Finite Group Databasebeta

← #25106851

Subgroups — #25106851

Order 11008.

1030 conjugacy classes of subgroups.

The subgroup lattice has 776 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14582865C211yesmaximal, characteristic
2C2×#14582864C211yesmaximal, characteristic
3#19137081C211yesmaximal, characteristic
4#19134780C211yesmaximal, characteristic, complemented
5#19134777C211yesmaximal, characteristic, complemented
6#19134776C211yesmaximal, characteristic, complemented
7#19134776C211yesmaximal, characteristic, complemented
8#19134774C211yesmaximal, characteristic, complemented
9#19134774C211yesmaximal, characteristic, complemented
10#19134773C211yesmaximal, characteristic, complemented
11#19134578C211yesmaximal, characteristic, complemented
12#19134576C211yesmaximal, characteristic, complemented
13#19134574C211yesmaximal, characteristic, complemented
14#19134572C211yesmaximal, characteristic, complemented
15C43×#1850C211yesmaximal, characteristic, complemented
16C22×#10621898C2211yescharacteristic
17C22×#10621877C2211yescharacteristic
18C22×#10621872C2211yescharacteristic
19C22×C8×D43C2211yescharacteristic
20C2×#13063282C2211yescharacteristic
21C2×C42×D43C2211yescharacteristic
22C2×C4⋊(C43⋊C8)C2211yescharacteristic
23C2×C4⋊(C43⋊C8)C2211yescharacteristic
24C2×Dic43⋊C8C2211yescharacteristic
25C2×Dic43⋊C8C2211yescharacteristic
26C2×Dic43⋊C8C2211yescharacteristic
27C2×Dic43⋊C8C2211yescharacteristic
28#14582865—24no—
29#14582864—24no—
30C2×C22⋊(C43⋊C8)C2211yescharacteristic
31C2×(C2×D43)⋊C8C2211yescharacteristic
32C2×(C2×D43)⋊C8C2211yescharacteristic
33C2×(C2×D43)⋊C8C2211yescharacteristic
34C2×(C2×D43)⋊C8C2211yescharacteristic
35C2×(C2×D43)⋊C8C2211yescharacteristic
36C2×(C2×D43)⋊C8C2211yescharacteristic
37#14582803C411yescharacteristic
38#14582803C411yescharacteristic
39#14582799C411yescharacteristic
40#14582799C411yescharacteristic
41#14582777C411yescharacteristic
42#14582777C411yescharacteristic
43#14582775C411yescharacteristic
44#14582775C411yescharacteristic
45C4×(C2×D43)⋊C4C2211yescharacteristic
46C4×(C2×D43)⋊C4C2211yescharacteristic
47C4×C22⋊Dic43C2211yescharacteristic
48#14582654C2211yescharacteristic
49#14582654C2211yescharacteristic
50#14582653C2211yescharacteristic
51#14582653C2211yescharacteristic
52#14582653C2211yescharacteristic
53#14582653C2211yescharacteristic
54C23×C8×C43C2211yescharacteristic
55C2×C4⋊C8×C43C2211yescharacteristic
56C2×C4⋊C8×C43C2211yescharacteristic
57C2×C22⋊C8×C43C2211yescharacteristic
58C4×C22⋊C4×C43C2211yescharacteristic
59C43×#336C2211yescharacteristic
60C43×#336C2211yescharacteristic
61C2×#10621898—41no—
62C2×#10621898—41no—
63C2×#10621898—41no—
64C2×#10621898—41no—
65C2×#10621898D414yes—
66C2×#10621898Q814yes—
67C22×Dic86C2×C411yescharacteristic
68C22×D172C2×C411yescharacteristic
69C22×C22⋊D43C2×C411yescharacteristic
70C22×C22⋊D43C2×C411yescharacteristic
71C22×C4×D43C2×C411yescharacteristic
72C22×C4×D43C2×C411yescharacteristic
73C22×C4×D43C2311yescharacteristic
74C22×C4×D43C2311yescharacteristic
75C2×#10621877—22no—
76C2×#10621877—41no—
77C2×#10621877—41no—
78C2×#10621872—22no—
79C2×#10621872—41no—
80C2×#10621872—41no—
81C22×C43⋊C8C2311yescharacteristic
82C22×C43⋊C8C2311yescharacteristic
83C22×C43⋊C8C2311yescharacteristic
84C22×C43⋊C8C2311yescharacteristic
85C2×C8×D43—22no—
86C2×C8×D43—41no—
87C2×C8×D43—41no—
88#13063282—41no—
89#13063282—41no—
90C2×Dic43⋊C4C2×C411yescharacteristic
91C2×Dic43⋊C4C2×C411yescharacteristic
92C2×C22⋊Dic43C2×C411yescharacteristic
93C2×C22⋊Dic43C2×C411yescharacteristic
94C2×(C2×D43)⋊C4C2×C411yescharacteristic
95C2×(C2×D43)⋊C4C2×C411yescharacteristic
96C2×(C2×D43)⋊C4C2×C411yescharacteristic
97C2×(C2×D43)⋊C4C2×C411yescharacteristic
98C2×(C2×D43)⋊C4C2×C411yescharacteristic
99C2×(C2×D43)⋊C4C2×C411yescharacteristic
100C2×C4×Dic43C2×C411yescharacteristic
101C2×C4×Dic43C2×C411yescharacteristic
102C2×C4×Dic43C2311yescharacteristic
103C2×C4×Dic43C2311yescharacteristic
104C42×D43—41no—
105C42×D43—41no—
106C4⋊(C43⋊C8)—41no—
107C4⋊(C43⋊C8)—41no—
108Dic43⋊C8—41no—
109Dic43⋊C8—41no—
110Dic43⋊C8—41no—
111Dic43⋊C8—41no—
112C22⋊(C43⋊C8)—22no—
113(C2×D43)⋊C8—22no—
114(C2×D43)⋊C8—22no—
115(C2×D43)⋊C8—22no—
116(C2×D43)⋊C8—22no—
117(C2×D43)⋊C8—22no—
118(C2×D43)⋊C8—22no—
119C43⋊#95C2×C411yescharacteristic
120C43⋊#95C2×C411yescharacteristic
121C43⋊#95C2×C411yescharacteristic
122C43⋊#95C2×C411yescharacteristic
123C43⋊#95C2×C411yescharacteristic
124C43⋊#95C2×C411yescharacteristic
125C23×C4×C43C2311yescharacteristic
126C22×C8×C43—22no—
127C22×C8×C43—41no—
128C22×C8×C43—41no—
129C22×C8×C43C2311yescharacteristic
130C22×C8×C43C2311yescharacteristic
131C22×C8×C43C2311yescharacteristic
132C22×C8×C43C2311yescharacteristic
133C2×C22⋊C4×C43C2×C411yescharacteristic
134C2×C22⋊C4×C43C2×C411yescharacteristic
135C2×C42×C43C2311yescharacteristic
136C2×C42×C43C2311yescharacteristic
137C4⋊C8×C43—41no—
138C4⋊C8×C43—41no—
139C22⋊C8×C43—22no—
140#95×C43C2×C411yescharacteristic
141#95×C43C2×C411yescharacteristic
142C24×C43C22×C411yescharacteristic
143C23×D43C22×C411yescharacteristic
144C23×D43C22×C411yescharacteristic
145C22×C4×C43—21no—
146C22×C4×C43—21no—
147C22×C4×C43—21no—
148C22×C4×C43—21no—
149C22×C4×C43C22×C411yescharacteristic
150C22×C4×C43C22×C411yescharacteristic
151C22×C4×C43C22×C411yescharacteristic
152C22×C4×C43C22×C411yescharacteristic
153C22×C4×C43C22×C411yescharacteristic
154C22×C4×C43C2×D412yes—
155C22×C4×C43C2×Q812yes—
156C22×C4×C43C2411yescharacteristic
157C2×C22⋊D43—41no—
158C2×C22⋊D43—41no—
159C2×C22⋊D43—41no—
160C2×C22⋊D43—41no—
161C2×C22⋊D43C4⋊C414yes—
162C2×C22⋊D43C4⋊C414yes—
163C22×Dic43C22×C411yescharacteristic
164C22×Dic43C22×C411yescharacteristic
165C22×Dic43C22×C411yescharacteristic
166C22×Dic43C22×C411yescharacteristic
167C22×Dic43C22×C411yescharacteristic
168C22×Dic43C22×C411yescharacteristic
169#10621898—44no—
170#10621898—44no—
171#10621898—44no—
172#10621898—44no—
173C2×D172—41no—
174C2×D172—41no—
175C2×D172C4⋊C414yes—
176C2×C4×D43—21no—
177C2×C4×D43—21no—
178C2×C4×D43—21no—
179C2×C4×D43—21no—
180C2×C4×D43—21no—
181C2×C4×D43—21no—
182C2×C4×D43—21no—
183C2×C4×D43—21no—
184C2×C4×D43—22no—
185C2×C4×D43—22no—
186C2×C4×D43—41no—
187C2×C4×D43—41no—
188C2×C4×D43—41no—
189C2×C4×D43—41no—
190C2×C4×D43C2×D412yes—
191C2×C4×D43C2×D412yes—
192C2×C4×D43C2×Q812yes—
193C2×C4×D43C2×Q812yes—
194C2×Dic86—41no—
195C2×Dic86—41no—
196C2×Dic86C4⋊C414yes—
197C2×C8×C43—21no—
198C2×C8×C43—21no—
199C2×C8×C43—21no—
200C2×C8×C43—21no—
201C2×C8×C43—21no—
202C2×C8×C43—21no—
203C2×C8×C43—21no—
204C2×C8×C43—21no—
205C2×C8×C43—21no—
206C2×C8×C43—21no—
207C2×C8×C43—21no—
208C2×C8×C43—21no—
209C2×C8×C43—44no—
210C22⋊C4×C43—22no—
211C22⋊C4×C43—41no—
212C42×C43—21no—
213C42×C43—21no—
214C42×C43—21no—
215C42×C43—21no—
216C22⋊Dic43—22no—
217C22⋊Dic43—41no—
218(C2×D43)⋊C4—22no—
219(C2×D43)⋊C4—22no—
220(C2×D43)⋊C4—41no—
221(C2×D43)⋊C4—41no—
222(C2×D43)⋊C4—41no—
223(C2×D43)⋊C4—41no—
224Dic43⋊C4—41no—
225Dic43⋊C4—41no—
226C4×Dic43—21no—
227C4×Dic43—21no—
228C4×Dic43—21no—
229C4×Dic43—21no—
230C4×Dic43—41no—
231C4×Dic43—41no—
232#10621877—44no—
233C2×C43⋊C8—21no—
234C2×C43⋊C8—21no—
235C2×C43⋊C8—21no—
236C2×C43⋊C8—21no—
237C2×C43⋊C8—21no—
238C2×C43⋊C8—21no—
239C2×C43⋊C8—21no—
240C2×C43⋊C8—21no—
241C2×C43⋊C8—21no—
242C2×C43⋊C8—21no—
243C2×C43⋊C8—21no—
244C2×C43⋊C8—21no—
245#10621872—44no—
246C8×D43—44no—
247C23×C43—21no—
248C23×C43—21no—
249C23×C43—21no—
250C23×C43—21no—
251C23×C43—21no—
252C23×C43—21no—
253C23×C43C2×C4⋊C412yes—
254C23×C43C23×C411yescharacteristic
255C22×D43—21no—
256C22×D43—21no—
257C22×D43—21no—
258C22×D43—21no—
259C22×D43—21no—
260C22×D43—21no—
261C22×D43—21no—
262C22×D43—21no—
263C22×D43—21no—
264C22×D43—21no—
265C22×D43—21no—
266C22×D43—21no—
267C22×D43C2×C4⋊C412yes—
268C22×D43C2×C4⋊C412yes—
269C2×C4×C43—21no—
270C2×C4×C43—21no—
271C2×C4×C43—21no—
272C2×C4×C43—21no—
273C2×C4×C43—22no—
274C2×C4×C43—22no—
275C2×C4×C43—22no—
276C2×C4×C43—22no—
277C2×C4×C43—21no—
278C2×C4×C43—21no—
279C2×C4×C43—21no—
280C2×C4×C43—21no—
281C2×C4×C43—21no—
282C2×C4×C43—21no—
283C2×C4×C43—21no—
284C2×C4×C43—21no—
285C2×C4×C43—21no—
286C2×C4×C43C2×C4⋊C412yes—
287C2×C4×C43#13112yes—
288C2×C4×C43C22×D411yescharacteristic
289C2×C4×C43C22×Q811yescharacteristic
290C2×C4×C43H(5,𝔽2)11yescharacteristic
291C2×C4×C43H(5,𝔽2)11yescharacteristic
292C2×C4×C43H(5,𝔽2)11yescharacteristic
293C2×C4×C43H(5,𝔽2)11yescharacteristic
294C22⋊D43—44no—
295C22⋊D43—44no—
296C2×Dic43—21no—
297C2×Dic43—21no—
298C2×Dic43—21no—
299C2×Dic43—21no—
300C2×Dic43—21no—
301C2×Dic43—21no—
302C2×Dic43—21no—
303C2×Dic43—21no—
304C2×Dic43—21no—
305C2×Dic43—21no—
306C2×Dic43—21no—
307C2×Dic43—21no—
308C2×Dic43—21no—
309C2×Dic43—21no—
310C2×Dic43—21no—
311C2×Dic43C2×C4⋊C412yes—
312C2×Dic43C2×C4⋊C412yes—
313C2×Dic43#13112yes—
314D172—44no—
315C4×D43—22no—
316C4×D43—22no—
317C4×D43—22no—
318C4×D43—22no—
319C4×D43—22no—
320C4×D43—22no—
321C4×D43—22no—
322C4×D43—22no—
323C4×D43—44no—
324C4×D43—44no—
325Dic86—44no—
326C8×C43—41no—
327C8×C43—41no—
328C8×C43—41no—
329C8×C43—41no—
330C43⋊C8—41no—
331C43⋊C8—41no—
332C43⋊C8—41no—
333C43⋊C8—41no—
334#21937—431nomaximal, Sylow
335C22×C43—22no—
336C22×C43—22no—
337C22×C43—22no—
338C22×C43—41no—
339C22×C43—41no—
340C22×C43—41no—
341C22×C43—41no—
342C22×C43C22×C4⋊C411yescharacteristic
343C22×C43#51811yescharacteristic
344C22×C43#51811yescharacteristic
345C22×C43C2×#13111yescharacteristic
346C22×C43C2×#13111yescharacteristic
347C22×C43#56811yescharacteristic
348C22×C43#56811yescharacteristic
349C2×D43—22no—
350C2×D43—22no—
351C2×D43—22no—
352C2×D43—22no—
353C2×D43—22no—
354C2×D43—22no—
355C2×D43—41no—
356C2×D43—41no—
357C2×D43—41no—
358C2×D43—41no—
359C2×D43—41no—
360C2×D43—41no—
361C2×D43—41no—
362C2×D43—41no—
363C4×C43—22no—
364C4×C43—22no—
365C4×C43—41no—
366C4×C43—41no—
367C4×C43—41no—
368C4×C43#53411yescharacteristic
369C4×C43#53411yescharacteristic
370C4×C43#54311yescharacteristic
371C4×C43#54311yescharacteristic
372Dic43—22no—
373Dic43—22no—
374Dic43—22no—
375Dic43—41no—
376Dic43—41no—
377Dic43—41no—
378C2×#408—431no—
379C2×#408—431no—
380#2297—431no—
381#1851—431no—
382#1851—431no—
383#1851—431no—
384#1851—431no—
385#1850—431no—
386#1850—431no—
387#1850—431no—
388#1850D4311yescharacteristic, complemented
389#1798—431no—
390#1798—431no—
391#1797—431no—
392#1797—431no—
393C2×C43—42no—
394C2×C43#231511yescharacteristic
395C2×C43#290611yescharacteristic
396C2×C43#290611yescharacteristic
397C2×C43#297711yescharacteristic
398C2×C43#297811yescharacteristic
399C2×C43#298111yescharacteristic
400C2×C43#298111yescharacteristic
401D43—42no—
402D43—42no—
403C22×#41—431no—
404C22×M16—431no—
405C22×M16—431no—
406C23×C8—431no—
407C23×C8C2×D4311yescharacteristic
408C2×#117—431no—
409C22×C42—431no—
410C2×C4⋊C8—431no—
411C2×C4⋊C8—431no—
412C2×C4⋊C8—431no—
413C2×C4⋊C8—431no—
414C2×C4⋊C8—431no—
415C2×C4⋊C8—431no—
416C2×C4⋊C8C2×D4311yescharacteristic
417C2×C4⋊C8C2×D4311yescharacteristic
418#408—864no—
419#408—864no—
420C2×C22⋊C8—431no—
421C2×C22⋊C8—431no—
422C2×C22⋊C8—431no—
423C2×C22⋊C8—431no—
424C2×C22⋊C8—431no—
425C2×C22⋊C8—431no—
426C2×C22⋊C8—431no—
427C2×C22⋊C8C2×D4311yescharacteristic
428#391—431no—
429#391—431no—
430#390—431no—
431#390—431no—
432#386—431no—
433#386—431no—
434#386—431no—
435#386—431no—
436C4×C22⋊C4—431no—
437C4×C22⋊C4—431no—
438C4×C22⋊C4—431no—
439C4×C22⋊C4C2×D4311yescharacteristic
440#336—431no—
441#336—431no—
442#336—431no—
443#336—431no—
444#336—431no—
445#336—431no—
446#336C2×D4311yescharacteristic
447#336C2×D4311yescharacteristic
448C43#2193711yescharacteristic, complemented, Sylow
449C2×#41—434no—
450C2×#41—434no—
451C2×#41—1721no—
452C2×#41—1721no—
453C2×#41—1721no—
454C2×#41—1721no—
455C22×Q8—431no—
456C22×D4—431no—
457C22×D4—431no—
458C22×D4—431no—
459C23×C4—431no—
460C23×C4—431no—
461C23×C4—431no—
462C23×C4—431no—
463C23×C4C22×D4311yescharacteristic
464C2×M16—862no—
465C2×M16—862no—
466C2×M16—1721no—
467C2×M16—1721no—
468C2×M16—1721no—
469C2×M16—1721no—
470C22×C8—22no—
471C22×C8—41no—
472C22×C8—41no—
473C22×C8—431no—
474C22×C8—431no—
475C22×C8—431no—
476C22×C8—431no—
477C22×C8—862no—
478C22×C8—1721no—
479C22×C8—1721no—
480C22×C8C22×D4311yescharacteristic
481C22×C8C22×D4311yescharacteristic
482C22×C8C22×D4311yescharacteristic
483C22×C8C22×D4311yescharacteristic
484#117—1721no—
485#117—1721no—
486C2×C4⋊C4—431no—
487C2×C4⋊C4—431no—
488C2×C22⋊C4—431no—
489C2×C22⋊C4—431no—
490C2×C22⋊C4—431no—
491C2×C22⋊C4—431no—
492C2×C22⋊C4—431no—
493C2×C22⋊C4—431no—
494C2×C22⋊C4—431no—
495C2×C22⋊C4—431no—
496C2×C22⋊C4C4×D4311yescharacteristic
497C2×C22⋊C4C4×D4311yescharacteristic
498C2×C42—431no—
499C2×C42—431no—
500C2×C42—431no—
501C2×C42—431no—
502C2×C42—1721no—
503C2×C42—1721no—
504C2×C42C22×D4311yescharacteristic
505C2×C42C22×D4311yescharacteristic
506C4⋊C8—41no—
507C4⋊C8—41no—
508C4⋊C8—1721no—
509C4⋊C8—1721no—
510C4⋊C8—1721no—
511C4⋊C8—1721no—
512C4⋊C8—1721no—
513C4⋊C8—1721no—
514C22⋊C8—22no—
515C22⋊C8—862no—
516C22⋊C8—862no—
517C22⋊C8—862no—
518C22⋊C8—862no—
519C22⋊C8—862no—
520C22⋊C8—862no—
521C22⋊C8—862no—
522#95—431no—
523#95—431no—
524#95—431no—
525#95—431no—
526#95—431no—
527#95—431no—
528#95C4×D4311yescharacteristic
529#95C4×D4311yescharacteristic
530C24—431no—
531C24—431no—
532C24C2×C4×D4311yescharacteristic
533#41—1724no—
534#41—1724no—
535#41—1724no—
536#41—1724no—
537C2×Q8—434no—
538C2×Q8—1721no—
539C2×Q8—1721no—
540C2×D4—434no—
541C2×D4—434no—
542C2×D4—434no—
543C2×D4—1721no—
544C2×D4—1721no—
545C2×D4—1721no—
546C2×D4—1721no—
547C2×D4—1721no—
548C2×D4—1721no—
549C22×C4—21no—
550C22×C4—21no—
551C22×C4—21no—
552C22×C4—21no—
553C22×C4—431no—
554C22×C4—431no—
555C22×C4—431no—
556C22×C4—432no—
557C22×C4—432no—
558C22×C4—432no—
559C22×C4—432no—
560C22×C4—431no—
561C22×C4—431no—
562C22×C4—431no—
563C22×C4—862no—
564C22×C4—861no—
565C22×C4—861no—
566C22×C4—861no—
567C22×C4—861no—
568C22×C4—861no—
569C22×C4—861no—
570C22×C4—861no—
571C22×C4—861no—
572C22×C4—862no—
573C22×C4—1721no—
574C22×C4—1721no—
575C22×C4—1721no—
576C22×C4—1721no—
577C22×C4C2×C4×D4311yescharacteristic
578C22×C4C2×C4×D4311yescharacteristic
579C22×C4C2×C4×D4311yescharacteristic
580C22×C4C2×C4×D4311yescharacteristic
581C22×C4C2×C4×D4311yescharacteristic
582C22×C4D4×D4312yes—
583C22×C4Q8×D4312yes—
584C22×C4C23×D4311yescharacteristic
585M16—1724no—
586M16—1724no—
587C2×C8—21no—
588C2×C8—21no—
589C2×C8—21no—
590C2×C8—21no—
591C2×C8—21no—
592C2×C8—21no—
593C2×C8—21no—
594C2×C8—21no—
595C2×C8—21no—
596C2×C8—21no—
597C2×C8—21no—
598C2×C8—21no—
599C2×C8—44no—
600C2×C8—861no—
601C2×C8—861no—
602C2×C8—861no—
603C2×C8—861no—
604C2×C8—861no—
605C2×C8—861no—
606C2×C8—861no—
607C2×C8—861no—
608C2×C8—861no—
609C2×C8—861no—
610C2×C8—861no—
611C2×C8—861no—
612C2×C8—1724no—
613C4⋊C4—1721no—
614C4⋊C4—1721no—
615C22⋊C4—22no—
616C22⋊C4—41no—
617C22⋊C4—862no—
618C22⋊C4—862no—
619C22⋊C4—862no—
620C22⋊C4—1721no—
621C22⋊C4—1721no—
622C22⋊C4—1721no—
623C22⋊C4—1721no—
624C22⋊C4—1721no—
625C42—21no—
626C42—21no—
627C42—21no—
628C42—21no—
629C42—861no—
630C42—861no—
631C42—861no—
632C42—861no—
633C42—1721no—
634C42—1721no—
635C23—21no—
636C23—21no—
637C23—21no—
638C23—21no—
639C23—21no—
640C23—21no—
641C23—432no—
642C23—432no—
643C23—861no—
644C23—861no—
645C23—861no—
646C23—861no—
647C23—861no—
648C23—861no—
649C23—861no—
650C23—861no—
651C23—861no—
652C23—861no—
653C23—861no—
654C23—861no—
655C23C4⋊C4×D4312yes—
656C23C22×C4×D4311yescharacteristic
657Q8—1724no—
658D4—1724no—
659D4—1724no—
660D4—1724no—
661C2×C4—21no—
662C2×C4—21no—
663C2×C4—21no—
664C2×C4—21no—
665C2×C4—22no—
666C2×C4—22no—
667C2×C4—22no—
668C2×C4—22no—
669C2×C4—21no—
670C2×C4—21no—
671C2×C4—21no—
672C2×C4—21no—
673C2×C4—21no—
674C2×C4—21no—
675C2×C4—21no—
676C2×C4—21no—
677C2×C4—21no—
678C2×C4—432no—
679C2×C4—432no—
680C2×C4—432no—
681C2×C4—861no—
682C2×C4—861no—
683C2×C4—861no—
684C2×C4—861no—
685C2×C4—861no—
686C2×C4—861no—
687C2×C4—862no—
688C2×C4—862no—
689C2×C4—862no—
690C2×C4—862no—
691C2×C4—862no—
692C2×C4—862no—
693C2×C4—862no—
694C2×C4—862no—
695C2×C4—861no—
696C2×C4—861no—
697C2×C4—861no—
698C2×C4—861no—
699C2×C4—861no—
700C2×C4—861no—
701C2×C4—861no—
702C2×C4—861no—
703C2×C4—861no—
704C2×C4—1724no—
705C2×C4—1724no—
706C2×C4C4⋊C4×D4312yes—
707C2×C4#1306333112yes—
708C2×C4C2×D4×D4311yescharacteristic
709C2×C4C2×Q8×D4311yescharacteristic
710C2×C4#1306337011yescharacteristic
711C2×C4#1306337011yescharacteristic
712C2×C4#1306337111yescharacteristic
713C2×C4#1306337111yescharacteristic
714C8—41no—
715C8—41no—
716C8—41no—
717C8—41no—
718C8—1721no—
719C8—1721no—
720C8—1721no—
721C8—1721no—
722C22—22no—
723C22—22no—
724C22—22no—
725C22—41no—
726C22—41no—
727C22—41no—
728C22—41no—
729C22—862no—
730C22—862no—
731C22—862no—
732C22—862no—
733C22—862no—
734C22—862no—
735C22—1721no—
736C22—1721no—
737C22—1721no—
738C22—1721no—
739C22—1721no—
740C22—1721no—
741C22—1721no—
742C22—1721no—
743C22C2×C4⋊C4×D4311yescharacteristic
744C22#1458337111yescharacteristic
745C22#1458337111yescharacteristic
746C22#131×D4311yescharacteristic
747C22C2×#1306333111yescharacteristic
748C22#1458366411yescharacteristic
749C22#1458366511yescharacteristic
750C4—22no—
751C4—22no—
752C4—41no—
753C4—41no—
754C4—41no—
755C4—862no—
756C4—862no—
757C4—862no—
758C4—1721no—
759C4—1721no—
760C4—1721no—
761C4#1458345911yescharacteristic
762C4#1458346011yescharacteristic
763C4#1458352411yescharacteristic
764C4#1458352411yescharacteristic
765C2—42no—
766C2—1722no—
767C2—1722no—
768C2#1913720611yescharacteristic
769C2#1914316011yescharacteristic
770C2#1914316211yescharacteristic
771C2#1914364811yescharacteristic
772C2#1914365411yescharacteristic
773C2#1914366711yescharacteristic
774C2#1914366911yescharacteristic
subgroupG/H
center, FrattiniC22×C4C23×D43
commutator, socleC23×C43C23×C4
FittingC43×#1850C2
prime radicalC22×#10621898C22
cosocleC22×C4×C43C24
hypercenter#1850D43
hypocenterC43#21937
LCSG ▷ C23×C43 ▷ C43
UCSC1 ◁ C22×C4 ◁ #1850

Complements

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

NH ≅ G/Ntype
4. #19134780C2semidirect
5. #19134777C2semidirect
6. #19134776C2semidirect
7. #19134776C2semidirect
8. #19134774C2semidirect
9. #19134774C2semidirect
10. #19134773C2semidirect
11. #19134578C2semidirect
12. #19134576C2semidirect
13. #19134574C2semidirect
14. #19134572C2semidirect
15. C43×#1850C2semidirect
388. #1850D43semidirect
448. C43#21937semidirect

Maximal subgroups

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

subgroupindex
C2×#145828652
C2×#145828642
#191370812
#191347802
#191347772
#191347762
#191347742
#191347732
#191345782
#191345762
#191345742
#191345722
C43×#18502
#2193743