Finite Group Databasebeta

← C2×#11731034 #13521911

Subgroups — C2×#11731034 #13521911

Order 1792.

3438 conjugacy classes of subgroups.

The subgroup lattice has 880 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#6492C211yesmaximal, characteristic, complemented
2C22×C4×D28C211yesmaximal, characteristic, complemented
3C2×C4×C7×C22⋊C4C211yesmaximal, characteristic, complemented
4C2×#89985C211yesmaximal, characteristic, complemented
5C2×#89732C211yesmaximal, characteristic
6C2×#89728C211yesmaximal, characteristic, complemented
7C2×#89728C211yesmaximal, characteristic, complemented
8C2×#89720C211yesmaximal, characteristic, complemented
9C2×#89712C211yesmaximal, characteristic, complemented
10C2×#89712C211yesmaximal, characteristic, complemented
11C2×#89705C211yesmaximal, characteristic, complemented
12#11731034C2116yesmaximal, direct product factor
13C2×#89436C211yesmaximal, characteristic, complemented
14C2×#89439C211yesmaximal, characteristic, complemented
15C2×#89432C211yesmaximal, characteristic, complemented
16C2×#89444C211yesmaximal, characteristic, complemented
17C24×C4×C7C2211yescharacteristic
18C23×C22⋊D7C2211yescharacteristic
19C23×C22⋊D7C2211yescharacteristic
20C23×D28C2211yescharacteristic
21C23×C4×D7C2211yescharacteristic
22C23×C4×D7C2211yescharacteristic
23C22×C7×C22⋊C4C2211yescharacteristic
24C22×C7×C22⋊C4C2211yescharacteristic
25C22×C42×C7C2211yescharacteristic
26C22×C42×C7C2211yescharacteristic
27C22×C22⋊Dic7C2211yescharacteristic
28C22×C22⋊Dic7C2211yescharacteristic
29C2×#6492—28no—
30C2×#6492C2218yescomplemented
31C22×(C2×D7)⋊C4C2211yescharacteristic
32C22×(C2×D7)⋊C4C2211yescharacteristic
33C22×(C2×D7)⋊C4C2211yescharacteristic
34C22×(C2×D7)⋊C4C2211yescharacteristic
35C22×(C2×D7)⋊C4C2211yescharacteristic
36C22×(C2×D7)⋊C4C2211yescharacteristic
37C22×(C2×D7)⋊C4C2211yescharacteristic
38C22×(C2×D7)⋊C4C2211yescharacteristic
39C22×C4⋊Dic7C2211yescharacteristic
40C22×Dic7⋊C4C2211yescharacteristic
41C22×Dic7⋊C4C2211yescharacteristic
42C22×Dic7⋊C4C2211yescharacteristic
43C22×Dic7⋊C4C2211yescharacteristic
44C2×C4×D28—28no—
45C2×C4×D28C2218yescomplemented
46C4×C7×C22⋊C4C2218yescomplemented
47C2×C7×#95C2211yescharacteristic
48C2×C7×#95C2211yescharacteristic
49#89985C2218yescomplemented
50C2×C7⋊#95C2211yescharacteristic
51C2×C7⋊#95C2211yescharacteristic
52C2×C7⋊#95C2211yescharacteristic
53C2×C7⋊#95C2211yescharacteristic
54C2×C7⋊#95C2211yescharacteristic
55C2×C7⋊#95C2211yescharacteristic
56C2×C7⋊#95C2211yescharacteristic
57C2×C7⋊#95C2211yescharacteristic
58#89732C2218yes—
59#89728C2218yescomplemented
60#89728C2218yescomplemented
61#89720C2218yescomplemented
62#89712C2218yescomplemented
63#89712C2218yescomplemented
64#89705C2218yescomplemented
65#89444C2218yescomplemented
66#89439C2218yescomplemented
67#89436C2218yescomplemented
68#89432C2218yescomplemented
69C2×#2457—71nomaximal, Sylow
70C25×C7C2311yescharacteristic
71C24×D7C2311yescharacteristic
72C24×D7C2311yescharacteristic
73C23×C4×C7—24no—
74C23×C4×C7—24no—
75C23×C4×C7—42no—
76C23×C4×C7C2311yescharacteristic
77C23×C4×C7C2311yescharacteristic
78C23×C4×C7C2311yescharacteristic
79C23×C4×C7C2314yes—
80C23×C4×C7C2311yescharacteristic
81C23×C4×C7C2311yescharacteristic
82C23×C4×C7C2311yescharacteristic
83C22×C22⋊D7—24no—
84C22×C22⋊D7—24no—
85C22×C22⋊D7—24no—
86C22×C22⋊D7—24no—
87C22×C22⋊D7—42no—
88C22×C22⋊D7—42no—
89C22×C22⋊D7C2314yes—
90C22×C22⋊D7C2314yes—
91C23×Dic7C2311yescharacteristic
92C23×Dic7C2311yescharacteristic
93C23×Dic7C2311yescharacteristic
94C23×Dic7C2311yescharacteristic
95C23×Dic7C2311yescharacteristic
96C23×Dic7C2311yescharacteristic
97C22×D28—24no—
98C22×D28—24no—
99C22×D28—24no—
100C22×D28C2314yes—
101C22×C4×D7—24no—
102C22×C4×D7—24no—
103C22×C4×D7—24no—
104C22×C4×D7—24no—
105C22×C4×D7—42no—
106C22×C4×D7—42no—
107C22×C4×D7C2314yes—
108C22×C4×D7C2314yes—
109C2×C7×C22⋊C4—24no—
110C2×C7×C22⋊C4—24no—
111C2×C7×C22⋊C4C2314yes—
112C2×C7×C22⋊C4C2314yes—
113C2×C42×C7—24no—
114C2×C42×C7—42no—
115C2×C42×C7C2314yes—
116C2×C42×C7C2314yes—
117C2×C22⋊Dic7—24no—
118C2×C22⋊Dic7—42no—
119C2×C22⋊Dic7C2314yes—
120C2×C22⋊Dic7C2314yes—
121#6492—232no—
122C2×(C2×D7)⋊C4—24no—
123C2×(C2×D7)⋊C4—24no—
124C2×(C2×D7)⋊C4—24no—
125C2×(C2×D7)⋊C4—42no—
126C2×(C2×D7)⋊C4—42no—
127C2×(C2×D7)⋊C4—42no—
128C2×(C2×D7)⋊C4—42no—
129C2×(C2×D7)⋊C4D418yescomplemented
130C2×(C2×D7)⋊C4C2314yes—
131C2×(C2×D7)⋊C4C2314yes—
132C2×(C2×D7)⋊C4C2314yes—
133C2×(C2×D7)⋊C4C2314yes—
134C2×(C2×D7)⋊C4C2314yes—
135C2×(C2×D7)⋊C4C2314yes—
136C2×(C2×D7)⋊C4C2314yes—
137C2×(C2×D7)⋊C4C2314yes—
138C2×C4⋊Dic7—24no—
139C2×C4⋊Dic7C2314yes—
140C2×Dic7⋊C4—24no—
141C2×Dic7⋊C4—24no—
142C2×Dic7⋊C4—24no—
143C2×Dic7⋊C4—42no—
144C2×Dic7⋊C4C2314yes—
145C2×Dic7⋊C4C2314yes—
146C2×Dic7⋊C4C2314yes—
147C2×Dic7⋊C4C2314yes—
148C4×D28—232no—
149C7×#95C2314yes—
150C7×#95C2314yes—
151C7⋊#95C2314yes—
152C7⋊#95C2314yes—
153C7⋊#95C2314yes—
154C7⋊#95C2314yes—
155C7⋊#95C2314yes—
156C7⋊#95C2314yes—
157C7⋊#95C2314yes—
158C7⋊#95C2314yes—
159C22×#123—71no—
160C22×C4×D4—71no—
161#2457—716no—
162C2×#400—71no—
163C2×#396—71no—
164C2×#394—71no—
165C2×#392—71no—
166C2×#388—71no—
167C2×#388—71no—
168C2×#387—71no—
169C2×#386—71no—
170C2×#386—71no—
171C2×#386—71no—
172C2×#381—71no—
173C2×#380—71no—
174C2×C4×C22⋊C4D711yescharacteristic, complemented
175C24×C7—22no—
176C24×C7—22no—
177C24×C7—22no—
178C24×C7—22no—
179C24×C7—22no—
180C24×C7—22no—
181C24×C7#4114yes—
182C24×C7C2412yes—
183C24×C7C2411yescharacteristic
184C23×D7—22no—
185C23×D7—22no—
186C23×D7—22no—
187C23×D7—22no—
188C23×D7—22no—
189C23×D7—22no—
190C23×D7—22no—
191C23×D7—22no—
192C23×D7—22no—
193C23×D7—22no—
194C23×D7—22no—
195C23×D7—22no—
196C23×D7C2×D414yes—
197C23×D7#4114yes—
198C23×D7C2412yes—
199C23×D7C2412yes—
200C22×C4×C7—22no—
201C22×C4×C7—22no—
202C22×C4×C7—22no—
203C22×C4×C7—22no—
204C22×C4×C7—22no—
205C22×C4×C7—22no—
206C22×C4×C7—22no—
207C22×C4×C7—22no—
208C22×C4×C7—22no—
209C22×C4×C7—22no—
210C22×C4×C7—28no—
211C22×C4×C7—22no—
212C22×C4×C7—22no—
213C22×C4×C7—22no—
214C22×C4×C7—22no—
215C22×C4×C7—22no—
216C22×C4×C7—28no—
217C22×C4×C7—44no—
218C22×C4×C7—416no—
219C22×C4×C7C2×D414yes—
220C22×C4×C7#4114yes—
221C22×C4×C7#4114yes—
222C22×C4×C7C2412yes—
223C22×C4×C7C2412yes—
224C22×C4×C7C2412yes—
225C22×C4×C7C2412yes—
226C22×C4×C7C2412yes—
227C22×C4×C7C2412yes—
228C2×C22⋊D7—28no—
229C2×C22⋊D7—28no—
230C2×C22⋊D7—28no—
231C2×C22⋊D7—28no—
232C2×C22⋊D7—44no—
233C2×C22⋊D7—44no—
234C2×C22⋊D7—416no—
235C2×C22⋊D7—416no—
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—22no—
245C22×Dic7—22no—
246C22×Dic7—22no—
247C22×Dic7—22no—
248C22×Dic7—22no—
249C22×Dic7—22no—
250C22×Dic7—22no—
251C22×Dic7—22no—
252C22×Dic7—22no—
253C22×Dic7C2×D414yes—
254C22×Dic7C2412yes—
255C22×Dic7C2412yes—
256C22×Dic7C2412yes—
257C22×Dic7C2412yes—
258C22×Dic7C2412yes—
259C22×Dic7C2412yes—
260C2×D28—232no—
261C2×D28—28no—
262C2×D28—28no—
263C2×D28—28no—
264C2×C4×D7—28no—
265C2×C4×D7—28no—
266C2×C4×D7—28no—
267C2×C4×D7—28no—
268C2×C4×D7—44no—
269C2×C4×D7—44no—
270C2×C4×D7—416no—
271C2×C4×D7—416no—
272C7×C22⋊C4—28no—
273C7×C22⋊C4—28no—
274C42×C7—28no—
275C42×C7—44no—
276C22⋊Dic7—28no—
277C22⋊Dic7—44no—
278(C2×D7)⋊C4—28no—
279(C2×D7)⋊C4—28no—
280(C2×D7)⋊C4—28no—
281(C2×D7)⋊C4—44no—
282(C2×D7)⋊C4—44no—
283(C2×D7)⋊C4—44no—
284(C2×D7)⋊C4—44no—
285(C2×D7)⋊C4C2×D4116yescomplemented
286C4⋊Dic7—28no—
287Dic7⋊C4—28no—
288Dic7⋊C4—28no—
289Dic7⋊C4—28no—
290Dic7⋊C4—44no—
291C23×D4—71no—
292C23×D4—71no—
293C23×D4—71no—
294C24×C4—71no—
295C24×C4—71no—
296C24×C4C2×D711yescharacteristic
297C2×#123—78no—
298C2×#123—148no—
299C2×C4×D4—78no—
300C2×C4×D4—148no—
301C22×C4⋊C4—71no—
302C22×C4⋊C4—71no—
303C22×C4⋊C4—71no—
304C22×C4⋊C4—71no—
305C22×C4⋊C4—71no—
306C22×C22⋊C4—71no—
307C22×C22⋊C4—71no—
308C22×C22⋊C4—71no—
309C22×C22⋊C4—71no—
310C22×C22⋊C4—71no—
311C22×C22⋊C4—71no—
312C22×C22⋊C4—71no—
313C22×C22⋊C4—71no—
314C22×C22⋊C4—71no—
315C22×C22⋊C4—71no—
316C22×C22⋊C4C2×D711yescharacteristic
317C22×C22⋊C4C2×D711yescharacteristic
318C22×C42C2×D711yescharacteristic
319C22×C42C2×D711yescharacteristic
320#400—78no—
321#396—78no—
322#394—78no—
323#392—78no—
324#388—78no—
325#388—78no—
326#387—78no—
327#386—78no—
328#386—78no—
329#386—78no—
330#381—78no—
331#380—78no—
332C4×C22⋊C4C2×D718yescomplemented
333C2×#95—71no—
334C2×#95—71no—
335C2×#95—71no—
336C2×#95—71no—
337C2×#95—71no—
338C2×#95—71no—
339C2×#95—71no—
340C2×#95—71no—
341C2×#95C2×D711yescharacteristic
342C2×#95C2×D711yescharacteristic
343C23×C7—28no—
344C23×C7—28no—
345C23×C7—28no—
346C23×C7—22no—
347C23×C7—22no—
348C23×C7—22no—
349C23×C7—22no—
350C23×C7—22no—
351C23×C7—22no—
352C23×C7—44no—
353C23×C7—44no—
354C23×C7—44no—
355C23×C7—44no—
356C23×C7C22×D412yes—
357C23×C7C2×#4114yes—
358C23×C7C2×#4112yes—
359C23×C7C2×#4112yes—
360C23×C7C2×#4112yes—
361C23×C7C2×#4112yes—
362C23×C7H(5,𝔽2)12yes—
363C23×C7H(5,𝔽2)12yes—
364C23×C7C2511yescharacteristic
365C22×D7—28no—
366C22×D7—28no—
367C22×D7—28no—
368C22×D7—28no—
369C22×D7—28no—
370C22×D7—28no—
371C22×D7—22no—
372C22×D7—22no—
373C22×D7—22no—
374C22×D7—22no—
375C22×D7—22no—
376C22×D7—22no—
377C22×D7—22no—
378C22×D7—22no—
379C22×D7—22no—
380C22×D7—22no—
381C22×D7—22no—
382C22×D7—22no—
383C22×D7—44no—
384C22×D7—44no—
385C22×D7—44no—
386C22×D7—44no—
387C22×D7—44no—
388C22×D7—44no—
389C22×D7—44no—
390C22×D7—44no—
391C22×D7C22×D414yes—
392C22×D7C2×#4114yes—
393C2×C4×C7—28no—
394C2×C4×C7—28no—
395C2×C4×C7—28no—
396C2×C4×C7—22no—
397C2×C4×C7—22no—
398C2×C4×C7—22no—
399C2×C4×C7—22no—
400C2×C4×C7—22no—
401C2×C4×C7—22no—
402C2×C4×C7—22no—
403C2×C4×C7—22no—
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—416no—
412C2×C4×C7—44no—
413C2×C4×C7—44no—
414C2×C4×C7—44no—
415C2×C4×C7C22×D414yes—
416C2×C4×C7C2×#4114yes—
417C2×C4×C7C2×#4114yes—
418C22⋊D7—416no—
419C22⋊D7—416no—
420C2×Dic7—28no—
421C2×Dic7—22no—
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—44no—
439C2×Dic7—44no—
440C2×Dic7—44no—
441C2×Dic7—44no—
442C2×Dic7—44no—
443C2×Dic7C22×D414yes—
444D28—232no—
445C4×D7—416no—
446C4×D7—416no—
447C25—71no—
448C25—71no—
449C25C22×D711yescharacteristic
450C22×D4—74no—
451C22×D4—74no—
452C22×D4—74no—
453C22×D4—144no—
454C22×D4—144no—
455C22×D4—144no—
456C22×D4—144no—
457C22×D4—144no—
458C22×D4—144no—
459C22×D4—144no—
460C22×D4—282no—
461C22×D4—282no—
462C23×C4—24no—
463C23×C4—24no—
464C23×C4—42no—
465C23×C4—71no—
466C23×C4—71no—
467C23×C4—71no—
468C23×C4—71no—
469C23×C4—71no—
470C23×C4—71no—
471C23×C4—74no—
472C23×C4—74no—
473C23×C4—144no—
474C23×C4—144no—
475C23×C4—144no—
476C23×C4—144no—
477C23×C4—282no—
478C23×C4—282no—
479C23×C4C22×D711yescharacteristic
480C23×C4C22×D711yescharacteristic
481C23×C4C22×D711yescharacteristic
482C23×C4C22×D714yes—
483C23×C4C22×D711yescharacteristic
484C23×C4C22×D711yescharacteristic
485C23×C4C22×D711yescharacteristic
486#123—1432no—
487C4×D4—1432no—
488C2×C4⋊C4—74no—
489C2×C4⋊C4—74no—
490C2×C4⋊C4—74no—
491C2×C4⋊C4—74no—
492C2×C4⋊C4—74no—
493C2×C4⋊C4—144no—
494C2×C4⋊C4—144no—
495C2×C4⋊C4—144no—
496C2×C4⋊C4—144no—
497C2×C4⋊C4—282no—
498C2×C22⋊C4—24no—
499C2×C22⋊C4—24no—
500C2×C22⋊C4—78no—
501C2×C22⋊C4—74no—
502C2×C22⋊C4—74no—
503C2×C22⋊C4—74no—
504C2×C22⋊C4—74no—
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—144no—
512C2×C22⋊C4—144no—
513C2×C22⋊C4—144no—
514C2×C22⋊C4—144no—
515C2×C22⋊C4—282no—
516C2×C22⋊C4—282no—
517C2×C22⋊C4—282no—
518C2×C22⋊C4—282no—
519C2×C22⋊C4—282no—
520C2×C22⋊C4C22×D714yes—
521C2×C22⋊C4C22×D714yes—
522C2×C42—24no—
523C2×C42—42no—
524C2×C42C22×D714yes—
525C2×C42C22×D714yes—
526#95—74no—
527#95—74no—
528#95—74no—
529#95—74no—
530#95—74no—
531#95—74no—
532#95—74no—
533#95—74no—
534#95C22×D714yes—
535#95C22×D714yes—
536C22×C7—24no—
537C22×C7—24no—
538C22×C7—24no—
539C22×C7—42no—
540C22×C7—42no—
541C22×C7—42no—
542C22×C7—42no—
543C22×C7—416no—
544C22×C7#52514yes—
545C22×C7#52914yes—
546C22×C7#54014yes—
547C22×C7#54614yes—
548C22×C7#54614yes—
549C22×C7#55114yes—
550C22×C7#55314yes—
551C22×C7C23×D411yescharacteristic
552C22×C7C22×#4111yescharacteristic
553C22×C7C22×#4111yescharacteristic
554C22×C7C22×#4111yescharacteristic
555C22×C7C22×#4111yescharacteristic
556C22×C7C2×H(5,𝔽2)11yescharacteristic
557C22×C7C2×H(5,𝔽2)11yescharacteristic
558C2×D7—24no—
559C2×D7—24no—
560C2×D7—24no—
561C2×D7—24no—
562C2×D7—24no—
563C2×D7—24no—
564C2×D7—42no—
565C2×D7—42no—
566C2×D7—42no—
567C2×D7—42no—
568C2×D7—42no—
569C2×D7—42no—
570C2×D7—42no—
571C2×D7—42no—
572C2×D7—416no—
573C2×D7—416no—
574C4×C7—24no—
575C4×C7—24no—
576C4×C7—24no—
577C4×C7—42no—
578C4×C7—42no—
579C4×C7—42no—
580Dic7—24no—
581Dic7—42no—
582Dic7—42no—
583Dic7—42no—
584Dic7—42no—
585Dic7—42no—
586C24—22no—
587C24—22no—
588C24—22no—
589C24—22no—
590C24—22no—
591C24—22no—
592C24—74no—
593C24—74no—
594C24—72no—
595C24—72no—
596C24—142no—
597C24—142no—
598C24—142no—
599C24—142no—
600C24—142no—
601C24—142no—
602C24—142no—
603C24—142no—
604C24—142no—
605C24—142no—
606C24—142no—
607C24—142no—
608C24#115714yes—
609C24C23×D712yes—
610C24C23×D711yescharacteristic
611C2×D4—148no—
612C2×D4—148no—
613C2×D4—1432no—
614C2×D4—148no—
615C2×D4—148no—
616C2×D4—148no—
617C2×D4—148no—
618C2×D4—148no—
619C2×D4—284no—
620C2×D4—284no—
621C2×D4—2816no—
622C2×D4—2816no—
623C22×C4—22no—
624C22×C4—22no—
625C22×C4—22no—
626C22×C4—22no—
627C22×C4—22no—
628C22×C4—22no—
629C22×C4—22no—
630C22×C4—22no—
631C22×C4—28no—
632C22×C4—22no—
633C22×C4—22no—
634C22×C4—22no—
635C22×C4—22no—
636C22×C4—22no—
637C22×C4—22no—
638C22×C4—22no—
639C22×C4—28no—
640C22×C4—44no—
641C22×C4—416no—
642C22×C4—74no—
643C22×C4—72no—
644C22×C4—72no—
645C22×C4—72no—
646C22×C4—72no—
647C22×C4—72no—
648C22×C4—72no—
649C22×C4—148no—
650C22×C4—148no—
651C22×C4—142no—
652C22×C4—142no—
653C22×C4—142no—
654C22×C4—142no—
655C22×C4—142no—
656C22×C4—142no—
657C22×C4—142no—
658C22×C4—142no—
659C22×C4—142no—
660C22×C4—142no—
661C22×C4—142no—
662C22×C4—142no—
663C22×C4—142no—
664C22×C4—142no—
665C22×C4—142no—
666C22×C4—142no—
667C22×C4—142no—
668C22×C4—148no—
669C22×C4—148no—
670C22×C4—284no—
671C22×C4—284no—
672C22×C4—2816no—
673C22×C4—2816no—
674C22×C4#115714yes—
675C22×C4#115714yes—
676C22×C4D4×D714yes—
677C22×C4C23×D712yes—
678C22×C4C23×D712yes—
679C22×C4C23×D712yes—
680C22×C4C23×D712yes—
681C22×C4C23×D712yes—
682C22×C4C23×D712yes—
683C4⋊C4—148no—
684C4⋊C4—148no—
685C4⋊C4—148no—
686C4⋊C4—148no—
687C4⋊C4—284no—
688C22⋊C4—28no—
689C22⋊C4—28no—
690C22⋊C4—716no—
691C22⋊C4—148no—
692C22⋊C4—148no—
693C22⋊C4—148no—
694C22⋊C4—148no—
695C22⋊C4—284no—
696C22⋊C4—284no—
697C22⋊C4—284no—
698C22⋊C4—284no—
699C22⋊C4—284no—
700C42—28no—
701C42—44no—
702C2×C7—44no—
703C2×C7#245718yescomplemented
704C2×C7C2×#52511yescharacteristic
705C2×C7C2×#52911yescharacteristic
706C2×C7C2×#54011yescharacteristic
707C2×C7C2×#54611yescharacteristic
708C2×C7C2×#54611yescharacteristic
709C2×C7C2×#55111yescharacteristic
710C2×C7C2×#55311yescharacteristic
711D7—44no—
712D7—44no—
713C23—28no—
714C23—28no—
715C23—28no—
716C23—22no—
717C23—22no—
718C23—22no—
719C23—22no—
720C23—22no—
721C23—22no—
722C23—44no—
723C23—44no—
724C23—44no—
725C23—44no—
726C23—74no—
727C23—74no—
728C23—148no—
729C23—148no—
730C23—148no—
731C23—148no—
732C23—148no—
733C23—148no—
734C23—142no—
735C23—142no—
736C23—142no—
737C23—142no—
738C23—142no—
739C23—142no—
740C23—142no—
741C23—142no—
742C23—142no—
743C23—142no—
744C23—142no—
745C23—142no—
746C23—284no—
747C23—284no—
748C23—284no—
749C23—284no—
750C23—284no—
751C23—284no—
752C23—284no—
753C23—284no—
754C23C2×#115714yes—
755C23C2×#115712yes—
756C23C2×#115712yes—
757C23C2×#115712yes—
758C23C2×D4×D712yes—
759C23#654812yes—
760C23D7×#4112yes—
761C23#655312yes—
762C23C24×D711yescharacteristic
763D4—1432no—
764D4—2816no—
765D4—2816no—
766C2×C4—28no—
767C2×C4—28no—
768C2×C4—28no—
769C2×C4—22no—
770C2×C4—22no—
771C2×C4—22no—
772C2×C4—22no—
773C2×C4—22no—
774C2×C4—22no—
775C2×C4—22no—
776C2×C4—22no—
777C2×C4—22no—
778C2×C4—22no—
779C2×C4—22no—
780C2×C4—22no—
781C2×C4—22no—
782C2×C4—22no—
783C2×C4—22no—
784C2×C4—416no—
785C2×C4—44no—
786C2×C4—44no—
787C2×C4—44no—
788C2×C4—74no—
789C2×C4—148no—
790C2×C4—142no—
791C2×C4—142no—
792C2×C4—142no—
793C2×C4—142no—
794C2×C4—142no—
795C2×C4—142no—
796C2×C4—142no—
797C2×C4—142no—
798C2×C4—142no—
799C2×C4—142no—
800C2×C4—142no—
801C2×C4—142no—
802C2×C4—142no—
803C2×C4—142no—
804C2×C4—142no—
805C2×C4—142no—
806C2×C4—142no—
807C2×C4—2816no—
808C2×C4—2816no—
809C2×C4—284no—
810C2×C4—284no—
811C2×C4—284no—
812C2×C4—284no—
813C2×C4—284no—
814C2×C4C2×#115714yes—
815C2×C4C2×#115714yes—
816C2×C4C2×D4×D714yes—
817C7C2×#245711yescharacteristic, complemented, Sylow
818C22—24no—
819C22—24no—
820C22—24no—
821C22—416no—
822C22—42no—
823C22—42no—
824C22—42no—
825C22—42no—
826C22—144no—
827C22—144no—
828C22—144no—
829C22—144no—
830C22—144no—
831C22—144no—
832C22—282no—
833C22—282no—
834C22—282no—
835C22—282no—
836C22—2816no—
837C22—2816no—
838C22—282no—
839C22—282no—
840C22—282no—
841C22—282no—
842C22#9017014yes—
843C22#9018114yes—
844C22#9021814yes—
845C22#9023814yes—
846C22#9024114yes—
847C22#9024914yes—
848C22#9025314yes—
849C22C22×#115711yescharacteristic
850C22C22×#115711yescharacteristic
851C22C22×#115711yescharacteristic
852C22C22×D4×D711yescharacteristic
853C22C2×#654811yescharacteristic
854C22C2×D7×#4111yescharacteristic
855C22C2×#655311yescharacteristic
856C4—24no—
857C4—24no—
858C4—24no—
859C4—42no—
860C4—42no—
861C4—42no—
862C4—144no—
863C4—282no—
864C4—282no—
865C4—282no—
866C4—282no—
867C4—282no—
868C2—44no—
869C2—284no—
870C2—284no—
871C2#1173103418yesdirect product factor
872C2C2×#9017011yescharacteristic
873C2C2×#9018111yescharacteristic
874C2C2×#9021811yescharacteristic
875C2C2×#9023811yescharacteristic
876C2C2×#9025311yescharacteristic
877C2C2×#9024111yescharacteristic
878C2C2×#9024911yescharacteristic
subgroupG/H
centerC24C23×D7
commutator, cosocleC23×C7C25
FrattiniC23C24×D7
FittingC2×C4×C7×C22⋊C4C2
socleC24×C7C24
prime radicalC2×#89732C2
hypercenterC2×C4×C22⋊C4D7
hypocenterC7C2×#2457
LCSG ▷ C23×C7 ▷ C7
UCSC1 ◁ C24 ◁ C2×C4×C22⋊C4

Complements

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

NH ≅ G/Ntype
1. C22×#6492C2semidirect
2. C22×C4×D28C2semidirect
3. C2×C4×C7×C22⋊C4C2semidirect
4. C2×#89985C2semidirect
6. C2×#89728C2semidirect
7. C2×#89728C2semidirect
8. C2×#89720C2semidirect
9. C2×#89712C2semidirect
10. C2×#89712C2semidirect
11. C2×#89705C2semidirect
12. #11731034C2direct (N × H)
13. C2×#89436C2semidirect
14. C2×#89439C2semidirect
15. C2×#89432C2semidirect
16. C2×#89444C2semidirect
30. C2×#6492C22semidirect
45. C2×C4×D28C22semidirect
46. C4×C7×C22⋊C4C22semidirect
49. #89985C22semidirect
59. #89728C22semidirect
60. #89728C22semidirect
61. #89720C22semidirect
62. #89712C22semidirect
63. #89712C22semidirect
64. #89705C22semidirect
65. #89444C22semidirect
66. #89439C22semidirect
67. #89436C22semidirect
68. #89432C22semidirect
129. C2×(C2×D7)⋊C4D4semidirect
174. C2×C4×C22⋊C4D7semidirect
285. (C2×D7)⋊C4C2×D4semidirect
332. C4×C22⋊C4C2×D7semidirect
703. C2×C7#2457semidirect
817. C7C2×#2457semidirect
871. C2#11731034direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#64922
C22×C4×D282
C2×C4×C7×C22⋊C42
C2×#899852
C2×#897322
C2×#897282
C2×#897202
C2×#897122
C2×#897052
#117310342
C2×#894362
C2×#894392
C2×#894322
C2×#894442
C2×#24577