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11721731C211yesmaximal, characteristic, complemented
2C9×#882C211yesmaximal, characteristic, complemented
3C3×#63447C211yesmaximal, characteristic, complemented
4#11721292C211yesmaximal, characteristic, complemented
5#11721287C211yesmaximal, characteristic, complemented
6#11721286C211yesmaximal, characteristic, complemented
7#11721263C211yesmaximal, characteristic, complemented
8#11721050C211yesmaximal, characteristic, complemented
9#11721050C211yesmaximal, characteristic, complemented
10#11721044C211yesmaximal, characteristic, complemented
11#11721042C211yesmaximal, characteristic, complemented
12#11721035C211yesmaximal, characteristic, complemented
13#11720967C211yesmaximal, characteristic, complemented
14#11720964C211yesmaximal, characteristic, complemented
15#11720956C211yesmaximal, characteristic, complemented
16#10594309—31nomaximal
17#10589696—31nomaximal
18C23×D3×C9C2211yescharacteristic, complemented
19C22×D3×D9C2211yescharacteristic, complemented
20C2×#6233C2211yescharacteristic
21C2×#6226C2211yescharacteristic, complemented
22C2×C9×#67C2211yescharacteristic
23C2×C3×#611C2211yescharacteristic
24C2×C9×D12C2211yescharacteristic
25C2×C9×D12C2211yescharacteristic
26C2×C3×Dic18C2211yescharacteristic, complemented
27C2×#6195C2211yescharacteristic
28C2×#6195C2211yescharacteristic
29C2×#6194C2211yescharacteristic
30C2×#6194C2211yescharacteristic
31C2×#6189C2211yescharacteristic, complemented
32C3×C9×C22⋊C4C2211yescharacteristic, complemented
33#88551C2211yescharacteristic, complemented
34#88536C2211yescharacteristic, complemented
35#88536C2211yescharacteristic, complemented
36C4×C3⋊Dic9C2211yescharacteristic, complemented
37C3×#3676C2211yescharacteristic, complemented
38C9×(C2×D3)⋊C4C2211yescharacteristic, complemented
39C9×(C2×D3)⋊C4C2211yescharacteristic, complemented
40C3×(C2×D9)⋊C4C2211yescharacteristic, complemented
41C3×(C2×D9)⋊C4C2211yescharacteristic, complemented
42C3×C4×Dic9C2211yescharacteristic, complemented
43(C2×D3)⋊Dic9C2211yescharacteristic, complemented
44(C2×D3)⋊Dic9C2211yescharacteristic, complemented
45(C2×D3)⋊Dic9C2211yescharacteristic, complemented
46(C2×D3)⋊Dic9C2211yescharacteristic, complemented
47(C2×D3)⋊Dic9C2211yescharacteristic, complemented
48(C2×D3)⋊Dic9C2211yescharacteristic, complemented
49(C2×D3)⋊Dic9C2211yescharacteristic, complemented
50#88445C2211yescharacteristic, complemented
51(C2×D9)⋊Dic3C2211yescharacteristic, complemented
52Dic3×Dic9C2211yescharacteristic, complemented
53#64094—31no—
54C3×#885—31no—
55C3×#882D311yescharacteristic
56#63983—31no—
57#63977—31no—
58#63976—31no—
59#63959—31no—
60#63922—31no—
61#63922—31no—
62#63915—31no—
63#63913—31no—
64#63907—31no—
65#63863—31no—
66#63860—31no—
67#63852—31no—
68C9×#120—31no—
69#63515—31no—
70#63515—31no—
71#63499—31no—
72#63499—31no—
73#63499—31no—
74#63498—31no—
75#63498—31no—
76#63498—31no—
77#63447—31no—
78#63447—31no—
79#63447—31no—
80#63447—31no—
81#63447—31no—
82#63447—61no—
83#63447D311yescharacteristic, complemented
84C23×C3×C9C2311yescharacteristic
85C22×C3⋊D9C2311yescharacteristic
86C22×D3×C9—41no—
87C22×D3×C9—41no—
88C22×D3×C9—41no—
89C22×D3×C9C2311yescharacteristic
90C22×D3×C9C2311yescharacteristic
91C22×D3×C9C2311yescharacteristic
92C22×C3×D9C2311yescharacteristic
93C2×D3×D9—41no—
94C2×D3×D9—41no—
95C2×D3×D9—41no—
96C2×C3×C4×C9C2311yescharacteristic
97C2×C3×C4×C9C2311yescharacteristic
98#6233—41no—
99C2×C3⋊Dic9C2311yescharacteristic
100C2×C3⋊Dic9C2311yescharacteristic
101C2×C3⋊Dic9C2311yescharacteristic
102#6226—41no—
103C9×#67—41no—
104C3×#611—41no—
105C2×C9×Dic3C2311yescharacteristic
106C2×C3×Dic9C2311yescharacteristic
107C2×C3×Dic9C2311yescharacteristic
108C2×C3×Dic9C2311yescharacteristic
109C9×D12—41no—
110C9×D12—41no—
111C3×Dic18—41no—
112#6195—41no—
113#6195—41no—
114#6194—41no—
115#6194—41no—
116#6189—41no—
117#5683—91no—
118#5594—91no—
119C23×C3×D3C2×D311yescharacteristic
120C22×D32—31no—
121C2×#638—31no—
122C2×#634—31no—
123C2×C3×#67—31no—
124C2×C3×#67C2×D311yescharacteristic
125C2×C3×D12C2×D311yescharacteristic
126C2×C3×D12C2×D311yescharacteristic
127C2×C3×Dic6—31no—
128C2×#627—31no—
129C2×#626—31no—
130C2×#626—31no—
131C2×#625—31no—
132C2×#625—31no—
133C24×C9—31no—
134C23×D9—31no—
135C32×C22⋊C4C2×D311yescharacteristic
136#3757—31no—
137#3752—31no—
138#3752—31no—
139C4×C3⋊Dic3—31no—
140C3×#217—31no—
141C3×(C2×D3)⋊C4—31no—
142C3×(C2×D3)⋊C4—31no—
143C3×(C2×D3)⋊C4C2×D311yescharacteristic
144C3×(C2×D3)⋊C4C2×D311yescharacteristic
145C3×C4×Dic3—31no—
146#3722—31no—
147(C2×D3)⋊Dic3—31no—
148(C2×D3)⋊Dic3—31no—
149(C2×D3)⋊Dic3—31no—
150(C2×D3)⋊Dic3—31no—
151(C2×D3)⋊Dic3—31no—
152(C2×D3)⋊Dic3—31no—
153(C2×D3)⋊Dic3—31no—
154(C2×D3)⋊Dic3—31no—
155Dic32—31no—
156C2×D4×C9—31no—
157C2×D4×C9—31no—
158C2×D4×C9—31no—
159C2×#611—31no—
160C2×#611—31no—
161C2×#611—31no—
162C2×#611—31no—
163C2×#611—31no—
164C2×#611—61no—
165C2×#611C2×D311yescharacteristic
166C2×Dic18—31no—
167C2×Dic18—31no—
168C2×Dic18—61no—
169C2×Dic18C2×D311yescharacteristic, complemented
170C9×C22⋊C4—21no—
171C9×C22⋊C4—31no—
172C9×C22⋊C4—31no—
173C9×C22⋊C4C2×D311yescharacteristic, complemented
174#3676—31no—
175#3676—31no—
176#3676—31no—
177#3676—31no—
178#3676—31no—
179#3676—31no—
180#3676—31no—
181#3676—31no—
182#3676—61no—
183#3676C2×D311yescharacteristic, complemented
184(C2×D9)⋊C4—31no—
185(C2×D9)⋊C4—31no—
186(C2×D9)⋊C4—31no—
187(C2×D9)⋊C4—31no—
188(C2×D9)⋊C4—61no—
189(C2×D9)⋊C4—61no—
190(C2×D9)⋊C4C2×D311yescharacteristic, complemented
191(C2×D9)⋊C4C2×D311yescharacteristic, complemented
192C4×Dic9—31no—
193C4×Dic9—31no—
194C4×Dic9—61no—
195C4×Dic9C2×D311yescharacteristic, complemented
196C22×C3×C9—21no—
197C22×C3×C9—21no—
198C22×C3×C9—21no—
199C22×C3×C9C2411yescharacteristic
200C2×C3⋊D9—21no—
201C2×C3⋊D9—21no—
202C2×C3⋊D9—21no—
203C2×D3×C9—21no—
204C2×D3×C9—21no—
205C2×D3×C9—21no—
206C2×D3×C9—21no—
207C2×D3×C9—21no—
208C2×D3×C9—21no—
209C2×D3×C9—21no—
210C2×D3×C9—21no—
211C2×D3×C9—21no—
212C2×D3×C9—44no—
213C2×C3×D9—21no—
214C2×C3×D9—21no—
215C2×C3×D9—21no—
216D3×D9—44no—
217C3×C4×C9—21no—
218C3×C4×C9—21no—
219C3⋊Dic9—21no—
220C3⋊Dic9—21no—
221C3⋊Dic9—21no—
222C9×Dic3—21no—
223C3×Dic9—21no—
224C3×Dic9—21no—
225C3×Dic9—21no—
226C3×#124—91no—
227C3×#120—31no—
228#953—91no—
229#953—91no—
230#947—91no—
231#947—91no—
232#937—91no—
233#937—91no—
234#937—91no—
235#937—91no—
236#937—91no—
237#936—91no—
238#936—91no—
239#936—91no—
240#885—31no—
241#885—91no—
242#885—91no—
243#885—91no—
244#885—91no—
245#885—91no—
246#885—91no—
247#885—91no—
248#885—91no—
249#885—91no—
250#885—181no—
251#882—91no—
252#882—91no—
253#882—91no—
254#882D911yescharacteristic, complemented
255#875—91no—
256#875—91no—
257C23×C32C22×D311yescharacteristic
258C22×C3⋊D3—31no—
259C22×C3×D3—31no—
260C22×C3×D3—41no—
261C22×C3×D3—41no—
262C22×C3×D3—41no—
263C22×C3×D3C22×D311yescharacteristic
264C22×C3×D3C22×D311yescharacteristic
265C22×C3×D3C22×D311yescharacteristic
266C2×D32—121no—
267C2×D32—121no—
268C2×D32—121no—
269C2×C32×C4C22×D311yescharacteristic
270C2×C32×C4C22×D311yescharacteristic
271#638—121no—
272C2×C3⋊Dic3—31no—
273C2×C3⋊Dic3—31no—
274C2×C3⋊Dic3—31no—
275#634—121no—
276C3×#67—41no—
277C3×#67—121no—
278C2×C3×Dic3—31no—
279C2×C3×Dic3—31no—
280C2×C3×Dic3—31no—
281C2×C3×Dic3C22×D311yescharacteristic
282C3×D12—41no—
283C3×D12—41no—
284C3×Dic6—121no—
285#627—121no—
286#626—121no—
287#626—121no—
288#625—121no—
289#625—121no—
290C23×C9—21no—
291C23×C9—31no—
292C23×C9—31no—
293C23×C9—31no—
294C23×C9—121no—
295C23×C9—121no—
296C23×C9—121no—
297C23×C9C22×D311yescharacteristic
298C22×D9—31no—
299C22×D9—61no—
300C22×D9—121no—
301C22×D9—121no—
302C22×D9—121no—
303C22×D9C22×D311yescharacteristic
304D4×C9—121no—
305D4×C9—121no—
306D4×C9—121no—
307C2×C4×C9—21no—
308C2×C4×C9—21no—
309C2×C4×C9—31no—
310C2×C4×C9C22×D311yescharacteristic
311C2×C4×C9C22×D311yescharacteristic
312#611—41no—
313#611—121no—
314#611—121no—
315#611—121no—
316#611—121no—
317#611—121no—
318#611—122no—
319C2×Dic9—31no—
320C2×Dic9—31no—
321C2×Dic9—31no—
322C2×Dic9—61no—
323C2×Dic9—61no—
324C2×Dic9—61no—
325C2×Dic9C22×D311yescharacteristic
326C2×Dic9C22×D311yescharacteristic
327C2×Dic9C22×D311yescharacteristic
328Dic18—41no—
329Dic18—121no—
330Dic18—121no—
331Dic18—122no—
332H(3,𝔽4)—271noSylow
333C2×C3×C9—41no—
334C2×C3×C9H(5,𝔽2)11yescharacteristic
335C2×C3×C9H(5,𝔽2)11yescharacteristic
336C2×C3×C9H(5,𝔽2)11yescharacteristic
337C3⋊D9—41no—
338D3×C9—41no—
339D3×C9—41no—
340D3×C9—41no—
341C3×D9—41no—
342C24×C3—31no—
343C23×D3—91no—
344C23×D3—91no—
345C23×D3C2×D911yescharacteristic, complemented
346C2×C3×Q8—91no—
347C2×C3×D4—31no—
348C2×C3×D4—31no—
349C2×C3×D4—31no—
350C2×C3×D4—91no—
351C2×#67—31no—
352C2×#67—91no—
353C2×#67—91no—
354C2×#67—91no—
355C2×#67—91no—
356C2×#67—91no—
357C2×#67—91no—
358C2×#67—91no—
359C2×#67—91no—
360C2×#67—181no—
361C2×#67C2×D911yescharacteristic
362C2×D12—91no—
363C2×D12—91no—
364C2×D12C2×D911yescharacteristic
365C2×D12C2×D911yescharacteristic
366C2×Dic6—31no—
367C2×Dic6—91no—
368C2×Dic6—91no—
369C2×Dic6—91no—
370C2×Dic6—91no—
371C2×Dic6—181no—
372C3×C22⋊C4—21no—
373C3×C22⋊C4—31no—
374C3×C22⋊C4—31no—
375C3×C22⋊C4—91no—
376C3×C22⋊C4—91no—
377C3×C22⋊C4—91no—
378C3×C22⋊C4C2×D911yescharacteristic, complemented
379C3×C22⋊C4D3211yescharacteristic
380C3×C42—91no—
381#217—31no—
382#217—91no—
383#217—91no—
384#217—91no—
385#217—91no—
386#217—91no—
387#217—91no—
388#217—91no—
389#217—91no—
390#217—91no—
391#217—91no—
392#217—181no—
393(C2×D3)⋊C4—31no—
394(C2×D3)⋊C4—31no—
395(C2×D3)⋊C4—91no—
396(C2×D3)⋊C4—91no—
397(C2×D3)⋊C4—91no—
398(C2×D3)⋊C4—91no—
399(C2×D3)⋊C4—91no—
400(C2×D3)⋊C4—91no—
401(C2×D3)⋊C4—91no—
402(C2×D3)⋊C4—91no—
403(C2×D3)⋊C4—91no—
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—181no—
410(C2×D3)⋊C4—181no—
411(C2×D3)⋊C4C2×D911yescharacteristic, complemented
412(C2×D3)⋊C4C2×D911yescharacteristic, complemented
413C4×Dic3—31no—
414C4×Dic3—91no—
415C4×Dic3—91no—
416C4×Dic3—91no—
417C4×Dic3—91no—
418C4×Dic3—181no—
419C22×C32—21no—
420C22×C32—21no—
421C22×C32—21no—
422C22×C32C23×D311yescharacteristic
423C2×C3⋊D3—61no—
424C2×C3⋊D3—61no—
425C2×C3⋊D3—61no—
426C2×C3×D3—21no—
427C2×C3×D3—21no—
428C2×C3×D3—21no—
429C2×C3×D3—21no—
430C2×C3×D3—21no—
431C2×C3×D3—21no—
432C2×C3×D3—21no—
433C2×C3×D3—21no—
434C2×C3×D3—21no—
435C2×C3×D3—44no—
436C2×C3×D3—61no—
437C2×C3×D3—61no—
438C2×C3×D3—61no—
439D32—124no—
440C32×C4—21no—
441C32×C4—21no—
442C3⋊Dic3—61no—
443C3⋊Dic3—61no—
444C3⋊Dic3—61no—
445C3×Dic3—21no—
446C3×Dic3—61no—
447C3×Dic3—61no—
448C3×Dic3—61no—
449C22×C9—21no—
450C22×C9—21no—
451C22×C9—21no—
452C22×C9—21no—
453C22×C9—41no—
454C22×C9—41no—
455C22×C9—41no—
456C22×C9—61no—
457C22×C9—61no—
458C22×C9—61no—
459C22×C9—61no—
460C22×C9—61no—
461C22×C9—61no—
462C22×C9—61no—
463C22×C9—61no—
464C22×C9—61no—
465C22×C9—124no—
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—
476C2×D9—124no—
477C4×C9—21no—
478C4×C9—21no—
479C4×C9—41no—
480C4×C9—41no—
481C4×C9—61no—
482Dic9—21no—
483Dic9—21no—
484Dic9—21no—
485Dic9—62no—
486Dic9—61no—
487Dic9—61no—
488Dic9—61no—
489Dic9—121no—
490Dic9—121no—
491#124—91no—
492#124—271no—
493#124—271no—
494#124—271no—
495#124—271no—
496#124—271no—
497#124—271no—
498#124—271no—
499#124—271no—
500#120—31no—
501#120—271no—
502#120—271no—
503#120—271no—
504#120—271no—
505#120—271no—
506C3×C9H(3,𝔽4)11yescharacteristic, complemented, Sylow
507C23×C3—21no—
508C23×C3—31no—
509C23×C3—31no—
510C23×C3—31no—
511C23×C3—91no—
512C23×C3—121no—
513C23×C3—121no—
514C23×C3—121no—
515C23×C3C22×D911yescharacteristic
516C23×C3C2×D3211yescharacteristic
517C22×D3—31no—
518C22×D3—41no—
519C22×D3—41no—
520C22×D3—41no—
521C22×D3—91no—
522C22×D3—91no—
523C22×D3—181no—
524C22×D3—361no—
525C22×D3—361no—
526C22×D3—361no—
527C22×D3—361no—
528C22×D3—361no—
529C22×D3—361no—
530C22×D3C22×D911yescharacteristic
531C22×D3C22×D911yescharacteristic
532C22×D3C22×D911yescharacteristic
533C3×Q8—361no—
534C3×D4—121no—
535C3×D4—121no—
536C3×D4—121no—
537C3×D4—361no—
538C2×C3×C4—21no—
539C2×C3×C4—21no—
540C2×C3×C4—31no—
541C2×C3×C4—91no—
542C2×C3×C4—91no—
543C2×C3×C4—91no—
544C2×C3×C4C22×D911yescharacteristic
545C2×C3×C4C22×D911yescharacteristic
546C2×C3×C4C2×D3211yescharacteristic
547C2×C3×C4C2×D3211yescharacteristic
548#67—41no—
549#67—121no—
550#67—361no—
551#67—361no—
552#67—361no—
553#67—361no—
554#67—361no—
555#67—361no—
556#67—361no—
557#67—361no—
558#67—362no—
559C2×Dic3—31no—
560C2×Dic3—31no—
561C2×Dic3—31no—
562C2×Dic3—91no—
563C2×Dic3—91no—
564C2×Dic3—91no—
565C2×Dic3—91no—
566C2×Dic3—91no—
567C2×Dic3—91no—
568C2×Dic3—181no—
569C2×Dic3—181no—
570C2×Dic3—181no—
571C2×Dic3C22×D911yescharacteristic
572D12—41no—
573D12—41no—
574D12—361no—
575D12—361no—
576Dic6—121no—
577Dic6—361no—
578Dic6—361no—
579Dic6—361no—
580Dic6—361no—
581Dic6—362no—
582C2×C32—41no—
583C2×C32#100411yescharacteristic
584C2×C32#100411yescharacteristic
585C2×C32#100411yescharacteristic
586C3⋊D3—121no—
587C3×D3—41no—
588C3×D3—41no—
589C3×D3—41no—
590C3×D3—121no—
591C2×C9—21no—
592C2×C9—21no—
593C2×C9—21no—
594C2×C9—41no—
595C2×C9—81no—
596C2×C9—121no—
597C2×C9—121no—
598C2×C9—121no—
599C2×C9#100411yescharacteristic
600C2×C9#100911yescharacteristic
601C2×C9#100911yescharacteristic
602D9—41no—
603D9—121no—
604D9—241no—
605C24—31no—
606C24—271no—
607C2×Q8—91no—
608C2×Q8—271no—
609C2×Q8—271no—
610C2×D4—31no—
611C2×D4—31no—
612C2×D4—31no—
613C2×D4—91no—
614C2×D4—271no—
615C2×D4—271no—
616C2×D4—271no—
617C2×D4—271no—
618C2×D4—271no—
619C22⋊C4—31no—
620C22⋊C4—31no—
621C22⋊C4—91no—
622C22⋊C4—91no—
623C22⋊C4—91no—
624C22⋊C4—271no—
625C22⋊C4—271no—
626C22⋊C4—271no—
627C22⋊C4—271no—
628C22⋊C4—271no—
629C22⋊C4—271no—
630C22⋊C4—271no—
631C22⋊C4—271no—
632C22⋊C4—271no—
633C22⋊C4—271no—
634C22⋊C4—271no—
635C22⋊C4—271no—
636C22⋊C4D3×D911yescharacteristic, complemented
637C42—91no—
638C42—271no—
639C42—271no—
640C22×C3—21no—
641C22×C3—21no—
642C22×C3—21no—
643C22×C3—21no—
644C22×C3—21no—
645C22×C3—21no—
646C22×C3—21no—
647C22×C3—41no—
648C22×C3—41no—
649C22×C3—41no—
650C22×C3—61no—
651C22×C3—61no—
652C22×C3—61no—
653C22×C3—61no—
654C22×C3—61no—
655C22×C3—61no—
656C22×C3—61no—
657C22×C3—61no—
658C22×C3—61no—
659C22×C3—124no—
660C22×C3—181no—
661C22×C3—181no—
662C22×C3—181no—
663C22×C3C23×D911yescharacteristic
664C22×C3C22×D3211yescharacteristic
665C2×D3—21no—
666C2×D3—21no—
667C2×D3—21no—
668C2×D3—21no—
669C2×D3—21no—
670C2×D3—21no—
671C2×D3—21no—
672C2×D3—21no—
673C2×D3—21no—
674C2×D3—44no—
675C2×D3—61no—
676C2×D3—61no—
677C2×D3—61no—
678C2×D3—181no—
679C2×D3—181no—
680C2×D3—181no—
681C2×D3—181no—
682C2×D3—181no—
683C2×D3—181no—
684C2×D3—361no—
685C2×D3—361no—
686C2×D3—361no—
687C2×D3—364no—
688C2×D3—364no—
689C3×C4—21no—
690C3×C4—21no—
691C3×C4—21no—
692C3×C4—21no—
693C3×C4—41no—
694C3×C4—41no—
695C3×C4—61no—
696C3×C4—181no—
697C3×C4—181no—
698C3×C4—181no—
699Dic3—21no—
700Dic3—61no—
701Dic3—61no—
702Dic3—61no—
703Dic3—182no—
704Dic3—181no—
705Dic3—181no—
706Dic3—181no—
707Dic3—181no—
708Dic3—181no—
709Dic3—181no—
710Dic3—361no—
711Dic3—361no—
712C32#559411yescharacteristic
713C9—21no—
714C9#568311yescharacteristic, complemented
715C23—31no—
716C23—31no—
717C23—31no—
718C23—91no—
719C23—121no—
720C23—121no—
721C23—121no—
722C23—271no—
723C23—1081no—
724C23—1081no—
725C23—1081no—
726C23C2×D3×D911yescharacteristic
727Q8—361no—
728Q8—1081no—
729Q8—1081no—
730D4—121no—
731D4—121no—
732D4—121no—
733D4—361no—
734D4—1081no—
735D4—1081no—
736D4—1081no—
737D4—1081no—
738D4—1081no—
739C2×C4—31no—
740C2×C4—91no—
741C2×C4—91no—
742C2×C4—91no—
743C2×C4—271no—
744C2×C4—271no—
745C2×C4—271no—
746C2×C4C2×D3×D911yescharacteristic
747C2×C4C2×D3×D911yescharacteristic
748C2×C3—21no—
749C2×C3—21no—
750C2×C3—21no—
751C2×C3—41no—
752C2×C3—41no—
753C2×C3—81no—
754C2×C3—121no—
755C2×C3—121no—
756C2×C3—121no—
757C2×C3—361no—
758C2×C3#6371011yescharacteristic
759C2×C3#6371011yescharacteristic
760C2×C3#6371011yescharacteristic
761C2×C3#6430711yescharacteristic
762C2×C3#6431311yescharacteristic
763C2×C3#6431411yescharacteristic
764D3—41no—
765D3—41no—
766D3—41no—
767D3—121no—
768D3—361no—
769D3—361no—
770D3—721no—
771C22—21no—
772C22—21no—
773C22—21no—
774C22—61no—
775C22—61no—
776C22—61no—
777C22—61no—
778C22—61no—
779C22—61no—
780C22—61no—
781C22—61no—
782C22—61no—
783C22—124no—
784C22—181no—
785C22—181no—
786C22—181no—
787C22—541no—
788C22—541no—
789C22—541no—
790C22—1084no—
791C22C22×D3×D911yescharacteristic
792C4—21no—
793C4—21no—
794C4—61no—
795C4—181no—
796C4—181no—
797C4—181no—
798C4—541no—
799C4—541no—
800C4—541no—
801C3—21no—
802C3#1058969611yescharacteristic, complemented
803C3#1059430911yescharacteristic
804C2—41no—
805C2—121no—
806C2—121no—
807C2—121no—
808C2—361no—
809C2—1081no—
810C2#1172247611yescharacteristic
811C2#1172249911yescharacteristic
812C2#1172250011yescharacteristic
subgroupG/H
centerC22C22×D3×D9
commutator, cosocleC22×C3×C9C24
FrattiniC22×C3C22×D32
FittingC3×C9×C22⋊C4C22
socleC22×C32C23×D3
hypercenterC22⋊C4D3×D9
hypocenterC3×C9H(3,𝔽4)
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. #11721731C2semidirect
2. C9×#882C2semidirect
3. C3×#63447C2semidirect
4. #11721292C2semidirect
5. #11721287C2semidirect
6. #11721286C2semidirect
7. #11721263C2semidirect
8. #11721050C2semidirect
9. #11721050C2semidirect
10. #11721044C2semidirect
11. #11721042C2semidirect
12. #11721035C2semidirect
13. #11720967C2semidirect
14. #11720964C2semidirect
15. #11720956C2semidirect
18. C23×D3×C9C22semidirect
19. C22×D3×D9C22semidirect
21. C2×#6226C22semidirect
26. C2×C3×Dic18C22semidirect
31. C2×#6189C22semidirect
32. C3×C9×C22⋊C4C22semidirect
33. #88551C22semidirect
34. #88536C22semidirect
35. #88536C22semidirect
36. C4×C3⋊Dic9C22semidirect
37. C3×#3676C22semidirect
38. C9×(C2×D3)⋊C4C22semidirect
39. C9×(C2×D3)⋊C4C22semidirect
40. C3×(C2×D9)⋊C4C22semidirect
41. C3×(C2×D9)⋊C4C22semidirect
42. C3×C4×Dic9C22semidirect
43. (C2×D3)⋊Dic9C22semidirect
44. (C2×D3)⋊Dic9C22semidirect
45. (C2×D3)⋊Dic9C22semidirect
46. (C2×D3)⋊Dic9C22semidirect
47. (C2×D3)⋊Dic9C22semidirect
48. (C2×D3)⋊Dic9C22semidirect
49. (C2×D3)⋊Dic9C22semidirect
50. #88445C22semidirect
51. (C2×D9)⋊Dic3C22semidirect
52. Dic3×Dic9C22semidirect
83. #63447D3semidirect
169. C2×Dic18C2×D3semidirect
173. C9×C22⋊C4C2×D3semidirect
183. #3676C2×D3semidirect
190. (C2×D9)⋊C4C2×D3semidirect
191. (C2×D9)⋊C4C2×D3semidirect
195. C4×Dic9C2×D3semidirect
254. #882D9semidirect
345. C23×D3C2×D9semidirect
378. C3×C22⋊C4C2×D9semidirect
411. (C2×D3)⋊C4C2×D9semidirect
412. (C2×D3)⋊C4C2×D9semidirect
506. C3×C9H(3,𝔽4)semidirect
636. C22⋊C4D3×D9semidirect
714. C9#5683semidirect
802. C3#10589696semidirect

Maximal subgroups

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

subgroupindex
#117217312
C9×#8822
C3×#634472
#117212922
#117212872
#117212862
#117212632
#117210502
#117210442
#117210422
#117210352
#117209672
#117209642
#117209562
#105943093
#105896963