Finite Group Databasebeta

← #13148207

Subgroups — #13148207

Order 1728.

956 conjugacy classes of subgroups.

The subgroup lattice has 796 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#88663C211yesmaximal, characteristic, complemented
2C2×#88638C211yesmaximal, characteristic, complemented
3#11721724C211yesmaximal, characteristic, complemented
4C9×#884C211yesmaximal, characteristic, complemented
5C3×#63446C211yesmaximal, characteristic, complemented
6#11721290C211yesmaximal, characteristic, complemented
7#11721281C211yesmaximal, characteristic, complemented
8#11721281C211yesmaximal, characteristic, complemented
9#11721037C211yesmaximal, characteristic, complemented
10#11721023C211yesmaximal, characteristic, complemented
11#11721016C211yesmaximal, characteristic, complemented
12D3×Dic9⋊C4C211yesmaximal, characteristic, complemented
13#11720996C211yesmaximal, characteristic, complemented
14#11720982C211yesmaximal, characteristic, complemented
15#11720939C211yesmaximal, characteristic, complemented
16#10594060—31nomaximal
17#10589699—31nomaximal
18C22×C3⋊Dic9C2211yescharacteristic
19C2×#6226C2211yescharacteristic
20C2×C9×#67C2211yescharacteristic
21C2×C9×#67C2211yescharacteristic
22C2×C3×#611C2211yescharacteristic
23C2×C3×#611C2211yescharacteristic
24C2×C9×D12C2211yescharacteristic
25C2×C4×D3×C9C2211yescharacteristic
26C2×C3×D36C2211yescharacteristic
27C2×C3×C4×D9C2211yescharacteristic
28C2×#6194C2211yescharacteristic
29C2×#6194C2211yescharacteristic
30C2×#6194C2211yescharacteristic
31C2×#6194C2211yescharacteristic
32#88663—24no—
33C2×D3×Dic9C2211yescharacteristic
34C2×D3×Dic9C2211yescharacteristic
35C2×D3×Dic9C2211yescharacteristic
36C2×Dic3×D9C2211yescharacteristic
37C2×#6189C2211yescharacteristic
38#88638—24no—
39C3×C9×C22⋊C4C2211yescharacteristic
40#88551C2211yescharacteristic
41C4⋊(C3⋊Dic9)C2211yescharacteristic
42#88534C2211yescharacteristic
43#88534C2211yescharacteristic
44C9×(C2×D3)⋊C4C2211yescharacteristic
45C3×(C2×D9)⋊C4C2211yescharacteristic
46C9×Dic3⋊C4C2211yescharacteristic
47C3×Dic9⋊C4C2211yescharacteristic
48(C2×D3)⋊Dic9C2211yescharacteristic
49(C2×D9)⋊Dic3C2211yescharacteristic
50(C2×D9)⋊Dic3C2211yescharacteristic
51(C2×D9)⋊Dic3C2211yescharacteristic
52#88442C2211yescharacteristic
53Dic9⋊Dic3C2211yescharacteristic
54Dic9⋊Dic3C2211yescharacteristic
55C2×#3805—31no—
56C2×#3795—31no—
57#64087—31no—
58C3×#884—31no—
59C3×#884D311yescharacteristic
60#63980—31no—
61#63970—31no—
62#63970—31no—
63#63908—31no—
64#63896—31no—
65#63893—31no—
66#63885—31no—
67#63885—31no—
68D3×Dic3⋊C4—31no—
69#63851—31no—
70C2×#3699—31no—
71C2×#3699—31no—
72C9×#121—31no—
73#63501—31no—
74#63501—31no—
75#63501—31no—
76#63501—31no—
77#63492—31no—
78C2×Dic9⋊C4—31no—
79#63458—31no—
80#63458—31no—
81#63446—31no—
82#63446D311yescharacteristic, complemented
83#63440—31no—
84#63440—31no—
85#63440—61no—
86C23×C3×C9C2311yescharacteristic
87C22×D3×C9C2311yescharacteristic
88C22×D3×C9C2311yescharacteristic
89C22×C3×D9C2311yescharacteristic
90C22×C3×D9C2311yescharacteristic
91C2×C3×C4×C9C2311yescharacteristic
92C2×C3×C4×C9C2311yescharacteristic
93C2×C3⋊Dic9—22no—
94C2×C3⋊Dic9C2311yescharacteristic
95C2×C3⋊Dic9C2311yescharacteristic
96C2×C3⋊Dic9C2311yescharacteristic
97C2×C3⋊Dic9C2311yescharacteristic
98#6226—22no—
99C9×#67—22no—
100C9×#67—41no—
101C3×#611—22no—
102C3×#611—41no—
103C2×C9×Dic3C2311yescharacteristic
104C2×C9×Dic3C2311yescharacteristic
105C2×C3×Dic9C2311yescharacteristic
106C2×C3×Dic9C2311yescharacteristic
107C9×D12—22no—
108C4×D3×C9—41no—
109C3×D36—41no—
110C3×C4×D9—22no—
111#6194—22no—
112#6194—22no—
113#6194—22no—
114#6194—41no—
115D3×Dic9—22no—
116D3×Dic9—41no—
117D3×Dic9D414yescomplemented
118Dic3×D9—22no—
119#6189—22no—
120#5608—91no—
121#5597—91no—
122C22×C3⋊Dic3—31no—
123C2×#634—31no—
124C2×C3×#67—31no—
125C2×C3×#67—31no—
126C2×C3×#67C2×D311yescharacteristic
127C2×C3×#67C2×D311yescharacteristic
128C2×C3×D12—31no—
129C2×C3×D12C2×D311yescharacteristic
130C2×C3×C4×D3—31no—
131C2×C3×C4×D3C2×D311yescharacteristic
132C2×#627—31no—
133C2×#625—31no—
134C2×#625—31no—
135C2×#625—31no—
136C2×#625—31no—
137#3805—64no—
138C2×D3×Dic3—31no—
139C2×D3×Dic3—31no—
140C2×D3×Dic3—31no—
141C2×D3×Dic3—31no—
142#3795—64no—
143C32×C22⋊C4C2×D311yescharacteristic
144#3757—31no—
145C4⋊(C3⋊Dic3)—31no—
146#3750—31no—
147#3750—31no—
148C3×(C2×D3)⋊C4—31no—
149C3×(C2×D3)⋊C4C2×D311yescharacteristic
150C3×Dic3⋊C4—31no—
151C3×Dic3⋊C4C2×D311yescharacteristic
152#3724—31no—
153Dic3⋊Dic3—31no—
154Dic3⋊Dic3—31no—
155(C2×D3)⋊Dic3—31no—
156(C2×D3)⋊Dic3—31no—
157(C2×D3)⋊Dic3—31no—
158(C2×D3)⋊Dic3—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×#611C2×D311yescharacteristic
168C2×#611C2×D311yescharacteristic
169C22×Dic9—31no—
170C22×Dic9—31no—
171C22×Dic9—31no—
172C22×Dic9—31no—
173C22×Dic9—61no—
174#3699—64no—
175#3699—64no—
176C2×D36C2×D311yescharacteristic
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)⋊C4C2×D311yescharacteristic
193C4⋊Dic9—31no—
194C4⋊Dic9—61no—
195Dic9⋊C4—31no—
196Dic9⋊C4—31no—
197Dic9⋊C4—31no—
198Dic9⋊C4—31no—
199Dic9⋊C4—31no—
200Dic9⋊C4—61no—
201Dic9⋊C4—61no—
202Dic9⋊C4C2×D311yescharacteristic
203C22×C3×C9—21no—
204C22×C3×C9—21no—
205C22×C3×C9—21no—
206C22×C3×C9C2411yescharacteristic
207C2×D3×C9—21no—
208C2×D3×C9—21no—
209C2×D3×C9—21no—
210C2×D3×C9—21no—
211C2×D3×C9—21no—
212C2×D3×C9C2×D412yes—
213C2×C3×D9—21no—
214C2×C3×D9—21no—
215C2×C3×D9—21no—
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⋊Dic9—21no—
224C3⋊Dic9C2×D412yes—
225C9×Dic3—21no—
226C9×Dic3—21no—
227C3×Dic9—21no—
228C3×Dic9C2×D412yes—
229C2×#237—91no—
230C2×#237—91no—
231C2×#237—91no—
232C2×#235—91no—
233C3×#121—31no—
234C3×#121—91no—
235#939—91no—
236#939—91no—
237#939—91no—
238#939—91no—
239#939—91no—
240#939—91no—
241#938—91no—
242#938—91no—
243#938—91no—
244#930—91no—
245#924—91no—
246C2×Dic3⋊C4—91no—
247#897—91no—
248#896—91no—
249#896—91no—
250D3×C4⋊C4—91no—
251#884—31no—
252#884—91no—
253#884—91no—
254#884D911yescharacteristic, complemented
255#878—91no—
256#878—91no—
257#878—91no—
258#878—91no—
259#878—181no—
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
267C2×C3⋊Dic3—31no—
268C2×C3⋊Dic3—31no—
269C2×C3⋊Dic3—31no—
270C2×C3⋊Dic3—31no—
271C2×C3⋊Dic3—62no—
272#634—62no—
273C3×#67—22no—
274C3×#67—41no—
275C3×#67—62no—
276C3×#67—121no—
277C2×C3×Dic3—31no—
278C2×C3×Dic3—31no—
279C2×C3×Dic3C22×D311yescharacteristic
280C2×C3×Dic3C22×D311yescharacteristic
281C3×D12—22no—
282C3×D12—121no—
283C3×C4×D3—41no—
284C3×C4×D3—62no—
285#627—62no—
286#625—62no—
287#625—62no—
288#625—62no—
289#625—121no—
290D3×Dic3—34no—
291D3×Dic3—62no—
292D3×Dic3—62no—
293D3×Dic3—121no—
294C23×C9—21no—
295C23×C9—31no—
296C23×C9—31no—
297C23×C9C22×D311yescharacteristic
298C22×D9C22×D311yescharacteristic
299C22×D9C22×D311yescharacteristic
300D4×C9—62no—
301D4×C9—62no—
302D4×C9—121no—
303C2×C4×C9—21no—
304C2×C4×C9—21no—
305C2×C4×C9—31no—
306C2×C4×C9—31no—
307C2×C4×C9—121no—
308C2×C4×C9C22×D311yescharacteristic
309C2×C4×C9C22×D311yescharacteristic
310#611—22no—
311#611—41no—
312#611—62no—
313#611—62no—
314#611—62no—
315#611—121no—
316C2×Dic9—31no—
317C2×Dic9—34no—
318C2×Dic9—31no—
319C2×Dic9—31no—
320C2×Dic9—31no—
321C2×Dic9—61no—
322C2×Dic9—61no—
323C2×Dic9—61no—
324C2×Dic9—61no—
325C2×Dic9—62no—
326C2×Dic9—62no—
327C2×Dic9—122no—
328C2×Dic9—121no—
329C2×Dic9C22×D311yescharacteristic
330C2×Dic9C22×D311yescharacteristic
331D36—41no—
332C4×D9—22no—
333C4×D9—62no—
334Dic18—62no—
335Dic18—62no—
336Dic18—122no—
337#537—271noSylow
338C2×C3×C9—41no—
339C2×C3×C9C22×D411yescharacteristic
340C2×C3×C9H(5,𝔽2)11yescharacteristic
341C2×C3×C92−1+411yescharacteristic
342D3×C9—22no—
343D3×C9—41no—
344C3×D9—41no—
345C3×D9—41no—
346C2×C3×D4—31no—
347C2×C3×D4—31no—
348C2×C3×D4—31no—
349C2×C3×D4—91no—
350C2×C3×D4—91no—
351C2×C3×D4—91no—
352C22×C3×C4—31no—
353C22×C3×C4—91no—
354C2×#67—31no—
355C2×#67—31no—
356C2×#67—91no—
357C2×#67—91no—
358C2×#67—91no—
359C2×#67—91no—
360C2×#67—91no—
361C2×#67—91no—
362C2×#67—91no—
363C2×#67—91no—
364C2×#67C2×D911yescharacteristic
365C2×#67C2×D911yescharacteristic
366C22×Dic3—91no—
367C22×Dic3—91no—
368C22×Dic3—91no—
369C22×Dic3—91no—
370C22×Dic3—91no—
371C22×Dic3—91no—
372C22×Dic3—181no—
373#237—184no—
374#237—184no—
375#237—184no—
376#235—184no—
377C2×D12—31no—
378C2×D12C2×D911yescharacteristic
379C2×C4×D3—31no—
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
397#217—91no—
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)⋊C4C2×D911yescharacteristic
410C4⋊Dic3—91no—
411C4⋊Dic3—91no—
412C4⋊Dic3—91no—
413C4⋊Dic3—91no—
414C4⋊Dic3—181no—
415Dic3⋊C4—31no—
416Dic3⋊C4—91no—
417Dic3⋊C4—91no—
418Dic3⋊C4—91no—
419Dic3⋊C4—91no—
420Dic3⋊C4—91no—
421Dic3⋊C4—91no—
422Dic3⋊C4—91no—
423Dic3⋊C4—91no—
424Dic3⋊C4—181no—
425Dic3⋊C4—181no—
426Dic3⋊C4C2×D911yescharacteristic
427C22×C32—21no—
428C22×C32—21no—
429C22×C32—21no—
430C22×C32C23×D311yescharacteristic
431C2×C3×D3—21no—
432C2×C3×D3—21no—
433C2×C3×D3—21no—
434C2×C3×D3—21no—
435C2×C3×D3—21no—
436C2×C3×D3—61no—
437C2×C3×D3—61no—
438C2×C3×D3—61no—
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—61no—
449C3×Dic3—21no—
450C3×Dic3—21no—
451C3×Dic3—32no—
452C3×Dic3—61no—
453C22×C9—22no—
454C22×C9—21no—
455C22×C9—21no—
456C22×C9—21no—
457C22×C9—21no—
458C22×C9—32no—
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—21no—
471C2×D9—21no—
472C2×D9—21no—
473C4×C9—21no—
474C4×C9—21no—
475C4×C9—41no—
476C4×C9—41no—
477C4×C9—61no—
478C4×C9—61no—
479Dic9—21no—
480Dic9—32no—
481Dic9—62no—
482Dic9—61no—
483Dic9—61no—
484Dic9—61no—
485Dic9—121no—
486Dic9—121no—
487Dic9—121no—
488Dic9D3×D412yes—
489C2×#41—271no—
490C2×#41—271no—
491C22⋊Q8—271no—
492C22⋊Q8—271no—
493C22⋊Q8—271no—
494C22⋊Q8—271no—
495#121—31no—
496#121—91no—
497#121—271no—
498#121—271no—
499#121—271no—
500#121—271no—
501#121—271no—
502#121—271no—
503C2×C4⋊C4—271no—
504C3×C9#53711yescharacteristic, complemented, Sylow
505C23×C3—21no—
506C23×C3—31no—
507C23×C3—31no—
508C23×C3—91no—
509C23×C3—91no—
510C23×C3C22×D911yescharacteristic
511C23×C3C2×D3211yescharacteristic
512C22×D3—31no—
513C22×D3—31no—
514C22×D3C22×D911yescharacteristic
515C22×D3C22×D911yescharacteristic
516C3×D4—62no—
517C3×D4—62no—
518C3×D4—121no—
519C3×D4—182no—
520C3×D4—361no—
521C3×D4—361no—
522C2×C3×C4—21no—
523C2×C3×C4—21no—
524C2×C3×C4—31no—
525C2×C3×C4—31no—
526C2×C3×C4—91no—
527C2×C3×C4—91no—
528C2×C3×C4—121no—
529C2×C3×C4—182no—
530C2×C3×C4C22×D911yescharacteristic
531C2×C3×C4C22×D911yescharacteristic
532C2×C3×C4C2×D3211yescharacteristic
533C2×C3×C4C2×D3211yescharacteristic
534#67—22no—
535#67—41no—
536#67—62no—
537#67—121no—
538#67—182no—
539#67—182no—
540#67—182no—
541#67—182no—
542#67—182no—
543#67—182no—
544#67—361no—
545#67—361no—
546C2×Dic3—31no—
547C2×Dic3—31no—
548C2×Dic3—94no—
549C2×Dic3—91no—
550C2×Dic3—91no—
551C2×Dic3—91no—
552C2×Dic3—91no—
553C2×Dic3—91no—
554C2×Dic3—91no—
555C2×Dic3—91no—
556C2×Dic3—91no—
557C2×Dic3—181no—
558C2×Dic3—181no—
559C2×Dic3—181no—
560C2×Dic3—181no—
561C2×Dic3—182no—
562C2×Dic3—182no—
563C2×Dic3—182no—
564C2×Dic3—182no—
565C2×Dic3—362no—
566C2×Dic3—361no—
567C2×Dic3C22×D911yescharacteristic
568C2×Dic3C22×D911yescharacteristic
569D12—22no—
570D12—121no—
571C4×D3—41no—
572C4×D3—62no—
573C4×D3—94no—
574C4×D3—182no—
575C4×D3—182no—
576C4×D3—361no—
577Dic6—182no—
578Dic6—182no—
579Dic6—182no—
580Dic6—182no—
581Dic6—362no—
582C2×C32—41no—
583C2×C32C2×D3×D411yescharacteristic
584C2×C32#100411yescharacteristic
585C2×C32#101011yescharacteristic
586C3×D3—22no—
587C3×D3—41no—
588C3×D3—121no—
589C3×D3—121no—
590C2×C9—21no—
591C2×C9—21no—
592C2×C9—21no—
593C2×C9—42no—
594C2×C9—41no—
595C2×C9—62no—
596C2×C9—121no—
597C2×C9C2×D3×D411yescharacteristic
598C2×C9#100411yescharacteristic
599C2×C9#101011yescharacteristic
600D9—41no—
601D9—41no—
602#41—544no—
603#41—544no—
604C2×Q8—271no—
605C2×Q8—271no—
606C2×D4—31no—
607C2×D4—31no—
608C2×D4—31no—
609C2×D4—91no—
610C2×D4—91no—
611C2×D4—91no—
612C2×D4—271no—
613C2×D4—271no—
614C2×D4—271no—
615C2×D4—271no—
616C22×C4—31no—
617C22×C4—91no—
618C22×C4—271no—
619C22×C4—271no—
620C22×C4—271no—
621C22×C4—271no—
622C22×C4—271no—
623C4⋊C4—31no—
624C4⋊C4—91no—
625C4⋊C4—271no—
626C4⋊C4—271no—
627C4⋊C4—271no—
628C4⋊C4—271no—
629C4⋊C4—271no—
630C4⋊C4—271no—
631C22⋊C4—31no—
632C22⋊C4—91no—
633C22⋊C4—271no—
634C22⋊C4—271no—
635C22⋊C4—271no—
636C22⋊C4—271no—
637C22⋊C4—271no—
638C22⋊C4D3×D911yescharacteristic
639C22×C3—22no—
640C22×C3—21no—
641C22×C3—21no—
642C22×C3—21no—
643C22×C3—21no—
644C22×C3—21no—
645C22×C3—21no—
646C22×C3—21no—
647C22×C3—32no—
648C22×C3—41no—
649C22×C3—41no—
650C22×C3—61no—
651C22×C3—61no—
652C22×C3—61no—
653C22×C3—61no—
654C22×C3—61no—
655C22×C3—181no—
656C22×C3—181no—
657C22×C3—181no—
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—61no—
672C2×D3—61no—
673C2×D3—61no—
674C2×D3D4×D912yes—
675C3×C4—21no—
676C3×C4—21no—
677C3×C4—21no—
678C3×C4—21no—
679C3×C4—41no—
680C3×C4—41no—
681C3×C4—61no—
682C3×C4—61no—
683C3×C4—92no—
684C3×C4—181no—
685Dic3—21no—
686Dic3—21no—
687Dic3—32no—
688Dic3—61no—
689Dic3—92no—
690Dic3—92no—
691Dic3—182no—
692Dic3—181no—
693Dic3—181no—
694Dic3—181no—
695Dic3—181no—
696Dic3—181no—
697Dic3—181no—
698Dic3—361no—
699Dic3—361no—
700Dic3—361no—
701C32#559711yescharacteristic
702C9—21no—
703C9#560811yescharacteristic, complemented
704C23—31no—
705C23—31no—
706C23—91no—
707C23—91no—
708C23C2×D3×D911yescharacteristic
709Q8—542no—
710Q8—542no—
711D4—62no—
712D4—62no—
713D4—121no—
714D4—182no—
715D4—361no—
716D4—361no—
717D4—542no—
718D4—542no—
719D4—542no—
720D4—1081no—
721C2×C4—31no—
722C2×C4—31no—
723C2×C4—91no—
724C2×C4—91no—
725C2×C4—121no—
726C2×C4—182no—
727C2×C4—274no—
728C2×C4—271no—
729C2×C4—271no—
730C2×C4—271no—
731C2×C4—271no—
732C2×C4—542no—
733C2×C4—542no—
734C2×C4—542no—
735C2×C4—1081no—
736C2×C4C2×D3×D911yescharacteristic
737C2×C4C2×D3×D911yescharacteristic
738C2×C3—21no—
739C2×C3—21no—
740C2×C3—21no—
741C2×C3—42no—
742C2×C3—41no—
743C2×C3—41no—
744C2×C3—62no—
745C2×C3—121no—
746C2×C3—361no—
747C2×C3—361no—
748C2×C3C2×D4×D911yescharacteristic
749C2×C3#6371011yescharacteristic
750C2×C3#6371611yescharacteristic
751C2×C3#6429811yescharacteristic
752C2×C3D32×D411yescharacteristic
753C2×C3#6431311yescharacteristic
754D3—22no—
755D3—41no—
756D3—121no—
757D3—121no—
758C22—21no—
759C22—21no—
760C22—21no—
761C22—32no—
762C22—61no—
763C22—61no—
764C22—61no—
765C22—61no—
766C22—61no—
767C22—181no—
768C22—181no—
769C22—181no—
770C22—181no—
771C22—181no—
772C22—181no—
773C22C22×D3×D911yescharacteristic
774C4—21no—
775C4—21no—
776C4—61no—
777C4—61no—
778C4—92no—
779C4—181no—
780C4—272no—
781C4—541no—
782C4—541no—
783C4—541no—
784C3—21no—
785C3#1058969911yescharacteristic, complemented
786C3#1059406011yescharacteristic
787C2—41no—
788C2—62no—
789C2—121no—
790C2—361no—
791C2—361no—
792C2#1172246511yescharacteristic
793C2D3×D4×D911yescharacteristic
794C2#1172249911yescharacteristic
subgroupG/H
centerC22C22×D3×D9
commutator, cosocleC22×C3×C9C24
FrattiniC22×C3C22×D32
FittingC3×C9×C22⋊C4C22
socleC22×C32C23×D3
hypercenterC22⋊C4D3×D9
hypocenterC3×C9#537
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×#88663C2semidirect
2. C2×#88638C2semidirect
3. #11721724C2semidirect
4. C9×#884C2semidirect
5. C3×#63446C2semidirect
6. #11721290C2semidirect
7. #11721281C2semidirect
8. #11721281C2semidirect
9. #11721037C2semidirect
10. #11721023C2semidirect
11. #11721016C2semidirect
12. D3×Dic9⋊C4C2semidirect
13. #11720996C2semidirect
14. #11720982C2semidirect
15. #11720939C2semidirect
82. #63446D3semidirect
117. D3×Dic9D4semidirect
254. #884D9semidirect
504. C3×C9#537semidirect
703. C9#5608semidirect
785. C3#10589699semidirect

Maximal subgroups

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

subgroupindex
C2×#886632
C2×#886382
#117217242
C9×#8842
C3×#634462
#117212902
#117212812
#117210372
#117210232
#117210162
D3×Dic9⋊C42
#117209962
#117209822
#117209392
#105940603
#105896993