Finite Group Databasebeta

← C2×#11731275 #13521404

Subgroups — C2×#11731275 #13521404

Order 1792.

4102 conjugacy classes of subgroups.

The subgroup lattice has 896 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×C22⋊Dic7C211yesmaximal, characteristic
2C22×#6442C211yesmaximal, characteristic, complemented
3C2×C7×#379C211yesmaximal, characteristic
4C2×#90019C211yesmaximal, characteristic
5C2×#89725C211yesmaximal, characteristic, complemented
6C2×#89724C211yesmaximal, characteristic, complemented
7C2×#89724C211yesmaximal, characteristic, complemented
8C2×#89720C211yesmaximal, characteristic, complemented
9C2×#89717C211yesmaximal, characteristic, complemented
10C2×#89716C211yesmaximal, characteristic, complemented
11C2×#89723C211yesmaximal, characteristic, complemented
12C2×#89722C211yesmaximal, characteristic, complemented
13C2×#89718C211yesmaximal, characteristic, complemented
14C2×#89714C211yesmaximal, characteristic, complemented
15C2×C22⋊C4×Dic7C211yesmaximal, characteristic, complemented
16#11731275C2116yesmaximal, direct product factor
17C26×C7C2211yescharacteristic
18C24×Dic7C2211yescharacteristic
19C24×Dic7C2211yescharacteristic
20C22×C7×C22⋊C4C2211yescharacteristic
21C22×C7×C22⋊C4C2211yescharacteristic
22C22×C7×C22⋊C4C2211yescharacteristic
23C22×C7×C22⋊C4C2211yescharacteristic
24C22×C7×C22⋊C4C2211yescharacteristic
25C22×C7×C22⋊C4C2211yescharacteristic
26C22×C22⋊Dic7—28no—
27C22×C22⋊Dic7C2211yescharacteristic
28C22×C22⋊Dic7C2218yes—
29C22×C22⋊Dic7C2211yescharacteristic
30C22×C22⋊Dic7C2211yescharacteristic
31C22×C22⋊Dic7C2211yescharacteristic
32C22×C22⋊Dic7C2211yescharacteristic
33C22×C22⋊Dic7C2211yescharacteristic
34C22×C22⋊Dic7C2211yescharacteristic
35C22×C22⋊Dic7C2211yescharacteristic
36C22×C22⋊Dic7C2211yescharacteristic
37C22×C22⋊Dic7C2211yescharacteristic
38C22×C4⋊Dic7C2211yescharacteristic, complemented
39C22×C4⋊Dic7C2211yescharacteristic, complemented
40C22×Dic7⋊C4C2211yescharacteristic, complemented
41C22×Dic7⋊C4C2211yescharacteristic, complemented
42C22×Dic7⋊C4C2211yescharacteristic, complemented
43C22×Dic7⋊C4C2211yescharacteristic, complemented
44C22×C4×Dic7C2211yescharacteristic, complemented
45C22×C4×Dic7C2211yescharacteristic, complemented
46C2×#6442—28no—
47C2×#6442C2218yescomplemented
48C7×#379C2218yes—
49#90019C2218yes—
50C2×C7⋊#95C2211yescharacteristic, complemented
51C2×C7⋊#95C2211yescharacteristic, complemented
52C2×C7⋊#95C2211yescharacteristic, complemented
53C2×C7⋊#95C2211yescharacteristic, complemented
54C2×C7⋊#95C2211yescharacteristic, complemented
55C2×C7⋊#95C2211yescharacteristic, complemented
56C2×C7⋊#95C2211yescharacteristic, complemented
57C2×C7⋊#95C2211yescharacteristic, complemented
58#89725C2218yescomplemented
59#89724C2218yescomplemented
60#89724C2218yescomplemented
61#89723C2218yescomplemented
62#89722C2218yescomplemented
63#89720C2218yescomplemented
64#89718C2218yescomplemented
65#89717C2218yescomplemented
66#89716C2218yescomplemented
67#89714C2218yescomplemented
68C22⋊C4×Dic7C2218yescomplemented
69C2×#2480—71nomaximal, Sylow
70C25×C7—24no—
71C25×C7—24no—
72C25×C7—24no—
73C25×C7—24no—
74C25×C7—24no—
75C25×C7—42no—
76C25×C7—42no—
77C25×C7C2311yescharacteristic
78C25×C7C2311yescharacteristic
79C25×C7C2314yes—
80C25×C7C2311yescharacteristic
81C23×C4×C7C2311yescharacteristic
82C23×C4×C7C2311yescharacteristic
83C23×C4×C7C2311yescharacteristic
84C23×C4×C7C2311yescharacteristic
85C23×Dic7—24no—
86C23×Dic7—24no—
87C23×Dic7—24no—
88C23×Dic7—24no—
89C23×Dic7—42no—
90C23×Dic7—42no—
91C23×Dic7C2311yescharacteristic
92C23×Dic7C2311yescharacteristic
93C23×Dic7C2311yescharacteristic
94C23×Dic7C2311yescharacteristic
95C23×Dic7C2311yescharacteristic
96C23×Dic7C2311yescharacteristic
97C23×Dic7C2314yes—
98C23×Dic7C2314yes—
99C23×Dic7C2311yescharacteristic
100C23×Dic7C2311yescharacteristic
101C2×C7×C22⋊C4—24no—
102C2×C7×C22⋊C4—24no—
103C2×C7×C22⋊C4—24no—
104C2×C7×C22⋊C4—24no—
105C2×C7×C22⋊C4—42no—
106C2×C7×C22⋊C4—42no—
107C2×C7×C22⋊C4C2314yes—
108C2×C7×C22⋊C4C2314yes—
109C2×C7×C22⋊C4C2314yes—
110C2×C7×C22⋊C4C2314yes—
111C2×C7×C22⋊C4C2314yes—
112C2×C7×C22⋊C4C2314yes—
113C2×C22⋊Dic7—24no—
114C2×C22⋊Dic7—24no—
115C2×C22⋊Dic7—24no—
116C2×C22⋊Dic7—24no—
117C2×C22⋊Dic7—24no—
118C2×C22⋊Dic7—24no—
119C2×C22⋊Dic7—24no—
120C2×C22⋊Dic7—232no—
121C2×C22⋊Dic7—42no—
122C2×C22⋊Dic7—42no—
123C2×C22⋊Dic7D418yes—
124C2×C22⋊Dic7C2314yes—
125C2×C22⋊Dic7C2314yes—
126C2×C22⋊Dic7C2314yes—
127C2×C22⋊Dic7C2314yes—
128C2×C22⋊Dic7C2314yes—
129C2×C22⋊Dic7C2314yes—
130C2×C22⋊Dic7C2314yes—
131C2×C22⋊Dic7C2314yes—
132C2×C22⋊Dic7C2314yes—
133C2×C22⋊Dic7C2314yes—
134C2×C4⋊Dic7—24no—
135C2×C4⋊Dic7—42no—
136C2×C4⋊Dic7C2314yescomplemented
137C2×C4⋊Dic7C2314yescomplemented
138C2×Dic7⋊C4—24no—
139C2×Dic7⋊C4—24no—
140C2×Dic7⋊C4—42no—
141C2×Dic7⋊C4—42no—
142C2×Dic7⋊C4C2314yescomplemented
143C2×Dic7⋊C4C2314yescomplemented
144C2×Dic7⋊C4C2314yescomplemented
145C2×Dic7⋊C4C2314yescomplemented
146C2×C4×Dic7—24no—
147C2×C4×Dic7—42no—
148C2×C4×Dic7C2314yescomplemented
149C2×C4×Dic7C2314yescomplemented
150#6442—232no—
151C7⋊#95C2314yescomplemented
152C7⋊#95C2314yescomplemented
153C7⋊#95C2314yescomplemented
154C7⋊#95C2314yescomplemented
155C7⋊#95C2314yescomplemented
156C7⋊#95C2314yescomplemented
157C7⋊#95C2314yescomplemented
158C7⋊#95C2314yescomplemented
159C22×#126—71no—
160C23×C22⋊C4—71no—
161#2480—716no—
162C2×#397—71no—
163C2×#397—71no—
164C2×#397—71no—
165C2×#396—71no—
166C2×#388—71no—
167C2×#388—71no—
168C2×#388—71no—
169C2×#385—71no—
170C2×#385—71no—
171C2×#380—71no—
172C2×#379—71no—
173C2×#379D711yescharacteristic
174C2×C4×C22⋊C4—71no—
175C24×C7—22no—
176C24×C7—22no—
177C24×C7—22no—
178C24×C7—22no—
179C24×C7—232no—
180C24×C7—28no—
181C24×C7—22no—
182C24×C7—28no—
183C24×C7—28no—
184C24×C7—22no—
185C24×C7—22no—
186C24×C7—22no—
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—28no—
196C24×C7—28no—
197C24×C7—44no—
198C24×C7—44no—
199C24×C7—416no—
200C24×C7—416no—
201C24×C7—416no—
202C24×C7—416no—
203C24×C7—416no—
204C24×C7—416no—
205C24×C7C2×D414yes—
206C24×C7#4114yes—
207C24×C7#4114yes—
208C24×C7#4114yes—
209C24×C7#4114yes—
210C24×C7C2412yes—
211C24×C7C2412yes—
212C24×C7C2412yes—
213C24×C7C2411yescharacteristic
214C22×C4×C7—22no—
215C22×C4×C7—22no—
216C22×C4×C7—22no—
217C22×C4×C7—22no—
218C22×C4×C7—22no—
219C22×C4×C7—22no—
220C22×C4×C7—22no—
221C22×C4×C7—22no—
222C22×C4×C7—22no—
223C22×C4×C7—22no—
224C22×C4×C7—22no—
225C22×C4×C7—22no—
226C22×C4×C7C2412yes—
227C22×C4×C7C2412yes—
228C22×C4×C7C2412yes—
229C22×C4×C7C2412yes—
230C22×Dic7—22no—
231C22×Dic7—22no—
232C22×Dic7—22no—
233C22×Dic7—22no—
234C22×Dic7—22no—
235C22×Dic7—22no—
236C22×Dic7—22no—
237C22×Dic7—22no—
238C22×Dic7—22no—
239C22×Dic7—22no—
240C22×Dic7—22no—
241C22×Dic7—22no—
242C22×Dic7—22no—
243C22×Dic7—22no—
244C22×Dic7—28no—
245C22×Dic7—28no—
246C22×Dic7—22no—
247C22×Dic7—22no—
248C22×Dic7—22no—
249C22×Dic7—22no—
250C22×Dic7—22no—
251C22×Dic7—22no—
252C22×Dic7—22no—
253C22×Dic7—22no—
254C22×Dic7—28no—
255C22×Dic7—28no—
256C22×Dic7—44no—
257C22×Dic7—44no—
258C22×Dic7—416no—
259C22×Dic7—416no—
260C22×Dic7C2×D414yes—
261C22×Dic7C2×D414yes—
262C22×Dic7C2412yes—
263C22×Dic7C2412yes—
264C22×Dic7C2412yes—
265C22×Dic7C2412yes—
266C22×Dic7C2412yes—
267C22×Dic7C2412yes—
268C22×Dic7C2412yes—
269C22×Dic7C2412yes—
270C7×C22⋊C4—28no—
271C7×C22⋊C4—28no—
272C7×C22⋊C4—28no—
273C7×C22⋊C4—28no—
274C7×C22⋊C4—44no—
275C7×C22⋊C4—44no—
276C22⋊Dic7—28no—
277C22⋊Dic7—28no—
278C22⋊Dic7—28no—
279C22⋊Dic7—28no—
280C22⋊Dic7—28no—
281C22⋊Dic7—28no—
282C22⋊Dic7—28no—
283C22⋊Dic7—44no—
284C22⋊Dic7—44no—
285C22⋊Dic7C2×D4116yes—
286C4⋊Dic7—28no—
287C4⋊Dic7—44no—
288Dic7⋊C4—28no—
289Dic7⋊C4—28no—
290Dic7⋊C4—44no—
291Dic7⋊C4—44no—
292C4×Dic7—28no—
293C4×Dic7—44no—
294C26C2×D711yescharacteristic
295C24×C4—71no—
296C24×C4—71no—
297C2×#126—78no—
298C2×#126—148no—
299C22×C4⋊C4—71no—
300C22×C4⋊C4—71no—
301C22×C4⋊C4—71no—
302C22×C4⋊C4—71no—
303C22×C4⋊C4—71no—
304C22×C4⋊C4—71no—
305C22×C22⋊C4—71no—
306C22×C22⋊C4—71no—
307C22×C22⋊C4—71no—
308C22×C22⋊C4—71no—
309C22×C22⋊C4—71no—
310C22×C22⋊C4—78no—
311C22×C22⋊C4—71no—
312C22×C22⋊C4—71no—
313C22×C22⋊C4—71no—
314C22×C22⋊C4—71no—
315C22×C22⋊C4—71no—
316C22×C22⋊C4—148no—
317C22×C22⋊C4C2×D711yescharacteristic
318C22×C22⋊C4C2×D711yescharacteristic
319C22×C22⋊C4C2×D711yescharacteristic
320C22×C22⋊C4C2×D711yescharacteristic
321C22×C22⋊C4C2×D711yescharacteristic
322C22×C22⋊C4C2×D711yescharacteristic
323C22×C42—71no—
324C22×C42—71no—
325#397—78no—
326#397—78no—
327#397—78no—
328#396—78no—
329#388—78no—
330#388—78no—
331#388—78no—
332#385—78no—
333#385—78no—
334#380—78no—
335#379—78no—
336#379C2×D718yes—
337C4×C22⋊C4—78no—
338C2×#95—71no—
339C2×#95—71no—
340C2×#95—71no—
341C2×#95—71no—
342C2×#95—71no—
343C2×#95—71no—
344C2×#95—71no—
345C2×#95—71no—
346C23×C7—28no—
347C23×C7—28no—
348C23×C7—28no—
349C23×C7—28no—
350C23×C7—28no—
351C23×C7—28no—
352C23×C7—22no—
353C23×C7—22no—
354C23×C7—22no—
355C23×C7—22no—
356C23×C7—232no—
357C23×C7—28no—
358C23×C7—28no—
359C23×C7—28no—
360C23×C7—28no—
361C23×C7—28no—
362C23×C7—28no—
363C23×C7—22no—
364C23×C7—22no—
365C23×C7—22no—
366C23×C7—22no—
367C23×C7—22no—
368C23×C7—22no—
369C23×C7—22no—
370C23×C7—22no—
371C23×C7—22no—
372C23×C7—22no—
373C23×C7—22no—
374C23×C7—22no—
375C23×C7—416no—
376C23×C7—416no—
377C23×C7—416no—
378C23×C7—416no—
379C23×C7—416no—
380C23×C7—4128no—
381C23×C7—44no—
382C23×C7—44no—
383C23×C7—416no—
384C23×C7—44no—
385C23×C7—44no—
386C23×C7—44no—
387C23×C7—44no—
388C23×C7—44no—
389C23×C7—44no—
390C23×C7#126116yescomplemented
391C23×C7C22×D414yes—
392C23×C7C22×D412yes—
393C23×C7C2×#4114yes—
394C23×C7C2×#4112yes—
395C23×C7C2×#4114yes—
396C23×C7C2×#4114yes—
397C23×C7C2×#4114yes—
398C23×C7C2×#4112yes—
399C23×C7C2×#4112yes—
400C23×C7C2×#4112yes—
401C23×C7H(5,𝔽2)12yes—
402C23×C7H(5,𝔽2)12yes—
403C23×C7C2511yescharacteristic
404C2×C4×C7—22no—
405C2×C4×C7—22no—
406C2×C4×C7—22no—
407C2×C4×C7—22no—
408C2×C4×C7—22no—
409C2×C4×C7—22no—
410C2×C4×C7—22no—
411C2×C4×C7—22no—
412C2×C4×C7—22no—
413C2×C4×C7—22no—
414C2×C4×C7—22no—
415C2×C4×C7—22no—
416C2×C4×C7—44no—
417C2×C4×C7—44no—
418C2×C4×C7—44no—
419C2×C4×C7—44no—
420C2×Dic7—28no—
421C2×Dic7—28no—
422C2×Dic7—22no—
423C2×Dic7—22no—
424C2×Dic7—22no—
425C2×Dic7—22no—
426C2×Dic7—22no—
427C2×Dic7—22no—
428C2×Dic7—22no—
429C2×Dic7—22no—
430C2×Dic7—22no—
431C2×Dic7—22no—
432C2×Dic7—22no—
433C2×Dic7—22no—
434C2×Dic7—22no—
435C2×Dic7—22no—
436C2×Dic7—22no—
437C2×Dic7—22no—
438C2×Dic7—22no—
439C2×Dic7—22no—
440C2×Dic7—22no—
441C2×Dic7—22no—
442C2×Dic7—22no—
443C2×Dic7—22no—
444C2×Dic7—416no—
445C2×Dic7—416no—
446C2×Dic7—44no—
447C2×Dic7—44no—
448C2×Dic7—44no—
449C2×Dic7—44no—
450C2×Dic7—44no—
451C2×Dic7—44no—
452C2×Dic7C22×D414yes—
453C2×Dic7C22×D414yes—
454C25—24no—
455C25—24no—
456C25—24no—
457C25—24no—
458C25—24no—
459C25—42no—
460C25—42no—
461C25C22×D711yescharacteristic
462C25C22×D711yescharacteristic
463C25C22×D714yes—
464C25C22×D711yescharacteristic
465C23×C4—71no—
466C23×C4—71no—
467C23×C4—71no—
468C23×C4—71no—
469C23×C4—71no—
470C23×C4—71no—
471C23×C4—71no—
472C23×C4—71no—
473C23×C4—74no—
474C23×C4—74no—
475C23×C4—144no—
476C23×C4—144no—
477C23×C4—144no—
478C23×C4—144no—
479C23×C4—282no—
480C23×C4—282no—
481C23×C4C22×D711yescharacteristic
482C23×C4C22×D711yescharacteristic
483C23×C4C22×D711yescharacteristic
484C23×C4C22×D711yescharacteristic
485#126—1432no—
486C2×C4⋊C4—74no—
487C2×C4⋊C4—74no—
488C2×C4⋊C4—74no—
489C2×C4⋊C4—74no—
490C2×C4⋊C4—74no—
491C2×C4⋊C4—74no—
492C2×C4⋊C4—144no—
493C2×C4⋊C4—144no—
494C2×C4⋊C4—144no—
495C2×C4⋊C4—282no—
496C2×C4⋊C4—282no—
497C2×C4⋊C4—282no—
498C2×C22⋊C4—24no—
499C2×C22⋊C4—24no—
500C2×C22⋊C4—24no—
501C2×C22⋊C4—24no—
502C2×C22⋊C4—42no—
503C2×C22⋊C4—42no—
504C2×C22⋊C4—78no—
505C2×C22⋊C4—74no—
506C2×C22⋊C4—74no—
507C2×C22⋊C4—74no—
508C2×C22⋊C4—74no—
509C2×C22⋊C4—74no—
510C2×C22⋊C4—74no—
511C2×C22⋊C4—74no—
512C2×C22⋊C4—74no—
513C2×C22⋊C4—74no—
514C2×C22⋊C4—74no—
515C2×C22⋊C4—1432no—
516C2×C22⋊C4—144no—
517C2×C22⋊C4—144no—
518C2×C22⋊C4—144no—
519C2×C22⋊C4—144no—
520C2×C22⋊C4—144no—
521C2×C22⋊C4—144no—
522C2×C22⋊C4—144no—
523C2×C22⋊C4—282no—
524C2×C22⋊C4—282no—
525C2×C22⋊C4C22×D714yes—
526C2×C22⋊C4C22×D714yes—
527C2×C22⋊C4C22×D714yes—
528C2×C22⋊C4C22×D714yes—
529C2×C22⋊C4C22×D714yes—
530C2×C22⋊C4C22×D714yes—
531C2×C42—74no—
532C2×C42—74no—
533C2×C42—144no—
534C2×C42—282no—
535#95—74no—
536#95—74no—
537#95—74no—
538#95—74no—
539#95—74no—
540#95—74no—
541#95—74no—
542#95—74no—
543C22×C7—24no—
544C22×C7—24no—
545C22×C7—24no—
546C22×C7—24no—
547C22×C7—24no—
548C22×C7—24no—
549C22×C7—232no—
550C22×C7—24no—
551C22×C7—24no—
552C22×C7—24no—
553C22×C7—24no—
554C22×C7—24no—
555C22×C7—24no—
556C22×C7—464no—
557C22×C7—42no—
558C22×C7—42no—
559C22×C7—42no—
560C22×C7—42no—
561C22×C7—42no—
562C22×C7—42no—
563C22×C7—42no—
564C22×C7—42no—
565C22×C7—416no—
566C22×C7—416no—
567C22×C7#52514yes—
568C22×C7C2×#12614yes—
569C22×C7C2×#12618yescomplemented
570C22×C7#53814yes—
571C22×C7#54614yes—
572C22×C7#54614yes—
573C22×C7#55114yes—
574C22×C7#55114yes—
575C22×C7C23×D411yescharacteristic
576C22×C7C22×#4111yescharacteristic
577C22×C7C22×#4111yescharacteristic
578C22×C7C22×#4111yescharacteristic
579C22×C7C22×#4111yescharacteristic
580C22×C7C2×H(5,𝔽2)11yescharacteristic
581C22×C7C2×H(5,𝔽2)11yescharacteristic
582C4×C7—42no—
583C4×C7—42no—
584C4×C7—42no—
585C4×C7—42no—
586Dic7—24no—
587Dic7—24no—
588Dic7—42no—
589Dic7—42no—
590Dic7—42no—
591Dic7—42no—
592Dic7—42no—
593Dic7—42no—
594C24—22no—
595C24—22no—
596C24—22no—
597C24—22no—
598C24—232no—
599C24—22no—
600C24—22no—
601C24—28no—
602C24—22no—
603C24—28no—
604C24—28no—
605C24—22no—
606C24—22no—
607C24—22no—
608C24—22no—
609C24—22no—
610C24—22no—
611C24—22no—
612C24—22no—
613C24—22no—
614C24—28no—
615C24—28no—
616C24—44no—
617C24—44no—
618C24—416no—
619C24—416no—
620C24—416no—
621C24—416no—
622C24—416no—
623C24—416no—
624C24#115714yes—
625C24D4×D714yes—
626C24#115914yes—
627C24#115914yes—
628C24#115914yes—
629C24C23×D712yes—
630C24C23×D712yes—
631C24C23×D712yes—
632C24C23×D711yescharacteristic
633C22×C4—22no—
634C22×C4—22no—
635C22×C4—22no—
636C22×C4—22no—
637C22×C4—22no—
638C22×C4—22no—
639C22×C4—22no—
640C22×C4—22no—
641C22×C4—22no—
642C22×C4—22no—
643C22×C4—22no—
644C22×C4—22no—
645C22×C4—74no—
646C22×C4—74no—
647C22×C4—72no—
648C22×C4—72no—
649C22×C4—72no—
650C22×C4—72no—
651C22×C4—72no—
652C22×C4—72no—
653C22×C4—72no—
654C22×C4—72no—
655C22×C4—148no—
656C22×C4—148no—
657C22×C4—142no—
658C22×C4—142no—
659C22×C4—142no—
660C22×C4—142no—
661C22×C4—142no—
662C22×C4—142no—
663C22×C4—148no—
664C22×C4—142no—
665C22×C4—142no—
666C22×C4—142no—
667C22×C4—142no—
668C22×C4—142no—
669C22×C4—142no—
670C22×C4—142no—
671C22×C4—142no—
672C22×C4—142no—
673C22×C4—148no—
674C22×C4—142no—
675C22×C4—142no—
676C22×C4—142no—
677C22×C4—142no—
678C22×C4—142no—
679C22×C4—142no—
680C22×C4—142no—
681C22×C4—284no—
682C22×C4—284no—
683C22×C4—2816no—
684C22×C4—2816no—
685C22×C4C23×D712yes—
686C22×C4C23×D712yes—
687C22×C4C23×D712yes—
688C22×C4C23×D712yes—
689C4⋊C4—148no—
690C4⋊C4—148no—
691C4⋊C4—148no—
692C4⋊C4—284no—
693C4⋊C4—284no—
694C4⋊C4—284no—
695C22⋊C4—28no—
696C22⋊C4—28no—
697C22⋊C4—28no—
698C22⋊C4—28no—
699C22⋊C4—44no—
700C22⋊C4—44no—
701C22⋊C4—716no—
702C22⋊C4—148no—
703C22⋊C4—148no—
704C22⋊C4—148no—
705C22⋊C4—148no—
706C22⋊C4—148no—
707C22⋊C4—148no—
708C22⋊C4—148no—
709C22⋊C4—284no—
710C22⋊C4—284no—
711C42—148no—
712C42—284no—
713C2×C7—28no—
714C2×C7—44no—
715C2×C7—44no—
716C2×C7#248018yescomplemented
717C2×C7C2×#52511yescharacteristic
718C2×C7C22×#12611yescharacteristic
719C2×C7C2×#53811yescharacteristic
720C2×C7C2×#54611yescharacteristic
721C2×C7C2×#54611yescharacteristic
722C2×C7C2×#55111yescharacteristic
723C2×C7C2×#55111yescharacteristic
724C23—28no—
725C23—28no—
726C23—28no—
727C23—28no—
728C23—28no—
729C23—28no—
730C23—22no—
731C23—22no—
732C23—22no—
733C23—22no—
734C23—232no—
735C23—28no—
736C23—28no—
737C23—28no—
738C23—28no—
739C23—28no—
740C23—28no—
741C23—22no—
742C23—22no—
743C23—22no—
744C23—22no—
745C23—22no—
746C23—22no—
747C23—22no—
748C23—22no—
749C23—22no—
750C23—22no—
751C23—22no—
752C23—22no—
753C23—416no—
754C23—416no—
755C23—416no—
756C23—416no—
757C23—416no—
758C23—4128no—
759C23—44no—
760C23—44no—
761C23—416no—
762C23—44no—
763C23—44no—
764C23—44no—
765C23—44no—
766C23—44no—
767C23—44no—
768C23#6442116yescomplemented
769C23C2×#115714yes—
770C23C2×#115712yes—
771C23C2×D4×D714yes—
772C23C2×D4×D712yes—
773C23C2×#115914yes—
774C23C2×#115914yes—
775C23C2×#115914yes—
776C23C2×#115912yes—
777C23C2×#115912yes—
778C23C2×#115912yes—
779C23#654812yes—
780C23#654812yes—
781C23C24×D711yescharacteristic
782C2×C4—22no—
783C2×C4—22no—
784C2×C4—22no—
785C2×C4—22no—
786C2×C4—22no—
787C2×C4—22no—
788C2×C4—22no—
789C2×C4—22no—
790C2×C4—22no—
791C2×C4—22no—
792C2×C4—22no—
793C2×C4—22no—
794C2×C4—44no—
795C2×C4—44no—
796C2×C4—44no—
797C2×C4—44no—
798C2×C4—74no—
799C2×C4—74no—
800C2×C4—148no—
801C2×C4—148no—
802C2×C4—142no—
803C2×C4—142no—
804C2×C4—142no—
805C2×C4—142no—
806C2×C4—142no—
807C2×C4—142no—
808C2×C4—142no—
809C2×C4—142no—
810C2×C4—142no—
811C2×C4—142no—
812C2×C4—142no—
813C2×C4—142no—
814C2×C4—142no—
815C2×C4—142no—
816C2×C4—142no—
817C2×C4—142no—
818C2×C4—142no—
819C2×C4—142no—
820C2×C4—142no—
821C2×C4—142no—
822C2×C4—142no—
823C2×C4—142no—
824C2×C4—2816no—
825C2×C4—2816no—
826C2×C4—284no—
827C2×C4—284no—
828C2×C4—284no—
829C2×C4—284no—
830C2×C4—284no—
831C2×C4—284no—
832C7C2×#248011yescharacteristic, complemented, Sylow
833C22—24no—
834C22—24no—
835C22—24no—
836C22—24no—
837C22—24no—
838C22—24no—
839C22—232no—
840C22—24no—
841C22—24no—
842C22—24no—
843C22—24no—
844C22—24no—
845C22—24no—
846C22—464no—
847C22—42no—
848C22—42no—
849C22—42no—
850C22—42no—
851C22—42no—
852C22—42no—
853C22—42no—
854C22—42no—
855C22—416no—
856C22—416no—
857C22C2×#644214yes—
858C22C2×#644218yescomplemented
859C22#9018114yes—
860C22#9018614yes—
861C22#9027714yes—
862C22#9027814yes—
863C22#9028214yes—
864C22#9028414yes—
865C22C22×#115711yescharacteristic
866C22C22×D4×D711yescharacteristic
867C22C22×#115911yescharacteristic
868C22C22×#115911yescharacteristic
869C22C22×#115911yescharacteristic
870C22C2×#654811yescharacteristic
871C22C2×#654811yescharacteristic
872C4—42no—
873C4—42no—
874C4—42no—
875C4—42no—
876C4—144no—
877C4—144no—
878C4—282no—
879C4—282no—
880C4—282no—
881C4—282no—
882C4—282no—
883C4—282no—
884C2—28no—
885C2—44no—
886C2—44no—
887C2#1173127518yesdirect product factor
888C2C22×#644211yescharacteristic
889C2C2×#9018611yescharacteristic
890C2C2×#9018111yescharacteristic
891C2C2×#9027711yescharacteristic
892C2C2×#9028411yescharacteristic
893C2C2×#9027811yescharacteristic
894C2C2×#9028211yescharacteristic
subgroupG/H
centerC24C23×D7
commutator, cosocleC23×C7C25
FrattiniC23C24×D7
FittingC2×C7×#379C2
socleC24×C7C24
prime radicalC26×C7C22
hypercenterC2×#379D7
hypocenterC7C2×#2480
LCSG ▷ C23×C7 ▷ C7
UCSC1 ◁ C24 ◁ C2×#379

Complements

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

NH ≅ G/Ntype
2. C22×#6442C2semidirect
5. C2×#89725C2semidirect
6. C2×#89724C2semidirect
7. C2×#89724C2semidirect
8. C2×#89720C2semidirect
9. C2×#89717C2semidirect
10. C2×#89716C2semidirect
11. C2×#89723C2semidirect
12. C2×#89722C2semidirect
13. C2×#89718C2semidirect
14. C2×#89714C2semidirect
15. C2×C22⋊C4×Dic7C2semidirect
16. #11731275C2direct (N × H)
38. C22×C4⋊Dic7C22semidirect
39. C22×C4⋊Dic7C22semidirect
40. C22×Dic7⋊C4C22semidirect
41. C22×Dic7⋊C4C22semidirect
42. C22×Dic7⋊C4C22semidirect
43. C22×Dic7⋊C4C22semidirect
44. C22×C4×Dic7C22semidirect
45. C22×C4×Dic7C22semidirect
47. C2×#6442C22semidirect
50. C2×C7⋊#95C22semidirect
51. C2×C7⋊#95C22semidirect
52. C2×C7⋊#95C22semidirect
53. C2×C7⋊#95C22semidirect
54. C2×C7⋊#95C22semidirect
55. C2×C7⋊#95C22semidirect
56. C2×C7⋊#95C22semidirect
57. C2×C7⋊#95C22semidirect
58. #89725C22semidirect
59. #89724C22semidirect
60. #89724C22semidirect
61. #89723C22semidirect
62. #89722C22semidirect
63. #89720C22semidirect
64. #89718C22semidirect
65. #89717C22semidirect
66. #89716C22semidirect
67. #89714C22semidirect
68. C22⋊C4×Dic7C22semidirect
136. C2×C4⋊Dic7C23semidirect
137. C2×C4⋊Dic7C23semidirect
142. C2×Dic7⋊C4C23semidirect
143. C2×Dic7⋊C4C23semidirect
144. C2×Dic7⋊C4C23semidirect
145. C2×Dic7⋊C4C23semidirect
148. C2×C4×Dic7C23semidirect
149. C2×C4×Dic7C23semidirect
151. C7⋊#95C23semidirect
152. C7⋊#95C23semidirect
153. C7⋊#95C23semidirect
154. C7⋊#95C23semidirect
155. C7⋊#95C23semidirect
156. C7⋊#95C23semidirect
157. C7⋊#95C23semidirect
158. C7⋊#95C23semidirect
390. C23×C7#126semidirect
569. C22×C7C2×#126semidirect
716. C2×C7#2480semidirect
768. C23#6442semidirect
832. C7C2×#2480semidirect
858. C22C2×#6442semidirect
887. C2#11731275direct (N × H)

Maximal subgroups

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

subgroupindex
C23×C22⋊Dic72
C22×#64422
C2×C7×#3792
C2×#900192
C2×#897252
C2×#897242
C2×#897202
C2×#897172
C2×#897162
C2×#897232
C2×#897222
C2×#897182
C2×#897142
C2×C22⋊C4×Dic72
#117312752
C2×#24807