Finite Group Databasebeta

← C2×#11736908 #14218876

Subgroups — C2×#11736908 #14218876

Order 1792.

1938 conjugacy classes of subgroups.

The subgroup lattice has 732 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#90229C211yesmaximal, characteristic
2C2×C7×#435C211yesmaximal, characteristic, complemented
3C2×#89899C211yesmaximal, characteristic, complemented
4C2×#89891C211yesmaximal, characteristic, complemented
5C2×#89883C211yesmaximal, characteristic, complemented
6C22×Dic7⋊C8C211yesmaximal, characteristic, complemented
7C2×D4×C7⋊C8C211yesmaximal, characteristic, complemented
8#11736908C2116yesmaximal, direct product factor
9C2×#89611C211yesmaximal, characteristic, complemented
10C2×#89603C211yesmaximal, characteristic, complemented
11C2×#89502C211yesmaximal, characteristic, complemented
12C2×(C22⋊D7)⋊C8C211yesmaximal, characteristic, complemented
13C2×#89492C211yesmaximal, characteristic, complemented
14C2×#89491C211yesmaximal, characteristic, complemented
15C2×#89481C211yesmaximal, characteristic, complemented
16C2×#89473C211yesmaximal, characteristic, complemented
17C22×C7×M16C2211yescharacteristic
18C23×C7×C8C2211yescharacteristic
19C2×C4×C7×D4C2211yescharacteristic
20C2×#6502C411yescharacteristic
21C2×#6498C411yescharacteristic
22C2×C4×C22⋊D7C2211yescharacteristic
23C2×C4×C22⋊D7C2211yescharacteristic
24C2×#6489C2211yescharacteristic
25C22×C4×Dic7C2211yescharacteristic
26C23×C7⋊C8C2211yescharacteristic
27C23×C7⋊C8C2211yescharacteristic
28C22×#1131C2211yescharacteristic
29C22×C8×D7C2211yescharacteristic
30#90229C418yes—
31#90229C2218yes—
32C2×#6461C411yescharacteristic
33C2×#6452C411yescharacteristic
34C2×#6449C411yescharacteristic
35C2×#6448C411yescharacteristic
36C2×#6442C411yescharacteristic
37C2×#6441C411yescharacteristic
38C2×#6435C2211yescharacteristic
39C2×C4×Dic14C2211yescharacteristic
40C7×#435C2218yescomplemented
41C2×C7×C4⋊C8C2211yescharacteristic
42C2×C7×C22⋊C8C2211yescharacteristic
43C2×C7×C22⋊C8C2211yescharacteristic
44C2×C7×#97C2211yescharacteristic
45C2×C22⋊(C7⋊C8)C2211yescharacteristic
46C2×C22⋊(C7⋊C8)C2211yescharacteristic
47#89899C2218yescomplemented
48#89891C2218yescomplemented
49#89883C2218yescomplemented
50C2×(C2×D7)⋊C8C2211yescharacteristic
51C2×(C2×D7)⋊C8C2211yescharacteristic
52C2×#6389C2211yescharacteristic
53C2×#6389C2211yescharacteristic
54C2×#6389C2211yescharacteristic
55C2×Dic7⋊C8C2211yescharacteristic
56C2×Dic7⋊C8C2211yescharacteristic
57C2×Dic7⋊C8C2211yescharacteristic
58C2×Dic7⋊C8C2211yescharacteristic
59C2×Dic7⋊C8C2211yescharacteristic
60C2×Dic7⋊C8C2211yescharacteristic
61C2×Dic7⋊C8C2211yescharacteristic
62C2×Dic7⋊C8C2211yescharacteristic
63C2×Dic7⋊C8C2218yescomplemented
64C2×C8×Dic7C2211yescharacteristic
65D4×C7⋊C8C2218yescomplemented
66C2×C4⋊(C7⋊C8)C2211yescharacteristic
67C2×C4×C7⋊C8C2211yescharacteristic
68#89611C2218yescomplemented
69#89603C2218yescomplemented
70#89502C2218yescomplemented
71(C22⋊D7)⋊C8C2218yescomplemented
72#89492C2218yescomplemented
73#89491C2218yescomplemented
74#89481C2218yescomplemented
75#89473C2218yescomplemented
76C2×#2992—71nomaximal, Sylow
77C22×C7×D4C2×C411yescharacteristic
78C23×C4×C7C2311yescharacteristic
79C23×C4×C7C2311yescharacteristic
80C22×C22⋊D7C2×C411yescharacteristic
81C22×C22⋊D7C2×C411yescharacteristic
82C23×Dic7C2×C411yescharacteristic
83C23×Dic7C2×C411yescharacteristic
84C22×C4×D7C2311yescharacteristic
85C22×Dic14C2×C411yescharacteristic
86C2×C7×M16—42no—
87C2×C7×M16C2314yes—
88C22×C7×C8—42no—
89C22×C7×C8C2311yescharacteristic
90C22×C7×C8C2311yescharacteristic
91C22×C7×C8C2311yescharacteristic
92C22×C7×C8C2311yescharacteristic
93C22×C7×C8C2314yes—
94C4×C7×D4C2×C414yes—
95C4×C7×D4C2314yes—
96C2×C7×C4⋊C4C2×C411yescharacteristic
97C2×C7×C22⋊C4C2×C411yescharacteristic
98C2×C7×C22⋊C4C2×C411yescharacteristic
99C2×C42×C7C2311yescharacteristic
100C2×C22⋊Dic7C2×C411yescharacteristic
101C2×C22⋊Dic7C2×C411yescharacteristic
102C2×C22⋊Dic7C2×C411yescharacteristic
103C2×C22⋊Dic7C2×C411yescharacteristic
104#6502C2×C418yes—
105#6498C2×C418yes—
106C4×C22⋊D7C2×C414yes—
107C4×C22⋊D7C2×C414yes—
108C4×C22⋊D7C2314yes—
109C4×C22⋊D7C2314yes—
110C2×(C2×D7)⋊C4C2×C411yescharacteristic
111C2×(C2×D7)⋊C4C2×C411yescharacteristic
112C2×(C2×D7)⋊C4C2×C411yescharacteristic
113C2×(C2×D7)⋊C4C2×C411yescharacteristic
114#6489C2×C414yes—
115#6489C2314yes—
116C2×C4⋊Dic7C2×C411yescharacteristic
117C2×C4⋊Dic7C2×C411yescharacteristic
118C2×C4⋊Dic7C2×C411yescharacteristic
119C2×Dic7⋊C4C2×C411yescharacteristic
120C2×Dic7⋊C4C2×C411yescharacteristic
121C2×Dic7⋊C4C2×C411yescharacteristic
122C2×Dic7⋊C4C2×C411yescharacteristic
123C2×Dic7⋊C4C2×C411yescharacteristic
124C2×Dic7⋊C4C2×C411yescharacteristic
125C2×C4×Dic7C2×C411yescharacteristic
126C2×C4×Dic7C2×C411yescharacteristic
127C2×C4×Dic7C2×C414yes—
128C2×C4×Dic7C2311yescharacteristic
129C2×C4×Dic7C2311yescharacteristic
130C2×C4×Dic7C2311yescharacteristic
131C2×C4×Dic7C2314yes—
132C22×C7⋊C8—42no—
133C22×C7⋊C8—42no—
134C22×C7⋊C8C2311yescharacteristic
135C22×C7⋊C8C2311yescharacteristic
136C22×C7⋊C8C2311yescharacteristic
137C22×C7⋊C8C2311yescharacteristic
138C22×C7⋊C8C2314yes—
139C22×C7⋊C8C2314yes—
140C2×#1131—42no—
141C2×#1131C2314yes—
142C2×C8×D7—42no—
143C2×C8×D7C2314yes—
144#6461C2×C418yes—
145#6452C2×C418yes—
146#6449C2×C418yes—
147#6448C2×C418yes—
148#6442C2×C418yes—
149#6441C2×C418yes—
150#6435C2×C414yes—
151#6435C2314yes—
152C4×Dic14C2×C414yes—
153C4×Dic14C2314yes—
154C7×C4⋊C8C2314yes—
155C7×C22⋊C8C2314yes—
156C7×C22⋊C8C2314yes—
157C7×#97C2314yes—
158C22⋊(C7⋊C8)C2314yes—
159C22⋊(C7⋊C8)C2314yes—
160(C2×D7)⋊C8C2314yes—
161(C2×D7)⋊C8C2314yes—
162#6389C2314yes—
163#6389C2314yes—
164#6389C2314yes—
165Dic7⋊C8C2314yes—
166Dic7⋊C8C2314yes—
167Dic7⋊C8C2314yes—
168Dic7⋊C8C2314yes—
169Dic7⋊C8C2314yes—
170Dic7⋊C8C2314yes—
171Dic7⋊C8C2314yes—
172Dic7⋊C8C2314yes—
173C8×Dic7C2314yes—
174C4⋊(C7⋊C8)C2314yes—
175C4×C7⋊C8C2314yes—
176C2×#529—71no—
177#2992—716no—
178C2×#446—71no—
179C2×#446—71no—
180C2×#435—71no—
181C2×#435—71no—
182C2×#435—71no—
183C2×#435D711yescharacteristic, complemented
184C2×C8×D4—71no—
185C2×C8×D4—71no—
186C2×#433—71no—
187C2×#433—71no—
188C2×#432—71no—
189C2×#424—71no—
190C2×#424—71no—
191C22×C4⋊C8—71no—
192C24×C7C22×C411yescharacteristic
193C24×C7C22×C411yescharacteristic
194C23×D7C22×C411yescharacteristic
195C2×C7×D4—24no—
196C2×C7×D4C22×C414yes—
197C22×C4×C7—22no—
198C22×C4×C7—22no—
199C22×C4×C7—22no—
200C22×C4×C7—22no—
201C22×C4×C7C22×C411yescharacteristic
202C22×C4×C7C22×C412yes—
203C22×C4×C7C22×C411yescharacteristic
204C22×C4×C7C22×C411yescharacteristic
205C22×C4×C7C22×C411yescharacteristic
206C22×C4×C7C22×C412yes—
207C22×C4×C7C2412yes—
208C22×C4×C7C2412yes—
209C22×C4×C7C2411yescharacteristic
210C2×C22⋊D7—24no—
211C2×C22⋊D7—42no—
212C2×C22⋊D7C22×C414yes—
213C2×C22⋊D7C22×C414yes—
214C22×Dic7—24no—
215C22×Dic7—42no—
216C22×Dic7C22×C414yes—
217C22×Dic7C22×C411yescharacteristic
218C22×Dic7C22×C411yescharacteristic
219C22×Dic7C22×C411yescharacteristic
220C22×Dic7C22×C411yescharacteristic
221C22×Dic7C22×C411yescharacteristic
222C22×Dic7C22×C411yescharacteristic
223C22×Dic7C22×C411yescharacteristic
224C22×Dic7C22×C414yes—
225C2×C4×D7—22no—
226C2×C4×D7—22no—
227C2×C4×D7C22×C412yes—
228C2×C4×D7C2412yes—
229C2×Dic14—42no—
230C2×Dic14C22×C414yes—
231C7×M16—44no—
232C2×C7×C8—22no—
233C2×C7×C8—22no—
234C2×C7×C8—22no—
235C2×C7×C8—22no—
236C2×C7×C8—44no—
237C2×C7×C8C2412yes—
238C2×C7×C8C2412yes—
239C2×C7×C8C2412yes—
240C2×C7×C8C2412yes—
241C7×C4⋊C4C22×C414yes—
242C7×C22⋊C4C22×C414yes—
243C7×C22⋊C4C22×C414yes—
244C42×C7C22×C412yes—
245C42×C7C2412yes—
246C22⋊Dic7C22×C414yes—
247C22⋊Dic7C22×C414yes—
248C22⋊Dic7C22×C414yes—
249C22⋊Dic7C22×C414yes—
250(C2×D7)⋊C4C22×C414yes—
251(C2×D7)⋊C4C22×C414yes—
252(C2×D7)⋊C4C22×C414yes—
253(C2×D7)⋊C4C22×C414yes—
254C4⋊Dic7C22×C414yes—
255C4⋊Dic7C22×C414yes—
256C4⋊Dic7C22×C414yes—
257Dic7⋊C4C22×C414yes—
258Dic7⋊C4C22×C414yes—
259Dic7⋊C4C22×C414yes—
260Dic7⋊C4C22×C414yes—
261Dic7⋊C4C22×C414yes—
262Dic7⋊C4C22×C414yes—
263C4×Dic7C22×C412yes—
264C4×Dic7C22×C412yes—
265C4×Dic7C22×C412yes—
266C4×Dic7C22×C414yes—
267C4×Dic7C22×C414yes—
268C4×Dic7C2412yes—
269C4×Dic7C2412yes—
270C4×Dic7C2412yes—
271C2×C7⋊C8—22no—
272C2×C7⋊C8—22no—
273C2×C7⋊C8—22no—
274C2×C7⋊C8—22no—
275C2×C7⋊C8—44no—
276C2×C7⋊C8—44no—
277C2×C7⋊C8C2412yes—
278C2×C7⋊C8C2412yes—
279C2×C7⋊C8C2412yes—
280C2×C7⋊C8C2412yes—
281#1131—44no—
282C8×D7—44no—
283C22×M16—71no—
284C22×M16C2×D711yescharacteristic
285C23×C8—71no—
286C23×C8—71no—
287C23×C8—71no—
288C23×C8C2×D711yescharacteristic
289#529—78no—
290#529—78no—
291C2×#126—71no—
292C2×#126—71no—
293C2×#125—71no—
294C2×#124—71no—
295C2×#123—71no—
296C2×#123—71no—
297C2×C22⋊Q8—71no—
298C2×#121—71no—
299C2×C4×Q8—71no—
300C2×C4×D4—71no—
301C2×C4×D4—71no—
302C2×C4×D4C2×D711yescharacteristic
303C2×#117—71no—
304C2×#117—71no—
305C22×C42—71no—
306#446—78no—
307#446—78no—
308#435—78no—
309#435—78no—
310#435—78no—
311#435C2×D718yescomplemented
312C8×D4—78no—
313C8×D4—78no—
314#433—78no—
315#433—78no—
316#432—78no—
317#424—78no—
318#424—78no—
319C2×C4⋊C8—71no—
320C2×C4⋊C8—71no—
321C2×C4⋊C8—71no—
322C2×C4⋊C8—71no—
323C2×C4⋊C8—71no—
324C2×C4⋊C8—71no—
325C2×C4⋊C8—71no—
326C2×C4⋊C8—71no—
327C2×C4⋊C8—78no—
328C2×C4⋊C8—71no—
329C2×C4⋊C8C2×D711yescharacteristic
330C2×C22⋊C8—71no—
331C2×C22⋊C8—71no—
332C2×C22⋊C8—71no—
333C2×C22⋊C8—71no—
334C2×C22⋊C8C2×D711yescharacteristic
335C2×C22⋊C8C2×D711yescharacteristic
336C2×#97—71no—
337C2×#97—71no—
338C2×#97—71no—
339C2×#97C2×D711yescharacteristic
340C2×C4×C8—71no—
341C2×C4×C8—71no—
342C23×C7—22no—
343C23×C7—22no—
344C23×C7—22no—
345C23×C7—22no—
346C23×C7—22no—
347C23×C7#13114yes—
348C23×C7C23×C412yes—
349C23×C7C23×C412yes—
350C23×C7C23×C411yescharacteristic
351C22×D7—22no—
352C22×D7—22no—
353C22×D7—22no—
354C22×D7C23×C412yes—
355C7×D4—28no—
356C2×C4×C7—22no—
357C2×C4×C7—22no—
358C2×C4×C7—22no—
359C2×C4×C7—22no—
360C2×C4×C7—24no—
361C2×C4×C7—24no—
362C2×C4×C7—22no—
363C2×C4×C7—22no—
364C2×C4×C7—22no—
365C2×C4×C7—22no—
366C2×C4×C7C23×C412yes—
367C2×C4×C7C23×C412yes—
368C2×C4×C7C23×C412yes—
369C2×C4×C7C23×C412yes—
370C2×C4×C7C23×C411yescharacteristic
371C2×C4×C7H(5,𝔽2)12yes—
372C2×C4×C72−1+412yes—
373C2×C4×C7C2511yescharacteristic
374C22⋊D7—28no—
375C22⋊D7—44no—
376C2×Dic7—22no—
377C2×Dic7—28no—
378C2×Dic7—22no—
379C2×Dic7—22no—
380C2×Dic7—22no—
381C2×Dic7—22no—
382C2×Dic7—22no—
383C2×Dic7—22no—
384C2×Dic7—44no—
385C2×Dic7C23×C412yes—
386C2×Dic7C23×C412yes—
387C2×Dic7C23×C412yes—
388C2×Dic7C23×C412yes—
389C2×Dic7C23×C412yes—
390C2×Dic7C23×C412yes—
391C2×Dic7C23×C412yes—
392C4×D7—24no—
393C4×D7—22no—
394C4×D7—22no—
395Dic14—44no—
396C7×C8—22no—
397C7×C8—22no—
398C7×C8—22no—
399C7×C8—22no—
400C7⋊C8—22no—
401C7⋊C8—22no—
402C7⋊C8—22no—
403C7⋊C8—22no—
404C22×Q8—71no—
405C22×D4—71no—
406C22×D4—71no—
407C22×D4C4×D711yescharacteristic
408C23×C4—71no—
409C23×C4—71no—
410C23×C4—71no—
411C23×C4C22×D711yescharacteristic
412C23×C4C22×D711yescharacteristic
413C2×M16—42no—
414C2×M16—74no—
415C2×M16—282no—
416C2×M16C22×D714yes—
417C22×C8—42no—
418C22×C8—71no—
419C22×C8—71no—
420C22×C8—71no—
421C22×C8—71no—
422C22×C8—74no—
423C22×C8—74no—
424C22×C8—74no—
425C22×C8—282no—
426C22×C8—282no—
427C22×C8—282no—
428C22×C8C22×D711yescharacteristic
429C22×C8C22×D711yescharacteristic
430C22×C8C22×D711yescharacteristic
431C22×C8C22×D711yescharacteristic
432C22×C8C22×D714yes—
433#126—78no—
434#126—78no—
435#125—78no—
436#124—78no—
437#123—78no—
438#123—78no—
439C22⋊Q8—78no—
440#121—78no—
441C4×Q8—74no—
442C4×Q8—74no—
443C4×D4—74no—
444C4×D4—74no—
445C4×D4—74no—
446C4×D4—74no—
447C4×D4C4×D714yes—
448C4×D4C22×D714yes—
449#117—74no—
450#117—74no—
451#117—74no—
452#117—74no—
453C2×C4⋊C4—71no—
454C2×C4⋊C4—71no—
455C2×C4⋊C4—71no—
456C2×C4⋊C4—71no—
457C2×C4⋊C4—71no—
458C2×C4⋊C4—71no—
459C2×C4⋊C4—71no—
460C2×C4⋊C4—71no—
461C2×C4⋊C4—71no—
462C2×C4⋊C4C4×D711yescharacteristic
463C2×C22⋊C4—71no—
464C2×C22⋊C4—71no—
465C2×C22⋊C4—71no—
466C2×C22⋊C4—71no—
467C2×C22⋊C4—71no—
468C2×C22⋊C4—71no—
469C2×C22⋊C4—71no—
470C2×C22⋊C4—71no—
471C2×C22⋊C4C4×D711yescharacteristic
472C2×C22⋊C4C4×D711yescharacteristic
473C2×C42—71no—
474C2×C42—71no—
475C2×C42—74no—
476C2×C42—74no—
477C2×C42—71no—
478C2×C42—71no—
479C2×C42—71no—
480C2×C42C22×D711yescharacteristic
481C4⋊C8—74no—
482C4⋊C8—74no—
483C4⋊C8—74no—
484C4⋊C8—74no—
485C4⋊C8—74no—
486C4⋊C8—74no—
487C4⋊C8—74no—
488C4⋊C8—74no—
489C4⋊C8—74no—
490C4⋊C8C22×D714yes—
491C22⋊C8—74no—
492C22⋊C8—74no—
493C22⋊C8—74no—
494C22⋊C8—74no—
495C22⋊C8C22×D714yes—
496C22⋊C8C22×D714yes—
497#97—74no—
498#97—74no—
499#97—74no—
500#97C22×D714yes—
501C4×C8—74no—
502C4×C8—74no—
503C22×C7—22no—
504C22×C7—28no—
505C22×C7—22no—
506C22×C7—22no—
507C22×C7—22no—
508C22×C7—22no—
509C22×C7—44no—
510C22×C7#52012yes—
511C22×C7C2×#13114yes—
512C22×C7C2×#13112yes—
513C22×C7#56812yes—
514C22×C7C24×C411yescharacteristic
515C2×D7—22no—
516C2×D7—22no—
517C2×D7—22no—
518C2×D7—44no—
519C4×C7—22no—
520C4×C7—22no—
521C4×C7—22no—
522C4×C7—22no—
523C4×C7#52012yes—
524C4×C7C2×H(5,𝔽2)11yescharacteristic
525C4×C7C2×2−1+411yescharacteristic
526Dic7—22no—
527Dic7—22no—
528Dic7—22no—
529Dic7—22no—
530Dic7—22no—
531Dic7—22no—
532Dic7—22no—
533C24—71no—
534C24C2×C4×D711yescharacteristic
535C24C2×C4×D711yescharacteristic
536C2×Q8—74no—
537C2×Q8—282no—
538C2×D4—24no—
539C2×D4—74no—
540C2×D4—74no—
541C2×D4—144no—
542C2×D4—282no—
543C2×D4C2×C4×D714yes—
544C22×C4—22no—
545C22×C4—22no—
546C22×C4—22no—
547C22×C4—22no—
548C22×C4—71no—
549C22×C4—71no—
550C22×C4—71no—
551C22×C4—71no—
552C22×C4—74no—
553C22×C4—71no—
554C22×C4—71no—
555C22×C4—71no—
556C22×C4—74no—
557C22×C4—72no—
558C22×C4—72no—
559C22×C4—144no—
560C22×C4—142no—
561C22×C4—142no—
562C22×C4—282no—
563C22×C4C2×C4×D711yescharacteristic
564C22×C4C2×C4×D712yes—
565C22×C4C2×C4×D711yescharacteristic
566C22×C4C2×C4×D711yescharacteristic
567C22×C4C2×C4×D711yescharacteristic
568C22×C4C2×C4×D712yes—
569C22×C4C23×D712yes—
570C22×C4C23×D712yes—
571C22×C4C23×D711yescharacteristic
572M16—44no—
573M16—284no—
574C2×C8—22no—
575C2×C8—22no—
576C2×C8—22no—
577C2×C8—22no—
578C2×C8—44no—
579C2×C8—72no—
580C2×C8—72no—
581C2×C8—72no—
582C2×C8—72no—
583C2×C8—142no—
584C2×C8—142no—
585C2×C8—142no—
586C2×C8—142no—
587C2×C8—284no—
588C2×C8—284no—
589C2×C8—284no—
590C2×C8C23×D712yes—
591C2×C8C23×D712yes—
592C2×C8C23×D712yes—
593C2×C8C23×D712yes—
594C4⋊C4—74no—
595C4⋊C4—74no—
596C4⋊C4—74no—
597C4⋊C4—74no—
598C4⋊C4—74no—
599C4⋊C4—74no—
600C4⋊C4—74no—
601C4⋊C4—74no—
602C4⋊C4—74no—
603C4⋊C4C2×C4×D714yes—
604C22⋊C4—74no—
605C22⋊C4—74no—
606C22⋊C4—74no—
607C22⋊C4—74no—
608C22⋊C4—74no—
609C22⋊C4—74no—
610C22⋊C4—74no—
611C22⋊C4—74no—
612C22⋊C4C2×C4×D714yes—
613C22⋊C4C2×C4×D714yes—
614C42—72no—
615C42—72no—
616C42—74no—
617C42—74no—
618C42—72no—
619C42—72no—
620C42—72no—
621C42—72no—
622C42C2×C4×D712yes—
623C42C23×D712yes—
624C2×C7—24no—
625C2×C7—42no—
626C2×C7#299214yescomplemented
627C2×C7C2×#52011yescharacteristic
628C2×C7C22×#13111yescharacteristic
629C2×C7C2×#56811yescharacteristic
630D7—42no—
631C23—22no—
632C23—22no—
633C23—22no—
634C23—22no—
635C23—22no—
636C23—72no—
637C23—142no—
638C23—142no—
639C23—142no—
640C23#647014yes—
641C23C22×C4×D712yes—
642C23C22×C4×D712yes—
643C23C22×C4×D711yescharacteristic
644Q8—284no—
645D4—28no—
646D4—148no—
647D4—284no—
648C2×C4—22no—
649C2×C4—22no—
650C2×C4—22no—
651C2×C4—22no—
652C2×C4—24no—
653C2×C4—24no—
654C2×C4—22no—
655C2×C4—22no—
656C2×C4—22no—
657C2×C4—22no—
658C2×C4—72no—
659C2×C4—72no—
660C2×C4—72no—
661C2×C4—72no—
662C2×C4—72no—
663C2×C4—72no—
664C2×C4—72no—
665C2×C4—148no—
666C2×C4—142no—
667C2×C4—142no—
668C2×C4—142no—
669C2×C4—142no—
670C2×C4—142no—
671C2×C4—142no—
672C2×C4—142no—
673C2×C4—144no—
674C2×C4—142no—
675C2×C4—142no—
676C2×C4—284no—
677C2×C4C22×C4×D712yes—
678C2×C4C22×C4×D712yes—
679C2×C4C22×C4×D712yes—
680C2×C4C22×C4×D712yes—
681C2×C4C22×C4×D711yescharacteristic
682C2×C4#654812yes—
683C2×C4#655412yes—
684C2×C4C24×D711yescharacteristic
685C8—22no—
686C8—22no—
687C8—22no—
688C8—22no—
689C8—142no—
690C8—142no—
691C8—142no—
692C8—142no—
693C7C2×#299211yescharacteristic, complemented, Sylow
694C22—28no—
695C22—22no—
696C22—22no—
697C22—22no—
698C22—22no—
699C22—22no—
700C22—44no—
701C22—142no—
702C22—142no—
703C22—142no—
704C22—284no—
705C22#9023712yes—
706C22C2×#647014yes—
707C22C2×#647012yes—
708C22#9044112yes—
709C22C23×C4×D711yescharacteristic
710C4—22no—
711C4—22no—
712C4—22no—
713C4—22no—
714C4—142no—
715C4—142no—
716C4—142no—
717C4—142no—
718C4—142no—
719C4—142no—
720C4—142no—
721C4#9023712yes—
722C4C2×#654811yescharacteristic
723C4C2×#655411yescharacteristic
724C2—24no—
725C2—42no—
726C2—282no—
727C2#1173690814yesdirect product factor
728C2C2×#9023711yescharacteristic
729C2C22×#647011yescharacteristic
730C2C2×#9044111yescharacteristic
subgroupG/H
centerC22×C4C23×D7
commutatorC22×C7C24×C4
FrattiniC2×C4C24×D7
FittingC2×C7×#435C2
socleC23×C7C23×C4
prime radicalC2×#6502C4
cosocleC2×C4×C7C25
hypercenterC2×#435D7
hypocenterC7C2×#2992
LCSG ▷ C22×C7 ▷ C7
UCSC1 ◁ C22×C4 ◁ C2×#435

Complements

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

NH ≅ G/Ntype
2. C2×C7×#435C2semidirect
3. C2×#89899C2semidirect
4. C2×#89891C2semidirect
5. C2×#89883C2semidirect
6. C22×Dic7⋊C8C2semidirect
7. C2×D4×C7⋊C8C2semidirect
8. #11736908C2direct (N × H)
9. C2×#89611C2semidirect
10. C2×#89603C2semidirect
11. C2×#89502C2semidirect
12. C2×(C22⋊D7)⋊C8C2semidirect
13. C2×#89492C2semidirect
14. C2×#89491C2semidirect
15. C2×#89481C2semidirect
16. C2×#89473C2semidirect
40. C7×#435C22semidirect
47. #89899C22semidirect
48. #89891C22semidirect
49. #89883C22semidirect
63. C2×Dic7⋊C8C22semidirect
65. D4×C7⋊C8C22semidirect
68. #89611C22semidirect
69. #89603C22semidirect
70. #89502C22semidirect
71. (C22⋊D7)⋊C8C22semidirect
72. #89492C22semidirect
73. #89491C22semidirect
74. #89481C22semidirect
75. #89473C22semidirect
183. C2×#435D7semidirect
311. #435C2×D7semidirect
626. C2×C7#2992semidirect
693. C7C2×#2992semidirect
727. C2#11736908direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#902292
C2×C7×#4352
C2×#898992
C2×#898912
C2×#898832
C22×Dic7⋊C82
C2×D4×C7⋊C82
#117369082
C2×#896112
C2×#896032
C2×#895022
C2×(C22⋊D7)⋊C82
C2×#894922
C2×#894912
C2×#894812
C2×#894732
C2×#29927