Finite Group Databasebeta

← D43×#2319 #25255239

Subgroups — D43×#2319 #25255239

Order 11008.

3046 conjugacy classes of subgroups.

The subgroup lattice has 744 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×D4×D43C211yesmaximal, characteristic
2#19137239C211yesmaximal, characteristic, complemented
3#19137238C211yesmaximal, characteristic, complemented
4#19137237C212yesmaximal, complemented
5#19137236C214yesmaximal, complemented
6#19137235C212yesmaximal, complemented
7#19137234C212yesmaximal, complemented
8#19137233C211yesmaximal, characteristic, complemented
9#19137232C212yesmaximal, complemented
10#390×D43C212yesmaximal
11#389×D43C212yesmaximal, complemented
12#388×D43C214yesmaximal, complemented
13#381×D43C212yesmaximal, complemented
14#380×D43C212yesmaximal, complemented
15C4×C4⋊C4×D43C211yesmaximal, characteristic, complemented
16#376×D43C211yesmaximal, characteristic, complemented
17C43×#2319C211yesmaximal, characteristic, complemented
18C22×D4×D43C2211yescharacteristic
19C23×C4×D43C2212yes—
20C2×C4×D172C2211yescharacteristic
21C2×D4×Dic43C2211yescharacteristic
22C2×#13063287C2211yescharacteristic
23C2×C4×C22⋊D43C2212yes—
24C2×(C22⋊D43)⋊C4C2212yes—
25C4×D4×D43C4116yescomplemented
26C2×C4⋊C4×D43C2212yes—
27C2×C4⋊C4×D43C2214yes—
28C2×C4⋊C4×D43C2211yescharacteristic
29C2×C22⋊C4×D43C2214yes—
30C2×C22⋊C4×D43C2214yes—
31C2×C22⋊C4×D43C2212yes—
32C2×C42×D43C2212yes—
33C2×C42×D43C2212yes—
34C2×C42×D43C2211yescharacteristic
35#14582802C2212yes—
36#14582801C2212yes—
37#14582800C2212yes—
38#14582799C2214yes—
39#14582799C2214yes—
40#14582798C2212yescomplemented
41#14582797C2212yescomplemented
42#14582796C2214yescomplemented
43#14582795C2212yescomplemented
44#14582794C2214yescomplemented
45#14582793C2214yescomplemented
46#14582792C2214yescomplemented
47#14582791C2214yescomplemented
48#14582790C2214yescomplemented
49#14582789C2214yescomplemented
50#14582788C2214yescomplemented
51#14582787C2214yescomplemented
52#14582762C2212yescomplemented
53#14582761C2212yescomplemented
54#14582761C2214yescomplemented
55#14582761C2212yescomplemented
56#14582760C2214yescomplemented
57#14582759C2212yescomplemented
58#14582758C2212yescomplemented
59#14582758C2212yescomplemented
60#14582757C2214yescomplemented
61#14582756C2214yescomplemented
62C4⋊C4×Dic43C2212yescomplemented
63C4×Dic43⋊C4C2212yescomplemented
64C4×C4⋊Dic43C2211yescharacteristic, complemented
65#14582750C2212yescomplemented
66#14582745C2212yescomplemented
67#14582745C2211yescharacteristic, complemented
68#14582744C2211yescharacteristic, complemented
69#14582744C2212yescomplemented
70#14582744C2211yescharacteristic, complemented
71#95×D43C2214yes—
72#95×D43C2211yescharacteristic
73#95×D43C2211yescharacteristic
74#95×D43C2212yes—
75#95×D43C2212yes—
76C2×C4×D4×C43C2211yescharacteristic
77C43×#390C2212yes—
78C43×#389C2212yescomplemented
79C43×#388C2214yescomplemented
80C43×#381C2212yescomplemented
81C43×#380C2212yescomplemented
82C4×C4⋊C4×C43C2211yescharacteristic, complemented
83C43×#376C2211yescharacteristic, complemented
84C24×D43C2312yes—
85C22×D172C2311yescharacteristic
86C22×C22⋊D43C2312yes—
87C2×D4×D43—28no—
88C2×D4×D43C2×C418yes—
89C23×Dic43C2312yes—
90C22×C4×D43—48no—
91C22×C4×D43C2×C4116yes—
92C22×C4×D43C2312yes—
93C22×C4×D43C2314yes—
94C22×C4×D43C2312yes—
95C22×C4×D43C2311yescharacteristic
96C22×C4×D43C2311yescharacteristic
97C22×C4×D43C2312yes—
98C22×C4×D43C2312yes—
99C22×C4×D43C2312yes—
100C22×C4×D43C2311yescharacteristic
101C4×D172C2×C418yescomplemented
102D4×Dic43C2×C418yescomplemented
103#13063287C2×C418yescomplemented
104C4×C22⋊D43C2×C4116yescomplemented
105(C22⋊D43)⋊C4C2×C4116yescomplemented
106C2×C4⋊Dic43C2312yes—
107C2×C4⋊Dic43C2314yes—
108C2×C4⋊Dic43C2311yescharacteristic
109C2×Dic43⋊C4C2314yes—
110C2×Dic43⋊C4C2314yes—
111C2×Dic43⋊C4C2314yes—
112C2×Dic43⋊C4C2312yes—
113C4⋊C4×D43—28no—
114C4⋊C4×D43—48no—
115C4⋊C4×D43C2×C418yes—
116C2×C22⋊Dic43C2314yes—
117C2×C22⋊Dic43C2314yes—
118C2×C22⋊Dic43C2312yes—
119C2×(C2×D43)⋊C4C2314yes—
120C2×(C2×D43)⋊C4C2314yes—
121C2×(C2×D43)⋊C4C2314yes—
122C2×(C2×D43)⋊C4C2314yes—
123C2×(C2×D43)⋊C4C2312yes—
124C2×(C2×D43)⋊C4C2312yes—
125C22⋊C4×D43—48no—
126C22⋊C4×D43—48no—
127C22⋊C4×D43C2×C4116yes—
128C2×C4×Dic43C2312yes—
129C2×C4×Dic43C2312yes—
130C2×C4×Dic43C2312yes—
131C2×C4×Dic43C2314yes—
132C2×C4×Dic43C2312yes—
133C2×C4×Dic43C2311yescharacteristic
134C2×C4×Dic43C2311yescharacteristic
135C2×C4×Dic43C2311yescharacteristic
136C42×D43—28no—
137C42×D43—44no—
138C42×D43C2×C418yes—
139C43⋊#95C2312yes—
140C43⋊#95C2314yes—
141C43⋊#95C2314yes—
142C43⋊#95C2314yes—
143C43⋊#95C2312yes—
144C43⋊#95C2312yes—
145C43⋊#95C2312yes—
146C43⋊#95C2311yescharacteristic
147C43⋊#95C2312yes—
148C43⋊#95C2311yescharacteristic
149C43⋊#95C2312yes—
150C43⋊#95C2314yes—
151C22×D4×C43C2311yescharacteristic
152C23×C4×C43C2312yes—
153C4×D4×C43C2×C418yescomplemented
154C2×C4⋊C4×C43C2312yes—
155C2×C4⋊C4×C43C2314yes—
156C2×C4⋊C4×C43C2311yescharacteristic
157C2×C22⋊C4×C43C2314yes—
158C2×C22⋊C4×C43C2314yes—
159C2×C22⋊C4×C43C2312yes—
160C2×C42×C43C2312yes—
161C2×C42×C43C2312yes—
162C2×C42×C43C2311yescharacteristic
163#95×C43C2312yes—
164#95×C43C2314yes—
165#95×C43C2311yescharacteristic
166#95×C43C2311yescharacteristic
167#95×C43C2312yes—
168C24×C43C2412yes—
169C23×D43—28no—
170C23×D43—24no—
171C23×D43—28no—
172C23×D43—24no—
173C23×D43C22×C418yes—
174C23×D43C2412yes—
175C23×D43C2411yescharacteristic
176C2×D4×C43—24no—
177C2×D4×C43C22×C414yes—
178C22×C4×C43—44no—
179C22×C4×C43C22×C418yes—
180C22×C4×C43C2412yes—
181C22×C4×C43C2412yes—
182C22×C4×C43C2414yes—
183C22×C4×C43C2411yescharacteristic
184C22×C4×C43C2411yescharacteristic
185C22×C4×C43C2412yes—
186C22×C4×C43C2411yescharacteristic
187C2×C22⋊D43—28no—
188C2×C22⋊D43C22×C418yes—
189C22×Dic43—44no—
190C22×Dic43C22×C418yes—
191C22×Dic43C2412yes—
192C22×Dic43C2412yes—
193C22×Dic43C2414yes—
194C22×Dic43C2411yescharacteristic
195C22×Dic43C2411yescharacteristic
196C22×Dic43C2412yes—
197C22×Dic43C2411yescharacteristic
198D4×D43—232no—
199C2×D172—24no—
200C2×D172C22×C414yes—
201C2×C4×D43—24no—
202C2×C4×D43—24no—
203C2×C4×D43—28no—
204C2×C4×D43—22no—
205C2×C4×D43—28no—
206C2×C4×D43—24no—
207C2×C4×D43—28no—
208C2×C4×D43—24no—
209C2×C4×D43—24no—
210C2×C4×D43—28no—
211C2×C4×D43—24no—
212C2×C4×D43—22no—
213C2×C4×D43—24no—
214C2×C4×D43—432no—
215C2×C4×D43—44no—
216C2×C4×D43—44no—
217C2×C4×D43C22×C414yes—
218C2×C4×D43C22×C414yes—
219C2×C4×D43C22×C418yes—
220C2×C4×D43C22×C418yes—
221C2×C4×D43C22×C418yes—
222C2×C4×D43C22×C414yes—
223C2×C4×D43#4118yes—
224C4⋊C4×C43—24no—
225C4⋊C4×C43—44no—
226C4⋊C4×C43C22×C414yes—
227C22⋊C4×C43—44no—
228C22⋊C4×C43—44no—
229C22⋊C4×C43C22×C418yes—
230C42×C43—24no—
231C42×C43—42no—
232C42×C43C22×C414yes—
233C22⋊Dic43—44no—
234C22⋊Dic43—44no—
235C22⋊Dic43C22×C418yes—
236(C2×D43)⋊C4—44no—
237(C2×D43)⋊C4—44no—
238(C2×D43)⋊C4—44no—
239(C2×D43)⋊C4—44no—
240(C2×D43)⋊C4C22×C418yes—
241(C2×D43)⋊C4C22×C418yes—
242C4⋊Dic43—24no—
243C4⋊Dic43—44no—
244C4⋊Dic43C22×C414yes—
245Dic43⋊C4—28no—
246Dic43⋊C4—44no—
247Dic43⋊C4—44no—
248Dic43⋊C4C22×C418yes—
249C4×Dic43—24no—
250C4×Dic43—24no—
251C4×Dic43—24no—
252C4×Dic43—44no—
253C4×Dic43—42no—
254C4×Dic43C22×C414yes—
255C4×Dic43C22×C414yes—
256C4×Dic43C22×C414yes—
257C23×C43—24no—
258C23×C43—22no—
259C23×C43—24no—
260C23×C43—22no—
261C23×C43C23×C414yes—
262C23×C43C2511yescharacteristic
263C22×D43—24no—
264C22×D43—22no—
265C22×D43—24no—
266C22×D43—22no—
267C22×D43—216no—
268C22×D43—216no—
269C22×D43—216no—
270C22×D43—416no—
271C22×D43—416no—
272C22×D43C23×C414yes—
273C22×D43C23×C412yes—
274C22×D43C2×#4114yes—
275C22×D43H(5,𝔽2)14yes—
276C22×D43H(5,𝔽2)12yes—
277C22×D432−1+412yes—
278D4×C43—28no—
279C2×C4×C43—21no—
280C2×C4×C43—24no—
281C2×C4×C43—22no—
282C2×C4×C43—21no—
283C2×C4×C43—22no—
284C2×C4×C43—22no—
285C2×C4×C43—24no—
286C2×C4×C43—24no—
287C2×C4×C43—22no—
288C2×C4×C43—24no—
289C2×C4×C43—22no—
290C2×C4×C43—22no—
291C2×C4×C43—22no—
292C2×C4×C43—48no—
293C2×C4×C43C23×C412yes—
294C2×C4×C43C23×C412yes—
295C2×C4×C43C23×C414yes—
296C2×C4×C43C23×C412yes—
297C2×C4×C43C2×#4114yes—
298C22⋊D43—216no—
299C2×Dic43—21no—
300C2×Dic43—24no—
301C2×Dic43—22no—
302C2×Dic43—21no—
303C2×Dic43—22no—
304C2×Dic43—22no—
305C2×Dic43—24no—
306C2×Dic43—24no—
307C2×Dic43—22no—
308C2×Dic43—24no—
309C2×Dic43—22no—
310C2×Dic43—22no—
311C2×Dic43—22no—
312C2×Dic43—48no—
313C2×Dic43C23×C412yes—
314C2×Dic43C23×C412yes—
315C2×Dic43C23×C414yes—
316C2×Dic43C23×C412yes—
317C2×Dic43C2×#4114yes—
318D172—28no—
319C4×D43—28no—
320C4×D43—216no—
321C4×D43—28no—
322C4×D43—48no—
323C4×D43—48no—
324C4×D43—48no—
325C4×D43—416no—
326C4×D43—48no—
327C4×D43#117116yes—
328C2×#2319—431nomaximal, Sylow
329C22×C43—24no—
330C22×C43—24no—
331C22×C43—24no—
332C22×C43—44no—
333C22×C43—44no—
334C22×C43C24×C411yescharacteristic
335C22×C43C22×#4112yes—
336C22×C43C2×H(5,𝔽2)12yes—
337C22×C43C2×H(5,𝔽2)11yescharacteristic
338C22×C43C2×2−1+411yescharacteristic
339C2×D43—24no—
340C2×D43—24no—
341C2×D43—24no—
342C2×D43—44no—
343C2×D43—44no—
344C2×D43—432no—
345C2×D43C2×#11714yes—
346C2×D43#51814yes—
347C2×D43#52014yes—
348C2×D43#54018yes—
349C2×D43#54218yes—
350C4×C43—22no—
351C4×C43—24no—
352C4×C43—22no—
353C4×C43—42no—
354C4×C43—44no—
355C4×C43—42no—
356C4×C43C2×#11714yes—
357Dic43—22no—
358Dic43—24no—
359Dic43—22no—
360Dic43—42no—
361Dic43—44no—
362Dic43—42no—
363Dic43C2×#11714yes—
364C22×C4×D4—431no—
365#2319—432no—
366#2319—432no—
367#2319—434no—
368#2319—432no—
369#2319—432no—
370#2319—431no—
371#2319—431no—
372#2319—431no—
373#2319D4311yescharacteristic, direct product factor
374C2×#390—432no—
375C2×#389—432no—
376C2×#388—434no—
377C2×#381—432no—
378C2×#380—432no—
379C2×C4×C4⋊C4—431no—
380C2×#376—431no—
381C2×C43—44no—
382C2×C43C22×#11711yescharacteristic
383C2×C43C2×#51811yescharacteristic
384C2×C43C2×#52011yescharacteristic
385C2×C43C2×#54012yes—
386C2×C43C2×#54212yes—
387D43—44no—
388D43#231918yesdirect product factor
389C23×D4—431no—
390C24×C4—432no—
391C2×C4×D4—431no—
392C2×C4×D4—432no—
393C2×C4×D4—4316no—
394C2×C4×D4—431no—
395C2×C4×D4—432no—
396C2×C4×D4—431no—
397C2×C4×D4C2×D4311yescharacteristic
398C22×C4⋊C4—431no—
399C22×C4⋊C4—432no—
400C22×C4⋊C4—434no—
401C22×C22⋊C4—432no—
402C22×C22⋊C4—434no—
403C22×C22⋊C4—434no—
404C22×C42—431no—
405C22×C42—432no—
406C22×C42—432no—
407#390—432no—
408#390—432no—
409#390—434no—
410#390—434no—
411#390—432no—
412#390C2×D4312yes—
413#389—434no—
414#389—432no—
415#389—432no—
416#389—432no—
417#389—434no—
418#389C2×D4312yescomplemented
419#388—434no—
420#388—434no—
421#388—434no—
422#388—434no—
423#388—434no—
424#388—434no—
425#388—434no—
426#388C2×D4314yescomplemented
427#381—432no—
428#381—434no—
429#381—434no—
430#381—432no—
431#381—432no—
432#381C2×D4312yescomplemented
433#380—432no—
434#380—434no—
435#380—434no—
436#380—432no—
437#380—432no—
438#380C2×D4312yescomplemented
439C4×C4⋊C4—432no—
440C4×C4⋊C4—431no—
441C4×C4⋊C4—432no—
442C4×C4⋊C4—432no—
443C4×C4⋊C4C2×D4311yescharacteristic, complemented
444#376—432no—
445#376—431no—
446#376—432no—
447#376—431no—
448#376—431no—
449#376C2×D4311yescharacteristic, complemented
450C2×#95—431no—
451C2×#95—431no—
452C2×#95—432no—
453C2×#95—432no—
454C2×#95—434no—
455C43C2×#231911yescharacteristic, complemented, Sylow
456C25—432no—
457C22×D4—432no—
458C22×D4—438no—
459C22×D4—431no—
460C22×D4—868no—
461C22×D4C22×D4311yescharacteristic
462C23×C4—431no—
463C23×C4—432no—
464C23×C4—431no—
465C23×C4—432no—
466C23×C4—431no—
467C23×C4—4316no—
468C23×C4—432no—
469C23×C4—432no—
470C23×C4—432no—
471C23×C4—434no—
472C23×C4—432no—
473C23×C4—1728no—
474C23×C4C22×D4312yes—
475C4×D4—438no—
476C4×D4—4316no—
477C4×D4—438no—
478C4×D4—4316no—
479C4×D4—438no—
480C4×D4C4×D4318yescomplemented
481C2×C4⋊C4—432no—
482C2×C4⋊C4—431no—
483C2×C4⋊C4—438no—
484C2×C4⋊C4—434no—
485C2×C4⋊C4—432no—
486C2×C4⋊C4—434no—
487C2×C4⋊C4—434no—
488C2×C4⋊C4—434no—
489C2×C4⋊C4—868no—
490C2×C4⋊C4—1728no—
491C2×C4⋊C4C22×D4312yes—
492C2×C4⋊C4C22×D4314yes—
493C2×C4⋊C4C22×D4311yescharacteristic
494C2×C22⋊C4—432no—
495C2×C22⋊C4—432no—
496C2×C22⋊C4—432no—
497C2×C22⋊C4—4316no—
498C2×C22⋊C4—434no—
499C2×C22⋊C4—434no—
500C2×C22⋊C4—434no—
501C2×C22⋊C4—434no—
502C2×C22⋊C4—434no—
503C2×C22⋊C4—434no—
504C2×C22⋊C4—1728no—
505C2×C22⋊C4—1728no—
506C2×C22⋊C4C22×D4314yes—
507C2×C22⋊C4C22×D4314yes—
508C2×C22⋊C4C22×D4312yes—
509C2×C42—431no—
510C2×C42—431no—
511C2×C42—431no—
512C2×C42—438no—
513C2×C42—432no—
514C2×C42—432no—
515C2×C42—432no—
516C2×C42—434no—
517C2×C42—432no—
518C2×C42—868no—
519C2×C42—1724no—
520C2×C42C22×D4312yes—
521C2×C42C22×D4312yes—
522C2×C42C22×D4311yescharacteristic
523#95—432no—
524#95—431no—
525#95—432no—
526#95—431no—
527#95—432no—
528#95—432no—
529#95—432no—
530#95—434no—
531#95—432no—
532#95—434no—
533#95—434no—
534#95—434no—
535#95C22×D4311yescharacteristic
536#95C22×D4311yescharacteristic
537#95C22×D4312yes—
538#95C22×D4312yes—
539#95C22×D4314yes—
540C24—431no—
541C24—438no—
542C24—432no—
543C24—864no—
544C24—868no—
545C24—868no—
546C24—864no—
547C24C23×D4312yes—
548C2×D4—24no—
549C2×D4—438no—
550C2×D4—434no—
551C2×D4—8632no—
552C2×D4—868no—
553C2×D4—864no—
554C2×D4C2×C4×D4314yes—
555C22×C4—44no—
556C22×C4—431no—
557C22×C4—434no—
558C22×C4—438no—
559C22×C4—431no—
560C22×C4—431no—
561C22×C4—432no—
562C22×C4—438no—
563C22×C4—434no—
564C22×C4—434no—
565C22×C4—438no—
566C22×C4—438no—
567C22×C4—438no—
568C22×C4—432no—
569C22×C4—432no—
570C22×C4—434no—
571C22×C4—862no—
572C22×C4—868no—
573C22×C4—864no—
574C22×C4—862no—
575C22×C4—864no—
576C22×C4—864no—
577C22×C4—868no—
578C22×C4—864no—
579C22×C4—864no—
580C22×C4—868no—
581C22×C4—868no—
582C22×C4—864no—
583C22×C4—864no—
584C22×C4—1724no—
585C22×C4—1724no—
586C22×C4—17232no—
587C22×C4—1724no—
588C22×C4C2×C4×D4318yes—
589C22×C4C23×D4312yes—
590C22×C4C23×D4312yes—
591C22×C4C23×D4314yes—
592C22×C4C23×D4311yescharacteristic
593C22×C4C23×D4311yescharacteristic
594C22×C4C23×D4312yes—
595C22×C4C23×D4311yescharacteristic
596C4⋊C4—24no—
597C4⋊C4—44no—
598C4⋊C4—438no—
599C4⋊C4—434no—
600C4⋊C4—868no—
601C4⋊C4—864no—
602C4⋊C4—1724no—
603C4⋊C4—1724no—
604C4⋊C4—1724no—
605C4⋊C4C2×C4×D4314yes—
606C22⋊C4—44no—
607C22⋊C4—44no—
608C22⋊C4—438no—
609C22⋊C4—438no—
610C22⋊C4—438no—
611C22⋊C4—1724no—
612C22⋊C4—1724no—
613C22⋊C4—1724no—
614C22⋊C4—1724no—
615C22⋊C4—1724no—
616C22⋊C4—1724no—
617C22⋊C4C2×C4×D4318yes—
618C42—24no—
619C42—42no—
620C42—434no—
621C42—434no—
622C42—434no—
623C42—864no—
624C42—864no—
625C42—864no—
626C42—1722no—
627C42—1724no—
628C42C2×C4×D4314yes—
629C23—24no—
630C23—22no—
631C23—24no—
632C23—22no—
633C23—432no—
634C23—434no—
635C23—434no—
636C23—432no—
637C23—432no—
638C23—434no—
639C23—8616no—
640C23—8616no—
641C23—8616no—
642C23—864no—
643C23—862no—
644C23—864no—
645C23—862no—
646C23—17216no—
647C23—17216no—
648C23C22×C4×D4314yes—
649C23C24×D4311yescharacteristic
650D4—28no—
651D4—8616no—
652D4—868no—
653C2×C4—21no—
654C2×C4—24no—
655C2×C4—22no—
656C2×C4—21no—
657C2×C4—22no—
658C2×C4—22no—
659C2×C4—24no—
660C2×C4—24no—
661C2×C4—22no—
662C2×C4—22no—
663C2×C4—24no—
664C2×C4—22no—
665C2×C4—22no—
666C2×C4—48no—
667C2×C4—432no—
668C2×C4—434no—
669C2×C4—4316no—
670C2×C4—432no—
671C2×C4—432no—
672C2×C4—434no—
673C2×C4—868no—
674C2×C4—8616no—
675C2×C4—868no—
676C2×C4—861no—
677C2×C4—864no—
678C2×C4—862no—
679C2×C4—861no—
680C2×C4—862no—
681C2×C4—862no—
682C2×C4—864no—
683C2×C4—864no—
684C2×C4—862no—
685C2×C4—862no—
686C2×C4—864no—
687C2×C4—862no—
688C2×C4—862no—
689C2×C4—1728no—
690C2×C4—1728no—
691C2×C4—1728no—
692C2×C4—17216no—
693C2×C4—1728no—
694C2×C4—1728no—
695C2×C4C22×C4×D4312yes—
696C2×C4C22×C4×D4312yes—
697C2×C4C22×C4×D4314yes—
698C2×C4C22×C4×D4312yes—
699C2×C4#41×D4314yes—
700C22—24no—
701C22—24no—
702C22—24no—
703C22—44no—
704C22—44no—
705C22—434no—
706C22—434no—
707C22—438no—
708C22—438no—
709C22—434no—
710C22—864no—
711C22—864no—
712C22—864no—
713C22—17232no—
714C22—1724no—
715C22—1724no—
716C22C23×C4×D4311yescharacteristic
717C22C2×#41×D4312yes—
718C22H(5,𝔽2)×D4312yes—
719C22H(5,𝔽2)×D4311yescharacteristic
720C222−1+4×D4311yescharacteristic
721C4—22no—
722C4—24no—
723C4—22no—
724C4—42no—
725C4—44no—
726C4—42no—
727C4—434no—
728C4—862no—
729C4—864no—
730C4—862no—
731C4—1722no—
732C4—1724no—
733C4—1722no—
734C4#117×D4314yes—
735C2—44no—
736C2—438no—
737C2—1724no—
738C2C2×#117×D4311yescharacteristic
739C2#518×D4311yescharacteristic
740C2#520×D4311yescharacteristic
741C2#540×D4312yes—
742C2#542×D4312yes—
subgroupG/H
center, FrattiniC23C24×D43
commutatorC22×C43C24×C4
FittingC43×#2319C2
socle, cosocleC23×C43C25
prime radicalC22×D4×D43C22
hypercenter#2319D43
hypocenterC43C2×#2319
LCSG ▷ C22×C43 ▷ C43
UCSC1 ◁ C23 ◁ #2319

Complements

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

NH ≅ G/Ntype
2. #19137239C2semidirect
3. #19137238C2semidirect
4. #19137237C2semidirect
5. #19137236C2semidirect
6. #19137235C2semidirect
7. #19137234C2semidirect
8. #19137233C2semidirect
9. #19137232C2semidirect
11. #389×D43C2semidirect
12. #388×D43C2semidirect
13. #381×D43C2semidirect
14. #380×D43C2semidirect
15. C4×C4⋊C4×D43C2semidirect
16. #376×D43C2semidirect
17. C43×#2319C2semidirect
25. C4×D4×D43C4semidirect
40. #14582798C22semidirect
41. #14582797C22semidirect
42. #14582796C22semidirect
43. #14582795C22semidirect
44. #14582794C22semidirect
45. #14582793C22semidirect
46. #14582792C22semidirect
47. #14582791C22semidirect
48. #14582790C22semidirect
49. #14582789C22semidirect
50. #14582788C22semidirect
51. #14582787C22semidirect
52. #14582762C22semidirect
53. #14582761C22semidirect
54. #14582761C22semidirect
55. #14582761C22semidirect
56. #14582760C22semidirect
57. #14582759C22semidirect
58. #14582758C22semidirect
59. #14582758C22semidirect
60. #14582757C22semidirect
61. #14582756C22semidirect
62. C4⋊C4×Dic43C22semidirect
63. C4×Dic43⋊C4C22semidirect
64. C4×C4⋊Dic43C22semidirect
65. #14582750C22semidirect
66. #14582745C22semidirect
67. #14582745C22semidirect
68. #14582744C22semidirect
69. #14582744C22semidirect
70. #14582744C22semidirect
78. C43×#389C22semidirect
79. C43×#388C22semidirect
80. C43×#381C22semidirect
81. C43×#380C22semidirect
82. C4×C4⋊C4×C43C22semidirect
83. C43×#376C22semidirect
101. C4×D172C2×C4semidirect
102. D4×Dic43C2×C4semidirect
103. #13063287C2×C4semidirect
104. C4×C22⋊D43C2×C4semidirect
105. (C22⋊D43)⋊C4C2×C4semidirect
153. C4×D4×C43C2×C4semidirect
373. #2319D43direct (N × H)
388. D43#2319direct (N × H)
418. #389C2×D43semidirect
426. #388C2×D43semidirect
432. #381C2×D43semidirect
438. #380C2×D43semidirect
443. C4×C4⋊C4C2×D43semidirect
449. #376C2×D43semidirect
455. C43C2×#2319semidirect
480. C4×D4C4×D43semidirect

Maximal subgroups

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

subgroupindex
C2×C4×D4×D432
#191372392
#191372382
#191372372
#191372362
#191372352
#191372342
#191372332
#191372322
#390×D432
#389×D432
#388×D432
#381×D432
#380×D432
C4×C4⋊C4×D432
#376×D432
C43×#23192
C2×#231943