Finite Group Databasebeta

← C2×#11739555 #13521219

Subgroups — C2×#11739555 #13521219

Order 1792.

4926 conjugacy classes of subgroups.

The subgroup lattice has 948 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×C7×C22⋊C4C211yesmaximal, characteristic
2C23×C22⋊Dic7C211yesmaximal, characteristic
3C22×#6487C211yesmaximal, characteristic, complemented
4C22×#6441C211yesmaximal, characteristic, complemented
5C2×#90019C211yesmaximal, characteristic
6C2×#89982C211yesmaximal, characteristic, complemented
7C2×#89982C211yesmaximal, characteristic, complemented
8C2×#89984C211yesmaximal, characteristic, complemented
9#11739555C2116yesmaximal, direct product factor
10C2×#89721C211yesmaximal, characteristic, complemented
11C2×#89720C211yesmaximal, characteristic, complemented
12C2×#89720C211yesmaximal, characteristic, complemented
13C2×#89719C211yesmaximal, characteristic, complemented
14C2×#89722C211yesmaximal, characteristic, complemented
15C2×#89718C211yesmaximal, characteristic, complemented
16C2×#89714C211yesmaximal, characteristic, complemented
17C26×C7C2211yescharacteristic
18C24×C4×C7C2211yescharacteristic
19C24×C4×C7C2211yescharacteristic
20C24×Dic7C2211yescharacteristic
21C24×Dic7C2211yescharacteristic
22C23×Dic14C2211yescharacteristic, complemented
23C22×C7×C22⋊C4—28no—
24C22×C7×C22⋊C4C2211yescharacteristic
25C22×C7×C22⋊C4C2211yescharacteristic
26C22×C7×C22⋊C4C2211yescharacteristic
27C22×C7×C22⋊C4C2218yes—
28C22×C7×C22⋊C4C2211yescharacteristic
29C22×C22⋊Dic7—28no—
30C22×C22⋊Dic7C2211yescharacteristic
31C22×C22⋊Dic7C2211yescharacteristic
32C22×C22⋊Dic7C2211yescharacteristic
33C22×C22⋊Dic7C2211yescharacteristic
34C22×C22⋊Dic7C2211yescharacteristic
35C22×C22⋊Dic7C2211yescharacteristic
36C22×C22⋊Dic7C2218yes—
37C22×C22⋊Dic7C2211yescharacteristic
38C22×C22⋊Dic7C2211yescharacteristic
39C22×C22⋊Dic7C2211yescharacteristic
40C22×C22⋊Dic7C2211yescharacteristic
41C22×C4⋊Dic7C2211yescharacteristic, complemented
42C22×C4⋊Dic7C2211yescharacteristic, complemented
43C22×C4⋊Dic7C2211yescharacteristic, complemented
44C2×#6487—28no—
45C2×#6487C2218yescomplemented
46C22×Dic7⋊C4C2211yescharacteristic, complemented
47C22×Dic7⋊C4C2211yescharacteristic, complemented
48C22×Dic7⋊C4C2211yescharacteristic, complemented
49C22×Dic7⋊C4C2211yescharacteristic, complemented
50C22×Dic7⋊C4C2211yescharacteristic, complemented
51C22×Dic7⋊C4C2211yescharacteristic, complemented
52C2×#6441—28no—
53C2×#6441C2218yescomplemented
54#90019C2218yes—
55#89984C2218yescomplemented
56#89982C2218yescomplemented
57#89982C2218yescomplemented
58C2×C7⋊#95C2211yescharacteristic, complemented
59C2×C7⋊#95C2211yescharacteristic, complemented
60C2×C7⋊#95C2211yescharacteristic, complemented
61C2×C7⋊#95C2211yescharacteristic, complemented
62C2×C7⋊#95C2211yescharacteristic, complemented
63C2×C7⋊#95C2211yescharacteristic, complemented
64#89722C2218yescomplemented
65#89721C2218yescomplemented
66#89720C2218yescomplemented
67#89720C2218yescomplemented
68#89719C2218yescomplemented
69#89718C2218yescomplemented
70#89714C2218yescomplemented
71C2×#2437—71nomaximal, Sylow
72C25×C7—24no—
73C25×C7—24no—
74C25×C7—24no—
75C25×C7—24no—
76C25×C7—42no—
77C25×C7—42no—
78C25×C7Q818yescomplemented
79C25×C7C2311yescharacteristic
80C25×C7C2314yes—
81C25×C7C2311yescharacteristic
82C25×C7C2311yescharacteristic
83C23×C4×C7—24no—
84C23×C4×C7—24no—
85C23×C4×C7—24no—
86C23×C4×C7—24no—
87C23×C4×C7—42no—
88C23×C4×C7—42no—
89C23×C4×C7C2311yescharacteristic
90C23×C4×C7C2311yescharacteristic
91C23×C4×C7C2314yes—
92C23×C4×C7C2314yes—
93C23×C4×C7C2311yescharacteristic
94C23×C4×C7C2311yescharacteristic
95C23×Dic7—24no—
96C23×Dic7—24no—
97C23×Dic7—24no—
98C23×Dic7—24no—
99C23×Dic7—42no—
100C23×Dic7—42no—
101C23×Dic7C2311yescharacteristic
102C23×Dic7C2311yescharacteristic
103C23×Dic7C2311yescharacteristic
104C23×Dic7C2311yescharacteristic
105C23×Dic7C2311yescharacteristic
106C23×Dic7C2311yescharacteristic
107C23×Dic7C2314yes—
108C23×Dic7C2314yes—
109C23×Dic7C2311yescharacteristic
110C23×Dic7C2311yescharacteristic
111C22×Dic14—24no—
112C22×Dic14—24no—
113C22×Dic14—42no—
114C22×Dic14C2314yescomplemented
115C2×C7×C22⋊C4—24no—
116C2×C7×C22⋊C4—24no—
117C2×C7×C22⋊C4—24no—
118C2×C7×C22⋊C4—232no—
119C2×C7×C22⋊C4D418yes—
120C2×C7×C22⋊C4C2314yes—
121C2×C7×C22⋊C4C2314yes—
122C2×C7×C22⋊C4C2314yes—
123C2×C7×C22⋊C4C2314yes—
124C2×C22⋊Dic7—24no—
125C2×C22⋊Dic7—24no—
126C2×C22⋊Dic7—24no—
127C2×C22⋊Dic7—24no—
128C2×C22⋊Dic7—24no—
129C2×C22⋊Dic7—24no—
130C2×C22⋊Dic7—24no—
131C2×C22⋊Dic7—232no—
132C2×C22⋊Dic7—42no—
133C2×C22⋊Dic7—42no—
134C2×C22⋊Dic7D418yes—
135C2×C22⋊Dic7C2314yes—
136C2×C22⋊Dic7C2314yes—
137C2×C22⋊Dic7C2314yes—
138C2×C22⋊Dic7C2314yes—
139C2×C22⋊Dic7C2314yes—
140C2×C22⋊Dic7C2314yes—
141C2×C22⋊Dic7C2314yes—
142C2×C22⋊Dic7C2314yes—
143C2×C22⋊Dic7C2314yes—
144C2×C22⋊Dic7C2314yes—
145C2×C4⋊Dic7—24no—
146C2×C4⋊Dic7—24no—
147C2×C4⋊Dic7—42no—
148C2×C4⋊Dic7C2314yescomplemented
149C2×C4⋊Dic7C2314yescomplemented
150C2×C4⋊Dic7C2314yescomplemented
151#6487—232no—
152C2×Dic7⋊C4—24no—
153C2×Dic7⋊C4—24no—
154C2×Dic7⋊C4—24no—
155C2×Dic7⋊C4—24no—
156C2×Dic7⋊C4—42no—
157C2×Dic7⋊C4—42no—
158C2×Dic7⋊C4C2314yescomplemented
159C2×Dic7⋊C4C2314yescomplemented
160C2×Dic7⋊C4C2314yescomplemented
161C2×Dic7⋊C4C2314yescomplemented
162C2×Dic7⋊C4C2314yescomplemented
163C2×Dic7⋊C4C2314yescomplemented
164#6441—232no—
165C7⋊#95C2314yescomplemented
166C7⋊#95C2314yescomplemented
167C7⋊#95C2314yescomplemented
168C7⋊#95C2314yescomplemented
169C7⋊#95C2314yescomplemented
170C7⋊#95C2314yescomplemented
171C22×C22⋊Q8—71no—
172C22×C22⋊Q8—71no—
173C23×C22⋊C4—71no—
174C23×C22⋊C4D711yescharacteristic
175#2437—716no—
176C2×#399—71no—
177C2×#396—71no—
178C2×#396—71no—
179C2×#393—71no—
180C2×#385—71no—
181C2×#385—71no—
182C2×#385—71no—
183C2×#385—71no—
184C2×#380—71no—
185C2×#380—71no—
186C2×#379—71no—
187C24×C7—22no—
188C24×C7—22no—
189C24×C7—22no—
190C24×C7—22no—
191C24×C7—22no—
192C24×C7—22no—
193C24×C7—22no—
194C24×C7—22no—
195C24×C7—232no—
196C24×C7—232no—
197C24×C7—28no—
198C24×C7—22no—
199C24×C7—28no—
200C24×C7—22no—
201C24×C7—28no—
202C24×C7—28no—
203C24×C7—22no—
204C24×C7—22no—
205C24×C7—22no—
206C24×C7—22no—
207C24×C7—416no—
208C24×C7—44no—
209C24×C7—44no—
210C24×C7—416no—
211C24×C7—416no—
212C24×C7—416no—
213C24×C7—416no—
214C24×C7C2×D414yes—
215C24×C7C2×D414yes—
216C24×C7C2×Q814yes—
217C24×C7C2×Q814yes—
218C24×C7C2×Q814yes—
219C24×C7C2×Q8116yescomplemented
220C24×C7#4114yes—
221C24×C7#4114yes—
222C24×C7C2412yes—
223C24×C7C2412yes—
224C24×C7C2412yes—
225C24×C7C2411yescharacteristic
226C22×C4×C7—22no—
227C22×C4×C7—22no—
228C22×C4×C7—22no—
229C22×C4×C7—22no—
230C22×C4×C7—22no—
231C22×C4×C7—28no—
232C22×C4×C7—22no—
233C22×C4×C7—22no—
234C22×C4×C7—28no—
235C22×C4×C7—22no—
236C22×C4×C7—22no—
237C22×C4×C7—22no—
238C22×C4×C7—28no—
239C22×C4×C7—28no—
240C22×C4×C7—44no—
241C22×C4×C7—44no—
242C22×C4×C7—416no—
243C22×C4×C7—416no—
244C22×C4×C7C2×D414yes—
245C22×C4×C7C2×D414yes—
246C22×C4×C7C2412yes—
247C22×C4×C7C2412yes—
248C22×C4×C7C2412yes—
249C22×C4×C7C2412yes—
250C22×Dic7—22no—
251C22×Dic7—22no—
252C22×Dic7—22no—
253C22×Dic7—22no—
254C22×Dic7—28no—
255C22×Dic7—22no—
256C22×Dic7—22no—
257C22×Dic7—22no—
258C22×Dic7—22no—
259C22×Dic7—22no—
260C22×Dic7—22no—
261C22×Dic7—22no—
262C22×Dic7—22no—
263C22×Dic7—22no—
264C22×Dic7—22no—
265C22×Dic7—22no—
266C22×Dic7—28no—
267C22×Dic7—22no—
268C22×Dic7—22no—
269C22×Dic7—22no—
270C22×Dic7—22no—
271C22×Dic7—22no—
272C22×Dic7—22no—
273C22×Dic7—22no—
274C22×Dic7—28no—
275C22×Dic7—28no—
276C22×Dic7—44no—
277C22×Dic7—44no—
278C22×Dic7—416no—
279C22×Dic7—416no—
280C22×Dic7C2×D414yes—
281C22×Dic7C2×D414yes—
282C22×Dic7C2412yes—
283C22×Dic7C2412yes—
284C22×Dic7C2412yes—
285C22×Dic7C2412yes—
286C22×Dic7C2412yes—
287C22×Dic7C2412yes—
288C22×Dic7C2412yes—
289C22×Dic7C2412yes—
290C2×Dic14—28no—
291C2×Dic14—28no—
292C2×Dic14—44no—
293C2×Dic14—416no—
294C7×C22⋊C4—28no—
295C7×C22⋊C4—28no—
296C7×C22⋊C4—28no—
297C7×C22⋊C4C2×D4116yes—
298C22⋊Dic7—28no—
299C22⋊Dic7—28no—
300C22⋊Dic7—28no—
301C22⋊Dic7—28no—
302C22⋊Dic7—28no—
303C22⋊Dic7—28no—
304C22⋊Dic7—28no—
305C22⋊Dic7—44no—
306C22⋊Dic7—44no—
307C22⋊Dic7C2×D4116yes—
308C4⋊Dic7—28no—
309C4⋊Dic7—28no—
310C4⋊Dic7—44no—
311Dic7⋊C4—28no—
312Dic7⋊C4—28no—
313Dic7⋊C4—28no—
314Dic7⋊C4—28no—
315Dic7⋊C4—44no—
316Dic7⋊C4—44no—
317C26C2×D711yescharacteristic
318C23×Q8—71no—
319C24×C4—71no—
320C24×C4—71no—
321C24×C4C2×D711yescharacteristic
322C24×C4C2×D711yescharacteristic
323C2×C22⋊Q8—78no—
324C2×C22⋊Q8—78no—
325C2×C22⋊Q8—148no—
326C2×C22⋊Q8—148no—
327C22×C4⋊C4—71no—
328C22×C4⋊C4—71no—
329C22×C4⋊C4—71no—
330C22×C4⋊C4—71no—
331C22×C4⋊C4—71no—
332C22×C4⋊C4—71no—
333C22×C4⋊C4—71no—
334C22×C4⋊C4—71no—
335C22×C4⋊C4—71no—
336C22×C22⋊C4—28no—
337C22×C22⋊C4—71no—
338C22×C22⋊C4—71no—
339C22×C22⋊C4—71no—
340C22×C22⋊C4—78no—
341C22×C22⋊C4—71no—
342C22×C22⋊C4—71no—
343C22×C22⋊C4—71no—
344C22×C22⋊C4—71no—
345C22×C22⋊C4—71no—
346C22×C22⋊C4—71no—
347C22×C22⋊C4—71no—
348C22×C22⋊C4—148no—
349C22×C22⋊C4C2×D711yescharacteristic
350C22×C22⋊C4C2×D711yescharacteristic
351C22×C22⋊C4C2×D718yes—
352C22×C22⋊C4C2×D711yescharacteristic
353C22×C22⋊C4C2×D711yescharacteristic
354#399—78no—
355#396—78no—
356#396—78no—
357#393—78no—
358#385—78no—
359#385—78no—
360#385—78no—
361#385—78no—
362#380—78no—
363#380—78no—
364#379—78no—
365C2×#95—71no—
366C2×#95—71no—
367C2×#95—71no—
368C2×#95—71no—
369C2×#95—71no—
370C2×#95—71no—
371C23×C7—28no—
372C23×C7—28no—
373C23×C7—28no—
374C23×C7—28no—
375C23×C7—28no—
376C23×C7—28no—
377C23×C7—28no—
378C23×C7—28no—
379C23×C7—28no—
380C23×C7—28no—
381C23×C7—28no—
382C23×C7—28no—
383C23×C7—22no—
384C23×C7—22no—
385C23×C7—22no—
386C23×C7—22no—
387C23×C7—22no—
388C23×C7—22no—
389C23×C7—22no—
390C23×C7—22no—
391C23×C7—28no—
392C23×C7—28no—
393C23×C7—232no—
394C23×C7—232no—
395C23×C7—28no—
396C23×C7—22no—
397C23×C7—22no—
398C23×C7—22no—
399C23×C7—22no—
400C23×C7—22no—
401C23×C7—22no—
402C23×C7—416no—
403C23×C7—4128no—
404C23×C7—416no—
405C23×C7—416no—
406C23×C7—416no—
407C23×C7—416no—
408C23×C7—44no—
409C23×C7—44no—
410C23×C7—44no—
411C23×C7—44no—
412C23×C7C22⋊Q8116yescomplemented
413C23×C7C22⋊Q8116yescomplemented
414C23×C7C22×D414yes—
415C23×C7C22×D412yes—
416C23×C7C22×D414yes—
417C23×C7C22×D412yes—
418C23×C7C22×Q814yes—
419C23×C7C22×Q814yes—
420C23×C7C22×Q814yes—
421C23×C7C22×Q812yes—
422C23×C7C2×#4114yes—
423C23×C7C2×#4112yes—
424C23×C7C2×#4114yes—
425C23×C7C2×#4112yes—
426C23×C7H(5,𝔽2)12yes—
427C23×C7H(5,𝔽2)12yes—
428C23×C7C2511yescharacteristic
429C2×C4×C7—28no—
430C2×C4×C7—28no—
431C2×C4×C7—22no—
432C2×C4×C7—22no—
433C2×C4×C7—22no—
434C2×C4×C7—22no—
435C2×C4×C7—22no—
436C2×C4×C7—22no—
437C2×C4×C7—22no—
438C2×C4×C7—22no—
439C2×C4×C7—22no—
440C2×C4×C7—22no—
441C2×C4×C7—416no—
442C2×C4×C7—416no—
443C2×C4×C7—44no—
444C2×C4×C7—44no—
445C2×C4×C7C22×D414yes—
446C2×C4×C7C22×D414yes—
447C2×Dic7—28no—
448C2×Dic7—28no—
449C2×Dic7—22no—
450C2×Dic7—22no—
451C2×Dic7—22no—
452C2×Dic7—22no—
453C2×Dic7—22no—
454C2×Dic7—22no—
455C2×Dic7—22no—
456C2×Dic7—22no—
457C2×Dic7—22no—
458C2×Dic7—22no—
459C2×Dic7—22no—
460C2×Dic7—22no—
461C2×Dic7—22no—
462C2×Dic7—22no—
463C2×Dic7—22no—
464C2×Dic7—22no—
465C2×Dic7—22no—
466C2×Dic7—22no—
467C2×Dic7—22no—
468C2×Dic7—22no—
469C2×Dic7—22no—
470C2×Dic7—22no—
471C2×Dic7—416no—
472C2×Dic7—416no—
473C2×Dic7—44no—
474C2×Dic7—44no—
475C2×Dic7—44no—
476C2×Dic7—44no—
477C2×Dic7—44no—
478C2×Dic7—44no—
479C2×Dic7C22×D414yes—
480C2×Dic7C22×D414yes—
481Dic14—416no—
482C25—24no—
483C25—24no—
484C25—24no—
485C25—24no—
486C25—42no—
487C25—42no—
488C25Dic1418yescomplemented
489C25C22×D711yescharacteristic
490C25C22×D714yes—
491C25C22×D711yescharacteristic
492C25C22×D711yescharacteristic
493C22×Q8—74no—
494C22×Q8—144no—
495C22×Q8—144no—
496C22×Q8—282no—
497C23×C4—24no—
498C23×C4—24no—
499C23×C4—24no—
500C23×C4—24no—
501C23×C4—42no—
502C23×C4—42no—
503C23×C4—71no—
504C23×C4—71no—
505C23×C4—71no—
506C23×C4—71no—
507C23×C4—71no—
508C23×C4—71no—
509C23×C4—71no—
510C23×C4—71no—
511C23×C4—74no—
512C23×C4—74no—
513C23×C4—144no—
514C23×C4—144no—
515C23×C4—144no—
516C23×C4—144no—
517C23×C4—282no—
518C23×C4—282no—
519C23×C4C22×D711yescharacteristic
520C23×C4C22×D711yescharacteristic
521C23×C4C22×D714yes—
522C23×C4C22×D714yes—
523C23×C4C22×D711yescharacteristic
524C23×C4C22×D711yescharacteristic
525C22⋊Q8—1432no—
526C22⋊Q8—1432no—
527C2×C4⋊C4—74no—
528C2×C4⋊C4—74no—
529C2×C4⋊C4—74no—
530C2×C4⋊C4—74no—
531C2×C4⋊C4—74no—
532C2×C4⋊C4—74no—
533C2×C4⋊C4—74no—
534C2×C4⋊C4—74no—
535C2×C4⋊C4—74no—
536C2×C4⋊C4—144no—
537C2×C4⋊C4—144no—
538C2×C4⋊C4—144no—
539C2×C4⋊C4—144no—
540C2×C4⋊C4—144no—
541C2×C4⋊C4—144no—
542C2×C4⋊C4—282no—
543C2×C4⋊C4—282no—
544C2×C4⋊C4—282no—
545C2×C22⋊C4—24no—
546C2×C22⋊C4—24no—
547C2×C22⋊C4—24no—
548C2×C22⋊C4—232no—
549C2×C22⋊C4—78no—
550C2×C22⋊C4—74no—
551C2×C22⋊C4—74no—
552C2×C22⋊C4—74no—
553C2×C22⋊C4—74no—
554C2×C22⋊C4—74no—
555C2×C22⋊C4—74no—
556C2×C22⋊C4—74no—
557C2×C22⋊C4—74no—
558C2×C22⋊C4—74no—
559C2×C22⋊C4—74no—
560C2×C22⋊C4—1432no—
561C2×C22⋊C4—144no—
562C2×C22⋊C4—144no—
563C2×C22⋊C4—144no—
564C2×C22⋊C4—144no—
565C2×C22⋊C4—144no—
566C2×C22⋊C4—144no—
567C2×C22⋊C4—144no—
568C2×C22⋊C4—282no—
569C2×C22⋊C4—282no—
570C2×C22⋊C4C22⋊D718yes—
571C2×C22⋊C4C22×D714yes—
572C2×C22⋊C4C22×D714yes—
573C2×C22⋊C4C22×D714yes—
574C2×C22⋊C4C22×D714yes—
575#95—74no—
576#95—74no—
577#95—74no—
578#95—74no—
579#95—74no—
580#95—74no—
581C22×C7—24no—
582C22×C7—24no—
583C22×C7—24no—
584C22×C7—24no—
585C22×C7—232no—
586C22×C7—232no—
587C22×C7—24no—
588C22×C7—24no—
589C22×C7—24no—
590C22×C7—24no—
591C22×C7—24no—
592C22×C7—24no—
593C22×C7—24no—
594C22×C7—24no—
595C22×C7—24no—
596C22×C7—24no—
597C22×C7—24no—
598C22×C7—464no—
599C22×C7—416no—
600C22×C7—42no—
601C22×C7—42no—
602C22×C7—42no—
603C22×C7—42no—
604C22×C7C2×C22⋊Q814yes—
605C22×C7C2×C22⋊Q814yes—
606C22×C7C2×C22⋊Q818yescomplemented
607C22×C7C2×C22⋊Q818yescomplemented
608C22×C7#54314yes—
609C22×C7D4214yes—
610C22×C7#54614yes—
611C22×C7#54614yes—
612C22×C7#55114yes—
613C22×C7C23×D411yescharacteristic
614C22×C7C23×D411yescharacteristic
615C22×C7C23×Q811yescharacteristic
616C22×C7C22×#4111yescharacteristic
617C22×C7C22×#4111yescharacteristic
618C22×C7C2×H(5,𝔽2)11yescharacteristic
619C22×C7C2×H(5,𝔽2)11yescharacteristic
620C4×C7—24no—
621C4×C7—24no—
622C4×C7—42no—
623C4×C7—42no—
624Dic7—24no—
625Dic7—24no—
626Dic7—42no—
627Dic7—42no—
628Dic7—42no—
629Dic7—42no—
630Dic7—42no—
631Dic7—42no—
632C24—22no—
633C24—22no—
634C24—22no—
635C24—22no—
636C24—22no—
637C24—22no—
638C24—22no—
639C24—22no—
640C24—232no—
641C24—232no—
642C24—28no—
643C24—22no—
644C24—28no—
645C24—22no—
646C24—28no—
647C24—22no—
648C24—22no—
649C24—22no—
650C24—28no—
651C24—22no—
652C24—416no—
653C24—44no—
654C24—44no—
655C24—416no—
656C24—416no—
657C24—416no—
658C24—416no—
659C24C2×Dic1414yes—
660C24C2×Dic1414yes—
661C24C2×Dic1414yes—
662C24C2×Dic14116yescomplemented
663C24#115714yes—
664C24D4×D714yes—
665C24#115914yes—
666C24C2×C22⋊D714yes—
667C24C23×D712yes—
668C24C23×D712yes—
669C24C23×D712yes—
670C24C23×D711yescharacteristic
671C2×Q8—148no—
672C2×Q8—148no—
673C2×Q8—284no—
674C2×Q8—2816no—
675C22×C4—22no—
676C22×C4—22no—
677C22×C4—22no—
678C22×C4—22no—
679C22×C4—22no—
680C22×C4—28no—
681C22×C4—28no—
682C22×C4—22no—
683C22×C4—22no—
684C22×C4—22no—
685C22×C4—22no—
686C22×C4—22no—
687C22×C4—28no—
688C22×C4—28no—
689C22×C4—44no—
690C22×C4—44no—
691C22×C4—416no—
692C22×C4—416no—
693C22×C4—74no—
694C22×C4—74no—
695C22×C4—72no—
696C22×C4—72no—
697C22×C4—72no—
698C22×C4—72no—
699C22×C4—72no—
700C22×C4—72no—
701C22×C4—72no—
702C22×C4—72no—
703C22×C4—148no—
704C22×C4—148no—
705C22×C4—142no—
706C22×C4—142no—
707C22×C4—142no—
708C22×C4—142no—
709C22×C4—142no—
710C22×C4—142no—
711C22×C4—148no—
712C22×C4—142no—
713C22×C4—142no—
714C22×C4—142no—
715C22×C4—142no—
716C22×C4—142no—
717C22×C4—142no—
718C22×C4—142no—
719C22×C4—142no—
720C22×C4—142no—
721C22×C4—142no—
722C22×C4—142no—
723C22×C4—142no—
724C22×C4—142no—
725C22×C4—142no—
726C22×C4—142no—
727C22×C4—142no—
728C22×C4—148no—
729C22×C4—284no—
730C22×C4—284no—
731C22×C4—2816no—
732C22×C4—2816no—
733C22×C4C2×C22⋊D714yes—
734C22×C4C2×C22⋊D714yes—
735C22×C4C23×D712yes—
736C22×C4C23×D712yes—
737C22×C4C23×D712yes—
738C22×C4C23×D712yes—
739C4⋊C4—148no—
740C4⋊C4—148no—
741C4⋊C4—148no—
742C4⋊C4—148no—
743C4⋊C4—148no—
744C4⋊C4—148no—
745C4⋊C4—284no—
746C4⋊C4—284no—
747C4⋊C4—284no—
748C22⋊C4—28no—
749C22⋊C4—28no—
750C22⋊C4—28no—
751C22⋊C4—716no—
752C22⋊C4—148no—
753C22⋊C4—148no—
754C22⋊C4—148no—
755C22⋊C4—148no—
756C22⋊C4—148no—
757C22⋊C4—148no—
758C22⋊C4—148no—
759C22⋊C4—284no—
760C22⋊C4—284no—
761C22⋊C4C2×C22⋊D7116yes—
762C2×C7—28no—
763C2×C7—28no—
764C2×C7—44no—
765C2×C7#243718yescomplemented
766C2×C7C22×C22⋊Q811yescharacteristic
767C2×C7C22×C22⋊Q811yescharacteristic
768C2×C7C2×#54311yescharacteristic
769C2×C7C2×D4211yescharacteristic
770C2×C7C2×#54611yescharacteristic
771C2×C7C2×#54611yescharacteristic
772C2×C7C2×#55111yescharacteristic
773C23—28no—
774C23—28no—
775C23—28no—
776C23—28no—
777C23—28no—
778C23—28no—
779C23—28no—
780C23—28no—
781C23—28no—
782C23—28no—
783C23—28no—
784C23—28no—
785C23—22no—
786C23—22no—
787C23—22no—
788C23—22no—
789C23—22no—
790C23—22no—
791C23—22no—
792C23—22no—
793C23—28no—
794C23—232no—
795C23—28no—
796C23—28no—
797C23—232no—
798C23—22no—
799C23—22no—
800C23—22no—
801C23—22no—
802C23—22no—
803C23—22no—
804C23—416no—
805C23—416no—
806C23—416no—
807C23—416no—
808C23—416no—
809C23—4128no—
810C23—44no—
811C23—44no—
812C23—44no—
813C23—44no—
814C23#6441116yescomplemented
815C23#6487116yescomplemented
816C23C22×Dic1414yes—
817C23C22×Dic1414yes—
818C23C22×Dic1414yes—
819C23C22×Dic1412yes—
820C23C2×#115714yes—
821C23C2×#115712yes—
822C23C2×D4×D714yes—
823C23C2×D4×D712yes—
824C23C2×#115914yes—
825C23C2×#115912yes—
826C23#654812yes—
827C23#654812yes—
828C23C22×C22⋊D714yes—
829C23C22×C22⋊D712yes—
830C23C24×D711yescharacteristic
831Q8—2816no—
832C2×C4—28no—
833C2×C4—28no—
834C2×C4—22no—
835C2×C4—22no—
836C2×C4—22no—
837C2×C4—22no—
838C2×C4—22no—
839C2×C4—22no—
840C2×C4—22no—
841C2×C4—22no—
842C2×C4—22no—
843C2×C4—22no—
844C2×C4—416no—
845C2×C4—416no—
846C2×C4—44no—
847C2×C4—44no—
848C2×C4—74no—
849C2×C4—74no—
850C2×C4—148no—
851C2×C4—148no—
852C2×C4—142no—
853C2×C4—142no—
854C2×C4—142no—
855C2×C4—142no—
856C2×C4—142no—
857C2×C4—142no—
858C2×C4—142no—
859C2×C4—142no—
860C2×C4—142no—
861C2×C4—142no—
862C2×C4—142no—
863C2×C4—142no—
864C2×C4—142no—
865C2×C4—142no—
866C2×C4—142no—
867C2×C4—142no—
868C2×C4—142no—
869C2×C4—142no—
870C2×C4—142no—
871C2×C4—142no—
872C2×C4—142no—
873C2×C4—142no—
874C2×C4—2816no—
875C2×C4—2816no—
876C2×C4—284no—
877C2×C4—284no—
878C2×C4—284no—
879C2×C4—284no—
880C2×C4—284no—
881C2×C4—284no—
882C2×C4C22×C22⋊D714yes—
883C2×C4C22×C22⋊D714yes—
884C7C2×#243711yescharacteristic, complemented, Sylow
885C22—24no—
886C22—24no—
887C22—24no—
888C22—24no—
889C22—24no—
890C22—24no—
891C22—24no—
892C22—24no—
893C22—24no—
894C22—24no—
895C22—24no—
896C22—24no—
897C22—232no—
898C22—232no—
899C22—24no—
900C22—24no—
901C22—24no—
902C22—464no—
903C22—42no—
904C22—42no—
905C22—42no—
906C22—42no—
907C22—416no—
908C22C2×#644114yes—
909C22C2×#644118yescomplemented
910C22#9017414yes—
911C22#9018114yes—
912C22#9018614yes—
913C22C2×#648714yes—
914C22C2×#648718yescomplemented
915C22D4×C22⋊D714yes—
916C22#9049714yes—
917C22C23×Dic1411yescharacteristic
918C22C22×#115711yescharacteristic
919C22C22×D4×D711yescharacteristic
920C22C22×#115911yescharacteristic
921C22C2×#654811yescharacteristic
922C22C2×#654811yescharacteristic
923C22C23×C22⋊D711yescharacteristic
924C4—24no—
925C4—24no—
926C4—42no—
927C4—42no—
928C4—144no—
929C4—144no—
930C4—282no—
931C4—282no—
932C4—282no—
933C4—282no—
934C4—282no—
935C4—282no—
936C2—28no—
937C2—28no—
938C2—44no—
939C2#1173955518yesdirect product factor
940C2C22×#644111yescharacteristic
941C2C2×#9017411yescharacteristic
942C2C2×#9018611yescharacteristic
943C2C2×#9018111yescharacteristic
944C2C22×#648711yescharacteristic
945C2C2×#9049711yescharacteristic
946C2C2×D4×C22⋊D711yescharacteristic
subgroupG/H
centerC24C23×D7
commutator, cosocleC23×C7C25
FrattiniC23C24×D7
FittingC23×C7×C22⋊C4C2
socleC24×C7C24
prime radicalC26×C7C22
hypercenterC23×C22⋊C4D7
hypocenterC7C2×#2437
LCSG ▷ C23×C7 ▷ C7
UCSC1 ◁ C24 ◁ C23×C22⋊C4

Complements

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

NH ≅ G/Ntype
3. C22×#6487C2semidirect
4. C22×#6441C2semidirect
6. C2×#89982C2semidirect
7. C2×#89982C2semidirect
8. C2×#89984C2semidirect
9. #11739555C2direct (N × H)
10. C2×#89721C2semidirect
11. C2×#89720C2semidirect
12. C2×#89720C2semidirect
13. C2×#89719C2semidirect
14. C2×#89722C2semidirect
15. C2×#89718C2semidirect
16. C2×#89714C2semidirect
22. C23×Dic14C22semidirect
41. C22×C4⋊Dic7C22semidirect
42. C22×C4⋊Dic7C22semidirect
43. C22×C4⋊Dic7C22semidirect
45. C2×#6487C22semidirect
46. C22×Dic7⋊C4C22semidirect
47. C22×Dic7⋊C4C22semidirect
48. C22×Dic7⋊C4C22semidirect
49. C22×Dic7⋊C4C22semidirect
50. C22×Dic7⋊C4C22semidirect
51. C22×Dic7⋊C4C22semidirect
53. C2×#6441C22semidirect
55. #89984C22semidirect
56. #89982C22semidirect
57. #89982C22semidirect
58. C2×C7⋊#95C22semidirect
59. C2×C7⋊#95C22semidirect
60. C2×C7⋊#95C22semidirect
61. C2×C7⋊#95C22semidirect
62. C2×C7⋊#95C22semidirect
63. C2×C7⋊#95C22semidirect
64. #89722C22semidirect
65. #89721C22semidirect
66. #89720C22semidirect
67. #89720C22semidirect
68. #89719C22semidirect
69. #89718C22semidirect
70. #89714C22semidirect
78. C25×C7Q8semidirect
114. C22×Dic14C23semidirect
148. C2×C4⋊Dic7C23semidirect
149. C2×C4⋊Dic7C23semidirect
150. C2×C4⋊Dic7C23semidirect
158. C2×Dic7⋊C4C23semidirect
159. C2×Dic7⋊C4C23semidirect
160. C2×Dic7⋊C4C23semidirect
161. C2×Dic7⋊C4C23semidirect
162. C2×Dic7⋊C4C23semidirect
163. C2×Dic7⋊C4C23semidirect
165. C7⋊#95C23semidirect
166. C7⋊#95C23semidirect
167. C7⋊#95C23semidirect
168. C7⋊#95C23semidirect
169. C7⋊#95C23semidirect
170. C7⋊#95C23semidirect
219. C24×C7C2×Q8semidirect
412. C23×C7C22⋊Q8semidirect
413. C23×C7C22⋊Q8semidirect
488. C25Dic14semidirect
606. C22×C7C2×C22⋊Q8semidirect
607. C22×C7C2×C22⋊Q8semidirect
662. C24C2×Dic14semidirect
765. C2×C7#2437semidirect
814. C23#6441semidirect
815. C23#6487semidirect
884. C7C2×#2437semidirect
909. C22C2×#6441semidirect
914. C22C2×#6487semidirect
939. C2#11739555direct (N × H)

Maximal subgroups

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

subgroupindex
C23×C7×C22⋊C42
C23×C22⋊Dic72
C22×#64872
C22×#64412
C2×#900192
C2×#899822
C2×#899842
#117395552
C2×#897212
C2×#897202
C2×#897192
C2×#897222
C2×#897182
C2×#897142
C2×#24377