Finite Group Databasebeta

← #11233524

Subgroups — #11233524

Order 768.

1422 conjugacy classes of subgroups.

The subgroup lattice has 838 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#2446C211yesmaximal, characteristic
2#83234C211yesmaximal, characteristic
3#83227C211yesmaximal, characteristic
4#82462C211yesmaximal, characteristic
5#82461C211yesmaximal, characteristic
6#78262C212yesmaximal
7#78175C212yesmaximal
8#77882C212yesmaximal
9#77880C212yesmaximal
10#76544C211yesmaximal, characteristic
11#76543C211yesmaximal, characteristic
12#76526C211yesmaximal, characteristic
13#76524C211yesmaximal, characteristic
14#76490C211yesmaximal, characteristic
15#76489C211yesmaximal, characteristic
16#76073C211yesmaximal, characteristic
17#75974C211yesmaximal, characteristic
18#75201C212yesmaximal
19#75071C212yesmaximal
20#75039C212yesmaximal
21#75038C212yesmaximal
22#73723C211yesmaximal, characteristic
23#73670C211yesmaximal, characteristic
24#45347—31nomaximal, Sylow
25C2×C3×C4⋊Q8C2211yescharacteristic
26C2×C3×C4×Q8C2211yescharacteristic
27C2×Q8×Dic3C2211yescharacteristic
28C2×Q8×Dic3C2211yescharacteristic
29C2×Q8×Dic3C2211yescharacteristic
30C2×#888C2211yescharacteristic
31C3×#400C2212yes—
32C3×#398C2212yes—
33C3×#391C2211yescharacteristic
34C3×#391C2211yescharacteristic
35C3×#391C2211yescharacteristic
36C3×#389C2211yescharacteristic
37C3×#387C2212yes—
38C3×#387C2212yes—
39C3×C4×C4⋊C4C2211yescharacteristic
40#5229C2211yescharacteristic
41#5229C2211yescharacteristic
42#5229C2211yescharacteristic
43#5229C2211yescharacteristic
44#5229C2211yescharacteristic
45#4986C2212yes—
46#4986C2212yes—
47#4985C2211yescharacteristic
48#4983C2212yes—
49#4983C2211yescharacteristic
50#4982C2212yes—
51#4982C2211yescharacteristic
52#4981C2211yescharacteristic
53#4981C2212yes—
54#4980C2212yes—
55#4980C2212yes—
56#4980C2212yes—
57#4980C2212yes—
58#4980C2212yes—
59#4980C2212yes—
60#4978C2212yes—
61#4978C2212yes—
62#4978C2212yes—
63#4978C2212yes—
64#4977C2211yescharacteristic
65#4977C2212yes—
66#4977C2211yescharacteristic
67#4975C2211yescharacteristic
68Dic3×C4⋊C4C2211yescharacteristic
69Dic3×C4⋊C4C2211yescharacteristic
70Dic3×C4⋊C4C2211yescharacteristic
71#4973C2212yes—
72#4972C2211yescharacteristic
73#4972C2212yes—
74#4936C2211yescharacteristic
75#4936C2211yescharacteristic
76#4936C2212yes—
77#4935C2211yescharacteristic
78C4×C4⋊Dic3C2212yes—
79C4×C4⋊Dic3C2211yescharacteristic
80C4×C4⋊Dic3C2211yescharacteristic
81#4932C2211yescharacteristic
82C4×Dic3⋊C4C2211yescharacteristic
83C4×Dic3⋊C4C2212yes—
84C4×Dic3⋊C4C2211yescharacteristic
85C4×Dic3⋊C4C2211yescharacteristic
86C4×Dic3⋊C4C2211yescharacteristic
87#4928C2212yes—
88#4928C2211yescharacteristic
89#4928C2211yescharacteristic
90C3⋊#401C2212yes—
91C3⋊#401C2212yes—
92#4660C2212yes—
93#4660C2212yes—
94#4659C2212yes—
95#4659C2211yescharacteristic
96#4658C2212yes—
97#4658C2212yes—
98#4658C2211yescharacteristic
99#4658C2211yescharacteristic
100#4657C2211yescharacteristic
101#4656C2212yes—
102#4656C2212yes—
103#4655C2212yes—
104#4655C2212yes—
105#4654C2212yes—
106#4654C2212yes—
107#4654C2212yes—
108#4653C2212yes—
109#4653C2212yes—
110#4652C2212yes—
111#4652C2212yes—
112#4652C2212yes—
113#4651C2212yes—
114#4651C2212yes—
115#4651C2212yes—
116#4650C2212yes—
117#4649C2212yes—
118#4648C2212yes—
119#4647C2212yes—
120#4647C2212yes—
121#4646C2212yes—
122#4646C2212yes—
123#4646C2212yes—
124#2766—32no—
125#2766—32no—
126#2762—32no—
127#2762—32no—
128#2570—31no—
129#2570—31no—
130#2568—31no—
131#2567—31no—
132#2533—32no—
133#2533—32no—
134#2520—32no—
135#2520—32no—
136#2514—31no—
137#2514—31no—
138#2446—31no—
139#2446D311yescharacteristic
140#2402—31no—
141#2356—31no—
142#2355—31no—
143#2355—31no—
144#2351—31no—
145#2331—31no—
146#2327—31no—
147C22×C3×Q8C2311yescharacteristic
148C22×C3×Q8C2311yescharacteristic
149C22×Dic6C2312yes—
150C3×C4⋊Q8—24no—
151C3×C4×Q8—24no—
152C2×C3×C4⋊C4C2311yescharacteristic
153C2×C3×C4⋊C4C2312yes—
154C2×C3×C4⋊C4C2311yescharacteristic
155C2×C3×C4⋊C4C2312yes—
156C2×C3×C4⋊C4C2312yes—
157C2×C3×C4⋊C4C2311yescharacteristic
158C2×C3×C4⋊C4C2312yes—
159C2×C3×C4⋊C4C2311yescharacteristic
160C2×C3×C42C2311yescharacteristic
161C2×C3×C42C2311yescharacteristic
162C2×C3×C42C2312yes—
163C2×C3×C42C2311yescharacteristic
164Q8×Dic3—24no—
165Q8×Dic3—24no—
166Q8×Dic3—24no—
167C2×C4⋊Dic3C2312yes—
168C2×C4⋊Dic3C2312yes—
169C2×C4⋊Dic3C2311yescharacteristic
170C2×C4⋊Dic3C2312yes—
171C2×C4⋊Dic3C2311yescharacteristic
172C2×C4⋊Dic3C2311yescharacteristic
173C2×C4⋊Dic3C2311yescharacteristic
174C2×C4⋊Dic3C2311yescharacteristic
175C2×C4⋊Dic3C2312yes—
176C2×C4⋊Dic3C2312yes—
177C2×C4⋊Dic3C2311yescharacteristic
178C2×Dic3⋊C4C2312yes—
179C2×Dic3⋊C4C2311yescharacteristic
180C2×Dic3⋊C4C2311yescharacteristic
181C2×Dic3⋊C4C2311yescharacteristic
182C2×Dic3⋊C4C2312yes—
183C2×Dic3⋊C4C2312yes—
184C2×Dic3⋊C4C2311yescharacteristic
185C2×Dic3⋊C4C2311yescharacteristic
186C2×Dic3⋊C4C2311yescharacteristic
187C2×Dic3⋊C4C2312yes—
188C2×Dic3⋊C4C2312yes—
189C2×Dic3⋊C4C2312yes—
190C2×Dic3⋊C4C2311yescharacteristic
191C2×Dic3⋊C4C2311yescharacteristic
192C2×C4×Dic3C2312yes—
193C2×C4×Dic3C2312yes—
194C2×C4×Dic3C2312yes—
195C2×C4×Dic3C2311yescharacteristic
196C2×C4×Dic3C2311yescharacteristic
197C2×C4×Dic3C2311yescharacteristic
198C2×C4×Dic3C2312yes—
199C2×C4×Dic3C2312yes—
200C2×C4×Dic3C2312yes—
201C2×C4×Dic3C2312yes—
202C2×C4×Dic3C2311yescharacteristic
203#888—24no—
204C3×#95C2312yes—
205C3×#95C2312yes—
206C3×#95C2312yes—
207C3×#95C2312yes—
208C3×#95C2312yes—
209C3×#95C2312yes—
210C3×#95C2312yes—
211C3×#95C2311yescharacteristic
212C3×#95C2311yescharacteristic
213C3⋊#95C2311yescharacteristic
214C3⋊#95C2312yes—
215C3⋊#95C2312yes—
216C3⋊#95C2312yes—
217C3⋊#95C2312yes—
218C3⋊#95C2312yes—
219C3⋊#95C2312yes—
220C3⋊#95C2312yes—
221C3⋊#95C2312yes—
222C3⋊#95C2312yes—
223C3⋊#95C2312yes—
224C3⋊#95C2311yescharacteristic
225C3⋊#95C2312yes—
226C3⋊#95C2312yes—
227C3⋊#95C2312yes—
228C3⋊#95C2312yes—
229C3⋊#95C2312yes—
230C3⋊#95C2311yescharacteristic
231C3⋊#95C2311yescharacteristic
232C3⋊#95C2311yescharacteristic
233C3⋊#95C2312yes—
234C3⋊#95C2312yes—
235C3⋊#95C2312yes—
236C3⋊#95C2312yes—
237C3⋊#95C2312yes—
238C3⋊#95C2312yes—
239C3⋊#95C2311yescharacteristic
240C3⋊#95C2311yescharacteristic
241C3⋊#95C2312yes—
242C3⋊#95C2312yes—
243C3⋊#95C2311yescharacteristic
244C3⋊#95C2312yes—
245C3⋊#95C2312yes—
246C3⋊#95C2311yescharacteristic
247C3⋊#95C2311yescharacteristic
248C3⋊#95C2311yescharacteristic
249C3⋊#95C2311yescharacteristic
250C3⋊#95C2311yescharacteristic
251C3⋊#95C2311yescharacteristic
252C2×C4⋊Q8—31no—
253C2×C4⋊Q8C2×D311yescharacteristic
254C2×C4×Q8—31no—
255C2×C4×Q8—31no—
256C2×C4×Q8—31no—
257C2×C4×Q8C2×D311yescharacteristic
258#401—32no—
259#401—32no—
260#400—32no—
261#400—31no—
262#400—32no—
263#400—32no—
264#400—32no—
265#400—32no—
266#400—31no—
267#400—31no—
268#400—32no—
269#400—31no—
270#400—32no—
271#400C2×D312yes—
272#398—32no—
273#398—32no—
274#398—31no—
275#398—31no—
276#398—31no—
277#398—32no—
278#398—31no—
279#398C2×D312yes—
280#395—32no—
281#395—32no—
282#391—31no—
283#391—31no—
284#391—31no—
285#391—31no—
286#391—31no—
287#391—32no—
288#391—32no—
289#391—32no—
290#391—32no—
291#391C2×D311yescharacteristic
292#391C2×D311yescharacteristic
293#391C2×D311yescharacteristic
294#389—31no—
295#389—32no—
296#389—31no—
297#389—31no—
298#389—32no—
299#389—32no—
300#389—32no—
301#389C2×D311yescharacteristic
302#387—32no—
303#387—32no—
304#387—32no—
305#387—32no—
306#387—32no—
307#387—32no—
308#387—32no—
309#387—32no—
310#387—32no—
311#387—32no—
312#387—32no—
313#387—32no—
314#387—32no—
315#387—32no—
316#387—32no—
317#387—32no—
318#387—32no—
319#387—32no—
320#387—32no—
321#387—32no—
322#387C2×D312yes—
323#387C2×D312yes—
324#384—31no—
325#384—31no—
326#383—32no—
327#383—32no—
328#383—32no—
329#382—31no—
330#382—31no—
331#382—32no—
332#382—31no—
333#382—31no—
334#382—32no—
335#382—32no—
336C4×C4⋊C4—31no—
337C4×C4⋊C4—31no—
338C4×C4⋊C4—31no—
339C4×C4⋊C4—31no—
340C4×C4⋊C4—31no—
341C4×C4⋊C4—31no—
342C4×C4⋊C4—31no—
343C4×C4⋊C4—32no—
344C4×C4⋊C4—31no—
345C4×C4⋊C4—31no—
346C4×C4⋊C4—32no—
347C4×C4⋊C4—32no—
348C4×C4⋊C4C2×D311yescharacteristic
349#376—31no—
350#376—32no—
351C2×C3×Q8—22no—
352C2×C3×Q8—22no—
353C2×C3×Q8—22no—
354C2×C3×Q8—22no—
355C2×C3×Q8—22no—
356C2×C3×Q8#4114yes—
357C22×C3×C4C2411yescharacteristic
358C22×C3×C4C2412yes—
359C22×C3×C4C2411yescharacteristic
360C22×C3×C4C2412yes—
361C22×C3×C4C2411yescharacteristic
362C22×C3×C4C2411yescharacteristic
363C22×C3×C4C2411yescharacteristic
364C22×C3×C4C2412yes—
365C22×C3×C4C2412yes—
366C22×C3×C4C2411yescharacteristic
367C22×C3×C4C2411yescharacteristic
368C22×Dic3C2411yescharacteristic
369C22×Dic3C2411yescharacteristic
370C22×Dic3C2411yescharacteristic
371C22×Dic3C2411yescharacteristic
372C22×Dic3C2412yes—
373C22×Dic3C2412yes—
374C22×Dic3C2411yescharacteristic
375C22×Dic3C2412yes—
376C22×Dic3C2412yes—
377C22×Dic3C2411yescharacteristic
378C22×Dic3C2411yescharacteristic
379C22×Dic3C2411yescharacteristic
380C2×Dic6—24no—
381C2×Dic6—42no—
382C2×Dic6—42no—
383C3×C4⋊C4—22no—
384C3×C4⋊C4—24no—
385C3×C4⋊C4—22no—
386C3×C4⋊C4—24no—
387C3×C4⋊C4—24no—
388C3×C4⋊C4—22no—
389C3×C4⋊C4—42no—
390C3×C4⋊C4—41no—
391C3×C42—24no—
392C3×C42—22no—
393C3×C42—22no—
394C3×C42—22no—
395C4⋊Dic3—22no—
396C4⋊Dic3—24no—
397C4⋊Dic3—22no—
398C4⋊Dic3—22no—
399C4⋊Dic3—22no—
400C4⋊Dic3—22no—
401C4⋊Dic3—24no—
402C4⋊Dic3—24no—
403C4⋊Dic3—41no—
404C4⋊Dic3—42no—
405C4⋊Dic3—42no—
406Dic3⋊C4—22no—
407Dic3⋊C4—24no—
408Dic3⋊C4—24no—
409Dic3⋊C4—22no—
410Dic3⋊C4—22no—
411Dic3⋊C4—24no—
412Dic3⋊C4—22no—
413Dic3⋊C4—41no—
414Dic3⋊C4—42no—
415Dic3⋊C4—41no—
416Dic3⋊C4—41no—
417Dic3⋊C4—42no—
418Dic3⋊C4—42no—
419Dic3⋊C4—41no—
420C4×Dic3—24no—
421C4×Dic3—22no—
422C4×Dic3—22no—
423C4×Dic3—22no—
424C4×Dic3—24no—
425C4×Dic3—24no—
426C4×Dic3—42no—
427C4×Dic3—42no—
428C4×Dic3—42no—
429C4×Dic3—42no—
430C4×Dic3#4114yes—
431C22×Q8—32no—
432C22×Q8C22×D311yescharacteristic
433C22×Q8C22×D311yescharacteristic
434C4⋊Q8—24no—
435C4⋊Q8—64no—
436C4×Q8—24no—
437C4×Q8—64no—
438C4×Q8—64no—
439C4×Q8—64no—
440C2×C4⋊C4—31no—
441C2×C4⋊C4—31no—
442C2×C4⋊C4—31no—
443C2×C4⋊C4—32no—
444C2×C4⋊C4—32no—
445C2×C4⋊C4—32no—
446C2×C4⋊C4—31no—
447C2×C4⋊C4—32no—
448C2×C4⋊C4—31no—
449C2×C4⋊C4—31no—
450C2×C4⋊C4—32no—
451C2×C4⋊C4—32no—
452C2×C4⋊C4—31no—
453C2×C4⋊C4—31no—
454C2×C4⋊C4—31no—
455C2×C4⋊C4—31no—
456C2×C4⋊C4—31no—
457C2×C4⋊C4—32no—
458C2×C4⋊C4—32no—
459C2×C4⋊C4—31no—
460C2×C4⋊C4—31no—
461C2×C4⋊C4—31no—
462C2×C4⋊C4—32no—
463C2×C4⋊C4—32no—
464C2×C4⋊C4—32no—
465C2×C4⋊C4C22×D311yescharacteristic
466C2×C4⋊C4C22×D312yes—
467C2×C4⋊C4C22×D311yescharacteristic
468C2×C4⋊C4C22×D312yes—
469C2×C4⋊C4C22×D312yes—
470C2×C4⋊C4C22×D311yescharacteristic
471C2×C4⋊C4C22×D311yescharacteristic
472C2×C4⋊C4C22×D312yes—
473C2×C42—31no—
474C2×C42—32no—
475C2×C42—31no—
476C2×C42—32no—
477C2×C42—32no—
478C2×C42—31no—
479C2×C42—31no—
480C2×C42—32no—
481C2×C42—32no—
482C2×C42—32no—
483C2×C42—32no—
484C2×C42C22×D311yescharacteristic
485C2×C42C22×D312yes—
486C2×C42C22×D311yescharacteristic
487C2×C42C22×D311yescharacteristic
488#95—31no—
489#95—32no—
490#95—32no—
491#95—31no—
492#95—31no—
493#95—31no—
494#95—31no—
495#95—31no—
496#95—32no—
497#95—31no—
498#95—32no—
499#95—32no—
500#95—32no—
501#95—32no—
502#95—32no—
503#95—32no—
504#95—31no—
505#95—31no—
506#95—31no—
507#95—31no—
508#95—32no—
509#95—31no—
510#95—31no—
511#95—31no—
512#95—32no—
513#95—32no—
514#95—32no—
515#95—32no—
516#95—32no—
517#95—32no—
518#95—32no—
519#95—32no—
520#95—32no—
521#95—32no—
522#95—32no—
523#95—32no—
524#95—32no—
525#95—32no—
526#95—32no—
527#95C22×D312yes—
528#95C22×D312yes—
529#95C22×D311yescharacteristic
530#95C22×D311yescharacteristic
531#95C22×D312yes—
532#95C22×D312yes—
533#95C22×D312yes—
534#95C22×D312yes—
535#95C22×D312yes—
536C23×C3C2511yescharacteristic
537C3×Q8—28no—
538C3×Q8—44no—
539C2×C3×C4—22no—
540C2×C3×C4—21no—
541C2×C3×C4—22no—
542C2×C3×C4—21no—
543C2×C3×C4—22no—
544C2×C3×C4—22no—
545C2×C3×C4—22no—
546C2×C3×C4—21no—
547C2×C3×C4—21no—
548C2×C3×C4—21no—
549C2×C3×C4—22no—
550C2×C3×C4—21no—
551C2×C3×C4—22no—
552C2×C3×C4—21no—
553C2×C3×C4—21no—
554C2×C3×C4—21no—
555C2×C3×C4—21no—
556C2×C3×C4—21no—
557C2×C3×C4—21no—
558C2×C3×C4—22no—
559C2×C3×C4—21no—
560C2×C3×C4—22no—
561C2×C3×C4—22no—
562C2×C3×C4—21no—
563C2×C3×C4—21no—
564C2×C3×C4—22no—
565C2×C3×C4—21no—
566C2×C3×C4—21no—
567C2×C3×C4C2×#4114yes—
568C2×C3×C4C2×#4112yes—
569C2×C3×C4C2×#4112yes—
570C2×C3×C42−1+412yes—
571C2×C3×C42−1+412yes—
572C2×Dic3—21no—
573C2×Dic3—21no—
574C2×Dic3—21no—
575C2×Dic3—21no—
576C2×Dic3—21no—
577C2×Dic3—21no—
578C2×Dic3—22no—
579C2×Dic3—21no—
580C2×Dic3—22no—
581C2×Dic3—22no—
582C2×Dic3—22no—
583C2×Dic3—21no—
584C2×Dic3—21no—
585C2×Dic3—21no—
586C2×Dic3—21no—
587C2×Dic3—22no—
588C2×Dic3—22no—
589C2×Dic3—21no—
590C2×Dic3—22no—
591C2×Dic3—21no—
592C2×Dic3—21no—
593C2×Dic3—21no—
594C2×Dic3—21no—
595C2×Dic3—21no—
596C2×Dic3—21no—
597C2×Dic3—22no—
598C2×Dic3—21no—
599C2×Dic3—22no—
600C2×Dic3—22no—
601C2×Dic3—22no—
602C2×Dic3—21no—
603C2×Dic3—21no—
604C2×Dic3—22no—
605C2×Dic3C2×#4112yes—
606C2×Dic3C2×#4112yes—
607C2×Dic32−1+412yes—
608Dic6—84no—
609C2×Q8—22no—
610C2×Q8—22no—
611C2×Q8—22no—
612C2×Q8—22no—
613C2×Q8—22no—
614C2×Q8—64no—
615C2×Q8—122no—
616C2×Q8—122no—
617C2×Q8#23714yes—
618C22×C4—31no—
619C22×C4—31no—
620C22×C4—31no—
621C22×C4—31no—
622C22×C4—31no—
623C22×C4—31no—
624C22×C4—32no—
625C22×C4—31no—
626C22×C4—32no—
627C22×C4—31no—
628C22×C4—32no—
629C22×C4—32no—
630C22×C4C23×D311yescharacteristic
631C22×C4C23×D312yes—
632C22×C4C23×D311yescharacteristic
633C22×C4C23×D312yes—
634C22×C4C23×D311yescharacteristic
635C22×C4C23×D311yescharacteristic
636C22×C4C23×D311yescharacteristic
637C22×C4C23×D312yes—
638C22×C4C23×D312yes—
639C22×C4C23×D311yescharacteristic
640C22×C4C23×D311yescharacteristic
641C4⋊C4—24no—
642C4⋊C4—22no—
643C4⋊C4—24no—
644C4⋊C4—24no—
645C4⋊C4—22no—
646C4⋊C4—22no—
647C4⋊C4—42no—
648C4⋊C4—41no—
649C4⋊C4—64no—
650C4⋊C4—64no—
651C4⋊C4—64no—
652C4⋊C4—62no—
653C4⋊C4—62no—
654C4⋊C4—64no—
655C4⋊C4—62no—
656C4⋊C4—64no—
657C4⋊C4—62no—
658C4⋊C4—62no—
659C4⋊C4—64no—
660C4⋊C4—62no—
661C4⋊C4—62no—
662C4⋊C4—62no—
663C4⋊C4—62no—
664C4⋊C4—121no—
665C4⋊C4—121no—
666C4⋊C4—122no—
667C4⋊C4—121no—
668C4⋊C4—122no—
669C4⋊C4—122no—
670C4⋊C4—121no—
671C4⋊C4—121no—
672C4⋊C4—122no—
673C4⋊C4—122no—
674C42—24no—
675C42—22no—
676C42—22no—
677C42—22no—
678C42—34no—
679C42—64no—
680C42—64no—
681C42—64no—
682C42—62no—
683C42—62no—
684C42—62no—
685C42—122no—
686C42—122no—
687C42—122no—
688C42—122no—
689C22×C3C22×#4111yescharacteristic
690C22×C3C22×#4111yescharacteristic
691C22×C3C2×2−1+411yescharacteristic
692C22×C3C2×2−1+411yescharacteristic
693C22×C3C2×2−1+411yescharacteristic
694C22×C3#58511yescharacteristic
695C22×C3#58511yescharacteristic
696C3×C4—24no—
697C3×C4—22no—
698C3×C4—42no—
699C3×C4—42no—
700C3×C4—42no—
701C3×C4—41no—
702C3×C4—41no—
703C3×C4—41no—
704C3×C4—41no—
705C3×C4—41no—
706C3×C4#55214yes—
707Dic3—22no—
708Dic3—22no—
709Dic3—22no—
710Dic3—42no—
711Dic3—42no—
712Dic3—42no—
713Dic3—42no—
714Dic3—41no—
715Dic3—41no—
716Dic3—41no—
717Dic3—41no—
718Dic3—41no—
719C23C24×D311yescharacteristic
720Q8—28no—
721Q8—44no—
722Q8—244no—
723C2×C4—21no—
724C2×C4—22no—
725C2×C4—22no—
726C2×C4—21no—
727C2×C4—22no—
728C2×C4—21no—
729C2×C4—21no—
730C2×C4—21no—
731C2×C4—22no—
732C2×C4—21no—
733C2×C4—21no—
734C2×C4—22no—
735C2×C4—22no—
736C2×C4—21no—
737C2×C4—21no—
738C2×C4—22no—
739C2×C4—22no—
740C2×C4—21no—
741C2×C4—21no—
742C2×C4—21no—
743C2×C4—22no—
744C2×C4—21no—
745C2×C4—22no—
746C2×C4—21no—
747C2×C4—21no—
748C2×C4—21no—
749C2×C4—22no—
750C2×C4—21no—
751C2×C4—32no—
752C2×C4—32no—
753C2×C4—32no—
754C2×C4—61no—
755C2×C4—61no—
756C2×C4—61no—
757C2×C4—61no—
758C2×C4—61no—
759C2×C4—61no—
760C2×C4—62no—
761C2×C4—61no—
762C2×C4—62no—
763C2×C4—61no—
764C2×C4—62no—
765C2×C4—61no—
766C2×C4—61no—
767C2×C4—62no—
768C2×C4—62no—
769C2×C4—62no—
770C2×C4—61no—
771C2×C4—61no—
772C2×C4—61no—
773C2×C4—61no—
774C2×C4—61no—
775C2×C4—61no—
776C2×C4—62no—
777C2×C4—62no—
778C2×C4—61no—
779C2×C4—61no—
780C2×C4—62no—
781C2×C4—62no—
782C2×C4—61no—
783C2×C4—62no—
784C2×C4—61no—
785C2×C4—61no—
786C2×C4—62no—
787C2×C4C2×#23714yes—
788C2×C4C2×#23712yes—
789C2×C4#100712yes—
790C2×C4D3×#4112yes—
791C2×C4#101012yes—
792C2×C3C2×#55211yescharacteristic
793C2×C3#350911yescharacteristic
794C2×C3#351011yescharacteristic
795C2×C3#351611yescharacteristic
796C2×C3#351611yescharacteristic
797C2×C3#355511yescharacteristic
798C2×C3#355511yescharacteristic
799C22C22×#23711yescharacteristic
800C22C2×#100711yescharacteristic
801C22C2×D3×#4111yescharacteristic
802C22C2×#101011yescharacteristic
803C22#596411yescharacteristic
804C22D3×2−1+411yescharacteristic
805C22#596811yescharacteristic
806C4—22no—
807C4—24no—
808C4—42no—
809C4—41no—
810C4—41no—
811C4—42no—
812C4—41no—
813C4—41no—
814C4—42no—
815C4—41no—
816C4—62no—
817C4—62no—
818C4—62no—
819C4—122no—
820C4—122no—
821C4—122no—
822C4—121no—
823C4—121no—
824C4—121no—
825C4—122no—
826C4—121no—
827C4—121no—
828C4#565014yes—
829C3#4534711yescharacteristic, complemented, Sylow
830C2C2×#565011yescharacteristic
831C2#8626811yescharacteristic
832C2#8650011yescharacteristic
833C2#8671911yescharacteristic
834C2#8674911yescharacteristic
835C2#8698411yescharacteristic
836C2#8702011yescharacteristic
subgroupG/H
center, FrattiniC23C24×D3
commutator, socle, prime radical, cosocleC23×C3C25
FittingC3×#2446C2
hypercenter#2446D3
hypocenterC3#45347
LCSG ▷ C23×C3 ▷ C3
UCSC1 ◁ C23 ◁ #2446

Complements

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

NH ≅ G/Ntype
829. C3#45347semidirect

Maximal subgroups

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

subgroupindex
C3×#24462
#832342
#832272
#824622
#824612
#782622
#781752
#778822
#778802
#765442
#765432
#765262
#765242
#764902
#764892
#760732
#759742
#752012
#750712
#750392
#750382
#737232
#736702
#453473