Finite Group Databasebeta

← C2×#11730980 #13523873

Subgroups — C2×#11730980 #13523873

Order 1792.

3158 conjugacy classes of subgroups.

The subgroup lattice has 872 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#6492C211yesmaximal, characteristic, complemented
2C22×#6439C211yesmaximal, characteristic, complemented
3C2×C4×C7×C22⋊C4C211yesmaximal, characteristic, complemented
4C2×#89985C211yesmaximal, characteristic, complemented
5C2×#89732C211yesmaximal, characteristic
6C2×#89720C211yesmaximal, characteristic, complemented
7C2×#89729C211yesmaximal, characteristic, complemented
8C2×#89729C211yesmaximal, characteristic, complemented
9C2×#89711C211yesmaximal, characteristic, complemented
10C2×#89712C211yesmaximal, characteristic, complemented
11C2×C4×Dic7⋊C4C211yesmaximal, characteristic, complemented
12#11730980C2116yesmaximal, direct product factor
13C2×#89429C211yesmaximal, characteristic, complemented
14C2×#89444C211yesmaximal, characteristic, complemented
15C2×#89441C211yesmaximal, characteristic, complemented
16C2×#89441C211yesmaximal, characteristic, complemented
17C24×C4×C7C2211yescharacteristic
18C23×C22⋊D7C2211yescharacteristic
19C23×C22⋊D7C2211yescharacteristic
20C23×D28C2211yescharacteristic
21C22×C7×C22⋊C4C2211yescharacteristic
22C22×C7×C22⋊C4C2211yescharacteristic
23C22×C42×C7C2211yescharacteristic
24C22×C42×C7C2211yescharacteristic
25C22×C22⋊Dic7C2211yescharacteristic
26C22×C22⋊Dic7C2211yescharacteristic
27C2×#6492—28no—
28C2×#6492C2218yescomplemented
29C22×(C2×D7)⋊C4C2211yescharacteristic
30C22×(C2×D7)⋊C4C2211yescharacteristic
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
44C22×Dic7⋊C4C2211yescharacteristic
45C22×Dic7⋊C4C2211yescharacteristic
46C22×C4×Dic7C2211yescharacteristic
47C22×C4×Dic7C2211yescharacteristic
48C2×#6439—28no—
49C2×#6439C2218yescomplemented
50C4×C7×C22⋊C4C2218yescomplemented
51C2×C7×#95C2211yescharacteristic
52C2×C7×#95C2211yescharacteristic
53#89985C2218yescomplemented
54C2×C7⋊#95C2211yescharacteristic
55C2×C7⋊#95C2211yescharacteristic
56C2×C7⋊#95C2211yescharacteristic
57C2×C7⋊#95C2211yescharacteristic
58#89732C2218yes—
59#89729C2218yescomplemented
60#89729C2218yescomplemented
61#89720C2218yescomplemented
62#89712C2218yescomplemented
63#89711C2218yescomplemented
64C4×Dic7⋊C4C2218yescomplemented
65#89444C2218yescomplemented
66#89441C2218yescomplemented
67#89441C2218yescomplemented
68#89429C2218yescomplemented
69C2×#2554—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—42no—
99C22×D28—42no—
100C22×D28C2314yes—
101C2×C7×C22⋊C4—24no—
102C2×C7×C22⋊C4—24no—
103C2×C7×C22⋊C4C2314yes—
104C2×C7×C22⋊C4C2314yes—
105C2×C42×C7—24no—
106C2×C42×C7—42no—
107C2×C42×C7C2314yes—
108C2×C42×C7C2314yes—
109C2×C22⋊Dic7—24no—
110C2×C22⋊Dic7—42no—
111C2×C22⋊Dic7C2314yes—
112C2×C22⋊Dic7C2314yes—
113#6492—232no—
114C2×(C2×D7)⋊C4—24no—
115C2×(C2×D7)⋊C4—24no—
116C2×(C2×D7)⋊C4—24no—
117C2×(C2×D7)⋊C4—24no—
118C2×(C2×D7)⋊C4—24no—
119C2×(C2×D7)⋊C4—24no—
120C2×(C2×D7)⋊C4—24no—
121C2×(C2×D7)⋊C4—24no—
122C2×(C2×D7)⋊C4—42no—
123C2×(C2×D7)⋊C4—42no—
124C2×(C2×D7)⋊C4C2314yes—
125C2×(C2×D7)⋊C4C2314yes—
126C2×(C2×D7)⋊C4C2314yes—
127C2×(C2×D7)⋊C4C2314yes—
128C2×(C2×D7)⋊C4C2314yes—
129C2×(C2×D7)⋊C4C2314yes—
130C2×(C2×D7)⋊C4C2314yes—
131C2×(C2×D7)⋊C4C2314yes—
132C2×(C2×D7)⋊C4C2314yes—
133C2×(C2×D7)⋊C4C2314yes—
134C2×C4⋊Dic7—42no—
135C2×C4⋊Dic7C2314yes—
136C2×Dic7⋊C4—24no—
137C2×Dic7⋊C4—24no—
138C2×Dic7⋊C4—24no—
139C2×Dic7⋊C4—24no—
140C2×Dic7⋊C4—42no—
141C2×Dic7⋊C4D418yescomplemented
142C2×Dic7⋊C4C2314yes—
143C2×Dic7⋊C4C2314yes—
144C2×Dic7⋊C4C2314yes—
145C2×Dic7⋊C4C2314yes—
146C2×Dic7⋊C4C2314yes—
147C2×Dic7⋊C4C2314yes—
148C2×C4×Dic7—24no—
149C2×C4×Dic7—42no—
150C2×C4×Dic7C2314yes—
151C2×C4×Dic7C2314yes—
152#6439—232no—
153C7×#95C2314yes—
154C7×#95C2314yes—
155C7⋊#95C2314yes—
156C7⋊#95C2314yes—
157C7⋊#95C2314yes—
158C7⋊#95C2314yes—
159C22×#126—71no—
160C22×#123—71no—
161#2554—716no—
162C2×#398—71no—
163C2×#396—71no—
164C2×#394—71no—
165C2×#392—71no—
166C2×#390—71no—
167C2×#390—71no—
168C2×#390—71no—
169C2×#388—71no—
170C2×#388—71no—
171C2×#388—71no—
172C2×#386—71no—
173C2×C4×C4⋊C4—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×D7—22no—
197C23×D7—22no—
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—22no—
211C22×C4×C7—22no—
212C22×C4×C7—28no—
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×Dic7C2×D414yes—
252C22×Dic7C2×D414yes—
253C22×Dic7#4114yes—
254C22×Dic7C2412yes—
255C22×Dic7C2412yes—
256C22×Dic7C2412yes—
257C22×Dic7C2412yes—
258C22×Dic7C2412yes—
259C22×Dic7C2412yes—
260C2×D28—28no—
261C2×D28—44no—
262C2×D28—44no—
263C2×D28—416no—
264C7×C22⋊C4—28no—
265C7×C22⋊C4—28no—
266C42×C7—28no—
267C42×C7—44no—
268C22⋊Dic7—28no—
269C22⋊Dic7—44no—
270(C2×D7)⋊C4—28no—
271(C2×D7)⋊C4—28no—
272(C2×D7)⋊C4—28no—
273(C2×D7)⋊C4—28no—
274(C2×D7)⋊C4—28no—
275(C2×D7)⋊C4—28no—
276(C2×D7)⋊C4—28no—
277(C2×D7)⋊C4—28no—
278(C2×D7)⋊C4—44no—
279(C2×D7)⋊C4—44no—
280C4⋊Dic7—44no—
281Dic7⋊C4—28no—
282Dic7⋊C4—28no—
283Dic7⋊C4—28no—
284Dic7⋊C4—28no—
285Dic7⋊C4—44no—
286Dic7⋊C4C2×D4116yescomplemented
287C4×Dic7—28no—
288C4×Dic7—44no—
289C23×D4—71no—
290C23×D4—71no—
291C23×D4—71no—
292C24×C4C2×D711yescharacteristic
293C2×#126—78no—
294C2×#126—148no—
295C2×#123—78no—
296C2×#123—148no—
297C22×C4⋊C4—71no—
298C22×C4⋊C4—71no—
299C22×C4⋊C4—71no—
300C22×C4⋊C4—71no—
301C22×C4⋊C4—71no—
302C22×C4⋊C4—71no—
303C22×C4⋊C4—71no—
304C22×C22⋊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—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×C42—71no—
319C22×C42—71no—
320C22×C42C2×D711yescharacteristic
321C22×C42C2×D711yescharacteristic
322#398—78no—
323#396—78no—
324#394—78no—
325#392—78no—
326#390—78no—
327#390—78no—
328#390—78no—
329#388—78no—
330#388—78no—
331#388—78no—
332#386—78no—
333C4×C4⋊C4—78no—
334C4×C22⋊C4C2×D718yescomplemented
335C2×#95—71no—
336C2×#95—71no—
337C2×#95—71no—
338C2×#95—71no—
339C2×#95C2×D711yescharacteristic
340C2×#95C2×D711yescharacteristic
341C23×C7—28no—
342C23×C7—28no—
343C23×C7—28no—
344C23×C7—22no—
345C23×C7—22no—
346C23×C7—22no—
347C23×C7—22no—
348C23×C7—22no—
349C23×C7—22no—
350C23×C7—44no—
351C23×C7—44no—
352C23×C7—44no—
353C23×C7—44no—
354C23×C7C22×D412yes—
355C23×C7C2×#4114yes—
356C23×C7C2×#4112yes—
357C23×C7C2×#4112yes—
358C23×C7C2×#4112yes—
359C23×C7C2×#4112yes—
360C23×C7H(5,𝔽2)12yes—
361C23×C7H(5,𝔽2)12yes—
362C23×C7C2511yescharacteristic
363C22×D7—22no—
364C22×D7—22no—
365C22×D7—22no—
366C22×D7—22no—
367C22×D7—22no—
368C22×D7—22no—
369C22×D7—22no—
370C22×D7—22no—
371C22×D7—22no—
372C22×D7—22no—
373C22×D7—22no—
374C22×D7—22no—
375C22×D7—22no—
376C22×D7—22no—
377C22×D7—44no—
378C22×D7—44no—
379C22×D7—44no—
380C22×D7—44no—
381C22×D7—44no—
382C22×D7—44no—
383C22×D7—44no—
384C22×D7—44no—
385C22×D7—44no—
386C22×D7—44no—
387C22×D7—44no—
388C22×D7—44no—
389C22×D7—44no—
390C22×D7—44no—
391C2×C4×C7—28no—
392C2×C4×C7—28no—
393C2×C4×C7—28no—
394C2×C4×C7—22no—
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—416no—
410C2×C4×C7—44no—
411C2×C4×C7—44no—
412C2×C4×C7—44no—
413C2×C4×C7C22×D414yes—
414C2×C4×C7C2×#4114yes—
415C2×C4×C7C2×#4114yes—
416C22⋊D7—416no—
417C22⋊D7—416no—
418C2×Dic7—28no—
419C2×Dic7—28no—
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—44no—
437C2×Dic7—44no—
438C2×Dic7—44no—
439C2×Dic7C22×D414yes—
440C2×Dic7C22×D414yes—
441C2×Dic7C2×#4114yes—
442D28—416no—
443C25—71no—
444C25—71no—
445C25C22×D711yescharacteristic
446C22×D4—74no—
447C22×D4—74no—
448C22×D4—74no—
449C22×D4—144no—
450C22×D4—144no—
451C22×D4—144no—
452C22×D4—144no—
453C22×D4—144no—
454C22×D4—282no—
455C22×D4—282no—
456C22×D4—282no—
457C22×D4—282no—
458C23×C4—24no—
459C23×C4—24no—
460C23×C4—42no—
461C23×C4—71no—
462C23×C4—71no—
463C23×C4—71no—
464C23×C4—71no—
465C23×C4—71no—
466C23×C4—71no—
467C23×C4C22×D711yescharacteristic
468C23×C4C22×D711yescharacteristic
469C23×C4C22×D711yescharacteristic
470C23×C4C22×D714yes—
471C23×C4C22×D711yescharacteristic
472C23×C4C22×D711yescharacteristic
473C23×C4C22×D711yescharacteristic
474#126—1432no—
475#123—1432no—
476C2×C4⋊C4—78no—
477C2×C4⋊C4—74no—
478C2×C4⋊C4—74no—
479C2×C4⋊C4—74no—
480C2×C4⋊C4—74no—
481C2×C4⋊C4—74no—
482C2×C4⋊C4—74no—
483C2×C4⋊C4—74no—
484C2×C4⋊C4—144no—
485C2×C4⋊C4—144no—
486C2×C4⋊C4—144no—
487C2×C4⋊C4—144no—
488C2×C4⋊C4—282no—
489C2×C4⋊C4—282no—
490C2×C22⋊C4—24no—
491C2×C22⋊C4—24no—
492C2×C22⋊C4—74no—
493C2×C22⋊C4—74no—
494C2×C22⋊C4—74no—
495C2×C22⋊C4—74no—
496C2×C22⋊C4—74no—
497C2×C22⋊C4—74no—
498C2×C22⋊C4—74no—
499C2×C22⋊C4—74no—
500C2×C22⋊C4—74no—
501C2×C22⋊C4—74no—
502C2×C22⋊C4—74no—
503C2×C22⋊C4—74no—
504C2×C22⋊C4—144no—
505C2×C22⋊C4—144no—
506C2×C22⋊C4—144no—
507C2×C22⋊C4—144no—
508C2×C22⋊C4—144no—
509C2×C22⋊C4—144no—
510C2×C22⋊C4—144no—
511C2×C22⋊C4—144no—
512C2×C22⋊C4—144no—
513C2×C22⋊C4—282no—
514C2×C22⋊C4—282no—
515C2×C22⋊C4—282no—
516C2×C22⋊C4C22×D714yes—
517C2×C22⋊C4C22×D714yes—
518C2×C42—24no—
519C2×C42—42no—
520C2×C42—74no—
521C2×C42—74no—
522C2×C42—144no—
523C2×C42—282no—
524C2×C42C22×D714yes—
525C2×C42C22×D714yes—
526#95—74no—
527#95—74no—
528#95—74no—
529#95—74no—
530#95C22×D714yes—
531#95C22×D714yes—
532C22×C7—24no—
533C22×C7—24no—
534C22×C7—24no—
535C22×C7—42no—
536C22×C7—42no—
537C22×C7—42no—
538C22×C7—42no—
539C22×C7—416no—
540C22×C7#52914yes—
541C22×C7#53214yes—
542C22×C7#53814yes—
543C22×C7#54614yes—
544C22×C7#55014yes—
545C22×C7#55114yes—
546C22×C7#55314yes—
547C22×C7C23×D411yescharacteristic
548C22×C7C22×#4111yescharacteristic
549C22×C7C22×#4111yescharacteristic
550C22×C7C22×#4111yescharacteristic
551C22×C7C22×#4111yescharacteristic
552C22×C7C2×H(5,𝔽2)11yescharacteristic
553C22×C7C2×H(5,𝔽2)11yescharacteristic
554C2×D7—42no—
555C2×D7—42no—
556C2×D7—42no—
557C2×D7—42no—
558C2×D7—42no—
559C2×D7—42no—
560C2×D7—42no—
561C2×D7—42no—
562C2×D7—42no—
563C2×D7—42no—
564C2×D7—42no—
565C2×D7—42no—
566C2×D7—42no—
567C2×D7—42no—
568C2×D7—88no—
569C2×D7—88no—
570C4×C7—24no—
571C4×C7—24no—
572C4×C7—24no—
573C4×C7—42no—
574C4×C7—42no—
575C4×C7—42no—
576Dic7—24no—
577Dic7—24no—
578Dic7—24no—
579Dic7—42no—
580Dic7—42no—
581Dic7—42no—
582C24—22no—
583C24—22no—
584C24—22no—
585C24—22no—
586C24—22no—
587C24—22no—
588C24—72no—
589C24—72no—
590C24—142no—
591C24—142no—
592C24—142no—
593C24—142no—
594C24—142no—
595C24—142no—
596C24—142no—
597C24—142no—
598C24—142no—
599C24—142no—
600C24—142no—
601C24—142no—
602C24—142no—
603C24—142no—
604C24#115714yes—
605C24C23×D712yes—
606C24C23×D711yescharacteristic
607C2×D4—148no—
608C2×D4—148no—
609C2×D4—148no—
610C2×D4—148no—
611C2×D4—148no—
612C2×D4—284no—
613C2×D4—284no—
614C2×D4—2816no—
615C2×D4—284no—
616C2×D4—284no—
617C2×D4—2816no—
618C2×D4—2816no—
619C22×C4—22no—
620C22×C4—22no—
621C22×C4—22no—
622C22×C4—22no—
623C22×C4—22no—
624C22×C4—22no—
625C22×C4—22no—
626C22×C4—22no—
627C22×C4—28no—
628C22×C4—22no—
629C22×C4—22no—
630C22×C4—22no—
631C22×C4—22no—
632C22×C4—22no—
633C22×C4—22no—
634C22×C4—22no—
635C22×C4—28no—
636C22×C4—44no—
637C22×C4—416no—
638C22×C4—74no—
639C22×C4—74no—
640C22×C4—74no—
641C22×C4—72no—
642C22×C4—72no—
643C22×C4—72no—
644C22×C4—72no—
645C22×C4—72no—
646C22×C4—72no—
647C22×C4—142no—
648C22×C4—142no—
649C22×C4—142no—
650C22×C4—142no—
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#115714yes—
663C22×C4#115714yes—
664C22×C4D4×D714yes—
665C22×C4C23×D712yes—
666C22×C4C23×D712yes—
667C22×C4C23×D712yes—
668C22×C4C23×D712yes—
669C22×C4C23×D712yes—
670C22×C4C23×D712yes—
671C4⋊C4—716no—
672C4⋊C4—148no—
673C4⋊C4—148no—
674C4⋊C4—148no—
675C4⋊C4—148no—
676C4⋊C4—284no—
677C4⋊C4—284no—
678C22⋊C4—28no—
679C22⋊C4—28no—
680C22⋊C4—148no—
681C22⋊C4—148no—
682C22⋊C4—148no—
683C22⋊C4—148no—
684C22⋊C4—148no—
685C22⋊C4—148no—
686C22⋊C4—148no—
687C22⋊C4—148no—
688C22⋊C4—148no—
689C22⋊C4—284no—
690C22⋊C4—284no—
691C22⋊C4—284no—
692C42—28no—
693C42—44no—
694C42—148no—
695C42—284no—
696C2×C7—44no—
697C2×C7#255418yescomplemented
698C2×C7C2×#52911yescharacteristic
699C2×C7C2×#53211yescharacteristic
700C2×C7C2×#53811yescharacteristic
701C2×C7C2×#54611yescharacteristic
702C2×C7C2×#55011yescharacteristic
703C2×C7C2×#55111yescharacteristic
704C2×C7C2×#55311yescharacteristic
705D7—82no—
706D7—82no—
707C23—28no—
708C23—28no—
709C23—28no—
710C23—22no—
711C23—22no—
712C23—22no—
713C23—22no—
714C23—22no—
715C23—22no—
716C23—44no—
717C23—44no—
718C23—44no—
719C23—44no—
720C23—142no—
721C23—142no—
722C23—142no—
723C23—142no—
724C23—142no—
725C23—142no—
726C23—142no—
727C23—142no—
728C23—142no—
729C23—142no—
730C23—142no—
731C23—142no—
732C23—142no—
733C23—142no—
734C23—284no—
735C23—284no—
736C23—284no—
737C23—284no—
738C23—284no—
739C23—284no—
740C23—284no—
741C23—284no—
742C23—284no—
743C23—284no—
744C23—284no—
745C23—284no—
746C23—284no—
747C23—284no—
748C23C2×#115714yes—
749C23C2×#115712yes—
750C23C2×#115712yes—
751C23C2×#115712yes—
752C23C2×D4×D712yes—
753C23#654812yes—
754C23D7×#4112yes—
755C23#655312yes—
756C23C24×D711yescharacteristic
757D4—2816no—
758D4—2816no—
759D4—2816no—
760C2×C4—28no—
761C2×C4—28no—
762C2×C4—28no—
763C2×C4—22no—
764C2×C4—22no—
765C2×C4—22no—
766C2×C4—22no—
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—416no—
779C2×C4—44no—
780C2×C4—44no—
781C2×C4—44no—
782C2×C4—74no—
783C2×C4—74no—
784C2×C4—74no—
785C2×C4—148no—
786C2×C4—148no—
787C2×C4—148no—
788C2×C4—142no—
789C2×C4—142no—
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—284no—
804C2×C4—284no—
805C2×C4—284no—
806C2×C4C2×#115714yes—
807C2×C4C2×#115714yes—
808C2×C4C2×D4×D714yes—
809C7C2×#255411yescharacteristic, complemented, Sylow
810C22—24no—
811C22—24no—
812C22—24no—
813C22—416no—
814C22—42no—
815C22—42no—
816C22—42no—
817C22—42no—
818C22—282no—
819C22—282no—
820C22—282no—
821C22—282no—
822C22—282no—
823C22—282no—
824C22—282no—
825C22—282no—
826C22—282no—
827C22—282no—
828C22—282no—
829C22—282no—
830C22—282no—
831C22—282no—
832C22—568no—
833C22—568no—
834C22#9017014yes—
835C22#9018114yes—
836C22#9021814yes—
837C22#9023114yes—
838C22#9023914yes—
839C22#9024414yes—
840C22#9025114yes—
841C22C22×#115711yescharacteristic
842C22C22×#115711yescharacteristic
843C22C22×#115711yescharacteristic
844C22C22×D4×D711yescharacteristic
845C22C2×#654811yescharacteristic
846C22C2×D7×#4111yescharacteristic
847C22C2×#655311yescharacteristic
848C4—24no—
849C4—24no—
850C4—24no—
851C4—42no—
852C4—42no—
853C4—42no—
854C4—144no—
855C4—144no—
856C4—144no—
857C4—282no—
858C4—282no—
859C4—282no—
860C2—44no—
861C2—562no—
862C2—562no—
863C2#1173098018yesdirect product factor
864C2C2×#9017011yescharacteristic
865C2C2×#9018111yescharacteristic
866C2C2×#9021811yescharacteristic
867C2C2×#9024411yescharacteristic
868C2C2×#9023111yescharacteristic
869C2C2×#9023911yescharacteristic
870C2C2×#9025111yescharacteristic
subgroupG/H
centerC24C23×D7
commutator, cosocleC23×C7C25
FrattiniC23C24×D7
FittingC2×C4×C7×C22⋊C4C2
socleC24×C7C24
prime radicalC2×#89732C2
hypercenterC2×C4×C22⋊C4D7
hypocenterC7C2×#2554
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×#6439C2semidirect
3. C2×C4×C7×C22⋊C4C2semidirect
4. C2×#89985C2semidirect
6. C2×#89720C2semidirect
7. C2×#89729C2semidirect
8. C2×#89729C2semidirect
9. C2×#89711C2semidirect
10. C2×#89712C2semidirect
11. C2×C4×Dic7⋊C4C2semidirect
12. #11730980C2direct (N × H)
13. C2×#89429C2semidirect
14. C2×#89444C2semidirect
15. C2×#89441C2semidirect
16. C2×#89441C2semidirect
28. C2×#6492C22semidirect
49. C2×#6439C22semidirect
50. C4×C7×C22⋊C4C22semidirect
53. #89985C22semidirect
59. #89729C22semidirect
60. #89729C22semidirect
61. #89720C22semidirect
62. #89712C22semidirect
63. #89711C22semidirect
64. C4×Dic7⋊C4C22semidirect
65. #89444C22semidirect
66. #89441C22semidirect
67. #89441C22semidirect
68. #89429C22semidirect
141. C2×Dic7⋊C4D4semidirect
174. C2×C4×C22⋊C4D7semidirect
286. Dic7⋊C4C2×D4semidirect
334. C4×C22⋊C4C2×D7semidirect
697. C2×C7#2554semidirect
809. C7C2×#2554semidirect
863. C2#11730980direct (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×#64392
C2×C4×C7×C22⋊C42
C2×#899852
C2×#897322
C2×#897202
C2×#897292
C2×#897112
C2×#897122
C2×C4×Dic7⋊C42
#117309802
C2×#894292
C2×#894442
C2×#894412
C2×#25547