Finite Group Databasebeta

← #11901233

Subgroups — #11901233

Order 1152.

3557 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
1C22×#3828C211yesmaximal, characteristic, complemented
2C22×C3×#235C211yesmaximal, characteristic, complemented
3C2×C3×#926C211yesmaximal, characteristic, complemented
4#10595519C214yesmaximal, complemented
5#10595045C212yesmaximal, complemented
6#10595043C214yesmaximal, complemented
7#10595042C212yesmaximal, complemented
8#10595034C214yesmaximal, complemented
9#10595029C214yesmaximal, complemented
10#10595023C214yesmaximal, complemented
11#10594866C212yesmaximal, complemented
12#10594856C212yesmaximal, complemented
13#87268—31nomaximal
14#85735—31nomaximal
15C23×C32×C4C2211yescharacteristic
16C22×#638C2212yes—
17C2×#3828—28no—
18C2×#3828C2212yes—
19C2×#3828C2212yes—
20C2×#3828C2212yescomplemented
21C2×#3828C2212yescomplemented
22C22×C4⋊(C3⋊D3)C2211yescharacteristic, complemented
23C22×C4×C3⋊D3C2212yescomplemented
24C22×#634C2211yescharacteristic, complemented
25C22×C3×#67C2212yes—
26C2×C3×#235—28no—
27C2×C3×#235C2212yes—
28C2×C3×#235C2212yes—
29C2×C3×#235C2212yescomplemented
30C2×C3×#235C2212yescomplemented
31C22×C3×D12C2211yescharacteristic, complemented
32C22×C3×C4×D3C2212yescomplemented
33C22×C3×Dic6C2211yescharacteristic, complemented
34C2×C3×#217C2212yes—
35C3×#926C2212yescomplemented
36C3×#926C2212yescomplemented
37C3×#926C2212yescomplemented
38C3×#926C2212yescomplemented
39C2×C3×C4⋊Dic3C2212yescomplemented
40C2×C3×C4×Dic3C2212yescomplemented
41#63981C2218yescomplemented
42#63978C22116yescomplemented
43#63977C2218yescomplemented
44#63966C2218yescomplemented
45#63962C2218yescomplemented
46#63916C2218yescomplemented
47#63911C2214yescomplemented
48#63909C2218yescomplemented
49C4×#626C22116yescomplemented
50#63871C2218yescomplemented
51#63866C2214yescomplemented
52#63864C2214yescomplemented
53#63860C2214yescomplemented
54#63857C2218yescomplemented
55C22×C3×#41—31no—
56C22×#235—31no—
57C22×#235—31no—
58C22×#235—61no—
59C22×#235D311yescharacteristic, complemented
60C2×C3×#117—31no—
61#5833—34no—
62#5832—34no—
63#5830—32no—
64#5828—34no—
65#5825—32no—
66#5816—32no—
67#5805—32no—
68#5804—34no—
69#5791—34no—
70C2×#926D311yescharacteristic, complemented
71#5526—32no—
72#5526—32no—
73#5525—32no—
74#5525—32no—
75#5524—34no—
76#5524—34no—
77#5510—34no—
78#5493—34no—
79#5477—34no—
80C24×C32C2311yescharacteristic
81C23×C3⋊D3C2312yes—
82C23×C3×D3C2312yes—
83C22×C32×C4D418yescomplemented
84C22×C32×C4C2311yescharacteristic
85C22×C32×C4C2311yescharacteristic
86C22×C32×C4C2311yescharacteristic
87C22×C32×C4C2311yescharacteristic
88C22×C32×C4C2311yescharacteristic
89C22×C32×C4C2311yescharacteristic
90C2×#638—28no—
91C2×#638C2314yes—
92C2×#638C2314yes—
93C22×C3⋊Dic3C2312yes—
94#3828—28no—
95#3828—28no—
96#3828—28no—
97#3828—28no—
98C2×C4⋊(C3⋊D3)—24no—
99C2×C4⋊(C3⋊D3)C2312yes—
100C2×C4⋊(C3⋊D3)C2312yes—
101C2×C4×C3⋊D3—28no—
102C2×C4×C3⋊D3C2314yes—
103C2×C4×C3⋊D3C2314yes—
104C2×#634—24no—
105C2×#634C2312yes—
106C2×#634C2312yes—
107C2×C3×#67—28no—
108C2×C3×#67C2314yes—
109C2×C3×#67C2314yes—
110C22×C3×Dic3C2312yes—
111C22×C3×Dic3C2314yes—
112C3×#235—28no—
113C3×#235—28no—
114C3×#235—28no—
115C3×#235—28no—
116C2×C3×D12—24no—
117C2×C3×D12C2312yes—
118C2×C3×D12C2312yes—
119C2×C3×C4×D3—28no—
120C2×C3×C4×D3C2314yes—
121C2×C3×C4×D3C2314yes—
122C2×C3×Dic6—24no—
123C2×C3×Dic6C2312yes—
124C2×C3×Dic6C2312yes—
125C2×#626C23116yes—
126C3×#217C2314yes—
127C3×#217C2314yes—
128C3×C4⋊Dic3C2314yes—
129C3×C4⋊Dic3C2314yes—
130C3×C4×Dic3C2314yes—
131C3×C4×Dic3C2314yes—
132Dic3⋊Dic3C23116yes—
133#3722C23116yes—
134(C2×D3)⋊Dic3C23116yes—
135#3449—91noSylow
136C2×C3×#41—32no—
137C2×C3×#41—32no—
138C2×C3×#41—32no—
139C2×C3×#41—32no—
140C2×C3×#41—68no—
141C22×C3×Q8—31no—
142C22×C3×D4—32no—
143C22×C3×D4—31no—
144C23×C3×C4—21no—
145C23×C3×C4—32no—
146C23×C3×C4C2×D311yescharacteristic
147C23×C3×C4C2×D311yescharacteristic
148C22×#67—32no—
149C22×#67—32no—
150C22×#67—62no—
151C22×#67C2×D312yes—
152C2×#235—28no—
153C2×#235—32no—
154C2×#235—32no—
155C2×#235—32no—
156C2×#235—32no—
157C2×#235—32no—
158C2×#235—32no—
159C2×#235—32no—
160C2×#235—32no—
161C2×#235—62no—
162C2×#235—62no—
163C2×#235—62no—
164C2×#235—62no—
165C2×#235—616no—
166C2×#235—68no—
167C2×#235—68no—
168C2×#235C2×D312yes—
169C2×#235C2×D312yes—
170C2×#235C2×D312yescomplemented
171C2×#235C2×D312yescomplemented
172C22×D12—31no—
173C22×D12—31no—
174C22×D12—61no—
175C22×D12C2×D311yescharacteristic, complemented
176C22×C4×D3—32no—
177C22×C4×D3—32no—
178C22×C4×D3—62no—
179C22×C4×D3C2×D312yescomplemented
180C22×Dic6—31no—
181C22×Dic6—31no—
182C22×Dic6—61no—
183C22×Dic6C2×D311yescharacteristic, complemented
184C3×#117—32no—
185C3×#117—32no—
186C3×#117—32no—
187C3×#117—32no—
188C2×C3×C4⋊C4—32no—
189C2×C3×C22⋊C4—32no—
190C2×C3×C42—32no—
191#953—38no—
192C2×#217C2×D312yes—
193#947—34no—
194#946—38no—
195#944—34no—
196#940—34no—
197#939—316no—
198#938—38no—
199#937—38no—
200#936—34no—
201#935—38no—
202#930—316no—
203#930—38no—
204#929—38no—
205C4×#67—316no—
206#926C2×D312yescomplemented
207#926C2×D312yescomplemented
208#926C2×D312yescomplemented
209#926C2×D312yescomplemented
210C2×C4⋊Dic3C2×D312yescomplemented
211#924—38no—
212C2×C4×Dic3C2×D312yescomplemented
213#897—38no—
214#897—38no—
215#895—38no—
216#895—38no—
217#886—38no—
218#886—38no—
219#882—38no—
220#882—38no—
221#875—34no—
222#875—34no—
223#874—34no—
224C4×D12—316no—
225#869—34no—
226C23×C32—42no—
227C23×C32C2×D414yes—
228C23×C32C2411yescharacteristic
229C23×C32C2411yescharacteristic
230C23×C32C2411yescharacteristic
231C22×C3⋊D3—24no—
232C22×C3⋊D3—44no—
233C22×C3⋊D3C2414yes—
234C22×C3×D3—24no—
235C22×C3×D3—44no—
236C22×C3×D3C2414yes—
237C2×C32×C4C2×D414yes—
238C2×C32×C4C2×D414yes—
239C2×C32×C4C2×D414yes—
240C2×C32×C4C2×D414yes—
241C2×C32×C4C2×D414yes—
242C2×C32×C4C2×D414yes—
243C2×C32×C4C2411yescharacteristic
244C2×C32×C4C2411yescharacteristic
245C2×C32×C4C2411yescharacteristic
246C2×C32×C4C2411yescharacteristic
247#638—28no—
248#638—28no—
249C2×C3⋊Dic3—24no—
250C2×C3⋊Dic3C2414yes—
251C4⋊(C3⋊D3)—24no—
252C4⋊(C3⋊D3)—24no—
253C4×C3⋊D3—28no—
254C4×C3⋊D3—28no—
255#634—24no—
256#634—24no—
257C3×#67—28no—
258C3×#67—28no—
259C2×C3×Dic3—24no—
260C2×C3×Dic3—44no—
261C2×C3×Dic3C2418yes—
262C2×C3×Dic3C2414yes—
263C3×D12—24no—
264C3×D12—24no—
265C3×C4×D3—28no—
266C3×C4×D3—28no—
267C3×Dic6—24no—
268C3×Dic6—24no—
269#626—416no—
270C22×#41—31no—
271C22×#41—91no—
272#537—94no—
273#536—92no—
274#536—92no—
275#535—92no—
276#535—92no—
277#534—94no—
278#532—94no—
279#525—94no—
280#525—94no—
281C2×#117—31no—
282C24×C3—21no—
283C24×C3—32no—
284C24×C3C22×D311yescharacteristic
285C24×C3C22×D311yescharacteristic
286C23×D3—32no—
287C23×D3—32no—
288C23×D3—62no—
289C23×D3C22×D312yes—
290C3×#41—68no—
291C3×#41—68no—
292C3×#41—68no—
293C3×#41—68no—
294C2×C3×Q8—32no—
295C2×C3×Q8—32no—
296C2×C3×Q8—64no—
297C2×C3×D4—34no—
298C2×C3×D4—34no—
299C2×C3×D4—32no—
300C2×C3×D4—32no—
301C2×C3×D4—68no—
302C2×C3×D4—64no—
303C22×C3×C4—28no—
304C22×C3×C4—21no—
305C22×C3×C4—21no—
306C22×C3×C4—21no—
307C22×C3×C4—21no—
308C22×C3×C4—21no—
309C22×C3×C4—21no—
310C22×C3×C4—32no—
311C22×C3×C4—34no—
312C22×C3×C4—34no—
313C22×C3×C4—34no—
314C22×C3×C4—68no—
315C22×C3×C4D1218yescomplemented
316C22×C3×C4#6718yescomplemented
317C22×C3×C4C22×D311yescharacteristic
318C22×C3×C4C22×D311yescharacteristic
319C22×C3×C4C22×D311yescharacteristic
320C22×C3×C4C22×D311yescharacteristic
321C22×C3×C4C22×D311yescharacteristic
322C22×C3×C4C22×D311yescharacteristic
323C22×C3×C4C22×D311yescharacteristic
324C22×C3×C4C22×D311yescharacteristic
325C22×C3×C4C22×D311yescharacteristic
326C22×C3×C4C22×D311yescharacteristic
327C22×C3×C4C22×D311yescharacteristic
328C22×C3×C4C22×D311yescharacteristic
329C2×#67—28no—
330C2×#67—34no—
331C2×#67—34no—
332C2×#67—34no—
333C2×#67—34no—
334C2×#67—316no—
335C2×#67—64no—
336C2×#67—64no—
337C2×#67—616no—
338C2×#67—68no—
339C2×#67—68no—
340C2×#67C22×D314yes—
341C2×#67C22×D314yes—
342C22×Dic3—32no—
343C22×Dic3—32no—
344C22×Dic3—62no—
345C22×Dic3C22×D312yes—
346C22×Dic3C22×D314yes—
347#235—28no—
348#235—28no—
349#235—28no—
350#235—28no—
351#235—616no—
352#235—616no—
353#235—616no—
354#235—616no—
355#235—68no—
356#235—68no—
357#235—68no—
358#235—68no—
359#235—68no—
360#235—68no—
361#235—68no—
362#235—68no—
363C2×D12—24no—
364C2×D12—32no—
365C2×D12—32no—
366C2×D12—32no—
367C2×D12—32no—
368C2×D12—316no—
369C2×D12—62no—
370C2×D12—62no—
371C2×D12—68no—
372C2×D12—64no—
373C2×D12—64no—
374C2×D12C22×D312yes—
375C2×D12C22×D312yes—
376C2×C4×D3—28no—
377C2×C4×D3—34no—
378C2×C4×D3—34no—
379C2×C4×D3—34no—
380C2×C4×D3—34no—
381C2×C4×D3—64no—
382C2×C4×D3—64no—
383C2×C4×D3—616no—
384C2×C4×D3—68no—
385C2×C4×D3—68no—
386C2×C4×D3C22×D314yes—
387C2×C4×D3C22×D314yes—
388C2×Dic6—24no—
389C2×Dic6—32no—
390C2×Dic6—32no—
391C2×Dic6—32no—
392C2×Dic6—32no—
393C2×Dic6—62no—
394C2×Dic6—62no—
395C2×Dic6—68no—
396C2×Dic6—64no—
397C2×Dic6—64no—
398C2×Dic6C22×D312yes—
399C2×Dic6C22×D312yes—
400C3×C4⋊C4—34no—
401C3×C4⋊C4—34no—
402C3×C22⋊C4—34no—
403C3×C22⋊C4—34no—
404C3×C42—34no—
405C3×C42—34no—
406#217—316no—
407#217C22×D314yes—
408#217C22×D314yes—
409(C2×D3)⋊C4—316no—
410(C2×D3)⋊C4—316no—
411(C2×D3)⋊C4—316no—
412C4⋊Dic3—316no—
413C4⋊Dic3C22×D314yes—
414C4⋊Dic3C22×D314yes—
415Dic3⋊C4—316no—
416C4×Dic3C22×D314yes—
417C4×Dic3C22×D314yes—
418C22×C32—22no—
419C22×C32—22no—
420C22×C32—22no—
421C22×C32—44no—
422C22×C32C22×D412yes—
423C22×C32C22×D412yes—
424C22×C32C22×D412yes—
425C22×C32C2511yescharacteristic
426C2×C3⋊D3—24no—
427C2×C3⋊D3—28no—
428C2×C3⋊D3—48no—
429C2×C3×D3—24no—
430C2×C3×D3—28no—
431C2×C3×D3—48no—
432C32×C4C22×D412yes—
433C32×C4C22×D412yes—
434C32×C4C22×D412yes—
435C32×C4C22×D412yes—
436C3⋊Dic3—24no—
437C3×Dic3—24no—
438C3×Dic3—28no—
439C2×#41—32no—
440C2×#41—32no—
441C2×#41—32no—
442C2×#41—32no—
443C2×#41—68no—
444C2×#41—92no—
445C2×#41—92no—
446C2×#41—92no—
447C2×#41—92no—
448C2×#41—188no—
449C22×Q8—31no—
450C22×Q8—91no—
451C22×D4—32no—
452C22×D4—31no—
453C22×D4—92no—
454C22×D4—91no—
455C23×C4—32no—
456C23×C4—92no—
457C23×C4D3211yescharacteristic
458C4⋊Q8—94no—
459#127—94no—
460#124—94no—
461#124—94no—
462#123—98no—
463#123—98no—
464C22⋊Q8—98no—
465C22⋊Q8—98no—
466#121—98no—
467#121—98no—
468#121—916no—
469#120—98no—
470#120—98no—
471C4×D4—916no—
472#117—32no—
473#117—32no—
474#117—32no—
475#117—32no—
476C2×C4⋊C4—32no—
477C2×C22⋊C4—32no—
478C2×C42—32no—
479C23×C3—21no—
480C23×C3—21no—
481C23×C3—21no—
482C23×C3—24no—
483C23×C3—34no—
484C23×C3—42no—
485C23×C3—42no—
486C23×C3—44no—
487C23×C3—64no—
488C23×C3—124no—
489C23×C3C2×D1214yes—
490C23×C3C2×#6714yes—
491C23×C3C23×D311yescharacteristic
492C23×C3C23×D311yescharacteristic
493C23×C3C23×D311yescharacteristic
494C23×C3C23×D311yescharacteristic
495C23×C3C23×D311yescharacteristic
496C23×C3C23×D311yescharacteristic
497C22×D3—24no—
498C22×D3—34no—
499C22×D3—34no—
500C22×D3—44no—
501C22×D3—64no—
502C22×D3—68no—
503C22×D3—64no—
504C22×D3—64no—
505C22×D3—124no—
506C22×D3—124no—
507C22×D3—128no—
508C22×D3C23×D314yes—
509C3×Q8—64no—
510C3×Q8—64no—
511C3×D4—68no—
512C3×D4—68no—
513C3×D4—64no—
514C3×D4—64no—
515C2×C3×C4—21no—
516C2×C3×C4—21no—
517C2×C3×C4—21no—
518C2×C3×C4—21no—
519C2×C3×C4—24no—
520C2×C3×C4—24no—
521C2×C3×C4—24no—
522C2×C3×C4—24no—
523C2×C3×C4—24no—
524C2×C3×C4—24no—
525C2×C3×C4—34no—
526C2×C3×C4—38no—
527C2×C3×C4—64no—
528C2×C3×C4—68no—
529C2×C3×C4—68no—
530C2×C3×C4—124no—
531C2×C3×C4C2×D1214yes—
532C2×C3×C4C2×D1214yes—
533C2×C3×C4C2×D1214yes—
534C2×C3×C4C2×D1214yes—
535C2×C3×C4C2×D1214yes—
536C2×C3×C4C2×D1214yes—
537C2×C3×C4C2×#6714yes—
538C2×C3×C4C2×#6714yes—
539C2×C3×C4C2×#6714yes—
540C2×C3×C4C2×#6714yes—
541C2×C3×C4C2×#6714yes—
542C2×C3×C4C2×#6714yes—
543C2×C3×C4C23×D311yescharacteristic
544C2×C3×C4C23×D311yescharacteristic
545C2×C3×C4C23×D311yescharacteristic
546C2×C3×C4C23×D311yescharacteristic
547C2×C3×C4C23×D311yescharacteristic
548C2×C3×C4C23×D311yescharacteristic
549C2×C3×C4C23×D311yescharacteristic
550C2×C3×C4C23×D311yescharacteristic
551#67—28no—
552#67—28no—
553#67—616no—
554#67—616no—
555#67—68no—
556#67—68no—
557#67—68no—
558#67—68no—
559#67—1216no—
560C2×Dic3—24no—
561C2×Dic3—34no—
562C2×Dic3—34no—
563C2×Dic3—44no—
564C2×Dic3—64no—
565C2×Dic3—68no—
566C2×Dic3—64no—
567C2×Dic3—64no—
568C2×Dic3C23×D318yes—
569C2×Dic3C23×D314yes—
570D12—24no—
571D12—24no—
572D12—68no—
573D12—68no—
574D12—64no—
575D12—64no—
576D12—64no—
577D12—64no—
578D12—1216no—
579C4×D3—28no—
580C4×D3—28no—
581C4×D3—616no—
582C4×D3—616no—
583C4×D3—68no—
584C4×D3—68no—
585C4×D3—68no—
586C4×D3—68no—
587Dic6—24no—
588Dic6—24no—
589Dic6—68no—
590Dic6—68no—
591Dic6—64no—
592Dic6—64no—
593Dic6—64no—
594Dic6—64no—
595C2×C32—22no—
596C2×C32—22no—
597C2×C32—22no—
598C2×C32C23×D411yescharacteristic
599C2×C32#58512yes—
600C3⋊D3—44no—
601C3×D3—44no—
602C24—32no—
603C24—92no—
604C24C2×D3211yescharacteristic
605#41—68no—
606#41—68no—
607#41—68no—
608#41—68no—
609#41—188no—
610#41—188no—
611#41—188no—
612#41—188no—
613C2×Q8—32no—
614C2×Q8—32no—
615C2×Q8—64no—
616C2×Q8—92no—
617C2×Q8—92no—
618C2×Q8—184no—
619C2×D4—34no—
620C2×D4—34no—
621C2×D4—32no—
622C2×D4—32no—
623C2×D4—68no—
624C2×D4—64no—
625C2×D4—916no—
626C2×D4—94no—
627C2×D4—94no—
628C2×D4—92no—
629C2×D4—92no—
630C2×D4—188no—
631C2×D4—184no—
632C22×C4—32no—
633C22×C4—34no—
634C22×C4—34no—
635C22×C4—34no—
636C22×C4—68no—
637C22×C4—92no—
638C22×C4—94no—
639C22×C4—94no—
640C22×C4—188no—
641C22×C4#62618yescomplemented
642C22×C4C2×D3211yescharacteristic
643C22×C4C2×D3211yescharacteristic
644C22×C4C2×D3211yescharacteristic
645C22×C4C2×D3211yescharacteristic
646C22×C4C2×D3211yescharacteristic
647C22×C4C2×D3211yescharacteristic
648C4⋊C4—34no—
649C4⋊C4—34no—
650C4⋊C4—916no—
651C22⋊C4—34no—
652C22⋊C4—34no—
653C22⋊C4—916no—
654C22⋊C4—916no—
655C42—34no—
656C42—34no—
657C22×C3—24no—
658C22×C3—22no—
659C22×C3—22no—
660C22×C3—22no—
661C22×C3—22no—
662C22×C3—22no—
663C22×C3—22no—
664C22×C3—22no—
665C22×C3—22no—
666C22×C3—22no—
667C22×C3—21no—
668C22×C3—42no—
669C22×C3—42no—
670C22×C3—44no—
671C22×C3—44no—
672C22×C3—48no—
673C22×C3—64no—
674C22×C3—68no—
675C22×C3—128no—
676C22×C3C22×D1212yes—
677C22×C3C22×D1212yes—
678C22×C3C22×D1212yes—
679C22×C3C22×#6712yes—
680C22×C3C22×#6712yes—
681C22×C3C22×#6712yes—
682C22×C3C24×D311yescharacteristic
683C22×C3C24×D311yescharacteristic
684C2×D3—28no—
685C2×D3—24no—
686C2×D3—48no—
687C2×D3—68no—
688C2×D3—64no—
689C2×D3—68no—
690C2×D3—68no—
691C2×D3—64no—
692C2×D3—128no—
693C2×D3—1216no—
694C2×D3—128no—
695C2×D3—128no—
696C3×C4—22no—
697C3×C4—22no—
698C3×C4—22no—
699C3×C4—22no—
700C3×C4—64no—
701C3×C4—68no—
702C3×C4C22×D1212yes—
703C3×C4C22×D1212yes—
704C3×C4C22×D1212yes—
705C3×C4C22×D1212yes—
706C3×C4C22×#6712yes—
707C3×C4C22×#6712yes—
708C3×C4C22×#6712yes—
709C3×C4C22×#6712yes—
710Dic3—28no—
711Dic3—24no—
712Dic3—68no—
713Dic3—64no—
714Dic3—64no—
715C32#344911yescharacteristic, complemented, Sylow
716C23—34no—
717C23—42no—
718C23—64no—
719C23—94no—
720C23—124no—
721C23—184no—
722C23—364no—
723C23C2×#62614yes—
724C23C22×D3211yescharacteristic
725C23C22×D3211yescharacteristic
726C23C22×D3211yescharacteristic
727Q8—64no—
728Q8—64no—
729Q8—184no—
730Q8—184no—
731D4—68no—
732D4—68no—
733D4—64no—
734D4—64no—
735D4—188no—
736D4—188no—
737D4—184no—
738D4—184no—
739D4—3616no—
740C2×C4—38no—
741C2×C4—34no—
742C2×C4—64no—
743C2×C4—68no—
744C2×C4—68no—
745C2×C4—94no—
746C2×C4—124no—
747C2×C4—184no—
748C2×C4—188no—
749C2×C4—188no—
750C2×C4C2×#62614yes—
751C2×C4C2×#62614yes—
752C2×C4C2×#62614yes—
753C2×C4C2×#62614yes—
754C2×C4C2×#62614yes—
755C2×C4C2×#62614yes—
756C2×C4C22×D3211yescharacteristic
757C2×C4C22×D3211yescharacteristic
758C2×C4C22×D3211yescharacteristic
759C2×C4C22×D3211yescharacteristic
760C2×C3—24no—
761C2×C3—22no—
762C2×C3—22no—
763C2×C3—22no—
764C2×C3—22no—
765C2×C3—22no—
766C2×C3—22no—
767C2×C3—22no—
768C2×C3—21no—
769C2×C3—42no—
770C2×C3—42no—
771C2×C3—124no—
772C2×C3C23×D1211yescharacteristic
773C2×C3#596412yes—
774C2×C3#596412yes—
775C2×C3C23×#6711yescharacteristic
776D3—44no—
777D3—128no—
778D3—124no—
779D3—124no—
780C22—22no—
781C22—22no—
782C22—22no—
783C22—44no—
784C22—68no—
785C22—64no—
786C22—128no—
787C22—188no—
788C22—184no—
789C22—368no—
790C22C22×#62612yes—
791C22C22×#62612yes—
792C22C22×#62612yes—
793C22C23×D3211yescharacteristic
794C4—68no—
795C4—64no—
796C4—184no—
797C4C22×#62612yes—
798C4C22×#62612yes—
799C4C22×#62612yes—
800C4C22×#62612yes—
801C3—21no—
802C3#8573511yescharacteristic, complemented
803C3#8726811yescharacteristic, complemented
804C2—22no—
805C2—22no—
806C2—22no—
807C2—124no—
808C2—364no—
809C2#1059666912yes—
810C2C23×#62611yescharacteristic
subgroupG/H
centerC2×C4C22×D32
commutator, socle, cosocleC22×C32C25
FrattiniC22C23×D32
FittingC23×C32×C4C22
hypercenterC23×C4D32
hypocenterC32#3449
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C2×C4 ◁ C23×C4

Complements

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

NH ≅ G/Ntype
1. C22×#3828C2semidirect
2. C22×C3×#235C2semidirect
3. C2×C3×#926C2semidirect
4. #10595519C2semidirect
5. #10595045C2semidirect
6. #10595043C2semidirect
7. #10595042C2semidirect
8. #10595034C2semidirect
9. #10595029C2semidirect
10. #10595023C2semidirect
11. #10594866C2semidirect
12. #10594856C2semidirect
20. C2×#3828C22semidirect
21. C2×#3828C22semidirect
22. C22×C4⋊(C3⋊D3)C22semidirect
23. C22×C4×C3⋊D3C22semidirect
24. C22×#634C22semidirect
29. C2×C3×#235C22semidirect
30. C2×C3×#235C22semidirect
31. C22×C3×D12C22semidirect
32. C22×C3×C4×D3C22semidirect
33. C22×C3×Dic6C22semidirect
35. C3×#926C22semidirect
36. C3×#926C22semidirect
37. C3×#926C22semidirect
38. C3×#926C22semidirect
39. C2×C3×C4⋊Dic3C22semidirect
40. C2×C3×C4×Dic3C22semidirect
41. #63981C22semidirect
42. #63978C22semidirect
43. #63977C22semidirect
44. #63966C22semidirect
45. #63962C22semidirect
46. #63916C22semidirect
47. #63911C22semidirect
48. #63909C22semidirect
49. C4×#626C22semidirect
50. #63871C22semidirect
51. #63866C22semidirect
52. #63864C22semidirect
53. #63860C22semidirect
54. #63857C22semidirect
59. C22×#235D3semidirect
70. C2×#926D3semidirect
83. C22×C32×C4D4semidirect
170. C2×#235C2×D3semidirect
171. C2×#235C2×D3semidirect
175. C22×D12C2×D3semidirect
179. C22×C4×D3C2×D3semidirect
183. C22×Dic6C2×D3semidirect
206. #926C2×D3semidirect
207. #926C2×D3semidirect
208. #926C2×D3semidirect
209. #926C2×D3semidirect
210. C2×C4⋊Dic3C2×D3semidirect
212. C2×C4×Dic3C2×D3semidirect
315. C22×C3×C4D12semidirect
316. C22×C3×C4#67semidirect
641. C22×C4#626semidirect
715. C32#3449semidirect
802. C3#85735semidirect
803. C3#87268semidirect

Maximal subgroups

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

subgroupindex
C22×#38282
C22×C3×#2352
C2×C3×#9262
#105955192
#105950452
#105950432
#105950422
#105950342
#105950292
#105950232
#105948662
#105948562
#872683
#857353