Finite Group Databasebeta

← C2×#11734961 #13523910

Subgroups — C2×#11734961 #13523910

Order 1792.

3330 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×#6446C211yesmaximal, characteristic, complemented
2C22×#6448C211yesmaximal, characteristic, complemented
3C2×C7×#397C211yesmaximal, characteristic, complemented
4C2×#89760C211yesmaximal, characteristic, complemented
5C2×#89753C211yesmaximal, characteristic, complemented
6C2×#89732C211yesmaximal, characteristic
7C2×#89730C211yesmaximal, characteristic, complemented
8C2×#89730C211yesmaximal, characteristic, complemented
9C2×C22⋊C4×Dic7C211yesmaximal, characteristic, complemented
10#11734961C2116yesmaximal, direct product factor
11C2×#89447C211yesmaximal, characteristic, complemented
12C2×#89445C211yesmaximal, characteristic, complemented
13C2×#89437C211yesmaximal, characteristic, complemented
14C2×#89418C211yesmaximal, characteristic, complemented
15C2×#89442C211yesmaximal, characteristic, complemented
16C2×#89438C211yesmaximal, characteristic, complemented
17C23×C22⋊D7C2211yescharacteristic
18C23×C22⋊D7C2211yescharacteristic
19C24×Dic7C2211yescharacteristic
20C23×D28C2211yescharacteristic
21C23×C4×D7C2211yescharacteristic
22C23×Dic14C2211yescharacteristic
23C22×C7×C4⋊C4C2211yescharacteristic
24C22×C7×C22⋊C4C2211yescharacteristic
25C22×C7×C22⋊C4C2211yescharacteristic
26C22×C7×C22⋊C4C2211yescharacteristic
27C22×C22⋊Dic7C2211yescharacteristic
28C22×(C2×D7)⋊C4C2211yescharacteristic
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×C4⋊Dic7C2211yescharacteristic
38C22×Dic7⋊C4C2211yescharacteristic
39C22×C4×Dic7C2211yescharacteristic
40C22×C4×Dic7C2211yescharacteristic
41C22×C4×Dic7C2211yescharacteristic
42C2×#6448—28no—
43C2×#6448C2218yescomplemented
44C2×#6446—28no—
45C2×#6446C2218yescomplemented
46C7×#397C2218yescomplemented
47C2×C7×#95C2211yescharacteristic
48C2×C7×#95C2211yescharacteristic
49C2×C7×#95C2211yescharacteristic
50C2×C7⋊#95C2211yescharacteristic
51C2×C7⋊#95C2211yescharacteristic
52C2×C7⋊#95C2211yescharacteristic
53C2×C7⋊#95C2211yescharacteristic
54C2×C7⋊#95C2211yescharacteristic
55C2×C7⋊#95C2211yescharacteristic
56C2×C7⋊#95C2211yescharacteristic
57#89760C2218yescomplemented
58#89753C2218yescomplemented
59#89732C2218yes—
60#89730C2218yescomplemented
61#89730C2218yescomplemented
62C22⋊C4×Dic7C2218yescomplemented
63#89447C2218yescomplemented
64#89445C2218yescomplemented
65#89442C2218yescomplemented
66#89438C2218yescomplemented
67#89437C2218yescomplemented
68#89418C2218yescomplemented
69C2×#2557—71nomaximal, Sylow
70C25×C7C2311yescharacteristic
71C24×D7C2311yescharacteristic
72C24×D7C2311yescharacteristic
73C23×C4×C7C2311yescharacteristic
74C23×C4×C7C2311yescharacteristic
75C23×C4×C7C2311yescharacteristic
76C23×C4×C7C2311yescharacteristic
77C23×C4×C7C2311yescharacteristic
78C23×C4×C7C2311yescharacteristic
79C22×C22⋊D7—24no—
80C22×C22⋊D7—24no—
81C22×C22⋊D7—24no—
82C22×C22⋊D7—24no—
83C22×C22⋊D7—42no—
84C22×C22⋊D7—42no—
85C22×C22⋊D7C2314yes—
86C22×C22⋊D7C2314yes—
87C23×Dic7—24no—
88C23×Dic7—42no—
89C23×Dic7—42no—
90C23×Dic7C2311yescharacteristic
91C23×Dic7C2311yescharacteristic
92C23×Dic7C2311yescharacteristic
93C23×Dic7C2311yescharacteristic
94C23×Dic7C2311yescharacteristic
95C23×Dic7C2311yescharacteristic
96C23×Dic7C2314yes—
97C22×D28—24no—
98C22×D28—24no—
99C22×D28—42no—
100C22×D28C2314yes—
101C22×C4×D7—24no—
102C22×C4×D7—24no—
103C22×C4×D7—42no—
104C22×C4×D7C2314yes—
105C22×Dic14—24no—
106C22×Dic14—24no—
107C22×Dic14—42no—
108C22×Dic14C2314yes—
109C2×C7×C4⋊C4—24no—
110C2×C7×C4⋊C4C2314yes—
111C2×C7×C22⋊C4—24no—
112C2×C7×C22⋊C4—24no—
113C2×C7×C22⋊C4—24no—
114C2×C7×C22⋊C4C2314yes—
115C2×C7×C22⋊C4C2314yes—
116C2×C7×C22⋊C4C2314yes—
117C2×C22⋊Dic7D418yescomplemented
118C2×C22⋊Dic7C2314yes—
119C2×(C2×D7)⋊C4—24no—
120C2×(C2×D7)⋊C4—24no—
121C2×(C2×D7)⋊C4—24no—
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)⋊C4C2314yes—
129C2×(C2×D7)⋊C4C2314yes—
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×C4⋊Dic7—24no—
138C2×C4⋊Dic7C2314yes—
139C2×Dic7⋊C4—24no—
140C2×Dic7⋊C4C2314yes—
141C2×C4×Dic7—24no—
142C2×C4×Dic7—42no—
143C2×C4×Dic7—42no—
144C2×C4×Dic7C2314yes—
145C2×C4×Dic7C2314yes—
146C2×C4×Dic7C2314yes—
147#6448—232no—
148#6446—232no—
149C7×#95C2314yes—
150C7×#95C2314yes—
151C7×#95C2314yes—
152C7⋊#95C2314yes—
153C7⋊#95C2314yes—
154C7⋊#95C2314yes—
155C7⋊#95C2314yes—
156C7⋊#95C2314yes—
157C7⋊#95C2314yes—
158C7⋊#95C2314yes—
159C22×#124—71no—
160C22×#123—71no—
161#2557—716no—
162C2×#397—71no—
163C2×#397D711yescharacteristic, complemented
164C2×#393—71no—
165C2×#392—71no—
166C2×#391—71no—
167C2×#390—71no—
168C2×#388—71no—
169C2×#387—71no—
170C2×#386—71no—
171C2×#386—71no—
172C2×#386—71no—
173C2×C4×C22⋊C4—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×C7C2×D414yes—
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#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—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#4114yes—
218C22×C4×C7C2412yes—
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—22no—
241C22×Dic7—22no—
242C22×Dic7—22no—
243C22×Dic7—22no—
244C22×Dic7—22no—
245C22×Dic7—22no—
246C22×Dic7—28no—
247C22×Dic7—44no—
248C22×Dic7—44no—
249C22×Dic7—416no—
250C22×Dic7C2×D414yes—
251C22×Dic7C2×D414yes—
252C22×Dic7#4114yes—
253C22×Dic7#4114yes—
254C22×Dic7C2412yes—
255C22×Dic7C2412yes—
256C22×Dic7C2412yes—
257C22×Dic7C2412yes—
258C22×Dic7C2412yes—
259C22×Dic7C2412yes—
260C2×D28—28no—
261C2×D28—28no—
262C2×D28—44no—
263C2×D28—416no—
264C2×C4×D7—28no—
265C2×C4×D7—28no—
266C2×C4×D7—44no—
267C2×C4×D7—416no—
268C2×Dic14—28no—
269C2×Dic14—28no—
270C2×Dic14—44no—
271C2×Dic14—416no—
272C7×C4⋊C4—28no—
273C7×C22⋊C4—28no—
274C7×C22⋊C4—28no—
275C7×C22⋊C4—28no—
276C22⋊Dic7C2×D4116yescomplemented
277(C2×D7)⋊C4—28no—
278(C2×D7)⋊C4—28no—
279(C2×D7)⋊C4—28no—
280(C2×D7)⋊C4—28no—
281(C2×D7)⋊C4—28no—
282(C2×D7)⋊C4—28no—
283(C2×D7)⋊C4—44no—
284(C2×D7)⋊C4—44no—
285(C2×D7)⋊C4—44no—
286C4⋊Dic7—28no—
287Dic7⋊C4—28no—
288C4×Dic7—28no—
289C4×Dic7—44no—
290C4×Dic7—44no—
291C23×Q8—71no—
292C23×D4—71no—
293C23×D4—71no—
294C23×D4—71no—
295C24×C4—71no—
296C24×C4—71no—
297C2×#124—78no—
298C2×#124—148no—
299C2×#123—78no—
300C2×#123—148no—
301C22×C4⋊C4—71no—
302C22×C4⋊C4—71no—
303C22×C4⋊C4C2×D711yescharacteristic
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⋊C4C2×D711yescharacteristic
315C22×C22⋊C4C2×D711yescharacteristic
316C22×C22⋊C4C2×D711yescharacteristic
317C22×C42—71no—
318C22×C42—71no—
319C22×C42—71no—
320#397—78no—
321#397C2×D718yescomplemented
322#393—78no—
323#392—78no—
324#391—78no—
325#390—78no—
326#388—78no—
327#387—78no—
328#386—78no—
329#386—78no—
330#386—78no—
331C4×C22⋊C4—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×#95C2×D711yescharacteristic
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×D414yes—
357C23×C7C22×D412yes—
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—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—22no—
378C22×D7—22no—
379C22×D7—22no—
380C22×D7—22no—
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—
391C22×D7—44no—
392C22×D7C2×#4114yes—
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—22no—
410C2×C4×C7—22no—
411C2×C4×C7—44no—
412C2×C4×C7—44no—
413C2×C4×C7—44no—
414C2×C4×C7—44no—
415C2×C4×C7—44no—
416C2×C4×C7C2×#4114yes—
417C22⋊D7—416no—
418C22⋊D7—416no—
419C2×Dic7—28no—
420C2×Dic7—28no—
421C2×Dic7—28no—
422C2×Dic7—28no—
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—44no—
439C2×Dic7—44no—
440C2×Dic7C22×D414yes—
441C2×Dic7C22×D414yes—
442C2×Dic7C2×#4114yes—
443C2×Dic7C2×#4114yes—
444D28—416no—
445C4×D7—416no—
446Dic14—416no—
447C25—71no—
448C25—71no—
449C25C22×D711yescharacteristic
450C22×Q8—74no—
451C22×Q8—144no—
452C22×Q8—144no—
453C22×Q8—282no—
454C22×D4—74no—
455C22×D4—74no—
456C22×D4—74no—
457C22×D4—144no—
458C22×D4—144no—
459C22×D4—144no—
460C22×D4—144no—
461C22×D4—144no—
462C22×D4—144no—
463C22×D4—282no—
464C22×D4—282no—
465C22×D4—282no—
466C23×C4—71no—
467C23×C4—71no—
468C23×C4—71no—
469C23×C4—71no—
470C23×C4—71no—
471C23×C4—71no—
472C23×C4—74no—
473C23×C4—74no—
474C23×C4—144no—
475C23×C4—144no—
476C23×C4—144no—
477C23×C4—282no—
478C23×C4—282no—
479C23×C4—282no—
480C23×C4C22×D711yescharacteristic
481C23×C4C22×D711yescharacteristic
482C23×C4C22×D711yescharacteristic
483C23×C4C22×D711yescharacteristic
484C23×C4C22×D711yescharacteristic
485C23×C4C22×D711yescharacteristic
486#124—1432no—
487#123—1432no—
488C2×C4⋊C4—24no—
489C2×C4⋊C4—74no—
490C2×C4⋊C4—74no—
491C2×C4⋊C4—144no—
492C2×C4⋊C4—144no—
493C2×C4⋊C4C22×D714yes—
494C2×C22⋊C4—24no—
495C2×C22⋊C4—24no—
496C2×C22⋊C4—24no—
497C2×C22⋊C4—78no—
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—74no—
505C2×C22⋊C4—74no—
506C2×C22⋊C4—74no—
507C2×C22⋊C4—74no—
508C2×C22⋊C4—144no—
509C2×C22⋊C4—144no—
510C2×C22⋊C4—144no—
511C2×C22⋊C4—144no—
512C2×C22⋊C4—144no—
513C2×C22⋊C4—144no—
514C2×C22⋊C4—282no—
515C2×C22⋊C4—282no—
516C2×C22⋊C4—282no—
517C2×C22⋊C4C22×D714yes—
518C2×C22⋊C4C22×D714yes—
519C2×C22⋊C4C22×D714yes—
520C2×C42—74no—
521C2×C42—74no—
522C2×C42—74no—
523C2×C42—144no—
524C2×C42—282no—
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#95C22×D714yes—
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#52914yes—
545C22×C7#53214yes—
546C22×C7#53814yes—
547C22×C7#54614yes—
548C22×C7#54614yes—
549C22×C7#55114yes—
550C22×C7#55914yes—
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—42no—
562C2×D7—42no—
563C2×D7—42no—
564C2×D7—42no—
565C2×D7—416no—
566C2×D7—42no—
567C2×D7—42no—
568C2×D7—42no—
569C2×D7—42no—
570C2×D7—42no—
571C2×D7—42no—
572C2×D7—42no—
573C2×D7—88no—
574C4×C7—24no—
575C4×C7—42no—
576C4×C7—42no—
577C4×C7—42no—
578C4×C7—42no—
579C4×C7—42no—
580Dic7—24no—
581Dic7—24no—
582Dic7—24no—
583Dic7—24no—
584Dic7—42no—
585Dic7—42no—
586C24—22no—
587C24—22no—
588C24—22no—
589C24—22no—
590C24—22no—
591C24—22no—
592C24—74no—
593C24—72no—
594C24—72no—
595C24—142no—
596C24—142no—
597C24—142no—
598C24—142no—
599C24—142no—
600C24—142no—
601C24—142no—
602C24—142no—
603C24—142no—
604C24—142no—
605C24—142no—
606C24—142no—
607C24—142no—
608C24D4×D714yes—
609C24C23×D712yes—
610C24C23×D711yescharacteristic
611C2×Q8—148no—
612C2×Q8—148no—
613C2×Q8—284no—
614C2×Q8—2816no—
615C2×D4—148no—
616C2×D4—148no—
617C2×D4—148no—
618C2×D4—148no—
619C2×D4—148no—
620C2×D4—148no—
621C2×D4—284no—
622C2×D4—2816no—
623C2×D4—284no—
624C2×D4—284no—
625C2×D4—2816no—
626C2×D4—2816no—
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—22no—
638C22×C4—22no—
639C22×C4—22no—
640C22×C4—22no—
641C22×C4—22no—
642C22×C4—22no—
643C22×C4—22no—
644C22×C4—74no—
645C22×C4—74no—
646C22×C4—74no—
647C22×C4—74no—
648C22×C4—72no—
649C22×C4—72no—
650C22×C4—72no—
651C22×C4—72no—
652C22×C4—72no—
653C22×C4—72no—
654C22×C4—148no—
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—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#115914yes—
677C22×C4C23×D712yes—
678C22×C4C23×D712yes—
679C22×C4C23×D712yes—
680C22×C4C23×D712yes—
681C22×C4C23×D712yes—
682C22×C4C23×D712yes—
683C4⋊C4—28no—
684C4⋊C4—148no—
685C4⋊C4—148no—
686C22⋊C4—28no—
687C22⋊C4—28no—
688C22⋊C4—28no—
689C22⋊C4—716no—
690C22⋊C4—148no—
691C22⋊C4—148no—
692C22⋊C4—148no—
693C22⋊C4—148no—
694C22⋊C4—148no—
695C22⋊C4—148no—
696C22⋊C4—284no—
697C22⋊C4—284no—
698C22⋊C4—284no—
699C42—148no—
700C42—284no—
701C42—284no—
702C2×C7—44no—
703C2×C7#255718yescomplemented
704C2×C7C2×#52911yescharacteristic
705C2×C7C2×#53211yescharacteristic
706C2×C7C2×#53811yescharacteristic
707C2×C7C2×#54611yescharacteristic
708C2×C7C2×#54611yescharacteristic
709C2×C7C2×#55111yescharacteristic
710C2×C7C2×#55911yescharacteristic
711D7—44no—
712D7—82no—
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—148no—
728C23—148no—
729C23—148no—
730C23—142no—
731C23—142no—
732C23—142no—
733C23—142no—
734C23—142no—
735C23—142no—
736C23—142no—
737C23—142no—
738C23—142no—
739C23—142no—
740C23—142no—
741C23—142no—
742C23—142no—
743C23—284no—
744C23—284no—
745C23—284no—
746C23—284no—
747C23—284no—
748C23—284no—
749C23—284no—
750C23—284no—
751C23—284no—
752C23—284no—
753C23—284no—
754C23C2×D4×D714yes—
755C23C2×D4×D712yes—
756C23C2×#115912yes—
757C23D7×#4112yes—
758C23D7×#4112yes—
759C23D7×#4112yes—
760C23#655312yes—
761C23#655312yes—
762C23C24×D711yescharacteristic
763Q8—2816no—
764D4—2816no—
765D4—2816no—
766D4—2816no—
767C2×C4—28no—
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—22no—
782C2×C4—22no—
783C2×C4—22no—
784C2×C4—22no—
785C2×C4—44no—
786C2×C4—44no—
787C2×C4—44no—
788C2×C4—44no—
789C2×C4—44no—
790C2×C4—74no—
791C2×C4—74no—
792C2×C4—74no—
793C2×C4—74no—
794C2×C4—148no—
795C2×C4—148no—
796C2×C4—148no—
797C2×C4—148no—
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—142no—
810C2×C4—142no—
811C2×C4—142no—
812C2×C4—2816no—
813C2×C4—2816no—
814C2×C4—284no—
815C2×C4—284no—
816C2×C4C2×#115914yes—
817C7C2×#255711yescharacteristic, complemented, Sylow
818C22—24no—
819C22—24no—
820C22—24no—
821C22—42no—
822C22—42no—
823C22—416no—
824C22—42no—
825C22—42no—
826C22—144no—
827C22—144no—
828C22—144no—
829C22—282no—
830C22—282no—
831C22—282no—
832C22—2816no—
833C22—282no—
834C22—282no—
835C22—282no—
836C22—282no—
837C22—282no—
838C22—282no—
839C22—282no—
840C22—282no—
841C22—568no—
842C22#9028714yes—
843C22#9034514yes—
844C22#9034514yes—
845C22#9034914yes—
846C22#9037214yes—
847C22#9039514yes—
848C22#9039714yes—
849C22C22×D4×D711yescharacteristic
850C22C22×#115911yescharacteristic
851C22C2×D7×#4111yescharacteristic
852C22C2×D7×#4111yescharacteristic
853C22C2×D7×#4111yescharacteristic
854C22C2×#655311yescharacteristic
855C22C2×#655311yescharacteristic
856C4—24no—
857C4—42no—
858C4—42no—
859C4—42no—
860C4—42no—
861C4—42no—
862C4—144no—
863C4—144no—
864C4—144no—
865C4—144no—
866C4—282no—
867C4—282no—
868C2—44no—
869C2—284no—
870C2—562no—
871C2#1173496118yesdirect product factor
872C2C2×#9028711yescharacteristic
873C2C2×#9034511yescharacteristic
874C2C2×#9034511yescharacteristic
875C2C2×#9034911yescharacteristic
876C2C2×#9037211yescharacteristic
877C2C2×#9039711yescharacteristic
878C2C2×#9039511yescharacteristic
subgroupG/H
centerC24C23×D7
commutator, cosocleC23×C7C25
FrattiniC23C24×D7
FittingC2×C7×#397C2
socleC24×C7C24
prime radicalC2×#89732C2
hypercenterC2×#397D7
hypocenterC7C2×#2557
LCSG ▷ C23×C7 ▷ C7
UCSC1 ◁ C24 ◁ C2×#397

Complements

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

NH ≅ G/Ntype
1. C22×#6446C2semidirect
2. C22×#6448C2semidirect
3. C2×C7×#397C2semidirect
4. C2×#89760C2semidirect
5. C2×#89753C2semidirect
7. C2×#89730C2semidirect
8. C2×#89730C2semidirect
9. C2×C22⋊C4×Dic7C2semidirect
10. #11734961C2direct (N × H)
11. C2×#89447C2semidirect
12. C2×#89445C2semidirect
13. C2×#89437C2semidirect
14. C2×#89418C2semidirect
15. C2×#89442C2semidirect
16. C2×#89438C2semidirect
43. C2×#6448C22semidirect
45. C2×#6446C22semidirect
46. C7×#397C22semidirect
57. #89760C22semidirect
58. #89753C22semidirect
60. #89730C22semidirect
61. #89730C22semidirect
62. C22⋊C4×Dic7C22semidirect
63. #89447C22semidirect
64. #89445C22semidirect
65. #89442C22semidirect
66. #89438C22semidirect
67. #89437C22semidirect
68. #89418C22semidirect
117. C2×C22⋊Dic7D4semidirect
163. C2×#397D7semidirect
276. C22⋊Dic7C2×D4semidirect
321. #397C2×D7semidirect
703. C2×C7#2557semidirect
817. C7C2×#2557semidirect
871. C2#11734961direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#64462
C22×#64482
C2×C7×#3972
C2×#897602
C2×#897532
C2×#897322
C2×#897302
C2×C22⋊C4×Dic72
#117349612
C2×#894472
C2×#894452
C2×#894372
C2×#894182
C2×#894422
C2×#894382
C2×#25577