Finite Group Databasebeta

← C2×#11734354 #13521904

Subgroups — C2×#11734354 #13521904

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×D4×Dic7C211yesmaximal, characteristic, complemented
2C22×#6446C211yesmaximal, characteristic, complemented
3C2×C7×#394C211yesmaximal, characteristic, complemented
4C2×#89995C211yesmaximal, characteristic
5C2×#89766C211yesmaximal, characteristic, complemented
6C2×#89753C211yesmaximal, characteristic, complemented
7C2×#89728C211yesmaximal, characteristic, complemented
8C2×#89716C211yesmaximal, characteristic, complemented
9C2×#89723C211yesmaximal, characteristic, complemented
10C2×#89730C211yesmaximal, characteristic, complemented
11C2×#89730C211yesmaximal, characteristic, complemented
12C2×#89715C211yesmaximal, characteristic, complemented
13C2×#89714C211yesmaximal, characteristic, complemented
14#11734354C2116yesmaximal, direct product factor
15C2×#89432C211yesmaximal, characteristic, complemented
16C2×#89438C211yesmaximal, characteristic, complemented
17C23×C7×D4C2211yescharacteristic
18C23×C22⋊D7C2211yescharacteristic
19C23×C22⋊D7C2211yescharacteristic
20C24×Dic7C2211yescharacteristic
21C24×Dic7C2211yescharacteristic
22C23×C4×D7C2211yescharacteristic
23C22×C7×C4⋊C4C2211yescharacteristic
24C22×C7×C22⋊C4C2211yescharacteristic
25C22×C7×C22⋊C4C2211yescharacteristic
26C22×C7×C22⋊C4C2211yescharacteristic
27C22×C7×C22⋊C4C2211yescharacteristic
28C22×C22⋊Dic7C2211yescharacteristic
29C22×C22⋊Dic7C2211yescharacteristic
30C22×C22⋊Dic7C2211yescharacteristic
31C22×C22⋊Dic7C2211yescharacteristic
32C2×D4×Dic7—28no—
33C2×D4×Dic7C2218yescomplemented
34C22×(C2×D7)⋊C4C2211yescharacteristic
35C22×(C2×D7)⋊C4C2211yescharacteristic
36C22×(C2×D7)⋊C4C2211yescharacteristic
37C22×(C2×D7)⋊C4C2211yescharacteristic
38C22×C4⋊Dic7C2211yescharacteristic
39C22×C4⋊Dic7C2211yescharacteristic
40C22×Dic7⋊C4C2211yescharacteristic
41C22×Dic7⋊C4C2211yescharacteristic
42C22×C4×Dic7C2211yescharacteristic
43C22×C4×Dic7C2211yescharacteristic
44C2×#6446—28no—
45C2×#6446C2218yescomplemented
46C7×#394C2218yescomplemented
47C2×C7×#95C2211yescharacteristic
48#89995C2218yes—
49C2×C7⋊#95C2211yescharacteristic
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#89766C2218yescomplemented
59#89753C2218yescomplemented
60#89730C2218yescomplemented
61#89730C2218yescomplemented
62#89728C2218yescomplemented
63#89723C2218yescomplemented
64#89716C2218yescomplemented
65#89715C2218yescomplemented
66#89714C2218yescomplemented
67#89438C2218yescomplemented
68#89432C2218yescomplemented
69C2×#2457—71nomaximal, Sylow
70C25×C7C2311yescharacteristic
71C25×C7C2311yescharacteristic
72C24×D7C2311yescharacteristic
73C22×C7×D4—24no—
74C22×C7×D4—24no—
75C22×C7×D4—24no—
76C22×C7×D4C2314yes—
77C23×C4×C7C2311yescharacteristic
78C23×C4×C7C2311yescharacteristic
79C23×C4×C7C2311yescharacteristic
80C23×C4×C7C2311yescharacteristic
81C23×C4×C7C2311yescharacteristic
82C22×C22⋊D7—24no—
83C22×C22⋊D7—24no—
84C22×C22⋊D7—24no—
85C22×C22⋊D7—24no—
86C22×C22⋊D7—42no—
87C22×C22⋊D7—42no—
88C22×C22⋊D7C2314yes—
89C22×C22⋊D7C2314yes—
90C23×Dic7—24no—
91C23×Dic7—24no—
92C23×Dic7—24no—
93C23×Dic7—24no—
94C23×Dic7—42no—
95C23×Dic7—42no—
96C23×Dic7C2311yescharacteristic
97C23×Dic7C2311yescharacteristic
98C23×Dic7C2311yescharacteristic
99C23×Dic7C2311yescharacteristic
100C23×Dic7C2314yes—
101C23×Dic7C2314yes—
102C23×Dic7C2311yescharacteristic
103C23×Dic7C2311yescharacteristic
104C23×Dic7C2311yescharacteristic
105C22×C4×D7—24no—
106C22×C4×D7—24no—
107C22×C4×D7—42no—
108C22×C4×D7C2314yes—
109C2×C7×C4⋊C4—24no—
110C2×C7×C4⋊C4C2314yes—
111C2×C7×C22⋊C4—24no—
112C2×C7×C22⋊C4—24no—
113C2×C7×C22⋊C4—42no—
114C2×C7×C22⋊C4—42no—
115C2×C7×C22⋊C4C2314yes—
116C2×C7×C22⋊C4C2314yes—
117C2×C7×C22⋊C4C2314yes—
118C2×C7×C22⋊C4C2314yes—
119C2×C22⋊Dic7—24no—
120C2×C22⋊Dic7—42no—
121C2×C22⋊Dic7—42no—
122C2×C22⋊Dic7D418yescomplemented
123C2×C22⋊Dic7C2314yes—
124C2×C22⋊Dic7C2314yes—
125C2×C22⋊Dic7C2314yes—
126C2×C22⋊Dic7C2314yes—
127D4×Dic7—232no—
128C2×(C2×D7)⋊C4—24no—
129C2×(C2×D7)⋊C4—24no—
130C2×(C2×D7)⋊C4—24no—
131C2×(C2×D7)⋊C4—42no—
132C2×(C2×D7)⋊C4C2314yes—
133C2×(C2×D7)⋊C4C2314yes—
134C2×(C2×D7)⋊C4C2314yes—
135C2×(C2×D7)⋊C4C2314yes—
136C2×C4⋊Dic7—24no—
137C2×C4⋊Dic7—24no—
138C2×C4⋊Dic7C2314yes—
139C2×C4⋊Dic7C2314yes—
140C2×Dic7⋊C4—24no—
141C2×Dic7⋊C4—42no—
142C2×Dic7⋊C4C2314yes—
143C2×Dic7⋊C4C2314yes—
144C2×C4×Dic7—24no—
145C2×C4×Dic7—42no—
146C2×C4×Dic7C2314yes—
147C2×C4×Dic7C2314yes—
148#6446—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×#394D711yescharacteristic, complemented
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⋊C4—71no—
175C24×C7—22no—
176C24×C7—22no—
177C24×C7—22no—
178C24×C7—22no—
179C24×C7—22no—
180C24×C7—22no—
181C24×C7—22no—
182C24×C7—22no—
183C24×C7—22no—
184C24×C7—22no—
185C24×C7—22no—
186C24×C7—22no—
187C24×C7C2×D414yes—
188C24×C7#4114yes—
189C24×C7C2412yes—
190C24×C7C2412yes—
191C24×C7C2411yescharacteristic
192C23×D7—22no—
193C23×D7—22no—
194C23×D7—22no—
195C23×D7—22no—
196C23×D7—22no—
197C23×D7—22no—
198C23×D7#4114yes—
199C23×D7C2412yes—
200C2×C7×D4—232no—
201C2×C7×D4—28no—
202C2×C7×D4—28no—
203C2×C7×D4—28no—
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—22no—
211C22×C4×C7—22no—
212C22×C4×C7—22no—
213C22×C4×C7—22no—
214C22×C4×C7—22no—
215C22×C4×C7—22no—
216C22×C4×C7—22no—
217C22×C4×C7—22no—
218C22×C4×C7#4114yes—
219C22×C4×C7C2412yes—
220C22×C4×C7C2412yes—
221C22×C4×C7C2412yes—
222C22×C4×C7C2412yes—
223C22×C4×C7C2412yes—
224C2×C22⋊D7—28no—
225C2×C22⋊D7—28no—
226C2×C22⋊D7—28no—
227C2×C22⋊D7—28no—
228C2×C22⋊D7—44no—
229C2×C22⋊D7—44no—
230C2×C22⋊D7—416no—
231C2×C22⋊D7—416no—
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—28no—
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—28no—
252C22×Dic7—28no—
253C22×Dic7—28no—
254C22×Dic7—44no—
255C22×Dic7—44no—
256C22×Dic7—416no—
257C22×Dic7—416no—
258C22×Dic7C2×D414yes—
259C22×Dic7C2×D414yes—
260C22×Dic7#4114yes—
261C22×Dic7C2412yes—
262C22×Dic7C2412yes—
263C22×Dic7C2412yes—
264C22×Dic7C2412yes—
265C22×Dic7C2412yes—
266C22×Dic7C2412yes—
267C22×Dic7C2412yes—
268C2×C4×D7—28no—
269C2×C4×D7—28no—
270C2×C4×D7—44no—
271C2×C4×D7—416no—
272C7×C4⋊C4—28no—
273C7×C22⋊C4—28no—
274C7×C22⋊C4—28no—
275C7×C22⋊C4—44no—
276C7×C22⋊C4—44no—
277C22⋊Dic7—28no—
278C22⋊Dic7—44no—
279C22⋊Dic7—44no—
280C22⋊Dic7C2×D4116yescomplemented
281(C2×D7)⋊C4—28no—
282(C2×D7)⋊C4—28no—
283(C2×D7)⋊C4—28no—
284(C2×D7)⋊C4—44no—
285C4⋊Dic7—28no—
286C4⋊Dic7—28no—
287Dic7⋊C4—28no—
288Dic7⋊C4—44no—
289C4×Dic7—28no—
290C4×Dic7—44no—
291C23×D4—71no—
292C23×D4—71no—
293C23×D4C2×D711yescharacteristic
294C24×C4—71no—
295C24×C4—71no—
296C24×C4—71no—
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⋊C4C2×D711yescharacteristic
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⋊C4C2×D711yescharacteristic
315C22×C22⋊C4C2×D711yescharacteristic
316C22×C22⋊C4C2×D711yescharacteristic
317C22×C22⋊C4C2×D711yescharacteristic
318C22×C42—71no—
319C22×C42—71no—
320#400—78no—
321#396—78no—
322#394C2×D718yescomplemented
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⋊C4—78no—
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×#95—71no—
342C2×#95C2×D711yescharacteristic
343C23×C7—28no—
344C23×C7—28no—
345C23×C7—28no—
346C23×C7—28no—
347C23×C7—28no—
348C23×C7—28no—
349C23×C7—22no—
350C23×C7—22no—
351C23×C7—22no—
352C23×C7—22no—
353C23×C7—22no—
354C23×C7—22no—
355C23×C7—22no—
356C23×C7—22no—
357C23×C7—22no—
358C23×C7—22no—
359C23×C7—22no—
360C23×C7—22no—
361C23×C7—44no—
362C23×C7—44no—
363C23×C7—44no—
364C23×C7—44no—
365C23×C7—44no—
366C23×C7—44no—
367C23×C7—44no—
368C23×C7—44no—
369C23×C7C22×D414yes—
370C23×C7C22×D412yes—
371C23×C7C2×#4114yes—
372C23×C7C2×#4112yes—
373C23×C7C2×#4112yes—
374C23×C7C2×#4112yes—
375C23×C7C2×#4112yes—
376C23×C7H(5,𝔽2)12yes—
377C23×C7H(5,𝔽2)12yes—
378C23×C7C2511yescharacteristic
379C22×D7—28no—
380C22×D7—28no—
381C22×D7—28no—
382C22×D7—22no—
383C22×D7—22no—
384C22×D7—22no—
385C22×D7—22no—
386C22×D7—22no—
387C22×D7—22no—
388C22×D7—44no—
389C22×D7—44no—
390C22×D7—44no—
391C22×D7—44no—
392C22×D7C2×#4114yes—
393C7×D4—232no—
394C2×C4×C7—28no—
395C2×C4×C7—22no—
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—44no—
410C2×C4×C7—44no—
411C2×C4×C7—44no—
412C2×C4×C7—44no—
413C2×C4×C7C2×#4114yes—
414C22⋊D7—416no—
415C22⋊D7—416no—
416C2×Dic7—28no—
417C2×Dic7—28no—
418C2×Dic7—28no—
419C2×Dic7—22no—
420C2×Dic7—22no—
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—416no—
438C2×Dic7—416no—
439C2×Dic7—44no—
440C2×Dic7—44no—
441C2×Dic7—44no—
442C2×Dic7—44no—
443C2×Dic7C22×D414yes—
444C2×Dic7C22×D414yes—
445C2×Dic7C2×#4114yes—
446C4×D7—416no—
447C25—71no—
448C25C22×D711yescharacteristic
449C25C22×D711yescharacteristic
450C22×D4—24no—
451C22×D4—24no—
452C22×D4—24no—
453C22×D4—74no—
454C22×D4—74no—
455C22×D4—144no—
456C22×D4—144no—
457C22×D4—144no—
458C22×D4—144no—
459C22×D4—282no—
460C22×D4—282no—
461C22×D4C22×D714yes—
462C23×C4—71no—
463C23×C4—71no—
464C23×C4—71no—
465C23×C4—71no—
466C23×C4—71no—
467C23×C4—71no—
468C23×C4—71no—
469C23×C4—74no—
470C23×C4—74no—
471C23×C4—74no—
472C23×C4—144no—
473C23×C4—144no—
474C23×C4—144no—
475C23×C4—144no—
476C23×C4—144no—
477C23×C4—144no—
478C23×C4—282no—
479C23×C4—282no—
480C23×C4—282no—
481C23×C4C22×D711yescharacteristic
482C23×C4C22×D711yescharacteristic
483C23×C4C22×D711yescharacteristic
484C23×C4C22×D711yescharacteristic
485C23×C4C22×D711yescharacteristic
486#123—1432no—
487C4×D4—1432no—
488C2×C4⋊C4—24no—
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—282no—
497C2×C4⋊C4C22×D714yes—
498C2×C22⋊C4—24no—
499C2×C22⋊C4—24no—
500C2×C22⋊C4—42no—
501C2×C22⋊C4—42no—
502C2×C22⋊C4—78no—
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⋊C4C22×D714yes—
519C2×C22⋊C4C22×D714yes—
520C2×C22⋊C4C22×D714yes—
521C2×C22⋊C4C22×D714yes—
522C2×C42—74no—
523C2×C42—74no—
524C2×C42—144no—
525C2×C42—282no—
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#95—74no—
535#95C22×D714yes—
536C22×C7—24no—
537C22×C7—24no—
538C22×C7—24no—
539C22×C7—24no—
540C22×C7—24no—
541C22×C7—24no—
542C22×C7—42no—
543C22×C7—42no—
544C22×C7—42no—
545C22×C7—42no—
546C22×C7—42no—
547C22×C7—42no—
548C22×C7—42no—
549C22×C7—42no—
550C22×C7—416no—
551C22×C7—416no—
552C22×C7#52514yes—
553C22×C7#52914yes—
554C22×C7#54014yes—
555C22×C7#54614yes—
556C22×C7#54614yes—
557C22×C7#55114yes—
558C22×C7#55314yes—
559C22×C7C23×D411yescharacteristic
560C22×C7C22×#4111yescharacteristic
561C22×C7C22×#4111yescharacteristic
562C22×C7C22×#4111yescharacteristic
563C22×C7C22×#4111yescharacteristic
564C22×C7C2×H(5,𝔽2)11yescharacteristic
565C22×C7C2×H(5,𝔽2)11yescharacteristic
566C2×D7—24no—
567C2×D7—24no—
568C2×D7—24no—
569C2×D7—42no—
570C2×D7—42no—
571C2×D7—42no—
572C2×D7—42no—
573C2×D7—416no—
574C4×C7—24no—
575C4×C7—42no—
576C4×C7—42no—
577C4×C7—42no—
578C4×C7—42no—
579Dic7—24no—
580Dic7—24no—
581Dic7—24no—
582Dic7—42no—
583Dic7—42no—
584Dic7—42no—
585Dic7—42no—
586C24—22no—
587C24—22no—
588C24—22no—
589C24—22no—
590C24—22no—
591C24—22no—
592C24—22no—
593C24—22no—
594C24—22no—
595C24—22no—
596C24—22no—
597C24—22no—
598C24—74no—
599C24—72no—
600C24—142no—
601C24—142no—
602C24—142no—
603C24—142no—
604C24—142no—
605C24—142no—
606C24D4×D714yes—
607C24#115914yes—
608C24C23×D712yes—
609C24C23×D712yes—
610C24C23×D711yescharacteristic
611C2×D4—232no—
612C2×D4—28no—
613C2×D4—28no—
614C2×D4—28no—
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—22no—
632C22×C4—22no—
633C22×C4—22no—
634C22×C4—22no—
635C22×C4—22no—
636C22×C4—22no—
637C22×C4—74no—
638C22×C4—74no—
639C22×C4—74no—
640C22×C4—72no—
641C22×C4—72no—
642C22×C4—72no—
643C22×C4—72no—
644C22×C4—72no—
645C22×C4—72no—
646C22×C4—72no—
647C22×C4—148no—
648C22×C4—148no—
649C22×C4—148no—
650C22×C4—148no—
651C22×C4—148no—
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—148no—
661C22×C4—142no—
662C22×C4—142no—
663C22×C4—142no—
664C22×C4—142no—
665C22×C4—142no—
666C22×C4—142no—
667C22×C4—142no—
668C22×C4—142no—
669C22×C4—142no—
670C22×C4—142no—
671C22×C4—284no—
672C22×C4—2816no—
673C22×C4—284no—
674C22×C4—284no—
675C22×C4—2816no—
676C22×C4—2816no—
677C22×C4#115914yes—
678C22×C4C23×D712yes—
679C22×C4C23×D712yes—
680C22×C4C23×D712yes—
681C22×C4C23×D712yes—
682C22×C4C23×D712yes—
683C4⋊C4—28no—
684C4⋊C4—148no—
685C4⋊C4—148no—
686C4⋊C4—148no—
687C4⋊C4—284no—
688C22⋊C4—28no—
689C22⋊C4—28no—
690C22⋊C4—44no—
691C22⋊C4—44no—
692C22⋊C4—716no—
693C22⋊C4—148no—
694C22⋊C4—148no—
695C22⋊C4—148no—
696C22⋊C4—148no—
697C22⋊C4—284no—
698C22⋊C4—284no—
699C22⋊C4—284no—
700C42—148no—
701C42—284no—
702C2×C7—44no—
703C2×C7—44no—
704C2×C7#245718yescomplemented
705C2×C7C2×#52511yescharacteristic
706C2×C7C2×#52911yescharacteristic
707C2×C7C2×#54011yescharacteristic
708C2×C7C2×#54611yescharacteristic
709C2×C7C2×#54611yescharacteristic
710C2×C7C2×#55111yescharacteristic
711C2×C7C2×#55311yescharacteristic
712D7—44no—
713C23—28no—
714C23—28no—
715C23—28no—
716C23—28no—
717C23—28no—
718C23—28no—
719C23—22no—
720C23—22no—
721C23—22no—
722C23—22no—
723C23—22no—
724C23—22no—
725C23—22no—
726C23—22no—
727C23—22no—
728C23—22no—
729C23—22no—
730C23—22no—
731C23—44no—
732C23—44no—
733C23—44no—
734C23—44no—
735C23—44no—
736C23—44no—
737C23—44no—
738C23—44no—
739C23—74no—
740C23—148no—
741C23—148no—
742C23—148no—
743C23—142no—
744C23—142no—
745C23—142no—
746C23—142no—
747C23—142no—
748C23—142no—
749C23—284no—
750C23—284no—
751C23—284no—
752C23—284no—
753C23C2×D4×D714yes—
754C23C2×D4×D712yes—
755C23C2×#115914yes—
756C23C2×#115912yes—
757C23C2×#115912yes—
758C23#654812yes—
759C23D7×#4112yes—
760C23D7×#4112yes—
761C23#655312yes—
762C23C24×D711yescharacteristic
763D4—232no—
764D4—2816no—
765D4—2816no—
766C2×C4—28no—
767C2×C4—22no—
768C2×C4—22no—
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—44no—
782C2×C4—44no—
783C2×C4—44no—
784C2×C4—44no—
785C2×C4—74no—
786C2×C4—74no—
787C2×C4—74no—
788C2×C4—148no—
789C2×C4—148no—
790C2×C4—148no—
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—142no—
808C2×C4—142no—
809C2×C4—2816no—
810C2×C4—2816no—
811C2×C4—2816no—
812C2×C4—284no—
813C2×C4—284no—
814C2×C4—284no—
815C2×C4—284no—
816C2×C4C2×#115914yes—
817C7C2×#245711yescharacteristic, complemented, Sylow
818C22—24no—
819C22—24no—
820C22—24no—
821C22—24no—
822C22—24no—
823C22—24no—
824C22—42no—
825C22—42no—
826C22—42no—
827C22—42no—
828C22—416no—
829C22—416no—
830C22—42no—
831C22—42no—
832C22—42no—
833C22—42no—
834C22—144no—
835C22—144no—
836C22—144no—
837C22—282no—
838C22—282no—
839C22—282no—
840C22—2816no—
841C22—282no—
842C22#9027714yes—
843C22#9029214yes—
844C22#9030114yes—
845C22#9031014yes—
846C22#9034514yes—
847C22#9034914yes—
848C22#9037114yes—
849C22C22×D4×D711yescharacteristic
850C22C22×#115911yescharacteristic
851C22C22×#115911yescharacteristic
852C22C2×#654811yescharacteristic
853C22C2×D7×#4111yescharacteristic
854C22C2×D7×#4111yescharacteristic
855C22C2×#655311yescharacteristic
856C4—24no—
857C4—42no—
858C4—42no—
859C4—42no—
860C4—42no—
861C4—144no—
862C4—144no—
863C4—144no—
864C4—282no—
865C4—282no—
866C4—282no—
867C4—282no—
868C2—44no—
869C2—44no—
870C2—284no—
871C2#1173435418yesdirect product factor
872C2C2×#9027711yescharacteristic
873C2C2×#9031011yescharacteristic
874C2C2×#9029211yescharacteristic
875C2C2×#9030111yescharacteristic
876C2C2×#9034511yescharacteristic
877C2C2×#9034911yescharacteristic
878C2C2×#9037111yescharacteristic
subgroupG/H
centerC24C23×D7
commutator, cosocleC23×C7C25
FrattiniC23C24×D7
FittingC2×C7×#394C2
socleC24×C7C24
prime radicalC2×#89995C2
hypercenterC2×#394D7
hypocenterC7C2×#2457
LCSG ▷ C23×C7 ▷ C7
UCSC1 ◁ C24 ◁ C2×#394

Complements

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

NH ≅ G/Ntype
1. C22×D4×Dic7C2semidirect
2. C22×#6446C2semidirect
3. C2×C7×#394C2semidirect
5. C2×#89766C2semidirect
6. C2×#89753C2semidirect
7. C2×#89728C2semidirect
8. C2×#89716C2semidirect
9. C2×#89723C2semidirect
10. C2×#89730C2semidirect
11. C2×#89730C2semidirect
12. C2×#89715C2semidirect
13. C2×#89714C2semidirect
14. #11734354C2direct (N × H)
15. C2×#89432C2semidirect
16. C2×#89438C2semidirect
33. C2×D4×Dic7C22semidirect
45. C2×#6446C22semidirect
46. C7×#394C22semidirect
58. #89766C22semidirect
59. #89753C22semidirect
60. #89730C22semidirect
61. #89730C22semidirect
62. #89728C22semidirect
63. #89723C22semidirect
64. #89716C22semidirect
65. #89715C22semidirect
66. #89714C22semidirect
67. #89438C22semidirect
68. #89432C22semidirect
122. C2×C22⋊Dic7D4semidirect
164. C2×#394D7semidirect
280. C22⋊Dic7C2×D4semidirect
322. #394C2×D7semidirect
704. C2×C7#2457semidirect
817. C7C2×#2457semidirect
871. C2#11734354direct (N × H)

Maximal subgroups

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

subgroupindex
C22×D4×Dic72
C22×#64462
C2×C7×#3942
C2×#899952
C2×#897662
C2×#897532
C2×#897282
C2×#897162
C2×#897232
C2×#897302
C2×#897152
C2×#897142
#117343542
C2×#894322
C2×#894382
C2×#24577