Finite Group Databasebeta

← C2×#11732206 #13523920

Subgroups — C2×#11732206 #13523920

Order 1792.

3266 conjugacy classes of subgroups.

The subgroup lattice has 876 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#6501C211yesmaximal, characteristic
2C22×#6442C211yesmaximal, characteristic, complemented
3C2×C7×#386C211yesmaximal, characteristic, complemented
4C2×#89994C211yesmaximal, characteristic, complemented
5C2×#89985C211yesmaximal, characteristic, complemented
6C2×C4×C22⋊Dic7C211yesmaximal, characteristic, complemented
7C2×#89731C211yesmaximal, characteristic, complemented
8C2×#89731C211yesmaximal, characteristic, complemented
9C2×#89729C211yesmaximal, characteristic, complemented
10C2×#89717C211yesmaximal, characteristic, complemented
11C2×#89723C211yesmaximal, characteristic, complemented
12#11732206C2116yesmaximal, direct product factor
13C2×#89440C211yesmaximal, characteristic, complemented
14C2×#89432C211yesmaximal, characteristic, complemented
15C2×#89419C211yesmaximal, characteristic, complemented
16C2×#89438C211yesmaximal, characteristic, complemented
17C23×C7×D4C2211yescharacteristic
18C24×C4×C7C2211yescharacteristic
19C23×C22⋊D7C2211yescharacteristic
20C23×C22⋊D7C2211yescharacteristic
21C23×C4×D7C2211yescharacteristic
22C22×C7×C22⋊C4C2211yescharacteristic
23C22×C7×C22⋊C4C2211yescharacteristic
24C22×C7×C22⋊C4C2211yescharacteristic
25C22×C22⋊Dic7C2211yescharacteristic
26C22×C22⋊Dic7C2211yescharacteristic
27C22×C22⋊Dic7C2211yescharacteristic
28C22×C22⋊Dic7C2211yescharacteristic
29C22×C22⋊Dic7C2211yescharacteristic
30C22×C22⋊Dic7C2211yescharacteristic
31C2×#6501—28no—
32C2×#6501C2218yes—
33C22×(C2×D7)⋊C4C2211yescharacteristic
34C22×(C2×D7)⋊C4C2211yescharacteristic
35C22×(C2×D7)⋊C4C2211yescharacteristic
36C22×(C2×D7)⋊C4C2211yescharacteristic
37C22×C4⋊Dic7C2211yescharacteristic
38C22×C4⋊Dic7C2211yescharacteristic
39C22×Dic7⋊C4C2211yescharacteristic
40C22×Dic7⋊C4C2211yescharacteristic
41C22×Dic7⋊C4C2211yescharacteristic
42C22×Dic7⋊C4C2211yescharacteristic
43C22×C4×Dic7C2211yescharacteristic
44C22×C4×Dic7C2211yescharacteristic
45C22×C4×Dic7C2211yescharacteristic
46C2×#6442—28no—
47C2×#6442C2218yescomplemented
48C7×#386C2218yescomplemented
49C2×C7×#95C2211yescharacteristic
50C2×C7×#95C2211yescharacteristic
51#89994C2218yescomplemented
52#89985C2218yescomplemented
53C4×C22⋊Dic7C2218yescomplemented
54C2×C7⋊#95C2211yescharacteristic
55C2×C7⋊#95C2211yescharacteristic
56C2×C7⋊#95C2211yescharacteristic
57C2×C7⋊#95C2211yescharacteristic
58C2×C7⋊#95C2211yescharacteristic
59C2×C7⋊#95C2211yescharacteristic
60#89731C2218yescomplemented
61#89731C2218yescomplemented
62#89729C2218yescomplemented
63#89723C2218yescomplemented
64#89717C2218yescomplemented
65#89440C2218yescomplemented
66#89438C2218yescomplemented
67#89432C2218yescomplemented
68#89419C2218yescomplemented
69C2×#2559—71nomaximal, Sylow
70C25×C7C2311yescharacteristic
71C25×C7C2311yescharacteristic
72C24×D7C2311yescharacteristic
73C22×C7×D4—24no—
74C22×C7×D4—24no—
75C22×C7×D4—42no—
76C22×C7×D4C2314yes—
77C23×C4×C7—24no—
78C23×C4×C7—42no—
79C23×C4×C7—42no—
80C23×C4×C7C2311yescharacteristic
81C23×C4×C7C2311yescharacteristic
82C23×C4×C7C2311yescharacteristic
83C23×C4×C7C2311yescharacteristic
84C23×C4×C7C2311yescharacteristic
85C23×C4×C7C2314yes—
86C22×C22⋊D7—24no—
87C22×C22⋊D7—24no—
88C22×C22⋊D7—24no—
89C22×C22⋊D7—24no—
90C22×C22⋊D7—42no—
91C22×C22⋊D7—42no—
92C22×C22⋊D7C2314yes—
93C22×C22⋊D7C2314yes—
94C23×Dic7C2311yescharacteristic
95C23×Dic7C2311yescharacteristic
96C23×Dic7C2311yescharacteristic
97C23×Dic7C2311yescharacteristic
98C23×Dic7C2311yescharacteristic
99C23×Dic7C2311yescharacteristic
100C23×Dic7C2311yescharacteristic
101C22×C4×D7—24no—
102C22×C4×D7—24no—
103C22×C4×D7—42no—
104C22×C4×D7C2314yes—
105C2×C7×C22⋊C4—24no—
106C2×C7×C22⋊C4—24no—
107C2×C7×C22⋊C4—42no—
108C2×C7×C22⋊C4C2314yes—
109C2×C7×C22⋊C4C2314yes—
110C2×C7×C22⋊C4C2314yes—
111C2×C22⋊Dic7—24no—
112C2×C22⋊Dic7—24no—
113C2×C22⋊Dic7—24no—
114C2×C22⋊Dic7—24no—
115C2×C22⋊Dic7—42no—
116C2×C22⋊Dic7D418yes—
117C2×C22⋊Dic7C2314yes—
118C2×C22⋊Dic7C2314yes—
119C2×C22⋊Dic7C2314yes—
120C2×C22⋊Dic7C2314yes—
121C2×C22⋊Dic7C2314yes—
122C2×C22⋊Dic7C2314yes—
123#6501—232no—
124C2×(C2×D7)⋊C4—24no—
125C2×(C2×D7)⋊C4—24no—
126C2×(C2×D7)⋊C4—24no—
127C2×(C2×D7)⋊C4—42no—
128C2×(C2×D7)⋊C4C2314yes—
129C2×(C2×D7)⋊C4C2314yes—
130C2×(C2×D7)⋊C4C2314yes—
131C2×(C2×D7)⋊C4C2314yes—
132C2×C4⋊Dic7—24no—
133C2×C4⋊Dic7—24no—
134C2×C4⋊Dic7C2314yes—
135C2×C4⋊Dic7C2314yes—
136C2×Dic7⋊C4—24no—
137C2×Dic7⋊C4—24no—
138C2×Dic7⋊C4—24no—
139C2×Dic7⋊C4—42no—
140C2×Dic7⋊C4C2314yes—
141C2×Dic7⋊C4C2314yes—
142C2×Dic7⋊C4C2314yes—
143C2×Dic7⋊C4C2314yes—
144C2×C4×Dic7—24no—
145C2×C4×Dic7—42no—
146C2×C4×Dic7—42no—
147C2×C4×Dic7C2314yes—
148C2×C4×Dic7C2314yes—
149C2×C4×Dic7C2314yes—
150#6442—232no—
151C7×#95C2314yes—
152C7×#95C2314yes—
153C7⋊#95C2314yes—
154C7⋊#95C2314yes—
155C7⋊#95C2314yes—
156C7⋊#95C2314yes—
157C7⋊#95C2314yes—
158C7⋊#95C2314yes—
159C22×#126—71no—
160C22×#121—71no—
161#2559—716no—
162C2×#400—71no—
163C2×#394—71no—
164C2×#394—71no—
165C2×#394—71no—
166C2×#390—71no—
167C2×#389—71no—
168C2×#388—71no—
169C2×#388—71no—
170C2×#386—71no—
171C2×#386D711yescharacteristic, complemented
172C2×#385—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×C7—22no—
182C24×C7—22no—
183C24×C7—22no—
184C24×C7—22no—
185C24×C7—22no—
186C24×C7—22no—
187C24×C7—22no—
188C24×C7C2×D414yes—
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—28no—
201C2×C7×D4—28no—
202C2×C7×D4—44no—
203C2×C7×D4—416no—
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—28no—
218C22×C4×C7—44no—
219C22×C4×C7—44no—
220C22×C4×C7—416no—
221C22×C4×C7#4114yes—
222C22×C4×C7#4114yes—
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×Dic7—22no—
254C22×Dic7C2×D414yes—
255C22×Dic7C2×D414yes—
256C22×Dic7#4114yes—
257C22×Dic7C2412yes—
258C22×Dic7C2412yes—
259C22×Dic7C2412yes—
260C22×Dic7C2412yes—
261C22×Dic7C2412yes—
262C22×Dic7C2412yes—
263C22×Dic7C2412yes—
264C2×C4×D7—28no—
265C2×C4×D7—28no—
266C2×C4×D7—44no—
267C2×C4×D7—416no—
268C7×C22⋊C4—28no—
269C7×C22⋊C4—28no—
270C7×C22⋊C4—44no—
271C22⋊Dic7—28no—
272C22⋊Dic7—28no—
273C22⋊Dic7—28no—
274C22⋊Dic7—28no—
275C22⋊Dic7—44no—
276C22⋊Dic7C2×D4116yes—
277(C2×D7)⋊C4—28no—
278(C2×D7)⋊C4—28no—
279(C2×D7)⋊C4—28no—
280(C2×D7)⋊C4—44no—
281C4⋊Dic7—28no—
282C4⋊Dic7—28no—
283Dic7⋊C4—28no—
284Dic7⋊C4—28no—
285Dic7⋊C4—28no—
286Dic7⋊C4—44no—
287C4×Dic7—28no—
288C4×Dic7—44no—
289C4×Dic7—44no—
290C23×D4—71no—
291C23×D4—71no—
292C23×D4C2×D711yescharacteristic
293C24×C4—71no—
294C24×C4C2×D711yescharacteristic
295C2×#126—78no—
296C2×#126—148no—
297C2×#121—78no—
298C2×#121—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—71no—
311C22×C22⋊C4—71no—
312C22×C22⋊C4—71no—
313C22×C22⋊C4—71no—
314C22×C22⋊C4—71no—
315C22×C22⋊C4C2×D711yescharacteristic
316C22×C22⋊C4C2×D711yescharacteristic
317C22×C22⋊C4C2×D711yescharacteristic
318C22×C42—71no—
319C22×C42—71no—
320C22×C42—71no—
321#400—78no—
322#394—78no—
323#394—78no—
324#394—78no—
325#390—78no—
326#389—78no—
327#388—78no—
328#388—78no—
329#386—78no—
330#386C2×D718yescomplemented
331#385—78no—
332C4×C22⋊C4—78no—
333C4×C22⋊C4—78no—
334C2×#95—71no—
335C2×#95—71no—
336C2×#95—71no—
337C2×#95—71no—
338C2×#95—71no—
339C2×#95—71no—
340C2×#95C2×D711yescharacteristic
341C2×#95C2×D711yescharacteristic
342C23×C7—28no—
343C23×C7—28no—
344C23×C7—28no—
345C23×C7—22no—
346C23×C7—22no—
347C23×C7—22no—
348C23×C7—22no—
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—44no—
359C23×C7—44no—
360C23×C7—44no—
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×#4112yes—
372C23×C7C2×#4112yes—
373C23×C7C2×#4112yes—
374C23×C7C2×#4112yes—
375C23×C7H(5,𝔽2)12yes—
376C23×C7H(5,𝔽2)12yes—
377C23×C7C2511yescharacteristic
378C22×D7—28no—
379C22×D7—28no—
380C22×D7—28no—
381C22×D7—22no—
382C22×D7—22no—
383C22×D7—22no—
384C22×D7—22no—
385C22×D7—22no—
386C22×D7—22no—
387C22×D7—44no—
388C22×D7—44no—
389C22×D7—44no—
390C22×D7—44no—
391C22×D7C2×#4114yes—
392C7×D4—416no—
393C2×C4×C7—28no—
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—416no—
409C2×C4×C7—44no—
410C2×C4×C7—44no—
411C2×C4×C7—44no—
412C2×C4×C7C2×#4114yes—
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—44no—
438C2×Dic7—44no—
439C2×Dic7—44no—
440C2×Dic7—44no—
441C2×Dic7C22×D414yes—
442C2×Dic7C22×D414yes—
443C2×Dic7C2×#4114yes—
444C4×D7—416no—
445C25—71no—
446C25C22×D711yescharacteristic
447C25C22×D711yescharacteristic
448C22×D4—24no—
449C22×D4—24no—
450C22×D4—42no—
451C22×D4—74no—
452C22×D4—74no—
453C22×D4—144no—
454C22×D4—144no—
455C22×D4—144no—
456C22×D4—144no—
457C22×D4—282no—
458C22×D4—282no—
459C22×D4C22×D714yes—
460C23×C4—24no—
461C23×C4—42no—
462C23×C4—42no—
463C23×C4—71no—
464C23×C4—71no—
465C23×C4—71no—
466C23×C4—71no—
467C23×C4—71no—
468C23×C4—71no—
469C23×C4—71no—
470C23×C4—74no—
471C23×C4—144no—
472C23×C4—144no—
473C23×C4—282no—
474C23×C4C22×D711yescharacteristic
475C23×C4C22×D711yescharacteristic
476C23×C4C22×D711yescharacteristic
477C23×C4C22×D711yescharacteristic
478C23×C4C22×D711yescharacteristic
479C23×C4C22×D714yes—
480#126—1432no—
481#121—1432no—
482C2×C4⋊C4—74no—
483C2×C4⋊C4—74no—
484C2×C4⋊C4—74no—
485C2×C4⋊C4—74no—
486C2×C4⋊C4—74no—
487C2×C4⋊C4—74no—
488C2×C4⋊C4—144no—
489C2×C4⋊C4—144no—
490C2×C4⋊C4—144no—
491C2×C4⋊C4—144no—
492C2×C4⋊C4—144no—
493C2×C4⋊C4—282no—
494C2×C22⋊C4—24no—
495C2×C22⋊C4—24no—
496C2×C22⋊C4—42no—
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—144no—
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#95C22×D714yes—
533#95C22×D714yes—
534C22×C7—24no—
535C22×C7—24no—
536C22×C7—24no—
537C22×C7—42no—
538C22×C7—42no—
539C22×C7—42no—
540C22×C7—42no—
541C22×C7—416no—
542C22×C7—42no—
543C22×C7—42no—
544C22×C7—42no—
545C22×C7—42no—
546C22×C7—42no—
547C22×C7—42no—
548C22×C7—42no—
549C22×C7—88no—
550C22×C7#52914yes—
551C22×C7#53214yes—
552C22×C7#53814yes—
553C22×C7#54614yes—
554C22×C7#54614yes—
555C22×C7#55314yes—
556C22×C7#55314yes—
557C22×C7C23×D411yescharacteristic
558C22×C7C22×#4111yescharacteristic
559C22×C7C22×#4111yescharacteristic
560C22×C7C22×#4111yescharacteristic
561C22×C7C22×#4111yescharacteristic
562C22×C7C2×H(5,𝔽2)11yescharacteristic
563C22×C7C2×H(5,𝔽2)11yescharacteristic
564C2×D7—24no—
565C2×D7—24no—
566C2×D7—24no—
567C2×D7—42no—
568C2×D7—42no—
569C2×D7—42no—
570C2×D7—42no—
571C2×D7—416no—
572C4×C7—24no—
573C4×C7—24no—
574C4×C7—42no—
575C4×C7—42no—
576C4×C7—42no—
577Dic7—24no—
578Dic7—24no—
579Dic7—24no—
580Dic7—42no—
581Dic7—42no—
582Dic7—42no—
583Dic7—42no—
584C24—22no—
585C24—22no—
586C24—22no—
587C24—22no—
588C24—22no—
589C24—22no—
590C24—22no—
591C24—22no—
592C24—22no—
593C24—22no—
594C24—22no—
595C24—22no—
596C24—22no—
597C24—74no—
598C24—72no—
599C24—142no—
600C24—142no—
601C24—142no—
602C24—142no—
603C24—142no—
604C24—142no—
605C24D4×D714yes—
606C24C23×D712yes—
607C24C23×D712yes—
608C24C23×D711yescharacteristic
609C2×D4—28no—
610C2×D4—28no—
611C2×D4—44no—
612C2×D4—416no—
613C2×D4—148no—
614C2×D4—148no—
615C2×D4—148no—
616C2×D4—148no—
617C2×D4—284no—
618C2×D4—284no—
619C2×D4—2816no—
620C2×D4—2816no—
621C22×C4—22no—
622C22×C4—22no—
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—28no—
635C22×C4—44no—
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—72no—
648C22×C4—148no—
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—142no—
663C22×C4—142no—
664C22×C4—142no—
665C22×C4—142no—
666C22×C4—142no—
667C22×C4—148no—
668C22×C4—284no—
669C22×C4—2816no—
670C22×C4#115714yes—
671C22×C4#115914yes—
672C22×C4C23×D712yes—
673C22×C4C23×D712yes—
674C22×C4C23×D712yes—
675C22×C4C23×D712yes—
676C22×C4C23×D712yes—
677C4⋊C4—148no—
678C4⋊C4—148no—
679C4⋊C4—148no—
680C4⋊C4—148no—
681C4⋊C4—148no—
682C4⋊C4—284no—
683C22⋊C4—28no—
684C22⋊C4—28no—
685C22⋊C4—44no—
686C22⋊C4—716no—
687C22⋊C4—148no—
688C22⋊C4—148no—
689C22⋊C4—148no—
690C22⋊C4—148no—
691C22⋊C4—148no—
692C22⋊C4—148no—
693C22⋊C4—148no—
694C22⋊C4—284no—
695C22⋊C4—284no—
696C42—148no—
697C42—284no—
698C42—284no—
699C2×C7—44no—
700C2×C7—82no—
701C2×C7#255918yescomplemented
702C2×C7C2×#52911yescharacteristic
703C2×C7C2×#53211yescharacteristic
704C2×C7C2×#53811yescharacteristic
705C2×C7C2×#54611yescharacteristic
706C2×C7C2×#54611yescharacteristic
707C2×C7C2×#55311yescharacteristic
708C2×C7C2×#55311yescharacteristic
709D7—44no—
710C23—28no—
711C23—28no—
712C23—28no—
713C23—22no—
714C23—22no—
715C23—22no—
716C23—22no—
717C23—22no—
718C23—22no—
719C23—22no—
720C23—22no—
721C23—22no—
722C23—22no—
723C23—22no—
724C23—22no—
725C23—22no—
726C23—44no—
727C23—44no—
728C23—44no—
729C23—44no—
730C23—44no—
731C23—44no—
732C23—44no—
733C23—44no—
734C23—44no—
735C23—44no—
736C23—44no—
737C23—74no—
738C23—148no—
739C23—148no—
740C23—142no—
741C23—142no—
742C23—148no—
743C23—142no—
744C23—142no—
745C23—142no—
746C23—142no—
747C23—284no—
748C23—284no—
749C23—284no—
750C23—284no—
751C23C2×#115712yes—
752C23C2×D4×D714yes—
753C23C2×D4×D712yes—
754C23C2×#115912yes—
755C23#654812yes—
756C23#654812yes—
757C23D7×#4112yes—
758C23D7×#4112yes—
759C23C24×D711yescharacteristic
760D4—416no—
761D4—2816no—
762D4—2816no—
763C2×C4—28no—
764C2×C4—28no—
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—142no—
804C2×C4—142no—
805C2×C4—142no—
806C2×C4—2816no—
807C2×C4—284no—
808C2×C4—284no—
809C2×C4—284no—
810C2×C4—284no—
811C2×C4C2×#115714yes—
812C2×C4C2×#115914yes—
813C7C2×#255911yescharacteristic, complemented, Sylow
814C22—24no—
815C22—24no—
816C22—24no—
817C22—42no—
818C22—42no—
819C22—42no—
820C22—42no—
821C22—416no—
822C22—42no—
823C22—42no—
824C22—42no—
825C22—42no—
826C22—42no—
827C22—42no—
828C22—42no—
829C22—88no—
830C22—144no—
831C22—144no—
832C22—144no—
833C22—282no—
834C22—282no—
835C22—282no—
836C22—282no—
837C22—2816no—
838C22#9018114yes—
839C22#9024814yes—
840C22#9024914yes—
841C22#9028414yes—
842C22#9028714yes—
843C22#9030114yes—
844C22#9035214yes—
845C22C22×#115711yescharacteristic
846C22C22×D4×D711yescharacteristic
847C22C22×#115911yescharacteristic
848C22C2×#654811yescharacteristic
849C22C2×#654811yescharacteristic
850C22C2×D7×#4111yescharacteristic
851C22C2×D7×#4111yescharacteristic
852C4—24no—
853C4—24no—
854C4—42no—
855C4—42no—
856C4—42no—
857C4—144no—
858C4—144no—
859C4—144no—
860C4—282no—
861C4—282no—
862C4—282no—
863C4—282no—
864C2—44no—
865C2—82no—
866C2—284no—
867C2#1173220618yesdirect product factor
868C2C2×#9018111yescharacteristic
869C2C2×#9024811yescharacteristic
870C2C2×#9024911yescharacteristic
871C2C2×#9028411yescharacteristic
872C2C2×#9028711yescharacteristic
873C2C2×#9030111yescharacteristic
874C2C2×#9035211yescharacteristic
subgroupG/H
centerC24C23×D7
commutator, cosocleC23×C7C25
FrattiniC23C24×D7
FittingC2×C7×#386C2
socleC24×C7C24
prime radicalC22×#6501C2
hypercenterC2×#386D7
hypocenterC7C2×#2559
LCSG ▷ C23×C7 ▷ C7
UCSC1 ◁ C24 ◁ C2×#386

Complements

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

NH ≅ G/Ntype
2. C22×#6442C2semidirect
3. C2×C7×#386C2semidirect
4. C2×#89994C2semidirect
5. C2×#89985C2semidirect
6. C2×C4×C22⋊Dic7C2semidirect
7. C2×#89731C2semidirect
8. C2×#89731C2semidirect
9. C2×#89729C2semidirect
10. C2×#89717C2semidirect
11. C2×#89723C2semidirect
12. #11732206C2direct (N × H)
13. C2×#89440C2semidirect
14. C2×#89432C2semidirect
15. C2×#89419C2semidirect
16. C2×#89438C2semidirect
47. C2×#6442C22semidirect
48. C7×#386C22semidirect
51. #89994C22semidirect
52. #89985C22semidirect
53. C4×C22⋊Dic7C22semidirect
60. #89731C22semidirect
61. #89731C22semidirect
62. #89729C22semidirect
63. #89723C22semidirect
64. #89717C22semidirect
65. #89440C22semidirect
66. #89438C22semidirect
67. #89432C22semidirect
68. #89419C22semidirect
171. C2×#386D7semidirect
330. #386C2×D7semidirect
701. C2×C7#2559semidirect
813. C7C2×#2559semidirect
867. C2#11732206direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#65012
C22×#64422
C2×C7×#3862
C2×#899942
C2×#899852
C2×C4×C22⋊Dic72
C2×#897312
C2×#897292
C2×#897172
C2×#897232
#117322062
C2×#894402
C2×#894322
C2×#894192
C2×#894382
C2×#25597