Finite Group Databasebeta

← #25257640

Subgroups — #25257640

Order 11008.

5682 conjugacy classes of subgroups.

The subgroup lattice has 772 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#13063371C211yesmaximal, characteristic
2C2×#14583381C211yesmaximal, characteristic, complemented
3C2×C4×#10621902C211yesmaximal, characteristic, complemented
4#19137436C211yesmaximal, characteristic, complemented
5#19137433C211yesmaximal, characteristic, complemented
6#19137433C211yesmaximal, characteristic, complemented
7C22⋊C4×D172C213yesmaximal, complemented
8#19137416C213yesmaximal, complemented
9#19137416C213yesmaximal, complemented
10#19137415C213yesmaximal, complemented
11#19137184C213yesmaximal, complemented
12#19137174C213yesmaximal, complemented
13#19137081C213yesmaximal, complemented
14#390×D43C213yesmaximal, complemented
15C43×#2341C211yesmaximal, characteristic, complemented
16C2×#13063371—28no—
17C2×#13063371—28no—
18C2×#13063371C4116yescomplemented
19C22×#10621902C2211yescharacteristic
20C22×#10621902C2211yescharacteristic
21C22×#10621898C2213yes—
22C23×D172C2213yes—
23C22×D4×D43C2213yes—
24C22×D4×D43C2213yes—
25#14583381—28no—
26C4×#10621902—28no—
27C2×Q8×Dic43C2211yescharacteristic, complemented
28C2×Q8×Dic43C2211yescharacteristic, complemented
29C2×C4×D172C2213yescomplemented
30C2×C4×D172C2213yescomplemented
31C2×#13063287C2213yescomplemented
32C2×#13063287C2213yescomplemented
33C2×#13063283C2213yescomplemented
34C2×#13063282C2213yescomplemented
35C2×C4⋊C4×D43C2213yescomplemented
36C2×C22⋊C4×D43C2216yescomplemented
37C2×C22⋊C4×D43C2216yescomplemented
38C2×C42×D43C2213yescomplemented
39#14582803C2211yescharacteristic, complemented
40#14582803C2213yescomplemented
41#14582802C2213yescomplemented
42#14582802C2213yescomplemented
43#14582801C2213yescomplemented
44#14582801C2213yescomplemented
45#14582800C2213yescomplemented
46#14582800C2213yescomplemented
47#14582799C2213yescomplemented
48#14582799C2216yescomplemented
49#14582799C2213yescomplemented
50#14582777C2213yescomplemented
51#14582777C2213yescomplemented
52#14582777C2216yescomplemented
53#14582775C2213yescomplemented
54#14582775C2213yescomplemented
55#14582775C2216yescomplemented
56#14582759C2213yescomplemented
57#14582756C2213yescomplemented
58#14582756C2213yescomplemented
59#14582754C2216yescomplemented
60#14582754C2216yescomplemented
61C4×(C2×D43)⋊C4C2213yescomplemented
62C4×(C2×D43)⋊C4C2213yescomplemented
63C4×C22⋊Dic43C2213yescomplemented
64C22×#41×C43C2211yescharacteristic
65C2×C4×Q8×C43C2211yescharacteristic, complemented
66C2×C4×Q8×C43C2211yescharacteristic, complemented
67C43×#390C2213yescomplemented
68C43×#390C2213yescomplemented
69C43×#380C2213yescomplemented
70C4×C22⋊C4×C43C2213yescomplemented
71C24×D43C2316yes—
72#13063371—2128no—
73C2×#10621902—24no—
74C2×#10621902—24no—
75C2×#10621902C2×C418yes—
76C2×#10621902C2×C418yescomplemented
77C2×#10621902D418yes—
78C2×#10621902D418yes—
79C2×#10621898—212no—
80C2×#10621898—212no—
81C2×#10621898C2×C4124yescomplemented
82C22×Dic86C2311yescharacteristic
83C22×D172—212no—
84C22×D172—212no—
85C22×D172C2×C4124yescomplemented
86C22×D172C2313yes—
87C22×D172C2313yes—
88C22×D172C2313yes—
89C22×C22⋊D43C2313yes—
90C22×C22⋊D43C2313yes—
91C2×D4×D43—212no—
92C2×D4×D43—212no—
93C2×D4×D43—212no—
94C2×D4×D43—212no—
95C2×D4×D43C2×C4124yescomplemented
96C2×D4×D43C2×C4124yescomplemented
97C22×C4×D43C2313yes—
98C22×C4×D43C2313yes—
99C22×C4×D43C2313yes—
100C22×C4×D43C2316yes—
101C22×C4×D43C2313yes—
102Q8×Dic43—24no—
103Q8×Dic43—24no—
104C4×D172—212no—
105C4×D172—212no—
106#13063287—212no—
107#13063287—212no—
108#13063283—212no—
109#13063282—212no—
110C2×C4⋊Dic43C2313yes—
111C2×C4⋊Dic43C2313yes—
112C2×Dic43⋊C4C2313yes—
113C2×Dic43⋊C4C2311yescharacteristic
114C4⋊C4×D43—212no—
115C2×C22⋊Dic43C2313yes—
116C2×C22⋊Dic43C2316yes—
117C2×C22⋊Dic43C2313yes—
118C2×(C2×D43)⋊C4C2313yes—
119C2×(C2×D43)⋊C4C2313yes—
120C2×(C2×D43)⋊C4C2313yes—
121C2×(C2×D43)⋊C4C2313yes—
122C2×(C2×D43)⋊C4C2316yes—
123C2×(C2×D43)⋊C4C2313yes—
124C2×(C2×D43)⋊C4C2316yes—
125C2×(C2×D43)⋊C4C2316yes—
126C2×(C2×D43)⋊C4C2313yes—
127C22⋊C4×D43—412no—
128C22⋊C4×D43—412no—
129C2×C4×Dic43C2311yescharacteristic
130C2×C4×Dic43C2313yes—
131C2×C4×Dic43C2313yes—
132C2×C4×Dic43C2313yes—
133C42×D43—212no—
134C43⋊#95C2311yescharacteristic
135C43⋊#95C2313yes—
136C43⋊#95C2311yescharacteristic
137C43⋊#95C2311yescharacteristic
138C43⋊#95C2313yes—
139C43⋊#95C2313yes—
140C2×#41×C43—24no—
141C2×#41×C43—24no—
142C2×#41×C43C2×C418yescomplemented
143C22×Q8×C43C2311yescharacteristic
144C22×D4×C43C2313yes—
145C23×C4×C43C2313yes—
146C4×Q8×C43—24no—
147C4×Q8×C43—24no—
148C2×C4⋊C4×C43C2313yes—
149C2×C4⋊C4×C43C2313yes—
150C2×C22⋊C4×C43C2313yes—
151C2×C22⋊C4×C43C2316yes—
152C2×C22⋊C4×C43C2313yes—
153C2×C42×C43C2313yes—
154C2×C42×C43C2313yes—
155#95×C43C2311yescharacteristic
156#95×C43C2313yes—
157C24×C43C2413yes—
158C23×D43—212no—
159C23×D43—212no—
160C23×D43—46no—
161C23×D43—46no—
162C23×D43—46no—
163C23×D43—46no—
164C23×D43C22×C4124yes—
165C23×D43C2413yes—
166C23×D43C2413yes—
167#41×C43—232no—
168C2×Q8×C43C22×C414yes—
169C2×Q8×C43C2×D414yes—
170C2×Q8×C43C2×D414yes—
171C2×D4×C43—26no—
172C2×D4×C43—26no—
173C2×D4×C43C22×C4112yes—
174C22×C4×C43—26no—
175C22×C4×C43—26no—
176C22×C4×C43C22×C4112yes—
177C22×C4×C43C2411yescharacteristic
178C22×C4×C43C2413yes—
179C22×C4×C43C2413yes—
180C22×C4×C43C2411yescharacteristic
181C22×C4×C43C2411yescharacteristic
182C22×C4×C43C2413yes—
183C2×C22⋊D43—26no—
184C2×C22⋊D43—26no—
185C2×C22⋊D43—26no—
186C2×C22⋊D43—26no—
187C2×C22⋊D43C22×C4112yes—
188C2×C22⋊D43C22×C4112yes—
189C22×Dic43C2411yescharacteristic
190C22×Dic43C2413yes—
191C22×Dic43C2413yes—
192C22×Dic43C2411yescharacteristic
193C22×Dic43C2411yescharacteristic
194C22×Dic43C2411yescharacteristic
195#10621902—232no—
196#10621902C22⋊C4164yescomplemented
197D4×D43—296no—
198D4×D43—296no—
199#10621898—296no—
200C2×D172—26no—
201C2×D172—26no—
202C2×D172—296no—
203C2×D172—26no—
204C2×D172—26no—
205C2×D172C22×C4112yes—
206C2×D172C22×C4112yes—
207C2×D172C22×C4112yes—
208C2×D172C2×D4112yes—
209C2×D172C2×D4112yes—
210C2×C4×D43—26no—
211C2×C4×D43—26no—
212C2×C4×D43—26no—
213C2×C4×D43—26no—
214C2×C4×D43—26no—
215C2×C4×D43—26no—
216C2×C4×D43—212no—
217C2×C4×D43—43no—
218C2×C4×D43—43no—
219C2×C4×D43—46no—
220C2×C4×D43—46no—
221C2×C4×D43C22×C4112yes—
222C2×C4×D43C22×C4112yes—
223C2×C4×D43C2×D4112yes—
224C2×C4×D43C2×D4112yes—
225C2×Dic86—22no—
226C2×Dic86—22no—
227C2×Dic86C22×C414yes—
228C4⋊C4×C43—26no—
229C4⋊C4×C43—26no—
230C22⋊C4×C43—26no—
231C22⋊C4×C43—43no—
232C22⋊C4×C43—46no—
233C42×C43—26no—
234C42×C43—26no—
235C22⋊Dic43—26no—
236C22⋊Dic43—46no—
237C22⋊Dic43—43no—
238(C2×D43)⋊C4—26no—
239(C2×D43)⋊C4—26no—
240(C2×D43)⋊C4—26no—
241(C2×D43)⋊C4—26no—
242(C2×D43)⋊C4—212no—
243(C2×D43)⋊C4—46no—
244(C2×D43)⋊C4—46no—
245(C2×D43)⋊C4—43no—
246(C2×D43)⋊C4—43no—
247C4⋊Dic43—26no—
248C4⋊Dic43—26no—
249Dic43⋊C4—26no—
250Dic43⋊C4—22no—
251C4×Dic43—26no—
252C4×Dic43—26no—
253C4×Dic43—22no—
254C4×Dic43—26no—
255C23×C43—23no—
256C23×C43—23no—
257C23×C43—23no—
258C23×C43—23no—
259C23×C43—23no—
260C23×C43—23no—
261C23×C43C23×C416yes—
262C23×C43C2511yescharacteristic
263C22×D43—23no—
264C22×D43—23no—
265C22×D43—23no—
266C22×D43—23no—
267C22×D43—23no—
268C22×D43—23no—
269C22×D43—23no—
270C22×D43—23no—
271C22×D43—23no—
272C22×D43—23no—
273C22×D43—248no—
274C22×D43—424no—
275C22×D43—424no—
276C22×D43—812no—
277C22×D43—812no—
278C22×D43—812no—
279C22×D43—812no—
280C22×D43C23×C416yes—
281C22×D43C23×C416yes—
282C22×D43C22×D416yes—
283C22×D43C22×D416yes—
284Q8×C43C2×C22⋊C4116yescomplemented
285D4×C43—224no—
286C2×C4×C43—21no—
287C2×C4×C43—21no—
288C2×C4×C43—21no—
289C2×C4×C43—21no—
290C2×C4×C43—224no—
291C2×C4×C43—23no—
292C2×C4×C43—21no—
293C2×C4×C43—23no—
294C2×C4×C43—23no—
295C2×C4×C43—23no—
296C2×C4×C43—23no—
297C2×C4×C43—21no—
298C2×C4×C43—23no—
299C2×C4×C43—21no—
300C2×C4×C43C23×C412yes—
301C2×C4×C43C23×C416yes—
302C2×C4×C43C22×D416yes—
303C2×C4×C43C22×D416yes—
304C2×C4×C43H(5,𝔽2)12yescomplemented
305C22⋊D43—224no—
306C22⋊D43—224no—
307C2×Dic43—21no—
308C2×Dic43—21no—
309C2×Dic43—21no—
310C2×Dic43—21no—
311C2×Dic43—21no—
312C2×Dic43—23no—
313C2×Dic43—23no—
314C2×Dic43—23no—
315C2×Dic43—23no—
316C2×Dic43—23no—
317C2×Dic43—21no—
318C2×Dic43—23no—
319C2×Dic43—21no—
320C2×Dic43C23×C412yes—
321C2×Dic43C23×C412yes—
322C2×Dic43C22×D412yes—
323C2×Dic43C22×D412yes—
324C2×Dic43H(5,𝔽2)12yescomplemented
325D172—224no—
326D172—224no—
327D172C2×C22⋊C4148yescomplemented
328C4×D43—224no—
329C4×D43—412no—
330C4×D43—412no—
331C4×D43—812no—
332C4×D43C2×C22⋊C4148yescomplemented
333Dic86—28no—
334#34258—431nomaximal, Sylow
335C22×C43—26no—
336C22×C43—26no—
337C22×C43—26no—
338C22×C43—43no—
339C22×C43—43no—
340C22×C43—43no—
341C22×C43—43no—
342C22×C43C24×C411yescharacteristic
343C22×C43C23×D411yescharacteristic
344C22×C43C23×D411yescharacteristic
345C22×C43C2×H(5,𝔽2)11yescharacteristic
346C22×C43C2×H(5,𝔽2)11yescharacteristic
347C22×C43#58511yescharacteristic
348C22×C43#58511yescharacteristic
349C2×D43—26no—
350C2×D43—26no—
351C2×D43—26no—
352C2×D43—26no—
353C2×D43—26no—
354C2×D43—26no—
355C2×D43—26no—
356C2×D43—26no—
357C2×D43—26no—
358C2×D43—43no—
359C2×D43—43no—
360C2×D43—43no—
361C2×D43—43no—
362C2×D43—848no—
363C2×D43C22×C22⋊C4112yes—
364C4×C43—22no—
365C4×C43—22no—
366C4×C43—43no—
367C4×C43—43no—
368C4×C43—41no—
369C4×C43C22×C22⋊C4112yes—
370Dic43—22no—
371Dic43—22no—
372Dic43—43no—
373Dic43—43no—
374Dic43—41no—
375Dic43C22×C22⋊C414yes—
376C22×H(5,𝔽2)—431no—
377C2×#520—431no—
378C2×C4×#41—431no—
379#2341—431no—
380#2341—431no—
381#2341—431no—
382#2341D4311yescharacteristic, complemented
383D4×C22⋊C4—433no—
384D4×C22⋊C4—433no—
385D4×C22⋊C4—433no—
386D4×C22⋊C4—433no—
387#2311—433no—
388#2309—433no—
389#2297—433no—
390C2×#390—433no—
391C2×C43—46no—
392C2×C43C23×C22⋊C411yescharacteristic
393C2×C43C4×H(5,𝔽2)11yescharacteristic
394C2×C43C4×H(5,𝔽2)11yescharacteristic
395C2×C43#348811yescharacteristic
396C2×C43#348811yescharacteristic
397C2×C43#349811yescharacteristic
398C2×C43#350011yescharacteristic
399D43—212no—
400D43—46no—
401C2×H(5,𝔽2)—4316no—
402C2×H(5,𝔽2)—868no—
403C2×H(5,𝔽2)—868no—
404C22×#41—431no—
405C22×#41—431no—
406C22×#41—433no—
407C22×#41C2×D4311yescharacteristic
408C23×D4—433no—
409C23×D4—433no—
410C23×D4—433no—
411#520—868no—
412C4×#41—868no—
413C2×C4×Q8—431no—
414C2×C4×Q8—431no—
415C2×C4×Q8C2×D4311yescharacteristic, complemented
416C2×C4×Q8C2×D4311yescharacteristic, complemented
417C2×C4×D4—433no—
418C2×C4×D4—433no—
419C2×C4×D4—433no—
420C2×C4×D4—433no—
421C2×#117—433no—
422C2×#117—433no—
423C22×C4⋊C4—433no—
424C22×C22⋊C4—436no—
425C22×C22⋊C4—436no—
426C22×C42—433no—
427#391—433no—
428#391—431no—
429#390—433no—
430#390—433no—
431#390—433no—
432#390—433no—
433#390—433no—
434#390—436no—
435#390—433no—
436#390—433no—
437#390—433no—
438#390C2×D4313yescomplemented
439#390C2×D4313yescomplemented
440#386—436no—
441#386—433no—
442#386—433no—
443#386—436no—
444#386—433no—
445#386—433no—
446#380—433no—
447#380—433no—
448#380—433no—
449#380C2×D4313yescomplemented
450#379—436no—
451#379—436no—
452C4×C22⋊C4—433no—
453C4×C22⋊C4—433no—
454C4×C22⋊C4—433no—
455C4×C22⋊C4C2×D4313yescomplemented
456C43#3425811yescharacteristic, complemented, Sylow
457C25—436no—
458H(5,𝔽2)—86128no—
459C2×#41—24no—
460C2×#41—24no—
461C2×#41—438no—
462C2×#41—438no—
463C2×#41—438no—
464C2×#41—438no—
465C2×#41—4324no—
466C2×#41—8612no—
467C2×#41—8612no—
468C2×#41—864no—
469C2×#41—864no—
470C2×#41C4×D4318yescomplemented
471C22×Q8—431no—
472C22×Q8C22×D4311yescharacteristic
473C22×D4—433no—
474C22×D4—433no—
475C22×D4—4324no—
476C22×D4—4324no—
477C22×D4—4324no—
478C22×D4—433no—
479C22×D4—433no—
480C22×D4—433no—
481C22×D4—8612no—
482C22×D4—8612no—
483C22×D4—8612no—
484C22×D4—8612no—
485C22×D4—8612no—
486C22×D4—8612no—
487C22×D4C22×D4313yes—
488C23×C4—433no—
489C23×C4—433no—
490C23×C4—433no—
491C23×C4—433no—
492C23×C4—436no—
493C23×C4C22×D4313yes—
494C4×Q8—24no—
495C4×Q8—24no—
496C4×Q8—864no—
497C4×Q8—864no—
498C4×D4—8612no—
499C4×D4—8612no—
500C4×D4—8612no—
501C4×D4—8612no—
502#117—8612no—
503#117—8612no—
504C2×C4⋊C4—433no—
505C2×C4⋊C4—433no—
506C2×C4⋊C4—431no—
507C2×C4⋊C4—433no—
508C2×C4⋊C4—8612no—
509C2×C4⋊C4C22×D4313yes—
510C2×C4⋊C4C22×D4313yes—
511C2×C22⋊C4—433no—
512C2×C22⋊C4—433no—
513C2×C22⋊C4—433no—
514C2×C22⋊C4—433no—
515C2×C22⋊C4—436no—
516C2×C22⋊C4—433no—
517C2×C22⋊C4—436no—
518C2×C22⋊C4—433no—
519C2×C22⋊C4—436no—
520C2×C22⋊C4—436no—
521C2×C22⋊C4—433no—
522C2×C22⋊C4—433no—
523C2×C22⋊C4—17212no—
524C2×C22⋊C4—17212no—
525C2×C22⋊C4C22×D4313yes—
526C2×C22⋊C4C22×D4316yes—
527C2×C22⋊C4C22×D4313yes—
528C2×C42—433no—
529C2×C42—433no—
530C2×C42—433no—
531C2×C42—431no—
532C2×C42—8612no—
533C2×C42C22×D4313yes—
534C2×C42C22×D4313yes—
535#95—431no—
536#95—431no—
537#95—431no—
538#95—433no—
539#95—433no—
540#95—433no—
541#95C22×D4311yescharacteristic
542#95C22×D4313yes—
543C24—433no—
544C24—433no—
545C24—4324no—
546C24—8612no—
547C24—8612no—
548C24—1726no—
549C24—1726no—
550C24—1726no—
551C24—1726no—
552C24C23×D4313yes—
553#41—232no—
554#41—4364no—
555#41—8696no—
556#41—8632no—
557C2×Q8—434no—
558C2×Q8—862no—
559C2×Q8—862no—
560C2×Q8C2×C4×D4314yes—
561C2×Q8D4×D4314yes—
562C2×Q8D4×D4314yes—
563C2×D4—26no—
564C2×D4—26no—
565C2×D4—4312no—
566C2×D4—4312no—
567C2×D4—4312no—
568C2×D4—4312no—
569C2×D4—4312no—
570C2×D4—4312no—
571C2×D4—4312no—
572C2×D4—8696no—
573C2×D4—866no—
574C2×D4—866no—
575C2×D4—8696no—
576C2×D4—866no—
577C2×D4—866no—
578C2×D4—8696no—
579C2×D4—866no—
580C2×D4—866no—
581C2×D4—866no—
582C2×D4—866no—
583C2×D4C2×C4×D43112yes—
584C22×C4—26no—
585C22×C4—26no—
586C22×C4—431no—
587C22×C4—4312no—
588C22×C4—4312no—
589C22×C4—4312no—
590C22×C4—431no—
591C22×C4—431no—
592C22×C4—4312no—
593C22×C4—431no—
594C22×C4—433no—
595C22×C4—433no—
596C22×C4—866no—
597C22×C4—8612no—
598C22×C4—866no—
599C22×C4—866no—
600C22×C4—866no—
601C22×C4—866no—
602C22×C4—866no—
603C22×C4—1726no—
604C22×C4—1726no—
605C22×C4—1723no—
606C22×C4—1723no—
607C22×C4C2×C4×D43112yes—
608C22×C4C23×D4313yes—
609C22×C4C23×D4311yescharacteristic
610C22×C4C23×D4313yes—
611C22×C4C23×D4311yescharacteristic
612C22×C4C23×D4311yescharacteristic
613C22×C4C23×D4313yes—
614C4⋊C4—26no—
615C4⋊C4—26no—
616C4⋊C4—866no—
617C4⋊C4—862no—
618C4⋊C4—866no—
619C4⋊C4—866no—
620C22⋊C4—26no—
621C22⋊C4—46no—
622C22⋊C4—43no—
623C22⋊C4—866no—
624C22⋊C4—866no—
625C22⋊C4—8612no—
626C22⋊C4—866no—
627C22⋊C4—866no—
628C22⋊C4—866no—
629C22⋊C4—1726no—
630C22⋊C4—1726no—
631C22⋊C4—1723no—
632C22⋊C4—1723no—
633C22⋊C4—1726no—
634C22⋊C4—1723no—
635C42—26no—
636C42—26no—
637C42—862no—
638C42—866no—
639C42—866no—
640C42—866no—
641C23—23no—
642C23—23no—
643C23—23no—
644C23—23no—
645C23—23no—
646C23—23no—
647C23—436no—
648C23—436no—
649C23—436no—
650C23—436no—
651C23—8648no—
652C23—863no—
653C23—863no—
654C23—863no—
655C23—863no—
656C23—863no—
657C23—863no—
658C23—863no—
659C23—863no—
660C23—863no—
661C23—863no—
662C23—34412no—
663C23—34412no—
664C23—34412no—
665C23—34412no—
666C23—17224no—
667C23—17224no—
668C23C22×C4×D4316yes—
669C23C24×D4311yescharacteristic
670Q8—868no—
671Q8C22⋊C4×D43116yescomplemented
672D4—224no—
673D4—4348no—
674D4—8624no—
675D4—8624no—
676D4—8624no—
677D4—8624no—
678C2×C4—21no—
679C2×C4—21no—
680C2×C4—21no—
681C2×C4—21no—
682C2×C4—224no—
683C2×C4—21no—
684C2×C4—23no—
685C2×C4—23no—
686C2×C4—23no—
687C2×C4—23no—
688C2×C4—23no—
689C2×C4—21no—
690C2×C4—23no—
691C2×C4—21no—
692C2×C4—432no—
693C2×C4—432no—
694C2×C4—432no—
695C2×C4—4348no—
696C2×C4—432no—
697C2×C4—432no—
698C2×C4—861no—
699C2×C4—861no—
700C2×C4—861no—
701C2×C4—861no—
702C2×C4—8624no—
703C2×C4—861no—
704C2×C4—863no—
705C2×C4—863no—
706C2×C4—863no—
707C2×C4—863no—
708C2×C4—863no—
709C2×C4—861no—
710C2×C4—861no—
711C2×C4—863no—
712C2×C4—34412no—
713C2×C4—17212no—
714C2×C4—17212no—
715C2×C4C22×C4×D4312yes—
716C2×C4C22×C4×D4316yes—
717C2×C4C2×D4×D4316yes—
718C2×C4C2×D4×D4316yes—
719C2×C4#1306337112yescomplemented
720C22—26no—
721C22—26no—
722C22—26no—
723C22—43no—
724C22—43no—
725C22—43no—
726C22—43no—
727C22—4312no—
728C22—866no—
729C22—866no—
730C22—866no—
731C22—866no—
732C22—866no—
733C22—866no—
734C22—866no—
735C22—866no—
736C22—866no—
737C22—34448no—
738C22—1723no—
739C22—1723no—
740C22—1723no—
741C22—1723no—
742C22C23×C4×D4311yescharacteristic
743C22C22×D4×D4311yescharacteristic
744C22C22×D4×D4311yescharacteristic
745C22H(5,𝔽2)×D4311yescharacteristic
746C22C2×#1306337111yescharacteristic
747C22#1458373511yescharacteristic
748C22#1458373611yescharacteristic
749C4—22no—
750C4—22no—
751C4—43no—
752C4—41no—
753C4—43no—
754C4—434no—
755C4—862no—
756C4—862no—
757C4—1723no—
758C4—1721no—
759C4—1723no—
760C4C2×C22⋊C4×D43112yes—
761C2—46no—
762C2—8612no—
763C2—1726no—
764C2C22×C22⋊C4×D4311yescharacteristic
765C2#1914780111yescharacteristic
766C2C4×#1306337111yescharacteristic
767C2#1914826111yescharacteristic
768C2#1914826311yescharacteristic
769C2#1914837211yescharacteristic
770C2#1914838611yescharacteristic
subgroupG/H
center, FrattiniC23C24×D43
commutatorC22×C43C24×C4
FittingC43×#2341C2
socle, cosocleC23×C43C25
prime radicalC22×#13063371C2
hypercenter#2341D43
hypocenterC43#34258
LCSG ▷ C22×C43 ▷ C43
UCSC1 ◁ C23 ◁ #2341

Complements

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

NH ≅ G/Ntype
2. C2×#14583381C2semidirect
3. C2×C4×#10621902C2semidirect
4. #19137436C2semidirect
5. #19137433C2semidirect
6. #19137433C2semidirect
7. C22⋊C4×D172C2semidirect
8. #19137416C2semidirect
9. #19137416C2semidirect
10. #19137415C2semidirect
11. #19137184C2semidirect
12. #19137174C2semidirect
13. #19137081C2semidirect
14. #390×D43C2semidirect
15. C43×#2341C2semidirect
18. C2×#13063371C4semidirect
27. C2×Q8×Dic43C22semidirect
28. C2×Q8×Dic43C22semidirect
29. C2×C4×D172C22semidirect
30. C2×C4×D172C22semidirect
31. C2×#13063287C22semidirect
32. C2×#13063287C22semidirect
33. C2×#13063283C22semidirect
34. C2×#13063282C22semidirect
35. C2×C4⋊C4×D43C22semidirect
36. C2×C22⋊C4×D43C22semidirect
37. C2×C22⋊C4×D43C22semidirect
38. C2×C42×D43C22semidirect
39. #14582803C22semidirect
40. #14582803C22semidirect
41. #14582802C22semidirect
42. #14582802C22semidirect
43. #14582801C22semidirect
44. #14582801C22semidirect
45. #14582800C22semidirect
46. #14582800C22semidirect
47. #14582799C22semidirect
48. #14582799C22semidirect
49. #14582799C22semidirect
50. #14582777C22semidirect
51. #14582777C22semidirect
52. #14582777C22semidirect
53. #14582775C22semidirect
54. #14582775C22semidirect
55. #14582775C22semidirect
56. #14582759C22semidirect
57. #14582756C22semidirect
58. #14582756C22semidirect
59. #14582754C22semidirect
60. #14582754C22semidirect
61. C4×(C2×D43)⋊C4C22semidirect
62. C4×(C2×D43)⋊C4C22semidirect
63. C4×C22⋊Dic43C22semidirect
65. C2×C4×Q8×C43C22semidirect
66. C2×C4×Q8×C43C22semidirect
67. C43×#390C22semidirect
68. C43×#390C22semidirect
69. C43×#380C22semidirect
70. C4×C22⋊C4×C43C22semidirect
76. C2×#10621902C2×C4semidirect
81. C2×#10621898C2×C4semidirect
85. C22×D172C2×C4semidirect
95. C2×D4×D43C2×C4semidirect
96. C2×D4×D43C2×C4semidirect
142. C2×#41×C43C2×C4semidirect
196. #10621902C22⋊C4semidirect
284. Q8×C43C2×C22⋊C4semidirect
304. C2×C4×C43H(5,𝔽2)semidirect
324. C2×Dic43H(5,𝔽2)semidirect
327. D172C2×C22⋊C4semidirect
332. C4×D43C2×C22⋊C4semidirect
382. #2341D43semidirect
415. C2×C4×Q8C2×D43semidirect
416. C2×C4×Q8C2×D43semidirect
438. #390C2×D43semidirect
439. #390C2×D43semidirect
449. #380C2×D43semidirect
455. C4×C22⋊C4C2×D43semidirect
456. C43#34258semidirect
470. C2×#41C4×D43semidirect
671. Q8C22⋊C4×D43semidirect
719. C2×C4#13063371semidirect

Maximal subgroups

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

subgroupindex
C22×#130633712
C2×#145833812
C2×C4×#106219022
#191374362
#191374332
C22⋊C4×D1722
#191374162
#191374152
#191371842
#191371742
#191370812
#390×D432
C43×#23412
#3425843