Finite Group Databasebeta

← C2×#11735234 #13523878

Subgroups — C2×#11735234 #13523878

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×#6457C211yesmaximal, characteristic, complemented
2C22×#6461C211yesmaximal, characteristic, complemented
3C2×C7×#398C211yesmaximal, characteristic, complemented
4C2×#89766C211yesmaximal, characteristic, complemented
5C2×#89760C211yesmaximal, characteristic, complemented
6C2×#89760C211yesmaximal, characteristic, complemented
7C2×#89760C211yesmaximal, characteristic, complemented
8C2×#89762C211yesmaximal, characteristic, complemented
9C2×#89762C211yesmaximal, characteristic, complemented
10#11735234C2116yesmaximal, direct product factor
11C2×#89443C211yesmaximal, characteristic
12C2×#89437C211yesmaximal, characteristic, complemented
13C2×#89444C211yesmaximal, characteristic, complemented
14C2×#89442C211yesmaximal, characteristic, complemented
15C2×#89421C211yesmaximal, characteristic, complemented
16C2×#89438C211yesmaximal, characteristic, complemented
17C23×D28C2211yescharacteristic
18C23×D28C2211yescharacteristic
19C23×D28C2211yescharacteristic
20C23×C4×D7C2211yescharacteristic
21C22×C7×C4⋊C4C2211yescharacteristic
22C22×C7×C4⋊C4C2211yescharacteristic
23C22×C7×C4⋊C4C2211yescharacteristic
24C22×C7×C4⋊C4C2211yescharacteristic
25C22×(C2×D7)⋊C4C2211yescharacteristic
26C22×(C2×D7)⋊C4C2211yescharacteristic
27C22×(C2×D7)⋊C4C2211yescharacteristic
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×(C2×D7)⋊C4C2211yescharacteristic
38C22×(C2×D7)⋊C4C2211yescharacteristic
39C22×C4⋊Dic7C2211yescharacteristic
40C22×Dic7⋊C4C2211yescharacteristic
41C22×Dic7⋊C4C2211yescharacteristic
42C22×C4×Dic7C2211yescharacteristic
43C22×C4×Dic7C2211yescharacteristic
44C22×C4×Dic7C2211yescharacteristic
45C22×C4×Dic7C2211yescharacteristic
46C2×#6461—28no—
47C2×#6461C2218yescomplemented
48C2×#6457—28no—
49C2×#6457C2218yescomplemented
50C7×#398C2218yescomplemented
51C2×C7×#95C2211yescharacteristic
52C2×C7×#95C2211yescharacteristic
53C2×C7×#95C2211yescharacteristic
54C2×C7⋊#95C2211yescharacteristic
55C2×C7⋊#95C2211yescharacteristic
56C2×C7⋊#95C2211yescharacteristic
57#89766C2218yescomplemented
58#89762C2218yescomplemented
59#89762C2218yescomplemented
60#89760C2218yescomplemented
61#89760C2218yescomplemented
62#89760C2218yescomplemented
63#89444C2218yescomplemented
64#89443C2218yes—
65#89442C2218yescomplemented
66#89438C2218yescomplemented
67#89437C2218yescomplemented
68#89421C2218yescomplemented
69C2×#2554—71nomaximal, Sylow
70C24×D7C2311yescharacteristic
71C24×D7C2311yescharacteristic
72C24×D7C2311yescharacteristic
73C23×C4×C7C2311yescharacteristic
74C23×C4×C7C2311yescharacteristic
75C23×C4×C7C2311yescharacteristic
76C23×C4×C7C2311yescharacteristic
77C23×C4×C7C2311yescharacteristic
78C23×C4×C7C2311yescharacteristic
79C23×C4×C7C2311yescharacteristic
80C23×Dic7C2311yescharacteristic
81C23×Dic7C2311yescharacteristic
82C23×Dic7C2311yescharacteristic
83C23×Dic7C2311yescharacteristic
84C23×Dic7C2311yescharacteristic
85C22×D28—24no—
86C22×D28—24no—
87C22×D28—24no—
88C22×D28—24no—
89C22×D28—24no—
90C22×D28—42no—
91C22×D28—42no—
92C22×D28—42no—
93C22×D28—42no—
94C22×D28C2314yes—
95C22×D28C2314yes—
96C22×D28C2314yes—
97C22×C4×D7—24no—
98C22×C4×D7—24no—
99C22×C4×D7—42no—
100C22×C4×D7C2314yes—
101C2×C7×C4⋊C4—24no—
102C2×C7×C4⋊C4—24no—
103C2×C7×C4⋊C4—42no—
104C2×C7×C4⋊C4—42no—
105C2×C7×C4⋊C4C2314yes—
106C2×C7×C4⋊C4C2314yes—
107C2×C7×C4⋊C4C2314yes—
108C2×C7×C4⋊C4C2314yes—
109C2×(C2×D7)⋊C4—24no—
110C2×(C2×D7)⋊C4—24no—
111C2×(C2×D7)⋊C4—24no—
112C2×(C2×D7)⋊C4—24no—
113C2×(C2×D7)⋊C4—24no—
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—42no—
121C2×(C2×D7)⋊C4—42no—
122C2×(C2×D7)⋊C4—42no—
123C2×(C2×D7)⋊C4C2314yes—
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×(C2×D7)⋊C4C2314yes—
135C2×(C2×D7)⋊C4C2314yes—
136C2×(C2×D7)⋊C4C2314yes—
137C2×C4⋊Dic7—24no—
138C2×C4⋊Dic7C2314yes—
139C2×Dic7⋊C4—24no—
140C2×Dic7⋊C4D418yescomplemented
141C2×Dic7⋊C4C2314yes—
142C2×Dic7⋊C4C2314yes—
143C2×C4×Dic7—24no—
144C2×C4×Dic7—24no—
145C2×C4×Dic7—42no—
146C2×C4×Dic7—42no—
147C2×C4×Dic7C2314yes—
148C2×C4×Dic7C2314yes—
149C2×C4×Dic7C2314yes—
150C2×C4×Dic7C2314yes—
151#6461—232no—
152#6457—232no—
153C7×#95C2314yes—
154C7×#95C2314yes—
155C7×#95C2314yes—
156C7⋊#95C2314yes—
157C7⋊#95C2314yes—
158C7⋊#95C2314yes—
159C22×#126—71no—
160C22×#123—71no—
161#2554—716no—
162C2×#398D711yescharacteristic, complemented
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⋊C4—71no—
175C24×C7C2411yescharacteristic
176C23×D7—22no—
177C23×D7—22no—
178C23×D7—22no—
179C23×D7—22no—
180C23×D7—22no—
181C23×D7—22no—
182C23×D7—22no—
183C23×D7—22no—
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#4114yes—
197C23×D7C2412yes—
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—22no—
218C22×C4×C7C2×D414yes—
219C22×C4×C7#4114yes—
220C22×C4×C7#4114yes—
221C22×C4×C7C2412yes—
222C22×C4×C7C2412yes—
223C22×C4×C7C2412yes—
224C22×C4×C7C2412yes—
225C22×C4×C7C2412yes—
226C22×C4×C7C2412yes—
227C22×C4×C7C2412yes—
228C22×Dic7—22no—
229C22×Dic7—22no—
230C22×Dic7—22no—
231C22×Dic7—22no—
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×Dic7C2×D414yes—
241C22×Dic7C2×D414yes—
242C22×Dic7#4114yes—
243C22×Dic7C2412yes—
244C22×Dic7C2412yes—
245C22×Dic7C2412yes—
246C22×Dic7C2412yes—
247C22×Dic7C2412yes—
248C2×D28—28no—
249C2×D28—28no—
250C2×D28—28no—
251C2×D28—28no—
252C2×D28—28no—
253C2×D28—44no—
254C2×D28—44no—
255C2×D28—44no—
256C2×D28—44no—
257C2×D28—416no—
258C2×D28—416no—
259C2×D28—416no—
260C2×C4×D7—28no—
261C2×C4×D7—28no—
262C2×C4×D7—44no—
263C2×C4×D7—416no—
264C7×C4⋊C4—28no—
265C7×C4⋊C4—28no—
266C7×C4⋊C4—44no—
267C7×C4⋊C4—44no—
268(C2×D7)⋊C4—28no—
269(C2×D7)⋊C4—28no—
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—28no—
279(C2×D7)⋊C4—44no—
280(C2×D7)⋊C4—44no—
281(C2×D7)⋊C4—44no—
282C4⋊Dic7—28no—
283Dic7⋊C4—28no—
284Dic7⋊C4C2×D4116yescomplemented
285C4×Dic7—28no—
286C4×Dic7—28no—
287C4×Dic7—44no—
288C4×Dic7—44no—
289C23×D4—71no—
290C23×D4—71no—
291C23×D4—71no—
292C24×C4—71no—
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⋊C4C2×D711yescharacteristic
301C22×C4⋊C4C2×D711yescharacteristic
302C22×C4⋊C4C2×D711yescharacteristic
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⋊C4—71no—
315C22×C22⋊C4—71no—
316C22×C22⋊C4—71no—
317C22×C22⋊C4—71no—
318C22×C42—71no—
319C22×C42—71no—
320C22×C42—71no—
321C22×C42—71no—
322#398C2×D718yescomplemented
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⋊C4—78no—
335C2×#95—71no—
336C2×#95—71no—
337C2×#95—71no—
338C2×#95C2×D711yescharacteristic
339C2×#95C2×D711yescharacteristic
340C2×#95C2×D711yescharacteristic
341C23×C7C22×D412yes—
342C23×C7C2×#4112yes—
343C23×C7C2×#4112yes—
344C23×C7C2×#4112yes—
345C23×C7C2×#4112yes—
346C23×C7H(5,𝔽2)12yes—
347C23×C7H(5,𝔽2)12yes—
348C23×C7C2511yescharacteristic
349C22×D7—28no—
350C22×D7—28no—
351C22×D7—28no—
352C22×D7—22no—
353C22×D7—22no—
354C22×D7—22no—
355C22×D7—22no—
356C22×D7—22no—
357C22×D7—22no—
358C22×D7—22no—
359C22×D7—22no—
360C22×D7—22no—
361C22×D7—22no—
362C22×D7—22no—
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—44no—
373C22×D7—44no—
374C22×D7—44no—
375C22×D7—44no—
376C22×D7—44no—
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×D7C2×#4114yes—
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—22no—
410C2×C4×C7—22no—
411C2×C4×C7—22no—
412C2×C4×C7—44no—
413C2×C4×C7—44no—
414C2×C4×C7—44no—
415C2×C4×C7—44no—
416C2×C4×C7C22×D414yes—
417C2×C4×C7C2×#4114yes—
418C2×C4×C7C2×#4114yes—
419C2×Dic7—28no—
420C2×Dic7—28no—
421C2×Dic7—28no—
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—44no—
435C2×Dic7—44no—
436C2×Dic7C22×D414yes—
437C2×Dic7C22×D414yes—
438C2×Dic7C2×#4114yes—
439D28—416no—
440D28—416no—
441D28—416no—
442C4×D7—416no—
443C25—71no—
444C25—71no—
445C25—71no—
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—71no—
459C23×C4—71no—
460C23×C4—71no—
461C23×C4—71no—
462C23×C4—71no—
463C23×C4—74no—
464C23×C4—144no—
465C23×C4—144no—
466C23×C4—282no—
467C23×C4C22×D711yescharacteristic
468C23×C4C22×D711yescharacteristic
469C23×C4C22×D711yescharacteristic
470C23×C4C22×D711yescharacteristic
471C23×C4C22×D711yescharacteristic
472C23×C4C22×D711yescharacteristic
473C23×C4C22×D711yescharacteristic
474#126—1432no—
475#123—1432no—
476C2×C4⋊C4—24no—
477C2×C4⋊C4—24no—
478C2×C4⋊C4—42no—
479C2×C4⋊C4—42no—
480C2×C4⋊C4—78no—
481C2×C4⋊C4—74no—
482C2×C4⋊C4—74no—
483C2×C4⋊C4—74no—
484C2×C4⋊C4—144no—
485C2×C4⋊C4—144no—
486C2×C4⋊C4C22×D714yes—
487C2×C4⋊C4C22×D714yes—
488C2×C4⋊C4C22×D714yes—
489C2×C4⋊C4C22×D714yes—
490C2×C22⋊C4—74no—
491C2×C22⋊C4—74no—
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—144no—
514C2×C22⋊C4—144no—
515C2×C22⋊C4—282no—
516C2×C22⋊C4—282no—
517C2×C22⋊C4—282no—
518C2×C42—74no—
519C2×C42—74no—
520C2×C42—74no—
521C2×C42—74no—
522C2×C42—144no—
523C2×C42—144no—
524C2×C42—282no—
525C2×C42—282no—
526#95—74no—
527#95—74no—
528#95—74no—
529#95C22×D714yes—
530#95C22×D714yes—
531#95C22×D714yes—
532C22×C7#52914yes—
533C22×C7#53214yes—
534C22×C7#53814yes—
535C22×C7#54614yes—
536C22×C7#55014yes—
537C22×C7#55114yes—
538C22×C7#55314yes—
539C22×C7C23×D411yescharacteristic
540C22×C7C22×#4111yescharacteristic
541C22×C7C22×#4111yescharacteristic
542C22×C7C22×#4111yescharacteristic
543C22×C7C22×#4111yescharacteristic
544C22×C7C2×H(5,𝔽2)11yescharacteristic
545C22×C7C2×H(5,𝔽2)11yescharacteristic
546C2×D7—24no—
547C2×D7—24no—
548C2×D7—24no—
549C2×D7—42no—
550C2×D7—42no—
551C2×D7—42no—
552C2×D7—42no—
553C2×D7—416no—
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—
576C4×C7—42no—
577Dic7—24no—
578Dic7—24no—
579Dic7—24no—
580Dic7—42no—
581Dic7—42no—
582C24—74no—
583C24—72no—
584C24—72no—
585C24—72no—
586C24—142no—
587C24—142no—
588C24—142no—
589C24—142no—
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—142no—
605C24—142no—
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—284no—
615C2×D4—284no—
616C2×D4—2816no—
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—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—148no—
646C22×C4—148no—
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—284no—
660C22×C4—2816no—
661C22×C4D4×D714yes—
662C22×C4#116114yes—
663C22×C4#116114yes—
664C22×C4C23×D712yes—
665C22×C4C23×D712yes—
666C22×C4C23×D712yes—
667C22×C4C23×D712yes—
668C22×C4C23×D712yes—
669C22×C4C23×D712yes—
670C22×C4C23×D712yes—
671C4⋊C4—28no—
672C4⋊C4—28no—
673C4⋊C4—44no—
674C4⋊C4—44no—
675C4⋊C4—716no—
676C4⋊C4—148no—
677C4⋊C4—148no—
678C22⋊C4—148no—
679C22⋊C4—148no—
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—148no—
693C42—148no—
694C42—284no—
695C42—284no—
696C2×C7#255418yescomplemented
697C2×C7C2×#52911yescharacteristic
698C2×C7C2×#53211yescharacteristic
699C2×C7C2×#53811yescharacteristic
700C2×C7C2×#54611yescharacteristic
701C2×C7C2×#55011yescharacteristic
702C2×C7C2×#55111yescharacteristic
703C2×C7C2×#55311yescharacteristic
704D7—44no—
705D7—82no—
706D7—82no—
707C23—74no—
708C23—148no—
709C23—148no—
710C23—148no—
711C23—142no—
712C23—142no—
713C23—142no—
714C23—142no—
715C23—142no—
716C23—142no—
717C23—142no—
718C23—142no—
719C23—142no—
720C23—142no—
721C23—142no—
722C23—142no—
723C23—142no—
724C23—142no—
725C23—142no—
726C23—142no—
727C23—142no—
728C23—142no—
729C23—142no—
730C23—142no—
731C23—284no—
732C23—284no—
733C23—284no—
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—
748C23—284no—
749C23C2×D4×D712yes—
750C23#654812yes—
751C23C2×#116112yes—
752C23C2×#116112yes—
753C23D7×#4112yes—
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—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—2816no—
804C2×C4—284no—
805C2×C4—284no—
806C2×C4C2×D4×D714yes—
807C2×C4C2×#116114yes—
808C2×C4C2×#116114yes—
809C7C2×#255411yescharacteristic, complemented, Sylow
810C22—144no—
811C22—144no—
812C22—144no—
813C22—282no—
814C22—282no—
815C22—282no—
816C22—282no—
817C22—2816no—
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#9029014yes—
835C22#9032814yes—
836C22#9033514yes—
837C22#9034514yes—
838C22#9038214yes—
839C22#9038614yes—
840C22#9041614yes—
841C22C22×D4×D711yescharacteristic
842C22C2×#654811yescharacteristic
843C22C22×#116111yescharacteristic
844C22C22×#116111yescharacteristic
845C22C2×D7×#4111yescharacteristic
846C22C2×D7×#4111yescharacteristic
847C22C2×#655311yescharacteristic
848C4—24no—
849C4—24no—
850C4—24no—
851C4—42no—
852C4—42no—
853C4—42no—
854C4—42no—
855C4—144no—
856C4—144no—
857C4—144no—
858C4—282no—
859C4—282no—
860C2—284no—
861C2—562no—
862C2—562no—
863C2#1173523418yesdirect product factor
864C2C2×#9029011yescharacteristic
865C2C2×#9033511yescharacteristic
866C2C2×#9032811yescharacteristic
867C2C2×#9034511yescharacteristic
868C2C2×#9038211yescharacteristic
869C2C2×#9038611yescharacteristic
870C2C2×#9041611yescharacteristic
subgroupG/H
centerC24C23×D7
commutator, cosocleC23×C7C25
FrattiniC23C24×D7
FittingC2×C7×#398C2
socleC24×C7C24
prime radicalC2×#89443C2
hypercenterC2×#398D7
hypocenterC7C2×#2554
LCSG ▷ C23×C7 ▷ C7
UCSC1 ◁ C24 ◁ C2×#398

Complements

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

NH ≅ G/Ntype
1. C22×#6457C2semidirect
2. C22×#6461C2semidirect
3. C2×C7×#398C2semidirect
4. C2×#89766C2semidirect
5. C2×#89760C2semidirect
6. C2×#89760C2semidirect
7. C2×#89760C2semidirect
8. C2×#89762C2semidirect
9. C2×#89762C2semidirect
10. #11735234C2direct (N × H)
12. C2×#89437C2semidirect
13. C2×#89444C2semidirect
14. C2×#89442C2semidirect
15. C2×#89421C2semidirect
16. C2×#89438C2semidirect
47. C2×#6461C22semidirect
49. C2×#6457C22semidirect
50. C7×#398C22semidirect
57. #89766C22semidirect
58. #89762C22semidirect
59. #89762C22semidirect
60. #89760C22semidirect
61. #89760C22semidirect
62. #89760C22semidirect
63. #89444C22semidirect
65. #89442C22semidirect
66. #89438C22semidirect
67. #89437C22semidirect
68. #89421C22semidirect
140. C2×Dic7⋊C4D4semidirect
162. C2×#398D7semidirect
284. Dic7⋊C4C2×D4semidirect
322. #398C2×D7semidirect
696. C2×C7#2554semidirect
809. C7C2×#2554semidirect
863. C2#11735234direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#64572
C22×#64612
C2×C7×#3982
C2×#897662
C2×#897602
C2×#897622
#117352342
C2×#894432
C2×#894372
C2×#894442
C2×#894422
C2×#894212
C2×#894382
C2×#25547