Finite Group Databasebeta

← #32868209

Subgroups — #32868209

Order 18176.

2342 conjugacy classes of subgroups.

The subgroup lattice has 1008 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#17986510C211yesmaximal, characteristic
2#22599170C214yesmaximal, complemented
3#22599161C212yesmaximal, complemented
4#22599142C212yesmaximal, complemented
5#22599121C214yesmaximal, complemented
6#22599112C212yesmaximal, complemented
7#22599093C212yesmaximal, complemented
8#22598284C212yesmaximal, complemented
9#22598263C212yesmaximal, complemented
10#22597966C214yesmaximal, complemented
11#22597598C212yesmaximal, complemented
12#22597574C212yesmaximal, complemented
13C2×#17985963C211yesmaximal, characteristic, complemented
14C22×C22⋊Q8×C71C211yesmaximal, characteristic, complemented
15C22×#11765865C2211yescharacteristic
16C2×#14556159C2214yescomplemented
17C22×#11765849C2212yescomplemented
18#17986510—21no—
19#17986510—21no—
20#17986510—21no—
21#17986510—21no—
22#17986510C2212yes—
23#17986510C2212yes—
24#17986510C2212yes—
25#17986510C2212yes—
26C2×#14556111—21no—
27C2×#14556107C2211yescharacteristic
28C2×#14556107C2211yescharacteristic
29C2×#14556102C2211yescharacteristic
30C2×#14556102C2211yescharacteristic
31C2×#14556097—21no—
32C2×C4×C22⋊D71—21no—
33C2×C4×C22⋊D71—21no—
34C2×#14556087C2211yescharacteristic
35#17986337C2218yescomplemented
36#17986334C2214yescomplemented
37#17986332C2214yescomplemented
38#17986329C2214yescomplemented
39#17986327C2214yescomplemented
40#17986317C2214yescomplemented
41#17986312C2214yescomplemented
42#17986255C2218yescomplemented
43#17986247C2218yescomplemented
44#17986238C2218yescomplemented
45#17986230C2218yescomplemented
46#17986159C2218yescomplemented
47#17986155C2214yescomplemented
48#17986155C2214yescomplemented
49#17986154C2214yescomplemented
50#17986149C2214yescomplemented
51#17986138C2214yescomplemented
52#17986138C2214yescomplemented
53#17986039C2214yescomplemented
54#17986008C2214yescomplemented
55#17985998C2214yescomplemented
56#17985963C2212yes—
57#17985963C2212yes—
58#17985963C2212yescomplemented
59#17985963C2212yescomplemented
60C2×C22⋊(C71⋊C8)C2212yes—
61C2×C22⋊(C71⋊C8)C2212yescomplemented
62C23×Q8×C71C2211yescharacteristic, complemented
63C24×C4×C71C2211yescharacteristic
64C2×C22⋊Q8×C71—21no—
65C2×C22⋊Q8×C71—21no—
66C2×C22⋊Q8×C71—21no—
67C2×C22⋊Q8×C71—21no—
68C2×C22⋊Q8×C71—21no—
69C2×C22⋊Q8×C71—21no—
70C2×C22⋊Q8×C71C2212yes—
71C2×C22⋊Q8×C71C2212yes—
72C2×C22⋊Q8×C71C2212yes—
73C2×C22⋊Q8×C71C2212yescomplemented
74C2×C22⋊Q8×C71C2212yescomplemented
75C2×C22⋊Q8×C71C2212yescomplemented
76C22×C4⋊C4×C71—21no—
77C22×C4⋊C4×C71C2211yescharacteristic, complemented
78C22×C22⋊C4×C71—21no—
79C2×#11765865—21no—
80C2×#11765865—21no—
81C2×#11765865—44no—
82C2×#11765865C2312yes—
83C2×#11765865C2312yes—
84C22×Dic142C2311yescharacteristic
85C22×D284C2311yescharacteristic
86C22×C22⋊D71—21no—
87C22×C22⋊D71—21no—
88C22×C22⋊D71—21no—
89C22×C4×D71—21no—
90#14556159—48no—
91C2×#11765855C2318yescomplemented
92C2×#11765852C2318yescomplemented
93C2×#11765849—44no—
94C2×#11765849C2314yes—
95C2×#11765849C2314yes—
96C22×C71⋊C8C2314yes—
97#14556111—22no—
98#14556111—22no—
99#14556111—22no—
100#14556111—22no—
101#14556107—21no—
102#14556107—21no—
103#14556107—21no—
104#14556107—21no—
105#14556107C2312yes—
106#14556107C2312yes—
107#14556107C2312yes—
108#14556107C2312yes—
109#14556102—21no—
110#14556102—21no—
111#14556102—21no—
112#14556102—21no—
113#14556102C2312yes—
114#14556102C2312yes—
115#14556102C2312yes—
116#14556102C2312yes—
117#14556097—22no—
118#14556097—22no—
119#14556097—22no—
120#14556097—22no—
121C4×C22⋊D71—22no—
122C4×C22⋊D71—22no—
123C4×C22⋊D71—22no—
124C4×C22⋊D71—22no—
125C4×C22⋊D71—22no—
126C4×C22⋊D71—22no—
127C4×C22⋊D71—22no—
128C4×C22⋊D71—22no—
129#14556087—21no—
130#14556087—21no—
131#14556087C2312yes—
132#14556087C2312yes—
133C2×C4⋊Dic71C2311yescharacteristic
134C2×C4⋊Dic71C2311yescharacteristic
135C2×Dic71⋊C4—21no—
136C2×Dic71⋊C4—21no—
137C2×C22⋊Dic71—21no—
138C2×C22⋊Dic71—21no—
139C2×C22⋊Dic71—21no—
140C2×(C2×D71)⋊C4—21no—
141C2×(C2×D71)⋊C4—21no—
142C2×C4×Dic71—21no—
143#14556061C2318yescomplemented
144#14556059C2318yescomplemented
145#14556052C2318yescomplemented
146#14556052C2318yescomplemented
147#14556051C2318yescomplemented
148#14556048C2318yescomplemented
149C22⋊(C71⋊C8)C2314yes—
150C22⋊(C71⋊C8)C2314yes—
151C22⋊(C71⋊C8)C2314yes—
152C22⋊(C71⋊C8)C2314yes—
153C25×C71D411yescharacteristic
154C22×Q8×C71—21no—
155C22×Q8×C71—21no—
156C22×Q8×C71—21no—
157C22×Q8×C71—44no—
158C22×Q8×C71C2312yes—
159C22×Q8×C71C2312yes—
160C22×Q8×C71C2312yes—
161C23×C4×C71—21no—
162C23×C4×C71—21no—
163C23×C4×C71—44no—
164C23×C4×C71D411yescharacteristic
165C23×C4×C71D411yescharacteristic
166C23×C4×C71D411yescharacteristic
167C23×C4×C71D411yescharacteristic
168C23×C4×C71D411yescharacteristic
169C23×C4×C71D411yescharacteristic
170C23×C4×C71D411yescharacteristic
171C23×C4×C71C2311yescharacteristic
172C23×C4×C71C2311yescharacteristic
173C23×C4×C71C2311yescharacteristic
174C23×C4×C71C2311yescharacteristic
175C23×C4×C71C2311yescharacteristic
176C23×C4×C71C2311yescharacteristic
177C23×C4×C71C2311yescharacteristic
178C22⋊Q8×C71—22no—
179C22⋊Q8×C71—22no—
180C22⋊Q8×C71—22no—
181C22⋊Q8×C71—22no—
182C22⋊Q8×C71—22no—
183C22⋊Q8×C71—22no—
184C22⋊Q8×C71—22no—
185C22⋊Q8×C71—22no—
186C22⋊Q8×C71—22no—
187C22⋊Q8×C71—22no—
188C22⋊Q8×C71—22no—
189C22⋊Q8×C71—22no—
190C22⋊Q8×C71C2314yes—
191C22⋊Q8×C71C2314yes—
192C22⋊Q8×C71C2314yes—
193C22⋊Q8×C71C2314yes—
194C2×C4⋊C4×C71—22no—
195C2×C4⋊C4×C71—22no—
196C2×C4⋊C4×C71—22no—
197C2×C4⋊C4×C71—22no—
198C2×C4⋊C4×C71—22no—
199C2×C4⋊C4×C71—22no—
200C2×C4⋊C4×C71—21no—
201C2×C4⋊C4×C71—21no—
202C2×C4⋊C4×C71—21no—
203C2×C4⋊C4×C71C2312yes—
204C2×C4⋊C4×C71C2312yes—
205C2×C4⋊C4×C71C2312yes—
206C2×C22⋊C4×C71—22no—
207C2×C22⋊C4×C71—22no—
208C2×C22⋊C4×C71—22no—
209C2×C22⋊C4×C71—22no—
210C2×C22⋊C4×C71—22no—
211C2×C22⋊C4×C71—22no—
212C23×D71—21no—
213#11765865—28no—
214#11765865—44no—
215#11765865—44no—
216#11765865—44no—
217C2×Dic142—21no—
218C2×Dic142—42no—
219C2×Dic142C2412yes—
220C2×D284—21no—
221C2×D284—42no—
222C2×D284C2412yes—
223C2×C22⋊D71—22no—
224C2×C22⋊D71—22no—
225C2×C22⋊D71—22no—
226C2×C22⋊D71—22no—
227C2×C22⋊D71—22no—
228C2×C22⋊D71—22no—
229C2×C22⋊D71—44no—
230C2×C22⋊D71—44no—
231C2×C22⋊D71—44no—
232C22×Dic71—21no—
233C22×Dic71—21no—
234C22×Dic71—21no—
235C2×C4×D71—22no—
236C2×C4×D71—22no—
237C2×C4×D71—44no—
238#11765855—48no—
239#11765852—48no—
240#11765849—28no—
241#11765849—44no—
242C2×C71⋊C8—44no—
243C2×C71⋊C8C2418yes—
244C4⋊Dic71—21no—
245C4⋊Dic71—21no—
246C4⋊Dic71C2412yes—
247C4⋊Dic71C2412yes—
248Dic71⋊C4—22no—
249Dic71⋊C4—22no—
250Dic71⋊C4—22no—
251Dic71⋊C4—22no—
252C22⋊Dic71—22no—
253C22⋊Dic71—22no—
254C22⋊Dic71—22no—
255C22⋊Dic71—22no—
256C22⋊Dic71—22no—
257C22⋊Dic71—22no—
258(C2×D71)⋊C4—22no—
259(C2×D71)⋊C4—22no—
260(C2×D71)⋊C4—22no—
261(C2×D71)⋊C4—22no—
262C4×Dic71—22no—
263C4×Dic71—22no—
264C24×C71—24no—
265C24×C71—42no—
266C24×C71—42no—
267C24×C71C2×D411yescharacteristic
268C24×C71C2×D411yescharacteristic
269C24×C71C2×D411yescharacteristic
270C24×C71C2×D411yescharacteristic
271C24×C71C2×D411yescharacteristic
272C24×C71C2×D411yescharacteristic
273C24×C71C2×D411yescharacteristic
274C2×Q8×C71—22no—
275C2×Q8×C71—22no—
276C2×Q8×C71—22no—
277C2×Q8×C71—28no—
278C2×Q8×C71—44no—
279C2×Q8×C71—44no—
280C2×Q8×C71—44no—
281C2×Q8×C71—44no—
282C2×Q8×C71—44no—
283C2×Q8×C71C2414yes—
284C22×C4×C71—24no—
285C22×C4×C71—24no—
286C22×C4×C71—24no—
287C22×C4×C71—22no—
288C22×C4×C71—22no—
289C22×C4×C71—22no—
290C22×C4×C71—22no—
291C22×C4×C71—22no—
292C22×C4×C71—22no—
293C22×C4×C71—42no—
294C22×C4×C71—42no—
295C22×C4×C71—42no—
296C22×C4×C71—42no—
297C22×C4×C71—42no—
298C22×C4×C71—42no—
299C22×C4×C71—42no—
300C22×C4×C71—42no—
301C22×C4×C71—42no—
302C22×C4×C71—42no—
303C22×C4×C71—42no—
304C22×C4×C71—44no—
305C22×C4×C71—44no—
306C22×C4×C71C2×D411yescharacteristic
307C22×C4×C71C2×D411yescharacteristic
308C22×C4×C71C2×D411yescharacteristic
309C22×C4×C71C2×D411yescharacteristic
310C22×C4×C71C2×D411yescharacteristic
311C22×C4×C71C2×D411yescharacteristic
312C22×C4×C71C2×D411yescharacteristic
313C22×C4×C71C2×D411yescharacteristic
314C22×C4×C71C2×D411yescharacteristic
315C22×C4×C71C2×D411yescharacteristic
316C22×C4×C71C2×D411yescharacteristic
317C22×C4×C71C2×D411yescharacteristic
318C22×C4×C71C2×D411yescharacteristic
319C22×C4×C71C2×D411yescharacteristic
320C22×C4×C71C2×D411yescharacteristic
321C22×C4×C71C2×D411yescharacteristic
322C22×C4×C71C2×D411yescharacteristic
323C22×C4×C71C2×D411yescharacteristic
324C22×C4×C71C2×D411yescharacteristic
325C22×C4×C71C2×D411yescharacteristic
326C22×C4×C71C2×D411yescharacteristic
327C22×C4×C71C2411yescharacteristic
328C22×C4×C71C2411yescharacteristic
329C22×C4×C71C2411yescharacteristic
330C22×C4×C71C2411yescharacteristic
331C22×C4×C71C2411yescharacteristic
332C22×C4×C71C2411yescharacteristic
333C22×C4×C71C2411yescharacteristic
334C4⋊C4×C71—24no—
335C4⋊C4×C71—24no—
336C4⋊C4×C71—24no—
337C4⋊C4×C71—24no—
338C4⋊C4×C71—22no—
339C4⋊C4×C71—22no—
340C4⋊C4×C71—22no—
341C4⋊C4×C71C2414yes—
342C22⋊C4×C71—24no—
343C22⋊C4×C71—24no—
344C22⋊C4×C71—24no—
345C22⋊C4×C71—24no—
346C23×C71—22no—
347C23×C71—22no—
348C23×C71—22no—
349C23×C71—22no—
350C23×C71—22no—
351C23×C71—22no—
352C23×C71—22no—
353C23×C71—22no—
354C23×C71—22no—
355C23×C71—22no—
356C23×C71—22no—
357C23×C71—22no—
358C23×C71—41no—
359C23×C71—41no—
360C23×C71—41no—
361C23×C71—41no—
362C23×C71—41no—
363C23×C71—41no—
364C23×C71—41no—
365C23×C71—41no—
366C23×C71—416no—
367C23×C71#13714yescomplemented
368C23×C71C22×D411yescharacteristic
369C23×C71C22×D411yescharacteristic
370C23×C71C22×D411yescharacteristic
371C23×C71C22×D411yescharacteristic
372C23×C71C22×D411yescharacteristic
373C23×C71C22×D411yescharacteristic
374C23×C71C22×D411yescharacteristic
375C22×D71—22no—
376C22×D71—42no—
377C22×D71—42no—
378C22×D71—42no—
379Q8×C71—28no—
380Q8×C71—44no—
381Q8×C71—44no—
382Q8×C71—44no—
383C2×C4×C71—22no—
384C2×C4×C71—22no—
385C2×C4×C71—22no—
386C2×C4×C71—22no—
387C2×C4×C71—22no—
388C2×C4×C71—22no—
389C2×C4×C71—22no—
390C2×C4×C71—22no—
391C2×C4×C71—22no—
392C2×C4×C71—22no—
393C2×C4×C71—22no—
394C2×C4×C71—22no—
395C2×C4×C71—22no—
396C2×C4×C71—22no—
397C2×C4×C71—22no—
398C2×C4×C71—24no—
399C2×C4×C71—24no—
400C2×C4×C71—41no—
401C2×C4×C71—41no—
402C2×C4×C71—41no—
403C2×C4×C71—41no—
404C2×C4×C71—41no—
405C2×C4×C71—41no—
406C2×C4×C71—41no—
407C2×C4×C71—41no—
408C2×C4×C71—41no—
409C2×C4×C71—41no—
410C2×C4×C71—41no—
411C2×C4×C71—41no—
412C2×C4×C71—44no—
413C2×C4×C71—44no—
414C2×C4×C71—44no—
415C2×C4×C71—44no—
416C2×C4×C71—44no—
417C2×C4×C71—44no—
418C2×C4×C71C22×D411yescharacteristic
419C2×C4×C71C22×D411yescharacteristic
420C2×C4×C71C22×D411yescharacteristic
421C2×C4×C71C22×D411yescharacteristic
422C2×C4×C71C22×D411yescharacteristic
423C2×C4×C71C22×D411yescharacteristic
424C2×C4×C71C22×D411yescharacteristic
425C2×C4×C71H(5,𝔽2)14yes—
426C2×C4×C71C2511yescharacteristic
427C22⋊D71—44no—
428C22⋊D71—44no—
429C22⋊D71—44no—
430C22⋊D71—44no—
431C22⋊D71—44no—
432C22⋊D71—44no—
433C2×Dic71—22no—
434C2×Dic71—22no—
435C2×Dic71—22no—
436C2×Dic71—42no—
437C2×Dic71—42no—
438C2×Dic71—42no—
439D284—24no—
440D284—42no—
441C4×D71—44no—
442C4×D71—44no—
443Dic142—24no—
444Dic142—42no—
445C71⋊C8—28no—
446C22×C71—28no—
447C22×C71—21no—
448C22×C71—21no—
449C22×C71—21no—
450C22×C71—21no—
451C22×C71—21no—
452C22×C71—21no—
453C22×C71—21no—
454C22×C71—21no—
455C22×C71—21no—
456C22×C71—21no—
457C22×C71—21no—
458C22×C71—21no—
459C22×C71—21no—
460C22×C71—21no—
461C22×C71—21no—
462C22×C71—21no—
463C22×C71—44no—
464C22×C71—44no—
465C22×C71—44no—
466C22×C71—44no—
467C22×C71—44no—
468C22×C71—44no—
469C22×C71#53412yes—
470C22×C71C2×#13712yes—
471C22×C71C2×#13712yes—
472C22×C71C2×#13712yes—
473C22×C71#57512yes—
474C22×C71C23×D411yescharacteristic
475C2×D71—42no—
476C2×D71—42no—
477C2×D71—42no—
478C2×D71—84no—
479C4×C71—21no—
480C4×C71—21no—
481C4×C71—21no—
482C4×C71—21no—
483C4×C71—21no—
484C4×C71—21no—
485C4×C71—44no—
486C4×C71—44no—
487C4×C71#53412yes—
488C4×C71C2×H(5,𝔽2)12yes—
489Dic71—42no—
490Dic71—42no—
491Dic71—42no—
492#60751—711nomaximal, Sylow
493C2×C71—22no—
494C2×C71—22no—
495C2×C71—22no—
496C2×C71—22no—
497C2×C71—22no—
498C2×C71—41no—
499C2×C71—41no—
500C2×C71C2×#53411yescharacteristic
501C2×C71C22×#13711yescharacteristic
502C2×C71C2×#57511yescharacteristic
503D71—82no—
504C2×#525—711no—
505C22×C22⋊Q8D7111yescharacteristic, complemented
506#3196—714no—
507#3195—712no—
508#3193—712no—
509#3190—714no—
510#3189—712no—
511#3187—712no—
512#3095—712no—
513#3092—712no—
514#3056—714no—
515#3007—712no—
516#3004—712no—
517C2×#407—711no—
518C71#6075111yescharacteristic, complemented, Sylow
519C22×#41—711no—
520C23×Q8C2×D7111yescharacteristic, complemented
521C24×C4C2×D7111yescharacteristic
522C2×#137—714no—
523C22×M16—712no—
524#525—712no—
525#525—712no—
526#525—712no—
527#525—712no—
528#525—1421no—
529#525—1421no—
530#525—1421no—
531#525—1421no—
532C2×#123—1421no—
533C2×C22⋊Q8—21no—
534C2×C22⋊Q8—21no—
535C2×C22⋊Q8—21no—
536C2×C22⋊Q8—21no—
537C2×C22⋊Q8—21no—
538C2×C22⋊Q8—21no—
539C2×C22⋊Q8—711no—
540C2×C22⋊Q8—711no—
541C2×C22⋊Q8C2×D7112yes—
542C2×C22⋊Q8C2×D7112yes—
543C2×C22⋊Q8C2×D7112yes—
544C2×C22⋊Q8C2×D7112yescomplemented
545C2×C22⋊Q8C2×D7112yescomplemented
546C2×C22⋊Q8C2×D7112yescomplemented
547C2×#121—711no—
548C2×#121—711no—
549C2×#120—1421no—
550C2×C4×D4—1421no—
551C2×C4×D4—1421no—
552C2×#117—711no—
553C22×C4⋊C4—21no—
554C22×C4⋊C4C2×D7111yescharacteristic, complemented
555C22×C22⋊C4—21no—
556#485—718no—
557#484—714no—
558#484—714no—
559#483—714no—
560#483—714no—
561#481—714no—
562#480—714no—
563#470—718no—
564#468—718no—
565#467—718no—
566#465—718no—
567#452—718no—
568#451—714no—
569#451—714no—
570#451—714no—
571#450—714no—
572#448—714no—
573#448—714no—
574#428—714no—
575#419—714no—
576#417—714no—
577#407—712no—
578#407—712no—
579#407—712no—
580#407—712no—
581C2×C22⋊C8—712no—
582C2×C22⋊C8—712no—
583C25C22⋊D7111yescharacteristic
584C2×#41—2844no—
585C2×#41—712no—
586C2×#41—712no—
587C2×#41—1421no—
588C2×#41—1421no—
589C22×Q8—21no—
590C22×Q8—21no—
591C22×Q8—21no—
592C22×Q8—44no—
593C22×Q8—711no—
594C22×Q8C22×D7112yes—
595C22×Q8C22×D7112yes—
596C22×Q8C22×D7112yes—
597C22×D4—711no—
598C22×D4—1421no—
599C22×D4—1421no—
600C22×D4—1421no—
601C23×C4—21no—
602C23×C4—21no—
603C23×C4—44no—
604C23×C4—1421no—
605C23×C4C22⋊D7111yescharacteristic
606C23×C4C22⋊D7111yescharacteristic
607C23×C4C22⋊D7111yescharacteristic
608C23×C4C22⋊D7111yescharacteristic
609C23×C4C22⋊D7111yescharacteristic
610C23×C4C22⋊D7111yescharacteristic
611C23×C4C22⋊D7111yescharacteristic
612C23×C4C22×D7111yescharacteristic
613C23×C4C22×D7111yescharacteristic
614C23×C4C22×D7111yescharacteristic
615C23×C4C22×D7111yescharacteristic
616C23×C4C22×D7111yescharacteristic
617C23×C4C22×D7111yescharacteristic
618C23×C4C22×D7111yescharacteristic
619#137—2848no—
620C2×Q16—718no—
621C2×SD16—718no—
622C2×M16—2844no—
623C2×M16—714no—
624C2×M16—714no—
625C22×C8—714no—
626#123—1422no—
627#123—1422no—
628#123—1422no—
629#123—1422no—
630C22⋊Q8—22no—
631C22⋊Q8—22no—
632C22⋊Q8—22no—
633C22⋊Q8—22no—
634C22⋊Q8—22no—
635C22⋊Q8—22no—
636C22⋊Q8—22no—
637C22⋊Q8—22no—
638C22⋊Q8—22no—
639C22⋊Q8—22no—
640C22⋊Q8—22no—
641C22⋊Q8—22no—
642C22⋊Q8—712no—
643C22⋊Q8—712no—
644C22⋊Q8—712no—
645C22⋊Q8—712no—
646C22⋊Q8—1421no—
647C22⋊Q8—1421no—
648C22⋊Q8—1421no—
649C22⋊Q8—1421no—
650C22⋊Q8C22×D7114yes—
651C22⋊Q8C22×D7114yes—
652C22⋊Q8C22×D7114yes—
653C22⋊Q8C22×D7114yes—
654#121—712no—
655#121—712no—
656#121—712no—
657#121—712no—
658#121—1421no—
659#121—1421no—
660#121—1421no—
661#121—1421no—
662#120—1422no—
663#120—1422no—
664#120—1422no—
665#120—1422no—
666C4×D4—1422no—
667C4×D4—1422no—
668C4×D4—1422no—
669C4×D4—1422no—
670C4×D4—1422no—
671C4×D4—1422no—
672C4×D4—1422no—
673C4×D4—1422no—
674#117—712no—
675#117—712no—
676#117—1421no—
677#117—1421no—
678C2×C4⋊C4—22no—
679C2×C4⋊C4—22no—
680C2×C4⋊C4—22no—
681C2×C4⋊C4—22no—
682C2×C4⋊C4—22no—
683C2×C4⋊C4—22no—
684C2×C4⋊C4—21no—
685C2×C4⋊C4—21no—
686C2×C4⋊C4—21no—
687C2×C4⋊C4—711no—
688C2×C4⋊C4—711no—
689C2×C4⋊C4—1421no—
690C2×C4⋊C4—1421no—
691C2×C4⋊C4C22×D7112yes—
692C2×C4⋊C4C22×D7112yes—
693C2×C4⋊C4C22×D7112yes—
694C2×C22⋊C4—22no—
695C2×C22⋊C4—22no—
696C2×C22⋊C4—22no—
697C2×C22⋊C4—22no—
698C2×C22⋊C4—22no—
699C2×C22⋊C4—22no—
700C2×C22⋊C4—1421no—
701C2×C22⋊C4—1421no—
702C2×C22⋊C4—1421no—
703C2×C22⋊C4—1421no—
704C2×C22⋊C4—1421no—
705C2×C42—1421no—
706#107—718no—
707#106—718no—
708#103—718no—
709#103—718no—
710#103—718no—
711#102—718no—
712C22⋊C8—714no—
713C22⋊C8—714no—
714C22⋊C8—714no—
715C22⋊C8—714no—
716C24—24no—
717C24—42no—
718C24—42no—
719C24—1421no—
720C24C2×C22⋊D7111yescharacteristic
721C24C2×C22⋊D7111yescharacteristic
722C24C2×C22⋊D7111yescharacteristic
723C24C2×C22⋊D7111yescharacteristic
724C24C2×C22⋊D7111yescharacteristic
725C24C2×C22⋊D7111yescharacteristic
726C24C2×C22⋊D7111yescharacteristic
727#41—2844no—
728#41—2844no—
729#41—2844no—
730#41—1428no—
731C2×Q8—22no—
732C2×Q8—22no—
733C2×Q8—22no—
734C2×Q8—28no—
735C2×Q8—44no—
736C2×Q8—44no—
737C2×Q8—44no—
738C2×Q8—44no—
739C2×Q8—44no—
740C2×Q8—2842no—
741C2×Q8—712no—
742C2×Q8—1421no—
743C2×Q8C23×D7114yes—
744C2×D4—2842no—
745C2×D4—2844no—
746C2×D4—2844no—
747C2×D4—2844no—
748C2×D4—712no—
749C2×D4—1422no—
750C2×D4—1422no—
751C2×D4—1422no—
752C2×D4—1422no—
753C2×D4—1422no—
754C2×D4—1422no—
755C2×D4—1421no—
756C22×C4—24no—
757C22×C4—24no—
758C22×C4—24no—
759C22×C4—22no—
760C22×C4—22no—
761C22×C4—22no—
762C22×C4—22no—
763C22×C4—22no—
764C22×C4—22no—
765C22×C4—42no—
766C22×C4—42no—
767C22×C4—42no—
768C22×C4—42no—
769C22×C4—42no—
770C22×C4—42no—
771C22×C4—42no—
772C22×C4—42no—
773C22×C4—42no—
774C22×C4—42no—
775C22×C4—42no—
776C22×C4—44no—
777C22×C4—44no—
778C22×C4—2844no—
779C22×C4—1421no—
780C22×C4—1421no—
781C22×C4—1421no—
782C22×C4—1422no—
783C22×C4—1422no—
784C22×C4C2×C22⋊D7111yescharacteristic
785C22×C4C2×C22⋊D7111yescharacteristic
786C22×C4C2×C22⋊D7111yescharacteristic
787C22×C4C2×C22⋊D7111yescharacteristic
788C22×C4C2×C22⋊D7111yescharacteristic
789C22×C4C2×C22⋊D7111yescharacteristic
790C22×C4C2×C22⋊D7111yescharacteristic
791C22×C4C2×C22⋊D7111yescharacteristic
792C22×C4C2×C22⋊D7111yescharacteristic
793C22×C4C2×C22⋊D7111yescharacteristic
794C22×C4C2×C22⋊D7111yescharacteristic
795C22×C4C2×C22⋊D7111yescharacteristic
796C22×C4C2×C22⋊D7111yescharacteristic
797C22×C4C2×C22⋊D7111yescharacteristic
798C22×C4C2×C22⋊D7111yescharacteristic
799C22×C4C2×C22⋊D7111yescharacteristic
800C22×C4C2×C22⋊D7111yescharacteristic
801C22×C4C2×C22⋊D7111yescharacteristic
802C22×C4C2×C22⋊D7111yescharacteristic
803C22×C4C2×C22⋊D7111yescharacteristic
804C22×C4C2×C22⋊D7111yescharacteristic
805C22×C4C23×D7111yescharacteristic
806C22×C4C23×D7111yescharacteristic
807C22×C4C23×D7111yescharacteristic
808C22×C4C23×D7111yescharacteristic
809C22×C4C23×D7111yescharacteristic
810C22×C4C23×D7111yescharacteristic
811C22×C4C23×D7111yescharacteristic
812Q16—2848no—
813SD16—2848no—
814M16—2844no—
815M16—1428no—
816C2×C8—2844no—
817C2×C8—718no—
818C4⋊C4—24no—
819C4⋊C4—24no—
820C4⋊C4—24no—
821C4⋊C4—24no—
822C4⋊C4—22no—
823C4⋊C4—22no—
824C4⋊C4—22no—
825C4⋊C4—712no—
826C4⋊C4—712no—
827C4⋊C4—1422no—
828C4⋊C4—1422no—
829C4⋊C4—1422no—
830C4⋊C4—1422no—
831C4⋊C4—1421no—
832C4⋊C4—1421no—
833C4⋊C4C23×D7114yes—
834C22⋊C4—24no—
835C22⋊C4—24no—
836C22⋊C4—24no—
837C22⋊C4—24no—
838C22⋊C4—1422no—
839C22⋊C4—1422no—
840C22⋊C4—1422no—
841C22⋊C4—1422no—
842C22⋊C4—1422no—
843C22⋊C4—1422no—
844C22⋊C4—1422no—
845C22⋊C4—1422no—
846C22⋊C4—1422no—
847C22⋊C4—1422no—
848C42—1422no—
849C42—1422no—
850C23—22no—
851C23—22no—
852C23—22no—
853C23—22no—
854C23—22no—
855C23—22no—
856C23—22no—
857C23—22no—
858C23—22no—
859C23—22no—
860C23—22no—
861C23—22no—
862C23—41no—
863C23—41no—
864C23—41no—
865C23—41no—
866C23—41no—
867C23—41no—
868C23—41no—
869C23—41no—
870C23—416no—
871C23—2842no—
872C23—2842no—
873C23—2842no—
874C23—1422no—
875C23#1455615914yescomplemented
876C23C22×C22⋊D7111yescharacteristic
877C23C22×C22⋊D7111yescharacteristic
878C23C22×C22⋊D7111yescharacteristic
879C23C22×C22⋊D7111yescharacteristic
880C23C22×C22⋊D7111yescharacteristic
881C23C22×C22⋊D7111yescharacteristic
882C23C22×C22⋊D7111yescharacteristic
883Q8—28no—
884Q8—44no—
885Q8—44no—
886Q8—44no—
887Q8—2842no—
888Q8—1424no—
889D4—2842no—
890D4—2844no—
891D4—2844no—
892D4—2844no—
893D4—2844no—
894D4—2844no—
895D4—2844no—
896D4—1424no—
897C2×C4—22no—
898C2×C4—22no—
899C2×C4—22no—
900C2×C4—22no—
901C2×C4—22no—
902C2×C4—22no—
903C2×C4—22no—
904C2×C4—22no—
905C2×C4—22no—
906C2×C4—22no—
907C2×C4—22no—
908C2×C4—22no—
909C2×C4—22no—
910C2×C4—22no—
911C2×C4—22no—
912C2×C4—24no—
913C2×C4—24no—
914C2×C4—41no—
915C2×C4—41no—
916C2×C4—41no—
917C2×C4—41no—
918C2×C4—41no—
919C2×C4—41no—
920C2×C4—41no—
921C2×C4—41no—
922C2×C4—41no—
923C2×C4—41no—
924C2×C4—41no—
925C2×C4—41no—
926C2×C4—44no—
927C2×C4—44no—
928C2×C4—44no—
929C2×C4—44no—
930C2×C4—44no—
931C2×C4—44no—
932C2×C4—2844no—
933C2×C4—2842no—
934C2×C4—2842no—
935C2×C4—2842no—
936C2×C4—2844no—
937C2×C4—1422no—
938C2×C4—1422no—
939C2×C4—1422no—
940C2×C4C22×C22⋊D7111yescharacteristic
941C2×C4C22×C22⋊D7111yescharacteristic
942C2×C4C22×C22⋊D7111yescharacteristic
943C2×C4C22×C22⋊D7111yescharacteristic
944C2×C4C22×C22⋊D7111yescharacteristic
945C2×C4C22×C22⋊D7111yescharacteristic
946C2×C4C22×C22⋊D7111yescharacteristic
947C2×C4#1455617314yes—
948C2×C4C24×D7111yescharacteristic
949C8—1428no—
950C22—28no—
951C22—21no—
952C22—21no—
953C22—21no—
954C22—21no—
955C22—21no—
956C22—21no—
957C22—21no—
958C22—21no—
959C22—21no—
960C22—21no—
961C22—21no—
962C22—21no—
963C22—21no—
964C22—21no—
965C22—21no—
966C22—21no—
967C22—44no—
968C22—44no—
969C22—44no—
970C22—44no—
971C22—44no—
972C22—44no—
973C22—2842no—
974C22—2842no—
975C22—2842no—
976C22—5684no—
977C22#1798655812yes—
978C22C2×#1455615912yes—
979C22C2×#1455615912yes—
980C22C2×#1455615912yes—
981C22#1798679712yes—
982C22C23×C22⋊D7111yescharacteristic
983C4—21no—
984C4—21no—
985C4—21no—
986C4—21no—
987C4—21no—
988C4—21no—
989C4—44no—
990C4—44no—
991C4—2842no—
992C4—2842no—
993C4—2842no—
994C4#1798655812yes—
995C4C2×#1455617312yes—
996C2—22no—
997C2—22no—
998C2—22no—
999C2—22no—
1000C2—22no—
1001C2—41no—
1002C2—41no—
1003C2—5682no—
1004C2C2×#1798655811yescharacteristic
1005C2C22×#1455615911yescharacteristic
1006C2C2×#1798679711yescharacteristic
subgroupG/H
centerC22C23×C22⋊D71
commutator, cosocleC2×C4×C71C25
FrattiniC2×C4C24×D71
FittingC22×C22⋊Q8×C71C2
socleC22×C71C23×D4
prime radicalC2×#17986510C2
hypercenterC22×C22⋊Q8D71
hypocenterC71#60751
LCSG ▷ C2×C4×C71 ▷ C2×C71 ▷ C71
UCSC1 ◁ C22 ◁ C24×C4 ◁ C22×C22⋊Q8

Complements

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

NH ≅ G/Ntype
2. #22599170C2semidirect
3. #22599161C2semidirect
4. #22599142C2semidirect
5. #22599121C2semidirect
6. #22599112C2semidirect
7. #22599093C2semidirect
8. #22598284C2semidirect
9. #22598263C2semidirect
10. #22597966C2semidirect
11. #22597598C2semidirect
12. #22597574C2semidirect
13. C2×#17985963C2semidirect
14. C22×C22⋊Q8×C71C2semidirect
16. C2×#14556159C22semidirect
17. C22×#11765849C22semidirect
35. #17986337C22semidirect
36. #17986334C22semidirect
37. #17986332C22semidirect
38. #17986329C22semidirect
39. #17986327C22semidirect
40. #17986317C22semidirect
41. #17986312C22semidirect
42. #17986255C22semidirect
43. #17986247C22semidirect
44. #17986238C22semidirect
45. #17986230C22semidirect
46. #17986159C22semidirect
47. #17986155C22semidirect
48. #17986155C22semidirect
49. #17986154C22semidirect
50. #17986149C22semidirect
51. #17986138C22semidirect
52. #17986138C22semidirect
53. #17986039C22semidirect
54. #17986008C22semidirect
55. #17985998C22semidirect
58. #17985963C22semidirect
59. #17985963C22semidirect
61. C2×C22⋊(C71⋊C8)C22semidirect
62. C23×Q8×C71C22semidirect
73. C2×C22⋊Q8×C71C22semidirect
74. C2×C22⋊Q8×C71C22semidirect
75. C2×C22⋊Q8×C71C22semidirect
77. C22×C4⋊C4×C71C22semidirect
91. C2×#11765855C23semidirect
92. C2×#11765852C23semidirect
143. #14556061C23semidirect
144. #14556059C23semidirect
145. #14556052C23semidirect
146. #14556052C23semidirect
147. #14556051C23semidirect
148. #14556048C23semidirect
367. C23×C71#137semidirect
505. C22×C22⋊Q8D71semidirect
518. C71#60751semidirect
520. C23×Q8C2×D71semidirect
544. C2×C22⋊Q8C2×D71semidirect
545. C2×C22⋊Q8C2×D71semidirect
546. C2×C22⋊Q8C2×D71semidirect
554. C22×C4⋊C4C2×D71semidirect
875. C23#14556159semidirect

Maximal subgroups

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

subgroupindex
C2×#179865102
#225991702
#225991612
#225991422
#225991212
#225991122
#225990932
#225982842
#225982632
#225979662
#225975982
#225975742
C2×#179859632
C22×C22⋊Q8×C712
#6075171